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Taye stephen Mogaji
Estudo teórico e experimental sobre
ebulição convectiva no interior de
tubos com fitas retorcidas
Tese apresentada à Escola de Engenharia
de São Carlos, Departamento de Engenharia
Mecânica, da Universidade de São Paulo, como
parte dos requisitos para obtenção do título de
Doutor em Engenharia Mecânica.
Área de Concentração: Térmica e Fluidos
Orientador: Prof. Dr. Gherhardt Ribatski
SÃO CARLOS-SP
2014
ESTE EXEMPLAR TRATA-SE DA VERSÃO CORRIGIDA. A VERSÃO ORIGINAL ENCONTRA-SE
DISPONÍVEL JUNTO AO DEPARTAMENTO DE ENGENHARIA MECANICA DA EESC-USP.
DEDICATION
This research work is dedicated to the Almigthy God, the author and finisher of my
faith and in memory of my late father Pa David Kolawole Mogaji.
ACKNOWNLEDGEMENT
This study has been carried out at Laboratory of Thermal and Fluids Engineering,
Department of Mechanical Engineering, School of Engineering of São Carlos (EESC-
USP) under the direction of Prof. Gherhardt Ribatski. The Doctoral scholarship has
been funded by the CAPES (Coordination for the Improvement of Higher Level - or
Education-Personnel, Brazil) under Contract Number 00011/07-0, and the financial
support to this study under Contract Number 474403/2008-4 given by CNPq (The
National Council for Scientific and Technological Development, Brazil), which are
gratefully acknowledge.
I would like to thank my University, Federal University of Technology Akure (FUTA),
Ondo State, Nigeria, for giving me the opportunity to carry out my Doctoral degree
study here in Brasil through study leave with pay support received from the
University.
I would like to thank Professor Gherhardt Ribatski for giving me the opportunity to
carry out this research work in his laboratory, for his excellent supervision, academic
training and guidance during this period. Finally, I would like to thank him for his
careful reading of this thesis.
To my family, my lovely wife, Mrs Josephine Bukola Mogaji, and my children, Favour
Emmanuela and Pedro Ayodeji Mogaji for their ultimate support and understanding
during this period.
Encouragement and prayer support from my twins brother and his family (Mr and Mrs
K.A. Mogaji), the entire family members of Mogaji’s, Fasina’s and Omoreige’s, my
Pastor and adviser (Dr.Engr.S. P. Ayodeji) are appreciated and recognized.
The technical support given to this investigation by Mr. Jose Roberto Bogni for
successful construction and maintenance of the experimental bench is also
appreciated and deeply recognized.
I also acknowledge my colleagues of the Laboratory of Refrigeration (EESC-USP),
Cristiano Bigonha Tibiriça, Daniel Sempertegui Tapia, Francisco Julio Nascimento,
Hugo Leonardo Leo, Jacqueline Diniz da Silva, Gustavo Rodriguez de Souza,
Anderson Ubices de Moraes, Francisco Loyola, Cristian Alfredo Chávez Toro, Thiago
Augosto Moreira, Felipe, Nourjane Namaca, Karime Barbarasanto Caminoto for their
helps and specially Kanizawa Fabio Toshio for his collaboration during this period.
To Professor Antonio Moreira, Oscar Rodriguez, Daniel Verala Mogalhães, for their
excellent academic training given to me during my course work period, technical
Jorge Nicolau do santo and Roberto for your collaboration during this period.
To Professor Enio Pedone Bandarra Filho for his candid contribution to this research
work and presentation of part of the results obtained in this study at ECI 8th
International Conference on Boiling and Condensation Heat Transfer, 2012,
Lausanne, Switzerland.
To friends and colleagues of the group Núcleo de Engenharia Térmica e Fluidos
(NETeF) for your contributions in terms of important discussions and suggestions
during this period: Marcelo Souza Castro, Marcia Regina Osaki, Evelise Corbalan,
Hugo Fernando Velasco Pena, Adriana Bonilla Riano,Iara Hernande Rodriguez,
Jonas Laerte Ansoni, Luis Enrique Ortiz-Vidal, Ricardo Pereria de Avila, Marlon
Mauricio Hernandez Cely, Glauber Cruz , Serginho and Daniela Andresa Mortari.
ABSTRACT
MOGAJI, Taye Stephen (2014). THEORETICAL AND EXPERIMENTAL STUDY ON
CONVECTIVE BOILING INSIDE TUBES CONTAINING TWISTED-TAPE INSERTS.
258 pages. Thesis (PhD) - Escola de Engenharia de São Carlos, University of São
Paulo, São Carlos.
This research comprises an experimental and theoretical study on convective boiling
inside tubes containing twisted-tape inserts. The demand for more compact and
efficient thermal systems, in which the heat exchangers plays an important role, has
led to the development and use of various heat transfer enhancement techniques.
Among them twisted-tape insert as a swirl flow device is one of the most used.
Twisted-tape inserts have been used for over more than one century ago as a
technique of heat transfer enhancement applied to heat exchangers. However, the
heat transfer augmentation comes together with pressure drop increment, impacting
the pumping power and, consequently, the system efficiency. Moreover, until now it
is not clear, the operational conditions under which the heat transfer coefficient
augmentation by the use of twisted-tape inserts overcomes pressure drop penalty. In
the present study, initially, extensive investigations of the literature concerning
convective boiling inside plain tubes with and without twisted-tape inserts were
performed. This literature review covers pressure drop, heat transfer coefficient and
the leading frictional pressure drop gradient and heat transfer coefficient predictive
methods during convective boiling inside tubes with and without twisted-tape inserts.
Then, pressure drop and heat transfer coefficient results acquired in the present
study were obtained in an experimental apparatus of 12.7 and 15.9 mm ID tubes
during flow boiling of R134a for twisted-tape ratios of 3, 4, 9, 14 and tubes without
inserts, mass velocities ranging from 75 to 200 kg / m2 s, saturation temperatures of 5
and 15 °C and heat fluxes of 5 and 10 kW / m2. The experimental results were
parametrically analyzed and compared against the predictive methods from literature.
An analysis of the enhancement of the heat transfer coefficient and the pressure drop
penalty is presented. Heat transfer coefficient increments up to 45 % keeping the
same pumping power and pressure drop penalty of about 35 % were obtained by
using twisted-tape relative to tubes without inserts. Additionally, through comparison
of the present study experimental results with the predictive methods from the
literature for heat transfer coefficient during two-phase flow inside tube containing
twisted-tape inserts, it was verified that non of these methods predict satisfactory well
the experimental results. However, a new method was develop for predicting the heat
transfer coefficient during flow boiling inside tubes containing twisted-tape inserts
based on the experimental results obtained in the present study. The predictive
method takes into account the physical picture of the swirl flow phenomenon by
including swirl flow effects promoted by the twisted-tape inserts. The proposed
method predicts satisfactorily well the data obtained in the present study, predicting
89.1% of the experimental data within an error band of ±30 % and absolute mean
deviation of 15.7 %.
Keywords: Convective boiling, twisted-tape, heat transfer enhancement, pressure
drop, swirl flow.
RESUMO
MOGAJI, Taye Stephen (2014). Estudo teórico e experimental sobre a ebulição
convectiva no interior de tubos com fitas retorcidas. 258 páginas. Tese (Doutorado) -
Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos.
A presente pesquisa trata-se de um estudo teórico e experimental sobre a ebulição
convectiva no interior de tubos com fitas retorcidas. A crescente demanda por
sistemas térmicos mais compactos e eficientes, nos quais os trocadores de calor
apresentam elevada relevância, tem motivado o desenvolvimento de inúmeras
técnicas de intensificação de troca de calor, sendo que a utilização de fitas
retorcidas é uma das técnicas mais adotadas. Fitas retorcidas são utilizadas como
técnicas de intensificação de troca de calor há mais de um século. Entretanto o
incremento da transferência de calor é acompanhado do aumento da perda de
pressão, que por sua vez implica em aumento da potência de bombeamento, e
consequentemente afeta a eficiência global do sistema. Adicionalmente, até os dias
de hoje não há consenso sobre as condições operacionais em que o ganho com o
incremento do coeficiente de transferência de calor é superior à perda devido ao
aumento da perda de pressão. Neste estudo, inicialmente foi realizada uma extensa
revisão da literatura sobre a ebulição convectiva no interior de tubos com e sem fitas
retorcidas. Esta revisão aborda aspectos relacionados à perda de pressão e ao
coeficiente de transferência de calor, juntamente com os métodos de previsão
destes parâmetros. Foram realizados experimentos para determinação experimental
de perda de pressão e coeficiente de transferência de calor, em aparato
experimental contando com tubos horizontais com diâmetros internos iguais a 12,7 e
15,9 mm, para escoamento bifásico de R134a, razões de retorcimento iguais a 3, 4,
9, 14 e tubo sem fita, velocidades mássicas entre 75 e 200 kg/m²s, temperaturas de
saturação iguais a 5 e 15 °C, e flux de calor iguais a 5 e 10 kW/m². Os resultados
experimentais foram analisados e comparados com estimativas segundo métodos
disponíveis na literatura. Uma análise do aumento do coeficiente de transferência de
calor e da perda de pressão friccional é apresentada. Foram verificados incrementos
do coeficiente de transferência de calor de até 45% para a mesma potência de
bombeamento, e aumento de perda de pressão de aproximadamente 35% para
tubos com fitas retorcidas em relação aos tubos sem fita. Adicionalmente, através da
comparação dos resultados experimentais com os métodos de previsão para
coeficiente de transferência de calor, foi verificado que nenhuma metodologia
apresentava previsões satisfatórias dos resultados. Portanto um novo método para
previsão do coeficiente de transferência de calor durante ebulição convectiva no
interior de tubos com fitas retorcidas foi desenvolvido com base nos resultados
experimentais obtidos durante o presente estudo. O método proposto é função de
parâmetros geométricos e do escoamento, e também de parâmetros físicos do
escoamento rotacional induzido pela fita. A metodologia desenvolvida apresenta
previsões satisfatórias dos resultados experimentais, prevendo 89,1% dos
resultados experimentais com erro inferior a ±30% e erro médio absoluto igual a
15,7%.
Palavras-chave: Ebulição convectiva, fitas retorcidas, intensificação de transferência
de calor, perda de pressão, escoamento rotacional.
LIST OF SYMBOLS
Latin Letters
di Internal diameter, m
E Electrical power, W
e Tape thickness,m
Fe Fin effect multiplier, dimensionless
fw Surface material parameter, dimensionless
F Convective enhancement factor, dimensionless
Fr Froude Number, dimensionless
g Acceleration due to gravity, m2 / s
G Mass velocity, kg / m2 s
Gr Grashof Number, dimensionless
h Heat transfer coefficient, W / m2 K
H Length of 180° tape turn, m
i Enthalpy, kJ / kg
k Thermal conductivity, W / m K
L Length, m
M Molecular mass, kg / kmol
Mass flow rate, kg / s
pr Reduced pressure, dimensionless
Pr Prandtl number, dimensionless
Heat transfer, W
Re Reynolds Number, dimensionless
Ra Peak-to-valley surface roughnesses, µm
V Velocity, m / s
T Temperature, oC
x Vapor quality, dimensionless
xdi Dryout completion quality, dimensionless
xde Dryout inception quality, dimensionless
We Weber Number, dimensionless
y Twist ratio
z Distance from inlet, m
Greek symbols
∆p Pressure drop, Pa
Liquid film thickness, m
Superficial void fraction, dimensionless
Surface roughness, µm
Enhancement parameter, dimensionless
Geometric parameter define by Eq.(2.132), dimensionless
Dynamic viscosity, kg / m s
η Absolute mean error, %
ζ Percentage of exp. data within an error band of ±30 %, dimensionless
ϕ Heat flux, kW / m2
Two phase multiplier for liquid, dimensionless
Two phase multiplier for vapor, dimensionless
Angle, rad
Density, kg / m3
Surface tension, N / m
Subscripts
acc Accelerational
env Heat transfer to the environment
fric Frictional
grav Gravitational
Hydraulic
Homogeneous
In Inlet
l Liquid
v Vapor
lv Liquid-vapor
Out Outlet
PH Pre-Heater
PT Plain tube
TS Test section
TT With twisted tape
w Wall
2φ Two–phase
V0 Mixture as vapor
L0 Mixture as Liquid
Dimensionless
Boiling Number
Convective Number
Froude Number
Grashof – Number
Nulsset Number
Reynolds Number
Weber Number
Martineli Parameter
LIST OF FIGURES Figure 2.1 - Two-phase flow (liquid-vapor) in a tube (Kanizawa, 2011). ................... 32
Figure 2.2 - Flow patterns observed in horizontal tubes, Cheng et al. (2008)........... 37
Figure 2.3 - Flow pattern map for horizontal flow (Baker 1954). ............................... 38
Figure 2.4 - Flow pattern map for R134a at Tsat = 30 oC in a 10 mm internal diameter
tube for ϕ = 10 kW / m2 using G = 100 kg / m2 s (Kattan et al. 1998)....................... 39
Figure 2.5 - Flow pattern map evaluated for R22 at Tsat = 5 oC in a 13.84 mm internal
diameter tube for ϕ = 2.1 kW/m2 using G = 100 kg / m2 s to calculate the void
fractions. (Wojtan et al. 2005). .................................................................................. 40
Figure 2.6 - Simplified stratified flow configuration, Kattan et al. (1998). .................. 41
Figure 2.7 – Comparison among the predictive methods for Nusselt Number during
during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C,
p=692 kPa Tsub =19.08 oC......................................................................................... 95
Figure 2.8 – Comparison among the predictive methods for Nusselt Number during
during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C,
p=692 kPa Tsub =19.08 oC......................................................................................... 95
Figure 3.1 - Photograph of the experimental bench................................................ 108
Figure 3.2 - Schematic diagram of the refrigerant circuit. ....................................... 109
Figure 3.3 - Thermodynamic process of the refrigerant along the refrigerant test
circuit. ..................................................................................................................... 110
Figure 3.4 - Schematic diagram of the test section and the thermocouples
distribution. ............................................................................................................. 111
Figure 3.5 - Positioning of thermocouples for each cross section along the test
section. ................................................................................................................... 112
Figure 3.6 - Visualisation section at the test section outlet. .................................... 112
Figure 3.7 - Illustration of fitting of differential pressure transducers....................... 113
Figure 3.8 - Photograph of the Pre-heater. ............................................................. 114
Figure 3.9 - Schematic diagram of the acquisition system and terminals. .............. 117
Figure 3.10 - Image of the program implemented for data acquisition.................... 118
Figure 3.11 - Photograph of the twisted-tape inserts used during the experimental
compaign. ............................................................................................................... 119
Figure 3.12 - Comparison between experimental friction factors and estimated friction
factors, for single-phase flow in tubes with 12.7 mm ID (filled symbols) and 15.9 mm
ID (empty symbols). ................................................................................................127
Figure 3.13 - Comparison of experimental and estimated heat transfer coefficient for
liquid single-phase flow, for 12.7 mm ID tube. Estimatives according to Dittus and
Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols). ..................127
Figure 3.14 - Comparison of experimental and estimated heat transfer coefficient for
liquid single-phase flow, for 15.9 mm ID tube. Estimatives according to Dittus and
Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols). ..................128
Figure 3.15 - Variation with mass velocity of the heat exchanged between the test
section and the surroundings. .................................................................................129
Figure 3.16 - Variation with mass velocity of the heat exchanged between the pre-
heater and the surroundings....................................................................................129
Figure 4.1 - Variation of frictional pressure drop gradient with vapor quality for
adiabatic two-phase flow in 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols)
and Tsat = 15 °C (filled symbols). .............................................................................133
Figure 4.2 - Variation of frictional pressure drop gradient with vapor quality for
adiabatic two-phase flow in 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols)
and Tsat = 15 °C (filled symbols). .............................................................................133
Figure 4.3 - Variation of frictional pressure drop gradient with vapor quality for R134a,
12.7 mm ID tube, G = 75 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). .......................................................................................................134
Figure 4.4 - Variation of frictional pressure drop gradient with vapor quality for R134a,
12.7 mm ID tube, G = 100 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). .......................................................................................................135
Figure 4.5 - Variation of frictional pressure drop gradient with vapor quality for R134a,
12.7 mm ID tube, G = 150 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). .......................................................................................................135
Figure 4.6 - Variation of frictional pressure drop gradient with vapor quality for R134a,
12.7 mm ID tube, G = 200 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). .......................................................................................................136
Figure 4.7 - Variation of frictional pressure drop gradient with vapor quality for R134a,
15.9 mm ID tube, G = 75 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). .......................................................................................................136
Figure 4.8 - Variation of frictional pressure drop gradient with vapor quality for R134a,
15.9 mm ID tube, G = 100 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). ....................................................................................................... 137
Figure 4.9 - Variation of frictional pressure drop gradient with vapor quality fo R134a,
15.9 mm ID tube, G = 150 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). ....................................................................................................... 137
Figure 4.10 - Variation of frictional pressure drop gradient with vapor quality for
R134a 15.9 mm ID tube, G = 200 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat =
15 °C (filled symbols). ............................................................................................. 138
Figure 4.11 - Comparison between estimated and experimental frictional pressure
drop, for 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). ....................................................................................................... 139
Figure 4.12 - Comparison between estimated and experimental frictional pressure
drop, for 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C
(filled symbols). ....................................................................................................... 139
Figure 4.13- Comparison of the trends of the frictional pressure drop according to
predictive methods and experimental data for plain tube without twisted-tape,for 15.9
mm ID plain tube, Tsat = 15 °C and G = 100 kg / m² s. ............................................ 140
Figure 4.14 - Comparison between estimated and experimental frictional pressure
drop gradient, for 12.7 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3,
4, 9 and 14.............................................................................................................. 142
Figure 4.15 - Comparison between estimated and experimental frictional pressure
drop gradient, for 15.9 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3,
4, 9 and 14.............................................................................................................. 142
Figure 4.16 - Comparison of the trends of the frictional pressure drop according to
predictive methods and experimental data for plain tube with twisted-tape, for 12.7
mm ID tube Tsat = 15 °C. ......................................................................................... 144
Figure 4.17 - Comparison of the trends of the frictional pressure drop according to
predictive methods and experimental data for plain tube with twisted-tape, for 15.9
mm, ID tube, Tsat = 15 °C. ....................................................................................... 144
Figure 4.18 – Illustration of the variation of pressure drop penalty with vapor quality,
for ID = 12.7 mm and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols)........ 145
Figure 4.19 - Illustration of the variation of pressure drop penalty with vapor quality
for ID = 15.9 mm, and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols)....... 146
Figure 4.20 – Variation of heat transfer coefficient with vapor quality during flow
boiling in tube without twisted-tape inserts, ϕ = 10 kW / m², Tsat = 5 °C, di = 12.7 mm
(empty symbols) and di = 15.9 mm (filled symbols).................................................148
Figure 4.21 - Variation of heat transfer coefficient with vapor quality during flow
boiling in tube without twisted-tape inserts, ϕ = 10 kW / m², di = 15.9 mm , Tsat = 5 °C
(empty symbols) and Tsat = 15 °C (filled symbols). ..................................................148
Figure 4.22 - Variation of heat transfer coefficient with vapor quality during flow
boiling in tube without twisted-tape inserts, Tsat = 15 °C ,di = 15.9 mm ,ϕ = 10 kW /
m² (empty symbols) and ϕ = 5 kW / m², (filled symbols).........................................149
Figure 4.23- Comparison between estimated and experimental heat transfer
coefficients for the12.7 mm ID tube without inserts according to Kandlikar (1990). 150
Figure 4.24 - Heat transfer coefficient variation with vapor quality during flow boiling
in 12.7 mm ID, .........................................................................................................151
Figure 4.25 - Heat transfer coefficient variation with vapor quality during flow boiling
in 12.7 mm ID, G = 150 kg / m2 s, φ = 10 kW / m², Tsat =5 oC. ................................152
Figure 4.26 - Heat transfer coefficient variation with vapor quality during flow boiling
in 15.9 mm ID, G = 75 kg / m2 s, φ = 10 kW / m², Tsat = 5 oC. .................................152
Figure 4.27 - Heat transfer coefficient variation with vapor quality during flow boiling
in 15.9 mm ID, G = 150 kg / m2 s,φ = 10 kW / m², Tsat = 5 oC. ................................153
Figure 4.28 - Illustration of the effect of heat flux on heat transfer coefficient for plain
tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 12.7
mm ID Tsat = 5 oC.....................................................................................................154
Figure 4.29 - Illustration of the effect of heat flux on heat transfer coefficient for plain
tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 15.9
mm ID Tsat = 5 oC.....................................................................................................154
Figure 4.30 - Heat transfer coefficient variation with vapor quality during flow boiling
in 15.9 mm ID, φ = 10 kW / m², Tsat = 15 oC; y = 14 (filled symbol) and y = 3 (empty
symbol)....................................................................................................................155
Figure 4.31 – Illustration of the effect of tube diameter on the heat transfer coefficient
with vapor quality inside tubes with twisted-tape inserts, G = 100 kg / m2 s, φ = 10
kW / m², Tsat = 15 oC................................................................................................156
Figure 4.32 - Effect of the saturation temperature on the heat transfer coefficient
during flow boiling in 15.9 mm ID, G = 75 kg / m2 s, φ = 10 kW / m², y = 14 (filled
symbol) and y = 4 (empty symbol). ......................................................................... 157
Figure 4.33 - Effect of the saturation temperature on the heat transfer coefficient for
during flow boiling in 15.9 mm ID, G = 150 kg / m2 s, φ = 10 kW / m², y = 14 (filled
symbol) and y = 4 (empty symbol). ......................................................................... 157
Figure 4.34 - Comparison between estimatives according to Akhavan-Behabadi et al.
(2009b) and experimental heat transfer coefficients. .............................................. 159
Figure 4.35 - Comparison of the trends of the heat transfer coefficient according to
predictive methods and experimental data for plain tube with twisted-tape, for 12.7
mm ID tube, Tsat = 5 °C, φ = 10 kW/m². ................................................................... 160
Figure 4.36 - Comparison of the trends of the heat transfer coefficient according to
predictive methods and experimental data for plain tube with twisted-tape, for 15.9
mm ID tube, Tsat= 5 °C, φ = 10 kW/m²..................................................................... 160
Figure 4.37 - Variation of enhancement factor 1ε for unit pumping power, for G = 75
kg/m²s, ϕ = 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
................................................................................................................................ 163
Figure 4.38 – Variation of enhancement factor 2ε for the same pumping power, for G
= 75 kg/m²s, ϕ = 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled
symbols). ................................................................................................................ 164
Figure 4.39 – Variation of enhancement factor 2ε for the same pumping power, for G
= 200 kg/m²s, ϕ = 10 kW/m², Tsat = 15 °C, d = 12.7 mm (empty symbols) and di =
15.9 mm (filled symbols). ........................................................................................ 164
Figure 5.1 - Comparison of the experimental vapor quality data for the dryout
inception in plain tubes and the predictions according to the method of Wojtan et al.
(2005), Tsat = 15 oC and φ = 10 kW / m2 . ............................................................... 168
Figure 5.2 - Comparison between the experimental and predicted values of the heat
transfer coefficient during single-phase flows inside tube with twisted-tape insert, ID
=12.7 mm................................................................................................................ 170
Figure 5.3 - Flow images. (a) Stratified flow (y = 14, G = 75 kg / m2 s, x = 0.25, Tsat =
5 oC); (b) stratified wavy flow (y =14,G = 100 kg / m2 s, x = 0.20, Tsat = 5 oC); (c)
Anular flow ( y = 3, G = 150 kg / m2 s, x = 0.35, Tsat = 5 oC); (d) Dryout (y = 3, G =
200 kg / m2 s, x = 0.45, Tsat = 5 oC). ........................................................................172
Figure 5.4 - Flow pattern Schematic diagram..........................................................173
Figure 5.5 - Comparison between the method proposed in the present study and the
experimental heat transfer results for tubes with twisted-tape inserts. ....................175
Figure 5.6 - Results of the statistical analyses of the comparison between
experimental and predicted results according to the present method for different
experimental conditions, G = 75-200 kg / m² s, y=3-14, Tsat = 5 and 15°C, φ = 5 and
10 kW / m². ..............................................................................................................176
Figure 5.7 - Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines), ϕ = 10 kW / m², Tsat= 5 °C, G = 75 kg / m2 s and ID = 12.7 mm..................177
Figure 5.8 – Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines) , ϕ= 10 kW/m², Tsat= 15 °C, G = 75 kg / m2 s and ID = 15.9 mm..................178
Figure 5.9 – Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines) , ϕ = 10 kW/m², Tsat= 5 °C, G = 100 kg / m2 s and ID = 12.7 mm.................178
Figure 5.10 – Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines) , ϕ = 10 kW/m², Tsat= 15 °C, G = 100 kg / m2 s and ID = 15.9 mm...............179
Figure 5.11– Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines), ϕ = 10 kW / m²,Tsat = 5 °C, G = 150 kg / m2 s and ID = 12.7 mm................179
Figure 5.12 – Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines) , ϕ = 10 kW/m², Tsat =15 °C, G = 150 kg / m2 s and ID = 15.9 mm...............180
Figure 5.13 – Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines) , ϕ = 10 kW/m², Tsat = 5 °C, G = 200 kg / m2 s and ID = 12.7 mm................180
Figure 5.14 – Evolution of the heat transfer coefficient with vapor quality according to
the experimental results (symbols) and predictions according to the proposed method
(lines) , ϕ = 10 kW/m², Tsat = 15 °C, G = 200 kg / m2 s and ID = 15.9 mm. ............ 181
Figure 5.15 - Comparism between experimental heat transfer data from Agrawal et
al. (1986) and the prediction by the present study proposed model. ...................... 182
Figure 5.16 - Comparism between experimental heat transfer data from Akhavan-
Behabadi et al. (2009b) and the prediction by the present study proposed model. 182
LIST OF TABLES
Table 2.1 – Coeficients for estimating two phase flow multipliers of Lockhart and
Martinelli (1949) apud Thome (2008)........................................................................ 49
Table 2.2 - Values of fluid dependent parameter . ............................................. 69
Table 2.3 - Values of the empirical constants of the Kandlikar (1990) method. ........ 69
Table 2.4 - Summary of predictive methods for the heat transfer coefficient during
flow boiling ................................................................................................................ 76
Table 2.5 - Variation of heat transfer coefficient estimated by the predictive methods
based on different experimental operating conditions............................................... 81
Table 2.6 - Summaries of some studies in the literature concerning single-phase
flows inside tubes containing twisted-tape inserts .................................................... 88
Table 2.7 - Description of the experimental studies concerning two-phase flow inside
tubes containing twisted-tape inserts........................................................................ 96
Table 3.1 - Uncertainty of the measured parameters.............................................. 130
Table 3.2 - Uncertainty of the calculated parameters ............................................. 130
Table 4.1 - Experimental conditions covered in the present study.......................... 131
Table 4.2 - Physical, chemical and thermodynamic properties of R134a ............... 132
Table 4.3 - Results of the statistical analysis of the comparison between experimental
data and predictive methods for frictional pressure drop in plain tubes. ................. 141
Table 4.4 – Results of the statistical analysis of the comparison between
experimental and predicted pressure drop data during two-phase flow in tubes with
twisted-tape inserts. ................................................................................................ 143
Table 4.5 – Results of the statistical analysis of the comparison between
experimental results for heat transfer coefficient during two-phase flow in plain tubes
and predictive methods from literature.................................................................... 150
Table 4.6 - Results of the statistical analysis of the comparison between experimental
results and predictive methods for heat transfer coefficient in tubes with twisted tape
inserts......................................................................................................................159
Table 5.1 - Results of the statistical analysis of the comparison between the
proposed method and the heat transfer experimental results, G = 75-200 kg / m² s,
Tsat = 5 and 15 °C, φ = 5 and 10 kW / m²................................................................175
Table A.1 - Coefficients of the equation for the pressure transducers and uncertainty
................................................................................................................................197
Table A.2 - Features of the thermometers used during calibration of the acquisition
system channel for temperature. .............................................................................198
Table A.3 - Coefficients for the reading temperature and estimated uncertainties for
the thermocouples channels....................................................................................198
Table A.4 - Characteristics of the multimeters used during the calibration of power
transducers..............................................................................................................200
Table A.5 - Coefficients and calculated uncertainty results of the active power
transducers..............................................................................................................200
Table B.1 – Flow boiling pressure drop experimental results for Tsat = 5oC under
adiabatic conditions inside 12.7 mm internal diameter tube ....................................202
Table B.2 - Flow boiling pressure drop experimental results for Tsat = 15oC under
adiabatic conditions inside 12.7 mm internal diameter tube ....................................207
Table B.3 - Flow boiling pressure drop experimental results for Tsat = 5oC under
adiabatic conditions inside 15.9 mm internal diameter tube ....................................213
Table B.4 - Flow boiling pressure drop experimental results for Tsat =15 oC under
adiabatic conditions inside 15.9 mm internal diameter tube ....................................221
Table B.5 - Flow boiling heat transfer coefficient experimental results with local
saturation temperature Tsat = 5 oC measured at each section of the of the test section
inside 12.7 mm internal diameter tube ....................................................................230
Table B.6 - Flow boiling heat transfer coefficient experimental results with local
saturation temperature Tsat = 15 oC measured at each section of the of the test
section inside 12.7 mm internal diameter tube ........................................................242
Table B.7 - Flow boiling heat transfer coefficient experimental results with local
saturation temperature Tsat = 5 oC measured at each section of the of the test section
inside 15.9 mm internal diameter tube.................................................................... 247
Table B.8 - Flow boiling heat transfer coefficient experimental results with local
saturation temperature Tsat = 15 oC measured at each section of the of the test
section inside 15.9 mm internal diameter tube........................................................ 258
SUMMARY _Toc387378716
1INTRODUCTION ..........................................................................................27
1.1 Objectives..............................................................................................29
1.2 Thesis structure .....................................................................................30
2 LITERATURE REVIEW ...............................................................................31
2.1 Introduction............................................................................................31
2.2 Definitions of terms used in two-phase flows.........................................31
2.3 Two-phase flow parameters ..................................................................32
2.4 Two-phase flow patterns during convective boiling ...............................35
2.4.1 Flow patterns in horizontal two-phase flows....................................35
2.4.2 Flow pattern predictive methods......................................................37
2.5 Fundamentals of convective boiling.......................................................43
2.6 Pressure drop ........................................................................................45
2.6.1 Correlations to predict single-phase frictional pressure drop inside
plain tube..................................................................................................46
2.6.2 Methods to predict two-phase flow pressure drop in plain tubes.....48
2.7 Comparisons from the literature of the two-phase frictional pressure drop
predictive methods ......................................................................................57
2.8 Heat transfer during convective boiling..................................................60
2.8.1 Introduction .....................................................................................60
2.8.2 Predictive methods for flow boiling heat transfer coefficient............61
2.9 Studies concerning twisted-tapes. .........................................................83
2.9.1 Introduction .....................................................................................83
2.9.2 Single-phase flow studies................................................................84
2.9.3 Flow boiling in tube contaninig twisted-tape insert ..........................97
2.9.4 Conclusions based on the literature review...................................106
3 EQUIPMENT, EXPERIMENTAL PROCEDURE AND DATA REDUCTION108
3.1 Introduction ......................................................................................... 108
3.2 Experimental bench ............................................................................ 109
3.2.1 Test section .................................................................................. 110
3.2.2 Visualization sections ................................................................... 112
3.2.3 Pressure drop measurement instruments..................................... 112
3.2.4 Temperature measurements......................................................... 113
3.2.5 Pre-Heater Section ....................................................................... 114
3.2.6 Flow Stabilization section.............................................................. 114
3.2.7 Sub-Cooler.................................................................................... 115
3.2.8 Condenser .................................................................................... 115
3.2.9 Reservoir ...................................................................................... 115
3.2.10 Micro Pump................................................................................. 116
3.2.11 Flow meter .................................................................................. 116
3.3 Ethylene-Glycol/Water Solution Circuit ............................................... 116
3.4 Control and Data Acquisition System.................................................. 116
3.5 Twisted-tape inserts ............................................................................ 118
3.6 Experimental procedure...................................................................... 120
3.6.1 Single-phase flow tests ................................................................. 120
3.6.2 Two-phase flow test...................................................................... 121
3.7 Data reduction Procedures ................................................................. 122
3.7.1 Pressure drop ............................................................................... 123
3.7.2 Heat Exchange with environment ................................................. 124
3.7.3 Heat transfer coefficient ................................................................ 125
3.8 Validation of the experimental bench and determination of the
uncertainty ................................................................................................ 126
3.8.1 Single-phase pressure drop experimental data validation ............ 126
3.8.2 Single-phase flow heat transfer experimental data validation....... 126
3.9 Uncertainty analysis ............................................................................129
4 EXPERIMENTAL RESULTS......................................................................131
4.1 Pressure drop results ..........................................................................132
4.1.1 Pressure drop for tubes without twisted-tape inserts.....................132
4.1.2 Pressure drop for tubes with twisted-tape inserts..........................134
4.1.3 Comparison between the experimental frictional pressure drop
results and the predictive methods.........................................................138
4.1.4 Evaluation of the pressure drop penalty due to twisted-tape inserts
..........................................................................................................................144
4.2 Heat transfer coefficient results ...........................................................146
4.2.1 Results for tubes without twisted-tape...........................................147
4.2.2 Comparison between the experimental heat transfer coefficients
results for tubes without twisted-tape inserts and the predictive methods.
...............................................................................................................149
4.2.3 Results for tubes with twisted-tape inserts ....................................150
4.2.4 Comparison between the experimental heat transfer coefficient
results for tubes with twisted-tape inserts and the predictive methods...157
4.2.5 Overall Performance of the heat transfer enhancement technique160
5 PREDICTIVE METHOD FOR HEAT TRANSFER COEFFICIENT DURING
FLOW BOILING INSIDE TUBES CONTAINING TWISTED-TAPE INSERTS166
6 CONCLUSIONS AND RECOMMENDATIONS..........................................183
6.1 Conclusions.........................................................................................183
6.2 Recommendations for future studies ...................................................185
REFERENCES .............................................................................................187
Appendix A – Calibration of the Experimental measuring equipments .........195
A.1 Uncertainty analysis ............................................................................195
A.2 Absolute pressure transducers............................................................196
A.3 Flowmeter ...........................................................................................197
A.4 Calibration of thermocouples channels ...............................................197
A.5 Calibration of the active power transducers........................................ 199
A.6 Characteristics of differential pressure transducers............................ 201
Appendix B – Experimental Data.................................................................. 202
Appendix C – Publications ........................................................................... 263
Introduction 27
1INTRODUCTION
The convective boiling mechanism has been under intense research over the
last three decades. This is initially result of the fact that most of refrigerants used in
the refrigeration and air-conditioning sectors until the 80’s were related to the
depletion of the ozone layer. During the 1980’s, the refrigerant R134a came up as
the solution and its use spreads rapidly, because its impact on the ozone layer is
negligible. From the mid-90’s, attention has been devoted to the global warming.
Therefore, based on the fact that R134a presents a high global warming potential,
researchers have started to focus on the development of new refrigerants, parallel to
the revival of natural fluids, e.g. ammonia and hydrocarbons.
Independently of the refrigerant choice, results have shown that the refrigerant
leakages, relative to the total refrigerant inventory in the system, increase with
increasing the refrigerant total charge. Ribatski (2008) have shown that leaks are
inevitable and can only be minimized. Most of the refrigerant inventory is located in
the heat exchangers. So, by minimizing the heat exchanger size, both the refrigerant
inventory and the material used for its manufacture are reduced resulting in lower
initial and operational costs. Moreover, the environmental impact during the system
lifetime is also reduced, since, as pointed out by Ribatski (2008), decreasing the
refrigerant inventory implies that the amount of refrigerant leakage decreases in both
relative and absolute values. Under this scenario, several researches have been
developed focusing on new refrigerants and heat transfer enhancement without
major pressure drop penalties in order to reduce the refrigerant inventory and
improving the system efficiency. One of the alternatives to achieve such an objective
is the use of twisted-tape inserts.
Bergles (1999) defines twisted-tape inserts as passive heat transfer
enhancement technique, i.e. it does not require external energy source to increase
the heat transfer coefficient. Sarviya and Veeresh (2012) reported twisted-tape
inserts as one of the important swirl flow devices for passive heat transfer
augmentation. The implementation of this technique occurs through the twisting of a
metal tape which is then fixed internally inside a smooth tube.
28 Introduction
According to Manglik and Bergles (1993), twisted-tape inserts have been used for
over a century, dating from 1896. This technique presents advantage over other
techniques due to the low manufacturing costs, easy installation and maintenance,
and according to Thome and Ribatski (2005) the possibility of being used to retrofit
heat exchangers already in use.
Similarly to most of the heat transfer enhancement techniques, the heat
transfer coefficient enhancement given by twisted-tape inserts is accompanied by a
drastic increase in the pressure drop, impacting the pumping power and,
consequently, the system efficiency. Bandarra-Filho and Saiz-Jabardo (2006) have
pointed out that the use of inserting devices especially in dry expansion evaporator
coils are in fact efficient in upgrading the heat transfer coefficient but at the cost of
significant pressure drop augmentation. However, Shatto and Peterson (1996)
highlighted the fact that the negative result of increasing the pressure drop gradient
by the use of inserts can be overcome by a reduction in the heat exchanger size due
to the heat transfer enhancement. Therefore, to effectively estimate the net benefits
of enhancing heat transfer rates through the use of this device in practical heat
exchangers, both the heat transfer and pressure drop characteristics must be known.
Moreover, since the results of the comparison among the predictive methods
from the literature for heat transfer coefficient during two-phase flow inside tube
containing twisted-tape inserts revealed notable discrepancies. Therefore, an
accurate heat transfer predictive method taken into account the swirl effects
promoted by the tape on the heat transfer coefficient inside horizontal tubes
containing twisted-tapes inserts is still necessary and is one of the objectives of the
present study.
The present study was developed in order to determine when the effect on the
heat exchanger efficiency of this heat transfer enhancement technique overcomes
pressure drop penalties. For this purpose, an experimental investigation has been
conducted to evaluate the effect of twisted-tape inserts on the heat transfer
coefficient and pressure drop augmentations during flow boiling inside horizontal
tubes. The experiments were performed for R134a in 12.7 and 15.9 mm ID tubes.
The overall performance was evaluated according to the following parameters: the
ratio between the heat transfer coefficients per unit of pumping power of the tube with
and without twisted-tape; and the ratio of heat transfer coefficients of the tube with
Introduction 29
and without twisted-tape for the same pumping power keeping the same tube
diameter, vapor quality, saturation temperature and heat flux.
1.1 Objectives
The present study has the general objective of investigating pressure drop and
heat transfer during convective boiling under saturated conditions inside tubes with
twisted-tape inserts.
The specific objectives are the following:
i. Perform an extensive review of the literature concerning flow boiling inside
horizontal plain tubes with and without twisted-tape inserts;
ii. Obtain a broad database for flow boiling inside horizontal tubes with and
without twisted-tapes including pressure drop and heat transfer coefficient
results and based on this database evaluate, the accuracy of heat transfer and
pressure drop predictive methods available in the literature;
iii. Characterize conditions under which the use of twisting tape is favourable,
considering the following parameters: the ratio between the heat transfer
coefficients per unit of pumping power of the tube with and without twisted-
tape and the ratio of heat transfer coefficients of the tube with and without
twisted-tape for the same pumping power. These parameters are given by the
following equations, respectively:
(1.1)
(1.2)
iv. Perform a parametric analysis of the experimental results;
v. Develop a heat transfer predictive method taken into account the swirl effects
promoted by the tape on the heat transfer coefficient.
30 Introduction
1.2 Thesis structure
The structure of this text is composed of literature review, description of the
experimental setup and procedures, presentation and discussion of the experimental
results, development of a new heat transfer model and conclusions.
Below, the chapters of this thesis are briefly described and contextualized.
Chapter 2 presents the review of the literature concerning this study. Definition
of terms applied to two-phase flows and fundamental aspects of convective boiling
are presented. A section is devoted to two-phase flow patterns during convective
boiling inside tubes without twisted-tape. A study of literature concerning flow boiling
pressure drop and heat transfer coefficient with and without twisted-tape is
presented. Description of twisted-tape and models to predict heat transfer coefficient
and pressure drop are also presented.
Chapter 3 presents a description of the apparatus used for the experimental
campaing. The experimental conditions tested are defined and data reduction
procedures are detailed. Validation of the experimental bench and the analyses of
experimental uncertainties are also presented in this chapter.
Chapter 4 presents the heat transfer coefficient and pressure drop
experimental results for convective boiling inside a horizontal tube for plain tubes with
and without twisted-tape inserts. This chapter also presents comparisons of the
experimental results against predictive methods from literature. Moreover, an
analysis of the experimental results given in terms of heat transfer enhancements
and pressure drop penalty factors is also presented.
Chapter 5 is dedicated to the development of a new predictive method based
on the experimental results obtained in present study for estimating the heat transfer
coefficient during convective boiling inside horizontal tubes containing twisted-tape
inserts.
Finally, in Chapter 6 conclusions from the present study are presented.
Suggestions and recommendations for future studies are also provided.
Literature review 31
2 LITERATURE REVIEW
2.1 Introduction
This chapter reviews the main aspects of the literature related to the present
study. Two-phase flow terms are defined and the fundamentals of convective boiling
are presented. A section is devoted to the literature concerning flow patterns,
pressure drop and heat transfer during convective boiling inside horizontal tubes
without twisted-tape. Leading correlations and models to predict heat transfer
coefficient and pressure drop for plain tubes without twisted-tapes are described.
Finally, a section dealing with the literatures concerning heat transfer and pressure
drop during flow boiling and single-phase flow inside horizontal tubes containing
twisted-tape inserts is also presented.
2.2 Definitions of terms used in two-phase flows
The term “phase” is a thermodynamic definition of a state of matter. Generally
the following three states of matter are defined: solid, liquid and gas. Thus, the
simplest case of multiphase flow in which two phases are present for a pure
component is reffered to as two-phase flow.
The following three analytical parameters are considered in the definition of
terms for two-phase flows:
1. Primary parameters:
• Thermal: power;
• Hydraulics: pressure, mass flow rate, fluid temperature, pressure drop;
• Geometry: flow and heated areas, hydraulic and equivalent diameters;
2. Calculated parameters:
• Mass velocity, heat flux, vapor quality and void fraction;
3. Fluid properties:
• Density, viscosity, enthalpy, surface tension, thermal conductivity and
heat capacity.
Below, the definitions of the calculated parameters in two-phase flow from the
primary parameters are given.
32 Literature review
2.3 Two-phase flow parameters
Consider the flow of liquid and vapor in a tube as shown in Fig. 2.1, the total
mass flow rate along the tube is equal to the sum of the mass flows of the liquid, ,
and vapor, phases as follows:
(2.1)
Figure 2.1 - Two-phase flow (liquid-vapor) in a tube (Kanizawa, 2011).
Vapor quality is defined as the ratio of vapor mass flow rate and the total mass
flow rate given as follows:
(2.2)
Thermodynamic equilibrium vapor quality can be deduced from an energy
balance along a tube length and is given as follows:
( ) Lth
LV
i z ix
i
−=
(2.3)
where Li is the enthalpy of the saturated liquid,
LVi is the latent heat of evaporation,
both estimated at the saturation temperature at the position z along the tube length.
In Eq. (2.3) ( )zi is the average local fluid enthalpy in a given cross section at
position z and th
x is the thermodynamic equilibrium vapor quality.
Literature review 33
In case of thermodynamic equilibrium the mass based vapor quality becomes
similar to the thermodynamic equilibrium vapor quality. Usually studies concerning
flow boiling of pure fluids assumes thermodynamic equilibrium and xxth = . So, in the
present study thermodynamic equilibrium will be assumed and thxx = .
The mass velocity of each phase is defined as the ratio between the
correspondent mass flow rate of the phase and the total cross-sectional area of the
tube. Therefore the mass velocity for the liquid phase and vapor phase are given by
the following equations, respectively:
( )A
xmGL
−=
1&
(2.4)
A
xmGV
&=
(2.5)
Hence, the mass velocity of the mixture is given by the sum of the mass
velocity of the two phases:
VL GGG += (2.6)
The mean velocity (insitu velocity) of each phases are the mean velocities at
which the phases actually travel. The mean cross-sectional velocities of the phases
are determined by the ratio of volumetric flow rates and the respective cross-
sectional areas occupied by each phase given as:
(2.7)
(2.8)
where is the superficial void fraction defined as the cross-sectional area occupied
by the vapor relative to the total area of the channel cross-section. This is an
important parameter used to determine the flow pattern transition, heat transfer
coefficient and two-phase pressure drop. The void fraction is defined as:
(2.9)
34 Literature review
where is the time averaged cross sectional area of the channel occupied by
vapor.
From the equation of continuity, it is possible to define liquid and vapor phase
means velocities as follows:
(2.10)
(2.11)
The superficial velocities L
j and Vj are defined as the ratio of the volumetric
flow rate of each phase and the total cross-sectional area of the channel. The
superficial velocities are given as follows:
(2.9)
(2.10)
The two-phase superficial velocity is the sum of the liquid and vapor superficial
velocities and is given as follows:
L Vj j j= + (2.11)
The local drift velocities are defined as the velocity of each phase relative to
the two-phase superficial velocity as follows:
Lj LV V j= − (2.12)
Vj VV V j= − (2.13)
The drift fluxes and are defined as follows:
(2.14)
(2.15)
Literature review 35
2.4 Two-phase flow patterns during convective boiling
Liquid-vapor flows inside tubes present different two-phase flow topologies as
the liquid phase evaporates. These topologies are commonly referred to as flow
pattern. The predominant mechanisms defining the heat transfer coefficient and
pressure drop are influenced by the flow pattern. So, to predict accurately heat
transfer and pressure drop, it is necessary that the prediction methods incorporate
flow pattern characteristics. The flow pattern depends on many parameters such as
liquid and vapor velocities, void fraction, tube inclination and geometry, surface
roughness, pressure and fluid properties. Different nomenclature and classifications
are adopted for flow patterns by distinct authors.
During convective boiling, different flow patterns occur and consequently
different heat transfer mechanisms may be dominant depending on the operating
conditions such as mass velocity, vapor quality and heat flux. Distinct two-phase flow
patterns can be observed depending on the orientation of the tube, whether vertical
or horizontal. One of the main differences is often a tendency to stratification that
occurs in horizontal flows and convectional tubes due to gravitational forces.
The settings of flow patterns in horizontal tubes are more complex than those
observed in vertical tubes. In vertical tubes, the annular flow pattern is almost
symmetrical and the distribution of the average liquid film thickness along the tube
perimeter is almost uniform. For horizontal tubes and reduced mass velocities,
gravitational force determines the two-phase distribution. For low mass velocities and
moderate vapor qualities, gravitational force pulls the liquid downward and makes the
vapor buoyant. Under these conditions, the lower region of the tube presents a
thicker liquid film, while in the upper part of tube the liquid is absent. In the present
study, emphasis is given to two-phase flow patterns occurring for horizontal flows.
2.4.1 Flow patterns in horizontal two-phase flows
The flow patterns observed in horizontal two-phase flows are asymmetrical due
to the influence of gravity. The generally accepted flow pattern are shown in Fig. 2.2
and characterized as follows:
• Bubbly flow: The gas (or vapor phase) is distributed as discrete
bubbles in a continuous liquid phase. The average size of bubbles is
36 Literature review
usually small compared with the tube diameter. At high mass velocities,
the bubbles distribution tend to be more uniform within the liquid.
• Stratified flow: This flow pattern is characterized by segregation of
liquid phase at the tube bottom (under normal gravity conditions) and
vapor at the top. Some authors subdivided this flow pattern into
stratified smooth and stratified wavy. The stratified smooth occurs for
lower vapor velocities. The stratified wavy is also known as wavy flow.
• Wavy flow: This flow pattern is also characterized by the liquid phase
flowing in the bottom and the vapor in the upper part of the tube and
occurs when the vapor velocity is high enough to induce waves on the
liquid-vapor interface. The amplitude of the waves depends on the
relative velocity between the phases and the properties of the fluids,
such as their density and surface tension.
• Plug flow: This is an intermittent flow that occurs at low vapor flow
rates and moderate liquid flow rates. For this flow pattern, liquid plugs,
free of entrained gas bubbles, are separated by zones of elongated
vapor bubbles. The coalescence of the small bubbles rise to larger
bubbles, elongated and occupying the top portion of the tube. Plug flow
is also termed as elongated bubbles.
• Slug flow: When the vapor velocity increases from plug flow, the liquid
slugs become aerated and contain small bubbles. The two-phase
distribution for slug flow is more chaotic compared with plug flow and
the interface between vapor and liquid is not clearly defined.
• Annular flow: Annular flow pattern is characterized by the presence of
a continuos liquid film along the inner surface of the tube and the vapor
phase in the core. For horizontal tubes, the film is asymmetric, with the
thicker liquid film at the bottom of the tube. This behavior is due to the
gravitational effects that tends to reduce the film thickness at the top of
the tube and increases its value on the lower part of the tube.
• Dryout (Not shown in Fig. 2.2): This flow pattern occurs when an
evaporating annular film progressively dries out from the upper part of
the tube with increasing vapor quality
Literature review 37
• Mist flow: This flow pattern occurs when all the liquid is entrained in the
vapor core under high vapor velocity conditions. The vapor phase flows
as a continuous phase and the liquid in the form of droplets is
continued.
In general, these flow patterns can be grouped according to the following:
(1) Dispersed flows: One phase is dispersed in the other that flows as a continuous
phase. The main flow patterns associated are bubbly and mist flows.
(2) Separated-phases: as the denomination suggests, the liquid-vapor interface is
well defined. Such flows are typical of stratified and annular patterns, which
include most of the applications in refrigeration.
(3) Mixed flows: The flow pattern are characterized by the combination of the groups
mentioned. This group includes the slug pattern where bubbles of reasonable
dimension flow intermittently, separated by liquid plugs containing small bubbles
dispersed within the liquid.
Figure 2.2 - Flow patterns observed in horizontal tubes, Cheng et al. (2008).
2.4.2 Flow pattern predictive methods
In the 50’s, two dimensional maps to predict flow pattern began to appears in
the literature. They are attempts to characterize flow patterns based on two-
dimensional plots containing transition lines segregating regions corresponding to the
different flow patterns. Generally, these maps were developed for adiabatic and
isotherm conditions and are based on liquid and gas velocities as coordinate axis.
Superficial velocities and dimensionless groups containing superficial and insitu
velocities of both phases are also used.
38 Literature review
In case of diabatic conditions, generally, the mass velocity and vapor quality are used
in the vertical and horizontal axis, respectively. This procedure allows to follow the
flow pattern transitions with vapor quality variation as the liquid evaporates.
The flow pattern maps available in literature were first developed for nuclear and
petrochemical industries, in this case for flow of oil and gas in large diameter pipes.
Figure 2.3 illustrates the map developed by Baker (1954), based on data for air-water
and oil-water flows.
Figure 2.3 - Flow pattern map for horizontal flow (Baker 1954).
Taitel and Dukler (1976) were the pioneers to develop a method for prediction
of flow patterns based on physical mechanisms present in two-phase flows. In this
method, all parameters of interest are dimensionless and compared with
phenomenological grounded transition curves. The method of Taitel and Duker
(1976) is based on the equations of conservation of mass and momentum assuming
equilibrium stratified flow in slightly inclined pipes. They transformed these equations
to dimensionless form and obtained their solution based on phenomenological
transition criterions. According to Taitel and Duker, transitions are based on the
following physical mecanisim i) Transition between stratified and intermittent or
annular flow patterns: it takes place when the interface becomes unstable as a result
of Kelvin-Helmholtz instability and a finite amplitude wave on the liquid surface
grows; ii) Transition between intermittent and dispersed regimes: taking place when
the turbulent flunctuations are strong enough to overcome buoyant forces acting in
the gas; iii) Transition beteewn intermittent and annular regimes: from the stratified
Literature review 39
flow pattern depending on the liquid level either intermittent or annular flow will
develop, 0.5 being the threshold value of the ratio between the liquid level and the
tube diameter.
In the late 90’s, Kattan et al. (1998) based on Steiner (1993) proposed two-
phase flow pattern predictive method for evaporation of halocarbon refrigerants in
horizontal tubes. A flow pattern map based on the predictive method of Kattan et al.
(1998) is illustrated in Fig. 2.4. This predictive method was developed based on flow
pattern data for five refrigerants covering a wide range of mass velocities and vapor
qualities containing about 700 data points. The method of Kattan et al. (1998)
characterizes the following flow patterns: fully stratified, stratified-wavy, intermittent,
annular flow and mist flow. Their new method predicted correctly 96.2 % of their
experimental data.
Figure 2.4 - Flow pattern map for R134a at Tsat = 30 oC in a 10 mm internal diameter tube for ϕ = 10 kW / m2 using G = 100 kg / m2 s (Kattan et al. 1998).
Zücher et al. (1999) modified the flow pattern transitions proposed by Kattan et
al. (1998) based on new observation for ammonia: stratified to stratified-wavy and
stratified-wavy to intermittent and annular. These modifications were based on the
fact that the authors noted that the heat flux effects according to Kattan et al. (1998)
method were over estimated by predicting the transition from annular to stratified-
wavy flow at too low vapor qualities. Later on, in order of obtaining better predictions
of their data , Zücher et al. (2000) and Zücher et al. (2002) proposed the use of Taitel
and Dukler (1976) void fraction models for fully stratified flow and the Rouhani and
Mas
s ve
loci
ty [
kg/m
2 s]
Vapor quality [-]
40 Literature review
Axelsson (1992) void fraction model for intermittent and annular flows and the
interpolations between both models for stratified-wavy flows. However, the gain of
accuracy by using this void fraction prediction procedure is neglible compared to the
gain of complexity for its implementation. As a practical option, a new and easier to
implement version of the method were proposed by Thome and El Hajal (2002).
These authors introduced the Rouhani and Axelsson (1993) correlation for the void
fraction instead of using Taitel and Dukler (1976) approach.
Wojtan et al. (2005) working with an optical procedure to measure the void
fraction, noted that the stratified/wavy region of the Kattan et al. (1998) method
should be divided into three sub-regions corresponding to the following flow patterns:
slug, slug-stratified/wavy and stratified/wavy. These regions occur at lower vapor
qualities than the intermittent-annular transition. Moreover new dryout and mist flow
patterns were also developed based on their experimental data. By adding these new
flow patterns Wojtan et al. (2005) modified the previous method of Kattan et al.
(1998), for determining flow patterns in conventional horizontal pipes. This method,
whose flows pattern are illustrated in the map shown in Fig. 2.5, is based on
experimental results for R22 and R410A gathered for tubes with internal diameters
between 8.00 and 13.84 mm.
In the method of Wojtan et al. (2005) and Kattan et al. (1998), the parameter
that defines the flow structure and the parcels of the tube perimeter in contact with
the liquid and gas is the dry angle defined as shown in Fig. 2.6:
Figure 2.5 - Flow pattern map evaluated for R22 at Tsat = 5 oC in a 13.84 mm internal diameter tube for
ϕ = 2.1 kW/m2 using G = 100 kg / m2 s to calculate the void fractions. (Wojtan et al. 2005).
Literature review 41
Figure 2.6 - Simplified stratified flow configuration, Kattan et al. (1998).
Wojtan et al. (2005) kept the equation proposed by Kattan et al. (1998) to
determine the stratified to stratified-wavy flow transition boundary given as follows:
(2.16)
The same equation proposed by Kattan et al. (1998) for the transition between
stratified-wavy to intermittent and annular flow was kept by Wojtan et al. (2005) and
is given as follow:
(2.17)
where the liquid Froude number and the liquid Weber number are defined
as:
(2.18)
(2.19)
The dimensionless geometrical parameters , and in Eqs. (2.19)
and (2.20) are determined as follows:
(2.20)
42 Literature review
(2.21)
(2.22)
The void fraction is calculated using the same equation proposed by
Rouhani and Axelsson (1970) and modified by Steiner (1993) given as follow:
(2.23)
where the stratified angle is calculated with the equation proposed by Biberg
(1999) given as follow:
(2.24)
Wojtan et al. (2005) obtained the new flow patterns: slug, slug-stratified/wavy
and stratified/wavy shown in Fig. 2.5 by modified the stratified-wavy flow patterns
proposed by Thome-El Hajal (2002) as follows:
1. A new transition line is added at Gstrat = Gstrat(xIA) at x < xIA (this creates a
new horizontal transition line to the left of xIA and modifies the boundary of the
stratified (S) regime).
2. The stratified-wavy region is divided into three subzones:
• For G > Gwavy(xIA) , this becomes the slug zone.
• For Gstrat < G < Gwavy(xIA) and x < xIA, this becomes the slug/stratified-
wavy zone.
• For x ≥ xIA, this remains as the stratified wavy zone.
Wojtan et al. (2005) developed correlations to predict dryout inception and
completion vapor qualities based on their experimental data keeping the same
dimensionless equations proposed by Mori et al. (2000). The dryout inception and
completion vapor qualities equations are given as follows:
( ) ( )[ ]70.0crit
25.0LV
37.0V
17.0V FrW235.052.0
di e58.0xφφρρ−= (2.25)
Literature review 43
( ) ( )[ ]27.0crit
.09.0LV
15.0V
38.0V
3FrW10.8.557.0
de e61.0xφφρρ −−−= (2.26)
where the is calculated using the same equation proposed by Kutateladze
(1948) given as follow:
(2.27)
After isolating the mass velocity as function of vapor quality in Eqs. (2.29) and
(2.30), the following flow pattern transitions equations were proposed by Wojtan et al.
(2005) for predicting dryout and mist flow pattern curves, respectively:
(2.28)
(2.29)
2.5 Fundamentals of convective boiling
According to Collier and Thome (1994), convective boiling also named in the
literature as flow boiling is defined as the addition of heat to a forced flow of liquid
such that vapor is generated. Convective boiling often combines high heat transfer at
low mass flow rates, as well as a nearly constant temperature along the heat
exchanger length due to the thermally saturated nature of a liquid-vapor mixture.
Convective boiling can occur under sub-cooled and saturated conditions, depending
on the fluid temperature. In case of sub-cooled condition, the bubble nucleation
occurs with the liquid average temperature lower than the saturation temperature. In
saturated condition, convective boiling occurs with liquid average temperature higher
than the liquid saturation temperature.
Figure 2.7 shows how the temperature, heat transfer coefficient and heat
transfer mechanisms varies with the flow pattern during the evaporation process.
Whilst the liquid is being heated up to the saturation temperature and the wall
44 Literature review
temperature remains below that necessary for nucleation, the process of heat
transfer is single phase convective heat transfer to the liquid phase (region A). At
some point along the tube, the wall superheat is enough such that the formation of
vapor from nucleation sites can occur. Initially vapor formation takes place in the
presence of subcooled liquid (region B). From the subcooled boiling region, the
variation of the wall temperature along the tube length is reduced when compared
with single-phase flow. As the vapor quality increases through the saturated nucleate
boiling region (region C) a point may be reached where the predominant heat
transfer mechanism changes from nucleate boiling to conduction through a thin film
and evaporation at the liquid-vapor interface. This transition is preceded by a change
in the flow pattern from bubbly or slug flow to annular flow (region D). In the latter
regions, the thickness of the thin liquid film on the heating surface is such that its
temperature gradient is high and bubble nucleation is suppressed. At some critical
value of the vapor quality the complete evaporation of the liquid film occurs. This
transition is known as ' dryout ' and is accompanied by a drastic rise in the wall
temperature for channels operating with a controlled surface heat flux. In this region
mist flow can occur due to entrainment and deposition of liquid droplets on the tube
surface in (region E). The region comprising the surface dryout and the transition to
dry saturated vapor (region F) is termed as the liquid deficient region. These effects,
and drying of the wall, are the mechanisms that limit the maximum heat transfer rate
for a given flow in a tube.
Literature review 45
Figure 2.7 - Heat transfer and flow pattern behavior during convective boiling (Collier and Thome, 1994).
2.6 Pressure drop
The accurate prediction of the pressure drop in direct expansion and flooded
evaporator as well as in tube-side and shell-side condensers is an important design
parameters for the optimization of refrigeration, air-conditioning and heat pump
systems. The pressure drop along heat exchangers may dramatically affects the
pumping power and the efficiency of the system.
The pressure drop during convective boiling inside a tube is made up of the
following parcels:
Gravitational pressure drop due to the pressure head ;
Accelerational pressure drop due to the variation of kinetic flow energy, which
may result from phase changes, compressibility and of cross section variation;
Frictional pressure drop due to viscous dissipation of the fluids at the tube wall
and between the phases, (interface).
The total pressure drop gradient is given by the sum of these parcels as
follows:
fricaccgravtotal dz
dp
dz
dp
dz
dp
dz
dp
+
+
=
(2.30)
46 Literature review
In horizontal flows, the gravitational parcel is null. The accelerational pressure drop
gradient for two-phase flows in tubes of constant cross-section and for constant mass
velocity is given by:
(2.31)
where for halocarbon refrigerant and convectional tubes can be
calculated from Steiner version of the Rouhani and Axelson drift flux model given by
Eq. (2.26) as suggested by Wojtan et al. (2005).
2.6.1 Correlations to predict single-phase frictional pressure drop inside plain
tube
In several methods from the literature the two-phase flow pressure drop is
generally given as a function of the single-phase flow of liquid or gas. So, in this item
a brief review on the predictive methods for single-phase frictional pressure drop
inside tubes is provided.
The frictional pressure drop gradient for single-phase flow is given as a
function of the friction factor as follows:
(2.32)
where f is the friction factor of Fanning Type.
For developed laminar flow regime inside circular tubes, characterized by
Reynolds number less than 2300, the frictional factor is given by:
Re
16f = (2.33)
where the Reynolds number is defined as follows:
µiGd
Re = (2.34)
Literature review 47
For fully developed turbulent flow characterize by Reynolds number higher
than 4000, the friction factor can be estimated through the Blasius’ equation for
smooth tube given by:
25.0Re
079.0f = (2.35)
The limiting values for using Eq. (2.38) is Reynolds number less than .
In case of tubes with rough surface, pressure drop predictive methods were
proposed based on the tube relative roughness given by ratio of the surface peak-to-
valley roughness and the characteristic dimension of the channel cross section.
Based on experimental data, Colebrook (1939) apud White (1998), adjusted the
following correlation for prediction of the friction factor in a tube with rough surface
during turbulent flow:
+−=
2/1
ir
2/1)4/fRe(
51.2
7.3
d/log0.2
)4/f(
1 ε (2.36)
According to White (1998), Eq. (2.39) is recommendable for Reynolds number
higher than 4000. In this method, the friction factor is obtained through iterative
process. Based on this, Haaland apud White (1998) proposed an alternative explicit
form to obtain the friction factor based on Colebrook, given by:
+−=
11.1
ir
2/17.3
d/
Re
9.6log8.1
)4/f(
1 ε (2.37)
Presenting maximum error less than 2 %, when compared against the original
correlation.
Churchill (1977) proposed the following correlation to estimate the friction
factor in rough surface tubes, valid for both laminar and turbulent flow regimes:
12/12/3
1616
9.0
ir
12
Re
37530
Re
7d27.0log457.2
Re
82f
+
++
=
−
ε (2.38)
48 Literature review
It is worth noting that the methodology proposed by Churchill is explicit, in the
sense that the method does not required iteration to determine the friction factor.
2.6.2 Methods to predict two-phase flow pressure drop in plain tubes
2.6.2.1 Separate-phase methods
The majority of predictive methods for two-phase frictional pressure drop in the
literature were proposed based on separate-phase flow approach. This method
considers that phases are artificially separated into two streams flowing in its own
pipe. The first of these analyses was performed by Lockhart and Martinelli (1949)
and then followed by many others.
Lockhart and Martinelli (1949)
Lockhart and Martinelli (1949) performed pioneering work to evaluate two-
phase friction pressure drop gradient using two-phase multipliers for adiabatic air-
water mixtures at atmospheric pressure. The two-phase multipliers were defined
according to the following equations:
L
22
L
dz
dp
dz
dp
= ΦΦ (2.39)
V
22
V
dz
dp
dz
dp
= ΦΦ (2.40)
In Eqs. (2.42) and (2.43), Φ is reffered to as a two-phase multiplier, 2
dp
dz Φ
is the
two-phase flow frictional pressure drop gradient, L
dp
dz
and V
dp
dz
are frictional
pressure drop gradients assuming that each phase flows alone in a tube of the same
diameter where occurs the two-phase flow.
Literature review 49
The single-phase pressure drop gradients L
dp
dz
and V
dp
dz
are estimated
according to Eq. (2.35) with the frictional factor given by Eq. (2.38).
The two phase flow multipliers are given by:
,X
1
X
C1
2
tttt
2
L ++=Φ for LRe < 4000 (2.41)
,XCX12
tttt
2
V ++=Φ for LRe > 4000 (2.42)
where ttX is the Martinelli parameter for both phases assumed as turbulent flow,
given as follows:
1.0
V
L
5.0
L
V
9.0
ttx
x1X
−=
µ
µ
ρ
ρ (2.43)
The values of the parameter C adjusted experimentally by Chisholm (1967)
are defined according to the flow regime of each phase as shown in Tab. 2.1
Table 2.1 – Coeficients for estimating two phase flow multipliers of Lockhart and Martinelli (1949) apud Thome (2008)
Liquid Gas C
Turbulent Turbulent 20
Laminar Turbulent 12
Turbulent Laminar 10
Laminar Laminar 5
Friedel (1979)
Friedel (1979) proposed an empirical correlation based on a two-phase
multiplier assuming the two-phase mixture flowing as liquid in a tube with the same
diameter for vertical upward and horizontal flows in round tubes given by:
035.0
0L
045.0
H
Fr
0L
22
0LWeFr
FH24.3C
dz
dp
dz
dp
+=
= ΦΦ (2.44)
50 Literature review
In which the parameters FrC , F and H are given by:
( )0L
0V
V
L22
Frf
fxx1C
+−=
ρ
ρ (2.45)
( ) 224.078.0 x1xF −= (2.46)
( )0.91 0.19 0.7
0.240.78 1 1V VL
V L L
H x xµ µρ
ρ µ µ
= − −
(2.47)
It can be noted that the term is a modified Martinelli parameter and so
correlates similar effect as turbulent flow.
The friction factor 0Lf and 0V
f are estimated according to Eq. (2.38) assuming
the two-phase mixture flowing as liquid in a tube of the same diameter. H
Fr is the
homogeneous Froude number relating inertial and gravitational effects and is given
by:
i
2
H
2
Hdg
GFr
ρ= (2.48)
The homogeneous density that takes into account vapor quality effects is
given by the equation below:
1
LV
H
x1x−
−+=
ρρρ (2.49)
The Froude number and Weber number of the two-phase mixture flowing as
liquid contemplate the inertial and surface tension effects related to the interface
disturbances and consequently related to the flow pattern transition. The Weber
number is calculated according to Eq. (2.22).
Friedel (1979) used an experimental database containing 25,000 data points
in order to adjust his method. He obtained a standard deviation of approximate 30 %
when comparing his method against his database. The correlation is recommended
for fluids with (µL / µV) < 1000.
Literature review 51
It is interesting to highlight that the methodology proposed by the Friedel
(1979) contemplates the two extreme values of the vapor quality, corresponding to
single-phase flows of liquid and vapor.
Grönnerud (1979)
In this method, the two-phase multiplier was adjusted based on experimental
results for R12 and ammonia. The two-phase multiplier is given as follows:
−
+=
= 1dz
dp1
dz
dp
dz
dp
25.0
V
L
V
L
Fr
0L
22
0L
µ
µ
ρ
ρ
Φ Φ (2.50)
In which 0L
dp
dz
is estimated according to Eq. (2.38) assuming the two-phase
mixture flowing as liquid in a tube with the same diameter.
The pressure drop term in the right hand side of Eq. (2.53) is a function of the
frictional factor and is defined by Grönnerud (1979) as follows:
( )[ ]5.0
Fr
108.1
Fr
Fr
fxx4xfdz
dp−+=
(2.51)
where the friction factor is given by:
2
0.3
0
10.0055 ln
Fr L
L
f FrFr
= +
(2.52)
The Froude number is calculated assuming the two-phase mixture flowing as
liquids according to Eq. (2.52) by replacing the homogeneous density by the liquid
density.
The Froude number was introduced in the correlation in order to capture the
flow pattern effects, in the sense that with increasing Froude number, the inertia
effects suppress the gravitational effect and the annular flow pattern will be prevalent
while a reduction of Froude number makes the gravitational effect to be prevalent
and hence favouring the occurrence of stratified flow.
52 Literature review
Grönnerud (1979) correlation is developed especially for refrigerants and is
applicable to the entire vapor quality range.
Whalley (1987)
Whalley (1987) has proposed a correlation based on homogeneous model for
determining the two phase multipliers, 2
0VΦ as follows:
2
H
V
0V
H
0V
22
0Vx
1
f
f
dz
dp
dz
dp
ρ
ρΦ Φ =
= (2.53)
where Hf is the friction factor according to the homogeneous model and 0Vf is the
friction factor assuming the two-phase mixture as vapor in a tube with the same
diameter. Two-phase dynamic viscosity is estimated as proposed by Beattie and
Whalley (1981) as follows:
(2.54)
Jung and Radermacher (1989)
Jung and Radermacher (1989) developed a correlation based on the work of
Martinelli and Nelson (1948) and Lockhart and Martinelli (1949) that consist in a
curve fitting of their data, based on the Martinelli parameter. Their correlation is given
as follows:
,X58.3
dz
dp
dz
dp
735.0
tt
0L
22
0L
−=
= ΦΦ for 1X tt ≤ (2.55)
The empirical exponent and multiplicative constant were obtained based on
convective boiling pressure drop data in horizontal tubes for R22, R12, R114 and
R152A. This database includes more than 600 experimental data points covering
saturation pressures from 200 to 800 kPa and mass velocity from 230 to 720 kg/m2 s.
The correlation presented an average deviation of 8.4 % in relation to the
experimental data used for its development.
Literature review 53
Bandarra Filho (2002)
Bandarra Filho (2002) proposed a correlation for the two-phase multiplier 2
0LΦ
based on data for horizontal plain tube for R134a evaporating at a saturature
temperature of 5 oC, mass velocities from 25 to 500 kg / m2 s and tube diameters of
7.0, 7.93, 9.52 and 17.4 mm. In his method as in Jung and Radermacher (1989), the
two-phase multiplier 2
0LΦ is given as a function of the Martinelli parameter. However,
Bandarra Filho (2002) has proposed a more consistent physical format by taking into
consideration the asymptotic condition corresponding to, ∞→ttX , that is related to
only liquid flow, 0=x . The correlation adjusted according to his data is given as:
,X6.21
dz
dp
dz
dp
85.0
tt
0L
22
0L
−+=
= ΦΦ for 1X tt ≤ and 200G ≥ smkg2 (2.56)
This correlation provided an absolute average deviation value of 6.4 % when
compared against the data used for its development.
2.6.2.2 Extrictly empirical method
Müller-Steinhagen and Heck (1986)
Müller-Steinhagen and Heck (1986) proposed a two-phase frictional pressure
drop correlation that is in essence an empirical interpolation as a function of the
vapor quality between all liquid and all vapor flows. Their method is given as follows:
( )1
33
2
1dp
S x Bxdz Φ
= − +
(2.57)
where the factor S is given as:
( )xAB2AS −+= (2.58)
A and B is calculated as follows:
2
0
0
2L
L L i
dp GA f
dz dρ
= =
(2.59)
54 Literature review
2
0
0
2V
V V i
dp GB f
dz dρ
= =
(2.60)
where 0Lf and 0Vf are estimated according to Blasius, Eq. (2.38)
Müller-Steinhagen and Heck (1986) method was developed based on a
comprehensive database including about 9300 experimental data points obtained for
air-water, vapor-water, water-oil and several refrigerants.
2.6.2.3 Flow pattern based predictive method
Moreno Quiben and Thome (2007)
Moreno Quiben and Thome (2007) proposed a method for predicting frictional
pressure drop during two-phase flows based on a phenomenological approach,
taking explicitly into account the flow patterns effects. The frictional pressure drop is
estimated taken into account the phases distribution based on the flow pattern
prediction method proposed by Wojtan et al. (2005). The method was developed
based on a database comprising 2543 experimental data points covering the
refrigerants R134a, R410A and R22, tubes with internal diameters of 8 and 13.8 mm,
mass velocities from 70 to 700 kg / m2 s and vapor qualities between 0 and 1.
For annular flow, the two-phase frictional pressure drop gradient is estimated
from the interfacial shear stress based on the relative velocity between the liquid and
vapor phases derived from the conservation of momentum considering that the
pressure drop gradients is similar for both phases. The pressure drop gradient is
given as follows:
i
iannular
d4
L
p τ∆= (2.61)
where the interfacial shear stress represents the shear stress exerted by the vapor
on the liquid phase calculated according to the following equation:
( )2
LVVii VV2
1f −= ρτ (2.62)
The terms LV and VV are the average velocities of the liquid and vapor phase,
given by Eqs. (2.9) and (2.10), respectively.
Literature review 55
The interfacial friction factor if is estimated by a correlation proposed by the
authors based on their two-phase frictional pressure drop database for annular flow.
The correlation is given by:
( ) [ ] 034.0
0L
08.0
L
V
4.02
VL
2.1
i Weg
R267.0f
−
−
−
=
µ
µ
σ
δρρδ (2.63)
where the liquid film thickness is estimated as follows:
(2.64)
The void fraction is calculated through Eq. (2.26).
The first term in Eq. (2.66) scales the interfacial friction factor to the ratio of the
film thickness to the tube diameter while the second term comes from the
manipulation of the Helmholtz instability equation using as the scaling factor for
the most dangerous wavelength for the formation of interfacial waves. The liquid
Weber is determined by Eq. (2.22).
For slug and intermittent flow pattern, the two-phase flow pressure drop
gradient is calculated considering an interpolation between the single-phase frictional
pressure drop and the two-phase frictional pressure drop for annular flow complying
within the limit of vapor quality tending to zero and , according to the following
equation:
(2.65)
where 0Lp∆ is the the single-phase frictional pressure drop (evaluated at x=0), is
the void fraction at the intermittent to annular transition boundary and ( )annularp∆ is
the two-phase frictional pressure drop evaluated at assuming annular flow and
using the Eqs. (2.64) to (2.68) with to calculate the corresponding film
thickness. The exponent 0.25 was estimated based on the authors’ experimental
results.
56 Literature review
For stratified-wavy flows, the composition of the friction factor for the dry
region and the region of the wall in contact with liquid was taken into account as a
function of the dry angle shown in Fig. 2.6.
So, the stratified-wavy flows frictional pressure drop is calculated from:
( )2
242
V V
stratified wavy stratified wavy
i
VLp f
d
ρ− Φ −
∆ =
(2.66)
The friction factor for stratified-wavy flow in Eq. (2.69) is obtained by a
proration around the perimeter of the tube taken into account wet and dry parcels, as
follows:
( ) ( )( )annulari
*
dryV
*
drywavystratified2 f1ff θθΦ −+=−
(2.67)
where πθθ 2*
drydry = , Vf is the single-phase friction factor for the vapor phase given by
Eq. (2.38), and the interfacial friction factor,i
f , is given by Eq. (2.66) for annular flow.
The dry angle is given by:
strat
61.0
stratwavy
wavy
dryGG
GGθθ
−
−= (2.68)
where stratθ is calculated according to Eq. (2.27)
For Slug+SW flow, the two-phase flow pressure drop gradient is calculated
considering an interpolation between the single-phase frictional pressure drop and
the two-phase frictional pressure drop . The interpolation was
obtained using as parameter the superficial void fraction as follows:
(2.69)
The exponent 0.25 was estimated based on the authors’ experimental results.
For mist flow, all the liquid is assumed flowing as droplet entrained in a continuous
vapor phase with the droplets travelling at nearly the same velocity as the vapor. So,
the authors adopted the homogeneous flow theory to predict two-phase frictional
pressure drop as follows:
Literature review 57
( )H
2
i
Hmist
G
d
Lf2p
ρ∆
= (2.70)
where Hρ is the homogeneous density given by Eq. (2.52)
The friction factor is given by Blasius correlation, according to Eq. (2.38)
with the viscosity estimated according to Cicchitti et al. (1960):
( ) LVH x1x µµµ −+= (2.71)
The process of dryout starts at the top of the tube, where the liquid film is
thinner, and takes place over a range of vapor quality (from the inception of dryout at
dix at the top of the tube to the completion of dryout at dex at the bottom of the tube)
and thus ends when the fully developed mist flow regime is reached. Based on this
behavior, the authors proposed a linear interpolation relation that captures pressure
drop variations between the annular and mist flows without jump in the frictional
pressure drop gradient. So, for dryout region, the pressure drop is given according to
the following equation:
( ) ( ) ( ) ( ) ( ) ( ) ( )[ ]demistditp
dide
di
ditpdryoutxpxp
xx
xxxpp ∆∆∆∆ −
−
−−= (2.72)
where dix and dex are calculated according to Eqs. (2.28) and (2.29) respectively.
2.7 Comparisons from the literature of the two-phase frictional pressure drop
predictive methods
Tribbe and Müller-Steinhagen (2000) reported an extensive comparison of 35
two-phase pressure drop predictive methods against a large database containing
experimental results for air-oil, cryogenics, steam-water, air-water fluid combinations
and several refrigerants. They observed that statistically, Müller-Steinhagen and
Heck (1986) method provides accurate predictions of the pressure drop data when
compared to the other methods. Ould-Didi et al (2002) compared seven of the most
quoted methods in the literature to their database (788 data points). They observed
that the method of Müller-Steinhagen and Heck (1986) and Grönnerud (1979)
consistently gave the best predictions while that of Friedel (1979) was only the third
best. They also mapped their experimental data using Kattan, Thome and Farvat’s
58 Literature review
flow pattern map (1998) and observed that the Müller-Steinhagen and Heck (1986)
correlation provides the best predictions for annular flow and Grönnerud (1979)
correlation for intermittent and stratified wavy flows.
Bandarra Filho (2002) presented a pressure drop study of R134a under flow
boiling conditions in horizontal smooth and microfin copper tubes. He observed that
the method by Jung and Radermacher (1989) was found to provide the best
prediction of his plain tube data.
Mauro et al. (2007) carried out pressure drop measurements for different
refrigerants (R22, R134a, R404A, R407C, R410A, R507A), mass velocities between
190 and 1100 kg / m2 s in horizontal tubes. They obtained 1160 experimental
pressure drop data. According to Mauro et al. (2007), the method proposed by
Friedel (1979) is statistically accurate but fails to capture the pressure drop trends
with changing of the flow patterns. The method underestimate the pressure drop for
intermittent flows and overestimate the values for annular flow and in the dryout
region. Müller-Steinhagen and Heck (1986) correlation gives better predictions than
Friedel (1979) for intermittent flow and under dryout conditions. The model by
Moreno-Quibén and Thome (2007) predicted 77 % of the pressure drop data within
error band of ±30 % and hence presented the best predictions.
Park and Hrnjak (2007) investigated experimentally flow boiling pressure drops
in a horizontal smooth tube of 6.10 mm inner diameter for R744, R410A and R22 and
saturation temperatures from -30 and -15 oC. The method of Müller-Steinhagen and
Heck (1986) was the best for predicting their data. According to Thome et al. (2008),
the method proposed by Friedel (1979) is unsatisfactory for the estimation of
pressure drop for ammonia in tube with diameter of 10 mm providing only 29 % of the
estimation within error band of ±30 %. The method of Müller-Steinhagen and Heck
(1986) gives better results, presenting 48 % of the prediction within error band of ±30
%. Moreno-Quiben and Thome (2007) predictive method poorly predicted the
pressure drop data, predicting only 17 % of the data correctly. According to Revellin
and Haberschill (2009), the method of Friedel (1979) presents satisfactory
predictions of the database gathered by them, predicting 63 % of their data within
error band of ±30 %. In general, Friedel (1979) provided the best prediction of the
high pressure drop data. The method of Müller-Steinhagen and Heck (1986),
presented an almost similar result predicting 62.9 % of the pressure drop data within
error band of ±30 %. In general, this method worked best for low pressure drop data.
Literature review 59
Hernandes (2010) performed a comparison between the leading plain-tube frictional
pressure drop predictive methods and a database gathered from literature containing
experimental results from independent laboratories. From his study, he found that the
predictive method by Müller-Steinhagen and Heck (1986) provided the best
agreement with his database.
Kanizawa (2011) carried out an experimental study on two-phase flow patterns
and pressure drop of R134a inside a 15.9 mm ID. The frictional pressure drop data
obtained from his experiment were compared against the predictions of Grönnerud
(1979), Müller-Steinhagen and Heck (1986), Friedel (1979) Lockhart and Martinelli
(1949) and Moreno-Quibén and Thome (2007). From his study, he found that the
predictive method by Grönnerud (1979) was the best predicting 90 % of the
experimental data within error band of ±30 %.
Grauso et al. ( 2013) investigated experimentally and assessment of predictive
methods available in literature focusing on flow pattern map, heat transfer and
pressure drops during evaporation of R1234ze (E) and R134a in a horizontal, circular
smooth tube. The authors observed that adiabatic frictional pressure gradients of the
two refrigerants were found to be very similar for all the investigated operating
conditions, showing the same trends with vapor quality. Also their results revealed
that the adiabatic frictional pressure gradients of R1234ze(E) is slightly higher than
those obtained for R134a at the same operating conditions. The frictional pressure
drop data obtained from their experiments were compared against the predictions of
Friedel (1979), Grönnerud (1979), Jung and Radermacher (1989), Müller-Steinhagen
and Heck (1986) and the phenomenological model by Moreno-Quibén and Thome
(2007). According to Grauso et al. (2013), the method proposed by Müller-
Steinhagen and Heck (1986) provided best prediction of their database, predicting
89.6 % of the experimental data within error band of ±30 %.
Several studies in the literature have compared experimental two-phase
pressure drop data and predictive methods. Based on the abovementioned
comparisons and according to the authors, it seems that the predictive methods work
better for certain databases. However, the predictive methods of Müller-Steinhagen
and Heck (1986) and Grönnerud (1979) are found to provide the best predictions of
various experimental databases obtained by authors from independent laboratories.
60 Literature review
2.8 Heat transfer during convective boiling
2.8.1 Introduction
Flow boiling heat transfer is a very complex process in which numerous
phenomenons are superimposed, i.e. the saturated liquid generates vapor, which
flows with higher velocity than the liquid phase. The two-phase topology flow
geometry varies due to the shear forces of accelerating vapor; nucleate boiling
generates bubbles that agitates the flow and the liquid film in the case of annular
flows.
Figure 2.8 illustrates qualitatively the typical behavior of the heat transfer
coefficient during in-tube flow boiling for high flow rates. In this figure, we observe
that the flow pattern and the heat transfer mechanisms varies along the evaporation
process with increasing vapor quality. Generally speaking, for vapor qualities below
30 %, the nucleate boiling mechanism is dominant and the heat transfer coefficient
increases with increasing heat flux and saturation pressure as occurs in pool boiling.
With increasing the amount of vapor, the void fraction increases and the annular flow
pattern is established for vapor quality of approximately 40 % then the process of
evaporation in the liquid-vapor interface becomes predominant for 40% <x < 80 %.
Heat transfer mechanism in horizontal flows is affected by the formation of an
asymmetric liquid film during annular flow. For annular flow, the liquid film thickness
reduce progressively due to the liquid evaporation in the liquid-vapor interface. This
results in the reduction of the liquid thermal resistance promoting an increase of heat
transfer coefficient as displayed in Fig. 2.8. The heat transfer coefficient increases
with vapor quality until a condition where occurs the wall dryout. When the inner
surface of the tube is partially dry, the heat transfer rate on the dry regions is much
lower compared to that of the wet portions reducing the perimeter average heat
transfer coefficient. Even after the complete evaporation of the liquid film, under
certain conditions, liquid droplets detached from the liquid film in the annular flow
region are kept flowing within the vapor phase, characterizing the mist flow. In this
region the heat transfer coefficient decreases with increasing vapor quality and after
entrainment deposition of the liquid droplets, the rate of heat transfer tends to be
reduced.
Literature review 61
Figure 2.8 - Schematic representation of the variation of the heat transfer coefficient during flow boiling.
Based on the brief analyses abovementioned, it can be concluded that
obtaining accurate and general methods for calculating heat transfer coefficient is a
difficult task. The heat transfer coefficient is a result of the influence of several
parameters such as the channel dimensions, the flow orientation, surface roughness
and material, mass velocity, fluid properties, saturation pressure, vapor quality, heat
flux and components of each phase in case of mixtures. Usually the methods to
estimate the heat transfer coefficient are based on dimensionless numbers relating
the properties of the fluid, the characteristics of the flow and the heat transfer rate.
The dimensionless numbers of Reynolds, Prandtl and Nusselt are generally used for
correlating single-phase flow inside tubes. Modified versions of these dimensionless
numbers are also considered for flow boiling heat transfer predictive methods plus
additional dimensionless numbers such as Weber and Froude. An approach used to
develop flow boiling heat transfer predictive methods that has been successful is the
superposition of nucleate boiling and forced convection effects and the method
based on the parcels of flow patterns. In the next item, some heat transfer predictive
methods available in the open literature are described.
2.8.2 Predictive methods for flow boiling heat transfer coefficient
Generally, the methods developed to predict the heat transfer coefficient
during flow boiling are based on the combination of the mechanisms of nucleate and
62 Literature review
convective boiling as initially proposed by Chen (1966). The nucleate boiling effect
depends strongly on the heat flux and saturation temperature while the convective
boiling contribution depends strongly on the mass velocity and vapor quality. As
identified and analyzed by Bandara Filho (1997) and Wojtan et al. (2005), the
methods for correlating the heat transfer coefficient under flow boiling conditions can
be classified into the following groups:
2.8.2.1 Convective correlations
Convective correlations: these methods are simple correlations given in terms
of dimensionless numbers such as Martineli parameter. Such correlations are
obtained by assuming annular flow pattern. Under this flow pattern condition,
convective effects are dominant and the Martineli parameter is appropriate to predict
them.
2.8.2.2 Superposition effects
Methods based on superposition effects: these predictive methods assume
that the flow boiling heat transfer coefficient is the superposition of nucleate and
convective boiling effects. The convective effects are given through the product
between the heat transfer coefficient for forced convection inside the tube and a
factor related to intensification of convective effects. Nucleate boiling effects are
correlated through the product between the heat transfer coefficient using a pool
boiling correlation and a factor related to nucleate boiling suppression.
2.8.2.3 Pure empirical methods
Pure empirical correlations: these type of correlations are based on
adjustment of dimensionless numbers based on experimental databases. This type
of predictive method was proposed by Shah (1982), Kandlikar (1990) and Bandarra
Filho (1997). The results provided by these correlations are accurate for the
experimental conditions considered in their development. They are not
recommended for conditions different than the database used for their development.
2.8.2.4 Flow pattern based methods
Flow pattern based predictive methods: these are flow pattern oriented
methods developed for flow boiling heat transfer predictions. These methods take
Literature review 63
into account the effect of the two-phase flow structure on the heat transfer coefficient
mechanisms.
Superposition effects based Group
Chen 1966
In convective boiling, different heat transfer mechanisms are dominant
according to the vapor quality range, heat flux, saturation temperature and mass
velocity levels. At low vapor qualities, nucleate boiling effects prevail while at high
vapor qualities, the heat transfer coefficient is controlled mainly by convective effects.
The predominance of these mechanisms was considered by Chen (1966) when
developing a method for prediction of convective boiling heat transfer coefficient
under condition of vertical flows. He postulated that both convective and nucleate
boiling heat transfer mechanisms play a role in flow boiling heat transfer and they are
additive such that the convective boiling heat transfer coefficient is calculated as
follows:
2 L NBh Fh ShΦ = + (2.73)
The first term on the right-hand side, LFh is the forced convective contribution
where Lh is the liquid-only heat transfer coefficient calculated according to Dittus and
Boelter (1930) correlation with only the liquid phase flowing in the same channel
given as follows:
i
L4.0
L
8.0
LLd
kPrRe023.0h = (2.74)
The second term, NBSh is the nucleate boiling contribution where NBh , is the
pool boiling heat transfer coefficient which is calculated from the Foster and Zuber
(1955) pool boiling correlation. The parameters F and S were defined by Chen
(1966) as the forced convective heat transfer enhancement and suppression factors,
respectively. The parameter F takes into account the increment of convective effects
relative to that of single-phase flow of the liquid. The enhancement of convective
effects is promoted by the flow acceleration due to the evaporation process itself and
in Chen’s method is a function of Martinelli parameter. The parameter S is the
nucleate boiling suppression factor that takes into account steeper temperature
64 Literature review
gradients near the wall due to the fluid motion which tends to suppress the number of
nucleation active sites and was assumed to be a function of the two-phase Reynolds
number,2Re Φ
.
The terms F and S are estimated according to the following equations:
1F = , for 1.0X1 tt < (2.75)
( ) 736.0
tt 213.0X135.2F += , for 1.0X1 tt ≥ (2.76)
where ttX is calculated by Eq. (2.46)
( )Φ2
6 Re10.53.211S −+= (2.77)
where the two-phase Reynolds number is defined as follows:
L
25.1
2 ReFRe =Φ (2.78)
Chen (1966) method was based on a database of 665 experimental data from
six different data sources.
Gungor and Winterton (1986)
Based on a study of the literature, Gungor and Winterton (1986) pointed out
the absence of procedures for determining the flow boiling heat transfer coefficient
that covers the whole range from subcooled to saturated flow boiling. So, they
developed a new method for subcooled and saturated flow boiling under conditions
of horizontal and vertical flows based on the same approach of Chen (1966) using
their experimental database containing more than 4300 data points including water,
refrigerants and ethylene glycol. On contrary to Chen (1966), Gungor and Winterton
(1986) took into account the effect of heat flux on the convective enhancement factor
by including the dimensionless Boiling Number in the equation for its prediction.
Literature review 65
Using the same approach of Chen (1966), Gungor and Winterton (1986)
estimated the liquid-only heat transfer coefficient Lh according to Eq. (2.77). The
Foster and Zuber (1955) pool boiling correlation adopted by Chen (1966) was
replaced by the correlation of Cooper (1984). The method of Cooper (1984) was
considered because of its simplicity and accuracy. The Cooper (1984) pool boiling
correlation is given as follows:
( )0.550.12 0.5 0.67
1055 logNB red redh P P M φ−= − (2.79)
The new convective enhancement factor is given as:
86.0
tt
16.1
X
137.1Bo240001F
++= (2.80)
where is calculated by:
(2.81)
The suppression factor is correlated as a function of convective enhancement
factor and the liquid only Reynolds number, LRe as follows:
17.1
L
26ReF10.15.11
1S
−+= (2.82)
According to the author, for horizontal flow, if the Froude number FrL0, (Eq.
2.21) is lower than 0.05, the values of the parameter as convective enhancement and
suppression factors, must be multiplied by the factors 1F and 1S respectively,
in order to capture flow stratification effects on the heat transfer coefficient present in
horizontal flows and low mass velocities. The factors 1F and 1S are given as follows:
( )0.1 2. 0
1 0
FrL
LF Fr−
= (2.83)
1 0LS Fr= (2.84)
Gungor and Winterton (1987)
66 Literature review
Later on, Gungor and Winterton (1987) modified this method in order of
making it simpler while keeping its accuracy. The modified method is given as
follows.
Fhh L2 =Φ (2.85)
The modified convective enhancement factor in Eq. (2.76) is given as:
0.410.75
0.861 3000 1.121
l
v
xF Bo
x
ρ
ρ
= + +
− (2.86)
where Lh is estimated according to Eq. (2.77).
Jung and Radermacher (1989)
Jung and Radermacher (1989) modified Chen (1966) method based on their
experimental database containing more than 3000 data points covering thirteen
halogenated refrigerants. In their method, the flow boiling heat transfer coefficient is
estimated according to Eq. (2.76) as proposed by Chen (1966). The liquid-only heat
transfer coefficient is calculated according to Dittus and Boelter (1930) correlation
given by Eq. (2.77).
The nucleate boiling heat transfer coefficient NBh is calculated through the
correlation of Stephan and Abdelsalam (1980) given as follows:
( ) 533.0
581.0745.0
Pr207 L
L
V
satL
b
b
LNB
Tk
D
D
kh
=
ρ
ρφ (2.87)
where,
( )
0.5
20.0146
b
L V
Dg
σϑ
ρ ρ
=
− and 35oϑ = (2.88)
The modified convective enhancement factor proposed by Jung and
Radermacher (1989) based on the regression analysis of their experimental data is
given as follows:
Literature review 67
85.0
ttX
129.037.2F
= (2.89)
A new correlation for the suppression factors was also developed by the
authors through the regression analysis of their experimental data. The suppression
factors is given as follow:
1.22 1.134048 ttS X Bo= for 1X tt ≤ (2.93)
0.28 0.332.0 0.1 ttS X Bo− −= − for 5X1 tt ≤< (2.94)
From Eqs. (2.93) and (2.94), it can be noticed that the author did not take into
account the Froude number to capture the effects of two-phase flow stratification due
to gravitational effects in horizontal flows.
Liu and Winterton (1991)
Based on the approach of Chen (1966) and on the method of Gungor and
Winterton (1986), Liu and Winterton (1991) developed a new method to predict
saturated and subcooled flow boiling heat transfer. They observed that predictive
methods for saturated flow boiling without an explicit nucleate boiling term, that rely
only on Boiling Number corrections, do not work for subcooled flow boiling.
Therefore, they proposed a method based on an explicit nucleate boiling term rather
than an empirical Boiling Number dependence. The authors used a database with
over 4200 experimental data points for saturated flow boiling and 991 experimental
data points for subcooled flow boiling. They proposed their method based on a
nonlinear superposition of nucleate boiling and convective effects as suggested by
Kutateladze (1961) using an assympotic exponent of 2. Their method is given as
follows:
( ) ( )2
1pool
2
10L
2
2 SShFFhh +=Φ (2.95)
where 0Lh is calculated from Dittus and Boelter (1930) correlation with the entire
mass flow rate flowing as liquid in the same channel and is given according to Eq.
(2.77) by replacing ReL with ReL0.
68 Literature review
The pool boiling heat transfer coefficient is estimated using Cooper (1984)
correlation given by Eq. (2.82).
The authors modified the enhancement factors proposed by Chen (1966) by
introducing the Prandtl Number, LPr , and the ratio between liquid and vapor densities.
This approach is physically consistent, since with increasing Prandtl Number, the
thickness of the laminar boundary sub-layer decreases, increasing the heat transfer
coefficient. The density ratio was introduced to capture the fact that the greater this
ratio, the greater the speed of the vapor-phase for a fixed mass velocity and vapor
quality, improving vaporization effects on the liquid-vapor interface. The
enhancement factor was defined by them as:
0.35
1 Pr 1LL
V
F xρ
ρ
= + −
(2.96)
The suppression factor was correlated based on the Reynolds number for the
two-phase mixture flowing as liquid in the same channel and the convective
enhancement parameter given by Eq. (2.96). The suppression factor is given as
follows:
( )0.1 0.160
1
1 0.055 ReL
SF
=+
(2.97)
In order to correct the gravity effects associated with the reduced mass
velocities responsible for stratification of the two-phase flow, the authors incorporate
the Froude number such that if 0 0.05L
Fr < , the enhancement and suppression factors
F and S must be multiplied by factor 1F and 1S respectively as, defined in Eqs.
(2.86) and (2.87).
Pure empirical based Group
Kandlikar (1990)
Kandlikar (1990) has pointed out that the correlations proposed until that time
were not suitable to new fluids and therefore, he proposed a new method including a
parameter characterizing the pair fluid-surface as proposed by Rohsenow (1952) for
Literature review 69
pool boiling. His predictive method was developed based on 5246 experimental data
from the literature is given according to the following equation as follows:
( ) ( ) LfL
D
L0L
B
2 hFCBohFr25ACoh +=Φ (2.98)
where 0LFr and Lh are given by Eqs.(2.21) and (2.77), respectively.
In the method of Kandlikar (1990), the convective enhancement and boiling
suppression factors were replaced by the Convective Number Co, and Boiling
Numbers Bo, respectively. As above mentioned, this method can be extended to
different fluids by evaluating only the fluid-dependent parameter fLF , for a specific
fluid based solely on one data point obtained from experiments for flow or pool
boiling. The values of the fLF , for different fluids as proposed by Kandlikar (1990),
are presented in Tab. 2.2.
Table 2.2 - Values of fluid dependent parameter .
Fluid Fluid
Water 1.00 R152a 1.10
R11 1.30 Nitrogen 4.70
R12 1.50 Neon 3.50
R13B1 1.31 R134a 1.63
R22 2.20 R404A 1.55
R113 1.30 R407C 1.50
The values of the constants A, B, C, D and E in Eq. (2.95) are given in Tab.
2.3. The values in the column corresponding to convective boiling dominant
mechanism are used if Co is less than 0.65 , while the value corresponding to
nucleate boiling dominant mechanism are used if Co is greater than 0.65.
Table 2.3 - Values of the empirical constants of the Kandlikar (1990) method.
Constant Convective boiling Nucleate boiling
A 1.1360 0.6683
B -0.9 -0.2
C 667.2 1058.0
D 0.7 0.7
E* 0.3 0.3
*The value of E should be fixed equal to 0 if 04.00 >LFr
Jabardo’s Group
70 Literature review
Based on dimensionless parameters Bandarra Filho (1997) proposed a simple
method to predict flow boiling heat transfer coefficients of halocarbon refrigerants.
The model was developed using experimental data obtained in the Laboratory of Air
Conditioning and Refrigeration Center of University of Illinois at Urban-Champaign,
USA. To capture convective effects and the influence of refrigerant properties such
as liquid and vapor viscosity and densities, Bandarra Filho included the Martinelli
Parameter in its correlation. The Boiling Number was also incorporated to capture
nucleate boiling effects associated with high heat flux under reduced vapor quality
conditions. The author finally included the Froude number to correlate the
experimental results obtained at reduced mass velocities capturing effects related to
the occurrence of both stratified and stratified wavy flow pattern. The proposed
method is given as follow:
(2.99)
(2.100)
In a subsequent study Bandarra Filho (2002) based on his experimental data
proposed different correlations for predicting heat transfer coefficients in horizontal
tubes according to mass velocities ranges and adopting a mass velocity threshold of
200 kg / m2 s. For mass velocity higher than this threshold, the heat transfer
coefficient is correlated as a function of the Martinelli Parameter and Boiling Number
while for lower mass velocities, the heat transfer coefficient is correlated as a function
of the dimensionless number and Froude Number. The dimensionless number
takes into account the heat flux applied to the tube wall and the conduction
through the liquid film. The method is given as follows:
( )23.066.0
ttL2 BoX201hh−+=Φ for 200≥G kg / m2 s (2.101)
+=
−3
1
0L3
2
L2 FrBj74.01hh Φ
for 200<G kg / m2 s (2.102)
where Lh is determined by Eq. (2.77) and the dimensionless Bj is given as follows:
satL
i
Tk
dBj
φ= (2.103)
Literature review 71
In Eq. (2.103) the saturation temperature, Tsat, should be in Kelvin
Barbieri (2005) based on Bandarra Filho (2002) has also proposed different
correlation according to the ranges of mass velocity, tube diameter and Martinelli
Parameter for estimating the heat transfer coefficient during flow boiling inside
horizontal tubes. The method is based on his results and previous data obtained by
Bandarra Filho (2002). The predictive method is given by the following equations:
( )0.76 0.172 1 2.62L tth h X Bo
−Φ = + for 1≤ttX , 150≥G kg / m2 s and 4.172.6 ≤≤ id mm (2.104)
( )0.56 0.702 1 7.35L tth h X Bo
−Φ = + for 1≤ttX , 100=G kg / m2 s and 4.172.6 ≤≤ id mm (2.105)
( )0.36 0.682 00.65L Lh h Fr Bj
−Φ = for 1≤ttX , 100<G kg / m2 s and 4.176.12 ≤≤ id mm (2.106)
where Lh is determined by Eq. (2.77) and Bj by Eq. (2.103).
Thome’s Group
Kattan et al. (1998) has pointed out that the flow boiling predictive methods
proposed until that time neglect mist flow and partial dryout flow pattern by
erroneously assuming conditions for evaporation under these conditions. Based on
this Statuo Quo, the authors developed a heat transfer predictive method for
horizontal flows that incorporates mist flow and dryout flow patterns besides
stratified, intermittent and annular flows. To estimate the flow boiling heat transfer
coefficients, Kattan et al. (1998) assumed that, the mean heat transfer around the
periphery of a evaporator tube in stratified, stratified-wavy and annular flow with
partial dryout regions of the tube is a direct proration of the liquid and vapor heat
transfer coefficients for wet and dry perimeter segments. Therefore, they proposed to
calculate the heat transfer coefficient a method that takes into account the relative
parcels of wet and dry perimeter given as follows:
2
(2 )
2
dry V dry weth hh
θ π θ
πΦ
+ −= (2.107)
where the dry angle, dryθ in Eq. (2.107) and schematically shown in Fig. 2.6, defined
the flow structures and the ratio of the tube perimeter in contact with liquid and vapor.
72 Literature review
For stratified flow, dryθ is equals to the stratified angle stratθ and is calculated
according to the following equation:
strat
stratwavy
wavy
dryGG
GGθθ
−
−= (2.108)
where stratθ is calculated by Eq. (2.27)
For annular (A), and intermittent (I) flows, dryθ = 0. For stratified-wavy flow,
dryθ varies from zero up to its maximum value, stratθ .
The vapor heat transfer coefficient Vh is calculated according to Dittus and
Boelter (1930) correlation, Eq. (2.77), for the vapor only. Reynolds Number given as
follows:
(2.109)
where is calculated through Eq. (2.26)
The heat transfer coefficient on the wet perimeter is calculated with an
asymptotic model that combines the nucleate boiling and convective boiling heat
transfer contributions using an asymptotic exponent of 3 as follows:
( ) ( )[ ] 313
NB
3
CBwet hhh += (2.110)
The convective boiling heat transfer coefficient CBh is calculated from the
following equation:
δδ
L4.0
L
69.0
CB
kPrRe0133.0h = (2.111)
where δ is calculated by Eq. (2.67).
The nucleate boiling heat transfer coefficient NBh is determined from Copper’s
pool boiling correlation given by Eq. (2.82).
Literature review 73
Wojtan et al. (2005) have proposed a flow pattern based method to predict
heat transfer coefficient during flow boiling inside horizontal tubes through
modification of the method proposed initially by Kattan et al. (1998). They observed
that the heat transfer coefficients predicted for stratified-wavy flow were not as
accurate as for annular flow and thereby developed a model to improve the accuracy
of predicting flow boiling heat transfer coefficient in stratified, dryout and mist flow
patterns. This new approach shows a good improvement in the heat transfer
prediction and extends the application of the model to vapor qualities below 0.15.
They kept the same procedure as proposed by Kattan et al. (1998) to calculate the
heat transfer coefficient for wet and dry perimeter of the tube given by Eqs. (2.107) to
(2.111)
For stratified-wavy flow, dryθ varies from zero up to its maximum value, stratθ .
The authors subdivided stratified-wavy flow into three sub zones (slug, slug/stratified-
wavy and stratified-wavy) to determine dryθ . For slug zone (slug), the high frequency
slugs maintain a continuous thin liquid layer on the upper tube perimeter. Thus,
similar to the intermittent and annular flow regimes, dryθ =0
For stratified-wavy zone (SW), the Eq. (2.71) was proposed.
For slug-stratified wavy zone (Slug + SW), the following interpolation between
the other two regimes is proposed forIA
xx < :
strat
61.0
stratwavy
wavy
IA
dryGG
GG
x
xθθ
−
−= (2.112)
The heat transfer coefficient for mist flow is calculated by a new correlation
developed in their study based on their experimental data which is a modification of
the correlation proposed by Groeneveld (1973). The mist flow heat transfer
correlation is given as follows :
i
V83.106.1
V
79.0
Hmistd
kYPrRe0117.0h −= (2.113)
74 Literature review
where the homogeneous Reynolds number HRe is given as:
( )
−+= x1x
GdRe
L
V
V
i
Hρ
ρ
µ (2.114)
and the multiplier factor Y is defined as:
4.0
V
L )x1(11.01Y
−
−−=
ρ
ρ (2.115)
As observed by the authors, the heat transfer coefficient fall sharply in the
dryout region and becomes nearly constant for mist flow. So, they proposed for the
heat transfer coefficient in the dryout region using the following linear interpolation
given as follows:
( ) ( ) ( )[ ]demistdi2
dide
didi2dryout xhxh
xx
xxxhh −
−
−−= ΦΦ (2.116)
where ( )2 dih xΦ is the two-phase heat transfer coefficient calculated from Eq. (2.107)
at the dryout inception quality dix , and ( )demist xh is the mist flow heat transfer
coefficient calculated with Eq. (2.113) at the dryout completion quality dex . Dryout
inception quality dix and dryout completion quality dex are respectively calculated by
Eqs. (2.28) and (2.29). According to the author, if dex is not defined at the considered
mass velocity, it should be assumed that, dex = 0.999.
Literature review 75
Presented in Tab. 2.4, is the summary of the predictive methods for the heat
transfer coefficient during flow boiling for plain tubes described in this Chapter.
76
Literature review
Table 2.4 - Summary of predictive methods for the heat transfer coefficient during flow boiling
Authors Fluids Tube
Orientation
G [kg/m2s]
φ [kW/m2]
i
d [mm] Comments
Chen
(1966)
Water, Methanol,
Cyclo hexane, pentane
Vertical G = 500 – 3600
Mean deviations of 12 % with data of six investigators. Large deviations observed for halocarbon refrigerants.
Gungor and Winterton
(1986)
Water, R11,
R12, R22
R113and R114
Vertical and
Horizontal
G = 60 – 8180
φ =1 - 2.6 3 – 32
The correlation gives mean deviation of 21.4 and 25.0 % for saturated and saturated flow boiling respectively relative to its database. The new correlation is simpler to apply and gives a closer fit to the data used in its development.
Gungor and Winterton
(1987)
Water, R11,
R12, R22
R113and R114
Vertical and
Horizontal
G = 60 – 8180
φ =1 - 2.6 3 – 32
The correlation was recommended as the best when compared with the flow boiling data of R134a of Thome (1997a).
Jung and Radermacher
(1989)
R11, R12, R13, R22, R32, R114, R123, R124, R134a, R141b, R142b,
R143a, R152a.
Horizontal G = 100 – 700
φ =5 - 40 8
The proposed method gives standard deviation in the order of 3 % while Chen (1966) of 70 % when compared to the authors’ database.
Kandlikar (1990)
Water, R11, R12, R22, R13B1, R113,R 114, R152a ,Nitrogen and
Neon
Horizontal G = 15 – 8180
φ =1.2 - 2.0 4.6 – 32
Mean deviation of 15.9 % for water and 18.8 % for the overall database. A fluid dependent parameter Ffl was introduced.
Liu and Winterton
(1991)
Water, R11, R12, R22, R113, R114 and Etileno-
glicol
Vertical and
Horizontal
G = 12.4 – 8180
φ =0.4 - 2.62 3 – 32 The new method can be used for saturated
subcooled boiling data.
Kattan et al. (1998)
R123, R134a, R402a, R404a and R502, Horizontal
G = 100 – 500
φ =0.44 – 7.83 10.92 – 12
This is a flow pattern based method. The method is better than the existing methods at high vapor qualities (x > 85 %) and for stratified types of flows.
Literature review
77
Table 2.4(Continuation) - Summary of predictive methods for the heat transfer coefficient during flow boiling
Authors Fluids Tube
Orientation
G [kg/m2s]
φ [kW/m2]
i
d [mm] Comments
Bandarra Filho (1997) R12, R22 andR134a Horizontal
G = 25 -500
φ =1.9-40 7.04- 10.92
The proposed method provide an absolute average deviation in the order of 12 % relative to the experimental data and the correlation is simpler to apply
Bandarra Filho (2002)
R22, R134a, R404a, R407C and R417A Horizontal
G = 25 -1100
φ =5 – 30 7.93- 17.4
The proposed method provide an absolute average deviation of 15 % and 5.9 % for high and reduced range of mass velocity, respectively.
Barbieri (2005) R134a Horizontal
G = 25 – 500
φ =5 and 10 6.2 - 17.4 The proposed models provided best predictions of the
experimental data obtained in his study
Wojtan et al. (2005b) R22 and R410A Horizontal
G = 70 – 700
φ =2.0 - 57.5 8.00 and 13.84
The new model reasonably predict most of the experimental data used in their study, extends the application of the model to vapor qualities below 0.15 and the heat transfer coefficients in the dryout and mist flows regions.
78 Literature review
2.8.2.5 Comparison between some of the predictive methods for heat transfer coefficient during two-phase flow
Figures 2.9 and 2.10 display comparisons among the predictive methods for
the heat transfer coefficient in plain tubes described in this Chapter. These figures
reveals notable discrepancies among the methods.
As shown in Fig. 2.9 for mass flow of 75 kg / m2 s, when stratified flow is
expected, Bandarra Filho (1997) method presented almost constant heat transfer
coefficient with increasing vapor qualities until the onset of dryout indicating a typical
behavior of stratified flow pattern. On the other hand, in Fig. 2.10 for mass velocity of
150 kg / m2 s, heat transfer coefficient initially increases with increasing vapor quality,
up to around 50 %, further vapor quality augmentation causes a progressive
reduction of the heat transfer coefficient. This behavior is significantly different from
those trends displayed by the other predictive methods.
Bandarra Filho (2002) and Barbieri (2005) methods display similar trends for
the heat transfer coefficient with increasing vapor quality as illustrated in Figs. 2.9
and 2.10, their methods provide an unexpected behavior according to which the heat
transfer coefficient keeps increasing with vapor quality even for x close to the unity.
The augmentation of the heat transfer coefficient with increasing vapor quality is a
typical behavior of annular flows in which the evaporation of liquid film and
convective effects are predominant. Such behavior is generally captured by the
predictive methods available in the literature as well as Bandarra Filho (2002) and
Barbieri (2005) by the Martineli Parameter.
Jung and Radermacher (1989) and Liu and Winterton (1991) correlations also
display that the heat transfer coefficient increases with increasing vapor quality.
However, in case of these authors the increment of the heat transfer coefficient with
vapor quality is less stepper than according to the methods of Bandarra Filho (2002)
and Barbieri (2005). Here, it is important to highlight that Jung and Radermacher
(1989), Liu and Winterton (1991), Bandarra Filho (2002) and Barbieri (2005) have
considered in the development of their methods, data obtained under electrical
heating conditions. Therefore, their methods does not include results for dryout and
mist flows and, so, these methods are not recommendable for vapor qualities close
to 1
Literature review 79
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
x [-]
h [
kW /
m2
oC
]
Jung and Radermacher (1989)Kandlikar (1990)Liu and Winterton (1991)Bandarra Filho (1997)Bandarra Filho (2002)Barbieri (2005)Wojtan et al. (2005b)
Figure 2.9 - Comparison among of the predictive method for heat transfer coefficient during convective
boiling of R245fa, ϕ = 7.5 kW / m², Tsat = 5 °C, G=75 kg / m2, and di = 6 mm.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
x [-]
h [
kW /
m2 o
C]
Jung and Radermacher (1989)Kandlikar (1990)Liu and Winterton (1991)Bandarra Filho (1997)Bandarra Filho (2002)Barbieri (2005)Wojtan et al. (2005b)
Figure 2.10 - Comparison among of the predictive method for heat transfer coefficient during
convective boiling R245fa, ϕ = 7.5 kW / m², Tsat = 5 °C, G=150 kg / m2, and di = 6 mm.
As shown in Figs. 2.9 and 2.10, it is interesting to note that according to
method of Kandlikar (1990) the heat transfer coefficient first decreases with
increasing vapor qualities up to 10 % and then the heat transfer coefficient
progressively increases up to a vapor quality of approximately 80 % with increasing
vapor qualities. These behaviors characterize the predominance of nucleate boiling
effect under low vapor quality conditions followed by annular flow and the
80 Literature review
predominance of convective effects under moderate and intermediary vapor quality
conditions. For vapor qualities higher than 80 %, the onset of dryout occurs drying
the tube wall internal surface and resulting in reduction of heat transfer coefficient.
The method of Wojtan et al. (2005b) seems to capture these behaviors as well but in
this case the flow patterns effect is more drastic.
Table 2.5 presents variation of heat transfer coefficient estimated by the
predictive methods based on different experimental operating conditions.
Table 2.5 - Variation of heat transfer coefficient estimated by the predictive methods based on different experimental operating conditions
G=75 kg / m2 s G=75 kg / m2 s
x=0.1 x=0.7 Predictive methods
R1=R134a R2=R245fa
Tsat1 =5o C Tsat2 =15o C
D1=6 mm D2=15 mm
=7.5 kW/m2
=20 kW/m2 R1=R134a
R2= R245fa Tsat1 =5o C Tsat2 =15o C
D1=6 mm D2=15 mm
=7.5 kW/m2
=20 kW/m2
Jung and Radermacher (1989) 12.7 16.9 -13.7 52.6 21.8 10.1 -16.7 2.3
Kandlikar (1990) - 5.6 -16.8 91.1 - 7.2 -16.7 26.8
Liu and Winterton (1991) 51.3 9.6 -31.8 43.6 52.8 10.1 -31.9 17.9
Bandarra Filho (1997) 19.4 0.4 -38.8 13.4 14.5 0.6 -42.3 19.2
Bandarra Filho (2002) 23.7 2.1 76.7 90.4 23.6 2.1 90.8 91.3
Barbieri (2005) 12.4 1.4 -16.7 7.2 8.0 6.4 -16.8 15.2
Wojtan et al. (2005b) 54.0 16.3 -4.1 91.2 15.7 7.7 -23.2 72.7
G=150 kg / m2 s G=150 kg / m2 s
x=0.1 x=0.7 Predictive methods
R1=R134a R2=R245fa
Tsat1 =5o C Tsat 2=15o C
D1=6 mm D2=15 mm
=7.5 kW/m2
=20 kW/m2 R1=R134a
R2= R245fa Tsat1 =5o C Tsat2 =15o C
D1=6 mm D2=15 mm
=7.5 kW/m2
=20 kW/m2
Jung and Radermacher (1989) 0.8 10.8 -15.5 33.1 22.2 9.9 -16.7 0.6
Kandlikar (1990) - 5.3 -16.8 86.7 - 8.8 -16.7 18.4
Liu and Winterton (1991) 49.9 9.3 -16.8 38.2 51.3 9.8 -16.7 21.6
Bandarra Filho (1997) 15.9 0.3 -25.5 17.5 11.3 1.4 -44.0 23.1
Bandarra Filho (2002) 23.8 2.1 64.6 89.3 23.7 2.1 82.7 90.8
Barbieri (2005) 13.7 1.1 -16.8 6.7 7.3 6.2 -16.8 14.9
Wojtan et al. (2005b) 41.9 14.1 -16.9 86.9 32.8 2.8 -28.6 50.2
*When not specified the calculations of, , were made for R134a based on the following conditions: Tsat=5 oC, , and di =9.5 mm
* ( ) %100*112 hhhh −=
* 1h refers to the condition characterized by subscript 1 and * 2h to the condition characterized by subscript 2
Literature review
77
82 Literature review
As can be noticed in Tab. 2.5, the effect of saturation temperature on heat
transfer coefficient increases with increasing saturation temperature under low vapor
quality condition. This effect becomes only marginal under high vapor quality
conditions. These behaviors are captured by the predictive methods of Jung and
Radermacher (1989) and Wojtan et al. (2005b). The predictive methods of Liu and
Winterton (1991), Kandlikar (1990), Bandarra Filho (1997), Bandarra Filho (2002)
and Barbieri (2005) were not able to capture these effects.
According to Tab. 2.5, the fact that the heat transfer coefficient increases with
decreasing tube diameter is well captured by the predictive methods of Jung and
Radermacher (1989), Bandarra Filho (1997), Barbieri (2005), Wojtan et al. (2005b),
Kandlikar (1990) and Liu and Winterton (1991). The predictive method of Bandarra
Filho (2002) fails to capture the effect of the tube diameter on the heat transfer
coefficient.
Considering the influence of fluid refrigerants on the heat transfer coefficient
increase, according to Tab. 2.5, the predictive methods of Wojtan et al. (2005b) and
Liu and Winterton (1991) shows highest effect among other predictive methods like
Jung and Radermacher (1989), Bandarra Filho (1997), Bandarra Filho (2002) and
Barbieri (2005) independent of the conditions displayed in Tab. 2.5. This effect is not
accertaing for predictive method of Kandlikar (1990) since the value of fluid
dependent parameter for R245fa is not provided by the author.
The effect of heat flux on heat transfer coefficient increases with increasing
heat flux under low vapor quality condition. For higher vapor quality conditions, this
effect causes heat transfer coefficient decreases independent of mass velocity. As
shown in Tab. 2.5, these behaviors are captured by the the predictive methods of
Kandlikar (1990), Liu and Winterton (1991), Wojtan et al. (2005b) and Jung and
Radermacher (1989). The predictive methods of Bandarra Filho (1997), Bandarra
Filho (2002) and Barbieri (2005) fails to capture the effect of the heat flux on the heat
transfer coefficient.
It is interesting to highlight that in Tab.2.5, the discrepancies among the results
provided by the different predictive methods characterized the perculiarity of each
method with respect to its mode of development.
Literature review 83
2.9 Studies concerning twisted-tapes.
2.9.1 Introduction
The process of improving the thermo hydraulic performance of heat
exchangers is referred in the literature as heat transfer enhancement. The
engineering cognisance of the need to increase the thermal performance of heat
exchanger, thereby effecting energy, material and cost savings, as well as a
consequential mitigation of environmental degradation, has led to the development
and use of many heat transfer enhancement techniques (Dalkilic and Wongwises,
2009). In general, enhancement techniques can be divided into two groups named by
Bergles (1999) as active and passive techniques. A detailed description of these
techniques is given by Webb (1994). Active techniques are heat transfer
augmentation methods which requires the addition of external energy to enhance the
heat transfer flux for a fixed wall superheating. An example of such a technique is the
vibration of tubes. Passive techniques are generally based on surface and
geometrical modifications by incorporating inserts and additional devices. Generally,
passive techniques promote higher heat transfer coefficients by disturbing and
altering the existing flow behavior. Passive techniques hold the advantage over the
active techniques due to the fact that they do not require any direct input of external
power to sustain the enhancements characteristics.
The use of heat transfer enhancement techniques lead to increase in heat
transfer coefficient but at the cost of increasing pressure drop. So, while designing a
heat exchanger using any of these techniques, analyses of both heat transfer
coefficient and pressure drop have to be done. Apart from this, issues like long term
performance and detailed economic analysis of heat exchanger has to be studied.
Bandarra Filho and Saiz-Jabardo (2006) reported that the use of devices for
intensification of heat transfer is not new in the refrigeration and air conditioning
industry, especially in the evaporators such as flooded or direct expansion type
among others. Twisted-tape is one of the passive techniques used for more than a
century and they are widely used due to the possibility of being used in a new and to
retrofit heat exchangers already in use. Twisted-tapes inserts have provided
significant heat transfer enhancement in past studies. However, until now it is not
clear, the operational conditions under which the heat transfer coefficient
84 Literature review
augmentation by the use of twisted-tape inserts overcomes pressure drop penalty
and its use is really brings benefits to the heat exchanger.
The twisted-tape insert, schematically presented in Fig. 2.12, is geometrically
characterized by the twist-ratio, defined as the ratio between 180° turn length H and
the internal diameter as follows:
i
Hy
d= (2.117)
Figure 2.11 - Schematic view of twisted-tape insert inside a tube (Kanizawa and Ribatski 2012).
2.9.2 Single-phase flow studies
An early evaluation of the status of swirl flow studies was presented by
Gambill and Bundi (1962). According to them, a large amount of data was collected
over a broad range of working fluids, Reynolds numbers and Nusselt numbers.
The emphasis of the present study was directed towards convective boiling inside
tubes containing twisted-tape inserts. However, single-phase flow heat transfer
research with twisted-tape inserts is the ground work for the development of a study
on convective boiling heat transfer in tubes with twisted-tape inserts. Therefore, this
item is initially dedicated to single-phase flow inside tubes containing twisted-tape
inserts.Then, the literature concerning twisted-tape during convective boiling in tubes
is critically described. Heat transfer and pressure drop predictive methods for single
and two-phase flow are also described.
2.9.2.1 Experimental studies concerning single-phase flow in tubes containing twisted-tape
Table 2.6 describes schematically the studies from the literature concerning
single-phase flows inside tubes containing twisted-tape inserts. According to this
table, experiments were performed for twist-ratios between 1.81 and 12 using the
Literature review 85
heating methods: (i) Joule effect by applying a direct current to the test section
surface; (ii) counter current flow (water glycol water mixture and steam). Test
sections made of stainless steel, Aluminium and Inconel.
Several researches have been carried out regarding augmentation of heat
transfer with twisted-tapes inserts for single-phase flow. Smithberg and Landis (1964)
analytically and experimentally studied pressure drop, velocity distribution and heat
transfer characteristics for fully developed turbulent flows in tubes containing twisted-
tape swirl generators. They observed that the use of twisted-tapes increases the
Heat transfer coefficients. Heat transfer coefficients increases especially for low twist-
ratios, but not without an increase in the friction factor. They concluded that twisted-
tapes is an inexpensive and efficient heat transfer enhancement technique
recommendable for tubular heat exchangers already in use.
The investigation of subcooled boiling by Gambill et al. (1968) yielded useful
information dealing with heat transfer and pressure drop for water flowing in tubes
with twisted-tape inserts. The results of their study showed that, the swirl flow
produced heat transfer coefficient enhancement as much as two times larger than for
axial flow of the same fluid in some ranges of Reynolds number and twist-ratios.
Lopina and Bergles (1969) found heat transfer coefficient enhancements above 20 %
for a given pumping power during both cooling and heating processes by using
twisted-tape compared to plain tubes without twisted-tape. They also proposed a
correlation for predicting single-phase flow heat transfer coefficient and the friction
factor inside tubes containing twisted-tape insert based on their experimental data.
The proposed correlations agree reasonably well with their experimental data points.
Date (1974) has investigated the twisted-tape performance for laminar single-
phase flows. Their experimental results revealed that, for high Reynolds and Prandtl
Numbers and low twist-ratios, the twisted-tape inserts increases the heat transfer
coefficients by a factor of 1.5 compared to tubes without twisted-tape at the same
experimental conditions. The study of Hong and Bergles (1976) on augmentation of
heat transfer during laminar flow in tubes containing twisted-tape inserts showed, as
expected, that the Nusselt Number is a function of the twist-ratio, and the Reynolds
and Prandtl Numbers. They observed that the heat transfer coefficient can be
improved by a factor of two to three by insertion of twisted-tapes when compared to
the flow through an empty tube at the same flow conditions
86 Literature review
Agrawal and Varma (1991) observed that the improvement of the heat transfer
coefficient by using twisted-tape is accompanied by a drastic increase of pressure
drop, impacting the system pumping power. They found heat transfer coefficient
enhancement from 27-133% for the tube with twisted-tape relative to the same tube
without twisted-tape inserts.
Manglik and Bergles (1993a, b) observed heat transfer and pressure drop
enhancements for laminar and turbulent single-phase flow inside tubes with twisted-
tape inserts. The following mechanisms were suggested by them as responsible for
this behavior: (i) partial cross-section obstruction; (ii) hydraulic diameter reduction;
(iii) augmentation of the flow effective length; (iv) swirl flow induced by the tape; and
(v) fin effect, if a good contact between the tape and the tube wall is attained.
Chakroun and Al-Fahed (1996) have investigated the effects of twisted-tape
width on the heat transfer and friction-factor performance for laminar flow in circular
tubes containing twisted-tapes. Their results revealed that the presence of twisted-
tape inserts inside the tubes caused the friction factor and heat transfer coefficient to
increase by factors of 3 to 7 times and 1.5 to 3 times, respectively, compared to the
data for the tube without twisted-tape. The authors recommended using loose-fit
tapes for low Reynolds numbers instead of tight-fit because they are easier to install
and remove for cleaning purposes.
Agarwal and Raja Rao (1996) obtained friction factor increments from 3.13 to
9.71 times compared to values for plain tubes without twisted-tapes. Nusselt
Numbers were found to be 2.28 to 5.35 and 1.21 to 3.70 times the values for plain
tubes without twisted-tape respectively based on similar flow rate and similar
pumping power for the twist-ratio of 2.41. They concluded that lower twist-ratios are
preferable to obtain maximum heat transfer enhancement. Maximum Nusselt
Numbers for the smallest twist-ratio were also obtained by Promvonge et al. (2006).
These authors have focused their study on heat transfer and friction factor
characteristics for tubes containing twisted-tape insert and Reynolds Number from
2000 to 12000.
Naphon (2006) observed higher heat transfer coefficients for tube with twisted-
tape insert compared to those obtained for tubes without twisted-tape insert at the
same Reynolds Number. He also found that the heat transfer coefficient increases
with decreasing the twist-ratio. Joshi et al. (2011) observed an increase in heat
Literature review 87
transfer coefficient accompany by an increase of friction factor. with decreasing the
twist-ratios.
Wongcharee and Eiamsa-Ard (2010) investigated friction and heat transfer
characteristics of laminar swirl flow for tubes inserted with alternate segment of
clockwise and counter-clockwise twisted-tapes. The experimental results revealed
that the heat transfer coefficient and friction factor associated by alternating
clockwise and counter-clockwise twisted-tapes are higher than those associated with
a single twisted-tape and plain tube without twisted-tape. They also observed that
friction factor and heat transfer coefficient increase with decreasing twist-ratio due to
the higher intensity of swirl flow and the longer flowing path.
Hata and Masuzaki (2011) have performed experiments for twisted-tape-
induced swirl flow in a short circular tube. The authors analysed the influence of the
twist-ratio, on swirl velocity, fanning friction factor and heat transfer coefficient. Their
results revealed that the friction factor and heat transfer coefficient for the tube
without twisted-tape are lower than those for the tube with twisted-tape. Moreover,
they found that this difference increases with decreasing twist-ratio for wide ranges of
Reynolds Number and swirl velocities.
Bas and Ozceyhan (2012) investigated the heat transfer enhancement for
tubes with twisted-tape inserts loosely placed in the tube. In their study, the effects of
twist-ratios and clearance ratios (ratio between the difference of the tube diameter
and the tape width and the tube diameter) on heat transfer coefficient and friction
factor. Their experimental results revealed that using twisted-tape losely positioned in
the tube instead of tightly fitted is advantageous to the heat transfer performance.
Moreover, they suggested that the best operating condition occurs for low Reynolds
Number.
Sarviya and Veeresh (2012) investigated heat transfer and friction factor
characteristics for tubes fitted with twisted casted screen. The authors found that the
heat transfer coefficient and friction factor increases with decreasing twist-ratio.
Moreover, the performance evaluation for tube with twisted casted screen is
observed to be greater than unity. They concluded that higher heat transfer rates can
be achieved using porous inserts at the expense of a reasonable pressure drop.
88
Literature review
Table 2.6 - Summaries of some studies in the literature concerning single-phase flows inside tubes containing twisted-tape inserts
Authors Fluids Tube
Orientation Internal Diameter
(mm) Twist-Ratio Material Heating Method
Objective of the Study
Smithberg and Landis (1964) Water and Air Horizontal 35.1 1.81, 2.17 and 22 -- -- f
Lopina and Bergles (1969) Water Vertical 4.92 2.48, 3.15, 3.52, 5.26 and
9.2 Inconel Direct DC
Agrawal and Varma (1991) R12 Horizontal 10 3.76, 5.58, 7.37, 10.15 and
∞ SS Direct AC ,f
Manglik and Bergles (1993 a, b)
Water and etiline-Glycol Horizontal 14 3.0; 4.5 and 6.0 -- Direct AC ,f
Agarwal and Raja Rao (1996). Oil Horizontal 25 2.41 and 4.84 SS Direct AC ,f
Chakroun and Al-Fahed (1996) Oil Horizontal 14 3.6, 5.4 and 7.1 Aluminium -- ,f
Naphon (2006) Water Horizontal 8.10 2.5 and 3 Aluminium Hot water ,f
Wongcharee and Eiamsa-Ard (2010) Water Horizontal 19 3,4 and 5 Aluminium Direct AC ,f
Joshi et al. (2011) Water Horizontal 20 9, 9.5, and 12 Aluminium Direct AC ,f
Hata and Masuzaki (2011) Water Vertical 6 2.39, 3.39 and 4.55 SUS304. Direct AC ,f
Bas and Ozceyhan (2012) Air Horizontal 56 2, 2.5, 3, 3.5 and 4 Aluminium Direct AC ,f
Sarviya and Veeresh (2012) Water Horizontal 9.5 5 and 7 Aluminium Hot water ,f
Literature review 89
2.9.2.2 Predictive methods for single-phase flow in tubes containing twisted-tape inserts
Friction factor
Lopina and Bergles (1969) based on their data described in Tab. 2.6
developed a method for predicting friction factor during single-phase flow inside
tubes containing twisted-tape inserts. The proposed method is given as follows:
406.0
ha
s
y
75.2
f
f=
(2.118)
where is the fanning friction factor for the plain tube and is calculated by:
2.0Re046.0=af
(2.119)
Chakroun and Al-Fahed (1996) explically included Swirl Number Sw in their
method and proposed a correlation for friction factor based on their experimental
data given as follows:
( ) ( )1 62 6 2.5515.767 2 2 4 1 10
i if e d e d Swπ π − = + − − + (2.120)
The Swirl Number describes the intensity of the secondary motion induced by
the twisted-tape and is given as follows:
y
ReS Sw
W = (2.121)
where,
L
iLs
Sw
dVRe
µ
ρ= (2.122)
The swirl velocity sV is given as follows:
( )[ ] 212
as y21VV π+= (2.123)
90 Literature review
where aV is the axial velocity given as:
c
aA
mV
ρ
&= (2.124)
cA is the axial cross-sectional area given as :
2( 4)c i iA d edπ = − (2.125)
Later on, Naphon (2006) based on his experimental data described in Tab. 2.6
and taken into account twist-ratio effects proposed a correlation for predicting friction
factor during single-phase flow inside tubes containing twisted-tape inserts. The
correlation predicted their friction factor experimental data within an error band of
±10 .The proposed correlation is given as follows:
[ ] 045.11414.0 y1Re517.3f −− += (2.126)
Wongcharee and Eiamsa-Ard (2010) developed also an empirical correlation
for the friction factor based on their experimental data given as follows:
0.304 0.89612.886Ref y− −= (2.127)
The proposed correlations agree quiet well with their experimental data and
predicted their friction factor experimental data within an error band of ±5 .
Similarly, based on their own experimental results Bas and Ozceyhan (2012)
propose a correlation for the friction factor given as follows:
( ) 65.0
i
45.0dyRe32.12f
−−= (2.128)
Hata and Masuzaki (2011) based on their experimental results proposed a
correlation for the prediction of single-phase friction factor. In their method, they took
into account twisted-tape-induced axial velocity created by the presence of twisted-
tape inserts. The proposed correlation is given as follows:
( )125.0 y17.41Re126.0f −− += (2.129)
Literature review 91
where, µ
ρ ia dV=Re with aV calculated through Eq. (2.124)
Figures 2.12 and 2.13 display comparisons of the friction factor versus the
Swirl Reynolds Number estimated according to the predictive methods described in
this Chapter, the comparison are perfomed for single-phase flow of R134a in a 12.7
ID tube for twist-ratios of 14 and 3. Except for the predictive method of Chakroun and
Al-Fahed (1996), it is observed that the friction factor decreases with increasing Swirl
Reynolds Number for all twist-ratios as expected. This behavior is also observed for
the plain tube without twisted-tape according to Blasius (1913).
The predictive method of Chakroun and Al-Fahed (1996) provides an
unrealistic results according to which the friction factor increases with increasing
Swirl Reynolds Number. It is important to highlight in Figs. 2.12 and 2.13, the
discrepancies among the results provided by the different predictive methods
achieving differences higher than one order of magnitude.
2,500 5,000 10,000 20,000 40,0002.5x10-3
1.0x10-2
1.0x10-1
1.0x100
1.0x101
Resw [-]
f [-
]
Hata and Masuzaki (2011)
Naphon (2006)Wongcharee and Eiamsa-Ard (2010)
Chakroun and Al-Fahed (1996)
Blasius (1913)
y=14Lopina and Bergles (1969)
Figure 2.12 – Comparison among predictive methods for friction factor during single-phase flow inside tube with twisted-tape insert for R134a, Tsub =10 oC.
92 Literature review
2,500 5,000 10,000 20,000 40,0002.5x10-3
1.0x10-2
1.0x10-1
1.0x100
1.0x101
4.0x101
Resw [-]
f [-
]
Lopina and Bergles (1969)
Wongcharee and Eiamsa-Ard (2010)Naphon (2006)Chakroun and Al-Fahed (1996)
Hata and Masuzaki (2011)
y=3
Blasius (1913)
Figure 2.13 – Comparison among predictive methods for friction factor during single-phase flow inside tube with twisted-tape insert for R134a, Tsub =10 oC.
Heat transfer coefficient (Nusselt Numbers)
Based on their experimental data Lopina and Bergles (1969) proposed a
correlation for the heat transfer taken into account swirl flow effects created by the
presence of twisted-tape inserts. The proposed correlation is given as follows:
( ) 4.08.0PrRe023.0 hd FeNu
iα=
(2.130)
where is the fin effect multiplier and Reh is the Reynolds number based on the
hydraulic diameter , hd
( )24 4
2
i i
hi i
d d ed
d d
π
π
−=
+ (2.131)
The geometric parameter α in Eq. (2.130) is defined as:
y
y
2
4 22 πα
+= (2.132)
Later on, Manglik and Bergles (1993b) have proposed a new predictive
method based on the ratio of Nusselt Numbers of the tube with twisted-tape and with
Literature review 93
straight tape inserts (y= ∞).Their method was developed for turbulent flow and is
given as follows:
+
−
−+
−∞=
y
769.01
de4
de22
de4PrRe023.0Nu
18.0
w
b
2.0
i
i
8.0
i
4.08.0
dy i µ
µ
π
π
π
π (2.133)
where, the exponent of the viscosity ratio 0.18 is a correction factor that takes into
account the effects on large temperature differences between the fluid and the tube
wall on the transport properties estimated based solely on the bulk temperature.
Chakroun and Al-Fahed (1996) based on their experimental results have also
proposed a correlation for the Nusselt Number during single-phase flow inside tubes
containing twisted-tape inserts given as follows:
( ) 14.0
wb
3.0569.0
d PrSw318.0Nui
µµ= (2.134)
where, the Swirl Number Sw is calculated through Eq. (2.121).
Naphon (2006) proposed a correlation for prediction of the Nusselt Number
based on his experimental data described in Tab. 2.6. The proposed correlation is
valid for 5.51.3 ≤≤ y and predicted their Nusselt Number data within an error band of
±15 . The proposed correlation is given as follows:
[ ] 31475.2136.0
dd Pry1Re648.0Nuii
−+= (2.135)
Wongcharee and Eiamsa-Ard (2010) developed an empirical correlation for
prediction of single-phase Nusselt Number inside tubes containing twisted-tape
inserts based on their experimental data given as follows:
594.04.0968.0
dd yPrRe032.0Nuii
−= (2.136)
The proposed correlation agree quiet well with their experimental data and
predicted their heat transfer coefficient experimental data within an error band of
±8 .
Bas and Ozceyhan (2012), using a procedure somewhat similar to
Wongcharee and Eiamsa-Ard (2010) proposed a correlation for prediction of single-
phase Nusselt Number based on their experimental data . The proposed correlation
is given as follows:
94 Literature review
( ) 4.045.0
i
57.0
dd PrdyRe6.0Nuii
−= (2.137)
Hata and Masuzaki (2011) proposed a correlation for the prediction of
turbulent heat transfer inside the tube containing twisted-tape by introducing the swirl
velocity swV instead of the flow velocity, V. The effects of tube diameter and length
were also take into account in the proposed correlation given as follows:
14.0
w
b
08.0
i
4.085.0
Swdd
LPrRe02.0Nu
ii
=
−
µ
µ (2.138)
where,the Swirl Reynolds Number is calculated through Eq. (2. 122)
Figures 2.14 and 2.15 illustrate comparisons of the Nusselt Numbers versus
Swirl Number estimated according to the the predictive methods described in this
Chapter for single-phase flow for R134a in 12.7 mm ID tube and twist-ratios of 14
and 3.
In general the methods proposed by Lopina and Bergles (1969) and
Wongcharee and Eiamsa-Ard (2010) provide higher Nusselt Numbers than the
methods of Manglik and Bergles (1993b), Chakroun and Al-Fahed (1996) and
Naphon (2006). The highest Nusselt Number are provided by the method of
Wongcharee and Eiamsa-Ard (2010), behavior that is intensified for the twist-ratio of
3. Additionally, unlike Lopina and Bergles (1969) and Wongcharee and Eiamsa-Ard
(2010) that present pronunced increment of Nusset Numbers with increasing Swirl
numbers, the methods of Manglik and Bergles (1993b), Chakroun and Al-Fahed
(1996) and Naphon (2006) present marginal increment of Nusselt Number with
increasing Swirl Number. It is interesting to note that in Figs. (2.14) and (2.15), the
results provided by the different predictive methods varies from one another
signifying notable descripancies among the methods.
Literature review 95
0 500 1000 1500 2000 2500 3000 35000
1000
2000
3000
4000
Sw [-]
Nu
[-]
Lopina and Bergles (1969)
Manglik and Bergles (1993b)
Chakroun and Al-Fahed (1996)
Naphon (2006)
Wongcharee and Eiamsa-Ard (2010)
y=14
Figure 2.7 – Comparison among the predictive methods for Nusselt Number during during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C, p=692 kPa Tsub =19.08 oC.
0 4000 8000 12000 160000
2000
4000
6000
8000
Sw [-]
Nu
[-]
Wongcharee and Eiamsa-Ard (2010)Naphon (2006)Chakroun and Al-Fahed (1996)
Lopina and Bergles (1969)Manglik and Bergles (1993b)
y=3
Figure 2.8 – Comparison among the predictive methods for Nusselt Number during during single-phase flow inside tubes containing twisted-tape insert, R134a, T=5 °C, p=692 kPa Tsub =19.08 oC.
Table 2.7 describes schematically the studies from the literature concerning
two-phase flows inside tubes containing twisted-tape inserts.
96
Literature review
Table 2.7 - Description of the experimental studies concerning two-phase flow inside tubes containing twisted-tape inserts.
Authors Fluids Tube
Orientation Internal Diameter
(mm) Twisted Tape Ratio
Tape
Material Heating Method
Objective of Study
Blatt and Adt (1963) Water Horizontal 3.81,6.35 and 12.7 2.5,5.0,7.5 S S Hot water and condensing Steam ,∆p
Cumo et al.(1974) R12 Vertical 7.56 4.4 -- Hot water
Agrawal et al.(1982) R12 Horizontal 10 3.76,5.58,7.37,10.15 S S Direct AC ∆p
Jensen et al. (1985) R113 Vertical 8.10 3.94,8.94,13.92 S S Direct DC ∆p
Agrawal et al. (1986) R12 Horizontal 10 3.76,5.58,7.3710.15 S S Direct AC
Jensen and Bensler (1986) R113 Vertical 8.10 3.94,8.94,13.92 S S Direct DC
Reid et al.(1991) R113 Horizontal 10.92 11.6 SS Direct DC ,∆p
Kedzierski and Kim(1998)
R12,R22,R152a,
R134a,R290,R32/R134a,R32/R152a,
R290/
R134a, R134a/
R600a
Horizontal 9.64 4.15 Aluminium Glycol/
Water mixture
Akhavan-Behabadi et al. (2009a) R134a Horizontal 12.6 6, 9, 12, and 15 Aluminium Direct AC ,∆p
Akhavan-Behabadi et al. (2009b) R134a Horizontal 7.5 6, 9, 12, and 15 Aluminium Direct AC ,∆p
Kanizawa and Ribatski (2012) R134a Horizontal 15.9 3, 4, 9, and 14 Aluminium Direct AC ∆p
Literature review 97
2.9.3 Flow boiling in tube contaninig twisted-tape insert
2.9.3.1 Experimental studies of two phase flow in tubes containing twisted-tape inserts.
Blatt and Adt (1963) based on the experimental conditions given in Tab. 2.7
investigated the effect of twisted-tape swirl generators on the heat transfer coefficient
and pressure drop during flow boiling inside horizontal tubes. They found that
twisted-tapes inserts improve significantly heat transfer only at low heat fluxes, low
vapor qualities and small radial accelerations and always increases substantially the
pressure drop. Cumo et al. (1974) found that the insertion of twisted-tape doubles
heat transfer coefficient. Agrawal et al. (1982) and Agrawal et al. (1986) studies
revealed that the smallest twisted-tape ratio outperformed the others, achieving
enhancement ratios up to 3.2 but at expense of pressure drop increment which
increases as the twisted-tape ratio decreases. Jensen et al. (1985) found that the
two-phase pressure drop increases from 1.2 to 3.5 times compared to empty tube for
the same flow conditions. A significant increase of the heat transfer coefficient in tube
with twisted-tape as compared to the plain tube counterpart was found by Jensen
and Bensler (1986). In the same study, they observed that the heat transfer
coefficient increase up to 2 times compared to the empty plain tube counterpart by
inserting twisted-tape. Additionally, they found that the increase in the heat transfer
coefficient is higher at high vapor qualities and mass velocities and for smaller twist-
ratios.
On contrary of Jensen and Bensler (1986) results, Kedzierski and Kim (1998)
observed an earlier falloff in the heat transfer coefficient at high vapor qualities due to
formation of partial dryout in the tube. The results from Reid et al. (1991) revealed
that the heat transfer enhancement factor decreases with increasing mass velocity.
Akhavan-Behabadi et al.(2009a) investigated the effect of twisted-tape inserts
on heat transfer enhancement and pressure drop in horizontal tubes. Their results
show that the insertion of twisted-tapes inside the tube enhances the heat transfer
coefficient by as much as 57 % above the results for plain tube without twisted-tape.
These authors also observed as much as 180 % pressure drop augmentation
compared to empty tube at low vapor quality region and mass velocity of 54 kg / m2 s
for the smallest twist-ratio. This behavior occurred due the fact that, flow pattern
changed to annular and as a result, the pressure drop increases relative to the plain
98 Literature review
tube in which the flow pattern is stratified-wavy. Moreover, contrary to Kedzierski and
Kim (1998) finding, Akhavan-Behabadi et al.(2009a) revealed that twisted-tapes are
more beneficial to the evaporator performance when installed at the end part of the
tube, preventing the formation of partial dryout and increasing the heat transfer
coefficient.
Highest enhancement in heat transfer coefficient for lowest twist-ratio of 6 was
obtained by Akhavan-Behabadi et al. (2009b). On performance evaluation basis for
similar pumping power, for low mass velocity conditions, best performance were
observed for highest twist-ratio of 15 while twist-ratios of 9 and 12 provided best
performance under high mass velocity conditions.
Kanizawa and Ribatski (2012) experimentally studied two-phase flow patterns
and pressure drop inside horizontal tubes containing twisted-tape inserts. The
authors observed that the frictional pressure drop penalty (defined as the ratio
between the experimental frictional pressure drop for the tube with twisted-tape insert
and its corresponding value for the plain tubes without inserts) due to the twisted-
tape is highly influenced by vapor quality and that this effect is more prominent for
reduced twist-ratios. The authors also found that the variation of the saturation
temperature from 5 to 15 °C have almost negligible effects on the pressure drop
penalty.
2.9.3.2 Predictive methods for two-phase flow and flow boiling inside tubes containing twisted-tape inserts.
This section presents some of the few available predictive methods from the
literature for the prediction of two-phase flow pressure drop and heat transfer
coefficient during flow boiling inside tubes containing twisted-tape inserts.
Pressure drop.
Most of the methods for predicting the frictional pressure drop during two-
phase flows inside tubes containing twisted-tape inserts are based on multipliers of
either pressure drop or friction factors for tubes without twisted-tape.
Literature review 99
Agrawal et al. (1982)
Based on the database described in Tab. 2.7, Agrawal et al. (1982) proposed
a method to estimate the pressure drop for two-phase flow inside tubes with twisted-
tapes. The proposed method is given as follows:
509.0
PT2
TT
y
12.5
p
p=
Φ∆
∆ (2.139)
where TT and PT indicates the pressure drop for the same tube with and without
twisted-tape, respectively. In this method, the pressure drop for two-phase flow in a
tube without twisted-tape inserts is calculated according to the Lockhart-Martinelli
and Nelson (1949), described in section 2.6.2.1 considering the internal diameter of
the tube.
Jensen et al. (1985)
These authors proposed a method to estimate the pressure drop for two-
phase flow inside tubes with twisted-tapes using a procedure somewhat similar to
Agrawal et al. (1982). In their method, the ratio of the friction factor for the same tube
with and without twisted-tape is given as a function of the twist-ratio. The method
proposed by Jensen et al. (1985) is given by the following equations:
(2.140)
(2.141)
where, the subindex h corresponds to the estimative of the friction factor based on
hydraulic diameter calculated according to Eq. (2.132).
The friction factor for tube without twisted-tape insert is estimated according to
correlation of Reddy et al. (1983) apud Jensen et al. (1985), and is given as follows:
(2.142)
where is the friction factor for the two-phase mixture as liquid calculated
according to Eq. (2.38). The two-phase multiplier in Eq. (2.142) is given by:
100 Literature review
(2.144)
where,
(2.144)
(2.145)
In Eqs. (2.144) and (2.145), is the reduced pressure.
Akhavan-Behabadi et al. (2009a)
Akhavan-Behabadi et al. (2009a) adopted a procedure similar to Agrawal et al.
(1982) in order of developing a new predictive method. Based on their data, they
proposed the following correlation to calculate the pressure drop inside tubes with
twisted-tape inserts:
28.0
PT2
TT
y
1.5
p
p=
Φ∆
∆ (2.146)
In the method of Akhavan-Behabadi et al. (2009a), the pressure drop during
two-phase flow in tubes without twisted-tape inserts is calculated according to the
method of Friedel (1979) described in section 2.6.2.1 considering as characteristic
dimension the internal diameter of the tube.
Kanizawa and Ribatski (2012)
Kanizawa and Ribatski (2012) have proposed a flow pattern based method to
predict pressure drop during two-phase flow in tubes with twisted-tape inserts. The
effect of vapor quality which is not contemplated by the aforementioned predictive
methods is capture by the proposed correlation. Their predictive method is given as
follows:
( )( )
1/55
5(1 )
0.65 1.88 2.10 0.1361.04 8.94 (1 )
6.68 1 19.381
m x
TT
xx m xPT L
ep
p y ey e Fr e
− −
− −
− ∆ − = + ∆ Π +
(2.147)
where the liquid Froude Number is given as follows:
Literature review 101
( )
h
2
L
2
Lgd
x1GFr
ρ
−=
(2.148)
The dimensionless Π in Eq. (2.147) corresponds to the ratio of inertial effects
according to the axial and radial directions. This dimensionless is given as follows:
( )VL
H
2y2
ρρ
ρΠ
−= (2.149)
where ρH is the density of the two-phase mixture estimated according to the
homogeneous model.
The value of the exponent m was imposed by the authors equal to 40 in order
of fitting single-phase flow conditions. The plain tube pressure drop is evaluated
based on the Grönnerud (1979) method described in section 2.6.2.1 and is
calculated based on the hydraulic diameter h
d defined according to Eq. (2.131).
Figures 2.16 to 2.17 illustrate comparisons among the pressure drop
predictive methods described in this Chapter for two-phase flow for R134a in tube
diameter of 15.9 mm, mass velocities of 75 and 150 kg / m² s, saturation temperature
of 5 oC and twist-ratios of 14 and 4. These figures reveals notable descripancies
among the methods.
As shown in Figs 2.16 and 2.17, predictive methods of Jensen et al. (1985),
Agrawal et al. (1982), Akhavan-Behabadi et al. (2009a) and Kanizawa and Ribatski
(2012) present pressure drop gradient increases with increasing vapor quality and
decreasing twist-ratio, independently of the mass velocity.
Agrawal et al. (1982) presents discontinuity in pressure drop gradient for high
vapor quality region according to Figs 2.16 and 2.17. This behavior is significantly
different from those trends displayed by the other predictive methods and is related
to change in flow pattern transitions with the increasing vapor qualities.
Additionally, unlike the other methods, the influence of flow pattern on
pressure drop is well captured by Kanizawa and Ribatski (2012) method, capturing
the pressure drop inflection related to the transition from stagnant flow to intermittent
flow patterns at low vapor quality region shown in Fig. 2.16, and pressure drop
gradient peak for high vapor quality region. This is due to the fact that this method is
a flow pattern based method.
102 Literature review
However, the predictive method of Kanizawa and Ribatski (2012) is observed
to be the best among other predictive methods abovementioned because, it
considered in details the influence of flow pattern on pressure drop gradient for both
low and high mass velocities conditions. Additionally, the effect of vapor quality, a
significant factor in the estimate of the increase in pressure drop was taken into
account by Kanizawa and Ribatski (2012) method what was absent in the predictive
methods of Agrawal et al. (1982) and Akhavan-Behabadi et al. (2009a).
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.5
1.0
1.5
[-]
∆∆ ∆∆p
/
L
[kP
a/m
]
Kanizawa and Ribatski (2012)
Agrawal et al. (1982)
Akhavan-Behabadi et al. (2009a)
Jensen et al. (1985)
G=75 kg/m2s, y=4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.5
1.0
[-]
∆∆ ∆∆p
/
L
[kP
a/m
]
Kanizawa and Ribatski (2012)
Agrawal et al. (1982)Jensen et al. (1985)Akhavan-Behabadi et al. (2009a)
G=75 kg/m2s, y=14
Figure 2.16 – Comparison among predictive methods for pressure drop during two-phase flow inside tube with twisted-tape insert for R134a, Tsat =5 oC, di = 15.9 mm.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
[-]
∆∆ ∆∆p
/
L
[kP
a/m
]
Kanizawa and Ribatski (2012)
Jensen et al. (1985)
Akhavan-Behabadi et al. (2009a)
Agrawal et al. (1982)
G=150 kg/m2s, y=4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
[-]
∆∆ ∆∆p
/
L
[kP
a/m
]
Kanizawa and Ribatski (2012)
Agrawal et al. (1982)
Jensen et al. (1985)
Akhavan-Behabadi et al. (2009a)
G=150 kg/m2s, y=14
Figure 2.17 – Comparison among predictive methods for pressure drop during two-phase flow inside tube with twisted-tape insert for R134a, Tsat =5 oC, di = 15.9 mm.
Heat transfer coefficient
Agrawal et al. (1986)
These authors based on their experimental data described in Tab. 2.7 found
that the heat transfer coefficient enhancement depends on the effect of twist-ratio,
heat flux and mass velocity. Based on this fact, they proposed a method according to
Literature review 103
which the ratio of the flow boiling heat transfer coefficients for the tube with and
without twisted-tapes inserts is correlated as a function of the Reynolds Number,
Boiling Number and twist-ratio. Their method is given as follows:
5219.0624.1247.2
2
TT yBoRe002944.0h
h −=Φ
(2.150)
where, Φ2h is the heat transfer coefficient for plain tube estimated according to Bo
Pierre (1964) correlation. Bo Pierre (1964) is a correlation for predicting average heat
transfer coefficient during flow boiling of refrigerant in a horizontal evaporator and is
given by:
n
LV2
L
i
L
2L
xhRe
d
kBh
=
∆Φ (2.151)
where for 9.0≤outx , B=0.0009 and n=0.5, for 9.0>outx , B=0.0082 and n=0.4.
Jensen and Bensler (1986)
Based on their data described in Tab.2.7, Jensen and Bensler (1986)
developed a predictive method for heat transfer coefficient during flow boiling in
tubes containing twisted-tape inserts according to the following procedure (i) Obtain a
reasonable prediction of plain tube data using well-established correlation from the
literature; (2) modify the plain tube correlation to predict the data for tubes with
twisted-tape.The method proposed by Jensen and Bensler (1986) is given as follows:
( ) 4.0
L
8.0
h
h
L
TT PrRe02.0d
kh α= (2.152)
where,
( )
l
h25.1
h
dx1GFRe
µ
−= (2.153)
1F = for 1.0X
1tt
< (2.154)
104 Literature review
736.0
tt
213.0X
135.2F
+= for 1.0
X1
tt
≥ (2.155)
α and hd are estimated using Eqs. (2.132) and (2.131) respectively
Akhavan-Behabadi et al. (2009b)
Akhavan-Behabadi et al. (2009b) proposed a method to estimate heat transfer
coefficient during flow boiling in tubes containing twisted-tape inserts. using a
procedure somewhat similar to Agrawal et al. (1986). Based on this fact, they
proposed a method according to which the ratio of the flow boiling heat transfer
coefficients for the tube with and without twisted-tapes inserts can be correlated as a
function of the Reynolds Number, Boiling Number and twist-ratio. The proposed
method is given as follows:
2156.1yBoRe0056.0h
h 5.0532.1214.2
2
TT += −
Φ
(2.156)
where, Φ2h is estimated using Eq. (2.88)
Figures 2.18 to 2.21 show comparisons among the heat transfer coefficient
methods described in Tab. 2.7 for the refrigerant R134a, tube diameters of 12.7 and
15.9 mm, mass velocities of 75 and 150 kg / m² s, saturation temperature of 5 oC and
twist-ratios of 9 and 4.
Generally speaking, according to the predictive methods described in this item
the heat transfer coefficient increases with decreasing twist-ratio and increasing
mass velocity and vapor quality.
According to Figs. 2.18 to 2.21, the methods of Akhavan-Behabadi et al.
(2009b) and Agrawal et al. (1986) reveals that the heat transfer coefficient decreases
with increasing vapor quality independent of the tube diameter. According to the
predictive method of Jensen and Bensler (1986), the heat transfer coefficient
increases with increasing vapor quality until a peak at vapor qualities close to 1. This
peak is relate to the onset of dryout that is responsible for a drastic falloff of heat
transfer coefficient. It can also be noted, according to the methods of Akhavan-
Behabadi et al. (2009b) and Agrawal et al. (1986) that, the heat transfer coefficient in
a 15.9 mm ID tube is higher than that in smaller 12.7 mm ID tube. On the other hand,
Literature review 105
Jensen and Bensler (1986) estimated higher heat transfer coefficients in the 12.7 mm
ID tube compared to the 15.9 mm ID tube, as expected. However, the predictive
method of Jensen and Bensler (1986) is observed to present best performance
among other predictive methods abovementioned, predicting the increase of heat
transfer coefficient with increasing vapor quality, decreasing tube diameter and twist
ratios, independently of the mass velocity.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
x [-]
h [
kW /
m2 o
C ]
Akhavan-Behabadi et al. (2009b)
Jensen and Bensler (1986)
Agrawal et al. (1986) y=4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
x [-]
h [
kW /
m2
oC
]
Akhavan-Behabadi et al. (2009b)Jensen and Bensler (1986) Agrawal et al. (1986) y=9
Figure 2.18 - Variation of the heat transfer coefficient with vapor quality according to predictive methods for heat transfer coefficient during flow boiling inside tubes containing twiste-tape, di = 12.7
mm, φ = 10 kW / m2, G = 75 kg / m² s, Tsat =5 oC
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
2.0
4.0
6.0
8.0
x [-]
h [
kW /
m2
oC
]
Akhavan-Behabadi et al. (2009b)
Jensen and Bensler (1986)
Agrawal et al. (1986) y=4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
5.0
x [-]
h [
kW /
m2
oC
]
Akhavan-Behabadi et al. (2009b)Jensen and Bensler (1986) Agrawal et al. (1986) y=9
Figure 2.19 - Variation of the heat transfer coefficient with vapor quality according to predictive methods for heat transfer coefficient during flow boiling inside tubes containing twiste-tape, di = 12.7
mm,φ = 10 kW / m2, G = 150 kg / m² s, Tsat = 5 oC.
106 Literature review
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
x [-]
h [
kW /
m2
oC
]
Akhavan-Behabadi iet al. (2009b)
Jensen and Bensler (1986) Agrawal et al. (1986) y=4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
x [-]
h [
kW /
m2
oC
]
Akhavan-Behabadi et al. (2009b)
Jensen and Bensler (1986) Agrawal et al. (1986) y=9
Figure 2.20 - Variation of the heat transfer coefficient with vapor quality according to predictive methods for heat transfer coefficient during flow boiling inside tubes containing twiste-tape, di = 15.9
mm, φ = 10 kW / m2, G = 75 kg / m² s, Tsat = 5 oC.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
2.0
4.0
6.0
8.0
10.0
12.0
x [-]
h [
kW /
m2
oC
]
Akhavan-Behabadi et al. (2009b)
Jensen and Bensler (1986)
Agrawal et al. (1986) y=4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
h [
kW /
m2 o
C ]
Akhavan-Behabadi et al. (2009b)Jensen and Bensler (1986) Agrawal et al. (1986) y=9
Figure 2.21 - Variation of the heat transfer coefficient with vapor quality according to predictive
methods for heat transfer coefficient during flow boiling inside tubes containing twiste-tape, di = 15.9 mm,φ = 10 kW / m2 ,
G = 150 kg / m² s, Tsat = 5 oC.
2.9.4 Conclusions based on the literature review.
Studies from the open literature revealed that flow boiling in tubes containing
twisted-tape inserts present higher heat transfer coefficients than plain tubes without
inserts. In general, the heat transfer coefficient increases with decreasing twist-ratio
due to high velocity of fluid in the vicinity of the tube wall generated by the twisted-
tape. It is also observed in the literature that the increase of the heat transfer
coefficient by the tape is always accompanied by a drastic increase in the pressure
drop and consequently augmentation of the pumping power of the system.
Comparison among the predictive methods from literature for heat transfer coefficient
during two-phase flow inside tube containing twisted-tape inserts presented in
section 2.9.3 have revealed notable discrepancies. Therefore, an accurate heat
Literature review 107
transfer predictive method taken into account the swirl effects promoted by the tape
on the heat transfer coefficient inside horizontal tubes containing twisted-tapes
inserts is still necessary and is one of the objectives of the next Chapters.
108 Equipment, experimental procedure and data reduction
3 EQUIPMENT, EXPERIMENTAL PROCEDURE AND
DATA REDUCTION
3.1 Introduction
This chapter describes the experimental bench and procedures adopted in the
present study. The data reduction procedures are detailed. Finally, the experimental
uncertainties of the measured and calculated parameters are presented.
The experimental apparatus is located at the Department of Mechanical
Engineering of the School of Engineering of São Carlos (EESC-USP) and was built
for the previous study of Kanizawa (2011). In the present study, results were
obtained for the heat transfer coefficient and pressure drop using two test sections
with internal diameters of 12.7 and 15.9 mm. In the study of Kanizawa (2011) flow
pattern and pressure drop results were obtained for the 15.9 mm ID test section for
R134a and the same twist-ratios considered in the present study. The photograph of
the experimental set up is presented in Fig. 3.1.
Figure 3.1 - Photograph of the experimental bench.
Equipment, experimental procedure and data reduction 109
3.2 Experimental bench
The experimental setup is comprised of refrigerant and ethylene-glycol/water
circuits, named also as primary and secondary circuits, respectively. Figure 3.2
presents schematically the refrigerant closed loop that globally comprises a micro-
pump to drive the working fluid through the test circuit, a sub-cooler, a pre-heater to
establish the experimental conditions at the inlet of the test section, a flow
stabilization section, a test section, two visualization sections, a heat exchanger to
condense the vapor generated in the heated sections and a refrigerant tank. The
secondary circuit, partially shown in Fig. 3.2, is responsible for the cooling effects in
the condenser and in the sub-cooler. This circuit contains a vapor compression
refrigeration cycle responsible for cooling the mixture of 60% of ethylene glycol in
water. This anti-freezing solution is driven by a centrifugal pump through the
condenser and the sub-cooler. The refrigeration cycle rejects heat to the external
environment through an evaporative cooling tower.
Figure 3.2 - Schematic diagram of the refrigerant circuit.
Figure 3.3 shows schematically the thermodynamic processes of the test fluid
along the refrigerant circuit. The numbers shown in Fig. 3.2 correspond to the
thermodynamic states indicated in Fig. 3.3.
The process 7-1 on the P - h diagram shown in Fig.3.3 corresponds to the
pumping process of the test fluid through the circuit by the micro-pump, increasing its
2
6
5
4
3
7 1
110 Equipment, experimental procedure and data reduction
pressure until the state 1. The process 1-2 is the local pressure drop of the fluid
across the Coriolis type flowmeter. The process 2-3 corresponds to sub-cooling of
the working fluid in the sub-cooler to ensure that the fluid is sub-cooled at the pre-
heater inlet. During process 3-4, the vapor quality at the pre-heater outlet is adjusted
by adding electrical power to the system, heating the fluid and establishing the
experimental conditions at the inlet of the test section of the state 4. The process
between states 4 and 5 is to supply heat to the refrigerant in the pre-heater and the
test sections. The change in slope of the process between states 4 and 5 from the
saturated liquid line is related to the higher pressure drop gradient in processes
involving evaporation when compared to single-phase flow. The evaporation process
continues until state 5 corresponding to the output of the test section. Expansion of
the fluid at the entrance of the condenser resulting in decreasing of the refrigerant
temperature and consequently, its pressure occurs during process 5-6. Finally, from
state 6, the condensation of the fluid occurs until it arrive at state 7 in a subcooled
liquid state .
-50 0 50 100 150 200 250 300 350101
102
103
104
105
h [kJ/kg]
15°C
5°C
0°C
0.2 0.4 0.6 0.8
0
0.2
0.5
0.7
0.9
kJ/
kg-K
P [
kPa]
15°C
5°C
0°C
0.2 0.4 0.6 0.8
0
0.2
0.5
0.7
0.9
kJ/
kg-K
R134a
1
23 4
7
5
6
Figure 3.3 - Thermodynamic process of the refrigerant along the refrigerant test circuit.
3.2.1 Test section
The test sections are 2 m long brass and copper tubes with nominal internal
diameter of 12.7 and 15.9 mm, respectively. Both tubes have the same wall
thickness of 3.2mm with peak-to-valley roughnesses of 7.65 and 9.5 µm for the 12.7
and 15.9 mm internal diameter, respectively. In the test section were installed a total
Equipment, experimental procedure and data reduction 111
of 16 thermocouples, evenly distributed in four cross sections. The first section is
positioned 460 mm from the test section inlet. The distances between neighbour
temperature measurement cross sections are 460 mm. Figure 3.4 shows the
schematic diagram of the test section and the thermocouples distribution.
Figure 3.4 - Schematic diagram of the test section and the thermocouples distribution.
In each section, the thermocouples were distributed at 90° apart, as indicated
in Fig. 3.5. The use of four thermocouples has the following objectives (i) obtain a
cross-sectional average heat transfer coefficient representative of the tube perimeter;
(ii) validate the measurements through comparison between the results given at the
sides; and (iii) to investigate the differences among local heat transfer coefficient
along the perimeter of the test section, related to stratification flow effects.
The test section heating effect was obtained by five electric heaters (tape type)
with nominal power of 624 W each, manufactured by Amptek, models AWH-052-
080D-Duo-Tape with width of 12 mm and length of 2400 mm. These resistors are
powered by a variable autotransformers (Variac) with maximum power of 3kW/220V.
The supplied electrical power is measured through active power transducers, model
2285A of Yokogawa. This heating system allows heat fluxes up to 30 kW / m². The
test section is insulated thermally with three layers of ceramic fibre with a density of
64 kg / m³ and nominal thickness of 50 mm, covered with a layer of Armaflex brand of
25 mm thickness rubber foam in order to reduce heat exchanges with the external
environment.
112 Equipment, experimental procedure and data reduction
Figure 3.5 - Positioning of thermocouples for each cross section along the test section.
3.2.2 Visualization sections
Two visualization sections are installed in the refrigerant circuit with the aim of
verify flow pattern transitions along the test section during the experiments. The first
one is installed between the outlet of the pre-heater and the test section inlet while
the second is located just downstream the test section outlet. The visualization
sections are 140 and 210 mm length, respectively. They are made of bore silicate
with internal diameter of 16.4 mm and wall thickness of 1.8 mm. Figure 3.6 shows the
visualization section just downstream the test section outlet.
Figure 3.6 - Visualisation section at the test section outlet.
3.2.3 Pressure drop measurement instruments
For the measurement of pressure drop along the test section, three
differentials pressure transducers from Endress–Hauser, PMD-75 model were
installed in the test section as shown in Fig. 3.7. Their nominal ranges are equal to ±
3, 10 and 300 kPa with accuracy equal to 0.075% of the set span. It is adopted more
Thermocouples positions 2 and 4 are Lateral, 1 is Upper and 3 is Bottom
Equipment, experimental procedure and data reduction 113
than one differential pressure transducer in order to reduce the relative error during
measurements since the experiments covers a wide pressure drop range. The
capiliarries tubes connecting the differential pressure transducers were heated up by
circulating hot water from a thermostatic bath through copper tubes
contacting the capillaries. The purpose of heating the capillary was preventing
formation of bubbles in the capillaries and to guarantee that the sensors are always
in contact with vapor at their both sides, otherwise they would provide erroneous
measurement.
Figure 3.7 - Illustration of fitting of differential pressure transducers.
3.2.4 Temperature measurements
Wall temperatures along the test section were measure with K-type
thermocouples of 120 m wire diameter with accuracy of 0.13oC. These
thermocouples were nested in longitudinal grooves 0.5 mm distant from the internal
surface, filled with high-conductive epoxy and distributed in four sections 460 mm
distant from each other. At each measuring cross section, the surface temperature
was read at four locations 90o spaced from the bottom to the top of the tube.
In the present study the thermocouples nested on the test section surface
were used for determining the heat transfer coefficient during diabatic tests and the
exchange of heat in the test section between the working fluid and the environment.
114 Equipment, experimental procedure and data reduction
3.2.5 Pre-Heater Section
The pre-heater is used to control and adjust the thermodynamic state, and
consequently the vapor quality, at the test section inlet. It consists of a 12.7 mm ID
copper tube, wrapped with 20 electrical resistances that totalize 12 kW. The system
is thermally insulated with ceramic fiber and elastomeric foam in order to reduce the
heat exchange with the environment. The pre-heater possess two thermocouples
(0.120 mm wire diameter) fixed within its tube wall. Additionally, absolute pressure
transducers and thermocouples were installed in the pre-heater inlet and outlet. The
heating effect in the pre-heater is controlled through electrical resistances powered
by two variable autotransformers (Variac), with power ratings of 3 and 9 kW. The
electrical power supplied to the pre-heater is measured by active power transducers,
model 2285A of Yokogawa. Figure 3.8 shows a photograph of the pre-heater, without
the elastomeric insulation foam, illustrating part of the ceramic fibre insulation and the
upper portion of the coil with the electrical resistances installed on its surface.
Figure 3.8 - Photograph of the Pre-heater.
3.2.6 Flow Stabilization section
The flow stabilization section consists of a horizontal 1.4 m long tube of the
same inner and outer diameters and material of the test section. The stabilization
section is used to guarantee that the flow at the test section inlet is fully developed.
For the setup with 15.9 mm ID tube, this length corresponds to approximately 90
diameters, and for 12.7 mm ID tube, it corresponds to 110 diameters. Both values
are considered sufficient for the two-phase flow development. The stabilization
section and the pre-heater are contained in the same thermal-insulation device
separated by a wide layer of ceramic fiber.
Equipment, experimental procedure and data reduction 115
3.2.7 Sub-Cooler
The sub-cooler is a tube-in-tube heat exchanger type with the test fluid flowing
in the internal tube. The sub-cooler is used to ensure that the fluid is sub-cooled at
the pre-heater inlet. Thus, the thermodynamic state of the fluid at the pre-heater inlet
is estimated based on the local temperature and pressure measurements. The
temperature of the refrigerant at the sub-cooler outlet and pre-heater inlet is
measured with a thermocouple (0.120 mm wire diameter), installed in a bulb
positioned in the center of the tube cross section. The inner tube has a nominal size
of ½ "(12.7 mm), and the outer 1 ½". The cooling effect in the sub-cooler is obtained
through the circulation of the anti-freezing solution from the ethylene-glycol circuit.
3.2.8 Condenser
The function of the condenser is to condense and subcool the working fluid
heated up in the test section and the pre-heater. It also allows controlling the
saturation temperature by adjusting the pressure in the system. It is a shell and tube
type heat exchanger and its cooling effect is obtained through the solution of
ethylene-glycol and water circulating inside the tubes. The flow rate of ethylene-
glycol and water solution through the condenser is controlled manually with the help
of a needle valve. The condenser is insulated with elastomeric foam manufactured by
Armaflex, with a thickness of 25 mm.
3.2.9 Reservoir
The refrigerant reservoir main objective is to adjust the refrigerant inventory
without adding any external refrigerant charge to the overall refrigerant circuit
(including the reservoir itself). It consists of a bottle of refrigerant wounded round with
a coil consisting of a copper tube inside which the solution of ethylene-glycol / water
from the chiller is circulated. The reservoir is insulated with elastomeric foam
(armaflex) of 25 mm thick and is suspended by a dynamometric balance (full scale
reading of 90 kg) for registering the amount of refrigerant in the main circuit. The
reservoir is connected to the refrigerant circuit through a ½ " copper tube. A ball valve
is installed in the connection line in order to isolate the reservoir from the refrigerant
circuit.
116 Equipment, experimental procedure and data reduction
3.2.10 Micro Pump
A micro-pump gear type that works without lubricant, drives the test fluid
through the refrigerant circuit. The micro pump is of 223/56C model with nominal
displacement of 3.48 ml per rotation. Its gear is made from a material commercially
known as Ryton and the coupling between the drive shaft and gears is magnetic. The
motor speed is controlled through a frequency converter, Danfoss VLT-2800 model
with frequencies from 0 to 60 Hz and output of 0 to 10 V using the communication
and data acquisition system control.
3.2.11 Flow meter
The mass flow in the refrigerant circuit is measured through a Coriolis type
mass flow meter. The Coriolis type mass flow meter is a flowmeter of 2100 model
with calculated uncertainty of ± 0.276 kg / m² s and measuring range from 1 to
52,000 kg / h or 867 kg / min
3.3 Ethylene-Glycol/Water Solution Circuit
The ethylene-glycol / water circuit, not completely illustrated in Fig. 3.2, is an
auxiliary circuit responsible for the cooling effects of the test fluid in the refrigerant
circuit. The solution is composed of 60% ethylene glycol in water and its freezing
temperature is about -55 °C. This solution is driven through the circuit by a centrifugal
pump and flows from a tank of 60 litters, through the closed loop containing the
condenser and the sub-cooler, both in the refrigerant circuit, and the evaporator of
the chiller. Electrical heaters of 12 kW were installed inside the tank. The power
supplied by the electrical heater is controlled by a PID controller actuating on solid-
state relay based on the temperature of the solution in the tank measured by a PT-
100 sensor and the temperature imposed to the control by the operator. The
electrical heater works in order to compensate the variation of the cooling power and
keep a minimal thermal load in the refrigerant circuit. Then, the chiller rejects the heat
to the external environment through an evaporative cooling tower.
3.4 Control and Data Acquisition System
Monitoring, controlling and recording of experimental results were conducted
using a data acquisition system from National Instruments installed on a personal
Equipment, experimental procedure and data reduction 117
computer of 3.0 GHz processor. The data acquisition system is comprised of 40
channels for voltage reading and 2 channels for output voltage; a chassis multiplexer
SCXI-1000, a board to communicate with the computer (NI PCI 6221); a SCXI 1302
terminal for acquisition and transmission of analog signals; SCXI 1303 terminal for
amplifying analog signals and SCXI 1112 terminal for amplifying the read enable
signal from the thermocouples and cold junction compensation.
A PI type controller is designed so that an analog signal is given by the data
acquisition system and acts on the variable-frequency drive base on the mass
velocity determine by the operator and the mass flow measurement provided by the
Coriolis flowmeter. Due to the fact that the absolute and differential pressure
transducers provide as an output signal of 4-20 mA, electrical resistors designed for
military application of 250 Ω were used with 0.1% error. The resistors were installed
in parallel with the terminals of the data acquisition system given voltage signals
between 1-5 V. These are precision resistors and present negligible variation in their
value with temperature.
Figure 3.9 shows schematically the components and the terminals of the
acquisition system.
Figure 3.9 - Schematic diagram of the acquisition system and terminals.
A LabVIEW version 8.2 from National Instruments was used to develop the
software for data acquisition and control of the apparatus. Calibration curves of the
sensors and transducers were also added to the program. Figure 3.10 shows the
interface of the LabVIEW software used to control and monitorate the test facility and
record the data.
118 Equipment, experimental procedure and data reduction
Figure 3.10 - Image of the program implemented for data acquisition.
3.5 Twisted-tape inserts
The twisted-tape inserts are made from an aluminum foil of 1.0 mm thick and
2.0 meters long, and are manufactured as suggested by Lopina and Bergles (1969).
A weight of approximately 20 kg was hanged at the free edge of the tape, while its
upper end is clamped in a fixed structure. Then, the weight is slowly twisted until the
desired twist-ratio is obtained. Due to the fact that the test section plus the
visualizations and stabilization sections are longer than the aluminum foil, for each
twist-ratio two strips were prepared and welded together in order to obtain a twisted-
tape length covering from the stabilization section until the downstream visualization
section. Twisted-tapes with twist-ratios, y, of 3, 4, 9 and 14 were manufactured for
each diameter. Figure 3.11 presents an image of the twisted-tapes inserts for 12.7
and 15.9 mm ID tubes. The tapes were loosly positioned in the test section, in order
to allow the change between different tapes, and are unmovable by the flow, due to
friction with the wall and to the fact that they are fixed by the curve of the piping
downstream the last visualization section. The clearance in diameter between the
tape and the tube wall is equal to 0.6 mm in average for the 15.9 mm ID tube, and
equal to 0.5 mm for the 12.7 mm ID tube.
Equipment, experimental procedure and data reduction 119
Twisted-tape inserts for 12.7 mm ID
Twisted-tape inserts for 15.9 mm ID
Figure 3.11 - Photograph of the twisted-tape inserts used during the experimental compaign.
y=3
y=3
y=4
y=4
y=9
y=9
y=14
y=14
120 Equipment, experimental procedure and data reduction
3.6 Experimental procedure
3.6.1 Single-phase flow tests
During single-phase flow experiments, firstly the valve connecting the main
circuit and the refrigerant reservoir was open. So, all the main circuit was filled with
liquid refrigerant corresponding to the addition of 18 kg of refrigerant to the main
circuit compared to two-phase flow experiments. Single-phase pressure drop
experiments were carried out under adiabatic conditions.
Before starting the experiments and after turning on the data acquisition
system, all the transducers and sensors were evaluated to check for possible
inconsistencies of their signal, i.e. null values of pressure drop, mass velocity and
heat flux, and almost similar absolute pressures along the refrigerant circuit. Then,
single-phase flow was imposed to the circuit by turning on the micro-pump through
the data acquisition system. Then under adiabatic conditions the temperatures given
by the thermocouples along the test section and pre-heater are compared and the
temperatures indicated by the thermocouples are considered correct if their
measurements indicate temperature differences less than 0.3 °C. After the check of
the measurements, the thermostatic bath was turned on and its temperature was set
equal to 70 °C to heat the capillary tubes connecting the pressure differential
transducers to the test circuit. Then, the mass velocity was set by act on the variable
frequency drive through the data acquisition system and the mass flow measurement
provided by the Coriolis flowmeter. The ethylene-glycol/water circuit and the electrical
heating system are activated only after the mass velocity was set.
In addition to the procedure adopted for single-phase pressure drop
experiment, during single-phase heat transfer experiment and energy balance
validation test, the electrical resistance for the pre-heater and test section were also
activated. Then, the fluid temperature at the test section was adjusted by
manipulating a needle valve that determines the flow rate of ethylene-glycol/water
solution through the condenser.
The electrical power supplied to both sections was manually adjusted through
variable transformers and measured with electrical power transducers. It is
interesting to note that, the abscense of vapor bubbles during single-phase
experiment was assured by maintaining a minimum of 10 oC of the subcooling of the
Equipment, experimental procedure and data reduction 121
test fluid at the test section outlet. The absence of the bubbles was also verified
through the visualization sections installed in the refrigerant circuit.
Steady state conditions were assumed when the variations of the
temperatures given by the thermocouples within the fluid at the inlet and outlet of the
test section were kept lower than twice the thermocouple uncertainty during a period
of at least 3 minutes. The recording system was initiated only after the establishment
of steady state conditions, and the experimental data were acquired during at least 1
minute with a recording rate of 25 Hz.
3.6.2 Two-phase flow test
Initially, the amount of refrigerant was adjusted by adding or draining
refrigerant from the main circuit to the refrigerant reservoir. The removal of refrigerant
from the main circuit was done by circulating the anti-freezing solution through the
coil in contact with the refrigerant reservoir, decreasing the refrigerant temperature
and consequently, its pressure. On the other hand, the addition of refrigerant was
implemented by circulating the anti-freezing solution through the condenser,
decreasing the temperature in the main circuit and consequently, its pressure. In the
container. So, the refrigerant was driven from the reservoir to the main circuit and
vice-versa by pressure gradient. Once the desired amount of refrigerant estimate
with the help of dynamometer was attained the ball valve connecting the reservoir
and the refrigerant circuit was closed. During the two-phase flow experiments, the
valve connecting the main circuit to the refrigerant tank was kept closed.
The procedures for the initiation of the experiments for two-phase flow are
similar to those adopted for the single-phase flow experiments. The consistency
among the different measurements of temperature and pressure were initially
observed. Subsequently, the mass velocity was set by act on the variable frequency
drive through the data acquisition system and the mass flow measurement provided
by the Coriolis flowmeter.
The ethylene-glycol/water circuit and the electrical heating system are
activated only after the mass velocity was set. The saturation temperature at the test
section was adjusted by manipulating a needle valve that determines the flow rate of
ethylene-glycol/water solution through the condenser. The vapor quality at the test
section inlet was obtained by imposing the appropriate heat flux to the pre-heater. By
varying the power supplied to the pre-heater, experimental results for distinct vapor
122 Equipment, experimental procedure and data reduction
qualities at the test section inlet were obtained keeping the remaining parameters
constant.
During the experiment, a sharp decline in the system pressure was observed
with increasing the fluid flow rate under higher vapor qualities conditions and for the
lowest saturation temperature of 5 oC. This is related to the fact that there is increase
in specific volume of the fluid and hence lead to a higher pressure drop, which
subsequently beyond the capacity of experimental bench component.
Experimental data were gathered for mass velocities (referred to the plain
tubes cross sectional area) of 75, 100, 150 and 200 kg / m² s saturation temperatures
Tsat equal to 5 and 15 °C, and heat fluxes of 0, 5 and 10 kW / m². For adiabatic
experiments, the inlet vapor quality was varied from 5 to 95 %, with increments of 5
%, and for diabatic experiments the inlet vapor quality were varied from 5 %, with
increment of 5 % with the outlet vapor quality depending on the energy balance along
the test section. The system was automatically turned off when dryout conditions at
the test section outlet were achieved. Dryout conditions were characterized by a
drastic increase in the wall temperature indicated by the thermocouples.
As for single-phase tests, steady state conditions were also assumed when
the variations of the temperatures given by the thermocouples within the fluid at the
inlet and outlet of the test section were kept lower than twice the thermocouple
uncertainty during a period of at least 3 minutes. The recording system was initiated
only after the establishment of steady state conditions, and the experimental data
were acquired during at least 1 minute with a recording rate of 25 Hz.
3.7 Data reduction Procedures
In the present item, the data regression procedure used to obtain the heat
transfer coefficient and pressure drop data from the measured parameters are
described. In the present study, an experimental procedure was initially adopted
based on single-phase energy balances in order of estimating the heat exchanges
with environment which are taken into account during the data regression analysis.
Transport and thermodynamic properties were obtained from the commercial
software EES (Engineering Equation Solver,1992)
The heat flux was assumed uniform along the entire test section and is given as
follows:
Equipment, experimental procedure and data reduction 123
Ld
E
i
TSTS
πφ = (3.1)
where ETS is the electrical power supplied to the test section minus the heat
exchanges with the external environment.
The mass velocity was defined as the ratio between the mass flow rate and
the cross sectional area for the tube without insert, as follows:
2
id
m4G
π
&= (3.2)
The vapor quality was determined based on the local thermodynamic state
given as follow:
( )
LV
L
i
izix
−= (3.3)
where Li is the enthalpy of the saturated liquid,
LVi is the latent heat of evaporation,
both estimated at the saturation temperature at the position z along the tube length.
In Eq. (3.3) ( )zi is the average local fluid enthalpy in a given cross section at position
z .
3.7.1 Pressure drop
The total pressure drop gradient is the sum of the frictional, accelerational, and
gravitational parcels given by Eq. (2.33).
Due to the fact that the test section is horizontal the gravitational parcel of the
pressure drop is null, therefore, the frictional pressure drop was assumed as equal to
the total pressure drop provided by the differential pressure transducer subtracted
the accelerational parcel. Consequently the frictional pressure drop is given by the
following relationship:
fric total acc
dp dp dp
dz dz dz
= −
(3.4)
It is important to highlight that Eq.(3.4) is related to the test section length of
2.0 m.
124 Equipment, experimental procedure and data reduction
where total
dp
dz
is the pressure drop provided by the differential pressure transducers.
Adiabatic experiments were performed for obtaining the pressure drop data.
Consequently the vapor quality variation along the test section is mainly due to the
pressure reduction. Acceleration parcel was estimated based on the inlet and outlet
vapor qualities and superficial void fraction estimated according to Eq. (2.34) and Eq.
(2.26), respectively.
3.7.2 Heat Exchange with environment
Correlations were developed in order of estimating the heat exchanged with
the environment and taking its value into account when calculating the heat flux. For
this, single-phase flow experiments were performed and the heat exchanged with the
environment determined as the difference between the power supplied to the
electrical heater and the product between the mass flow rate and the variation of
enthalpy of the fluid along the pre-heater and test section length. The heat
exchanged with the environment is calculated as follows:
(3.5)
(3.6)
where , and , are the refrigerant enthalpies estimated from
the measurements of the temperature and pressure (P,T) at the test section and pre-
heater inlet and just downstream the test section and pre-heater respectively based
on and corresponds to electrical power supplied to the test section and pre-
heater, respectively, taken into account the heat exchanges with the external
environment. Then, empirical equations were obtained for the ratio between the heat
exchanged with the environment and the electrical power as a function of Grashof
number and tube average temperature as follows:
(3.7)
(3.8)
Equipment, experimental procedure and data reduction 125
where is the Grashof number estimated for air properties at the film temperature
(mean value of wall and external temperature). In Eq. (3.7) refers to the wall
average temperature (2 thermocouples in the pre-heater), while corresponds to
the fluid average temperature between the inlet and outlet positions. In Eq. (3.8),
refers to the wall average temperature (16 thermocouples in test section
corresponds to the fluid average temperature between the inlet and outlet of the test
section. The coefficients and exponents of Eqs (3.7) and (3.8) were obtained from
the least square regression analysis of the single-phase pressure drop and heat
transfer coefficient experimental data realized during the validation of the test
section.
It is interesting to note that Eqs. (3.7) and (3.8) used to calculate the rate of
heat transfer exchanged with the environment for the pre-heater and the test section
for the 15.9 mm ID tube were also considered applicable for the 12.7mm ID tube,
because the same insulation configuration were used for both tubes. Thus, it is
expected that the thermal resistances are similar.
3.7.3 Heat transfer coefficient
The local heat transfer coefficient was calculated according to the Newton’s
cooling law as follows:
( )( )zTTh
satW
TS
−=
φ (3.9)
where WT is cross-sectional arithmetic average surface temperature of the inner tube
wall estimated according to the Fourier’s law assuming one-dimensional conduction
and based on the four wall temperature measurements at each cross section. The
internal average wall temperature is given as follows:
( )
Cu
ioi
i,TPW
k
rrlnrTT φ−= (3.10)
where iTPT , is the average temperature of the measurements by the thermocouple at
each cross section, is the internal radius of the section, is the distance between
126 Equipment, experimental procedure and data reduction
the section centre and the thermocouples ( Tio rr δ+= and Tδ =0.5 mm) and Cu
k is the
thermal conductivity of the tube (copper or brass).
In Eq. (3.9), ( )zTsat is the local saturation temperature of the refrigerant
evaluated from the local saturation pressure assuming a constant pressure gradient
along the test section and based on the measurements of the absolute pressure
transducer at the test section inlet and differential pressure transducer.
3.8 Validation of the experimental bench and determination of the uncertainty
In the present study, procedures were performed to validate the experimental
data and evaluate the accuracy of their measurements through comparisons of
experimental results with consolidated methods available in the literature for single-
phase flows. The validation of the apparatus and experimental procedures involved
also checking the heat losses through energy balance along the pre-heater and test
section to assure the correct estimation of the heat flux and vapor quality.
3.8.1 Single-phase pressure drop experimental data validation
Single-phase frictional pressure drop experiments for plain tube without inserts
were performed in order to assure the accuracy of the pressure drop measurements.
Figure 3.12 presents the comparison between experimental Fanning friction factor, f
for single-phase adiabatic flow in tubes with 12.7 and 15.9 mm internal diameter, for
Reynolds number Re varying from 3200 to 35000, and estimatives according to
methods of Blasius (1913), Churchill (1977), and Colebrook (1939). As can be
observed from Fig. 3.12, the experimental results present good agreement with the
theoretical estimatives, with all data predicted within an error band less than ± 10 %.
3.8.2 Single-phase flow heat transfer experimental data validation
In order to evaluate the accuracy of the data and validate the flow boiling heat
transfer coefficient measurements, diabatic single-phase experiments were carried
out in plain tubes, for sub-cooling temperature at the test section inlet of 10 and 20
°C, Reynolds number varying from 4000 to 35000, and heat flux from 0.16 to 6.2 kW
/ m² for both diameters. Figures 3.13 and 3.14 present comparisons among the
experimental heat transfer coefficient data and predictions according to Gnielinski
(1976) and Dittus and Boelter (1930) correlations. As can be observed in Figs. 3.13
Equipment, experimental procedure and data reduction 127
and 3.14, the experimental results agreed quiet well with the predictive methods for
the 12.7 mm ID tube, i.e., Dittus and Boelter (1930) and Gnielinski (1976) predicted
94.2 and 98.1 % of the experimental data within an error band of ±30 %. For the 15.9
mm ID tube, 98.4 % of the data was predicted within an error band of ±30 % by both
methods.
0.005 0.006 0.007 0.008 0.009 0.010 0.0110.005
0.006
0.007
0.008
0.009
0.010
0.011
fexperimental [-]
f est
imat
ed [
-]
+10 %
-10%
Blasius (1913)
Churchill (1977)
Colebrook (1939)
Figure 3.12 - Comparison between experimental friction factors and estimated friction factors, for single-phase flow in tubes with 12.7 mm ID (filled symbols) and 15.9 mm ID (empty symbols).
0.0 0.5 1.0 1.50.0
0.5
1.0
1.5
hexperimental [kW/m2 oC]
hes
tim
ated
[k
W/m
2 oC
]
+30%
-30%
Figure 3.13 - Comparison of experimental and estimated heat transfer coefficient for liquid single-
phase flow, for 12.7 mm ID tube. Estimatives according to Dittus and Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols).
128 Equipment, experimental procedure and data reduction
0.0 0.5 1.00.0
0.5
1.0
hexperimental [kW/m2 oC]
hes
tim
ated
[k
W/m
2 o
C]
+30%
-30%
Figure 3.14 - Comparison of experimental and estimated heat transfer coefficient for liquid single-
phase flow, for 15.9 mm ID tube. Estimatives according to Dittus and Boelter (1930) (filled symbols) and Gnielinski (1976) (empty symbols).
The accuracy of the estimated vapor quality was ascertained from evaluation
of the effective rate of heat exchanges between pre-heater, test section and
environment during the single-phase experiments. The analyses of the parcel of
energy exchanged with environment relative to the total energy supplied can be
calculated for the pre-heater and the test section as follows,respectively:
(3.10)
(3.11)
Figures 3.15 and 3.16 present the variation of the ratio of along the test
section and pre-heater respectively with mass velocity. According to Figs. 3.15 and
3.16, the relative value of the heat exchanged with environment increases with
decreasing the mass velocity. Heat exchanges lower than 10 % were achieved for G
≥ 125 kg / m2 s and lower than 5 % for G ≥ 400 kg / m2 s. Also, in Figs. 3.15 and
3.16, reasonable heat losses were observed in the test section and pre-heater for G
≤ 100 kg / m2 s and G ≤ 275 kg / m2 s, respectively.
Based on the above analyses, it can be concluded that the experimental
facility is satisfactorily accurate for obtaining pressure drop and heat transfer
coefficient results during flow boiling inside tubes with and without twisted-tapes.
Equipment, experimental procedure and data reduction 129
50 100 150 200 250 300 350 400 450
0.0
0.1
0.2
0.3
G [kg / m2 s]
∆∆ ∆∆E
/E [
-]
Figure 3.15 - Variation with mass velocity of the heat exchanged between the test section and the
surroundings.
100 150 200 250 300 350 400 450-0.05
0
0.05
0.1
0.15
0.2
G [kg / m2 s]
∆∆ ∆∆E
/E [
-]
Figure 3.16 - Variation with mass velocity of the heat exchanged between the pre-heater and the
surroundings.
3.9 Uncertainty analysis
An uncertainty analysis of the experimental results and their propagation was
performed for the pressure drop, heat transfer. The uncertainty of the measuring
instrument was evaluated using the methodology presented by Abernethy and
Thompson (1973) taken into account the technical specifications provided by the
manufacturer.
The evaluation of the uncertainty of the temperature measurement was also
performed using 5 calibration curves obtained from the thermocouples. Table 3.1
130 Equipment, experimental procedure and data reduction
presents uncertainties associated with measured parameters and detailed in
Appendix A.
Table 3.1 - Uncertainty of the measured parameters
The method developed by Taylor and Kuyatt (1994) was used to estimate
the uncertainty propagation of the calculated parameters. The estimation was
performed with the aid of the EES. Software. Table 3.2 shows the uncertainty
associated with the estimated parameters.
Table 3.2 - Uncertainty of the calculated parameters
Parameters Uncertainty
Heat flux 3.0%
Heat transfer coefficient <10%
Mass velocity 0.276 kg / m2 s
Vapor quality 0.032
Parameters Uncertainty
TPH,inlet 0.1 °C
TPH,outlet 0.1 °C
TST,outlet 0.1 °C
m& 5.45.10-5 kg / s
Power 3.04 %
PPH,inlet 1.4 kPa
PPH,outlet 1.6 kPa
∆p 0.075 %
Experimental results 131
4 EXPERIMENTAL RESULTS
This chapter presents the flow boiling experimental results obtained in the
present study for pressure drop and heat transfer coefficient in tubes with and without
twisted-tape inserts. The results were obtained using two test sections with internal
diameters of 12.7 and 15.9 mm from the experimental apparatus located at the
Department of Mechanical Engineering of the School of Engineering of São Carlos
(EESC-USP), built for the previous study of Kanizawa (2011). In the study of
Kanizawa (2011) flow pattern and pressure drop results were obtained for the 15.9
mm ID test section for R134a and the same twist-ratios considered in the present
study. A parametric analysis and critical discussion of the effect of experimental
parameters is also presented. Moreover, the results obtained in the present study are
compared with the predictive methods available in the literature.
The experimental data were obtained for the conditions described in Tab. 4.1.
Results for wider ranges of conditions were not possible due to limitation of the
apparatus as a sharp decline in the system pressure was observed with increasing
the fluid flow rate under higher vapor qualities conditions and for the lower saturation
temperature considered in the present study. This is related to the fact that there is
increase in specific volume of the fluid and hence lead to a higher pressure drop,
which subsequently beyond the capacity of experimental bench component.
Table 4.1 - Experimental conditions covered in the present study.
Paramters Conditions
Mass velocity 75,100, 150 and 200 kg / m2 s
Saturation temperature 5 o and 15 oC
Internal diameter 12.7 and15.9 mm
Vapor quality 0.05 to 0.95
Twist ratios 3,4,9,14 and
Heat flux 5 and 10 kW / m2
Working fluid R134a
In the present study, the thermo-hydraulic performance of refrigerant R134a is
analyzed during convective boiling inside tubes containing twisted-tape inserts. The
refrigerant R134a (tetrafluoroethane) is a halogenated hydrocarbon developed to
132 Experimental results
replace CFCs (chlorofluorocarbons) in refrigeration system. It is a medium-to-high
pressure refrigerant and its impact on the ozone layer is null. Table 4.2 presents the
thermodynamic and transport properties of R134a.
Table 4.2 - Physical, chemical and thermodynamic properties of R134a
Properties Ranges
Molecular weight [g / mol] 102.03
Boiling point 1 atm [° C] -26.1
Critical Temperature [° C] 101.1
Critical pressure [kPa (abs)] 4060
Saturated liquid density 25 ° C [kg / m³] 1206
Saturated vapor density 25 ° C [kg / m³] 32.34
Specific heat of saturated liquid 25 ° C [kJ / kg • K] 1.44
Specific heat of vapor 25 ° C and 1 atm [kJ / kg • K] 0.85
Saturated liquid pressure 25 ° C [kPa (abs)] 666
Thermal conductivity of saturated liquid 25 ° C [W / m • K] 0.08325
Thermal conductivity of saturated vapor 25 ° C [W / m • K] 0.01456
Viscosity of saturated liquid 25 ° C [Pa • s] 1.944*10-4
Viscosity of saturated vapor 25 ° C [Pa • s] 1.197*10-5
Surface tension [N / m] 8.081*10-3
4.1 Pressure drop results
This item describes the results of adiabatic two-phase flow experiments
performed focusing on determination of frictional pressure drop in tubes with and
without twisted-tape inserts. Additionally, predictive methods available in the
literature and described in Chapter 2 are compared against these data.
4.1.1 Pressure drop for tubes without twisted-tape inserts
A total of 284 experimental pressure drop data were obtained in the present
study, being 129 for the 12.7mm ID tube and 155 for the 15.9 mm ID tube.
Figures 4.1 and 4.2 display experimental results illustrating the variation of
frictional pressure drop gradient with vapor quality. These results were obtained for
R134a and saturation temperatures of 5 and 15 °C in 12.7 and 15.9 mm ID tubes.
According to Figs. 4.1 and 4.2, the frictional pressure drop increases with increasing
the mass velocity and decreasing the tube diameter and saturation temperature. By
decreasing the saturation temperature from 15 to 5 °C, the vapor specific volume
Experimental results 133
varies from 0.0421 to 0.0584 m³/kg. This behavior implies higher two-phase flow
velocities for lower saturation temperature and, consequently, higher pressure drops.
The liquid viscosity also increases with decreasing saturation temperature
contributing to the pressure drop augmentation.
Figures 4.1 and 4.2 also show that the pressure drop increases with the vapor
quality for low and intermediary vapor quality values. Moreover, pressure drop peaks
at high vapor qualities are displayed in Figs. 4.1 and 4.2 which seems to move to
lower vapor qualities with increasing the mass velocity and decreasing tube diameter.
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
G = 75 kg / m² s
G = 100 kg / m² s
G = 150 kg / m² s
G = 200 kg / m² s
Figure 4.1 - Variation of frictional pressure drop gradient with vapor quality for adiabatic two-phase
flow in 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
G = 75 kg / m² s
G = 100 kg / m² s
G = 150 kg / m² s
G = 200 kg / m² s
Figure 4.2 - Variation of frictional pressure drop gradient with vapor quality for adiabatic two-phase
flow in 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
134 Experimental results
4.1.2 Pressure drop for tubes with twisted-tape inserts
Figures 4.3 to 4.10 present experimental results of frictional pressure drop
during two-phase flow in tubes with twisted-tape inserts for saturation temperatures
of 5 and 15 °C, mass velocities from 75 to 200 kg / m² s, and twist-ratios equal to 3,
4, 9 and 14. In general as expected, the frictional pressure drop gradient increases
with decreasing twist-ratio, saturation temperature and tube diameter. Moreover, the
pressure drop increases with increasing the mass velocity. These trends are in
agreement with those observed by the study of Kanizawa and Ribatski (2012).
Figures. 4.3, 4.4 and 4.7 also display inflections in the trends of the pressure drop
gradient with increasing vapor quality for reduced mass velocities and twist-ratios.
The same behavior is not displayed in Figs. 4.9 and 4.10 for mass velocities of 150
and 200 kg / m² s. Kanizawa and Ribatski (2012) presented an analysis on the
influence of flow pattern on the pressure drop, concluding that these inflections are
related to the transition from stagnant flow to intermittent flow patterns. It is also
observed that the pressure drop gradient presents peaks for vapor qualities close to
0.73 and 0.87 for 12.7 and 15.9 mm ID tubes, respectively . The pressure drop
augmentation by the twisted-tape is related to the fact that, additionally to the
reduction of the cross sectional area, the insert induces turbulence and swirl effects
on the liquid film and vapor core.
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 4
y = 9
y = 14
Inflection
Figure 4.3 - Variation of frictional pressure drop gradient with vapor quality for R134a, 12.7 mm ID tube, G = 75 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
Experimental results 135
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
x [-]
∆∆ ∆∆p
fric
/ L
[kP
a / m
]
y = 4
y = 9y = 14
y=3
Inflection
Figure 4.4 - Variation of frictional pressure drop gradient with vapor quality for R134a, 12.7 mm ID tube, G = 100 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 9
y = 14
y=4
Figure 4.5 - Variation of frictional pressure drop gradient with vapor quality for R134a, 12.7 mm ID tube, G = 150 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
136 Experimental results
0.0 0.2 0.4 0.6 0.8 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 4
y = 9
y = 14
Figure 4.6 - Variation of frictional pressure drop gradient with vapor quality for R134a, 12.7 mm ID tube, G = 200 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 4
y = 9
y = 14
Inflection
Figure 4.7 - Variation of frictional pressure drop gradient with vapor quality for R134a, 15.9 mm ID tube, G = 75 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
Experimental results 137
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5
2.0
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 4
y = 9
y = 14
Figure 4.8 - Variation of frictional pressure drop gradient with vapor quality for R134a, 15.9 mm ID tube, G = 100 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
0.0 0.2 0.4 0.6 0.8 1.00.0
1.0
2.0
3.0
4.0
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 4
y = 9
y = 14
Figure 4.9 - Variation of frictional pressure drop gradient with vapor quality fo R134a, 15.9 mm ID tube, G = 150 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
138 Experimental results
0.0 0.2 0.4 0.6 0.8 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
x [-]
∆∆ ∆∆p
fric
/ L
[k
Pa
/ m
]
y = 3
y = 4y = 9
y = 14
Figure 4.10 - Variation of frictional pressure drop gradient with vapor quality for R134a 15.9 mm ID tube, G = 200 kg / m² s, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
4.1.3 Comparison between the experimental frictional pressure drop results
and the predictive methods
In this section, the experimental results of the two-phase flow frictional
pressure drop data obtained in the present study for plain tubes and tubes with
twisted-tape inserts are compared against estimatives according to predictive
methods available in the literature described in Chapter 2.
In Figs 4.11 and 4.12, the experimental pressure drop data for the 12.7 and
15.9 mm ID plain tubes, respectively, are compared against the predictive methods
of Friedel (1979), Grönnerud (1979), Müller-Steinhagen and Heck (1986) and
Moreno-Quibén and Thome (2007). According to these figures the method proposed
by Friedel (1979) and Moreno-Quibén and Thome (2007) presents higher deviation
from the experimental data. For higher mass velocity conditions, the predictive
methods of Friedel (1979), Grönnerud (1979), Müller-Steinhagen and Heck (1986)
perfomed better independent of the saturation temperature. On the other hand, the
predictive method of Moreno-Quibén and Thome (2007) underpridicts most of the
experimental data. Figure 4.13 displays comparisons of the behaviors of the pressure
drop data obtained in the present study with varying the vapor quality and the results
provided by the predictive methods. According to this figure, the methods of
Grönnerud (1979) and Müller-Steinhagen and Heck (1986) capture reasonable well
the pressure drop trends of the experimental data. Friedel (1979) over predicts most
Experimental results 139
of the experimental results, however captures reasonably the pressure drop peak
according to Fig. 4.13.
0.0 0.5 1.0 1.5 2.0 2.50.0
0.5
1.0
1.5
2.0
2.5
(∆∆∆∆pfric / L)experimental [kPa / m]
( ∆∆ ∆∆p
fric
/ L
) est
imat
ed
[kP
a /
m]
Friedel (1979)Grönnerud (1979)Müller-Steinhagen and Heck (1986)
-30 %
+30 %
Moreno-Quibén and Thome (2007)
Figure 4.11 - Comparison between estimated and experimental frictional pressure drop, for 12.7 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
(∆∆∆∆pfric / L)experimental [kPa / m]
( ∆∆ ∆∆p
fric
/ L
) est
imat
ed
[kP
a /
m] Friedel (1979)
Grönnerud (1979)Müller-Steinhagen and Heck (1986)
+30 %
-30 %
Moreno-Quibén and Thome (2007)
Figure 4.12 - Comparison between estimated and experimental frictional pressure drop, for 15.9 mm ID plain tube, for Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
140 Experimental results
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
0.4
x [-]
( ∆∆ ∆∆p
fric
/ L
) [
kPa
/ m
] Friedel (1979)
Exprimental data
Grönnerud (1979)
Müller-Steinhagen and Heck (1986)
Moreno-Quibén and Thome (2007)
Figure 4.13- Comparison of the trends of the frictional pressure drop according to predictive methods and experimental data for plain tube without twisted-tape,for 15.9 mm ID plain tube, Tsat = 15 °C and G
= 100 kg / m² s.
Table 4.3 presents the results of the statistical analysis of the comparison
between experimental results and predictive methods for two-phase pressure drop in
plain tubes without twisted-tape. The results are given in terms of the parcel of
experimental data predicted within an error band of ±30 % and the mean absolute
error defined as follows:
( ) ( )( ) points data
of number
Lp
LpLp
points data of number erimentalexpfric
erimentalexpfricestimatedfric
∑−
=∆
∆∆η (4.1)
Based on the results provided in Tab. 4.3, it is concluded that the method of
Grönnerud (1979) provides the best prediction of the overall database with mean
absolute deviation of 13 % and predicting 88 % of experimental data within an error
band of ±30 %. Müller-Steinhagen and Heck (1986) provides also reasonable
predictions. The abovementioned behaviors and the results displayed in Tab. 4.3 are
in agreement with the observations of Kanizawa and Ribatski (2012).
Experimental results 141
Table 4.3 - Results of the statistical analysis of the comparison between experimental data and predictive methods for frictional pressure drop in plain tubes.
Authors ζ30 [%] η [%]
Friedel (1979) 33 56
Grönnerud (1979) 88 13
Müller-Steinhagen and Heck (1986) 72 24
Moreno-Quibén and Thome (2007) 32 42
In Figs 4.14 and 4.15 the experimental results of frictional pressure drop in
12.7 and 15.9 mm tubes with twisted-tape inserts are compared with the predictive
methods of Jensen et al. (1985), Agrawal et al. (1982), Akhavan-Behabadi et al.
(2009a) and Kanizawa and Ribatski (2012). The statistics of the comparison are
presented in Tab. 4.4. In general, the predictive methods of Jensen et al. (1985),
Agrawal et al. (1982) and Akhavan-Behabadi et al. (2009a) provide reasonable
predictions of the experimental data only for high mass velocities corresponding to
annular flows. Poor predictions of the present database by the methods from
literature were already expected, considering the relatively wide range of operational
conditions covered in the present study and the fact that some of these methods are
based on fluids different than R134a. It should also be highlighted that these
methods do not take into account the influence of twisted-tape on the transitions
among stagnant, stratified and intermittent flow patterns, and so are not suitable for
reduced mass flow conditions.
According to Tab. 4.4, the method of Kanizawa and Ribatski (2012) provides
accurate prediction of the data obtained in the present study, predicting 99 % of
experimental data within an error band of ±30 %, and providing mean absolute
deviation of 7 %. The good predictions provided by the method of Kanizawa and
Ribatski (2012) is related to the fact that the method was developed considering in
detail the influence of flow pattern transitions on the pressure drop capturing its
tendencies under low and high mass velocity conditions. It is important mentioning
that the method of Kanizawa and Ribatski (2012) is based on experimental data
different from the data obtained in the present study.
142 Experimental results
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
(∆∆∆∆pfric / L)experimental [kPa/m]
( ∆∆ ∆∆p
fric
/ L
) est
imat
ed
[kP
a /
m]
+30 %
-30 %
Agrawal et al. (1982)
Akhavan-Behabadi et al. (2009a)
Jensen et al. (1985)
Kanizawa and Ribatski (2012)
Figure 4.14 - Comparison between estimated and experimental frictional pressure drop gradient, for 12.7 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3, 4, 9 and 14.
0.0 1.0 2.0 3.0 4.0 5.0 6.00.0
1.0
2.0
3.0
4.0
5.0
6.0
(∆∆∆∆pfric / L)experimental [kPa / m]
( ∆∆ ∆∆p
fric
/ L
) est
imat
ed
[kP
a /
m] +30 %
-30 %
Kanizawa and Ribatski (2012)
Agrawal et al. (1982)
Akhavan-Behabadi et al. (2009a)
Jensen et al. (1985)
Figure 4.15 - Comparison between estimated and experimental frictional pressure drop gradient, for 15.9 mm ID tube, Tsat = 5 °C, G from 75 to 200 kg / m² s, and y = 3, 4, 9 and 14.
Experimental results 143
Table 4.4 – Results of the statistical analysis of the comparison between experimental and predicted pressure drop data during two-phase flow in tubes with twisted-tape inserts.
ζ30 [%] η [%] Authors
di = 12.7 mm di = 15.9 mm Overall di = 12.7 mm di = 15.9 mm Overall
Akhavan-Behabadi et al.(2009a) 62 66 64 25 26 26
Jensen et al. (1985) 64 69 66 25 24 24
Agrawal et al (1982) 63 57 60 25 28 26
Kanizawa and Ribatski (2012) 99 99 99 8 7 7.5
Figures 4.16 and 4.17 display comparisons of the behaviors of pressure drop
with varying the vapor quality for the experimental data obtained in the present study
and the predictive methods. According to Figs. 4.16a and 4.17a, for mass velocity of
75 kg / m2 s, the predictive methods of Jensen et al. (1985), Agrawal et al. (1982)
and Akhavan-Behabadi et al. (2009a) fails to capture the pressure drop trends of the
experimental data independent of the vapor quality conditions. These methods,
under predict and over predict the data for low vapor qualities and for vapor qualities
higher than 0.4.
For mass velocity of 150 kg / m2 s, it can be noted in Fig. 4.17b that the
predictive methods of Jensen et al. (1985) and Akhavan-Behabadi et al. (2009a)
capture reasonably well the pressure drop trends of the experimental data while
Agrawal et al. (1982) method under predicts the data for high vapor qualities.
Significant differences between the database obtained in the present study and the
experimental data used by these authors when developing their methods can
partially explain their unsatisfactory performance. Moreover, these methods do not
take into account the influence of twisted-tape on the flow pattern transitions among
stagnant, stratified and intermittent flow and so they cannot be considered suitable
for reduced mass flow conditions.
Contrary to the predictive methods of Jensen et al. (1985), Agrawal et al.
(1982) and Akhavan-Behabadi et al. (2009a), it can be noted in Figs. 4.16 and 4.17,
that the predictive method of Kanizawa and Ribatski (2012) captures well the
experimental pressure drop data and their trend with increasing vapor quality and
twist-ratio, independently of the mass velocity. It can be noticed that the method
obeys the inflection in the pressure drop for vapor qualities about 0.2 related to the
transition from the stagnant to intermittent flow pattern. The method predicts
accurately well also the data under conditions of high vapor quality and twist-ratios.
144 Experimental results
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0
0.5
1.0
1.5
x [-]
∆∆ ∆∆p
fri
c /
L
[kP
a/m
]
Experimental
Kanizawa and Ribatski (2012)Akhavan-Behabadi et al. (2009a)
Jensen et al. (1985)Agrawal et al. (1982)
G=75 kg/m2s, y=3
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.5
1.0
1.5
2.0
x [-]
∆∆ ∆∆p
fri
c /
L
[kP
a/m
]
Experimental
Kanizawa and Ribatski (2012)
Agrawal et al. (1982)Akhavan-Behabadi et al. (2009a)Jensen et al. (1985)
G=150 kg/m2s, y=14
(b)
Figure 4.16 - Comparison of the trends of the frictional pressure drop according to predictive methods and experimental data for plain tube with twisted-tape, for 12.7 mm ID tube Tsat = 15 °C.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.5
1.0
1.5
x [-]
∆∆ ∆∆p
fri
c /
L
[kP
a/m
]
Experimental
Kanizawa and Ribatski (2012)
Agrawal et al. (1982)
Akhavan-Behabadi et al. (2009a)
Jensen et al. (1985)
G=75 kg/m2s, y=3
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
x [-]
∆∆ ∆∆p
fric
/ L
[kP
a/m
]
Experimental
Kanizawa and Ribatski (2012)
Akhavan-Behabadi et al. (2009a)
Agrawal et al. (1982)
Jensen et al. (1985)
G=150 kg/m2s, y=14
(b)
Figure 4.17 - Comparison of the trends of the frictional pressure drop according to predictive methods and experimental data for plain tube with twisted-tape, for 15.9 mm, ID tube, Tsat = 15 °C.
4.1.4 Evaluation of the pressure drop penalty due to twisted-tape inserts
Figures 4.18 and 4.19 illustrate the variation of the pressure drop penalty with
the vapor quality for different mass velocities, saturation temperatures and twist-
ratios for tubes with internal diameters of 12.7 and 15.9 mm. The pressure drop
penalty illustrated in these figures is defined as the ratio between the experimental
frictional pressure drop for the tube with twisted-tape insert and its corresponding
value for the plain tubes without inserts, estimated according to the correlation of
Grönnerud (1979), keeping the same experimental conditions. The predictive method
of Grönnerud (1979) was used in this comparison because it provided the best
prediction of the pressure drop data for the tube without twisted-tape insert.
Experimental results 145
According to Figs. 4.18 and 4.19 and as observed by Salimpour and Yarmohammadi
(2012) and Kanizawa and Ribatski (2012), the pressure drop penalty increases with
decreasing mass velocity and twist-ratio. Moreover, the pressure drop penalty tends
to a similar value independently of the twist-ratio as the vapor quality approaches to
the unity.
From Figs. 4.18 and 4.19 pressure drop penalties values higher than 30 are
observed for both tubes diameter under conditions of reduced vapor qualities and
mass velocities. By comparing Figs. 4.18 and 4.19, it is also noted under similar
experimental conditions that the 15.9 mm ID tube presents higher pressure drop
penalties than the 12.7 mm ID tube. Moreover, the effect of saturation temperature
on the pressure drop penalty seems only marginal for the range of experimental
conditions evaluated in the present study.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-]
y = 3
y = 4
y = 9
y = 14
G = 75 kg / m2 s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-]
y=14
y=9
y=4
y=3G = 100 kg / m2 s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-]
y=3
y=4
y=9
y=14
G = 150 kg / m2 s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-] y = 3
y = 4
y = 9
y = 14
G = 200 kg / m2 s
Figure 4.18 – Illustration of the variation of pressure drop penalty with vapor quality, for ID = 12.7 mm and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols).
146 Experimental results
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-]
y=14
y=9
y=4
y=3G =75 kg / m2 s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
35
x [-]∆∆ ∆∆
pfr
ic,T
T /
∆∆ ∆∆p
fric
,Pla
in [
-] y=3
y=4
y=9
y=14
G =100 kg / m2 s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-]
y=14
y=9
y=4
y=3
G =150 kg / m2 s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
35
x [-]
∆∆ ∆∆p
fric
,TT /
∆∆ ∆∆p
fric
,Pla
in [
-]
y=3
y=4
y=9
y=14
G =200 kg / m2 s
Figure 4.19 - Illustration of the variation of pressure drop penalty with vapor quality for ID = 15.9 mm, and Tsat = 5 °C (empty symbols) and 15 °C (filled symbols).
4.2 Heat transfer coefficient results
Initially, this section presents an analyses of the heat transfer coefficient results
for tubes without twisted-tapes. Then, a parametric discussion into the effect of the
experimental variables on the heat transfer coefficient for tubes with and without
twisted-tape inserts is presented. Additionally, the experimental data for tubes with
and without twisted-tapes are compared against the predictive methods available in
the literature described in Chapter 2.
Experimental results 147
4.2.1 Results for tubes without twisted-tape
Figures 4.20 and 4.21 illustrate the variation of the heat transfer coefficient
with vapor quality according to the experimental results. These data were obtained
during two-phase flows of R134a in tubes without twisted-tape inserts for saturation
temperatures of 5 and 15 °C, heat flux values of 5 and 10 kW / m² and mass
velocities from 75 to 200 kg / m² s. According to Figs. 4.20 and 4.21, the heat transfer
coefficient increases with increasing the mass velocity and decreasing the tube
diameter and saturation temperature. For mass velocities of 75 and 100 kg / m² s, the
heat transfer coefficient remains almost constant over a wide range of vapor quality.
This behavior is due to the occurrence of stratified flows for low mass velocities and
is related to the presence of a dry region on the tube upper part and a significant
layer of liquid on the bottom of the tube with occurrence of nucleate boiling in this
region. For intermediary and high mass velocities and prior to the surface dryout, the
heat transfer coefficient increases with increasing vapor quality. As illustrated in Fig.
4.20, this effect is more pronounced for the tube with smaller diameter compared to
the tube with larger diameter due to the higher vapor shear stress on the liquid film,
enhancing convective effects for the former. This behavior is typical of intermittent
and annular flow patterns as already pointed out by Saiz-Jabardo and Bandarra Filho
(2006), Wojtan et al. (2005) and Cheng et al. (2008).
According to Fig. 4.21, the heat transfer coefficient increases with increasing
the mass velocity and decreasing saturation temperature. For lower saturation
temperature, higher heat transfer coefficient is observed with increasing vapor quality
especially for intermediary and high mass velocities. Such behavior is related to the
fact that the vapor specific volume increases by decreasing the saturation
temperature, causing an increase in two-phase flow velocity.
According to Fig. 4.22, under high mass velocity conditions, the heat transfer
coefficient increases with increasing heat flux over the whole range of vapor quality.
Almost constant heat transfer coefficient is also observed in the lower vapor quality
region especially for mass velocities of 75 and 100 kg / m² s independent of the heat
flux effect, due to the predominance of nucleate boiling effects.
148 Experimental results
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
x [-]
h
[kW
/ m
2 o C
] G = 200kg / m2 s
G = 150 kg / m2 s
G = 100 kg / m2 s
G = 75 kg / m2 s
Figure 4.20 – Variation of heat transfer coefficient with vapor quality during flow boiling in tube without
twisted-tape inserts, ϕ = 10 kW / m², Tsat = 5 °C, di = 12.7 mm (empty symbols) and di = 15.9 mm (filled symbols).
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
x [-]
h
[kW
/ m
2 o C
] G = 200kg / m2 s
G = 150 kg / m2 s
G = 100 kg / m2 s
G = 75 kg / m2 s
Figure 4.21 - Variation of heat transfer coefficient with vapor quality during flow boiling in tube without
twisted-tape inserts, ϕ = 10 kW / m², di = 15.9 mm , Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
Experimental results 149
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
x [-]
h
[kW
/ m
2 o C
]G = 200 kg / m2 s
G = 150 kg / m2 s
G = 100 kg / m2 s
G = 75 kg / m2 s
Figure 4.22 - Variation of heat transfer coefficient with vapor quality during flow boiling in tube without
twisted-tape inserts, Tsat = 15 °C ,di = 15.9 mm ,ϕ = 10 kW / m² (empty symbols) and ϕ = 5 kW / m², (filled symbols).
4.2.2 Comparison between the experimental heat transfer coefficients results
for tubes without twisted-tape inserts and the predictive methods.
In this section, the experimental results of the two-phase flow heat transfer
coefficient data obtained in the present study for tubes without twisted-tape inserts
are compared against estimatives obtained using the predictive methods described in
Chapter 2.
In the present study, 420 and 342 experimental data for heat transfer
coefficient in 12.7 and 15.9 mm ID plain tubes without twisted-tape, respectively,
were obtained. Table 4.5 presents the results of statistical analysis of the
comparisons between experimental results and predictive methods for heat transfer
coefficient, namely Kandlikar (1990), Liu and Winterton (1991), Bandarra Filho (2002)
and Wojtan et al. (2005b). As can be observed in Tab. 4.5, Kandlikar (1990) presents
the best prediction of the experimental dataset for the plain tubes, predicting 64.6 %
of the experimental data within an error band of ±30 % and mean absolute deviation
of 25.9 %. Liu and Winterton (1991) and Wojtan et al. (2005b) also provide
predictions as accurate as Kandlikar (1990). However, considering only experimental
results for 12.7 mm ID tube, Kandlikar (1990) and Liu and Winterton (1991) methods
150 Experimental results
predicted respectively 82 and 71 % of the experimental data obtained in the present
study within an error band of ±30 %. This result suggested that these methods are
more appropriate to smaller diameter tubes. On the hand, Wojtan et al. (2005b)
predicts almost the same parcel of the data within an error band of ±30 % for larger
tube. Figure 4.23 shows a comparison of the experimental heat transfer coefficient
data and calculated values according to the predictive method of Kandlikar (1990).
Table 4.5 – Results of the statistical analysis of the comparison between experimental results for heat transfer coefficient during two-phase flow in plain tubes and predictive methods from literature.
ζ30 [%] η [%] Authors
di = 12.7 mm di = 15.9 mm Overall di = 12.7 mm di = 15.9 mm Overall
Kandlikar (1990) 82 47 65 24 28 26
Liu and Winterton (1991) 71 58 64 23 29 26
Bandarra Filho (2002) 32 35 34 88 83 85
Wojtan et al. (2005b) 62 66 64 29 27 28
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
hexperimental [kW / m2 oC]
hes
tim
ated
[kW
/ m
2 oC
]
+30 %
-30 %
Figure 4.23- Comparison between estimated and experimental heat transfer coefficients for the12.7 mm ID tube without inserts according to Kandlikar (1990).
4.2.3 Results for tubes with twisted-tape inserts
4.2.3.1 Twisted-tape effect
The twisted-tape effect on the heat transfer coefficient is illustrated in Figs.
4.24 and 4.25 for the 12.7 mm ID tube, and in Figs. 4.26 and 4.27 for the 15.9 mm ID
tube for heat flux of 10 kW / m2 and saturation temperature of 5 oC. According to
these figures, inserting twisted-tape inside a plain tube increase significantly the heat
Experimental results 151
transfer coefficient compared to tube without the swirl flow device, independently of
the mass velocity. This behavior is due to the promotion by the tape of better fluid
mixing and higher flow velocity of fluid in the vicinity of the tube wall compared to that
of the tube without tape.
It can be observed in Figs. 4.24 and 4.26 for mass velocity of 75 kg / m2 s,
heat transfer coefficients almost constant over nearly the whole range of vapor
qualities for tubes with twist-ratios of 9 and 14. This effect is more pronounced for
larger diameter. This trend is in agreement with the observations posted by Akhavan-
Behabadi et al. (2009b).
Generally speaking, for mass velocity of 150 kg / m2 s the heat transfer
coefficient increases with increasing the vapor quality for the plain tube and the tube
with twisted-tape inserts as illustrated in Figs. 4.25 and 4.27. According to Fig. 4.25,
for the reduced twist-ratios of 3 and 4 in both tubes, the heat transfer coefficient
increases with vapor quality also for the low mass velocity of 75 kg / m2 s. This
behavior can be related to an earlier transition from stratified to intermittent and
annular flow patterns for low twist-ratios due to the presence of twisted-tapes.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
x [-]
h
[kW
/ m
2 o C
]
Plain tube
y=4
y=3
y=9
y=14
Figure 4.24 - Heat transfer coefficient variation with vapor quality during flow boiling in 12.7 mm ID,
G = 75 kg / m2 s, φ = 10 kW / m², Tsat = 5 oC.
152 Experimental results
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
h
[kW
/ m
2 o C
]
Plain tube
y=3
y=4
y=9
y=14
Figure 4.25 - Heat transfer coefficient variation with vapor quality during flow boiling in 12.7 mm ID, G
= 150 kg / m2 s, φ = 10 kW / m², Tsat =5 oC.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
x [-]
h
[kW
/ m
2 o C
]
Plain tube
y=3
y=4
y=14
y=9
Figure 4.26 - Heat transfer coefficient variation with vapor quality during flow boiling in 15.9 mm ID, G
= 75 kg / m2 s, φ = 10 kW / m², Tsat = 5 oC.
Experimental results 153
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
h
[kW
/ m
2 o C
]Plain tube
y=3
y=4
y=9
y=14
Figure 4.27 - Heat transfer coefficient variation with vapor quality during flow boiling in 15.9 mm ID, G
= 150 kg / m2 s,φ = 10 kW / m², Tsat = 5 oC.
4.2.3.2 Heat flux
Figures 4.28 and 4.29 display the effect of heat flux on the heat transfer
coefficient for 12.7 and 15.9 mm ID tubes, respectively, with and without twisted-tape
inserts for mass velocity of 150 kg / m2 s, twist-ratio of 3 and heat flux values of 5 and
10 kW / m2. According to Figs. 4.28 and 4.29, the heat transfer coefficient increases
with increasing the heat flux for tubes with twisted-tape and without twisted-tape
inserts. For tubes without twisted-tape inserts, the heat flux affects the heat transfer
coefficient at lower vapor quality conditions, indicating the occurrence of stratified
wavy flow pattern and predominance of nucleate boiling effects. Moreover, from Figs.
4.28 and 4.29, higher heat transfer coefficient is observed at lower vapor quality
region for the tube with twisted-tape inserts than the tube without inserts,
independent of the heat flux values. This may be due to intense swirl flow promoted
by the twisted-tape, improving convective effects even at lower vapor qualities.
These trends are in agreement with those observed in the study of Agrawal and
Varma (1990).
154 Experimental results
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
h
[kW
/ m
2 o C
]
q = 10 kW / m2
q = 5 kW / m2
Figure 4.28 - Illustration of the effect of heat flux on heat transfer coefficient for plain tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 12.7 mm ID Tsat = 5 oC.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
x [-]
h
[kW
/ m
2 o C
]
q= 10 kW / m2
q= 5 kW / m2
Figure 4.29 - Illustration of the effect of heat flux on heat transfer coefficient for plain tube (filled symbol) and tube with twisted-tape insert, y = 3 (empty symbol) in 15.9 mm ID Tsat = 5 oC.
4.2.3.3 Mass Velocity
Figure 4.30 displays the heat transfer results for the 15.9 mm ID tube for twist-
ratios of 3 and 14, saturation temperature of 15 oC, heat flux of 10 kW / m² and
diferent mass velocities. In general, the heat transfer coefficient increases with
increasing mass velocity and decreasing twist-ratio. According to this figure and as
observed by Akhavan-Behabadi et al. (2009b) for mass velocities of 75 and 100 kg /
Experimental results 155
m² s and twist-ratio of 14, the heat transfer coefficient remains almost constant over a
wide range of vapor quality. This behavior is due to the occurrence of stratified flow
for low mass velocities. For mass velocities of 150 and 200 kg / m² s, the heat
transfer coefficient increases with increasing vapor quality. This behavior is typical of
annular flow patterns and is more pronounced for the lowest twist-ratio of 3.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
x [-]
h [
kW /
m2 o
C]
G =200 kg / m2 s
G =150 kg / m2 s
G =100 kg / m2 s
G =75 kg / m2 s
Figure 4.30 - Heat transfer coefficient variation with vapor quality during flow boiling in 15.9 mm ID, φ = 10 kW / m², Tsat = 15 oC; y = 14 (filled symbol) and y = 3 (empty symbol).
4.2.3.4 Tube diameter
Figure 4.31 shows for both tube diameters, the variation of the heat transfer
coefficient with vapor quality, for heat flux of 10 kW / m2, mass velocity of 100 kg / m2
s, saturation temperature of 15 °C and twist-ratios of 3 and 14. According to this
figure, in general, the heat transfer coefficient increases with decreasing tube
diameter. This effect is more pronounced for lower twist-ratios. These behavior may
be attributed to the higher vapor shear stress in 12.7 mm ID tube and lower twist-
ratio. The insertion of twisted-tape inside the 12.7 mm ID tube is more effective in
order of promoting an earlier transition of flow pattern from stratified-wavy to annular
flow. This behavior is clearly indicated by the sudden increase of the heat transfer
coefficient at vapor quality of approximately 0.32 and 0.16 according to the data of
12.7 mm ID tube and twist-ratio of 14 and 3, respectively. The augmentation of heat
transfer coefficient inside tubes with twisted-tape is related to the fact that,
additionally to the reduction of the cross sectional area, the insert induces swirl
156 Experimental results
effects on the liquid film and vapor core, increasing the total wetted perimeter and
improving the heat transfer coefficient of the tube with smaller diameter compared to
the tube with larger diameter.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
x [-]
h
[kW
/ m
2 o
C]
y=3, di=12.7 mm
y=3, di=15.9 mm
y=14, di=12.7 mm
y=14, di=15.9 mm
Figure 4.31 – Illustration of the effect of tube diameter on the heat transfer coefficient with vapor
quality inside tubes with twisted-tape inserts, G = 100 kg / m2 s, φ = 10 kW / m², Tsat = 15 oC.
4.2.3.5 Saturation temperature
Figures 4.32 and 4.33 illustrate the effects of the saturation temperature on the
heat transfer coefficient during flow boiling in tubes with twisted-tape inserts for mass
velocities of 75 and 150 kg / m2 s, heat flux of 10 kW / m2 and saturation
temperatures of 5 and 15 oC. From these figures, it can be noted that the heat
transfer coefficient increases with increasing vapor quality independent of saturation
temperatures. This behavior is more pronounced for the twist-ratio of 4. For lower
saturation temperature, higher heat transfer coefficient is observed with increasing
vapor quality. Such behaviour is related to the fact that the vapor specific volume
increases by decreasing the saturation temperature, causing an increase in the flow
velocity, and consequently in its longitudinal and centrifugal effects responsible for
increasing convective effects.
Experimental results 157
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
x [-]
h
[kW
/ m
2 o C
]
Tsat=5 o C
Tsat=15 o C
Figure 4.32 - Effect of the saturation temperature on the heat transfer coefficient during flow boiling in 15.9 mm ID, G = 75 kg / m2 s, φ = 10 kW / m², y = 14 (filled symbol) and y = 4 (empty symbol).
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
x [-]
h
[kW
/ m
2 o C
]
Tsat=5 o C
Tsat=15 o C
Figure 4.33 - Effect of the saturation temperature on the heat transfer coefficient for during flow boiling in 15.9 mm ID, G = 150 kg / m2 s, φ = 10 kW / m², y = 14 (filled symbol) and y = 4 (empty symbol).
4.2.4 Comparison between the experimental heat transfer coefficient results for
tubes with twisted-tape inserts and the predictive methods.
In this section, the experimental flow boiling results for the heat transfer
coefficient obtained in the present study for tubes with twisted-tape inserts are
158 Experimental results
compared against estimatives provided by the predictive methods available in the
literature.
In the present study, 1263 and 1098 heat transfer coefficient data were
obtained for 12.7 and 15.9 mm ID tubes, respectively for tubes with twisted-tape
inserts. Table 4.6 presents the results of the statistical analysis of the comparisons
between experimental and predicted data for tubes with twisted-tape inserts. This
analyses includes predictive methods of Akhavan-Behabadi et al. (2009b), Jensen
and Bensler (1986) and Agrawal et al. (1986). According to this table, it can be
concluded that Akhavan-Behabadi et al. (2009b) presents the best prediction of the
present experimental database. This can be related to the fact that their correlation
was developed based on database obtained for R134a, mass velocities between 54
and 136 kg / m² s and saturation temperature between -19 and -3 °C. Considering
only experimental results for 12.7 mm ID tube, Akhavan-Behabadi et al. (2009b),
methods predicted 79 % of the experimental data obtained in the present study within
an error band of ±30 %, indicating that this method is also more appropriate to
smaller diameter tubes. This can be related to the fact that, these authors have
performed experiments for 7.5 mm ID tube which value is closer to 12.7 than 15.9
mm. Figure 4.34 shows a comparison of the experimental heat transfer coefficient
data and the calculated values according to the predictive method of Akhavan-
Behabadi et al. (2009b).
The predictive methods proposed by Jensen and Bensler (1986) and Agrawal
et al. (1986) under predicts the experimental results obtained in the present study for
the entire database. Such a result was expected, given significant differences of
experimental conditions between the present study and the experimental data
obtained in their studies.
Figures 4.35 and 4.36 illustrate comparisons of the behaviors of the heat
transfer coefficient according to the experimental data and the counterparts results
provided by the predictive methods of Akhavan-Behabadi et al. (2009b), Jensen and
Bensler (1986) and Agrawal et al. (1986). It can be noted in Figs 4.35 and 4.36 that
the predictive methods of Akhavan-Behabadi et al. (2009b) and Agrawal et al. (1986)
provide an unexpected behavior corresponding to heat transfer coefficient reduction
with increasing vapor quality. This behavior is more pronounced for the 15.9 mm ID
tube. According to Fig. 4.35a, Akhavan-Behabadi et al. (2009b) captures reasonably
the main trend of the experimental data. The fact that the method of Akhavan-
Experimental results 159
Behabadi et al. (2009b) provided worst predictions of the trend of the heat transfer
coefficient with vapor quality for y=3 as shown in Fig. 4.35b can be also related to the
limitations of their database which minimum evaluated twist-ratio was 6.
As can be observed in Figs. 4.35 and 4.36, Jensen and Bensler (1986) under
predicts most of the heat transfer coefficient data independently of the mass velocity
and twist-ratio. However, under high mass velocity conditions and low twist-ratios, it
seems that the method of Jensen and Bensler (1986) captures reasonably well the
heat transfer coefficient trends with increasing vapor quality as shown in Figs. 4.35b,
4.36a and 4.36b. This result can be related to the fact that Jensen and Bensler
(1986) based their method on data for upwards flow in a vertical tube when the
effects of gravitational forces on the flow stratification are absent. For horizontal
tubes, two-phase flow stratification effects are reduced relatively to inertial forces with
increasing mass velocity.
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
hexperimental [kW / m2 oC]
hes
tim
ated
[kW
/ m
2 o
C] y=9
+30%
-30%
y=4
y=3
y=14
Figure 4.34 - Comparison between estimatives according to Akhavan-Behabadi et al. (2009b) and experimental heat transfer coefficients.
Table 4.6 - Results of the statistical analysis of the comparison between experimental results and predictive methods for heat transfer coefficient in tubes with twisted tape inserts.
ζ30 [%] η [%] Authors
di = 12.7 mm di = 15.9 mm Overall di = 12.7 mm di = 15.9 mm Overall
Akhavan-Behabadi et al.(2009b) 79 62 71 20 34 26
Jensen and Bensler (1986) 8 30 18 54 36 46
Agrawal et al. (1986) 31 24 28 54 78 65
160 Experimental results
0.0 0.1 0.2 0.3 0.4 0.50.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
x [-]
h
[kW
/ m
2 o C
]
ExperimentalAkhavan-Behabadi et al. (2009b)Jensen and Bensler (1986)Agrawal et al. (1986)
G=75 kg/m2s, y=14
(a)
0.0 0.1 0.2 0.3
0.0
3.0
6.0
9.0
x [-]
h
[kW
/ m
2 o C
]
ExperimentalAkhavan-Behabadi et al. (2009b)Jensen and Bensler (1986)Agrawal et al. (1986)
G=150 kg/m2s, y=3
(b)
Figure 4.35 - Comparison of the trends of the heat transfer coefficient according to predictive methods and experimental data for plain tube with twisted-tape, for 12.7 mm ID tube, Tsat = 5 °C, φ = 10 kW/m².
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
h
[kW
/ m
2 o C
]
Experimental
Akhavan-Behabadi et al. (2009b)
Agrawal et al. (1986)
Jensen and Bensler (1986)
G=75 kg/m2s, y=3
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
x [-]
h
[kW
/ m
2 o C
]
Experimental
Akhavan-Behabadi et al. (2009b)
Agrawal et al. (1986)
Jensen and Bensler (1986)
G=150 kg/m2s, y=14
(b)
Figure 4.36 - Comparison of the trends of the heat transfer coefficient according to predictive methods and experimental data for plain tube with twisted-tape, for 15.9 mm ID tube, Tsat= 5 °C, φ = 10 kW/m².
4.2.5 Overall Performance of the heat transfer enhancement technique
In order to determine the working conditions under which the use of twisted-
tape would present advantage over plain tube, parameters providing an overall view
of the performance enhancement are necessary. These parameters must include
pressure drop and heat transfer characteristics, keeping similar operational
constraints. Agarwal and Raja Rao (1996) have analyzed the enhancement
performance for single-phase flows inside tubes containing twisted-tape inserts
based on the heat transfer coefficient per unit of pumping power keeping fixed the
Reynolds number. Webb (1981) has presented a broad discussion on different
approaches to evaluate the heat transfer enhancement for heat exchangers
Experimental results 161
operating under single-phase flow conditions. His analysis takes into account the
heat exchanger characteristics by fixing different design constrains. For each group
of design constraints, he has imposed additional restrictions by keeping fixed
parameter as the pumping power, heat transfer capacity, mass flow rate and
temperature difference between the fluids given in terms of the logarithmic mean
temperature difference. For two-phase flows, Webb (1981) also argued that the
hypothesis of fixing the logarithmic mean temperature difference is not suitable due
to the reduced variation of fluid temperature. Shah (1978) has also analyzed the
different parameters of enhancement performance and from his study he has
suggested a thermodynamic analysis based on the minimum entropy generation for
evaluation of heat transfer enhancement technique.
In the present study, the overall performance enhancement technique was
evaluated according to the following parameters: the ratio between the heat transfer
coefficients per unit of pumping power of the tube with and without twisted-tape; and
the ratio of heat transfer coefficients of the tube with and without twisted-tape for the
same pumping power. These parameters are given, respectively, as follows:
dimensionless (4.2)
dimensionless (4.3)
In the equations above, the sub indexes TT and Plain correspond to tubes with
and without twisted-tape inserts, respectively. The subscripts of the terms between
parentheses represent the conditions adopted as reference and, so, kept fixed for
evaluation of the twisted-tape performance. In Eqs. (4.2) and (4.3), hTT is the heat
transfer coefficient for the tube with twisted-tape based on the experimental results.
The pumping power in Eq. (4.2) was estimated as the product between the
experimental frictional pressure drop, ,over the test section defined by Eq.
(3.2) and the volumetric flow rate of the liquid at its saturation temperature.
In Eq. (4.3) the mass flow rate for the plain tube was estimated based on the
pumping power based on the experimental results for the tubes with twisted-tape
162 Experimental results
inserts. For the estimation of both performance parameters ( and ), plain tube
heat transfer coefficient, hPT, and frictional pressure drop, ∆pPT, were evaluated
according to Kandlikar (1990) and Grönnerud (1979) methodologies, respectively.
Frictional pressure drop for tube with twisted-tape insert ∆pTT was estimated
according to Kanizawa and Ribatski (2012) correlation. These predictive methods
were chosen based on the fact that they have provided the best predictions of the
experimental data obtained in the present study.
The enhancement parameters and were chosen with the aim of
analyzing the gain in heat transfer for a given heat exchanger with fixed geometry
due to the installation of twisted-tape inserts, keeping the same pumping power or
per unit of pumping power. These approaches were considered since they are based
on characteristics directly applied by system designers such as pumping power,
temperature differences and heat exchanger size.
Figure 4.37 illustrates the behavior of the performance factor based on heat
transfer coefficient per unit of pumping power, 1ε , with increasing vapor quality for G
= 75 kg/m²s. As can be observed in this figure, 1ε increases with increasing vapor
quality and twist-ratio. Moreover, it is also noted that 1ε decreases with decreasing
saturation temperature and the tube diameter from 12.7 to 15.9 mm. Analyses of the
experimental results for other conditions (not shown in Fig. 4.37) revealed that 1ε
increases with increasing mass velocity and that the effect of augmenting the heat
flux from 5 to 10 kW / m² is only marginal on 1ε .
Figures 4.38 and 4.39 display the variation of the performance factor 2ε with
vapor quality for 12.7 and 15.9 mm ID tubes, respectively. According to these figures,
performance enhancements based on 2ε factor up to 45 % can be obtained keeping
the same pumping power through the use of twisted-tape inserts. Generally
speaking, Figs. 4.38 and 4.39 display that the performance factor 2ε increases with
increasing mass velocity and decreasing tube diameter. Moreover, initially the
performance factor 2ε increases with increasing vapor quality then passes through a
peak under intermediary to moderate-high vapor qualities. After the peak, 2ε
decreases drastically with further vapor quality augmentation. Although not shown for
all experimental conditions displayed in Figs. 4.38 and 4.39, the peak is an expected
behavior due to the fact that twisted-tapes promote earlier transitions to dryout
Experimental results 163
compared with tubes without twisted-tapes as displayed in Figs. 4.20 and 4.21. This
behavior moves the drastic reduction of the heat transfer coefficient to lower vapor
qualities. For reduced vapor quality values, it can be also noticed that the
enhancement factor is lower than unity for majority of conditions. This behavior is due
to high pressure drop penalty that the insert causes in the system. Based on section
4.1.4, pressure drop penalty values higher than 30 were obtained for reduced twist-
ratios and low vapor quality, while the heat transfer coefficient increment is about one
order of magnitude lower.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.2
0.4
0.6
0.8
1.0
x [-]
εε εε1
[-]
y = 3, di = 12.7 mm
y = 9, di = 12.7 mm
y = 3, di = 15.9 mm
y = 9, di = 15.9 mm
Figure 4.37 - Variation of enhancement factor 1ε for unit pumping power, for G = 75 kg/m²s, ϕ = 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
In general, the performance factor 2ε increases with increasing saturation
temperature from 5 to 15 °C. This behavior can be attributed to the fact that at high
saturation temperature conditions, the volumetric flow rate is lower than at low
saturation temperature conditions. This pose little effect on the system pumping
power resulting in increasing the overall performance factor.
Finally, based on Figs. 4.38 and 4.39, it can be concluded that higher twist-
tape-ratios are recommendable for high mass velocities and low vapor quality
conditions while lower twist-tape ratios are recommendable for high mass velocities
and intermediary vapor qualities prior the dryout. On the other hand, under low mass
velocity conditions, lower twist-ratios are recommendable for intermediary vapor
164 Experimental results
qualities. This is related to the fact that for reduced mass velocities, the twisted-tape
promotes the transition from stratified to annular flow what is absent for the tube
without swirl promoter devices. Annular flows are characterized by higher heat
transfer coefficients than stratified flows.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.5
1.0
1.5
2.0
x [-]
εε εε2
[-]
y = 3, di = 12.7 mmy = 4, di = 12.7 mmy = 14, di = 12.7 mmy = 3, di = 15.9 mmy = 4, di = 15.9 mmy = 14, di = 15.9 mm
Figure 4.38 – Variation of enhancement factor 2ε for the same pumping power, for G = 75 kg/m²s, ϕ
= 10 kW / m², Tsat = 5 °C (empty symbols) and Tsat = 15 °C (filled symbols).
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.5
1.0
1.5
2.0
2.5
x [-]
εε εε2
[-]
y = 4
y = 14
y = 3
Figure 4.39 – Variation of enhancement factor 2ε for the same pumping power, for G = 200 kg/m²s, ϕ
= 10 kW/m², Tsat = 15 °C, d = 12.7 mm (empty symbols) and di = 15.9 mm (filled symbols).
Experimental results 165
166 Heat transfer predictive method
5 PREDICTIVE METHOD FOR HEAT TRANSFER
COEFFICIENT DURING FLOW BOILING INSIDE
TUBES CONTAINING TWISTED-TAPE INSERTS
This chapter deals with the development of a new method for predicting heat
transfer coefficient during flow boiling inside tubes containing twisted-tape inserts.
The proposed method takes into account the swirl flow effects of the twisted-tape
inserts on the enhancement of convective effects and nucleate boiling suppression.
The new method was developed based on the following suggestions posted
by Shatto and Peterson (1996): (1) Obtain a reasonable prediction of experimental
data for plain tube without twisted-tape using well-established correlation from the
literature; (2) modify this correlation to predict the twisted-tape heat transfer data.
Taken into accounts the suggestion (1) of Shatto and Peterson (1996), the
new predictive method was developed based on the Liu and Winterton (1991)
method. This method was chosen because it predicted the data for tubes without
twisted-tape inserts gathered in the present study satisfactorily well. Moreover, the
method of Liu and Winterton (1991) was developed based on a wide range of
saturated and subcooled flow boiling data collected from 30 different literature
sources involving various types of fluids. Additionally, instead of the method of
Kandlikar (1990) that has provided also a reasonable prediction of the data obtained
in the present study, but is purely empirical, the method of Liu and Winterton (1991)
is based on the superposition of convective and nucleate boiling effects. So, following
the same approach of Liu and Winterton (1991) the effects of swirl flow on nucleate
boiling suppression and convection enhancement can be taken into account.
Based on the second suggestion of Shatto and Peterson (1996), the method
of Liu and Winterton (1991) was modified based on the data obtained in the present
study for flow boiling inside horizontal tubes containing twisted-tape inserts.
The following paragraphs describe the predictive method developed in the
present study to estimate the heat transfer coefficient during flow boiling inside tubes
containing twisted-tape inserts.
Heat transfer predictive method 167
Dryout inception and completion
As revealed in Figs. 4.24 and 4.25 and already discussed in Chapter 4, the
dryout inception for tubes with twisted-tape inserts occurs under lower vapor qualities
than for plain tubes without twisted-tapes. So, the prediction of dryout inception is
more relevant for tubes with twisted-tape inserts than for empty tubes and should be
taken into account in a predictive method for the heat transfer coefficient during flow
boiling inside tubes containing twisted-tape.
Based on the abovementioned, the method developed in the present study
considers the following three heat transfer regions: (i) Flow boiling region,
characterized by vapor qualities lower than dryout inception; (ii) Dryout region
covering vapor qualities between dryout inception and dryout completion; and (iii)
Mist flow region that occurs for vapor qualities higher than the vapor quality
corresponding to the dryout completion. The earlier dryout under swirl flow conditions
is due to centrifugal acceleration that detach the liquid droplets from the liquid film as
the vapor quality and two-phase flow velocity increase. Figure 5.1 presents a
comparison between the predictive method of Wojtan et al. (2005) for dryout
inception vapor quality given by Eq. (2.28) and the experimental dryout inception
data for plain tubes obtained in the present study. According to this figure, the
method of Wojtan et al. (2005) provides accurate prediction of the present study
experimental data. So, in the present study, a new predictive method for dryout
inception inside tubes with twisted-tape inserts was proposed based on the previous
method of Wojtan et al. (2005). In the new method, the dryout inception vapor quality
is given as follows:
(5.1)
where 1Π is a dimensionless parameter that takes into account the effects of twist-
ratio, heat flux, tube diameter and fluid properties on the dryout inception. The
parameter 1Π was correlated based on the regression analysis of the vapor quality
168 Heat transfer predictive method
data for the onset of dryout obtained in the present study. The parameter 1Π is given
by the following correlation:
(5.2)
where 2Π is defined as the ratio between the internal tube diameter and the
maximum tube diameter evaluated in the present study (15.9 mm) as follows:
)Max(i
i
2d
d=Π (5.3)
50 75 100 125 1500.5
0.6
0.7
0.8
0.9
1.0
G [kg / m2 s]
x di [
-]
Experimental , di=12.7 mm
Wojtan et al. (2005) Eq. (2.28)
Experimental , di=15.9 mm
Figure 5.1 - Comparison of the experimental vapor quality data for the dryout inception in plain tubes and the predictions according to the method of Wojtan et al. (2005), Tsat = 15 oC and φ = 10 kW / m2 .
It can be expected that the augmentation by the twisted-tape of the shear
effects on the film due to the increase of vapor velocity near the interface gas-liquid
affects equally the vapor qualities for dryout inception and completion. So, it seems
logical to propose the following correlation for the dryout completion vapor quality:
(5.4)
Flow boiling region
Heat transfer predictive method 169
Prior to the dryout inception and as above mentioned, the predictive method
proposed in the present study for the heat transfer coefficient during flow boiling
inside tubes containing twisted-tapes is based on the superposition of convective and
nucleate boiling effects. Analogous to Liu and Winterton (1991), an asymptotic
exponent of 2 is assumed and the flow boiling heat transfer coefficient is given
according to the following equation:
(5.5)
where the sub index refers to tubes with twisted-tape.
On contrary to Liu and Winterton (1991) that have correlated the single-phase
heat transfer coefficient in Eq. (5.5) according to Dittus and Boelter (1930) method, in
the present study the predictive method of Lopina and Bergles (1969), Eq. (2.130),
for single-phase flow inside tubes with twisted-tape inserts was adopted. The Lopina
and Bergles (1969) method is described in Chapter 2 and was selected because as
shown in Fig. 5.2 provided the best predictions of the single-phase heat transfer
coefficient data for swirl flow gathered in the present study. The method of Lopina
and Bergles (1969) is adopted considering the Reynolds number of the two-phase
mixture as liquid and using the internal diameter instead of hydraulic diameter as
follows:
( )i
L4.0
L
8.0
0LTT,Ld
kPrReFe023.0h α= (5.6)
where:
1.10Fe = (5.7)
Instead of the method of Cooper (1984) used by Liu and Winterton (1991) to
predict the pool boiling heat transfer coefficient in Eq. (5.5), in the present study the
method of Ribatski and Saiz-Jarbado (2003) was adopted because this method is
based on a broad database only for halocarbon refrigerants and, so, can be
considered more adequate to predict the present database for R134a. The method
proposed by Ribatski and Saiz-Jarbado (2003) is given as follows:
( )[ ]( )5.02.08.0
r
45.0
rW
m
nb MRaplogpfh−−
−= φ (5.8)
170 Heat transfer predictive method
where:
0.2r0.9 0.3m p= − (5.9)
and Wf is the surface material parameter and presents the following values for
copper, brass and stainless steel 100, 110 and 85, respectively.
1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
3000
3500
4000
Sw [-]
Nu
[-]
Wongcharee and Eiamsa-Ard (2010)
Naphon (2006)
Lopina and Bergles (1969)
Manglik and Bergles (1993b)
Experimental y=9
2000 4000 6000 8000 10000 12000 140000
1000
2000
3000
4000
5000
6000
7000
Sw [-]
Nu
[-]
Wongcharee and Eiamsa-Ard (2010)
Lopina and Bergles (1969)
Naphon (2006)
Manglik and Bergles (1993b)
Experimental y=3
Figure 5.2 - Comparison between the experimental and predicted values of the heat transfer coefficient during single-phase flows inside tube with twisted-tape insert, ID =12.7 mm.
New correlations were adjusted for convective enhancement and nucleate
boiling suppression factors based on the database obtained in the present study.
Heat transfer predictive method 171
New coefficients and exponents were obtained based on a least square regression
analyses keeping the same dimensionless numbers as proposed by Liu and
Winterton (1991). The new convective enhancement and nucleate boiling
suppression factors are given as follows:
37.0
V
L75.0
TT 1Prx1F
−+=
ρ
ρ (5.10)
( ) 116.0
0L
1.0
TTTT ReF055.01S−
+= (5.11)
Figures 5.3 and 5.4 present flow images and the schematic diagram
corresponding to the flow pattern observed in the present study. Both stratified and
stratified wavy flows were observed only under conditions of high twist-ratios and
reduced flow velocities, indicating the predominance of gravitational effects on the
two-phase distribution. Annular flow is observed for high vapor qualities and
becomes predominant under conditions of high mass velocities and reduced twist-
ratios. As mentioned in Chapter 4, the twisted-tapes promote transition from stratified
to annular flow pattern under lower mass velocities when compared to the plain tube
without twisted-tape. These effects are intensified with decreasing the tube diameter.
It is well known in the literature that the two-phase topology and heat transfer
coefficient are intrinsically related.
So, new correlations were adjusted for the parameters Se and Fe
which took
into account the stratification effects for empty tube in the method proposed by Liu
and Winterton (1991). The correlations for the parameters TTSe , and TTFe , were
obtained based on the present study database. If the tube is horizontal for
, then and in
Eq. (5.5) should be multiplied by TTSe , and TTFe , respectively.
The TTSe , and TTFe , , are given as follows:
( ) ( )( )( )Bo6.51x611.0
TT,S2ee
Π−−= (5.12)
( ) 44.0
r
6.3x15.1
TT,F pe468.0e−−= α (5.13)
172 Heat transfer predictive method
where 2Π is the dimensionless number given in Eq. (5.3) and Bo is the Boiling
number calculated according to Eq. (2.84).
The parameter α defined by Eq. (2.132), takes into account the swirl velocity effect.
Figure 5.3 - Flow images. (a) Stratified flow (y = 14, G = 75 kg / m2 s, x = 0.25, Tsat = 5 oC); (b) stratified wavy flow (y =14,G = 100 kg / m2 s, x = 0.20, Tsat = 5 oC); (c) Anular flow ( y = 3, G = 150 kg /
m2 s, x = 0.35, Tsat = 5 oC); (d) Dryout (y = 3, G = 200 kg / m2 s, x = 0.45, Tsat = 5 oC).
(a)
(b)
(c)
(d)
Heat transfer predictive method 173
Figure 5.4 - Flow pattern Schematic diagram
Mist flow region
For vapor qualities higher than the dryout completion, mist flow is assumed. In
the present study, the heat transfer coefficient in the mist flow region is obtained
using a modified version of Groeneveld (1973) correlation for mist flow heat transfer
coefficient used by Wojtan et al. (2005) for plain tubes without twisted-tapes. In the
modified version the fin effect generated by the twisted-tape inserts is taken into
account. The homogenous Reynold number considered by Wojtan et al. (2005)
method is also modified in order of taking into consideration the twisted-tape swirl
velocity effect. A modified version of Wojtan et al. (2005) method was adopted since
no data was obtained for mist flow region in the present study. This method seems
the most accurate for this flow pattern according to literature in case of empty tubes.
The heat transfer coefficient during mist flow for tubes with twisted-tape inserts is
given as follows:
Fed
kPrRe0117.0h
i
V83.1
3
06.1
V
79.0
TT,HTT,mist
−= Π (5.14)
where
( ) αρ
ρ
µ
−+= x1x
GdRe
L
V
V
i
TT,H (5.15)
(a
(b
(c)
(d
174 Heat transfer predictive method
( )0.4
3 1 0.1 1 1L
V
xρ
ρ
Π = − − −
(5.16)
Fe and α are estimated by Eq. (5.7) and Eq. (2.132) respectively.
Dryout flow region
The heat transfer coefficient in the dryout region is obtained using the same
approach used by Wojtan et al. (2005) for plain tubes without twisted-tapes. The heat
transfer coefficient is calculated from the following interpolating equation:
( ) ( ) ( )[ ]TT,deTT,mistdiTTTT,2
TT,diTT,de
TT,di
diTTTT,2TT,dryout xhxhxx
xxxhh −
−
−−= ΦΦ (5.17)
where ( )diTTTT xh ,2Φ is the two-phase flows heat transfer coefficient calculated from Eq.
(5.5) at the dryout inception vapor quality TTdix , and ( )TTdeTTmist xh ,, is the mist flow heat
transfer coefficient calculated from Eq. (5.14) at the dryout completion vapor quality
TTdex , . If the dryout completion vapor quality given by Eq. (5.4) is higher than 1, it
should be assumed that 999.0=dex as proposed by Wojtan et al. (2005).
Comparison of the proposed predictive method with experimental results
Figure 5.4 shows a comparison between the heat transfer data obtained in the
present study and the predictions given by Eq. (5.5). According to this figure, the
method seems accurate, predicting most of the data within an error band of ±30 %.
Table 5.1 presents the results of the statistical analyses of the comparison between
experimental and predicted results according to the proposed method. According to
Tab. 5.1, the new method predicted 89.1 % of the database obtained in the present
Heat transfer predictive method 175
study within an error band of ±30 %, and absolute mean deviation of 15.7 %. It
should be highlighted that the best predictive method from the literature predicted
only 70.9 % of the same database within an error band of ±30 % and absolute mean
deviation of 26.4 % as shown in Chapter 4. This scenario is reinforced by Fig. 5.5,
that illustrates the parcels of the database predicted by the new method within an
error band of ±30 % and the respective absolute mean deviation according to
different experimental parameters. According to this figure, it can be noticed that the
proposed method is well weighed predicting the experimental data for different
conditions with approximately similar error margins.
0.0 1.0 2.0 3.0 4.0 5.0 6.00.0
1.0
2.0
3.0
4.0
5.0
6.0
hexperimental [kW / m2 oC]
hes
tim
ated
[kW
/ m
2 o
C]
-30%
+30%
Figure 5.5 - Comparison between the method proposed in the present study and the experimental heat transfer results for tubes with twisted-tape inserts.
Table 5.1 - Results of the statistical analysis of the comparison between the proposed method and the heat transfer experimental results, G = 75-200 kg / m² s, Tsat = 5 and 15 °C, φ = 5 and 10 kW / m².
ζ30 [%] η [%] Authors
di = 12.7 mm di = 15.9 mm Overall di = 12.7 mm di = 15.9 mm Overall
Present study (2013) 92 87 89 16 16 16
176 Heat transfer predictive method
Figure 5.6 - Results of the statistical analyses of the comparison between experimental and predicted results according to the present method for different experimental conditions, G = 75-200 kg / m² s,
y=3-14, Tsat = 5 and 15°C, φ = 5 and 10 kW / m².
Considering the fact that a good predictive method should not only be
statistically accurate, but also be able of capturing the main trends of the
experimental results, Figs. 5.6 to 5.13 display comparisons of the evolution of the
heat transfer coefficient with vapor quality according to the experimental results and
Kg/m2 s
η, ζ
30 [%
] η, ζ
30 [%
] η, ζ
30 [%
] η, ζ
30 [%
]
Heat transfer predictive method 177
estimatives by the predictive method proposed in the present study. From this
figures, it can be noted that the proposed method captures the main trend of the
experimental data predicting the increase of the heat transfer coefficient with
increasing vapor quality, decreasing tube diameter and twist-ratios, independently of
the mass velocity. By analysing Figs. 5.6 and 5.7 for G = 75 kg / m2 s, it can be
noticed that the method also captures reasonably well the typical behaviour of
stratified flows corresponding to an almost constant heat transfer coefficient with
varying the vapor quality until the onset of dryout. According to these figures, the
effect of twist-ratio on heat transfer coefficient and the onset of dryout are also well
predicted. The same behavior are also captured for a mass velocity of 100 kg / m2 s
as shown in Figs. 5.8 and 5.9.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
[x]
h [
kW /
m2 o
C]
y=3y=3y=4y=4y=9y=9
y=14y=14
Figure 5.7 - Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines), ϕ = 10 kW / m², Tsat= 5 °C, G = 75 kg / m2 s and ID = 12.7 mm.
178 Heat transfer predictive method
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
[x]
h [
kW /
m2
oC
]y=3y=3y=4y=4y=9
y=14 y=14y=9
Figure 5.8 – Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines) , ϕ= 10 kW/m², Tsat= 15 °C, G = 75 kg / m2 s and ID = 15.9 mm.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
[x]
h [
kW /
m2
oC
]
y=3y=3y=4y=4y=9y=9
y=14y=14
Figure 5.9 – Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat= 5 °C, G = 100 kg / m2 s and ID = 12.7 mm.
Heat transfer predictive method 179
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
[x]
h [
kW /
m2
oC
]
y=3y=3y=4y=4y=9y=9
y=14y=14
Figure 5.10 – Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat= 15 °C, G = 100 kg / m2 s and ID = 15.9 mm.
Figures 5.10 to 5.13 present comparisons between predictions and
experimental data for mass velocities of 150 and 200 kg / m2 s corresponding to
annular flows. Again, the method proposed in the present study captures
satisfactorily the experimental trends corresponding to the heat transfer coefficient
augmentation with increasing vapor quality. Moreover, the method also captures the
facts that the vapor quality for the onset of dryout decreases with increasing the
mass velocity and decreasing the twist-ratio.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
[x]
h [
kW /
m2 o
C]
y=3y=3y=4y=4y=9y=9
y=14y=14
Figure 5.11– Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines), ϕ = 10 kW / m²,Tsat = 5 °C, G = 150 kg / m2 s and ID = 12.7 mm.
180 Heat transfer predictive method
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
[x]
h [
kW /
m2 o
C]
y=3y=3y=4y=4y=9y=9
y=14y=14
Figure 5.12 – Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat =15 °C, G = 150 kg / m2 s and ID = 15.9 mm.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
[x]
h [
kW /
m2 o
C]
y=4y=4y=3 y=3
y=9y=9
y=14y=14
Figure 5.13 – Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat = 5 °C, G = 200 kg / m2 s and ID = 12.7 mm.
Heat transfer predictive method 181
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
1.0
2.0
3.0
4.0
5.0
6.0
[x]
h [
kW /
m2
oC
]
y=3y=3y=4y=4y=9y=9
y=14y=14
Figure 5.14 – Evolution of the heat transfer coefficient with vapor quality according to the experimental
results (symbols) and predictions according to the proposed method (lines) , ϕ = 10 kW/m², Tsat = 15 °C, G = 200 kg / m2 s and ID = 15.9 mm.
The performance of the proposed method has also been evaluated through
comparisons with experimental results of Agrawal et al. (1986) and Akhavan-
Behabadi et al. (2009b). According to Fig. 5.14, the proposed method provides in
average reasonable predictions of the data from Agrawal et al. (1986) despite the
fact that the method is based on data for R12 while the method developed in the
present study considers only results for R134a. However, it should be highlighted
that the data of Agrawal et al. (1986) provides an unexpected behavior,
corresponding to heat transfer coefficient reduction with increasing vapor quality as
revealed in Figs. 2.17 to 2.20 and already discussed in Chapter 2
Data from Akhavan-Behabadi et al. (2009b) for R134a, the same refrigerant of
the present study, have also been considered for comparison. Figure 5.15 shows the
comparison between the estimated versus the experimental heat transfer coefficient
data. According to this figure, the method proposed in present study satisfactorily
predicted the database of Akhavan-Behabadi et al. (2009b) predicting 79 % of the
data points within an error band of ±30 % and absolute mean deviation of 23 %.
However, Akhavan-Behabadi et al. (2009b) have obtained averaged heat transfer
coefficient over the test section while in the present study local heat transfer
182 Heat transfer predictive method
coefficient results were obtained. This difference between data regression
procedures can be related to the disagreements between the experimental data of
these authors and the predictive method developed in the present study. It should be
highlighted that average heat transfer coefficients are typical of the experimental
conditions and test section characteristics as the tube length and, so, are not the best
approach to be considered for the development of design tools for heat exchangers.
0.0 1.0 2.0 3.0 4.0 5.0 6.00.0
1.0
2.0
3.0
4.0
5.0
6.0
hexperimental [kW / m2 oC]
Pro
po
sed
met
ho
d [
kW/
m2 o
C]
+30%
-30%
y=10.15
y=7.37
y=5.58
y=3.76
Agrawal et al. (1986) (ζζζζ30=67%)
Figure 5.15 - Comparism between experimental heat transfer data from Agrawal et al. (1986) and the prediction by the present study proposed model.
0.0 1.0 2.0 3.0 4.0 5.00.0
1.0
2.0
3.0
4.0
5.0
hexperimental [kW / m2 oC]
Pro
po
sed
met
ho
d [
kW/
m2 o
C]
+30%
-30%
y=9
y=12
y=15
y=6
Akhavan-Behabadi et al. (2009) (ζζζζ30=79%)
Figure 5.16 - Comparism between experimental heat transfer data from Akhavan-Behabadi et al. (2009b) and the prediction by the present study proposed model.
Conclusions and recommendations 183
6 CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
In the present study, flow boiling inside tubes (12.7 and 15.9 mm) containing
twisted-tape inserts was investigated. A broad literature review was performed. Heat
transfer and pressure drop data were collected for tubes without and with twisted-
tape inserts for four twist-ratios. Based on these experimental results, a new model
for predicting flow boiling heat transfer inside tubes containing twisted-tape has been
developed. From the present study, the following main conclusions can be draw:
• Based on the analyses of experimental results obtained in the present study, it
was observed that the frictional pressure drop increases for tubes with and
without twisted-tape inserts with increasing the mass velocity, vapor quality
and decreasing the tube diameter, saturation temperature and twist-ratio.
Pressure drop peaks were also observed at high vapor qualities
corresponding to conditions close to the flow pattern transition from annular to
mist flow. Additionally, a significant influence of flow pattern on pressure drop
was also observed. The transition from stratified flow to annular flow in tubes
with twisted-tape inserts occurs for lower vapor qualities and mass velocities
when compared with the plain tube counterparts independent of the tube
diameter;
• Experimental pressure drop data were compared against predictive methods
available in the literature. From this analyses it was concluded that Kanizawa
and Ribatski (2012) and Grönnerud (1979) methods provide the best results,
predicting 99.6 and 88.0 % of experimental data within an error band of ±30
%, for tubes with and without twisted-tape inserts, respectively;
• Based on the analyses of experimental results obtained in the present study, it
was observed that the heat transfer coefficient increases with increasing the
mass velocity and decreasing the tube diameter and saturation temperature
for tubes with and without twisted-tape inserts. Significant influence of flow
pattern on the heat transfer coefficient were also observed. The heat transfer
coefficient was almost constant for stratified flow pattern while its value
increases significantly with vapor quality under annular flow conditions.
184 Conclusions and recommendations
Moreover, a sharply decrease of the heat transfer coefficient with increasing
vapor quality was observed under high vapor qualities corresponding to the
onset of dryout. These behaviors are more pronounced by decreasing twist-
ratio and tube diameter;
• The heat transfer experimental results were compared against predictive
methods from literature. It was concluded from these comparisons that the
methods of Kandlikar (1990) and Akhavan-Behabadi et al. (2009b) provide the
best predictions of the experimental results for plain tubes and tubes with
twisted-tape inserts, respectively, predicting 64.6 and 70.9 % of the
experimental data gathered in the present study within an error band of ±30 %,
respectively;
• Pressure drop penalties of about 35 % were observed for low mass velocities
and twist-ratios. The pressure drop penalty is found to decrease sharply with
increasing vapor quality;
• Analysis of the enhancement factor was carried out in order to identify
operational conditions under which the use of twisted tape-inserts would be
advantageous. Heat transfer coefficient increments up to 45 % keeping the
same pumping power were obtained by using twisted-tape relative to tubes
without inserts. Additionally, according to the parameter defined by Eq.
(4.3), the use of twisted-tape insert is advantageous for most of the
operational conditions evaluated in the present study;
• The results from Tab. (4.4) revealed that both predictive method of Jensen
and Bensler (1986) and Agrawal et al. (1986) fail to predict the trends of the
data obtained in the present study. However, it is worth noting that the method
of Akhavan-Behabadi et al. (2009b) present satisfactory results but was
unable to capture well the data obtained for reduce twist-ratios. In this way, a
new predictive method for heat transfer coefficient inside tubes containing
twisted-tape inserts has been developed. The predictive method of Liu and
Winterton (1991) was modified in order of taking into account the effects of the
swirl flow induced by the twisted-tape on the heat transfer coefficient. The new
method includes the prediction of the dryout inception observed to be
dependent on the tubes diameter and twist-ratios. Moreover, the method is
flow pattern based and predicts the heat transfer coefficient under dryout and
mist flow conditions. The proposed method predicts satisfactorily well the data
Conclusions and recommendations 185
obtained in the present study, predicting 89.1 % of the experimental data
within an error band of ±30 % and absolute mean deviation of 15.7 %. It
should be highlighted that the dryout inception displayed by the experimental
data is also well captured by the method proposed in the present study.
6.2 Recommendations for future studies
The present study concerns a broad evaluation of the effect of twisted-tape
inserts on augmentation of heat transfer coefficient and pressure drop during flow
boiling of R134a inside horizontal tubes. However, several additional aspects were
not explored in the present study which are recommended for future studies:
• Conduct experimental test with low pressure refrigerants as R245fa. Usually,
these refrigerants present higher vapor specific volume and the two-phase
velocity increases with increasing this property. So, it is expected that this
effect combined with the twisted-tape improves the swirl effects affecting,
consequently, the nucleate boiling suppression and convective enhancement.
These data would be useful in order to extend the predictive method proposed
in the present study to broader conditions;
• Perform experimental tests for refrigerant/lubricant oil mixtures with the
objective of evaluating the effect of oil lubricant on pressure drop and heat
transfer coefficient during flow boiling inside tubes containing twisted-tape
inserts. It is expected that the twisted-tape improves the mixing effect due to
swirl flow. Thus, it can avoid the formation of a layer of liquid richer of lubricant
on the wall, favouring nucleate boiling under low vapor quality conditions and
reducing the thermal resistance across the liquid film during annular flow. For
both cases, a heat transfer coefficient enhancement is expected with the use
of twisted-tape due to the improvement of mixing. The same effect is expected
for the case of zeotropic mixtures as R407C;
• Conduct experimental test with natural refrigerants as ammonia, cabon dioxide
and hydrocarbons. These refrigerants are candidates to replace R134a in
some applications since this refrigerant although is not harmful to the ozone
layer but presents a high global warming potential (GWP). The like of natural
fluid as carbon dioxide and hydrocarbons are found to present low global
186 Conclusions and recommendations
warming potential. Additionally, the impact of ammonia on ozone layer (ODP)
and global warming potential (GWP) is null;
• Perform experimental test for mist flow data, since no data was obtained for
this flow pattern in the present study. In the actual configuration of the test
facility, the heating effect is obtained by imposing the heat flux through
electrical heaters. So, reaching post dryout conditions means damaging the
test section. Thus, a new experimental bench should be designed and
constructed using hot water as heating source and having the wall
temperature as boundary condition instead of heat flux. In this case, heat
transfer and pressure drop measurements can be made under safety
conditions. Moreover, the dryout phenomena can also be studied. This new
facility would be able also of running condensation test by using the water as
cooling medium instead of heating source;
• Perform pressure drop and heat transfer coefficient experimental tests during
condensation inside tubes containing twisted-tape inserts. Results from the
present study revealed that for higher saturation temperature, higher heat
transfer enhancement than pressure drop penalties can be obtained. It is
expected that pressure drop penalties inside tubes containing twisted-tape
inserts during condensation process will be lower compare to that in
evaporation process due to low vapor specific volume for high saturation
temperature conditions. It is also knows that pressure drop in the evaporator
are more detrimental to the system performance than in the condenser. This
corroborate the fact that the use of twisted-tape is more profitable to be use in
the condenser.
References 187
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STEPHAN, K., ABDELSALA, M. (1980). Heat transfer correlation for natural convective boiling. Int. J. Heat Mass Transfer, v. 23, p. 73-87
THOME, J.R., RIBATSKI, G. (2005). Boiling and evaporation: Augmentation of boiling and evaporation. In: Geoffrey F. Hewit. (Org.). HEDU Heat Exchanger Design Update, 1st ed. Wallingford: Begell House Inc,v. 12.
THOME, J. R., EL HAJAL, J. (2002). Two-phase flow pattern map for evaporation in horizontal tubes: latest version, 1st International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Kruger Park, South Africa: 2002 p. 182–188.
TAITEL, Y., DUKLER, A. E. (1976). A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE Journal, v. 22, p. 47–55.
TAITEL, Y., BORNEA, D. AND DUKLER, A. E. (1980). Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes, AIChE Journal, v. 26 p. 345 - 354.
TRIBBE. C., MÜLLER-STEINHAGEN. H. (2000). An evaluation of the performance of phenomenological models for predicting pressure gradient during gas-liquid flow in horizontal pipelines, Int. J. Multiphase Flow. v. 26, p. 1019-1036.
TAYLOR, B.N., KUYATT, C.E. (1994). Guidelines for evaluating and expressing the uncertainty of NIST Measurement Results. 1297. 1994 Edition.Gaithersburg, NIST Technical Note.
WEBB, R. L. (1981). Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transfer, v. 24-n. 4, p. 715-726.
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WHALLEY,P.B. (1987). Boiling condensation and gas-liquid flow. Oxford: Clarendon Press.
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WONGCHAREE, K., EIAMSA-ARD, S. (2011). Friction and heat transfer characteristics of laminar swirl flow through the round tubes inserted with alternate clockwise and counter-clockwise twisted-tapes. Int. Communications in Heat Mass Transfer, v. 38, p. 348-352.
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Appendix A 195
Appendix A – Calibration of the Experimental
measuring equipments
This section describes the methods and results related to the verification steps
and calibration of the components of the experimental apparatus.
A.1 Uncertainty analysis
Estimation of the experimental apparatus uncertainties as mentioned in
section 3.9 are given in detail as follow:
Measurement of uncertainty is given by:
( )StBU 95+±= (Appendix A.1)
The parameter B corresponds to the instrument uncertainty (or accuracy)
reference for measurement, 95t is the 95th point for the Student t -distribution with two
tails (two-tailed), which depends on the number of degrees of freedom of the
measured quantity. The term S corresponds to the precision obtained through
experimental tests, according to the following equation:
2
1
k
j
j
S
Sk
== ±
∑ (Appendix A.2)
where k is the number of the experimental points obtained from the curve and it
depends on the increment between the consecutive measurements and jS
is the
mean standard deviation for each point considered, given as follows:
( )2
1
1
N
ij ij
ij
x x
SN
=
−
=−
∑ (Appendix A.3)
N is equal to the number of curve plotted, ijx is the estimated value for each
curve i for the point j, and ijx is the average of the ijx . Each curve i obtained
196 Appendix A
experimentally corresponds to the lines that provide the estimated value of point j,
considering the actual reading, given by:
ij i j ix a x b= + (Appendix A.4)
where ia and ib are the coefficients of the line and jx is the real value of the reading
given by the calibrated instrument.
The degree of freedom of the parameter S depends on the type of magnitude
considered for pressure and temperature; the number of degrees of freedom is given
by:
( )1NKdfTS −= (Appendix A.5)
In the following subsections the calculated uncertainties for each type of
transduser is presented.
A.2 Absolute pressure transducers
The absolute pressure transducers are AKS-33 model manufactured by
Danfoss, with output 4-20 mA. The transduser is of nominal pressure measurement
from 0 to 11bar. The measurement was performed using a column manometer of
mercury, with approximately 1.4 meters high and 2.0 mm wide in conjunction with a
mercury column barometer for verification of atmospheric pressure. The maximum
height of the mercury column results in strain gauge pressure of 185 kPa, making it
impossible to cover the entire measurement range of the transducer.
During the calibration step, the transducers were connected to the data
aquisition system, by the use of precision resistors of 250 ohms. And the pipe
connected to one end of the column manometer, the calibration of the three
transdusers were perfomed simultaneously.
Table A.1 shows the coefficient and uncertainties obtained by the method
described in Section A.1:
Appendix A 197
Table A.1 - Coefficients of the equation for the pressure transducers and uncertainty
Parameters Pre-heater inlet Pre-heater outlet Test section inlet
[ ]a kPa V 326.7 326.0 326.2
[ ]b kPa -326.7 -326.5 -324.2
[ ]U kPa± 1.4 1.5 1.6
with the pressure given by the following equation:
p aV b= + (Appendix A.6)
A.3 Flowmeter
The main characteristics of the flowmeter are:
Flow meter type Coriolis FLOWMETER Model 2100 analyzer with signal MASSFLO
3000 Danfoss;
• Output current of 4 to 20 mA;
• Measure up to 52000 kg / h;
• Nominal connection of ½ inches.
The measurement was performed using water supplied by a reservoir of large
volume, balance and stopwatch. The scales used for the measurement is from the
manufacturer Toledo with 0.1 grams., and the container used for each measurement
has a maximum nominal volume of 12 liters. For the tests, a registry downstream of
the flowmeter was adjusted in order to obtain flow near the objective value. After
obtaining the steady-state condition, the output of the flowmeter was directed to the
container and the timer was activated with consequent measurement of the mass of
water.
The uncertainty analysis of the flow transductor after the tests was however
estimated using the methodology presented in section A.1. As a result, calculated
uncertainty of ± 0.276 kg / m² s was obtained considering the area for a nominal
diameter of the tube.
A.4 Calibration of thermocouples channels
Thermocouples channels calibration was performed between -4 and 52 °C
with increments of 4 °C. The calibration of the channels occurred with the use of a
198 Appendix A
thermostatic bath brand HAAKE, Model F6-C35 shown in Figure A. 01, together with
NIST (National Institute of Standards and Technology) and traceable thermometers.
The characteristics of the traceable thermometers are shown in Table A.2.
Table A.2 - Features of the thermometers used during calibration of the acquisition system channel for temperature.
Model Measuring range Resolution
3543Y -35 to 25 oC 0.1 oC
3570Y 20 to 60 oC 0.1 oC
Table A.3 - Coefficients for the reading temperature and estimated uncertainties for the thermocouples channels
Channel [ ]oa C V [ ]ob C [ ]oU C±
0 0.99 -0.20 0.10
1 0.99 -0.01 0.09
2 0.99 -0.14 0.09
13 0.99 -1.22 0.13
14 0.99 -1.25 0.12
15 0.99 -1.09 0.12
16 0.99 -1.14 0.12
17 0.99 -0.97 0.12
18 0.99 -1.10 0.12
19 0.99 -1.08 0.13
20 0.99 -1.14 0.13
21 0.99 -0.99 0.13
22 0.99 -1.07 0.12
23 0.99 -0.86 0.13
24 0.99 -0.68 0.12
25 0.99 -0.49 0.11
26 0.99 -0.73 0.12
27 0.99 -0.53 0.12
28 0.99 -0.74 0.11
Appendix A 199
Figure A.1 - Thermostatic bath used to calibrate the system thermocouple channels
To perform the calibration measurement, the temperature of the thermostatic
bath was set and after stabilization, the voltage at the terminals was recorded for
minimum of one minute, in conjunction with the direct reading of the temperature
values via thermometers.
From the data obtained experimentally, the temperature uncertainty was
estimated , according to the methodology presented in section A.1, resulting to the
values shown in Tab A.3, together with the coefficients for reading temperature
according to the following equation:
real measuredT aT b= + (Appendix A. 7)
A.5 Calibration of the active power transducers
Calibration of the active power transducers, for reading the electrical power
added to the system, was carried out while the refrigerant circuit micro pump with
frequency of 60Hz and the antifreeze solution circuit were activated.
The main characteristics of the active power transducers are given as follows:
• Transducer Yokogawa, model 2285A;
• output current of 4 to 20 Ma;
• Two transducers with full scale of 3 and 9 kW
200 Appendix A
The calibration was performed with the use of digital multimeters, linked to
output terminals of the electrical resistance (VARIACS). The power transducers were
connected to the acquisition system, using 250 ohm resistors. Characteristics of the
multimeters used during the calibration are shown in Table A.4
Table A.4 - Characteristics of the multimeters used during the calibration of power transducers
Model Voltage accuracy/range Current accuracy/range
Minipa ET-2042C ±0.8% / 200V ±2.0% / 20A
Minipa ET-3200 ±1.2% / 200V ±3.0% / 20A
Fluke 8050A ±0.5% / 200V
Due to the fact that the output current of the electrical resistance (VARIACS)
with nominal output of 9 kW surpass the maximum allowable current for the
multimeters, corresponding to 20A, the calibration of the entire measurement range
of this was not possible.
The electrical power of the instruments calibrated is given by the product of
voltage and current.
VIPower = (Appendix A.8)
Analysis was performed to estimate the uncertainty of the measured electrical
power based on the data obtained experimentally according to the methodology
presented in section A.1. The calculated uncertainties are shown in Table A.5,
together with the coefficients from the equation given as follows:
bmVPower += (Appendix A. 9)
Table A.5 - Coefficients and calculated uncertainty results of the active power transducers
Transducer Pre-heater
9 kW
Pre-heater
3 kW Test section
maq [W/V] 2180.1 914.9 971.0
baq [W] -2191.9 -915.0 -968.0
ST [±W] 5.1 6.5 0.9
t95.ST [±W] 10.1 13.0 1.7
B1/VI*100 (%) 3.0 3.0 3.0
Appendix A 201
A.6 Characteristics of differential pressure transducers
The differential pressure transducers used in the experimental setup are
manufactured by Endress-Hauser with PMD75 model.
The main characteristics of the differential pressure transducers are as listed
below:
• Transducers Endress-Hauser, PMD75 model;
• Measuring ranges up to 3, 10 and 300 kPa;
• Precision of 0.075 % of full scale, according to the manufacturer;
• Output with current, 4-20 mA;
Calibration of transducers was not carried due to the fact that, the transducers
are new, and indicated the same value of pressure loss during preliminary tests, with
the curve considered by the manufacturer.
202 Appendix B
Appendix B – Experimental Data
In this section raw experimental results obtained for the flow boiling pressure
drop and heat transfer coefficient for both tubes with and without twisted-tape inserts
during the experimental campain of this study are presented
Table B.1 – Flow boiling pressure drop experimental results for Tsat = 5oC under adiabatic conditions inside 12.7 mm internal diameter tube
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 5.0 5.2 Plain tube 74.6 0.052 0.041
0.0127 4.8 5.1 Plain tube 75.2 0.102 0.047
0.0127 5.0 5.3 Plain tube 75.3 0.151 0.050
0.0127 4.8 5.1 Plain tube 74.9 0.209 0.061
0.0127 4.8 5.1 Plain tube 75.5 0.251 0.072
0.0127 5.0 5.2 Plain tube 75.8 0.299 0.080
0.0127 4.8 5.0 Plain tube 74.7 0.360 0.113
0.0127 4.9 5.1 Plain tube 74.9 0.406 0.131
0.0127 5.0 5.2 Plain tube 75.3 0.458 0.154
0.0127 5.0 5.1 Plain tube 75.0 0.506 0.175
0.0127 4.8 4.9 Plain tube 75.3 0.556 0.202
0.0127 5.1 5.2 Plain tube 75.0 0.612 0.214
0.0127 4.9 5.0 Plain tube 74.7 0.661 0.235
0.0127 5.0 5.0 Plain tube 74.7 0.706 0.250
0.0127 5.1 5.1 Plain tube 75.3 0.761 0.271
0.0127 5.2 5.2 Plain tube 76.1 0.800 0.276
0.0127 5.1 5.1 Plain tube 75.9 0.864 0.299
0.0127 5.2 5.2 Plain tube 75.6 0.910 0.233
0.0127 5.0 5.2 Plain tube 100.1 0.051 0.052
0.0127 4.8 5.1 Plain tube 100.2 0.103 0.072
0.0127 5.1 5.2 Plain tube 100.3 0.155 0.075
0.0127 4.8 5.0 Plain tube 100.7 0.201 0.106
0.0127 5.0 5.2 Plain tube 99.5 0.254 0.128
0.0127 4.9 5.0 Plain tube 99.9 0.306 0.167
0.0127 4.9 5.0 Plain tube 100.3 0.356 0.210
0.0127 4.9 5.0 Plain tube 99.5 0.413 0.245
0.0127 5.0 5.0 Plain tube 99.2 0.459 0.275
0.0127 5.0 5.0 Plain tube 99.3 0.513 0.317
0.0127 5.1 5.1 Plain tube 99.9 0.558 0.346
0.0127 5.1 5.1 Plain tube 99.7 0.616 0.391
0.0127 5.1 5.1 Plain tube 100.5 0.653 0.427
0.0127 5.2 5.2 Plain tube 101.1 0.712 0.477
Appendix B 203
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 5.0 5.2 Plain tube 149.8 0.053 0.105
0.0127 5.1 5.3 Plain tube 150.1 0.104 0.130
0.0127 5.1 5.2 Plain tube 150.7 0.151 0.161
0.0127 4.9 5.0 Plain tube 150.0 0.209 0.262
0.0127 5.0 5.1 Plain tube 150.5 0.253 0.297
0.0127 4.9 4.9 Plain tube 149.4 0.309 0.404
0.0127 5.1 5.0 Plain tube 149.5 0.356 0.445
0.0127 5.1 5.0 Plain tube 149.6 0.410 0.549
0.0127 5.3 5.1 Plain tube 150.2 0.460 0.658
0.0127 5.0 4.8 Plain tube 149.6 0.513 0.767
0.0127 5.2 5.0 Plain tube 151.2 0.555 0.864
0.0127 5.1 4.9 Plain tube 150.7 0.609 1.010
0.0127 5.3 5.0 Plain tube 149.5 0.667 1.122
0.0127 5.3 4.9 Plain tube 148.9 0.725 1.275
0.0127 5.2 4.8 Plain tube 151.1 0.758 1.345
0.0127 5.4 5.0 Plain tube 148.5 0.825 1.401
0.0127 4.9 5.1 Plain tube 200.6 0.052 0.158
0.0127 5.1 5.2 Plain tube 200.1 0.103 0.210
0.0127 4.8 4.9 Plain tube 200.0 0.151 0.325
0.0127 4.9 4.9 Plain tube 200.6 0.202 0.439
0.0127 5.1 5.0 Plain tube 199.7 0.253 0.552
0.0127 5.1 4.9 Plain tube 199.3 0.309 0.715
0.0127 5.1 4.8 Plain tube 200.1 0.353 0.908
0.0127 5.2 4.8 Plain tube 200.3 0.409 1.109
0.0127 5.3 4.9 Plain tube 201.2 0.450 1.300
0.0127 5.4 4.8 Plain tube 200.0 0.511 1.529
0.0127 5.5 4.9 Plain tube 198.8 0.567 1.822
0.0127 5.3 4.5 Plain tube 202.1 0.604 2.047
0.0127 5.4 4.6 Plain tube 203.9 0.637 2.109
0.0127 5.7 4.8 Plain tube 197.6 0.727 2.386
0.0127 5.0 5.2 14 75.3 0.053 0.178
0.0127 5.0 5.1 14 75.0 0.102 0.193
0.0127 5.0 5.1 14 75.4 0.151 0.217
0.0127 5.0 5.1 14 75.4 0.205 0.239
0.0127 5.0 5.1 14 75.3 0.252 0.255
0.0127 5.1 5.2 14 74.9 0.308 0.281
0.0127 5.1 5.2 14 75.7 0.350 0.321
0.0127 5.1 5.1 14 75.2 0.404 0.367
0.0127 5.2 5.2 14 75.3 0.453 0.409
0.0127 5.1 5.1 14 74.6 0.511 0.468
0.0127 5.0 4.9 14 75.1 0.567 0.505
0.0127 5.2 5.2 14 75.2 0.610 0.537
0.0127 5.2 5.1 14 74.5 0.660 0.565
204 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 5.0 4.9 14 75.8 0.706 0.659
0.0127 5.1 4.9 14 74.5 0.774 0.640
0.0127 5.0 5.1 14 100.5 0.053 0.237
0.0127 5.1 5.2 14 100.1 0.102 0.276
0.0127 5.0 5.1 14 100.9 0.151 0.323
0.0127 4.9 5.0 14 99.3 0.208 0.407
0.0127 5.1 5.1 14 100.7 0.254 0.443
0.0127 5.1 5.1 14 100.8 0.303 0.498
0.0127 5.0 4.9 14 100.3 0.356 0.605
0.0127 5.1 5.1 14 100.3 0.406 0.677
0.0127 5.2 5.1 14 100.5 0.453 0.759
0.0127 4.9 4.7 14 99.6 0.520 0.893
0.0127 5.2 5.0 14 100.5 0.554 0.970
0.0127 5.0 4.8 14 101.0 0.606 1.054
0.0127 5.1 4.9 14 99.4 0.662 1.058
0.0127 5.0 5.1 14 150.4 0.052 0.329
0.0127 5.2 5.2 14 150.3 0.104 0.463
0.0127 5.2 5.1 14 150.9 0.153 0.609
0.0127 5.0 4.8 14 150.4 0.207 0.852
0.0127 5.1 4.9 14 150.0 0.255 0.993
0.0127 5.1 4.8 14 151.6 0.298 1.191
0.0127 5.3 5.0 14 152.6 0.343 1.357
0.0127 5.1 5.2 14 200.4 0.054 0.492
0.0127 5.0 5.0 14 199.9 0.104 0.807
0.0127 5.1 4.9 14 200.6 0.155 1.149
0.0127 5.2 4.8 14 199.4 0.211 1.558
0.0127 5.2 4.7 14 200.5 0.254 1.948
0.0127 5.3 4.6 14 200.4 0.306 2.452
0.0127 5.6 4.7 14 199.5 0.357 2.972
0.0127 5.6 4.5 14 200.0 0.410 3.529
0.0127 5.8 4.5 14 200.5 0.456 4.025
0.0127 5.6 4.1 14 199.7 0.523 4.680
0.0127 6.0 4.3 14 196.6 0.576 5.010
0.0127 5.8 3.9 14 197.5 0.629 5.265
0.0127 6.0 4.1 14 194.6 0.680 5.094
0.0127 5.1 5.2 9 75.1 0.054 0.189
0.0127 4.8 4.9 9 75.1 0.105 0.224
0.0127 5.1 5.2 9 75.3 0.152 0.267
0.0127 5.1 5.2 9 74.3 0.205 0.262
0.0127 5.2 5.2 9 75.1 0.256 0.278
0.0127 4.8 4.8 9 75.0 0.307 0.289
0.0127 4.9 4.9 9 75.1 0.360 0.330
0.0127 5.3 5.3 9 75.1 0.402 0.387
Appendix B 205
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 5.3 5.3 9 75.0 0.464 0.434
0.0127 5.1 5.0 9 75.1 0.509 0.476
0.0127 5.0 4.9 9 74.9 0.555 0.531
0.0127 5.1 5.0 9 75.0 0.610 0.562
0.0127 5.1 5.0 9 75.1 0.659 0.615
0.0127 5.2 5.0 9 75.7 0.707 0.614
0.0127 4.9 5.0 9 100.6 0.054 0.257
0.0127 4.9 5.0 9 100.7 0.102 0.299
0.0127 4.9 5.0 9 101.1 0.151 0.349
0.0127 5.1 5.2 9 100.4 0.206 0.418
0.0127 4.9 4.9 9 100.2 0.254 0.464
0.0127 5.1 5.1 9 100.5 0.302 0.518
0.0127 5.0 4.9 9 100.8 0.358 0.598
0.0127 5.1 4.9 9 101.2 0.407 0.711
0.0127 5.2 5.0 9 99.8 0.456 0.826
0.0127 4.9 4.7 9 100.2 0.506 0.924
0.0127 5.1 4.8 9 99.3 0.567 0.988
0.0127 5.2 4.9 9 99.0 0.618 1.079
0.0127 5.0 5.0 9 149.6 0.053 0.431
0.0127 5.1 5.1 9 148.7 0.107 0.554
0.0127 5.0 4.9 9 150.7 0.154 0.681
0.0127 5.1 5.0 9 149.6 0.205 0.867
0.0127 5.2 4.9 9 150.9 0.254 1.095
0.0127 5.0 4.7 9 150.0 0.357 1.294
0.0127 5.2 4.7 9 149.7 0.431 1.405
0.0127 5.0 4.6 9 152.5 0.495 1.468
0.0127 5.2 5.2 9 200.1 0.052 0.564
0.0127 5.2 5.2 9 200.3 0.101 0.842
0.0127 5.0 4.7 9 200.5 0.155 1.288
0.0127 5.3 4.8 9 200.1 0.208 1.664
0.0127 5.5 4.9 9 200.4 0.256 2.099
0.0127 5.5 4.7 9 200.3 0.312 2.727
0.0127 5.4 4.5 9 200.1 0.355 3.162
0.0127 5.6 4.4 9 200.3 0.409 3.802
0.0127 5.6 4.2 9 199.8 0.461 4.387
0.0127 5.6 4.1 9 200.5 0.517 4.569
0.0127 6.0 4.4 9 201.8 0.551 4.850
0.0127 6.3 4.4 9 196.5 0.637 5.053
0.0127 5.0 5.0 4 75.2 0.052 0.406
0.0127 5.0 5.0 4 75.4 0.106 0.425
0.0127 5.2 5.2 4 75.5 0.149 0.448
0.0127 5.2 5.2 4 74.4 0.210 0.468
0.0127 4.9 4.9 4 74.9 0.258 0.483
206 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 4.8 4.8 4 76.1 0.300 0.489
0.0127 5.2 5.1 4 75.2 0.359 0.548
0.0127 5.2 5.1 4 74.9 0.412 0.594
0.0127 5.1 4.9 4 75.1 0.456 0.663
0.0127 5.2 5.1 4 74.0 0.512 0.694
0.0127 4.9 4.7 4 74.7 0.555 0.770
0.0127 4.9 4.8 4 74.6 0.614 0.831
0.0127 5.3 5.2 4 75.6 0.659 0.863
0.0127 5.3 5.1 4 75.8 0.726 0.996
0.0127 5.1 5.1 4 100.3 0.053 0.499
0.0127 4.9 4.9 4 100.4 0.105 0.542
0.0127 5.0 4.9 4 100.4 0.153 0.619
0.0127 5.2 5.2 4 100.4 0.202 0.656
0.0127 5.2 5.1 4 100.2 0.253 0.745
0.0127 5.2 5.1 4 99.8 0.311 0.891
0.0127 5.1 4.9 4 100.5 0.354 0.980
0.0127 5.1 4.8 4 100.4 0.403 1.082
0.0127 5.2 4.9 4 100.4 0.451 1.193
0.0127 5.1 4.8 4 100.5 0.508 1.354
0.0127 5.1 4.7 4 99.7 0.558 1.458
0.0127 5.1 5.1 4 150.4 0.052 0.705
0.0127 5.1 5.0 4 150.0 0.101 0.831
0.0127 5.3 5.1 4 150.2 0.153 1.078
0.0127 5.1 4.8 4 150.4 0.203 1.271
0.0127 5.3 4.9 4 150.3 0.255 1.632
0.0127 5.3 4.7 4 150.6 0.305 1.932
0.0127 5.2 4.7 4 150.6 0.354 2.174
0.0127 5.3 4.6 4 150.2 0.413 2.546
0.0127 5.5 4.6 4 149.9 0.466 2.960
0.0127 5.3 5.2 4 199.7 0.076 0.847
0.0127 5.1 4.9 4 201.0 0.102 1.312
0.0127 5.1 4.7 4 200.7 0.153 1.821
0.0127 5.4 4.8 4 200.8 0.208 2.416
0.0127 5.6 4.7 4 200.6 0.254 2.924
0.0127 5.5 4.3 4 200.0 0.315 3.876
0.0127 5.7 4.3 4 200.0 0.362 4.384
0.0127 5.8 4.3 4 199.9 0.408 4.872
0.0127 5.9 4.1 4 199.9 0.461 5.704
0.0127 6.2 4.2 4 200.4 0.510 6.178
0.0127 5.1 5.2 3 75.1 0.053 0.362
0.0127 5.0 5.0 3 75.7 0.104 0.476
0.0127 5.1 5.1 3 75.7 0.154 0.547
0.0127 4.9 4.9 3 75.2 0.210 0.612
Appendix B 207
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 5.2 5.2 3 74.5 0.256 0.636
0.0127 5.0 5.0 3 75.0 0.305 0.655
0.0127 4.9 4.9 3 75.0 0.355 0.679
0.0127 5.0 4.9 3 75.1 0.401 0.737
0.0127 5.0 4.8 3 75.1 0.458 0.807
0.0127 5.0 4.9 3 75.5 0.519 0.849
0.0127 5.0 4.8 3 75.7 0.552 0.932
0.0127 5.1 4.9 3 75.2 0.614 0.981
0.0127 5.1 4.8 3 75.1 0.680 1.008
0.0127 4.9 4.9 3 100.1 0.053 0.519
0.0127 5.1 5.1 3 99.8 0.104 0.628
0.0127 5.0 4.9 3 100.0 0.154 0.732
0.0127 5.1 5.0 3 100.0 0.204 0.774
0.0127 5.2 5.1 3 100.2 0.258 0.914
0.0127 5.2 5.0 3 100.3 0.308 1.043
0.0127 5.2 5.0 3 100.8 0.354 1.200
0.0127 5.0 4.8 3 100.4 0.401 1.224
0.0127 5.1 4.8 3 100.8 0.468 1.393
0.0127 5.3 4.9 3 100.6 0.504 1.435
0.0127 5.1 5.0 3 150.4 0.054 0.844
0.0127 5.1 4.9 3 149.2 0.103 0.986
0.0127 5.1 4.8 3 150.1 0.154 1.382
0.0127 5.1 4.8 3 150.6 0.203 1.660
0.0127 5.0 4.6 3 150.9 0.255 1.861
0.0127 5.4 4.8 3 150.7 0.310 2.216
0.0127 5.4 4.7 3 149.0 0.355 2.460
0.0127 5.0 4.8 3 200.7 0.052 1.133
0.0127 5.3 4.9 3 199.8 0.104 1.609
0.0127 5.2 4.7 3 200.5 0.153 2.133
0.0127 5.5 4.7 3 200.1 0.208 2.736
0.0127 5.4 4.4 3 200.5 0.255 3.470
0.0127 5.6 4.3 3 200.1 0.313 4.400
0.0127 5.9 4.4 3 200.1 0.360 4.906
0.0127 6.0 4.2 3 200.3 0.408 5.511
0.0127 6.0 4.1 3 200.3 0.459 6.010
0.0127 6.1 3.7 3 196.7 0.525 6.704
Table B.2 - Flow boiling pressure drop experimental results for Tsat = 15oC under adiabatic conditions inside 12.7 mm internal diameter tube
D [m]
TTS,in
[oC] TTS,out
[oC] y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 15.1 15.2 Plain tube 74.7 0.053 0.039
0.0127 14.8 15.0 Plain tube 75.5 0.105 0.044
0.0127 15.1 15.2 Plain tube 75.9 0.153 0.044
208 Appendix B
0.0127 14.8 14.9 Plain tube 75.3 0.204 0.051
0.0127 14.9 15.0 Plain tube 76.2 0.249 0.056
0.0127 15.1 15.2 Plain tube 75.6 0.304 0.061
0.0127 14.9 15.0 Plain tube 74.7 0.355 0.081
0.0127 15.1 15.2 Plain tube 75.0 0.398 0.083
0.0127 15.0 15.1 Plain tube 75.1 0.456 0.104
0.0127 15.0 15.1 Plain tube 74.6 0.511 0.129
0.0127 15.1 15.2 Plain tube 75.1 0.549 0.139
0.0127 15.1 15.2 Plain tube 74.9 0.613 0.153
0.0127 15.2 15.3 Plain tube 75.1 0.651 0.168
0.0127 15.0 15.0 Plain tube 74.9 0.716 0.187
0.0127 15.0 15.0 Plain tube 75.3 0.757 0.196
0.0127 15.0 15.0 Plain tube 74.5 0.832 0.186
0.0127 15.0 15.1 Plain tube 76.2 0.840 0.210
0.0127 15.3 15.1 Plain tube 75.4 0.905 0.168
0.0127 14.9 15.1 Plain tube 100.3 0.050 0.049
0.0127 15.1 15.2 Plain tube 100.9 0.102 0.052
0.0127 15.0 15.1 Plain tube 100.8 0.150 0.060
0.0127 14.9 15.1 Plain tube 100.5 0.206 0.074
0.0127 14.9 15.1 Plain tube 100.9 0.255 0.094
0.0127 14.9 15.0 Plain tube 99.9 0.308 0.120
0.0127 15.1 15.2 Plain tube 99.9 0.353 0.132
0.0127 15.2 15.2 Plain tube 100.0 0.407 0.165
0.0127 15.1 15.2 Plain tube 100.4 0.454 0.190
0.0127 15.0 15.0 Plain tube 100.3 0.507 0.228
0.0127 15.0 15.1 Plain tube 100.3 0.551 0.248
0.0127 15.1 15.1 Plain tube 100.0 0.604 0.267
0.0127 15.2 15.2 Plain tube 100.0 0.659 0.292
0.0127 14.9 14.9 Plain tube 99.5 0.712 0.320
0.0127 15.0 15.0 Plain tube 100.1 0.764 0.345
0.0127 15.1 15.1 Plain tube 99.9 0.820 0.364
0.0127 15.0 15.0 Plain tube 101.5 0.840 0.392
0.0127 15.0 15.0 Plain tube 103.1 0.865 0.363
0.0127 15.1 15.3 Plain tube 150.6 0.053 0.072
0.0127 15.1 15.3 Plain tube 150.6 0.102 0.105
0.0127 15.1 15.2 Plain tube 149.5 0.152 0.130
0.0127 14.9 15.0 Plain tube 149.5 0.201 0.171
0.0127 15.1 15.2 Plain tube 150.2 0.251 0.209
0.0127 14.9 15.0 Plain tube 149.8 0.304 0.284
0.0127 15.0 15.1 Plain tube 149.8 0.353 0.309
0.0127 15.0 15.0 Plain tube 150.3 0.404 0.372
0.0127 15.1 15.1 Plain tube 150.8 0.454 0.420
0.0127 15.2 15.2 Plain tube 151.2 0.507 0.485
0.0127 15.2 15.2 Plain tube 150.5 0.555 0.553
0.0127 15.1 15.0 Plain tube 150.8 0.607 0.653
Appendix B 209
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 15.2 15.1 Plain tube 151.1 0.646 0.682
0.0127 15.2 15.1 Plain tube 149.6 0.705 0.771
0.0127 15.2 15.1 Plain tube 149.3 0.768 0.832
0.0127 15.1 15.2 Plain tube 200.5 0.051 0.104
0.0127 15.0 15.1 Plain tube 200.3 0.101 0.163
0.0127 15.1 15.2 Plain tube 200.7 0.151 0.220
0.0127 14.9 14.9 Plain tube 200.4 0.202 0.325
0.0127 15.1 15.1 Plain tube 200.4 0.251 0.373
0.0127 15.0 15.0 Plain tube 199.7 0.306 0.486
0.0127 15.0 14.9 Plain tube 199.7 0.354 0.563
0.0127 15.1 15.0 Plain tube 199.8 0.408 0.693
0.0127 15.2 15.1 Plain tube 200.2 0.451 0.783
0.0127 15.1 14.9 Plain tube 200.0 0.502 0.953
0.0127 15.2 15.0 Plain tube 199.3 0.553 1.108
0.0127 15.2 14.9 Plain tube 200.0 0.608 1.320
0.0127 15.1 14.7 Plain tube 200.5 0.653 1.477
0.0127 15.4 15.0 Plain tube 199.9 0.704 1.554
0.0127 15.2 14.8 Plain tube 201.4 0.754 1.784
0.0127 15.2 14.8 Plain tube 202.0 0.796 1.826
0.0127 14.9 15.0 14 74.9 0.051 0.155
0.0127 14.8 14.9 14 75.3 0.106 0.174
0.0127 14.9 15.0 14 75.2 0.152 0.186
0.0127 15.2 15.3 14 74.9 0.207 0.188
0.0127 14.9 15.0 14 75.1 0.251 0.204
0.0127 15.0 15.1 14 75.6 0.304 0.227
0.0127 15.1 15.2 14 74.3 0.358 0.238
0.0127 15.1 15.1 14 74.9 0.405 0.268
0.0127 15.0 15.0 14 75.0 0.455 0.302
0.0127 15.1 15.1 14 75.1 0.500 0.323
0.0127 15.0 15.0 14 75.2 0.557 0.358
0.0127 15.1 15.1 14 75.0 0.611 0.400
0.0127 15.0 15.0 14 75.3 0.654 0.423
0.0127 15.1 15.1 14 75.6 0.708 0.445
0.0127 15.0 15.0 14 75.7 0.750 0.450
0.0127 15.2 15.2 14 75.5 0.795 0.491
0.0127 15.1 15.1 14 75.2 0.891 0.430
0.0127 15.0 15.1 14 100.8 0.051 0.192
0.0127 15.0 15.1 14 100.6 0.102 0.215
0.0127 15.0 15.1 14 100.9 0.149 0.255
0.0127 14.8 14.9 14 100.9 0.205 0.290
0.0127 15.0 15.1 14 100.9 0.244 0.320
0.0127 14.8 14.8 14 100.9 0.301 0.333
0.0127 15.1 15.1 14 100.7 0.351 0.467
210 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 15.0 15.0 14 100.1 0.406 0.491
0.0127 15.1 15.1 14 101.1 0.446 0.534
0.0127 15.0 14.9 14 100.3 0.508 0.599
0.0127 15.1 15.0 14 100.7 0.551 0.628
0.0127 14.9 14.8 14 100.7 0.612 0.765
0.0127 15.0 15.0 14 150.5 0.050 0.277
0.0127 15.1 15.1 14 150.5 0.102 0.338
0.0127 15.2 15.2 14 150.4 0.151 0.436
0.0127 15.1 15.1 14 150.5 0.201 0.551
0.0127 15.1 15.0 14 150.9 0.251 0.724
0.0127 15.0 14.9 14 150.1 0.302 0.778
0.0127 14.9 14.8 14 148.3 0.373 1.032
0.0127 14.9 14.9 14 199.6 0.052 0.402
0.0127 15.0 15.0 14 199.9 0.101 0.568
0.0127 14.8 14.8 14 200.3 0.153 0.849
0.0127 14.9 14.7 14 199.7 0.203 1.105
0.0127 15.3 15.0 14 199.9 0.253 1.327
0.0127 15.0 14.6 14 200.2 0.306 1.655
0.0127 15.2 14.8 14 199.8 0.355 1.952
0.0127 15.3 14.7 14 199.3 0.405 2.328
0.0127 15.4 14.8 14 199.5 0.456 2.742
0.0127 15.5 14.7 14 199.1 0.504 3.200
0.0127 15.6 14.6 14 199.4 0.569 3.796
0.0127 14.9 15.1 9 74.9 0.051 0.181
0.0127 14.9 15.0 9 75.0 0.104 0.195
0.0127 15.1 15.2 9 74.9 0.150 0.204
0.0127 15.1 15.2 9 75.1 0.200 0.207
0.0127 15.0 15.0 9 75.2 0.252 0.230
0.0127 15.2 15.3 9 75.2 0.310 0.239
0.0127 15.1 15.1 9 75.1 0.348 0.263
0.0127 15.1 15.1 9 75.1 0.401 0.283
0.0127 15.3 15.3 9 75.0 0.450 0.295
0.0127 15.0 15.0 9 74.6 0.514 0.344
0.0127 15.1 15.1 9 75.2 0.557 0.378
0.0127 15.2 15.1 9 75.2 0.605 0.402
0.0127 14.9 14.9 9 75.5 0.648 0.423
0.0127 15.2 15.1 9 75.1 0.712 0.437
0.0127 15.1 15.1 9 76.2 0.746 0.481
0.0127 15.2 15.1 9 75.5 0.802 0.532
0.0127 15.1 15.0 9 74.8 0.865 0.496
0.0127 14.9 14.8 9 75.4 0.891 0.472
0.0127 15.2 15.3 9 100.6 0.052 0.218
0.0127 14.9 14.9 9 100.9 0.101 0.256
Appendix B 211
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 15.1 15.1 9 101.0 0.150 0.276
0.0127 15.2 15.3 9 100.6 0.202 0.305
0.0127 15.0 15.0 9 100.7 0.245 0.366
0.0127 15.2 15.2 9 100.8 0.308 0.382
0.0127 15.0 15.0 9 100.6 0.351 0.420
0.0127 14.9 14.9 9 100.4 0.401 0.513
0.0127 15.0 14.9 9 101.0 0.452 0.569
0.0127 15.1 15.0 9 100.3 0.504 0.631
0.0127 15.3 15.1 9 100.8 0.550 0.663
0.0127 14.9 14.8 9 101.4 0.610 0.706
0.0127 15.0 15.1 9 150.5 0.051 0.302
0.0127 14.8 14.9 9 149.9 0.106 0.425
0.0127 15.0 15.0 9 149.7 0.153 0.526
0.0127 14.9 14.8 9 150.7 0.206 0.653
0.0127 15.2 15.1 9 151.1 0.249 0.748
0.0127 15.0 14.8 9 151.5 0.309 0.897
0.0127 15.1 14.9 9 150.7 0.354 0.939
0.0127 15.0 14.8 9 152.1 0.404 1.019
0.0127 15.0 15.0 9 200.5 0.052 0.495
0.0127 15.2 15.2 9 200.8 0.101 0.632
0.0127 14.9 14.8 9 200.1 0.152 0.887
0.0127 15.2 15.0 9 200.1 0.205 1.121
0.0127 15.2 14.9 9 200.3 0.253 1.450
0.0127 15.2 14.8 9 200.0 0.302 1.763
0.0127 15.2 14.7 9 200.3 0.353 2.140
0.0127 15.4 14.8 9 200.3 0.407 2.555
0.0127 15.5 14.8 9 200.9 0.454 2.928
0.0127 15.5 14.7 9 200.1 0.512 3.356
0.0127 15.6 14.6 9 200.0 0.561 3.698
0.0127 15.6 14.5 9 200.8 0.605 3.904
0.0127 15.5 14.4 9 200.6 0.663 4.092
0.0127 15.0 15.1 4 75.0 0.053 0.408
0.0127 15.1 15.2 4 75.6 0.107 0.429
0.0127 14.9 15.0 4 75.4 0.158 0.444
0.0127 15.0 15.0 4 74.7 0.205 0.457
0.0127 15.2 15.2 4 75.2 0.255 0.440
0.0127 14.9 14.9 4 74.8 0.309 0.457
0.0127 14.9 14.9 4 73.9 0.363 0.454
0.0127 14.9 14.9 4 75.3 0.405 0.467
0.0127 15.1 15.1 4 75.2 0.452 0.517
0.0127 15.0 15.0 4 74.7 0.519 0.534
0.0127 14.9 14.9 4 74.8 0.557 0.576
0.0127 15.2 15.2 4 100.2 0.052 0.466
212 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 15.0 15.0 4 100.5 0.109 0.504
0.0127 15.0 15.0 4 100.3 0.149 0.529
0.0127 15.0 15.0 4 100.2 0.204 0.563
0.0127 15.1 15.1 4 101.6 0.248 0.568
0.0127 15.2 15.2 4 100.0 0.309 0.615
0.0127 15.0 15.0 4 100.2 0.357 0.712
0.0127 14.9 14.9 4 100.9 0.400 0.794
0.0127 15.1 15.0 4 100.2 0.454 0.897
0.0127 15.2 15.0 4 99.2 0.512 0.927
0.0127 15.0 14.9 4 99.6 0.564 0.897
0.0127 15.0 15.0 4 149.5 0.052 0.564
0.0127 14.9 14.9 4 150.2 0.100 0.648
0.0127 15.3 15.2 4 150.3 0.153 0.861
0.0127 15.2 15.1 4 149.5 0.205 1.000
0.0127 15.2 15.0 4 150.6 0.250 1.156
0.0127 15.0 14.8 4 150.7 0.304 1.439
0.0127 15.2 14.8 4 151.5 0.353 1.912
0.0127 15.3 14.9 4 148.9 0.409 1.983
0.0127 15.3 15.3 4 201.0 0.051 0.645
0.0127 15.1 15.0 4 201.0 0.100 0.906
0.0127 15.1 14.9 4 200.0 0.153 1.364
0.0127 15.2 14.9 4 200.6 0.201 1.659
0.0127 15.3 14.8 4 200.5 0.253 2.212
0.0127 15.4 14.9 4 199.4 0.306 2.428
0.0127 15.3 14.8 4 198.5 0.350 2.731
0.0127 15.0 15.0 3 75.0 0.051 0.401
0.0127 14.8 14.9 3 74.9 0.107 0.452
0.0127 14.9 15.0 3 75.2 0.151 0.466
0.0127 15.1 15.1 3 75.3 0.201 0.492
0.0127 14.9 14.9 3 75.2 0.265 0.478
0.0127 14.8 14.8 3 75.2 0.306 0.511
0.0127 15.2 15.2 3 76.0 0.352 0.553
0.0127 14.9 14.9 3 74.9 0.402 0.588
0.0127 15.0 15.0 3 75.0 0.451 0.597
0.0127 15.3 15.2 3 75.3 0.501 0.613
0.0127 15.1 15.1 3 75.7 0.556 0.631
0.0127 15.0 15.0 3 75.7 0.602 0.646
0.0127 15.2 15.2 3 75.8 0.658 0.677
0.0127 14.9 14.9 3 100.3 0.052 0.457
0.0127 15.0 15.0 3 100.4 0.104 0.573
0.0127 15.1 15.1 3 99.9 0.151 0.644
0.0127 15.0 15.0 3 100.9 0.198 0.705
0.0127 14.8 14.8 3 100.1 0.254 0.772
Appendix B 213
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0127 15.0 14.9 3 99.6 0.336 0.918
0.0127 15.2 15.2 3 150.1 0.051 0.628
0.0127 15.2 15.1 3 150.1 0.104 0.853
0.0127 15.2 15.1 3 150.2 0.152 1.044
0.0127 15.3 15.1 3 150.4 0.203 1.259
0.0127 15.2 14.9 3 150.4 0.251 1.517
0.0127 15.1 14.8 3 149.0 0.316 1.714
0.0127 15.5 15.1 3 150.0 0.356 1.886
0.0127 15.1 15.0 3 199.8 0.051 0.948
0.0127 15.0 14.8 3 199.8 0.102 1.342
0.0127 15.1 14.9 3 200.4 0.152 1.618
0.0127 15.3 14.9 3 200.5 0.203 2.090
0.0127 15.4 14.9 3 200.2 0.253 2.605
0.0127 15.5 14.8 3 199.7 0.313 3.084
0.0127 15.2 14.4 3 201.7 0.338 3.452
0.0127 15.5 14.5 3 193.3 0.433 3.752
Table B.3 - Flow boiling pressure drop experimental results for Tsat = 5oC under adiabatic conditions inside 15.9 mm internal diameter tube
D
[m]
TTS,in
[oC]
TTS,out
[oC]
y
[-]
G
[kg/m2 s]
x
[-]
∆p
[kPa/m]
0.0159 5.2 4.7 Plain tube 75.1 0.053 0.043
0.0159 5.5 5.0 Plain tube 75.2 0.108 0.046
0.0159 5.3 4.8 Plain tube 76.4 0.150 0.047
0.0159 5.2 4.6 Plain tube 74.6 0.208 0.049
0.0159 5.1 4.6 Plain tube 75.1 0.253 0.056
0.0159 5.2 4.6 Plain tube 75.3 0.304 0.066
0.0159 5.2 4.7 Plain tube 75.0 0.352 0.079
0.0159 5.4 5.0 Plain tube 74.9 0.409 0.094
0.0159 5.3 4.9 Plain tube 75.2 0.457 0.116
0.0159 5.3 4.9 Plain tube 75.0 0.506 0.130
0.0159 5.4 5.0 Plain tube 75.0 0.553 0.149
0.0159 5.1 4.7 Plain tube 74.5 0.612 0.170
0.0159 5.2 4.7 Plain tube 74.8 0.654 0.186
0.0159 5.2 4.7 Plain tube 74.8 0.707 0.203
0.0159 5.4 4.8 Plain tube 74.8 0.756 0.216
0.0159 5.3 4.8 Plain tube 74.8 0.808 0.233
0.0159 5.5 4.9 Plain tube 74.8 0.859 0.244
0.0159 5.5 5.0 Plain tube 74.8 0.908 0.248
0.0159 5.4 4.9 Plain tube 74.9 0.960 0.238
0.0159 5.2 4.7 Plain tube 99.8 0.053 0.051
0.0159 5.3 4.8 Plain tube 100.5 0.104 0.052
0.0159 5.1 4.6 Plain tube 100.0 0.153 0.062
214 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.3 4.8 Plain tube 99.8 0.208 0.079
0.0159 5.1 4.6 Plain tube 100.3 0.254 0.098
0.0159 5.3 4.8 Plain tube 100.3 0.304 0.118
0.0159 5.2 4.8 Plain tube 100.0 0.353 0.148
0.0159 5.3 4.8 Plain tube 99.8 0.405 0.173
0.0159 5.3 4.8 Plain tube 100.4 0.455 0.202
0.0159 5.1 4.7 Plain tube 100.3 0.504 0.232
0.0159 5.5 5.0 Plain tube 100.5 0.553 0.259
0.0159 5.4 4.8 Plain tube 100.4 0.606 0.296
0.0159 5.5 5.0 Plain tube 100.1 0.653 0.320
0.0159 5.5 4.9 Plain tube 100.2 0.708 0.358
0.0159 5.3 4.7 Plain tube 99.7 0.755 0.393
0.0159 5.5 4.9 Plain tube 99.6 0.807 0.421
0.0159 5.5 4.9 Plain tube 100.4 0.856 0.457
0.0159 5.4 4.8 Plain tube 99.7 0.910 0.464
0.0159 5.5 4.9 Plain tube 99.8 0.952 0.454
0.0159 5.5 4.9 Plain tube 149.5 0.053 0.084
0.0159 5.3 4.7 Plain tube 150.6 0.103 0.098
0.0159 5.1 4.5 Plain tube 149.9 0.155 0.138
0.0159 5.3 4.7 Plain tube 149.7 0.207 0.178
0.0159 5.2 4.7 Plain tube 150.6 0.253 0.217
0.0159 5.1 4.5 Plain tube 150.4 0.307 0.278
0.0159 5.4 4.8 Plain tube 149.8 0.354 0.320
0.0159 5.4 4.8 Plain tube 149.7 0.404 0.378
0.0159 5.4 4.8 Plain tube 149.8 0.456 0.452
0.0159 5.6 4.9 Plain tube 149.1 0.511 0.522
0.0159 5.5 4.8 Plain tube 149.7 0.554 0.609
0.0159 5.6 4.9 Plain tube 149.4 0.605 0.699
0.0159 5.6 4.8 Plain tube 150.0 0.653 0.808
0.0159 5.4 4.6 Plain tube 149.3 0.709 0.940
0.0159 5.6 4.7 Plain tube 149.1 0.757 1.036
0.0159 5.3 4.4 Plain tube 150.0 0.807 1.181
0.0159 5.6 4.7 Plain tube 149.3 0.854 1.235
0.0159 5.5 4.6 Plain tube 150.6 0.900 1.281
0.0159 5.8 4.8 Plain tube 149.7 0.953 1.309
0.0159 5.4 4.9 Plain tube 199.9 0.053 0.117
0.0159 5.2 4.6 Plain tube 200.9 0.104 0.162
0.0159 5.4 4.8 Plain tube 199.9 0.153 0.233
0.0159 5.4 4.8 Plain tube 199.5 0.204 0.305
0.0159 5.3 4.7 Plain tube 200.0 0.256 0.394
0.0159 5.1 4.4 Plain tube 200.1 0.309 0.505
0.0159 5.5 4.8 Plain tube 200.0 0.353 0.596
Appendix B 215
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.5 4.8 Plain tube 200.0 0.407 0.749
0.0159 5.4 4.7 Plain tube 200.1 0.451 0.890
0.0159 5.3 4.5 Plain tube 200.8 0.501 1.084
0.0159 5.5 4.6 Plain tube 200.0 0.557 1.255
0.0159 5.6 4.7 Plain tube 200.0 0.607 1.405
0.0159 5.5 4.9 14 75.3 0.053 0.139
0.0159 5.4 4.8 14 74.9 0.105 0.154
0.0159 5.4 4.9 14 75.4 0.155 0.163
0.0159 5.4 4.9 14 75.5 0.211 0.185
0.0159 5.4 4.9 14 75.1 0.254 0.199
0.0159 5.5 4.9 14 75.4 0.307 0.216
0.0159 5.5 4.9 14 75.2 0.356 0.247
0.0159 5.2 4.7 14 75.4 0.409 0.275
0.0159 5.5 4.9 14 75.7 0.455 0.304
0.0159 5.5 4.9 14 75.5 0.513 0.342
0.0159 5.3 4.7 14 75.1 0.556 0.381
0.0159 5.5 4.9 14 75.5 0.605 0.410
0.0159 5.3 4.7 14 75.4 0.657 0.452
0.0159 5.5 4.9 14 75.0 0.712 0.483
0.0159 5.6 4.9 14 74.9 0.758 0.511
0.0159 5.6 4.9 14 74.7 0.814 0.539
0.0159 5.4 4.8 14 74.8 0.859 0.555
0.0159 5.4 4.8 14 74.9 0.914 0.558
0.0159 5.4 4.8 14 75.0 0.961 0.547
0.0159 5.5 4.9 14 100.4 0.053 0.175
0.0159 5.1 4.6 14 100.4 0.104 0.208
0.0159 5.3 4.7 14 100.6 0.153 0.232
0.0159 5.5 4.9 14 100.3 0.204 0.251
0.0159 5.4 4.8 14 99.9 0.255 0.309
0.0159 5.5 4.9 14 99.9 0.309 0.334
0.0159 5.5 4.9 14 101.3 0.351 0.407
0.0159 5.3 4.7 14 100.0 0.405 0.472
0.0159 5.5 4.9 14 101.1 0.453 0.520
0.0159 5.5 4.9 14 100.8 0.508 0.609
0.0159 5.5 4.9 14 100.4 0.553 0.683
0.0159 5.6 4.9 14 99.9 0.613 0.770
0.0159 5.6 4.9 14 100.0 0.657 0.846
0.0159 5.6 4.9 14 99.4 0.706 0.910
0.0159 5.5 4.8 14 99.3 0.756 0.989
0.0159 5.6 4.9 14 99.3 0.808 1.045
0.0159 5.5 4.7 14 100.3 0.854 1.113
0.0159 5.2 4.4 14 100.2 0.911 1.135
216 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.6 4.8 14 99.7 0.963 1.123
0.0159 5.3 4.7 14 149.9 0.053 0.275
0.0159 5.2 4.6 14 150.0 0.104 0.357
0.0159 5.4 4.8 14 151.3 0.152 0.394
0.0159 5.5 4.8 14 150.7 0.205 0.542
0.0159 5.6 4.9 14 150.6 0.254 0.675
0.0159 5.5 4.8 14 150.5 0.308 0.865
0.0159 5.7 4.9 14 150.3 0.357 1.025
0.0159 5.7 4.8 14 149.6 0.408 1.191
0.0159 5.6 4.7 14 150.3 0.453 1.435
0.0159 5.7 4.7 14 149.5 0.510 1.650
0.0159 5.7 4.6 14 149.8 0.557 1.899
0.0159 5.8 4.7 14 149.4 0.607 2.092
0.0159 5.6 4.4 14 149.6 0.658 2.364
0.0159 5.8 4.6 14 150.4 0.708 2.539
0.0159 5.6 4.3 14 149.8 0.762 2.729
0.0159 5.9 4.6 14 150.3 0.803 2.791
0.0159 5.9 4.5 14 150.9 0.853 2.924
0.0159 5.9 4.4 14 149.5 0.909 2.884
0.0159 5.5 4.8 14 201.5 0.053 0.367
0.0159 5.4 4.7 14 200.7 0.105 0.560
0.0159 5.4 4.7 14 200.6 0.154 0.744
0.0159 5.6 4.8 14 199.5 0.208 0.982
0.0159 5.5 4.6 14 200.6 0.255 1.320
0.0159 5.7 4.8 14 200.2 0.308 1.608
0.0159 5.6 4.5 14 199.9 0.356 2.034
0.0159 5.8 4.6 14 199.9 0.412 2.449
0.0159 5.8 4.4 14 200.3 0.454 2.913
0.0159 5.7 4.2 14 200.3 0.510 3.370
0.0159 5.3 4.8 9 75.0 0.053 0.165
0.0159 5.3 4.7 9 74.9 0.105 0.180
0.0159 5.5 5.0 9 74.8 0.154 0.206
0.0159 5.3 4.8 9 74.7 0.207 0.226
0.0159 5.3 4.7 9 75.0 0.256 0.239
0.0159 5.5 4.9 9 75.1 0.310 0.255
0.0159 5.4 4.8 9 74.9 0.356 0.280
0.0159 5.0 4.5 9 75.5 0.412 0.312
0.0159 5.4 4.8 9 75.5 0.411 0.307
0.0159 5.5 4.9 9 75.3 0.456 0.338
0.0159 5.4 4.8 9 75.0 0.509 0.371
0.0159 5.2 4.5 9 75.3 0.557 0.410
0.0159 5.2 4.5 9 74.8 0.611 0.441
Appendix B 217
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.4 4.7 9 75.4 0.657 0.472
0.0159 5.4 4.8 9 74.9 0.709 0.500
0.0159 5.5 4.8 9 75.2 0.756 0.535
0.0159 5.3 4.6 9 75.1 0.815 0.568
0.0159 5.6 4.9 9 74.9 0.859 0.583
0.0159 5.5 4.8 9 74.7 0.917 0.588
0.0159 5.4 4.9 9 100.2 0.053 0.200
0.0159 5.5 4.9 9 100.3 0.102 0.239
0.0159 5.3 4.7 9 101.0 0.153 0.289
0.0159 5.4 4.8 9 101.0 0.208 0.317
0.0159 5.1 4.5 9 100.7 0.253 0.356
0.0159 5.5 4.8 9 101.0 0.309 0.422
0.0159 5.5 4.8 9 101.0 0.355 0.462
0.0159 5.5 4.9 9 100.2 0.405 0.510
0.0159 5.5 4.8 9 100.5 0.455 0.591
0.0159 5.5 4.8 9 100.6 0.505 0.686
0.0159 5.6 4.8 9 100.0 0.604 0.828
0.0159 5.2 4.4 9 101.3 0.655 0.990
0.0159 5.7 4.9 9 99.9 0.713 1.020
0.0159 5.6 4.7 9 99.7 0.754 1.085
0.0159 5.7 4.9 9 100.0 0.804 1.146
0.0159 5.2 4.3 9 99.9 0.855 1.212
0.0159 5.5 4.7 9 99.7 0.911 1.188
0.0159 5.6 4.8 9 99.8 0.959 1.164
0.0159 5.6 4.9 9 150.1 0.053 0.327
0.0159 5.5 4.9 9 150.5 0.103 0.420
0.0159 5.6 4.9 9 150.4 0.154 0.508
0.0159 5.5 4.8 9 150.8 0.208 0.611
0.0159 5.2 4.5 9 150.4 0.254 0.797
0.0159 5.6 4.8 9 149.4 0.312 0.941
0.0159 5.6 4.7 9 150.5 0.354 1.145
0.0159 5.4 4.5 9 149.9 0.407 1.410
0.0159 5.6 4.6 9 150.7 0.452 1.621
0.0159 5.4 4.4 9 149.7 0.510 1.891
0.0159 5.6 4.5 9 149.8 0.559 2.113
0.0159 5.7 4.5 9 149.2 0.613 2.337
0.0159 5.7 4.4 9 150.7 0.656 2.593
0.0159 5.8 4.5 9 149.0 0.714 2.730
0.0159 5.9 4.5 9 150.4 0.754 2.911
0.0159 5.8 4.4 9 150.7 0.804 3.062
0.0159 5.7 4.2 9 150.7 0.854 3.133
0.0159 5.8 4.2 9 148.3 0.903 3.044
218 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.5 4.9 9 200.2 0.054 0.455
0.0159 5.4 4.6 9 199.4 0.106 0.651
0.0159 5.5 4.7 9 200.5 0.154 0.863
0.0159 5.5 4.7 9 199.7 0.211 1.169
0.0159 5.4 4.4 9 200.8 0.255 1.526
0.0159 5.6 4.5 9 200.1 0.306 1.899
0.0159 5.6 4.4 9 199.2 0.356 2.295
0.0159 5.8 4.5 9 199.7 0.410 2.763
0.0159 5.9 4.4 9 200.1 0.455 3.195
0.0159 5.8 4.2 9 200.0 0.507 3.515
0.0159 5.9 4.2 9 200.6 0.556 4.057
0.0159 5.4 4.9 4 75.3 0.052 0.310
0.0159 5.4 4.9 4 75.7 0.106 0.312
0.0159 5.4 4.8 4 74.9 0.156 0.353
0.0159 5.3 4.7 4 75.6 0.206 0.384
0.0159 5.3 4.7 4 75.4 0.256 0.402
0.0159 5.4 4.8 4 75.3 0.311 0.405
0.0159 5.2 4.6 4 75.3 0.360 0.412
0.0159 5.4 4.8 4 74.7 0.413 0.437
0.0159 5.2 4.6 4 75.1 0.457 0.480
0.0159 5.4 4.8 4 74.8 0.507 0.518
0.0159 5.5 4.8 4 75.2 0.557 0.568
0.0159 5.6 4.9 4 75.1 0.611 0.608
0.0159 5.6 4.9 4 75.1 0.663 0.655
0.0159 5.3 4.6 4 75.3 0.714 0.711
0.0159 5.5 4.8 4 75.3 0.754 0.739
0.0159 5.6 4.8 4 74.8 0.815 0.761
0.0159 5.5 4.8 4 75.2 0.889 0.769
0.0159 5.3 4.7 4 100.5 0.055 0.376
0.0159 5.4 4.8 4 99.9 0.112 0.434
0.0159 5.6 4.9 4 100.4 0.153 0.478
0.0159 5.2 4.5 4 100.8 0.204 0.511
0.0159 5.5 4.8 4 100.0 0.258 0.554
0.0159 5.5 4.8 4 101.0 0.305 0.588
0.0159 5.6 4.9 4 100.3 0.358 0.699
0.0159 5.4 4.7 4 99.9 0.414 0.799
0.0159 5.4 4.6 4 100.0 0.459 0.903
0.0159 5.5 4.6 4 99.5 0.512 0.993
0.0159 5.6 4.7 4 100.9 0.558 1.097
0.0159 5.5 4.6 4 100.4 0.607 1.214
0.0159 5.5 4.6 4 100.8 0.656 1.333
0.0159 5.7 4.8 4 100.0 0.711 1.401
Appendix B 219
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.7 4.7 4 99.9 0.758 1.460
0.0159 5.5 4.5 4 99.7 0.814 1.518
0.0159 5.6 4.6 4 100.6 0.857 1.567
0.0159 5.6 4.6 4 101.6 0.895 1.499
0.0159 5.7 4.7 4 101.4 0.949 1.440
0.0159 5.3 4.7 4 150.6 0.053 0.541
0.0159 5.6 4.9 4 149.6 0.104 0.634
0.0159 5.6 4.8 4 150.5 0.154 0.766
0.0159 5.6 4.8 4 150.8 0.206 0.952
0.0159 5.4 4.5 4 149.9 0.257 1.202
0.0159 5.7 4.7 4 150.2 0.305 1.400
0.0159 5.6 4.7 4 150.0 0.355 1.645
0.0159 5.6 4.6 4 150.1 0.408 1.958
0.0159 5.7 4.5 4 149.7 0.460 2.282
0.0159 5.7 4.4 4 150.3 0.516 2.659
0.0159 5.6 4.2 4 150.8 0.558 2.915
0.0159 5.6 4.2 4 149.9 0.610 3.119
0.0159 6.0 4.5 4 149.5 0.659 3.251
0.0159 6.0 4.4 4 150.6 0.715 3.497
0.0159 5.9 4.2 4 149.8 0.758 3.633
0.0159 6.0 4.3 4 150.6 0.804 3.718
0.0159 5.9 4.3 4 149.4 0.859 3.721
0.0159 5.6 4.8 4 199.7 0.054 0.704
0.0159 5.5 4.7 4 199.2 0.105 0.968
0.0159 5.5 4.6 4 200.4 0.156 1.309
0.0159 5.5 4.4 4 200.7 0.214 1.840
0.0159 5.7 4.6 4 199.9 0.256 2.165
0.0159 5.7 4.4 4 200.8 0.306 2.718
0.0159 6.0 4.6 4 200.0 0.355 3.174
0.0159 5.3 4.8 3 75.5 0.054 0.380
0.0159 5.4 4.8 3 75.0 0.107 0.409
0.0159 5.5 4.9 3 75.2 0.155 0.437
0.0159 5.3 4.6 3 74.8 0.212 0.485
0.0159 5.2 4.5 3 74.9 0.258 0.483
0.0159 5.3 4.7 3 75.1 0.308 0.490
0.0159 5.5 4.9 3 74.8 0.358 0.501
0.0159 5.2 4.6 3 75.1 0.414 0.552
0.0159 5.6 5.0 3 75.6 0.454 0.570
0.0159 5.3 4.7 3 75.2 0.513 0.641
0.0159 5.5 4.9 3 75.1 0.558 0.674
0.0159 5.3 4.6 3 74.8 0.612 0.739
0.0159 5.4 4.7 3 75.1 0.657 0.780
220 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 5.3 4.6 3 74.9 0.711 0.848
0.0159 5.5 4.8 3 75.1 0.759 0.878
0.0159 5.3 4.6 3 75.3 0.810 0.904
0.0159 5.5 4.8 3 75.0 0.859 0.892
0.0159 5.5 4.8 3 75.4 0.910 0.849
0.0159 5.6 4.9 3 75.5 0.970 0.730
0.0159 5.4 4.8 3 100.5 0.054 0.427
0.0159 5.4 4.8 3 99.9 0.106 0.495
0.0159 5.3 4.6 3 99.7 0.153 0.575
0.0159 5.2 4.5 3 100.0 0.209 0.618
0.0159 5.5 4.8 3 100.1 0.257 0.649
0.0159 5.3 4.6 3 100.2 0.306 0.752
0.0159 5.5 4.7 3 99.9 0.355 0.833
0.0159 5.6 4.8 3 99.9 0.408 0.940
0.0159 5.4 4.6 3 100.0 0.457 1.059
0.0159 5.7 4.8 3 100.0 0.509 1.156
0.0159 5.5 4.6 3 100.0 0.557 1.315
0.0159 5.7 4.7 3 99.9 0.609 1.437
0.0159 5.7 4.7 3 100.2 0.657 1.555
0.0159 5.8 4.8 3 100.2 0.708 1.645
0.0159 5.5 4.5 3 100.4 0.754 1.723
0.0159 5.6 4.6 3 100.6 0.808 1.762
0.0159 5.8 4.7 3 100.6 0.855 1.746
0.0159 5.3 4.6 3 150.9 0.054 0.658
0.0159 5.6 4.9 3 150.6 0.102 0.767
0.0159 5.5 4.7 3 150.5 0.154 0.943
0.0159 5.6 4.8 3 151.0 0.202 1.157
0.0159 5.5 4.6 3 150.0 0.255 1.418
0.0159 5.7 4.7 3 150.1 0.306 1.696
0.0159 5.6 4.5 3 150.1 0.356 2.023
0.0159 5.7 4.5 3 150.6 0.410 2.413
0.0159 5.6 4.3 3 150.3 0.454 2.694
0.0159 5.7 4.3 3 149.0 0.515 3.059
0.0159 5.9 4.4 3 151.5 0.571 3.232
0.0159 5.4 4.6 3 200.2 0.054 0.871
0.0159 5.5 4.6 3 200.4 0.104 1.157
0.0159 5.7 4.7 3 200.2 0.155 1.553
0.0159 5.5 4.4 3 200.2 0.205 2.017
0.0159 5.9 4.6 3 199.7 0.255 2.502
0.0159 5.8 4.3 3 200.3 0.309 3.098
0.0159 6.0 4.5 3 200.8 0.357 3.600
Appendix B 221
Table B.4 - Flow boiling pressure drop experimental results for Tsat =15 oC under adiabatic conditions inside 15.9 mm internal diameter tube
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.4 14.9 Plain tube 75.1 0.051 0.049
0.0159 15.3 14.9 Plain tube 75.2 0.101 0.043
0.0159 15.4 14.9 Plain tube 74.9 0.152 0.041
0.0159 15.4 14.9 Plain tube 75.1 0.203 0.042
0.0159 15.3 14.9 Plain tube 75.2 0.251 0.046
0.0159 15.4 14.9 Plain tube 75.0 0.306 0.053
0.0159 15.4 15.0 Plain tube 74.9 0.350 0.059
0.0159 15.2 14.8 Plain tube 75.6 0.399 0.069
0.0159 15.3 14.8 Plain tube 74.7 0.457 0.081
0.0159 15.1 14.7 Plain tube 75.0 0.497 0.089
0.0159 15.4 15.0 Plain tube 75.4 0.553 0.103
0.0159 15.3 14.9 Plain tube 74.9 0.597 0.118
0.0159 15.4 14.9 Plain tube 75.8 0.650 0.135
0.0159 15.1 14.7 Plain tube 75.7 0.704 0.148
0.0159 15.1 14.7 Plain tube 74.5 0.753 0.156
0.0159 15.2 14.8 Plain tube 75.2 0.797 0.167
0.0159 15.2 14.7 Plain tube 74.8 0.858 0.174
0.0159 15.3 14.9 Plain tube 75.1 0.897 0.179
0.0159 15.0 14.6 Plain tube 75.1 0.954 0.175
0.0159 15.1 14.7 Plain tube 99.8 0.054 0.049
0.0159 15.1 14.7 Plain tube 100.2 0.107 0.051
0.0159 15.4 15.0 Plain tube 100.1 0.151 0.052
0.0159 15.4 15.0 Plain tube 100.2 0.204 0.055
0.0159 15.3 14.9 Plain tube 100.7 0.251 0.071
0.0159 15.2 14.8 Plain tube 100.7 0.304 0.089
0.0159 15.0 14.6 Plain tube 100.3 0.352 0.108
0.0159 15.3 14.9 Plain tube 100.4 0.404 0.123
0.0159 15.2 14.8 Plain tube 99.7 0.455 0.150
0.0159 15.0 14.6 Plain tube 99.8 0.508 0.171
0.0159 15.2 14.7 Plain tube 99.7 0.552 0.193
0.0159 15.4 15.0 Plain tube 100.9 0.600 0.208
0.0159 15.4 14.9 Plain tube 99.9 0.652 0.232
0.0159 15.5 15.0 Plain tube 100.5 0.703 0.254
0.0159 15.3 14.8 Plain tube 100.4 0.755 0.279
0.0159 15.1 14.6 Plain tube 100.4 0.811 0.305
0.0159 15.3 14.8 Plain tube 100.3 0.855 0.320
0.0159 15.3 14.8 Plain tube 100.6 0.898 0.336
0.0159 15.3 14.8 Plain tube 100.0 0.950 0.332
0.0159 15.6 15.1 Plain tube 100.5 0.982 0.326
0.0159 15.2 14.7 Plain tube 150.7 0.052 0.062
0.0159 15.3 14.8 Plain tube 150.2 0.104 0.077
222 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.3 14.9 Plain tube 150.2 0.152 0.095
0.0159 15.1 14.6 Plain tube 149.9 0.206 0.131
0.0159 15.4 14.9 Plain tube 150.0 0.250 0.156
0.0159 15.3 14.8 Plain tube 150.7 0.305 0.195
0.0159 15.3 14.8 Plain tube 150.3 0.350 0.227
0.0159 15.4 14.9 Plain tube 148.7 0.406 0.271
0.0159 15.4 14.9 Plain tube 149.8 0.450 0.307
0.0159 15.4 14.9 Plain tube 150.2 0.501 0.355
0.0159 15.2 14.6 Plain tube 149.7 0.552 0.408
0.0159 15.1 14.5 Plain tube 150.1 0.604 0.468
0.0159 15.3 14.7 Plain tube 149.7 0.653 0.525
0.0159 15.4 14.9 Plain tube 150.2 0.703 0.588
0.0159 15.3 14.7 Plain tube 150.3 0.753 0.670
0.0159 15.3 14.7 Plain tube 149.4 0.807 0.742
0.0159 15.5 14.8 Plain tube 149.9 0.852 0.807
0.0159 15.5 14.8 Plain tube 149.9 0.905 0.868
0.0159 15.2 14.5 Plain tube 149.2 0.954 0.887
0.0159 15.2 14.7 Plain tube 199.9 0.052 0.099
0.0159 15.1 14.6 Plain tube 199.4 0.105 0.130
0.0159 15.3 14.8 Plain tube 200.5 0.152 0.171
0.0159 15.2 14.7 Plain tube 200.9 0.203 0.234
0.0159 15.3 14.8 Plain tube 199.4 0.254 0.286
0.0159 15.4 14.9 Plain tube 201.5 0.301 0.343
0.0159 15.3 14.7 Plain tube 200.3 0.354 0.418
0.0159 15.4 14.8 Plain tube 199.1 0.415 0.497
0.0159 15.1 14.5 Plain tube 201.5 0.453 0.608
0.0159 15.5 14.9 Plain tube 200.7 0.501 0.682
0.0159 15.3 14.6 Plain tube 200.2 0.561 0.825
0.0159 15.6 14.9 Plain tube 198.8 0.610 0.925
0.0159 15.2 14.5 Plain tube 200.5 0.651 1.094
0.0159 15.2 14.3 Plain tube 200.5 0.708 1.255
0.0159 15.5 14.7 Plain tube 199.0 0.759 1.353
0.0159 15.6 14.8 Plain tube 199.5 0.809 1.456
0.0159 15.4 14.5 Plain tube 199.7 0.854 1.603
0.0159 15.6 14.7 Plain tube 199.7 0.910 1.654
0.0159 15.7 14.7 Plain tube 199.9 0.952 1.679
0.0159 15.3 14.8 14 75.8 0.056 0.135
0.0159 15.3 14.8 14 75.5 0.110 0.139
0.0159 15.3 14.8 14 75.2 0.153 0.148
0.0159 15.2 14.7 14 75.1 0.203 0.161
0.0159 15.1 14.7 14 74.8 0.253 0.173
0.0159 15.4 14.9 14 75.1 0.304 0.177
0.0159 15.5 15.0 14 74.9 0.352 0.199
Appendix B 223
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.2 14.7 14 75.3 0.407 0.216
0.0159 15.4 14.9 14 74.6 0.454 0.234
0.0159 15.4 14.9 14 75.2 0.503 0.242
0.0159 15.5 15.0 14 74.6 0.556 0.276
0.0159 15.1 14.6 14 76.0 0.602 0.320
0.0159 15.6 15.0 14 77.0 0.641 0.327
0.0159 15.0 14.6 14 74.6 0.716 0.350
0.0159 15.4 14.8 14 75.9 0.753 0.374
0.0159 15.6 15.0 14 76.2 0.813 0.389
0.0159 15.1 14.6 14 75.5 0.854 0.421
0.0159 15.1 14.6 14 75.2 0.906 0.413
0.0159 15.0 14.7 14 74.9 0.957 0.398
0.0159 15.4 15.0 14 100.1 0.052 0.170
0.0159 15.1 14.7 14 100.6 0.104 0.182
0.0159 15.3 14.8 14 100.2 0.153 0.204
0.0159 15.3 14.9 14 100.6 0.206 0.211
0.0159 15.2 14.7 14 100.6 0.252 0.245
0.0159 15.5 15.0 14 99.8 0.304 0.254
0.0159 15.4 14.9 14 100.2 0.353 0.309
0.0159 15.3 14.8 14 101.0 0.404 0.346
0.0159 15.1 14.6 14 100.0 0.451 0.404
0.0159 15.4 14.9 14 100.9 0.504 0.420
0.0159 15.5 15.0 14 100.5 0.552 0.480
0.0159 15.4 14.9 14 100.7 0.604 0.504
0.0159 15.3 14.8 14 100.9 0.653 0.594
0.0159 15.5 14.9 14 100.3 0.705 0.651
0.0159 15.4 14.8 14 99.9 0.752 0.663
0.0159 15.1 14.5 14 99.9 0.806 0.702
0.0159 15.4 14.8 14 100.0 0.853 0.705
0.0159 15.5 14.9 14 100.0 0.906 0.685
0.0159 15.5 14.9 14 100.2 0.954 0.649
0.0159 15.4 14.9 14 150.5 0.054 0.229
0.0159 15.5 15.0 14 149.8 0.104 0.276
0.0159 15.4 14.9 14 150.2 0.152 0.330
0.0159 15.3 14.8 14 149.9 0.204 0.378
0.0159 15.4 14.9 14 150.7 0.252 0.480
0.0159 15.3 14.8 14 150.3 0.304 0.596
0.0159 15.5 14.9 14 150.4 0.353 0.708
0.0159 15.5 14.9 14 150.7 0.408 0.825
0.0159 15.5 14.8 14 150.2 0.452 0.964
0.0159 15.5 14.8 14 150.3 0.506 1.097
0.0159 15.4 14.7 14 150.6 0.555 1.294
0.0159 15.5 14.8 14 149.9 0.613 1.441
224 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.3 14.5 14 150.3 0.656 1.563
0.0159 15.6 14.8 14 149.1 0.708 1.670
0.0159 15.4 14.5 14 150.6 0.758 1.890
0.0159 15.4 14.5 14 149.7 0.809 1.975
0.0159 15.5 14.6 14 150.1 0.857 2.055
0.0159 15.7 14.8 14 148.8 0.909 2.021
0.0159 15.5 14.6 14 149.6 0.957 1.956
0.0159 15.4 14.9 14 200.7 0.053 0.302
0.0159 15.5 14.9 14 199.9 0.103 0.411
0.0159 15.5 15.0 14 200.7 0.153 0.538
0.0159 15.5 15.0 14 201.8 0.203 0.701
0.0159 15.3 14.7 14 200.3 0.254 0.933
0.0159 15.6 14.9 14 200.3 0.308 1.100
0.0159 15.5 14.7 14 200.3 0.353 1.358
0.0159 15.5 14.7 14 200.5 0.407 1.631
0.0159 15.6 14.7 14 200.1 0.461 1.964
0.0159 15.5 14.5 14 201.1 0.508 2.290
0.0159 15.7 14.7 14 200.2 0.557 2.515
0.0159 15.6 14.5 14 200.1 0.606 2.760
0.0159 15.6 14.4 14 198.4 0.692 3.151
0.0159 15.7 14.4 14 197.1 0.754 3.384
0.0159 15.5 14.2 14 200.2 0.754 3.582
0.0159 15.9 14.6 14 199.1 0.810 3.655
0.0159 15.5 14.1 14 200.8 0.852 3.771
0.0159 15.9 14.5 14 199.7 0.907 3.711
0.0159 15.9 14.6 14 198.4 0.973 3.459
0.0159 15.5 14.9 9 75.1 0.053 0.175
0.0159 15.4 14.8 9 75.5 0.101 0.180
0.0159 15.3 14.7 9 75.1 0.154 0.188
0.0159 15.3 14.7 9 74.9 0.207 0.200
0.0159 15.5 14.9 9 75.8 0.253 0.210
0.0159 15.5 14.9 9 74.6 0.309 0.225
0.0159 15.2 14.7 9 75.5 0.357 0.235
0.0159 15.3 14.8 9 75.0 0.412 0.248
0.0159 15.3 14.8 9 75.4 0.450 0.255
0.0159 15.5 15.0 9 74.7 0.507 0.280
0.0159 15.3 14.8 9 75.4 0.553 0.293
0.0159 15.6 15.0 9 74.8 0.605 0.318
0.0159 15.1 14.6 9 75.2 0.654 0.341
0.0159 15.2 14.6 9 75.5 0.701 0.368
0.0159 15.3 14.7 9 74.8 0.753 0.373
0.0159 15.2 14.6 9 74.8 0.813 0.404
0.0159 15.4 14.8 9 76.1 0.849 0.418
Appendix B 225
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.4 14.8 9 74.8 0.904 0.417
0.0159 15.3 14.7 9 75.4 0.947 0.417
0.0159 15.4 14.9 9 100.1 0.053 0.207
0.0159 15.3 14.8 9 100.3 0.105 0.225
0.0159 15.3 14.9 9 100.3 0.151 0.235
0.0159 15.5 15.0 9 100.4 0.209 0.255
0.0159 15.4 14.9 9 100.2 0.254 0.293
0.0159 15.3 14.8 9 100.2 0.305 0.313
0.0159 15.5 14.9 9 101.0 0.354 0.348
0.0159 15.5 15.0 9 100.9 0.405 0.395
0.0159 15.5 14.9 9 100.2 0.455 0.437
0.0159 15.3 14.8 9 100.9 0.502 0.460
0.0159 15.4 14.8 9 100.4 0.552 0.523
0.0159 15.5 14.9 9 99.6 0.608 0.588
0.0159 15.4 14.9 9 100.9 0.650 0.608
0.0159 15.3 14.7 9 100.5 0.701 0.670
0.0159 15.4 14.8 9 100.7 0.754 0.745
0.0159 15.5 14.8 9 100.8 0.803 0.798
0.0159 15.5 14.9 9 100.6 0.854 0.815
0.0159 15.1 14.5 9 100.2 0.905 0.844
0.0159 15.3 14.7 9 100.1 0.963 0.824
0.0159 15.3 14.8 9 149.8 0.053 0.285
0.0159 15.3 14.7 9 150.2 0.102 0.347
0.0159 15.4 14.8 9 150.8 0.152 0.399
0.0159 15.1 14.6 9 150.4 0.204 0.469
0.0159 15.1 14.5 9 150.4 0.253 0.583
0.0159 15.5 14.9 9 149.7 0.315 0.693
0.0159 15.2 14.6 9 150.5 0.355 0.827
0.0159 15.4 14.8 9 150.4 0.402 0.927
0.0159 15.4 14.7 9 150.9 0.447 1.089
0.0159 15.2 14.5 9 149.7 0.505 1.271
0.0159 15.3 14.5 9 150.1 0.547 1.370
0.0159 15.5 14.7 9 150.0 0.601 1.546
0.0159 15.7 14.9 9 151.5 0.652 1.731
0.0159 15.3 14.3 9 150.6 0.708 1.940
0.0159 15.7 14.7 9 149.1 0.756 1.955
0.0159 15.4 14.4 9 151.2 0.801 2.186
0.0159 15.8 14.8 9 150.4 0.850 2.192
0.0159 15.2 14.2 9 149.3 0.911 2.225
0.0159 15.8 14.7 9 150.1 0.955 2.164
0.0159 15.4 14.8 9 200.7 0.053 0.389
0.0159 15.5 14.9 9 199.8 0.106 0.505
0.0159 15.3 14.7 9 200.4 0.154 0.647
226 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.5 14.9 9 199.4 0.209 0.802
0.0159 15.4 14.7 9 201.5 0.251 1.023
0.0159 15.3 14.5 9 200.4 0.312 1.355
0.0159 15.3 14.5 9 202.0 0.352 1.610
0.0159 15.2 14.3 9 201.1 0.411 1.964
0.0159 15.5 14.5 9 201.0 0.454 2.172
0.0159 15.7 14.7 9 199.7 0.513 2.456
0.0159 15.8 14.6 9 199.6 0.559 2.773
0.0159 15.7 14.5 9 199.2 0.616 3.101
0.0159 15.5 14.2 9 200.1 0.656 3.344
0.0159 15.8 14.4 9 201.1 0.707 3.684
0.0159 15.9 14.5 9 199.5 0.756 3.771
0.0159 15.8 14.3 9 199.6 0.818 4.011
0.0159 15.8 14.3 9 199.4 0.856 4.102
0.0159 15.6 14.1 9 200.1 0.906 4.083
0.0159 15.8 14.3 9 198.9 0.951 4.034
0.0159 15.3 14.8 4 75.1 0.053 0.272
0.0159 15.4 14.9 4 76.2 0.102 0.299
0.0159 15.2 14.7 4 75.7 0.152 0.328
0.0159 15.4 14.9 4 75.3 0.204 0.345
0.0159 15.5 14.9 4 74.6 0.254 0.366
0.0159 15.5 15.0 4 75.1 0.306 0.371
0.0159 15.4 14.9 4 74.7 0.370 0.370
0.0159 15.2 14.7 4 74.8 0.401 0.364
0.0159 15.4 14.9 4 74.9 0.455 0.363
0.0159 15.5 15.0 4 74.6 0.510 0.372
0.0159 15.3 14.7 4 75.4 0.557 0.430
0.0159 15.4 14.9 4 75.4 0.605 0.441
0.0159 15.5 14.9 4 75.3 0.659 0.474
0.0159 15.4 14.8 4 75.0 0.703 0.474
0.0159 15.1 14.5 4 74.8 0.750 0.523
0.0159 15.6 15.0 4 74.7 0.807 0.543
0.0159 15.4 14.8 4 74.5 0.864 0.519
0.0159 15.4 14.8 4 74.6 0.911 0.526
0.0159 15.3 14.8 4 100.8 0.052 0.362
0.0159 15.4 14.8 4 100.4 0.104 0.379
0.0159 15.3 14.8 4 100.4 0.153 0.427
0.0159 15.5 14.9 4 100.6 0.204 0.456
0.0159 15.2 14.7 4 101.0 0.253 0.462
0.0159 15.4 14.8 4 99.7 0.305 0.484
0.0159 15.4 14.9 4 100.1 0.353 0.521
0.0159 15.5 14.9 4 100.4 0.407 0.587
0.0159 15.3 14.7 4 100.5 0.451 0.639
Appendix B 227
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.4 14.8 4 99.5 0.505 0.708
0.0159 15.4 14.8 4 100.7 0.554 0.766
0.0159 15.4 14.8 4 100.2 0.607 0.849
0.0159 15.4 14.7 4 99.8 0.658 0.913
0.0159 15.5 14.8 4 100.9 0.702 0.968
0.0159 15.6 14.9 4 100.4 0.757 1.032
0.0159 15.5 14.8 4 100.3 0.804 1.074
0.0159 15.3 14.6 4 100.1 0.855 1.117
0.0159 15.5 14.8 4 99.9 0.905 1.080
0.0159 15.6 14.9 4 100.0 0.955 1.038
0.0159 15.4 14.8 4 150.4 0.054 0.509
0.0159 15.5 14.8 4 150.0 0.105 0.555
0.0159 15.4 14.7 4 150.8 0.153 0.631
0.0159 15.4 14.8 4 149.5 0.210 0.739
0.0159 15.5 14.8 4 150.8 0.253 0.863
0.0159 15.4 14.7 4 150.5 0.305 1.037
0.0159 15.5 14.8 4 151.5 0.352 1.205
0.0159 15.4 14.6 4 150.7 0.409 1.440
0.0159 15.4 14.5 4 150.5 0.455 1.593
0.0159 15.4 14.4 4 150.6 0.506 1.799
0.0159 15.6 14.6 4 150.3 0.556 2.005
0.0159 15.4 14.4 4 151.4 0.609 2.295
0.0159 15.7 14.7 4 150.5 0.654 2.375
0.0159 15.6 14.5 4 150.2 0.707 2.531
0.0159 15.4 14.2 4 150.5 0.756 2.684
0.0159 15.4 14.3 4 149.9 0.808 2.744
0.0159 15.5 14.3 4 150.6 0.856 2.792
0.0159 15.6 14.4 4 149.8 0.905 2.742
0.0159 15.7 14.6 4 150.0 0.957 2.522
0.0159 15.4 14.7 4 200.0 0.054 0.620
0.0159 15.4 14.7 4 201.4 0.105 0.757
0.0159 15.5 14.8 4 200.9 0.153 0.954
0.0159 15.3 14.5 4 199.6 0.205 1.315
0.0159 15.6 14.8 4 200.3 0.254 1.572
0.0159 15.5 14.6 4 200.3 0.308 1.916
0.0159 15.6 14.6 4 200.1 0.356 2.322
0.0159 15.6 14.5 4 199.8 0.406 2.692
0.0159 15.6 14.4 4 201.0 0.456 3.136
0.0159 15.8 14.5 4 199.6 0.508 3.420
0.0159 15.7 14.3 4 200.3 0.556 3.773
0.0159 15.7 14.2 4 199.5 0.607 3.942
0.0159 15.7 14.1 4 200.0 0.656 4.330
0.0159 15.8 14.2 4 199.7 0.704 4.535
228 Appendix B
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 16.0 14.4 4 200.0 0.755 4.721
0.0159 15.9 14.2 4 199.5 0.806 4.843
0.0159 15.9 14.2 4 200.0 0.855 4.797
0.0159 15.9 14.2 4 199.4 0.912 4.585
0.0159 15.3 14.8 3 74.5 0.053 0.468
0.0159 15.3 14.8 3 75.3 0.104 0.375
0.0159 15.4 14.9 3 74.8 0.154 0.396
0.0159 15.4 14.8 3 75.5 0.202 0.422
0.0159 15.4 14.9 3 74.9 0.254 0.438
0.0159 15.4 14.9 3 74.3 0.313 0.435
0.0159 15.4 14.9 3 75.6 0.352 0.436
0.0159 15.4 14.9 3 75.8 0.401 0.433
0.0159 15.4 14.9 3 75.2 0.453 0.430
0.0159 15.5 14.9 3 74.7 0.507 0.476
0.0159 15.3 14.8 3 75.4 0.555 0.500
0.0159 15.4 14.8 3 75.4 0.605 0.531
0.0159 15.3 14.8 3 75.1 0.659 0.563
0.0159 15.5 14.9 3 74.7 0.703 0.578
0.0159 15.4 14.8 3 75.0 0.755 0.618
0.0159 15.5 14.9 3 75.2 0.815 0.638
0.0159 15.2 14.6 3 75.3 0.855 0.656
0.0159 15.1 14.6 3 75.7 0.900 0.656
0.0159 15.4 14.9 3 75.5 0.956 0.571
0.0159 15.3 14.8 3 99.9 0.053 0.431
0.0159 15.2 14.7 3 100.4 0.106 0.465
0.0159 15.3 14.8 3 100.6 0.153 0.506
0.0159 15.4 14.9 3 99.6 0.203 0.527
0.0159 15.3 14.8 3 100.6 0.251 0.542
0.0159 15.2 14.6 3 100.0 0.305 0.577
0.0159 15.2 14.6 3 100.4 0.351 0.627
0.0159 15.4 14.8 3 100.3 0.405 0.661
0.0159 15.5 14.9 3 100.2 0.451 0.726
0.0159 15.2 14.6 3 100.2 0.504 0.831
0.0159 15.5 14.8 3 100.7 0.553 0.894
0.0159 15.4 14.7 3 99.5 0.607 0.976
0.0159 15.4 14.7 3 100.6 0.651 1.071
0.0159 15.4 14.7 3 100.1 0.707 1.155
0.0159 15.4 14.7 3 100.1 0.754 1.238
0.0159 15.4 14.6 3 100.6 0.808 1.284
0.0159 15.5 14.8 3 100.4 0.851 1.285
0.0159 15.3 14.6 3 100.3 0.907 1.240
0.0159 15.5 14.8 3 100.2 0.956 1.080
0.0159 15.4 14.8 3 150.4 0.053 0.572
Appendix B 229
D [m]
TTS,in
[oC] TTS,out
[oC] Y [-]
G [kg/m2 s]
x [-]
∆p [kPa/m]
0.0159 15.3 14.6 3 150.4 0.109 0.678
0.0159 15.5 14.9 3 149.8 0.153 0.751
0.0159 15.6 14.9 3 150.3 0.203 0.876
0.0159 15.5 14.9 3 150.6 0.252 1.031
0.0159 15.5 14.7 3 150.0 0.308 1.281
0.0159 15.5 14.7 3 150.5 0.353 1.431
0.0159 15.6 14.8 3 150.0 0.407 1.691
0.0159 15.4 14.5 3 150.3 0.456 1.976
0.0159 15.6 14.6 3 149.6 0.514 2.182
0.0159 15.7 14.7 3 150.1 0.554 2.392
0.0159 15.6 14.6 3 149.9 0.612 2.588
0.0159 15.6 14.5 3 150.4 0.653 2.740
0.0159 15.7 14.5 3 150.1 0.707 2.850
0.0159 15.6 14.4 3 150.4 0.754 2.974
0.0159 15.8 14.6 3 150.6 0.803 2.980
0.0159 15.6 14.4 3 150.1 0.855 3.010
0.0159 15.8 14.6 3 150.9 0.908 2.886
0.0159 15.6 14.5 3 149.7 0.969 2.468
0.0159 15.4 14.8 3 199.5 0.053 0.704
0.0159 15.5 14.8 3 199.9 0.107 0.956
0.0159 15.4 14.7 3 200.5 0.153 1.208
0.0159 15.6 14.8 3 199.7 0.208 1.519
0.0159 15.7 14.8 3 200.3 0.254 1.859
0.0159 15.7 14.7 3 200.2 0.307 2.288
0.0159 15.7 14.7 3 200.1 0.354 2.623
0.0159 15.7 14.5 3 200.8 0.404 3.055
0.0159 15.7 14.4 3 200.2 0.454 3.443
0.0159 15.8 14.4 3 200.6 0.508 3.875
0.0159 15.9 14.4 3 200.5 0.554 4.223
0.0159 16.0 14.4 3 200.5 0.609 4.584
0.0159 16.1 14.5 3 199.4 0.643 4.720
230
Appendix B
Table B.5 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 5 oC measured at each section of the of the test section inside 12.7 mm internal diameter tube
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 Plain tube 4.96 75.1 9.7 9.3 9.0 9.7 4.8 4.8 4.8 4.8 0.10 0.15 0.20 0.25 1.02 1.11 1.18 1.01
0.0127 Plain tube 4.99 74.9 9.8 9.6 9.2 9.8 5.0 5.0 5.0 5.0 0.15 0.20 0.25 0.30 1.03 1.08 1.19 1.03
0.0127 Plain tube 4.96 75.2 9.7 9.2 8.9 9.5 4.8 4.8 4.8 4.8 0.20 0.25 0.30 0.35 1.01 1.12 1.20 1.04
0.0127 Plain tube 4.95 74.6 9.7 9.3 9.0 9.8 4.9 4.9 4.9 4.8 0.25 0.30 0.35 0.40 1.03 1.11 1.20 1.00
0.0127 Plain tube 5.02 75.7 9.8 9.4 9.1 9.9 5.0 5.0 5.0 5.0 0.30 0.35 0.40 0.45 1.04 1.13 1.22 1.02
0.0127 Plain tube 4.98 75.5 9.8 9.4 9.1 10.0 4.9 4.9 4.9 4.9 0.36 0.41 0.45 0.50 1.03 1.11 1.21 0.99
0.0127 Plain tube 4.96 75.2 9.8 9.5 9.2 10.1 4.9 4.9 4.9 4.9 0.41 0.46 0.51 0.56 1.02 1.09 1.16 0.96
0.0127 Plain tube 4.96 75.3 10.0 9.7 9.4 10.3 5.1 5.1 5.1 5.0 0.45 0.50 0.55 0.60 1.02 1.08 1.14 0.95
0.0127 Plain tube 4.99 74.9 9.8 9.6 9.3 10.2 5.0 5.0 5.0 5.0 0.50 0.55 0.60 0.65 1.04 1.09 1.15 0.96
0.0127 Plain tube 5.01 75.8 10.0 9.7 9.4 10.3 5.0 5.0 5.0 5.0 0.55 0.60 0.65 0.70 1.02 1.07 1.14 0.94
0.0127 Plain tube 4.95 75.6 9.9 9.7 9.4 10.3 5.0 5.0 5.0 4.9 0.61 0.66 0.71 0.75 1.01 1.06 1.12 0.93
0.0127 Plain tube 4.96 74.6 9.9 9.7 9.4 10.3 4.9 4.9 4.8 4.8 0.67 0.72 0.77 0.82 1.00 1.04 1.09 0.91
0.0127 Plain tube 4.94 75.0 9.9 9.8 9.9 10.5 5.1 5.1 5.0 5.0 0.72 0.77 0.82 0.86 1.03 1.04 1.02 0.91
0.0127 Plain tube 4.95 75.1 9.9 9.9 10.0 10.6 5.0 5.0 5.0 5.0 0.77 0.82 0.87 0.92 1.02 1.02 0.99 0.88
0.0127 Plain tube 5.00 100.3 9.6 9.3 8.9 9.2 4.8 4.8 4.8 4.8 0.09 0.13 0.16 0.20 1.06 1.13 1.23 1.15
0.0127 Plain tube 4.94 101.8 9.5 9.1 8.6 9.1 4.8 4.8 4.8 4.8 0.14 0.18 0.21 0.25 1.06 1.16 1.32 1.15
0.0127 Plain tube 4.96 100.0 9.6 9.1 8.6 9.3 5.0 5.0 5.0 5.0 0.19 0.23 0.26 0.30 1.09 1.21 1.39 1.16
0.0127 Plain tube 5.00 100.4 9.5 9.1 8.6 9.5 5.1 5.1 5.1 5.1 0.24 0.28 0.32 0.36 1.13 1.24 1.42 1.13
0.0127 Plain tube 5.00 100.1 9.2 8.9 8.5 9.4 5.0 5.0 5.0 5.0 0.29 0.33 0.37 0.41 1.18 1.27 1.43 1.12
0.0127 Plain tube 5.01 100.7 9.3 9.0 8.5 9.5 5.0 5.0 5.0 5.0 0.34 0.38 0.42 0.45 1.19 1.28 1.43 1.13
0.0127 Plain tube 4.97 100.1 9.3 9.0 8.6 9.5 5.1 5.1 5.0 5.0 0.39 0.43 0.47 0.50 1.19 1.26 1.40 1.11
0.0127 Plain tube 5.00 101.1 9.3 9.1 8.7 9.6 5.1 5.1 5.1 5.0 0.44 0.48 0.51 0.55 1.18 1.25 1.39 1.10
0.0127 Plain tube 5.02 100.9 9.2 9.0 8.6 9.4 5.0 5.0 5.0 5.0 0.49 0.53 0.57 0.60 1.20 1.27 1.42 1.13
0.0127 Plain tube 4.99 100.2 9.2 9.0 8.6 9.4 5.0 5.0 5.0 4.9 0.54 0.58 0.62 0.65 1.20 1.26 1.40 1.13
0.0127 Plain tube 4.99 99.6 9.2 9.0 8.6 9.4 5.1 5.1 5.1 5.1 0.60 0.64 0.68 0.71 1.23 1.28 1.43 1.15
0.0127 Plain tube 4.99 101.0 9.2 9.0 8.6 9.4 5.1 5.1 5.1 5.1 0.64 0.67 0.71 0.75 1.24 1.29 1.44 1.16
A
ppendix B
231
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 Plain tube 5.00 100.2 9.1 9.0 8.6 9.3 5.0 5.0 5.0 5.0 0.70 0.74 0.78 0.81 1.24 1.28 1.41 1.17
0.0127 Plain tube 5.01 99.7 9.3 9.1 8.7 9.3 5.2 5.2 5.2 5.2 0.75 0.79 0.83 0.86 1.25 1.30 1.45 1.21
0.0127 Plain tube 4.96 150.2 9.0 8.7 8.5 8.9 5.0 5.0 5.0 5.0 0.08 0.10 0.13 0.15 1.24 1.35 1.43 1.27
0.0127 Plain tube 5.02 150 9.1 8.7 8.5 8.9 5.0 4.9 4.9 4.9 0.13 0.16 0.18 0.21 1.23 1.36 1.42 1.27
0.0127 Plain tube 5.01 150 8.8 8.5 8.4 8.8 5.0 5.0 5.0 5.0 0.18 0.20 0.23 0.25 1.31 1.42 1.48 1.30
0.0127 Plain tube 4.98 149.5 8.8 8.6 8.5 8.9 5.0 5.0 4.9 4.9 0.23 0.26 0.28 0.31 1.32 1.39 1.43 1.26
0.0127 Plain tube 4.94 150.4 8.8 8.5 8.4 8.8 5.0 5.0 4.9 4.9 0.28 0.30 0.33 0.35 1.31 1.39 1.45 1.27
0.0127 Plain tube 5.02 150.2 8.8 8.6 8.4 8.8 5.0 5.0 5.0 4.9 0.33 0.36 0.38 0.41 1.33 1.41 1.45 1.31
0.0127 Plain tube 5.01 150.4 8.9 8.6 8.4 8.8 5.2 5.2 5.2 5.1 0.38 0.41 0.43 0.46 1.38 1.47 1.57 1.37
0.0127 Plain tube 4.98 149.8 8.6 8.4 8.2 8.6 5.1 5.1 5.1 5.1 0.43 0.46 0.48 0.50 1.45 1.52 1.63 1.42
0.0127 Plain tube 4.94 150.1 8.3 8.2 7.9 8.4 5.1 5.1 5.1 5.0 0.48 0.50 0.53 0.55 1.57 1.61 1.77 1.50
0.0127 Plain tube 5.01 150.7 7.9 7.8 7.5 8.0 5.0 5.0 4.9 4.9 0.53 0.55 0.58 0.60 1.76 1.79 2.00 1.64
0.0127 Plain tube 4.97 150.1 7.6 7.6 7.2 7.6 5.1 5.1 5.0 5.0 0.58 0.60 0.63 0.65 1.97 2.00 2.28 1.90
0.0127 Plain tube 4.94 148.8 7.1 6.9 6.5 7.1 5.1 5.1 5.0 5.0 0.64 0.66 0.69 0.71 2.50 2.80 3.32 2.34
0.0127 Plain tube 4.94 150.1 6.7 6.7 6.5 7.1 5.2 5.2 5.1 5.1 0.68 0.70 0.73 0.75 3.46 3.29 3.57 2.42
0.0127 Plain tube 4.96 150.3 6.7 6.8 6.6 7.1 5.3 5.2 5.2 5.1 0.73 0.75 0.78 0.80 3.58 3.32 3.66 2.50
0.0127 Plain tube 4.99 150.1 6.6 6.6 6.4 7.0 5.3 5.2 5.2 5.1 0.78 0.81 0.83 0.86 3.78 3.57 3.97 2.62
0.0127 Plain tube 5.00 151.2 6.4 6.5 6.4 7.3 5.1 5.1 5.0 5.0 0.84 0.87 0.89 0.92 3.94 3.62 3.59 2.15
0.0127 Plain tube 4.93 199.9 8.6 8.6 8.4 8.6 4.9 4.9 4.9 4.9 0.07 0.09 0.11 0.12 1.35 1.35 1.43 1.34
0.0127 Plain tube 4.97 199.6 8.3 8.4 8.1 8.4 4.9 4.9 4.9 4.9 0.12 0.14 0.16 0.18 1.51 1.44 1.57 1.42
0.0127 Plain tube 4.98 199.7 8.4 8.4 8.2 8.4 5.1 5.1 5.1 5.0 0.17 0.19 0.21 0.23 1.53 1.49 1.60 1.50
0.0127 Plain tube 5.01 200.3 8.1 8.2 7.9 8.1 5.0 4.9 4.9 4.9 0.22 0.24 0.26 0.28 1.58 1.52 1.71 1.56
0.0127 Plain tube 4.98 199.5 8.0 8.1 7.6 7.9 5.0 5.0 4.9 4.9 0.27 0.29 0.31 0.33 1.65 1.61 1.91 1.69
0.0127 Plain tube 4.97 199.9 7.8 7.8 7.4 7.8 5.3 5.2 5.2 5.2 0.32 0.34 0.36 0.38 1.98 1.97 2.25 1.88
0.0127 Plain tube 4.94 200.1 7.2 7.4 7.0 7.4 5.3 5.2 5.2 5.1 0.37 0.39 0.41 0.43 2.52 2.24 2.73 2.21
0.0127 Plain tube 4.96 200.2 6.8 6.9 6.8 7.2 5.3 5.2 5.2 5.1 0.42 0.44 0.46 0.48 3.21 2.92 3.08 2.34
0.0127 Plain tube 5.01 201 6.8 6.9 6.7 7.1 5.3 5.2 5.1 5.1 0.47 0.49 0.51 0.53 3.23 2.93 3.17 2.45
0.0127 Plain tube 4.99 200.3 6.7 6.8 6.6 7.0 5.3 5.2 5.1 5.1 0.53 0.54 0.56 0.58 3.50 3.14 3.38 2.64
232
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 Plain tube 4.97 200.6 6.7 6.7 6.5 6.9 5.3 5.2 5.2 5.1 0.57 0.59 0.61 0.63 3.79 3.42 3.70 2.82
0.0127 Plain tube 4.97 200.3 6.7 6.8 6.6 6.9 5.5 5.4 5.3 5.3 0.62 0.64 0.66 0.68 4.15 3.72 4.02 3.00
0.0127 Plain tube 9.95 75.5 10.7 10.5 10.4 11.2 4.9 4.9 4.9 4.9 0.16 0.25 0.35 0.45 1.75 1.80 1.83 1.59
0.0127 Plain tube 9.94 75.9 10.9 10.7 10.6 11.4 5.1 5.1 5.1 5.1 0.20 0.30 0.40 0.49 1.72 1.79 1.83 1.59
0.0127 Plain tube 9.98 74.3 10.6 10.4 10.2 11.1 5.0 5.0 5.0 5.0 0.26 0.36 0.46 0.56 1.81 1.88 1.94 1.66
0.0127 Plain tube 9.89 75.6 10.9 10.6 10.5 11.2 5.0 5.0 5.0 5.0 0.31 0.40 0.50 0.60 1.70 1.79 1.82 1.61
0.0127 Plain tube 9.99 75.5 10.9 10.6 10.6 11.2 5.1 5.1 5.1 5.1 0.36 0.46 0.56 0.65 1.74 1.82 1.84 1.64
0.0127 Plain tube 9.89 76.2 11.0 10.8 10.8 11.4 5.0 5.0 5.0 5.0 0.42 0.52 0.61 0.71 1.66 1.71 1.72 1.57
0.0127 Plain tube 9.90 75.2 10.9 10.7 10.7 11.2 4.9 4.9 4.8 4.8 0.46 0.56 0.66 0.76 1.65 1.70 1.71 1.55
0.0127 Plain tube 9.97 76.4 11.2 11.0 11.0 11.8 5.1 5.0 5.0 5.0 0.51 0.60 0.70 0.80 1.64 1.67 1.68 1.48
0.0127 Plain tube 9.91 74.3 11.2 10.9 10.9 12.1 5.1 5.1 5.1 5.0 0.58 0.68 0.77 0.87 1.64 1.70 1.72 1.42
0.0127 Plain tube 9.93 74.6 11.1 10.9 10.9 12.6 4.9 4.9 4.9 4.9 0.57 0.67 0.77 0.87 1.62 1.68 1.67 1.29
0.0127 Plain tube 9.97 100.2 10.3 10.0 9.8 10.4 4.9 4.8 4.8 4.8 0.13 0.20 0.28 0.35 1.86 1.97 2.04 1.80
0.0127 Plain tube 9.97 102.0 10.5 10.3 10.1 10.8 5.0 5.0 5.0 5.0 0.17 0.25 0.32 0.39 1.83 1.92 1.98 1.74
0.0127 Plain tube 9.96 100.6 10.6 10.4 10.4 11.0 5.2 5.2 5.2 5.1 0.23 0.30 0.37 0.45 1.86 1.90 1.92 1.72
0.0127 Plain tube 9.94 99.1 10.6 10.3 10.3 10.9 5.2 5.2 5.2 5.2 0.29 0.37 0.44 0.51 1.84 1.96 1.95 1.75
0.0127 Plain tube 9.92 101.9 10.6 10.4 10.3 10.8 4.9 4.9 4.9 4.9 0.33 0.40 0.47 0.55 1.77 1.83 1.87 1.70
0.0127 Plain tube 9.94 99.9 10.7 10.4 10.4 10.8 5.0 5.0 5.0 5.0 0.38 0.46 0.53 0.61 1.78 1.85 1.87 1.73
0.0127 Plain tube 10.01 100.7 10.7 10.5 10.3 10.7 5.1 5.1 5.1 5.1 0.43 0.50 0.58 0.65 1.80 1.88 1.92 1.78
0.0127 Plain tube 9.93 100.2 10.7 10.5 10.3 10.7 5.1 5.0 5.0 5.0 0.49 0.56 0.64 0.71 1.77 1.85 1.90 1.76
0.0127 Plain tube 9.88 101.0 10.8 10.4 10.3 10.8 5.1 5.1 5.1 5.1 0.53 0.61 0.68 0.75 1.76 1.88 1.93 1.75
0.0127 Plain tube 9.93 99.4 10.7 10.3 10.1 10.8 5.0 5.0 5.0 5.0 0.59 0.67 0.74 0.82 1.77 1.89 1.94 1.71
0.0127 Plain tube 9.96 99.7 10.8 10.4 10.3 11.1 5.1 5.1 5.1 5.1 0.65 0.72 0.79 0.87 1.79 1.92 1.95 1.67
0.0127 Plain tube 9.99 99.3 10.6 10.3 10.2 12.1 5.0 5.0 5.0 5.0 0.70 0.77 0.85 0.92 1.81 1.93 1.93 1.42
0.0127 Plain tube 150.6 9.90 9.8 9.3 9.2 9.7 4.9 4.9 4.9 4.8 0.10 0.15 0.20 0.25 2.02 2.24 2.31 2.05
0.0127 Plain tube 149.6 9.96 10.0 9.6 9.4 10.0 5.1 5.1 5.1 5.1 0.15 0.20 0.25 0.30 2.04 2.22 2.30 2.03
0.0127 Plain tube 150.2 9.96 9.8 9.6 9.4 9.9 5.0 5.0 5.0 4.9 0.20 0.25 0.30 0.35 2.07 2.19 2.28 2.01
0.0127 Plain tube 150.6 9.96 9.8 9.6 9.4 9.9 5.0 5.0 5.0 5.0 0.26 0.31 0.35 0.40 2.11 2.19 2.29 2.03
A
ppendix B
233
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 Plain tube 149.8 9.90 9.9 9.6 9.4 9.8 5.0 5.0 5.0 5.0 0.30 0.35 0.40 0.45 2.04 2.16 2.28 2.06
0.0127 Plain tube 150.4 9.92 9.8 9.3 9.0 9.4 5.0 5.0 5.0 4.9 0.36 0.41 0.46 0.51 2.09 2.30 2.50 2.27
0.0127 Plain tube 150.7 9.97 9.8 9.4 9.0 9.3 5.0 5.0 5.0 5.0 0.40 0.45 0.50 0.55 2.10 2.31 2.51 2.32
0.0127 Plain tube 149.9 9.97 9.8 9.3 8.9 9.2 5.1 5.1 5.1 5.0 0.45 0.50 0.55 0.60 2.15 2.39 2.65 2.43
0.0127 Plain tube 151.2 9.94 9.6 9.1 8.6 8.7 5.1 5.1 5.0 5.0 0.50 0.55 0.60 0.65 2.25 2.51 2.82 2.66
0.0127 Plain tube 150.5 9.89 9.5 8.9 8.3 8.5 5.3 5.2 5.2 5.1 0.56 0.61 0.66 0.71 2.36 2.68 3.21 2.92
0.0127 Plain tube 150.8 9.93 9.3 8.7 8.0 8.5 5.3 5.3 5.2 5.2 0.61 0.66 0.71 0.76 2.52 2.88 3.59 3.03
0.0127 Plain tube 149.5 9.90 8.9 8.3 7.9 8.6 5.1 5.1 5.0 5.0 0.66 0.71 0.76 0.81 2.68 3.17 3.57 2.74
0.0127 Plain tube 151.1 9.92 8.2 8.1 7.8 8.8 5.1 5.0 5.0 4.9 0.72 0.77 0.81 0.86 3.28 3.33 3.56 2.56
0.0127 Plain tube 150.2 9.89 8.2 8.1 7.9 9.0 5.3 5.2 5.1 5.1 0.75 0.80 0.85 0.90 3.47 3.51 3.64 2.54
0.0127 Plain tube 200.7 9.92 9.7 9.3 9.1 9.5 5.1 5.1 5.1 5.0 0.09 0.13 0.16 0.20 2.15 2.35 2.51 2.26
0.0127 Plain tube 199.6 9.95 9.5 9.1 8.8 9.2 4.9 4.9 4.9 4.9 0.14 0.18 0.21 0.25 2.22 2.42 2.59 2.33
0.0127 Plain tube 199.1 9.94 9.4 9.2 8.9 9.3 5.1 5.1 5.0 5.0 0.19 0.23 0.27 0.30 2.31 2.44 2.59 2.35
0.0127 Plain tube 200.3 9.96 9.5 9.2 8.9 9.2 5.2 5.1 5.1 5.1 0.24 0.28 0.32 0.35 2.29 2.47 2.67 2.41
0.0127 Plain tube 199.4 9.99 9.5 9.0 8.6 8.9 5.1 5.0 5.0 5.0 0.30 0.34 0.38 0.41 2.29 2.54 2.80 2.56
0.0127 Plain tube 200 10.00 9.3 8.9 8.4 8.6 5.1 5.1 5.0 5.0 0.34 0.38 0.42 0.45 2.40 2.65 2.99 2.80
0.0127 Plain tube 199.3 10.01 9.1 8.7 8.0 8.5 5.2 5.2 5.1 5.1 0.40 0.43 0.47 0.51 2.58 2.86 3.46 2.96
0.0127 Plain tube 199.2 9.95 8.7 8.2 7.9 8.5 5.4 5.3 5.2 5.2 0.45 0.49 0.52 0.56 2.99 3.48 3.75 3.02
0.0127 Plain tube 200.6 10.00 7.9 7.8 7.5 8.1 5.1 5.0 5.0 4.9 0.50 0.53 0.57 0.61 3.69 3.63 3.97 3.18
0.0127 Plain tube 200.5 9.95 8.0 7.9 7.6 8.1 5.3 5.2 5.1 5.0 0.55 0.58 0.62 0.66 3.78 3.72 4.06 3.24
0.0127 Plain tube 199.5 9.98 8.0 8.0 7.7 8.2 5.5 5.4 5.3 5.2 0.61 0.64 0.68 0.72 3.98 3.89 4.27 3.33
0.0127 Plain tube 200.2 10.02 8.0 7.9 7.6 8.2 5.5 5.4 5.3 5.2 0.65 0.68 0.72 0.76 4.15 4.04 4.44 3.41
0.0127 Plain tube 199.4 9.98 7.8 7.8 7.5 8.1 5.6 5.5 5.4 5.3 0.69 0.72 0.76 0.80 4.47 4.27 4.70 3.60
0.0127 14 74.9 4.99 8.2 8.1 7.8 8.3 4.9 4.9 4.9 4.8 0.11 0.16 0.21 0.26 1.50 1.57 1.68 1.46
0.0127 14 75.8 4.94 8.3 8.2 7.9 8.4 5.1 5.1 5.1 5.0 0.16 0.20 0.25 0.30 1.54 1.61 1.73 1.49
0.0127 14 75.0 4.97 8.5 8.3 8.0 8.6 5.0 5.0 5.0 4.9 0.21 0.25 0.30 0.35 1.43 1.52 1.64 1.38
0.0127 14 75.4 5.01 8.3 8.3 8.1 8.6 5.0 5.0 5.0 5.0 0.26 0.31 0.36 0.41 1.53 1.55 1.64 1.39
0.0127 14 75.4 4.96 8.4 8.1 8.2 8.6 4.9 4.8 4.8 4.8 0.31 0.35 0.40 0.45 1.40 1.53 1.46 1.32
234
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 14 75.7 4.98 8.4 8.1 8.4 8.5 4.9 4.9 4.9 4.9 0.35 0.40 0.45 0.50 1.46 1.57 1.43 1.39
0.0127 14 75.0 4.96 8.2 8.1 8.5 8.3 4.9 4.9 4.9 4.9 0.41 0.46 0.51 0.56 1.52 1.58 1.38 1.46
0.0127 14 75.1 5.00 8.2 8.1 8.6 8.3 4.9 4.9 4.9 4.9 0.48 0.53 0.58 0.63 1.55 1.60 1.36 1.47
0.0127 14 75.4 4.96 8.3 8.2 8.8 8.4 5.1 5.1 5.1 5.1 0.50 0.55 0.60 0.65 1.58 1.62 1.36 1.49
0.0127 14 74.3 4.95 8.3 8.0 8.6 8.3 4.8 4.7 4.7 4.7 0.59 0.64 0.69 0.74 1.43 1.55 1.27 1.39
0.0127 14 75.6 4.93 8.2 8.0 8.6 8.2 4.8 4.8 4.8 4.8 0.62 0.67 0.72 0.77 1.48 1.58 1.29 1.45
0.0127 14 75.8 4.99 8.6 8.3 9.1 9.4 5.0 5.0 5.0 4.9 0.67 0.72 0.76 0.81 1.42 1.51 1.22 1.13
0.0127 14 75.8 5.00 8.6 8.6 9.4 11.1 4.9 4.9 4.9 4.9 0.74 0.79 0.84 0.88 1.37 1.36 1.10 0.80
0.0127 14 73.0 4.99 8.6 8.7 9.5 10.7 5.1 5.1 5.0 5.0 0.81 0.86 0.91 0.96 1.42 1.39 1.13 0.88
0.0127 14 100.6 4.97 8.0 7.8 7.6 8.0 5.0 5.0 4.9 4.9 0.09 0.13 0.16 0.20 1.68 1.77 1.89 1.64
0.0127 14 100.5 4.96 8.3 8.1 7.8 8.2 5.2 5.2 5.2 5.2 0.14 0.18 0.21 0.25 1.61 1.75 1.91 1.67
0.0127 14 99.1 4.97 7.8 7.7 7.6 8.0 5.0 5.0 5.0 5.0 0.20 0.23 0.27 0.31 1.79 1.84 1.93 1.67
0.0127 14 102.3 4.98 7.5 7.4 7.4 7.6 4.9 4.8 4.8 4.8 0.25 0.28 0.32 0.35 1.90 1.98 1.92 1.76
0.0127 14 149.9 4.95 7.8 7.7 7.4 7.8 5.1 5.1 5.0 5.0 0.08 0.10 0.13 0.15 1.82 1.91 2.07 1.81
0.0127 14 149.7 4.96 7.5 7.5 7.3 7.7 5.1 5.1 5.1 5.1 0.13 0.15 0.18 0.20 2.08 2.10 2.23 1.92
0.0127 14 149.8 4.98 7.4 7.5 7.2 7.5 5.2 5.2 5.2 5.1 0.18 0.20 0.23 0.25 2.32 2.24 2.47 2.08
0.0127 14 150.3 5.00 7.1 7.2 6.9 7.3 5.0 5.0 5.0 4.9 0.23 0.25 0.28 0.30 2.50 2.28 2.56 2.14
0.0127 14 151.4 5.00 7.2 7.4 7.0 7.5 5.3 5.2 5.2 5.1 0.28 0.30 0.32 0.35 2.63 2.36 2.76 2.16
0.0127 14 151.9 4.98 6.8 7.0 6.7 7.1 5.2 5.1 5.0 5.0 0.33 0.36 0.38 0.40 2.98 2.64 3.01 2.33
0.0127 14 199.7 5.02 7.4 7.3 7.1 7.5 5.0 5.0 5.0 5.0 0.07 0.09 0.11 0.13 2.15 2.18 2.42 2.03
0.0127 14 200.2 5.01 7.1 7.2 6.9 7.3 5.0 5.0 5.0 5.0 0.12 0.14 0.16 0.18 2.45 2.36 2.78 2.18
0.0127 14 199.9 4.93 6.9 7.0 6.7 7.2 5.1 5.1 5.0 5.0 0.17 0.19 0.21 0.22 2.74 2.51 3.03 2.30
0.0127 14 199.6 4.94 7.0 7.1 6.7 7.3 5.3 5.3 5.3 5.3 0.23 0.24 0.26 0.28 3.05 2.81 3.43 2.48
0.0127 14 200 4.97 6.8 6.8 6.5 7.0 5.3 5.2 5.2 5.2 0.27 0.29 0.31 0.33 3.36 3.18 3.92 2.70
0.0127 14 199.7 5.01 6.6 6.7 6.4 6.8 5.3 5.2 5.2 5.1 0.33 0.34 0.36 0.38 3.76 3.54 4.17 3.00
0.0127 14 199.8 4.98 6.7 6.6 6.4 6.8 5.5 5.4 5.3 5.3 0.37 0.39 0.41 0.43 4.27 4.11 4.84 3.33
0.0127 14 75.6 9.90 9.8 9.3 9.1 10.2 4.9 4.9 4.9 4.8 0.15 0.25 0.34 0.44 2.03 2.27 2.33 1.86
0.0127 14 75.6 9.87 9.8 9.3 9.2 10.1 5.1 5.1 5.1 5.1 0.20 0.30 0.40 0.49 2.13 2.38 2.47 1.99
A
ppendix B
235
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 14 75.5 9.96 10.1 9.3 9.6 10.3 5.0 5.0 4.9 4.9 0.25 0.35 0.45 0.55 1.97 2.34 2.17 1.86
0.0127 14 75.3 9.93 10.1 9.4 9.8 10.3 5.1 5.1 5.0 5.0 0.31 0.41 0.51 0.60 1.98 2.34 2.09 1.89
0.0127 14 76.3 9.95 10.2 9.3 9.7 9.7 5.1 5.1 5.1 5.0 0.34 0.44 0.54 0.63 1.97 2.37 2.17 2.13
0.0127 14 75.6 9.95 9.7 8.9 9.5 9.5 4.9 4.9 4.8 4.8 0.39 0.49 0.59 0.69 2.09 2.49 2.18 2.14
0.0127 14 74.4 9.93 9.6 8.9 9.5 9.4 4.9 4.9 4.9 4.8 0.44 0.54 0.64 0.74 2.12 2.47 2.17 2.21
0.0127 14 75.4 9.92 9.8 9.0 9.7 9.7 4.9 4.9 4.8 4.8 0.46 0.56 0.66 0.76 2.04 2.40 2.07 2.04
0.0127 14 100.4 9.89 9.4 8.9 8.8 9.3 5.0 5.0 5.0 5.0 0.13 0.20 0.28 0.35 2.28 2.56 2.62 2.28
0.0127 14 100.5 9.90 9.5 8.9 9.0 9.4 5.1 5.1 5.1 5.0 0.18 0.25 0.33 0.40 2.29 2.62 2.53 2.31
0.0127 14 99.47 9.98 9.3 8.9 9.1 9.2 5.1 5.1 5.0 5.0 0.23 0.30 0.38 0.45 2.37 2.65 2.46 2.38
0.0127 14 100.1 9.97 9.0 8.7 9.2 9.0 5.0 5.0 4.9 4.9 0.29 0.36 0.43 0.51 2.48 2.71 2.38 2.42
0.0127 14 97.81 10.01 8.8 8.6 8.6 8.7 5.2 5.2 5.2 5.1 0.34 0.42 0.50 0.57 2.85 3.01 2.92 2.81
0.0127 14 102.1 9.92 8.5 8.3 8.6 8.4 5.0 5.0 4.9 4.9 0.37 0.45 0.52 0.59 2.92 3.05 2.73 2.87
0.0127 14 150.4 9.93 9.0 8.6 8.6 8.7 5.2 5.1 5.1 5.1 0.10 0.15 0.20 0.25 2.61 2.88 2.92 2.74
0.0127 14 150.8 9.96 8.8 8.6 8.5 8.7 5.3 5.2 5.2 5.2 0.15 0.20 0.25 0.30 2.82 3.04 3.05 2.87
0.0127 14 149.7 9.94 8.3 8.2 8.0 8.2 5.0 4.9 4.9 4.8 0.20 0.25 0.30 0.35 3.02 3.13 3.23 2.95
0.0127 14 150.8 9.96 8.3 8.2 8.0 8.2 5.1 5.0 5.0 4.9 0.25 0.30 0.35 0.40 3.12 3.21 3.34 3.03
0.0127 14 148.7 9.87 7.9 7.9 7.6 7.7 5.5 5.4 5.3 5.2 0.41 0.46 0.51 0.56 4.07 4.03 4.50 4.01
0.0127 14 200.5 9.89 8.6 8.3 8.1 8.3 5.1 5.1 5.1 5.1 0.09 0.13 0.16 0.20 2.89 3.10 3.32 3.06
0.0127 14 199.7 9.98 8.39 8.30 8.01 8.30 5.22 5.20 5.19 5.17 0.14 0.18 0.22 0.25 3.19 3.26 3.59 3.23
0.0127 14 200.1 9.88 8.23 8.22 7.91 8.19 5.27 5.25 5.22 5.19 0.19 0.23 0.27 0.30 3.38 3.38 3.74 3.34
0.0127 14 200.4 9.91 8.22 8.17 7.84 8.17 5.44 5.41 5.37 5.33 0.24 0.28 0.31 0.35 3.61 3.65 4.08 3.53
0.0127 14 200.4 9.93 8.11 8.03 7.72 8.04 5.48 5.44 5.39 5.33 0.29 0.33 0.37 0.40 3.84 3.91 4.34 3.71
0.0127 14 198.8 9.94 8.12 8.02 7.70 8.02 5.63 5.57 5.50 5.42 0.35 0.39 0.42 0.46 4.07 4.14 4.62 3.89
0.0127 14 200.6 9.82 8.02 7.89 7.60 7.86 5.74 5.67 5.58 5.48 0.39 0.43 0.47 0.50 4.39 4.51 4.97 4.20
0.0127 14 201.6 9.87 7.80 7.70 7.41 7.68 5.61 5.52 5.42 5.30 0.44 0.47 0.51 0.55 4.60 4.63 5.07 4.23
0.0127 14 200.9 9.98 7.82 7.73 7.45 7.75 5.64 5.54 5.42 5.29 0.48 0.52 0.55 0.59 4.68 4.64 5.02 4.13
0.0127 9 75.5 5.02 8.92 8.15 8.03 8.73 5.00 4.99 4.98 4.97 0.10 0.15 0.20 0.25 1.29 1.60 1.66 1.34
0.0127 9 76.5 5.00 8.81 8.05 7.93 8.56 4.97 4.96 4.95 4.94 0.16 0.20 0.25 0.30 1.31 1.63 1.69 1.39
236
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 9 75.2 5.01 8.59 8.19 7.85 8.60 4.94 4.93 4.92 4.91 0.20 0.25 0.30 0.35 1.38 1.55 1.73 1.37
0.0127 9 75.3 4.98 8.69 8.68 8.13 9.03 5.25 5.24 5.23 5.21 0.26 0.31 0.35 0.40 1.46 1.46 1.73 1.31
0.0127 9 74.8 4.93 8.52 8.63 8.13 8.68 5.22 5.20 5.19 5.17 0.31 0.36 0.41 0.45 1.50 1.45 1.69 1.41
0.0127 9 76.0 4.99 8.59 8.73 8.10 8.74 5.15 5.14 5.12 5.11 0.35 0.40 0.45 0.50 1.46 1.40 1.69 1.38
0.0127 9 75.8 4.99 8.67 8.62 8.10 8.62 5.12 5.11 5.09 5.07 0.40 0.45 0.50 0.55 1.42 1.43 1.67 1.41
0.0127 9 74.3 4.96 8.71 8.68 8.25 8.85 5.18 5.16 5.14 5.12 0.46 0.51 0.56 0.61 1.41 1.42 1.61 1.33
0.0127 9 74.9 4.97 8.71 8.44 8.01 8.52 4.92 4.90 4.88 4.86 0.50 0.55 0.60 0.65 1.32 1.41 1.60 1.36
0.0127 9 75.8 4.98 9.02 8.71 8.35 8.74 5.20 5.18 5.16 5.13 0.56 0.61 0.66 0.70 1.31 1.42 1.57 1.39
0.0127 9 75.7 4.96 8.73 8.36 7.96 8.23 4.86 4.83 4.81 4.78 0.61 0.66 0.71 0.76 1.29 1.41 1.59 1.45
0.0127 9 75.5 4.95 8.84 8.44 8.13 8.66 5.02 5.00 4.97 4.94 0.66 0.71 0.76 0.81 1.31 1.45 1.58 1.34
0.0127 9 101.1 4.95 8.50 8.07 7.21 7.96 4.79 4.78 4.77 4.75 0.09 0.12 0.16 0.20 1.34 1.51 2.04 1.55
0.0127 9 99.4 4.94 8.24 7.99 7.10 7.76 4.72 4.71 4.69 4.67 0.15 0.19 0.22 0.26 1.42 1.52 2.07 1.61
0.0127 9 101.5 4.98 8.51 8.46 7.48 8.18 5.09 5.08 5.06 5.04 0.18 0.22 0.26 0.29 1.47 1.48 2.07 1.60
0.0127 9 100.0 4.96 8.40 8.52 7.57 8.03 5.25 5.23 5.21 5.19 0.24 0.28 0.31 0.35 1.58 1.52 2.12 1.76
0.0127 9 100.9 4.96 8.11 8.17 7.04 7.50 4.82 4.80 4.78 4.75 0.29 0.33 0.37 0.40 1.52 1.48 2.22 1.82
0.0127 9 100.0 4.97 8.31 8.29 7.16 7.56 5.05 5.03 5.00 4.97 0.34 0.38 0.42 0.46 1.54 1.53 2.32 1.94
0.0127 9 99.7 4.96 8.19 8.17 7.00 7.27 5.02 5.00 4.96 4.93 0.39 0.43 0.46 0.50 1.58 1.57 2.46 2.14
0.0127 9 100.0 4.96 7.99 7.96 6.83 7.05 4.92 4.89 4.85 4.81 0.44 0.48 0.52 0.55 1.63 1.63 2.53 2.23
0.0127 9 99.8 5.02 8.09 8.05 6.93 7.21 5.15 5.11 5.07 5.03 0.49 0.53 0.57 0.61 1.72 1.72 2.74 2.33
0.0127 9 99.9 5.02 8.05 7.78 6.98 7.22 5.18 5.14 5.10 5.06 0.55 0.58 0.62 0.66 1.77 1.92 2.70 2.34
0.0127 9 150.2 4.96 8.13 8.03 7.43 7.93 5.25 5.23 5.21 5.18 0.08 0.10 0.13 0.15 1.74 1.78 2.25 1.82
0.0127 9 149.8 5.00 7.27 7.39 6.92 7.32 4.88 4.85 4.82 4.79 0.13 0.16 0.18 0.21 2.11 1.98 2.41 1.99
0.0127 9 150.7 4.99 7.22 7.29 7.08 7.41 5.12 5.09 5.05 5.01 0.18 0.20 0.23 0.25 2.40 2.29 2.48 2.10
0.0127 9 150.9 4.94 6.97 6.95 6.85 7.17 5.02 4.98 4.93 4.88 0.23 0.26 0.28 0.30 2.56 2.52 2.61 2.18
0.0127 9 149.6 5.00 7.13 7.05 6.89 7.30 5.22 5.17 5.12 5.07 0.29 0.31 0.34 0.36 2.64 2.69 2.85 2.26
0.0127 9 200.4 5.00 7.32 7.37 7.11 7.47 5.07 5.04 5.01 4.97 0.07 0.09 0.11 0.13 2.25 2.17 2.40 2.02
0.0127 9 200.1 5.01 7.07 7.16 6.84 7.32 5.07 5.03 4.98 4.93 0.12 0.14 0.16 0.18 2.53 2.37 2.73 2.12
0.0127 9 200.4 4.98 7.10 7.14 6.84 7.33 5.24 5.19 5.12 5.06 0.17 0.19 0.21 0.23 2.72 2.57 2.94 2.21
A
ppendix B
237
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 9 199.6 4.97 7.08 7.08 6.83 7.22 5.34 5.27 5.19 5.10 0.22 0.24 0.26 0.28 2.89 2.78 3.06 2.36
0.0127 9 202 4.98 6.96 6.93 6.72 7.14 5.23 5.14 5.04 4.93 0.27 0.28 0.30 0.32 2.91 2.81 2.99 2.28
0.0127 9 74.9 9.94 10.20 9.84 9.28 10.5 5.21 5.20 5.18 5.17 0.15 0.25 0.35 0.45 2.02 2.16 2.45 1.87
0.0127 9 75.2 9.92 9.82 9.71 9.11 10.4 4.99 4.98 4.96 4.95 0.20 0.30 0.40 0.49 2.07 2.12 2.42 1.83
0.0127 9 74.8 9.98 9.89 9.79 9.25 10.4 5.13 5.12 5.10 5.08 0.26 0.36 0.46 0.55 2.12 2.16 2.43 1.90
0.0127 9 76.3 9.96 9.66 9.37 9.13 10.1 4.99 4.97 4.96 4.93 0.30 0.40 0.50 0.59 2.15 2.29 2.41 1.94
0.0127 9 101.1 9.93 9.39 9.20 8.59 9.51 4.99 4.97 4.95 4.93 0.13 0.20 0.27 0.34 2.28 2.37 2.76 2.19
0.0127 9 98.2 9.89 9.44 9.32 8.79 9.49 5.11 5.09 5.07 5.05 0.19 0.26 0.34 0.41 2.31 2.36 2.69 2.25
0.0127 9 100.5 9.90 9.35 9.24 8.77 9.21 5.14 5.12 5.10 5.07 0.23 0.30 0.37 0.45 2.38 2.43 2.73 2.42
0.0127 9 101.6 9.87 9.07 8.69 8.42 8.49 5.05 5.02 5.00 4.96 0.27 0.35 0.42 0.49 2.48 2.73 2.92 2.83
0.0127 9 99.3 9.91 8.84 8.53 8.23 8.39 5.00 4.97 4.94 4.90 0.34 0.41 0.48 0.56 2.61 2.82 3.05 2.87
0.0127 9 100.0 9.96 9.20 8.65 8.45 8.61 5.23 5.19 5.16 5.11 0.40 0.47 0.55 0.62 2.53 2.91 3.06 2.89
0.0127 9 101.6 9.95 9.64 8.76 8.37 8.43 5.02 4.98 4.94 4.90 0.45 0.53 0.60 0.67 2.17 2.66 2.94 2.85
0.0127 9 150.4 9.94 9.33 9.07 8.42 8.91 5.13 5.11 5.08 5.04 0.10 0.15 0.20 0.25 2.39 2.54 3.01 2.60
0.0127 9 150.9 9.88 9.07 8.92 8.32 8.76 5.18 5.15 5.11 5.07 0.15 0.20 0.25 0.30 2.57 2.65 3.12 2.70
0.0127 9 150.3 9.92 8.52 8.42 8.04 8.47 5.03 4.99 4.94 4.89 0.21 0.25 0.30 0.35 2.87 2.92 3.24 2.80
0.0127 9 150.1 9.89 8.66 8.63 8.28 8.70 5.32 5.27 5.22 5.16 0.25 0.30 0.35 0.40 3.00 2.98 3.28 2.84
0.0127 9 151.2 9.90 8.33 8.33 8.02 8.47 5.13 5.08 5.02 4.96 0.30 0.35 0.40 0.45 3.13 3.09 3.35 2.86
0.0127 9 147.8 9.94 8.08 8.02 7.74 8.38 5.08 5.02 4.96 4.90 0.39 0.44 0.49 0.54 3.36 3.36 3.63 2.89
0.0127 9 200.1 9.95 8.48 8.29 8.00 8.39 5.02 4.99 4.94 4.88 0.09 0.13 0.17 0.20 2.92 3.05 3.29 2.87
0.0127 9 199.9 9.89 8.16 8.06 7.71 8.17 4.95 4.90 4.84 4.76 0.14 0.18 0.22 0.25 3.12 3.17 3.49 2.93
0.0127 9 200.9 9.90 8.28 8.23 7.87 8.31 5.28 5.21 5.13 5.04 0.19 0.23 0.26 0.30 3.34 3.33 3.68 3.07
0.0127 9 200 9.88 8.24 8.13 7.79 8.18 5.34 5.25 5.15 5.03 0.24 0.28 0.32 0.35 3.46 3.49 3.81 3.18
0.0127 9 199.6 9.92 8.06 7.99 7.68 7.99 5.31 5.21 5.08 4.95 0.29 0.33 0.37 0.40 3.66 3.61 3.88 3.31
0.0127 9 200.1 9.92 7.89 7.81 7.46 7.76 5.27 5.14 4.99 4.84 0.34 0.38 0.42 0.45 3.84 3.77 4.10 3.44
0.0127 9 200.7 9.90 7.75 7.70 7.36 7.65 5.34 5.20 5.04 4.87 0.39 0.42 0.46 0.50 4.18 4.02 4.35 3.61
0.0127 9 201.4 9.89 7.72 7.60 7.25 7.61 5.38 5.21 5.04 4.85 0.44 0.48 0.51 0.55 4.30 4.22 4.56 3.64
0.0127 9 199.3 9.91 7.75 7.64 7.24 7.47 5.63 5.45 5.26 5.06 0.49 0.53 0.57 0.60 4.76 4.62 5.12 4.19
238
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 4 75.4 4.95 7.14 7.45 7.14 7.64 4.87 4.85 4.83 4.82 0.10 0.15 0.20 0.25 2.21 1.93 2.17 1.77
0.0127 4 74.8 4.97 7.35 7.54 7.23 7.76 5.07 5.06 5.04 5.02 0.16 0.21 0.26 0.30 2.21 2.02 2.30 1.83
0.0127 4 75.4 4.99 7.21 7.38 7.11 7.60 5.00 4.98 4.96 4.94 0.20 0.25 0.30 0.35 2.28 2.09 2.34 1.89
0.0127 4 75.3 4.99 7.12 7.30 7.02 7.48 4.93 4.91 4.89 4.87 0.26 0.31 0.35 0.40 2.30 2.11 2.37 1.93
0.0127 4 76.2 4.97 7.18 7.39 7.08 7.55 5.14 5.12 5.10 5.07 0.30 0.35 0.40 0.45 2.46 2.21 2.53 2.03
0.0127 4 75.4 5.02 7.19 7.45 7.16 7.57 5.22 5.20 5.17 5.15 0.35 0.40 0.45 0.50 2.58 2.25 2.55 2.09
0.0127 4 74.9 4.93 6.83 7.07 6.78 7.22 4.93 4.90 4.88 4.85 0.41 0.46 0.51 0.56 2.63 2.29 2.61 2.09
0.0127 4 74.7 4.96 7.02 7.22 6.89 7.39 5.13 5.11 5.08 5.05 0.47 0.51 0.56 0.61 2.66 2.38 2.77 2.14
0.0127 4 75.3 4.99 7.02 7.14 6.92 7.38 5.16 5.13 5.10 5.07 0.50 0.55 0.60 0.65 2.72 2.52 2.77 2.18
0.0127 4 75.0 4.98 7.04 7.19 7.01 7.41 5.26 5.23 5.20 5.16 0.57 0.62 0.66 0.71 2.85 2.58 2.78 2.24
0.0127 4 100.2 5.00 7.11 7.38 7.13 7.58 4.97 4.95 4.93 4.90 0.09 0.13 0.16 0.20 2.36 2.07 2.29 1.88
0.0127 4 101.1 4.98 7.29 7.54 7.28 7.74 5.18 5.15 5.13 5.10 0.14 0.17 0.21 0.25 2.38 2.11 2.33 1.91
0.0127 4 99.7 5.01 6.99 7.18 6.96 7.42 4.92 4.89 4.86 4.83 0.19 0.23 0.27 0.30 2.44 2.21 2.42 1.95
0.0127 4 99.4 4.99 7.06 7.25 7.05 7.47 5.11 5.08 5.04 5.01 0.25 0.28 0.32 0.36 2.58 2.32 2.51 2.05
0.0127 4 100.0 5.00 7.02 7.12 6.98 7.41 5.06 5.02 4.99 4.95 0.29 0.33 0.36 0.40 2.58 2.41 2.54 2.05
0.0127 4 100.3 5.01 7.08 7.15 7.02 7.45 5.15 5.11 5.07 5.03 0.34 0.38 0.41 0.45 2.63 2.49 2.60 2.08
0.0127 4 98.9 4.99 6.83 6.88 6.77 7.19 4.97 4.92 4.87 4.82 0.40 0.44 0.48 0.52 2.71 2.57 2.67 2.13
0.0127 4 100.5 5.06 7.03 7.10 6.96 7.40 5.16 5.11 5.06 5.01 0.45 0.49 0.53 0.56 2.73 2.58 2.69 2.13
0.0127 4 97.9 5.03 6.96 7.06 6.86 7.39 5.22 5.16 5.11 5.06 0.51 0.55 0.59 0.62 2.92 2.68 2.91 2.17
0.0127 4 150.3 4.95 7.22 7.43 7.24 7.62 5.20 5.17 5.13 5.10 0.08 0.10 0.13 0.15 2.47 2.21 2.38 1.97
0.0127 4 149.8 4.94 7.20 7.38 7.18 7.55 5.23 5.19 5.15 5.10 0.13 0.15 0.18 0.20 2.54 2.28 2.46 2.04
0.0127 4 149.5 4.97 6.98 7.08 6.89 7.25 5.05 5.01 4.95 4.89 0.18 0.20 0.23 0.25 2.61 2.42 2.59 2.12
0.0127 4 149.8 4.94 6.90 6.96 6.73 7.13 5.07 5.01 4.94 4.87 0.23 0.26 0.28 0.31 2.72 2.56 2.80 2.21
0.0127 4 201.1 5.01 7.16 7.34 7.09 7.46 5.17 5.14 5.09 5.04 0.07 0.09 0.11 0.13 2.55 2.30 2.54 2.08
0.0127 4 200.5 4.99 7.11 7.18 6.92 7.30 5.20 5.14 5.07 5.00 0.12 0.14 0.16 0.18 2.64 2.47 2.73 2.19
0.0127 4 200.5 4.95 6.86 6.92 6.67 7.00 5.17 5.09 5.00 4.90 0.17 0.19 0.21 0.23 2.97 2.73 2.99 2.38
0.0127 4 199.9 4.95 6.83 6.89 6.59 6.94 5.35 5.25 5.13 5.01 0.22 0.24 0.26 0.28 3.39 3.06 3.45 2.59
0.0127 4 199.9 4.96 6.79 6.87 6.61 6.93 5.41 5.28 5.14 5.00 0.27 0.29 0.31 0.33 3.63 3.17 3.43 2.59
A
ppendix B
239
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 4 200.1 4.99 6.51 6.60 6.30 6.60 5.37 5.21 5.04 4.87 0.33 0.35 0.37 0.39 4.42 3.66 4.04 2.92
0.0127 4 199.2 4.83 6.75 6.78 6.47 6.81 5.66 5.49 5.31 5.12 0.36 0.38 0.40 0.42 4.49 3.80 4.25 2.90
0.0127 4 197.9 4.97 6.71 6.73 6.41 6.73 5.71 5.52 5.31 5.09 0.41 0.43 0.45 0.47 5.08 4.17 4.60 3.08
0.0127 4 75.7 10.0 8.81 8.77 8.59 8.92 5.07 5.05 5.03 5.00 0.15 0.25 0.35 0.44 2.7 2.7 2.8 2.6
0.0127 4 75.6 10.1 8.87 8.80 8.59 8.86 5.21 5.19 5.17 5.14 0.21 0.31 0.41 0.51 2.8 2.8 3.0 2.7
0.0127 4 75.4 10.0 8.41 8.34 8.04 8.32 4.84 4.82 4.79 4.76 0.26 0.36 0.45 0.55 2.8 2.9 3.1 2.8
0.0127 4 74.6 9.9 8.49 8.43 8.14 8.44 5.03 5.01 4.98 4.95 0.32 0.42 0.52 0.62 2.9 2.9 3.2 2.9
0.0127 4 74.9 10.0 8.61 8.60 8.34 8.70 5.37 5.34 5.31 5.28 0.38 0.48 0.58 0.67 3.1 3.1 3.4 3.0
0.0127 4 100.3 9.87 8.66 8.57 8.34 8.79 5.17 5.14 5.11 5.08 0.12 0.20 0.27 0.34 2.8 2.9 3.1 2.7
0.0127 4 100.4 9.86 8.49 8.43 8.17 8.61 5.10 5.07 5.04 5.00 0.18 0.25 0.33 0.40 2.9 2.9 3.2 2.7
0.0127 4 99.3 9.86 8.38 8.30 8.03 8.49 5.06 5.03 4.99 4.94 0.23 0.31 0.38 0.45 3.0 3.0 3.3 2.8
0.0127 4 99.1 9.86 8.10 8.06 7.79 8.21 5.01 4.97 4.92 4.87 0.31 0.38 0.45 0.53 3.2 3.2 3.4 3.0
0.0127 4 99.5 9.93 8.34 8.33 8.15 8.57 5.36 5.31 5.26 5.20 0.38 0.46 0.53 0.61 3.3 3.3 3.4 3.0
0.0127 4 150.7 9.97 8.42 8.35 8.10 8.43 5.12 5.08 5.03 4.98 0.10 0.15 0.20 0.25 3.0 3.1 3.3 2.9
0.0127 4 150.1 9.96 8.45 8.39 8.14 8.49 5.32 5.27 5.21 5.14 0.15 0.20 0.25 0.30 3.2 3.2 3.4 3.0
0.0127 4 150.1 9.99 8.03 7.94 7.70 8.04 4.96 4.91 4.84 4.75 0.21 0.26 0.30 0.35 3.3 3.3 3.5 3.1
0.0127 4 149.6 9.93 7.99 7.97 7.73 8.02 5.09 5.02 4.94 4.85 0.26 0.31 0.36 0.41 3.4 3.4 3.6 3.1
0.0127 4 150 9.91 8.02 8.05 7.81 8.13 5.40 5.32 5.22 5.12 0.31 0.36 0.41 0.46 3.8 3.6 3.9 3.3
0.0127 4 200.6 10.0 8.49 8.45 8.28 8.63 5.36 5.31 5.24 5.15 0.09 0.13 0.17 0.20 3.2 3.2 3.3 2.9
0.0127 4 200.1 9.9 8.01 7.95 7.72 8.09 5.09 5.02 4.92 4.82 0.14 0.18 0.22 0.25 3.5 3.4 3.6 3.1
0.0127 4 200.6 9.9 8.17 8.09 7.84 8.16 5.42 5.32 5.21 5.08 0.19 0.23 0.27 0.30 3.7 3.6 3.8 3.3
0.0127 4 199.8 10.0 7.86 7.81 7.48 7.79 5.34 5.22 5.08 4.92 0.25 0.29 0.32 0.36 4.0 3.9 4.2 3.5
0.0127 4 200.7 9.9 8.05 8.01 7.67 7.96 5.70 5.56 5.40 5.22 0.29 0.33 0.37 0.40 4.3 4.1 4.4 3.7
0.0127 4 199.2 9.9 7.73 7.66 7.26 7.50 5.69 5.51 5.32 5.11 0.35 0.39 0.43 0.46 5.0 4.7 5.2 4.2
0.0127 4 199.3 10.0 7.75 7.72 7.31 7.53 5.84 5.64 5.42 5.19 0.41 0.44 0.48 0.52 5.3 4.9 5.4 4.3
0.0127 4 200.1 9.85 7.57 7.50 7.03 7.31 5.89 5.67 5.44 5.19 0.45 0.48 0.52 0.56 6.0 5.5 6.3 4.7
0.0127 4 201.7 9.89 7.37 7.23 6.74 7.08 5.69 5.45 5.20 4.94 0.49 0.53 0.56 0.60 6.0 5.7 6.6 4.7
0.0127 3 75.6 5.01 8.07 8.12 7.70 8.03 5.26 5.24 5.22 5.19 0.09 0.14 0.19 0.24 1.79 1.75 2.04 1.78
240
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 3 75.5 5.03 7.55 7.70 7.42 7.67 4.96 4.94 4.92 4.89 0.15 0.20 0.25 0.30 1.96 1.84 2.03 1.83
0.0127 3 75.1 4.95 7.31 7.45 7.20 7.46 4.84 4.81 4.79 4.76 0.21 0.26 0.30 0.35 2.02 1.89 2.07 1.85
0.0127 3 74.6 5.00 7.38 7.53 7.29 7.61 5.04 5.01 4.99 4.96 0.26 0.31 0.36 0.41 2.16 2.00 2.19 1.90
0.0127 3 75.0 5.00 7.22 7.33 7.07 7.49 4.94 4.91 4.88 4.85 0.31 0.36 0.41 0.46 2.21 2.09 2.30 1.91
0.0127 3 74.5 4.96 7.33 7.43 7.27 7.66 5.23 5.20 5.17 5.14 0.36 0.41 0.46 0.51 2.39 2.25 2.39 1.99
0.0127 3 75.7 5.06 7.17 7.31 7.10 7.50 5.07 5.03 5.00 4.97 0.41 0.46 0.51 0.56 2.43 2.25 2.44 2.02
0.0127 3 74.8 5.00 7.31 7.47 7.28 7.66 5.27 5.24 5.20 5.17 0.47 0.52 0.57 0.62 2.48 2.26 2.44 2.03
0.0127 3 75.5 5.00 7.07 7.30 7.09 7.48 5.11 5.07 5.04 5.00 0.50 0.55 0.60 0.65 2.58 2.26 2.45 2.03
0.0127 3 74.4 4.97 7.15 7.36 7.13 7.51 5.30 5.26 5.22 5.18 0.57 0.62 0.67 0.72 2.71 2.39 2.62 2.15
0.0127 3 100.3 4.98 7.55 7.67 7.34 7.61 4.94 4.92 4.89 4.86 0.07 0.11 0.14 0.18 1.92 1.82 2.05 1.82
0.0127 3 100.3 4.98 7.67 7.81 7.51 7.79 5.17 5.14 5.11 5.08 0.10 0.14 0.17 0.21 2.01 1.88 2.10 1.86
0.0127 3 100.1 4.99 7.37 7.46 7.24 7.56 5.03 5.01 4.98 4.94 0.14 0.18 0.21 0.25 2.16 2.05 2.23 1.92
0.0127 3 100.7 4.95 7.12 7.22 7.01 7.39 4.90 4.87 4.84 4.80 0.17 0.21 0.24 0.28 2.26 2.13 2.31 1.94
0.0127 3 101.1 4.94 7.35 7.42 7.22 7.61 5.23 5.20 5.16 5.12 0.22 0.25 0.29 0.33 2.36 2.24 2.43 2.00
0.0127 3 101.2 4.97 7.12 7.24 7.04 7.43 5.05 5.01 4.97 4.92 0.28 0.32 0.35 0.39 2.43 2.26 2.42 2.00
0.0127 3 101.9 4.95 7.16 7.35 7.18 7.50 5.19 5.14 5.09 5.04 0.35 0.39 0.43 0.46 2.54 2.27 2.40 2.03
0.0127 3 150.2 4.96 9.01 8.67 8.45 8.89 4.97 4.97 4.96 4.95 0.08 0.10 0.13 0.15 1.24 1.35 1.43 1.27
0.0127 3 150.0 5.02 9.07 8.67 8.49 8.91 4.96 4.95 4.94 4.93 0.13 0.16 0.18 0.21 1.23 1.36 1.42 1.27
0.0127 3 150.0 5.01 8.84 8.54 8.39 8.85 5.01 5.00 4.99 4.98 0.18 0.20 0.23 0.25 1.31 1.42 1.48 1.30
0.0127 3 149.5 4.98 8.78 8.57 8.45 8.90 4.98 4.96 4.95 4.93 0.23 0.26 0.28 0.31 1.32 1.39 1.43 1.26
0.0127 3 150.4 4.94 8.77 8.55 8.38 8.83 4.98 4.97 4.95 4.93 0.28 0.30 0.33 0.35 1.31 1.39 1.45 1.27
0.0127 3 150.2 5.02 8.79 8.55 8.43 8.80 5.00 4.98 4.96 4.94 0.33 0.36 0.38 0.41 1.33 1.41 1.45 1.31
0.0127 3 150.4 5.01 8.86 8.62 8.38 8.81 5.21 5.19 5.17 5.14 0.38 0.41 0.43 0.46 1.38 1.47 1.57 1.37
0.0127 3 149.8 4.98 8.59 8.42 8.15 8.57 5.13 5.11 5.08 5.05 0.43 0.46 0.48 0.50 1.45 1.52 1.63 1.42
0.0127 3 150.1 4.94 8.30 8.18 7.88 8.35 5.13 5.10 5.07 5.03 0.48 0.50 0.53 0.55 1.57 1.61 1.77 1.50
0.0127 3 150.7 5.01 7.89 7.80 7.48 7.98 5.02 4.98 4.94 4.91 0.53 0.55 0.58 0.60 1.76 1.79 2.00 1.64
0.0127 3 150.1 4.97 7.65 7.57 7.23 7.62 5.10 5.06 5.02 4.98 0.58 0.60 0.63 0.65 1.97 2.00 2.28 1.90
0.0127 3 148.8 4.94 7.13 6.87 6.55 7.12 5.13 5.08 5.04 4.99 0.64 0.66 0.69 0.71 2.50 2.80 3.32 2.34
A
ppendix B
241
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 3 150.1 4.94 6.67 6.69 6.52 7.13 5.22 5.17 5.12 5.07 0.68 0.70 0.73 0.75 3.46 3.29 3.57 2.42
0.0127 3 150.3 4.96 6.71 6.77 6.57 7.14 5.30 5.25 5.20 5.14 0.73 0.75 0.78 0.80 3.58 3.32 3.66 2.50
0.0127 3 150.1 4.99 6.61 6.63 6.43 7.02 5.26 5.21 5.15 5.09 0.78 0.81 0.83 0.86 3.78 3.57 3.97 2.62
0.0127 3 151.2 5.00 6.43 6.48 6.44 7.31 5.14 5.08 5.02 4.96 0.84 0.87 0.89 0.92 3.94 3.62 3.59 2.15
0.0127 3 199.9 4.93 8.57 8.57 8.36 8.56 4.89 4.89 4.88 4.86 0.07 0.09 0.11 0.12 1.35 1.35 1.43 1.34
0.0127 3 199.6 4.97 8.27 8.39 8.11 8.43 4.95 4.93 4.92 4.91 0.12 0.14 0.16 0.18 1.51 1.44 1.57 1.42
0.0127 3 199.7 4.98 8.37 8.45 8.20 8.39 5.09 5.08 5.06 5.04 0.17 0.19 0.21 0.23 1.53 1.49 1.60 1.50
0.0127 3 200.3 5.01 8.14 8.24 7.86 8.12 4.95 4.93 4.91 4.88 0.22 0.24 0.26 0.28 1.58 1.52 1.71 1.56
0.0127 3 199.5 4.98 8.02 8.07 7.57 7.88 4.99 4.96 4.93 4.90 0.27 0.29 0.31 0.33 1.65 1.61 1.91 1.69
0.0127 3 199.9 4.97 7.79 7.78 7.42 7.82 5.26 5.23 5.19 5.16 0.32 0.34 0.36 0.38 1.98 1.97 2.25 1.88
0.0127 3 200.1 4.94 7.25 7.45 7.01 7.38 5.26 5.22 5.18 5.13 0.37 0.39 0.41 0.43 2.52 2.24 2.73 2.21
0.0127 3 200.2 4.96 6.83 6.93 6.79 7.25 5.26 5.21 5.16 5.10 0.42 0.44 0.46 0.48 3.21 2.92 3.08 2.34
0.0127 3 201 5.01 6.83 6.93 6.74 7.14 5.26 5.20 5.14 5.08 0.47 0.49 0.51 0.53 3.23 2.93 3.17 2.45
0.0127 3 200.3 4.99 6.72 6.81 6.63 6.97 5.27 5.20 5.13 5.06 0.53 0.54 0.56 0.58 3.50 3.14 3.38 2.64
0.0127 3 200.6 4.97 6.65 6.72 6.53 6.87 5.32 5.24 5.17 5.08 0.57 0.59 0.61 0.63 3.79 3.42 3.70 2.82
0.0127 3 200.3 4.97 6.73 6.79 6.60 6.93 5.51 5.43 5.34 5.25 0.62 0.64 0.66 0.68 4.15 3.72 4.02 3.00
0.0127 3 73.9 9.93 9.02 8.98 8.59 8.81 5.20 5.18 5.15 5.12 0.14 0.24 0.34 0.44 2.63 2.64 2.93 2.72
0.0127 3 74.6 9.88 9.00 8.95 8.70 9.06 5.07 5.04 5.02 4.99 0.15 0.25 0.35 0.45 2.54 2.56 2.72 2.45
0.0127 3 75.8 9.85 8.67 8.54 8.08 8.35 4.84 4.82 4.79 4.76 0.19 0.29 0.38 0.48 2.60 2.68 3.03 2.77
0.0127 3 74.3 9.90 8.87 8.78 8.30 8.60 5.12 5.09 5.06 5.03 0.24 0.34 0.44 0.54 2.67 2.72 3.10 2.80
0.0127 3 75.9 9.90 8.48 8.34 8.01 8.30 4.87 4.84 4.81 4.77 0.28 0.38 0.47 0.57 2.77 2.87 3.13 2.84
0.0127 3 76.5 9.88 8.67 8.74 8.42 8.71 5.32 5.29 5.26 5.22 0.31 0.41 0.50 0.60 2.99 2.90 3.17 2.87
0.0127 3 100.1 9.92 8.53 8.41 8.04 8.35 4.90 4.87 4.84 4.80 0.11 0.18 0.25 0.33 2.76 2.84 3.14 2.83
0.0127 3 100.2 9.92 8.68 8.53 8.13 8.47 5.03 5.00 4.96 4.92 0.12 0.20 0.27 0.34 2.75 2.84 3.18 2.83
0.0127 3 100.3 9.91 8.66 8.53 8.15 8.48 5.07 5.04 5.00 4.96 0.17 0.24 0.31 0.39 2.80 2.88 3.19 2.85
0.0127 3 101.6 9.87 8.53 8.48 8.23 8.52 5.17 5.14 5.10 5.05 0.20 0.27 0.34 0.41 2.98 2.98 3.19 2.87
0.0127 3 99.9 9.93 8.20 8.15 7.93 8.22 4.87 4.83 4.79 4.73 0.23 0.31 0.38 0.46 3.02 3.03 3.20 2.89
0.0127 3 100.6 9.94 8.42 8.36 8.16 8.44 5.24 5.20 5.15 5.10 0.27 0.34 0.41 0.49 3.17 3.19 3.35 3.02
242
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 3 99.2 9.93 8.32 8.27 8.06 8.38 5.25 5.20 5.15 5.09 0.32 0.39 0.47 0.54 3.28 3.28 3.47 3.06
0.0127 3 150.4 9.93 8.56 8.41 8.10 8.43 5.18 5.14 5.09 5.02 0.08 0.13 0.18 0.23 2.98 3.08 3.35 2.95
0.0127 3 150.1 9.95 8.69 8.49 8.21 8.57 5.34 5.29 5.22 5.15 0.12 0.17 0.22 0.27 3.01 3.15 3.38 2.95
0.0127 3 150.3 9.98 8.27 8.08 7.78 8.13 5.06 5.00 4.93 4.85 0.16 0.21 0.26 0.31 3.16 3.29 3.55 3.09
0.0127 3 150.4 9.92 8.33 8.12 7.82 8.19 5.20 5.13 5.05 4.96 0.20 0.25 0.30 0.35 3.22 3.36 3.64 3.11
0.0127 3 149.5 9.90 8.40 8.21 7.88 8.23 5.39 5.31 5.22 5.12 0.25 0.30 0.35 0.40 3.34 3.47 3.79 3.23
0.0127 3 148.5 10.00 8.34 8.14 7.87 8.12 5.45 5.35 5.25 5.10 0.31 0.36 0.41 0.46 3.51 3.64 3.88 3.36
0.0127 3 199.7 9.87 8.38 8.27 8.00 8.34 5.20 5.14 5.07 4.98 0.08 0.12 0.16 0.19 3.15 3.20 3.42 2.97
0.0127 3 199.1 9.85 8.44 8.32 8.02 8.39 5.30 5.23 5.15 5.05 0.10 0.14 0.17 0.21 3.18 3.24 3.48 2.99
0.0127 3 200.9 10.00 8.19 8.04 7.71 7.88 5.08 5.00 4.90 4.79 0.12 0.16 0.20 0.23 3.25 3.33 3.62 3.28
0.0127 3 200.7 9.92 8.13 8.04 7.74 7.90 5.17 5.09 4.98 4.85 0.14 0.18 0.22 0.26 3.40 3.41 3.65 3.31
0.0127 3 200.4 9.90 8.28 8.19 7.87 8.05 5.40 5.30 5.18 5.04 0.17 0.21 0.24 0.28 3.49 3.48 3.74 3.34
0.0127 3 200.4 9.92 8.31 8.22 7.88 8.07 5.61 5.49 5.36 5.20 0.20 0.24 0.28 0.31 3.73 3.69 3.99 3.51
0.0127 3 201.1 9.98 8.05 7.95 7.59 7.81 5.49 5.36 5.20 5.02 0.24 0.28 0.31 0.35 3.97 3.92 4.26 3.64
0.0127 3 200.5 9.99 7.77 7.69 7.28 7.54 5.39 5.23 5.05 4.85 0.28 0.32 0.36 0.39 4.27 4.13 4.57 3.78
0.0127 3 199.2 10.12 7.58 7.49 7.08 7.30 5.39 5.22 5.02 4.81 0.31 0.35 0.39 0.43 4.71 4.53 5.03 4.14 Table B.6 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 15 oC measured at each section of the of
the test section inside 12.7 mm internal diameter tube Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 Plain tube 75.0 9.92 20.2 20.2 20.4 21.0 15.0 15.0 15.0 15.0 0.21 0.31 0.42 0.52 1.95 1.95 1.87 1.67
0.0127 Plain tube 75.1 9.88 20.4 20.4 20.6 21.2 15.1 15.1 15.1 15.1 0.31 0.41 0.52 0.62 1.89 1.91 1.82 1.62
0.0127 Plain tube 75.1 9.90 20.5 20.6 20.9 21.4 15.1 15.1 15.1 15.1 0.41 0.52 0.62 0.72 1.85 1.82 1.73 1.57
0.0127 Plain tube 75.4 9.94 20.6 20.7 21.0 21.6 15.1 15.1 15.1 15.1 0.46 0.56 0.66 0.76 1.83 1.81 1.71 1.56
0.0127 Plain tube 75.1 9.94 20.8 20.9 21.1 21.8 15.2 15.2 15.2 15.2 0.52 0.62 0.72 0.83 1.79 1.78 1.70 1.51
0.0127 Plain tube 100.2 9.94 19.8 19.7 19.9 20.3 15.0 15.0 15.0 15.0 0.18 0.26 0.34 0.41 2.09 2.12 2.05 1.89
0.0127 Plain tube 100.8 9.95 20.1 20.1 20.3 20.7 15.1 15.1 15.1 15.1 0.28 0.36 0.43 0.51 2.02 2.00 1.91 1.77
A
ppendix B
243
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 Plain tube 100.3 9.95 20.2 20.2 20.4 20.8 15.1 15.1 15.1 15.1 0.39 0.46 0.54 0.62 1.98 1.98 1.89 1.76
0.0127 Plain tube 150.6 9.92 19.3 19.1 19.2 19.5 14.9 14.9 14.9 14.9 0.15 0.20 0.25 0.31 2.32 2.39 2.35 2.19
0.0127 Plain tube 150.8 9.96 19.3 19.3 19.4 19.7 15.1 15.1 15.0 15.0 0.25 0.31 0.36 0.41 2.37 2.37 2.33 2.13
0.0127 Plain tube 149.9 9.91 19.4 19.4 19.5 19.8 15.0 15.0 15.0 15.0 0.36 0.41 0.46 0.51 2.28 2.27 2.23 2.08
0.0127 Plain tube 150.2 9.88 19.6 19.5 19.5 19.7 15.1 15.1 15.1 15.1 0.46 0.51 0.56 0.61 2.23 2.25 2.24 2.15
0.0127 Plain tube 150.4 9.90 19.5 19.4 19.3 19.4 15.1 15.1 15.1 15.1 0.55 0.60 0.65 0.71 2.29 2.34 2.40 2.33
0.0127 Plain tube 150.5 9.94 19.4 19.2 19.1 19.1 15.2 15.2 15.2 15.1 0.66 0.71 0.76 0.81 2.41 2.50 2.58 2.51
0.0127 Plain tube 150.4 9.92 19.0 18.8 18.7 19.0 15.1 15.1 15.1 15.0 0.74 0.79 0.84 0.89 2.58 2.70 2.78 2.51
0.0127 Plain tube 200 10.01 18.8 18.7 18.5 19.0 14.9 14.9 14.9 14.9 0.09 0.13 0.17 0.21 2.60 2.66 2.78 2.44
0.0127 Plain tube 200.3 9.92 19.0 18.9 18.8 19.2 15.1 15.1 15.0 15.0 0.14 0.18 0.22 0.25 2.56 2.60 2.63 2.43
0.0127 Plain tube 200.6 9.88 18.8 18.7 18.6 19.0 14.9 14.9 14.9 14.9 0.19 0.23 0.27 0.30 2.61 2.61 2.68 2.43
0.0127 Plain tube 200.2 9.94 18.9 18.9 18.8 19.1 15.1 15.0 15.0 15.0 0.24 0.28 0.32 0.36 2.61 2.62 2.64 2.44
0.0127 Plain tube 201 9.96 19.0 18.9 18.8 19.1 15.1 15.0 15.0 15.0 0.29 0.33 0.37 0.40 2.56 2.59 2.64 2.47
0.0127 Plain tube 199.5 9.92 19.1 18.9 18.8 19.1 15.1 15.1 15.1 15.0 0.34 0.38 0.42 0.46 2.53 2.60 2.65 2.46
0.0127 Plain tube 200.9 9.87 19.0 18.9 18.8 18.9 15.1 15.1 15.0 15.0 0.39 0.43 0.47 0.50 2.55 2.63 2.67 2.56
0.0127 Plain tube 200.5 9.96 18.9 18.7 18.5 18.5 15.1 15.1 15.0 15.0 0.44 0.48 0.52 0.56 2.62 2.74 2.91 2.88
0.0127 Plain tube 200.1 9.93 18.8 18.7 18.3 18.3 15.2 15.1 15.1 15.1 0.49 0.53 0.57 0.61 2.76 2.85 3.11 3.13
0.0127 Plain tube 200.5 9.91 18.6 18.4 18.0 18.2 15.2 15.1 15.1 15.1 0.54 0.58 0.62 0.66 2.94 3.10 3.48 3.24
0.0127 Plain tube 200.7 9.96 18.2 18.0 18.0 18.2 15.2 15.2 15.1 15.1 0.59 0.63 0.67 0.71 3.35 3.59 3.58 3.27
0.0127 Plain tube 199.8 9.95 17.8 18.0 18.0 18.2 15.3 15.3 15.2 15.1 0.64 0.68 0.72 0.76 4.01 3.66 3.60 3.33
0.0127 14 74.3 9.85 19.2 19.0 18.7 20.1 15.2 15.1 15.1 15.1 0.16 0.26 0.37 0.47 2.44 2.61 2.77 1.99
0.0127 14 75.9 9.88 19.3 18.9 18.6 20.0 14.8 14.8 14.8 14.8 0.21 0.31 0.41 0.51 2.21 2.41 2.58 1.89
0.0127 14 75.4 9.96 19.6 19.1 18.9 20.1 15.2 15.1 15.1 15.1 0.26 0.36 0.46 0.56 2.26 2.55 2.65 2.00
0.0127 14 75.6 9.94 19.5 18.9 19.1 20.0 15.0 15.0 15.0 15.0 0.31 0.41 0.51 0.61 2.23 2.62 2.48 2.02
0.0127 14 75.4 9.92 19.6 18.8 19.2 20.0 15.0 15.0 15.0 15.0 0.36 0.46 0.56 0.66 2.19 2.61 2.38 2.00
0.0127 14 101.6 9.96 18.8 18.3 18.1 19.1 14.9 14.9 14.9 14.9 0.13 0.20 0.28 0.36 2.60 2.96 3.14 2.37
0.0127 14 100.4 9.90 18.8 18.4 18.3 19.0 15.0 15.0 15.0 15.0 0.18 0.26 0.33 0.41 2.65 2.99 3.07 2.49
0.0127 14 100.7 10.00 18.8 18.4 18.5 19.0 15.1 15.1 15.0 15.0 0.23 0.31 0.39 0.47 2.68 3.02 2.94 2.53
244
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 14 100.4 9.95 18.8 18.4 18.7 19.0 15.1 15.1 15.1 15.0 0.29 0.36 0.44 0.52 2.71 3.01 2.78 2.57
0.0127 14 99.5 9.89 18.6 18.2 18.6 18.7 15.0 15.0 15.0 14.9 0.34 0.41 0.49 0.57 2.78 3.06 2.76 2.68
0.0127 14 101.1 9.91 18.4 18.2 18.4 18.5 15.3 15.3 15.2 15.2 0.38 0.46 0.53 0.61 3.18 3.47 3.15 3.03
0.0127 14 101.2 9.95 18.2 18.0 18.0 18.2 15.3 15.3 15.3 15.2 0.44 0.52 0.60 0.67 3.53 3.69 3.63 3.36
0.0127 14 97.8 9.93 18.2 18.1 18.1 18.3 15.4 15.4 15.4 15.4 0.52 0.59 0.67 0.75 3.60 3.73 3.74 3.47
0.0127 14 150.9 9.90 18.4 18.2 18.1 18.5 15.2 15.2 15.1 15.1 0.10 0.15 0.21 0.26 3.08 3.27 3.36 2.95
0.0127 14 148.7 9.88 18.1 18.0 17.9 18.2 14.9 14.9 14.9 14.9 0.16 0.21 0.26 0.32 3.20 3.29 3.27 3.02
0.0127 14 150.3 9.92 18.1 18.0 18.1 18.2 15.1 15.1 15.0 15.0 0.21 0.26 0.31 0.36 3.29 3.40 3.31 3.11
0.0127 14 150.6 9.89 18.0 17.9 18.0 18.1 15.1 15.1 15.0 15.0 0.25 0.30 0.36 0.41 3.42 3.54 3.44 3.20
0.0127 14 151.9 9.92 18.1 18.1 18.4 18.3 15.2 15.2 15.2 15.1 0.35 0.40 0.45 0.50 3.49 3.53 3.13 3.15
0.0127 14 150.1 9.96 18.0 18.0 18.1 18.0 15.3 15.3 15.2 15.1 0.42 0.47 0.52 0.58 3.71 3.70 3.40 3.38
0.0127 14 201.1 9.90 18.1 17.9 17.7 18.1 15.0 15.0 15.0 15.0 0.09 0.13 0.17 0.20 3.28 3.47 3.66 3.20
0.0127 14 201.9 9.96 18.1 18.1 17.9 18.2 15.3 15.2 15.2 15.2 0.14 0.18 0.22 0.26 3.52 3.60 3.78 3.30
0.0127 14 200.8 9.98 18.0 17.9 17.7 18.1 15.2 15.2 15.1 15.1 0.19 0.23 0.27 0.30 3.65 3.69 3.91 3.38
0.0127 14 200 9.88 17.6 17.7 17.5 17.8 15.0 15.0 14.9 14.9 0.25 0.28 0.32 0.36 3.86 3.74 3.97 3.44
0.0127 14 200.3 9.91 17.7 17.7 17.5 17.8 15.1 15.1 15.0 15.0 0.29 0.33 0.37 0.41 3.99 3.85 4.08 3.52
0.0127 14 199.8 9.88 17.8 17.9 17.7 18.0 15.4 15.3 15.3 15.2 0.34 0.38 0.42 0.46 4.15 3.92 4.15 3.56
0.0127 14 200.2 9.90 17.6 17.6 17.4 17.7 15.2 15.2 15.1 15.0 0.39 0.43 0.47 0.51 4.28 4.08 4.31 3.68
0.0127 9 75.1 9.93 19.6 19.3 19.2 19.4 15.2 15.2 15.2 15.2 0.16 0.26 0.36 0.47 2.29 2.47 2.49 2.41
0.0127 9 75.1 9.92 19.1 19.2 18.7 19.1 14.9 14.9 14.9 14.9 0.21 0.31 0.41 0.52 2.38 2.33 2.60 2.39
0.0127 9 75.0 9.96 19.5 19.5 19.1 19.4 15.1 15.0 15.0 15.0 0.26 0.36 0.46 0.57 2.28 2.27 2.49 2.31
0.0127 9 74.7 9.93 19.3 19.5 18.6 19.2 14.9 14.8 14.8 14.8 0.31 0.42 0.52 0.62 2.26 2.18 2.67 2.30
0.0127 9 100.6 9.93 19.2 19.0 18.2 19.0 15.2 15.2 15.2 15.2 0.13 0.21 0.28 0.36 2.52 2.63 3.30 2.60
0.0127 9 100.8 9.94 19.2 19.1 18.3 19.0 15.2 15.1 15.1 15.1 0.18 0.25 0.33 0.41 2.50 2.53 3.23 2.57
0.0127 9 98.62 9.88 19.1 19.1 18.1 18.9 15.1 15.1 15.0 15.0 0.24 0.32 0.39 0.47 2.50 2.48 3.30 2.57
0.0127 9 100.4 9.87 19.1 19.1 18.0 18.9 15.1 15.1 15.0 15.0 0.28 0.35 0.43 0.50 2.44 2.47 3.40 2.56
0.0127 9 100.4 9.94 19.1 19.2 18.1 19.0 15.1 15.1 15.1 15.1 0.33 0.41 0.48 0.56 2.53 2.48 3.41 2.59
0.0127 9 101.6 9.86 19.2 19.1 18.0 18.6 15.1 15.1 15.1 15.1 0.37 0.44 0.52 0.59 2.44 2.51 3.46 2.84
A
ppendix B
245
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 9 98.9 9.96 18.8 19.0 17.9 19.2 15.0 15.0 15.0 15.0 0.46 0.54 0.62 0.70 2.66 2.50 3.50 2.39
0.0127 9 151.1 9.92 18.6 18.5 17.9 18.4 15.2 15.2 15.2 15.1 0.10 0.15 0.20 0.26 2.92 3.07 3.68 3.09
0.0127 9 149.9 9.88 18.6 18.5 17.8 18.3 15.1 15.1 15.1 15.1 0.15 0.21 0.26 0.31 2.93 3.00 3.74 3.11
0.0127 9 150 9.95 18.1 18.1 17.4 17.9 14.9 14.8 14.8 14.8 0.21 0.26 0.31 0.36 3.13 3.12 3.84 3.23
0.0127 9 150.6 9.90 18.1 18.1 17.6 18.0 15.1 15.0 15.0 15.0 0.26 0.31 0.36 0.41 3.35 3.28 3.92 3.31
0.0127 9 149.5 9.92 18.1 18.2 17.8 18.2 15.3 15.3 15.2 15.2 0.31 0.36 0.41 0.46 3.52 3.38 3.94 3.36
0.0127 9 149.2 9.95 17.9 17.9 17.5 17.9 15.1 15.1 15.1 15.0 0.37 0.42 0.47 0.52 3.62 3.64 4.11 3.47
0.0127 9 200.8 9.92 18.3 18.0 17.8 18.3 15.1 15.1 15.1 15.0 0.09 0.13 0.17 0.20 3.20 3.50 3.72 3.10
0.0127 9 200.6 9.89 18.3 18.1 17.9 18.3 15.3 15.3 15.3 15.2 0.14 0.18 0.22 0.25 3.42 3.64 3.89 3.24
0.0127 9 200.2 9.94 18.1 18.0 17.8 18.2 15.3 15.3 15.2 15.2 0.19 0.23 0.27 0.31 3.66 3.73 3.98 3.33
0.0127 9 199.8 9.96 18.1 17.9 17.7 18.2 15.4 15.3 15.3 15.2 0.24 0.28 0.32 0.36 3.79 3.87 4.19 3.37
0.0127 9 199.6 9.89 17.9 17.8 17.5 18.0 15.3 15.2 15.2 15.1 0.29 0.33 0.37 0.41 3.89 4.00 4.33 3.45
0.0127 9 201.8 9.93 17.7 17.6 17.3 17.9 15.1 15.0 15.0 14.9 0.33 0.37 0.41 0.45 3.94 3.96 4.24 3.34
0.0127 4 75.0 9.92 18.0 18.0 17.8 18.3 15.0 15.0 15.0 15.0 0.13 0.24 0.34 0.44 3.36 3.34 3.57 3.04
0.0127 4 75.3 9.91 17.9 17.9 17.7 18.1 14.8 14.8 14.8 14.8 0.15 0.25 0.35 0.45 3.23 3.27 3.49 2.99
0.0127 4 75.2 9.90 18.0 18.0 17.8 18.2 14.9 14.9 14.9 14.9 0.16 0.26 0.37 0.47 3.21 3.24 3.43 2.98
0.0127 4 75.9 9.90 18.1 18.0 17.8 18.2 14.9 14.9 14.9 14.9 0.20 0.30 0.40 0.50 3.18 3.19 3.39 3.01
0.0127 4 76.2 9.88 18.2 18.1 17.9 18.3 15.0 15.0 15.0 15.0 0.22 0.32 0.42 0.52 3.17 3.24 3.43 2.98
0.0127 4 74.5 9.89 18.2 18.1 17.9 18.3 15.0 15.0 14.9 14.9 0.27 0.37 0.47 0.58 3.13 3.20 3.44 3.00
0.0127 4 75.2 9.89 18.2 18.1 17.9 18.3 15.0 15.0 15.0 15.0 0.30 0.40 0.50 0.61 3.15 3.24 3.41 3.05
0.0127 4 75.1 9.92 18.3 18.3 18.1 18.5 15.2 15.1 15.1 15.1 0.33 0.43 0.53 0.64 3.15 3.19 3.35 2.95
0.0127 4 100.5 9.86 17.8 17.9 17.7 18.1 14.9 14.9 14.9 14.9 0.08 0.16 0.23 0.31 3.43 3.38 3.53 3.13
0.0127 4 100.4 9.95 18.0 18.0 17.8 18.2 15.0 15.0 15.0 15.0 0.10 0.18 0.25 0.33 3.43 3.38 3.55 3.15
0.0127 4 100.5 9.94 18.2 18.1 18.0 18.3 15.2 15.2 15.1 15.1 0.13 0.20 0.28 0.36 3.39 3.38 3.57 3.20
0.0127 4 100.7 9.91 18.0 17.9 17.8 18.1 15.0 15.0 15.0 14.9 0.16 0.24 0.32 0.39 3.38 3.38 3.57 3.20
0.0127 4 101.3 9.96 18.1 18.0 17.8 18.1 15.0 15.0 15.0 14.9 0.20 0.27 0.35 0.43 3.30 3.37 3.60 3.20
0.0127 4 100.3 9.94 18.0 18.0 17.7 18.1 15.0 15.0 15.0 15.0 0.25 0.33 0.40 0.48 3.38 3.40 3.65 3.25
0.0127 4 100.1 9.95 18.1 18.1 17.9 18.2 15.2 15.2 15.2 15.1 0.31 0.39 0.46 0.54 3.47 3.47 3.75 3.28
246
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 4 99.83 9.96 17.8 17.8 17.7 18.0 15.0 15.0 15.0 15.0 0.37 0.45 0.53 0.60 3.64 3.60 3.77 3.32
0.0127 4 150.8 9.88 17.9 17.9 17.7 18.0 15.1 15.0 15.0 15.0 0.05 0.10 0.16 0.21 3.53 3.49 3.72 3.29
0.0127 4 149.8 9.97 17.8 17.8 17.6 17.9 14.9 14.9 14.9 14.9 0.07 0.12 0.17 0.22 3.57 3.53 3.76 3.35
0.0127 4 150.8 9.94 18.1 18.1 17.9 18.3 15.3 15.3 15.2 15.2 0.09 0.14 0.19 0.24 3.55 3.52 3.74 3.30
0.0127 4 150.9 9.91 18.1 18.1 17.9 18.2 15.2 15.2 15.2 15.1 0.13 0.18 0.23 0.28 3.54 3.51 3.74 3.34
0.0127 4 150.1 9.91 17.9 17.9 17.7 18.0 15.1 15.1 15.0 15.0 0.18 0.23 0.28 0.33 3.60 3.59 3.81 3.37
0.0127 4 150.4 9.88 18.0 18.0 17.8 18.1 15.3 15.2 15.2 15.1 0.23 0.28 0.33 0.38 3.70 3.66 3.87 3.42
0.0127 4 150.3 9.87 17.7 17.7 17.5 17.7 15.0 15.0 14.9 14.9 0.27 0.32 0.37 0.42 3.75 3.74 3.95 3.47
0.0127 4 150.5 9.89 17.8 17.8 17.7 17.9 15.2 15.2 15.1 15.1 0.32 0.37 0.42 0.47 3.88 3.77 3.97 3.50
0.0127 4 149.2 9.85 17.7 17.7 17.5 17.7 15.2 15.2 15.1 15.1 0.38 0.43 0.49 0.54 4.06 3.91 4.20 3.83
0.0127 4 200.8 9.90 17.8 17.8 17.6 17.9 15.0 15.0 15.0 14.9 0.07 0.11 0.15 0.19 3.60 3.62 3.84 3.40
0.0127 4 200.5 9.92 17.9 17.8 17.6 17.9 15.1 15.1 15.1 15.0 0.09 0.13 0.17 0.21 3.62 3.68 3.95 3.45
0.0127 4 199.9 9.91 18.0 17.9 17.7 18.0 15.2 15.2 15.2 15.1 0.12 0.16 0.20 0.24 3.71 3.73 3.95 3.46
0.0127 4 199.7 9.87 17.9 17.8 17.6 17.9 15.3 15.2 15.2 15.1 0.16 0.19 0.23 0.27 3.78 3.84 4.10 3.57
0.0127 4 200 9.88 17.7 17.6 17.4 17.7 15.1 15.1 15.0 14.9 0.21 0.25 0.29 0.32 3.96 3.94 4.22 3.65
0.0127 4 200.6 9.87 17.6 17.6 17.3 17.6 15.2 15.1 15.0 14.9 0.26 0.29 0.33 0.37 4.15 4.06 4.38 3.77
0.0127 4 199.2 9.98 17.7 17.7 17.4 17.7 15.4 15.3 15.2 15.1 0.31 0.35 0.39 0.43 4.36 4.29 4.68 3.96
0.0127 3 74.7 9.96 18.1 18.1 17.8 18.1 14.9 14.9 14.9 14.9 0.14 0.24 0.34 0.45 3.16 3.19 3.50 3.14
0.0127 3 75.3 9.95 18.3 18.3 18.0 18.3 15.2 15.2 15.2 15.1 0.17 0.27 0.38 0.48 3.25 3.26 3.58 3.22
0.0127 3 75.5 9.93 18.0 18.0 17.6 18.0 14.8 14.7 14.7 14.7 0.22 0.32 0.42 0.53 3.12 3.09 3.47 3.05
0.0127 3 74.3 9.90 18.3 18.3 17.9 18.3 15.1 15.1 15.1 15.1 0.27 0.37 0.48 0.58 3.10 3.17 3.53 3.13
0.0127 3 101.0 9.92 18.0 17.9 17.7 18.0 14.9 14.9 14.9 14.9 0.11 0.18 0.26 0.34 3.30 3.36 3.64 3.25
0.0127 3 99.6 9.89 18.0 17.9 17.6 17.9 14.9 14.9 14.9 14.8 0.13 0.21 0.28 0.36 3.29 3.38 3.68 3.27
0.0127 3 100.9 9.93 18.1 17.9 17.7 18.0 15.0 15.0 15.0 14.9 0.17 0.25 0.32 0.40 3.29 3.40 3.71 3.25
0.0127 3 100.0 9.93 18.1 18.1 17.8 18.1 15.2 15.2 15.1 15.1 0.22 0.29 0.37 0.45 3.42 3.46 3.75 3.33
0.0127 3 100.0 9.97 18.2 18.1 17.9 18.2 15.3 15.2 15.2 15.2 0.26 0.34 0.42 0.50 3.47 3.48 3.73 3.30
0.0127 3 99.8 9.95 17.8 17.7 17.6 17.9 14.9 14.9 14.9 14.9 0.31 0.39 0.47 0.55 3.53 3.52 3.74 3.34
0.0127 3 101.7 9.92 18.1 18.2 18.0 18.3 15.3 15.3 15.3 15.3 0.35 0.42 0.50 0.57 3.54 3.50 3.73 3.36
A
ppendix B
247
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0127 3 150.7 9.96 17.9 17.9 17.7 18.1 15.0 15.0 14.9 14.9 0.07 0.12 0.17 0.22 3.52 3.48 3.61 3.12
0.0127 3 150.1 9.94 17.8 17.9 17.7 18.1 15.0 15.0 15.0 14.9 0.10 0.15 0.20 0.25 3.58 3.52 3.64 3.17
0.0127 3 149.7 9.94 18.1 18.1 18.0 18.3 15.3 15.3 15.2 15.2 0.14 0.19 0.24 0.29 3.61 3.54 3.68 3.21
0.0127 3 151 9.91 17.7 17.8 17.6 18.0 15.0 15.0 14.9 14.9 0.16 0.22 0.27 0.32 3.65 3.58 3.68 3.24
0.0127 3 150.4 9.96 17.8 17.9 17.8 18.1 15.1 15.1 15.0 15.0 0.20 0.25 0.31 0.36 3.74 3.60 3.69 3.27
0.0127 3 150.3 9.92 18.0 18.1 17.9 18.2 15.4 15.3 15.3 15.2 0.25 0.30 0.35 0.40 3.79 3.68 3.80 3.33
0.0127 3 149.5 9.90 17.9 18.0 17.9 18.2 15.4 15.4 15.3 15.2 0.30 0.35 0.40 0.45 3.96 3.80 3.91 3.42
0.0127 3 200.5 9.88 17.8 17.8 17.6 18.0 15.0 15.0 14.9 14.9 0.07 0.11 0.15 0.18 3.65 3.57 3.72 3.26
0.0127 3 199.3 9.91 17.9 17.9 17.7 18.0 15.2 15.1 15.1 15.0 0.10 0.14 0.18 0.21 3.72 3.69 3.83 3.35
0.0127 3 199.6 9.91 17.9 17.9 17.8 18.1 15.3 15.2 15.2 15.1 0.14 0.17 0.21 0.25 3.80 3.73 3.85 3.33
0.0127 3 200.2 9.90 17.9 17.9 17.7 18.0 15.3 15.2 15.2 15.1 0.16 0.20 0.24 0.28 3.89 3.84 4.00 3.43
0.0127 3 199.4 9.90 17.8 17.8 17.7 18.0 15.3 15.3 15.2 15.1 0.19 0.23 0.27 0.31 4.03 3.92 4.06 3.51
0.0127 3 200 9.91 17.7 17.7 17.5 17.9 15.3 15.2 15.1 15.0 0.24 0.28 0.32 0.36 4.23 4.06 4.20 3.58
0.0127 3 200.2 9.88 17.4 17.5 17.3 17.6 15.2 15.1 15.0 14.9 0.29 0.32 0.36 0.40 4.47 4.19 4.34 3.69
0.0127 3 200.9 9.88 17.5 17.5 17.3 17.7 15.3 15.2 15.1 15.0 0.32 0.36 0.40 0.44 4.61 4.30 4.49 3.74
0.0127 3 199.6 9.91 17.5 17.5 17.3 17.6 15.4 15.3 15.2 15.1 0.37 0.40 0.44 0.48 4.86 4.54 4.75 3.98 Table B.7 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 5 oC measured at each section of the of the
test section inside 15.9 mm internal diameter tube. Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 Plain tube 5.00 74.8 10.2 11.2 11.4 11.7 4.65 4.65 4.64 4.64 0.14 0.18 0.22 0.26 0.897 0.768 0.741 0.710
0.0159 Plain tube 5.03 74.9 11.4 11.1 11.3 11.4 4.62 4.62 4.61 4.61 0.25 0.29 0.33 0.37 0.741 0.775 0.756 0.739
0.0159 Plain tube 5.01 75.4 11.1 11.0 11.3 11.3 4.67 4.66 4.66 4.65 0.35 0.38 0.42 0.46 0.778 0.787 0.756 0.758
0.0159 Plain tube 5.03 74.8 10.8 10.8 11.1 11.0 4.62 4.62 4.61 4.60 0.44 0.48 0.52 0.56 0.820 0.816 0.777 0.787
0.0159 Plain tube 5.00 74.7 10.6 10.7 11.0 10.8 4.70 4.70 4.69 4.68 0.55 0.59 0.63 0.67 0.854 0.837 0.799 0.824
0.0159 Plain tube 5.01 75.3 10.1 10.3 10.5 10.3 4.45 4.44 4.43 4.42 0.65 0.69 0.73 0.77 0.889 0.861 0.830 0.855
0.0159 Plain tube 5.03 74.7 10.1 10.3 10.5 10.5 4.56 4.55 4.54 4.53 0.75 0.79 0.83 0.87 0.914 0.871 0.840 0.840
248
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 Plain tube 5.00 74.9 9.4 10.0 10.6 11.0 4.12 4.11 4.10 4.09 0.85 0.89 0.93 0.97 0.942 0.857 0.773 0.721
0.0159 Plain tube 5.03 101.1 10.0 11.2 11.7 11.3 4.89 4.89 4.88 4.88 0.13 0.16 0.19 0.22 0.99 0.80 0.74 0.79
0.0159 Plain tube 5.02 100.0 11.0 10.8 11.0 10.7 4.91 4.91 4.90 4.89 0.23 0.26 0.29 0.32 0.83 0.85 0.83 0.86
0.0159 Plain tube 5.00 100.6 10.4 10.3 10.5 10.2 4.57 4.56 4.55 4.54 0.33 0.36 0.39 0.42 0.85 0.88 0.85 0.89
0.0159 Plain tube 5.01 99.6 10.4 10.2 10.4 10.1 4.82 4.81 4.79 4.78 0.44 0.47 0.50 0.53 0.90 0.92 0.90 0.95
0.0159 Plain tube 5.03 99.8 10.1 10.0 10.0 9.7 4.93 4.91 4.90 4.88 0.54 0.57 0.60 0.63 0.98 0.99 0.99 1.04
0.0159 Plain tube 5.02 100.1 9.7 9.6 9.7 9.5 5.12 5.10 5.08 5.06 0.64 0.67 0.70 0.73 1.11 1.11 1.09 1.14
0.0159 Plain tube 5.04 100.8 8.9 9.1 9.1 8.9 4.79 4.78 4.76 4.74 0.74 0.77 0.80 0.83 1.22 1.16 1.16 1.21
0.0159 Plain tube 4.98 99.9 8.5 8.8 9.0 9.2 4.77 4.76 4.75 4.75 0.84 0.87 0.89 0.92 1.34 1.24 1.17 1.11
0.0159 Plain tube 5.03 99.6 8.7 9.1 9.4 9.8 4.99 4.98 4.98 4.99 0.89 0.92 0.95 0.98 1.36 1.23 1.13 1.05
0.0159 Plain tube 4.99 150.0 9.49 10.05 10.12 9.55 4.84 4.84 4.83 4.82 0.12 0.14 0.16 0.18 1.07 0.96 0.94 1.06
0.0159 Plain tube 5.03 150.4 9.46 9.91 9.98 9.56 5.00 4.98 4.97 4.96 0.22 0.24 0.26 0.28 1.13 1.02 1.01 1.09
0.0159 Plain tube 4.97 150.0 9.66 9.96 9.86 9.38 5.21 5.19 5.17 5.15 0.32 0.34 0.36 0.38 1.12 1.04 1.06 1.18
0.0159 Plain tube 5.02 149.9 8.90 9.11 8.91 8.49 5.03 5.01 4.98 4.95 0.43 0.45 0.46 0.48 1.30 1.23 1.28 1.42
0.0159 Plain tube 5.04 149.8 8.48 8.65 8.49 8.16 5.32 5.29 5.25 5.21 0.53 0.55 0.57 0.59 1.60 1.50 1.56 1.71
0.0159 Plain tube 4.99 149.7 7.70 7.80 7.65 7.40 5.28 5.23 5.19 5.14 0.63 0.65 0.67 0.69 2.06 1.95 2.03 2.22
0.0159 Plain tube 4.99 149.6 6.90 7.15 7.12 7.00 5.00 4.95 4.90 4.84 0.73 0.75 0.77 0.79 2.64 2.28 2.26 2.32
0.0159 Plain tube 5.00 150.7 6.87 7.13 7.09 6.97 5.07 5.01 4.95 4.89 0.82 0.84 0.86 0.88 2.78 2.37 2.35 2.41
0.0159 Plain tube 5.05 149.1 7.14 7.40 7.41 7.36 5.33 5.27 5.21 5.15 0.88 0.90 0.92 0.94 2.79 2.37 2.30 2.30
0.0159 Plain tube 4.97 148.7 6.94 7.31 7.34 7.33 5.18 5.12 5.06 5.01 0.93 0.95 0.97 0.99 2.82 2.27 2.19 2.14
0.0159 Plain tube 5.03 200.0 8.60 9.04 9.07 8.86 4.82 4.81 4.80 4.79 0.07 0.08 0.10 0.11 1.33 1.19 1.18 1.24
0.0159 Plain tube 5.01 200.1 8.30 8.38 8.49 8.42 4.89 4.88 4.87 4.85 0.12 0.13 0.15 0.16 1.47 1.43 1.39 1.41
0.0159 Plain tube 4.95 200.2 8.30 8.45 8.35 8.27 4.90 4.89 4.87 4.85 0.17 0.18 0.20 0.21 1.46 1.40 1.43 1.45
0.0159 Plain tube 5.03 199.9 8.52 8.53 8.44 8.18 5.08 5.06 5.03 5.01 0.22 0.24 0.25 0.27 1.46 1.45 1.48 1.59
0.0159 Plain tube 4.98 200.0 8.22 8.30 8.12 7.81 5.10 5.08 5.05 5.02 0.27 0.28 0.30 0.31 1.60 1.55 1.62 1.79
0.0159 Plain tube 5.03 199.7 8.02 8.12 7.92 7.67 5.27 5.24 5.21 5.17 0.32 0.33 0.35 0.36 1.84 1.75 1.86 2.02
0.0159 Plain tube 5.00 200.0 7.57 7.71 7.59 7.35 5.27 5.23 5.19 5.14 0.37 0.38 0.40 0.41 2.18 2.02 2.09 2.27
0.0159 Plain tube 4.97 199.8 7.38 7.42 7.39 7.24 5.43 5.39 5.34 5.29 0.42 0.43 0.45 0.46 2.56 2.46 2.43 2.55
A
ppendix B
249
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 Plain tube 5.08 200.0 7.09 7.21 7.23 7.17 5.34 5.29 5.23 5.17 0.47 0.48 0.50 0.51 2.91 2.65 2.55 2.54
0.0159 Plain tube 4.97 199.9 6.56 6.66 6.63 6.65 5.03 4.97 4.90 4.83 0.52 0.53 0.55 0.56 3.27 2.95 2.88 2.73
0.0159 Plain tube 4.91 200.7 6.53 6.62 6.59 6.55 5.05 4.98 4.90 4.83 0.57 0.58 0.60 0.61 3.35 3.00 2.92 2.85
0.0159 Plain tube 5.28 197.9 6.93 6.98 6.98 6.94 5.43 5.35 5.26 5.17 0.63 0.64 0.66 0.68 3.54 3.24 3.09 3.00
0.0159 Plain tube 10.07 75.2 11.8 12.5 12.8 13.2 4.47 4.47 4.46 4.46 0.10 0.18 0.26 0.34 1.38 1.26 1.21 1.15
0.0159 Plain tube 9.95 76.3 11.9 12.3 12.6 13.1 4.33 4.33 4.33 4.32 0.16 0.24 0.31 0.39 1.32 1.25 1.20 1.14
0.0159 Plain tube 9.98 75.4 11.7 12.2 12.7 13.2 4.40 4.40 4.39 4.38 0.22 0.30 0.38 0.46 1.36 1.28 1.21 1.13
0.0159 Plain tube 9.90 75.5 11.7 12.1 12.6 13.2 4.38 4.37 4.37 4.36 0.28 0.36 0.44 0.52 1.35 1.29 1.21 1.13
0.0159 Plain tube 9.97 75.3 11.7 12.1 12.6 13.2 4.29 4.29 4.28 4.27 0.38 0.46 0.54 0.62 1.36 1.28 1.20 1.12
0.0159 Plain tube 9.99 75.4 11.7 12.3 12.8 13.7 4.35 4.34 4.33 4.32 0.48 0.56 0.64 0.72 1.36 1.26 1.19 1.07
0.0159 Plain tube 9.89 75.2 11.6 12.4 13.0 14.7 4.12 4.11 4.10 4.09 0.59 0.67 0.74 0.82 1.33 1.19 1.12 0.93
0.0159 Plain tube 9.92 74.8 11.8 12.7 13.3 14.8 4.26 4.25 4.24 4.23 0.61 0.69 0.77 0.85 1.32 1.17 1.10 0.94
0.0159 Plain tube 10.01 75.2 11.6 12.6 13.3 15.2 3.96 3.94 3.93 3.91 0.67 0.75 0.83 0.91 1.32 1.16 1.07 0.89
0.0159 Plain tube 9.9 100.3 11.6 12.1 12.1 12.4 4.50 4.50 4.49 4.48 0.16 0.22 0.28 0.34 1.39 1.32 1.30 1.26
0.0159 Plain tube 10.0 99.6 11.7 11.8 12.1 12.5 4.67 4.66 4.65 4.64 0.26 0.32 0.38 0.44 1.44 1.40 1.35 1.29
0.0159 Plain tube 10.0 99.8 11.7 12.0 12.5 12.8 4.71 4.70 4.69 4.67 0.36 0.42 0.48 0.54 1.42 1.37 1.28 1.23
0.0159 Plain tube 10.0 99.4 12.0 12.4 12.7 12.8 4.81 4.80 4.78 4.76 0.47 0.53 0.59 0.65 1.41 1.33 1.27 1.25
0.0159 Plain tube 10.0 100.4 11.9 12.2 12.5 12.6 4.87 4.85 4.83 4.81 0.56 0.62 0.68 0.74 1.43 1.36 1.31 1.29
0.0159 Plain tube 10.0 100.0 11.7 12.0 12.4 12.8 4.80 4.78 4.76 4.74 0.67 0.73 0.79 0.85 1.44 1.38 1.31 1.25
0.0159 Plain tube 10.1 99.9 11.3 11.7 12.3 12.1 4.57 4.55 4.54 4.54 0.78 0.84 0.90 0.96 1.51 1.42 1.31 1.34
0.0159 Plain tube 9.99 150.3 11.5 11.6 11.7 11.8 4.88 4.87 4.86 4.85 0.08 0.12 0.16 0.20 1.51 1.50 1.46 1.44
0.0159 Plain tube 10.08 149.4 11.3 11.4 11.6 11.7 4.84 4.83 4.82 4.80 0.14 0.18 0.22 0.26 1.55 1.54 1.50 1.47
0.0159 Plain tube 9.91 149.6 11.1 11.1 11.4 11.5 4.92 4.91 4.89 4.87 0.24 0.28 0.32 0.36 1.60 1.61 1.53 1.51
0.0159 Plain tube 9.89 150.0 11.2 11.1 11.4 11.3 4.96 4.94 4.92 4.89 0.34 0.38 0.42 0.46 1.58 1.61 1.54 1.55
0.0159 Plain tube 9.91 149.9 11.0 10.8 10.9 10.7 4.91 4.88 4.85 4.81 0.44 0.48 0.52 0.56 1.63 1.69 1.65 1.70
0.0159 Plain tube 9.92 150.1 10.6 10.3 10.3 10.0 5.10 5.06 5.02 4.97 0.54 0.58 0.62 0.66 1.82 1.90 1.89 1.97
0.0159 Plain tube 9.96 149.8 9.7 9.4 9.4 9.2 5.04 4.99 4.94 4.89 0.65 0.69 0.73 0.76 2.16 2.26 2.25 2.31
0.0159 Plain tube 9.99 151.9 8.5 8.6 9.0 9.0 4.95 4.89 4.83 4.77 0.81 0.84 0.88 0.92 2.84 2.68 2.41 2.34
250
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 Plain tube 9.84 149.3 8.6 8.7 9.1 9.2 5.07 5.01 4.95 4.88 0.82 0.86 0.90 0.94 2.83 2.65 2.37 2.26
0.0159 Plain tube 10.02 200.3 11.1 11.1 11.4 11.4 4.68 4.67 4.65 4.64 0.07 0.10 0.13 0.16 1.58 1.55 1.50 1.48
0.0159 Plain tube 9.93 200.8 10.8 10.6 10.8 10.7 4.93 4.92 4.90 4.88 0.16 0.19 0.22 0.25 1.70 1.74 1.70 1.70
0.0159 Plain tube 9.96 200.3 10.8 10.5 10.5 10.3 5.00 4.97 4.94 4.90 0.26 0.29 0.32 0.35 1.73 1.81 1.81 1.85
0.0159 Plain tube 9.93 199.4 10.8 10.9 10.5 10.4 5.17 5.13 5.08 5.03 0.36 0.39 0.41 0.44 1.76 1.72 1.84 1.85
0.0159 Plain tube 9.99 199.9 9.4 9.5 9.4 9.1 5.22 5.17 5.10 5.03 0.46 0.49 0.52 0.55 2.40 2.30 2.33 2.47
0.0159 Plain tube 9.91 200.9 8.8 8.9 9.0 8.8 5.28 5.20 5.12 5.04 0.56 0.59 0.61 0.64 2.82 2.69 2.54 2.65
0.0159 14 4.99 75.1 8.78 8.79 9.35 8.74 4.85 4.84 4.84 4.82 0.14 0.18 0.22 0.26 1.27 1.27 1.11 1.28
0.0159 14 5.01 75.1 8.33 8.66 9.29 8.61 4.98 4.96 4.95 4.94 0.25 0.29 0.33 0.37 1.50 1.36 1.16 1.37
0.0159 14 5.04 74.8 8.55 8.75 9.26 8.57 4.97 4.96 4.95 4.93 0.34 0.39 0.43 0.47 1.41 1.33 1.17 1.38
0.0159 14 5.00 74.7 8.80 8.64 9.01 8.44 5.00 4.98 4.97 4.95 0.44 0.48 0.52 0.56 1.32 1.37 1.24 1.43
0.0159 14 5.02 74.7 8.85 8.47 8.90 8.29 4.91 4.89 4.87 4.84 0.54 0.58 0.62 0.66 1.28 1.41 1.25 1.46
0.0159 14 5.02 74.5 9.42 8.69 9.37 8.61 5.09 5.07 5.04 5.02 0.65 0.69 0.73 0.77 1.16 1.39 1.16 1.40
0.0159 14 5.02 74.8 9.45 8.38 9.56 8.91 4.81 4.78 4.76 4.74 0.75 0.79 0.83 0.87 1.08 1.40 1.05 1.21
0.0159 14 5.00 75.1 9.38 8.60 9.57 10.10 4.50 4.48 4.47 4.47 0.85 0.89 0.93 0.97 1.02 1.22 0.98 0.89
0.0159 14 5.01 100.3 8.33 8.49 8.65 8.39 5.21 5.19 5.18 5.16 0.13 0.16 0.19 0.22 1.61 1.52 1.45 1.56
0.0159 14 5.03 100.4 7.86 8.20 8.35 7.99 5.10 5.08 5.06 5.04 0.23 0.26 0.29 0.32 1.82 1.61 1.53 1.71
0.0159 14 5.02 100.3 7.78 8.00 7.96 7.68 5.04 5.02 5.00 4.97 0.34 0.37 0.40 0.43 1.84 1.69 1.70 1.85
0.0159 14 5.00 100.6 7.63 7.77 7.56 7.48 5.04 5.01 4.98 4.95 0.44 0.47 0.50 0.53 1.94 1.82 1.94 1.98
0.0159 14 5.00 100.1 7.73 7.77 7.55 7.56 5.17 5.13 5.09 5.05 0.54 0.56 0.59 0.62 1.95 1.90 2.03 2.00
0.0159 14 5.02 99.4 7.81 7.71 7.60 7.62 5.26 5.22 5.18 5.14 0.64 0.67 0.70 0.73 1.97 2.02 2.07 2.02
0.0159 14 5.01 99.9 7.97 7.64 7.65 7.70 5.19 5.15 5.12 5.09 0.74 0.77 0.80 0.83 1.81 2.02 1.98 1.92
0.0159 14 5.02 99.3 8.42 7.57 8.00 8.28 5.17 5.15 5.14 5.15 0.84 0.87 0.90 0.93 1.55 2.08 1.76 1.60
0.0159 14 5.01 150.5 7.42 7.70 7.68 7.54 5.05 5.03 5.00 4.97 0.12 0.14 0.16 0.18 2.12 1.88 1.87 1.95
0.0159 14 5.00 149.5 7.48 7.77 7.68 7.61 5.33 5.30 5.26 5.21 0.23 0.25 0.27 0.29 2.33 2.03 2.07 2.09
0.0159 14 5.00 150.3 7.05 7.39 7.29 7.21 5.18 5.13 5.08 5.02 0.33 0.35 0.37 0.39 2.68 2.22 2.27 2.29
0.0159 14 4.98 149.6 7.02 7.45 7.31 7.18 5.35 5.28 5.21 5.13 0.43 0.45 0.47 0.49 2.99 2.30 2.38 2.44
0.0159 14 5.03 150.9 6.83 7.23 7.10 6.99 5.40 5.31 5.21 5.10 0.53 0.55 0.57 0.59 3.53 2.63 2.67 2.66
A
ppendix B
251
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 14 4.97 150.4 6.55 6.91 6.77 6.64 5.22 5.08 4.93 4.76 0.63 0.64 0.66 0.68 3.76 2.72 2.71 2.66
0.0159 14 5.00 149.0 6.77 7.13 6.99 6.87 5.45 5.22 4.96 4.68 0.73 0.75 0.77 0.79 3.81 2.62 2.48 2.29
0.0159 14 5.01 149.3 6.61 7.04 6.91 6.85 5.31 4.95 4.54 4.08 0.82 0.84 0.86 0.88 3.88 2.40 2.11 1.81
0.0159 14 5.00 150.0 6.50 6.96 6.88 6.86 5.20 4.72 4.19 3.59 0.88 0.90 0.91 0.93 3.85 2.24 1.86 1.53
0.0159 14 5.00 200.4 7.72 7.91 7.85 7.77 5.51 5.51 5.50 5.49 0.12 0.13 0.15 0.16 2.27 2.08 2.13 2.20
0.0159 14 5.01 199.7 7.07 7.35 7.25 7.11 5.26 5.24 5.22 5.19 0.22 0.24 0.25 0.27 2.77 2.39 2.48 2.63
0.0159 14 4.99 199.8 7.10 7.42 7.25 7.08 5.58 5.54 5.49 5.44 0.32 0.34 0.35 0.37 3.30 2.66 2.85 3.04
0.0159 14 4.99 200.5 6.75 6.99 6.83 6.65 5.56 5.48 5.40 5.31 0.42 0.43 0.45 0.46 4.21 3.33 3.50 3.75
0.0159 14 5.03 200.7 6.60 6.76 6.56 6.38 5.62 5.51 5.39 5.27 0.52 0.54 0.55 0.57 5.18 4.04 4.33 4.55
0.0159 14 10.0 75.4 10.51 9.41 9.94 10.51 4.64 4.63 4.62 4.60 0.19 0.26 0.34 0.42 1.71 2.10 1.88 1.70
0.0159 14 10.0 75.2 10.17 9.32 9.85 10.48 4.66 4.65 4.63 4.61 0.29 0.37 0.44 0.52 1.82 2.15 1.92 1.71
0.0159 14 10.0 74.5 10.69 9.57 10.15 10.78 4.89 4.87 4.85 4.83 0.39 0.47 0.55 0.63 1.73 2.13 1.89 1.68
0.0159 14 10.0 74.8 10.52 9.04 9.69 10.44 4.39 4.37 4.35 4.32 0.49 0.57 0.65 0.73 1.64 2.15 1.88 1.64
0.0159 14 10.0 74.6 11.04 9.38 10.30 11.18 4.49 4.47 4.44 4.42 0.59 0.67 0.75 0.83 1.53 2.04 1.71 1.48
0.0159 14 10.0 74.8 11.29 9.25 10.73 12.71 4.06 4.03 4.01 3.99 0.69 0.77 0.85 0.93 1.39 1.92 1.49 1.15
0.0159 14 10.0 100 9.9 10.2 10.3 10.1 4.88 4.86 4.84 4.82 0.16 0.22 0.28 0.34 1.98 1.88 1.83 1.92
0.0159 14 10.0 100 9.8 10.2 10.2 9.9 5.01 4.99 4.97 4.94 0.26 0.32 0.38 0.44 2.10 1.93 1.91 2.02
0.0159 14 10.0 100 9.9 10.1 10.1 9.8 4.95 4.93 4.89 4.86 0.36 0.42 0.48 0.54 2.03 1.93 1.94 2.03
0.0159 14 10.0 99 10.1 10.2 10.1 10.0 5.05 5.02 4.98 4.94 0.47 0.53 0.59 0.65 1.99 1.95 1.95 2.00
0.0159 14 10.0 99 9.9 10.0 9.9 9.9 4.89 4.85 4.81 4.76 0.57 0.63 0.69 0.75 2.01 1.96 1.98 1.96
0.0159 14 10.0 100 9.9 9.8 9.9 10.0 4.79 4.74 4.70 4.67 0.67 0.73 0.79 0.85 1.96 1.97 1.94 1.88
0.0159 14 10.0 99 10.7 10.0 10.8 11.4 4.80 4.77 4.75 4.75 0.77 0.83 0.89 0.95 1.72 1.92 1.66 1.51
0.0159 14 10.0 150.4 9.48 9.89 9.83 9.75 5.22 5.19 5.16 5.12 0.14 0.18 0.22 0.26 2.36 2.14 2.15 2.17
0.0159 14 10.0 150.0 8.98 9.35 9.27 9.30 5.03 4.99 4.94 4.88 0.24 0.28 0.32 0.36 2.55 2.31 2.33 2.28
0.0159 14 10.0 150.6 9.10 9.46 9.42 9.38 5.37 5.31 5.25 5.18 0.34 0.38 0.42 0.46 2.68 2.41 2.40 2.38
0.0159 14 10.0 149.8 8.94 9.24 9.21 9.18 5.42 5.34 5.26 5.16 0.44 0.48 0.52 0.56 2.86 2.57 2.54 2.50
0.0159 14 10.0 150.7 8.24 8.72 8.70 8.64 5.17 5.07 4.94 4.80 0.54 0.58 0.62 0.66 3.27 2.75 2.67 2.61
0.0159 14 10.1 150.6 7.97 8.43 8.47 8.41 5.10 4.93 4.73 4.49 0.65 0.69 0.73 0.77 3.52 2.89 2.70 2.57
252
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 14 10.0 150.1 8.09 8.61 8.67 8.67 5.25 4.98 4.66 4.26 0.75 0.79 0.83 0.86 3.54 2.77 2.51 2.28
0.0159 14 10.0 149.8 7.35 7.96 8.17 8.24 4.65 4.19 3.64 2.95 0.85 0.89 0.93 0.97 3.72 2.66 2.21 1.89
0.0159 14 10.1 200.2 9.27 9.71 9.58 9.50 5.31 5.30 5.29 5.27 0.13 0.16 0.19 0.22 2.55 2.29 2.35 2.39
0.0159 14 10.0 199.9 8.68 9.13 8.98 8.89 5.26 5.23 5.20 5.16 0.24 0.27 0.30 0.33 2.94 2.58 2.66 2.69
0.0159 14 10.0 199.9 8.50 8.97 8.83 8.67 5.50 5.45 5.39 5.32 0.33 0.36 0.39 0.42 3.36 2.86 2.93 3.01
0.0159 14 10.0 199.8 8.20 8.49 8.36 8.17 5.49 5.41 5.31 5.20 0.44 0.47 0.50 0.53 3.73 3.27 3.30 3.39
0.0159 14 10.0 199.4 7.78 7.96 7.83 7.64 5.40 5.28 5.15 5.01 0.54 0.57 0.60 0.62 4.23 3.74 3.74 3.83
0.0159 9 4.98 75.0 8.73 9.07 8.80 8.78 4.93 4.92 4.91 4.90 0.14 0.18 0.22 0.26 1.32 1.20 1.29 1.29
0.0159 9 5.00 75.3 8.75 9.09 8.99 8.90 5.03 5.01 5.00 4.99 0.24 0.28 0.32 0.36 1.35 1.23 1.25 1.28
0.0159 9 4.99 74.9 9.39 9.43 9.50 8.99 5.10 5.08 5.07 5.05 0.35 0.39 0.43 0.47 1.16 1.15 1.13 1.27
0.0159 9 4.99 74.8 9.20 9.33 9.50 8.82 5.05 5.03 5.01 4.99 0.45 0.48 0.52 0.56 1.21 1.16 1.11 1.31
0.0159 9 4.98 75.1 8.92 9.51 9.67 8.76 5.18 5.16 5.14 5.11 0.55 0.59 0.63 0.67 1.33 1.15 1.10 1.37
0.0159 9 4.99 75.1 7.95 9.16 9.30 8.56 5.05 5.02 5.00 4.97 0.65 0.69 0.73 0.77 1.73 1.21 1.16 1.39
0.0159 9 4.97 75.0 7.54 8.94 9.22 9.01 4.77 4.74 4.71 4.68 0.75 0.79 0.83 0.87 1.80 1.19 1.11 1.15
0.0159 9 5.01 76.2 8.10 9.61 10.02 10.32 4.97 4.94 4.91 4.88 0.77 0.81 0.85 0.88 1.61 1.08 0.98 0.92
0.0159 9 5.03 99.1 8.36 8.60 8.37 8.20 5.07 5.05 5.04 5.02 0.13 0.16 0.19 0.22 1.53 1.42 1.51 1.58
0.0159 9 5.03 100.1 8.58 8.45 8.15 7.94 5.14 5.12 5.10 5.08 0.23 0.26 0.29 0.32 1.46 1.51 1.65 1.76
0.0159 9 5.03 100.2 8.33 8.16 7.85 7.66 5.17 5.15 5.12 5.09 0.34 0.37 0.40 0.43 1.59 1.67 1.85 1.96
0.0159 9 4.99 99.9 7.92 7.95 7.73 7.63 5.29 5.26 5.22 5.19 0.44 0.47 0.50 0.53 1.90 1.86 1.99 2.05
0.0159 9 5.00 100.0 7.28 7.56 7.44 7.36 5.10 5.06 5.02 4.98 0.54 0.57 0.60 0.63 2.30 2.00 2.07 2.10
0.0159 9 4.99 100.0 7.27 7.55 7.43 7.52 5.15 5.11 5.07 5.03 0.64 0.67 0.69 0.72 2.36 2.05 2.12 2.01
0.0159 9 4.99 99.7 6.87 7.16 7.12 7.25 4.94 4.91 4.87 4.85 0.74 0.77 0.80 0.83 2.60 2.22 2.23 2.09
0.0159 9 4.99 149.9 7.61 7.71 7.72 7.50 5.08 5.06 5.03 5.00 0.12 0.14 0.16 0.18 1.98 1.89 1.86 2.01
0.0159 9 4.99 149.3 7.48 7.78 7.59 7.36 5.19 5.15 5.11 5.06 0.22 0.24 0.26 0.28 2.19 1.90 2.01 2.18
0.0159 9 5.00 149.8 7.19 7.61 7.39 7.20 5.26 5.21 5.16 5.10 0.32 0.34 0.36 0.38 2.60 2.09 2.25 2.40
0.0159 9 5.01 150.5 7.08 7.49 7.28 7.09 5.35 5.30 5.24 5.19 0.43 0.44 0.46 0.48 2.90 2.29 2.46 2.63
0.0159 9 4.99 150.2 7.00 7.30 7.17 7.00 5.50 5.44 5.38 5.32 0.52 0.54 0.56 0.58 3.34 2.70 2.79 2.98
0.0159 9 5.02 150.3 6.78 7.11 6.94 6.76 5.42 5.34 5.25 5.16 0.63 0.65 0.67 0.69 3.70 2.84 2.99 3.15
A
ppendix B
253
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 9 5.03 152.4 6.64 6.91 6.78 6.61 5.44 5.31 5.17 5.00 0.72 0.74 0.76 0.78 4.21 3.16 3.14 3.14
0.0159 9 5.00 149.8 6.19 6.47 6.34 6.19 4.99 4.85 4.69 4.51 0.73 0.75 0.77 0.79 4.20 3.10 3.04 2.99
0.0159 9 5.02 200.2 7.64 7.78 7.70 7.44 5.40 5.37 5.32 5.28 0.12 0.13 0.15 0.16 2.25 2.08 2.12 2.33
0.0159 9 5.01 199.9 7.07 7.23 7.18 7.04 5.33 5.25 5.18 5.09 0.22 0.24 0.25 0.27 2.88 2.54 2.50 2.58
0.0159 9 4.98 199.7 6.69 6.85 6.80 6.64 5.30 5.18 5.06 4.93 0.33 0.34 0.36 0.37 3.58 3.00 2.87 2.93
0.0159 9 4.99 200.5 6.61 6.78 6.79 6.54 5.52 5.37 5.21 5.05 0.43 0.44 0.46 0.47 4.58 3.54 3.17 3.36
0.0159 9 5.02 201.3 6.53 6.66 6.66 6.37 5.68 5.50 5.31 5.13 0.52 0.53 0.55 0.56 5.90 4.32 3.75 4.04
0.0159 9 9.99 75.1 10.9 11.3 11.6 12.1 4.60 4.59 4.58 4.56 0.18 0.26 0.34 0.42 1.59 1.49 1.42 1.32
0.0159 9 10.00 74.9 11.0 11.3 12.5 12.3 4.66 4.65 4.63 4.61 0.29 0.37 0.45 0.52 1.59 1.52 1.27 1.30
0.0159 9 10.04 75.0 11.3 11.6 12.8 12.3 4.74 4.73 4.71 4.68 0.39 0.47 0.55 0.63 1.53 1.46 1.25 1.32
0.0159 9 9.99 74.7 11.3 11.8 12.8 12.5 4.78 4.76 4.74 4.71 0.48 0.56 0.64 0.72 1.54 1.43 1.24 1.29
0.0159 9 10.02 74.6 10.5 11.6 12.9 13.0 4.56 4.54 4.51 4.48 0.59 0.67 0.75 0.83 1.70 1.42 1.19 1.18
0.0159 9 10.0 99.4 10.3 10.2 10.4 10.5 4.84 4.83 4.81 4.79 0.17 0.23 0.29 0.35 1.83 1.87 1.81 1.76
0.0159 9 10.0 99.8 10.7 10.2 10.4 10.1 4.88 4.86 4.83 4.80 0.27 0.33 0.39 0.45 1.73 1.89 1.80 1.89
0.0159 9 10.0 100.1 10.6 10.0 10.1 9.8 5.05 5.03 4.99 4.96 0.36 0.42 0.48 0.54 1.82 2.02 1.95 2.05
0.0159 9 10.0 99.6 9.9 9.9 9.9 9.8 5.11 5.08 5.04 4.99 0.47 0.53 0.59 0.65 2.10 2.08 2.07 2.09
0.0159 9 10.0 99.6 9.3 9.6 9.6 9.7 5.04 5.00 4.95 4.91 0.57 0.63 0.69 0.75 2.37 2.19 2.14 2.10
0.0159 9 10.0 100.0 8.9 9.4 9.8 9.9 4.71 4.66 4.63 4.60 0.67 0.73 0.78 0.84 2.39 2.12 1.94 1.90
0.0159 9 10.0 149.9 9.36 9.09 9.13 9.22 4.90 4.87 4.83 4.79 0.15 0.19 0.23 0.27 2.25 2.38 2.34 2.27
0.0159 9 10.0 149.8 9.36 9.19 9.15 9.29 5.34 5.29 5.24 5.19 0.25 0.29 0.33 0.36 2.50 2.58 2.57 2.45
0.0159 9 10.1 149.9 8.69 8.92 8.94 8.87 5.23 5.17 5.12 5.06 0.35 0.39 0.43 0.47 2.91 2.69 2.64 2.65
0.0159 9 10.0 149.9 8.34 8.74 8.77 8.63 5.20 5.14 5.08 5.01 0.45 0.49 0.53 0.57 3.19 2.79 2.71 2.77
0.0159 9 10.0 150 7.72 7.72 7.98 8.05 5.15 5.08 5.01 4.92 0.55 0.59 0.63 0.67 3.91 3.82 3.39 3.21
0.0159 9 10.0 150.9 7.82 7.89 8.13 8.19 5.27 5.18 5.07 4.92 0.64 0.68 0.72 0.76 3.93 3.69 3.27 3.07
0.0159 9 10.1 149.9 7.72 7.91 8.15 8.26 5.19 5.02 4.79 4.50 0.75 0.79 0.83 0.87 4.00 3.49 3.00 2.68
0.0159 9 10.0 150.9 7.50 7.76 8.08 8.09 5.01 4.77 4.46 4.06 0.80 0.84 0.88 0.92 4.04 3.36 2.78 2.49
0.0159 9 10.1 199.2 9.43 9.43 9.41 9.19 5.32 5.27 5.22 5.15 0.13 0.16 0.19 0.22 2.46 2.43 2.40 2.50
0.0159 9 10.0 199.2 9.05 9.13 9.00 8.83 5.41 5.33 5.24 5.14 0.23 0.26 0.29 0.32 2.75 2.63 2.66 2.71
254
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 9 10.0 199.9 8.56 8.63 8.57 8.39 5.51 5.39 5.25 5.11 0.34 0.37 0.40 0.43 3.31 3.10 3.03 3.06
0.0159 9 10.0 199.3 7.95 8.07 7.94 7.71 5.27 5.11 4.93 4.75 0.44 0.47 0.50 0.53 3.74 3.38 3.33 3.39
0.0159 9 9.9 200 7.88 8.03 7.96 7.73 5.38 5.20 5.00 4.81 0.53 0.56 0.59 0.62 4.01 3.52 3.38 3.41
0.0159 4 4.99 75.5 7.59 7.88 8.07 7.99 4.85 4.83 4.81 4.79 0.15 0.19 0.23 0.27 1.82 1.64 1.53 1.56
0.0159 4 5.03 75.4 7.38 7.74 7.97 7.84 5.07 5.05 5.03 5.01 0.25 0.29 0.33 0.37 2.19 1.87 1.71 1.78
0.0159 4 5.01 75.0 7.25 7.67 7.88 7.62 5.09 5.07 5.05 5.02 0.35 0.39 0.43 0.47 2.33 1.93 1.77 1.94
0.0159 4 4.98 74.7 7.10 7.43 7.55 7.46 5.04 5.01 4.98 4.95 0.45 0.49 0.53 0.57 2.42 2.07 1.95 2.00
0.0159 4 5.01 74.6 6.97 7.23 7.35 7.39 4.96 4.93 4.89 4.86 0.55 0.59 0.63 0.67 2.50 2.19 2.04 1.98
0.0159 4 5.05 74.7 6.97 7.27 7.42 7.52 4.96 4.93 4.89 4.85 0.65 0.69 0.73 0.77 2.52 2.16 2.00 1.90
0.0159 4 5.00 74.8 6.97 7.30 7.57 7.69 5.00 4.96 4.92 4.87 0.75 0.79 0.83 0.87 2.55 2.14 1.89 1.78
0.0159 4 5.00 75.4 6.64 6.97 7.32 7.68 4.66 4.62 4.57 4.52 0.82 0.86 0.90 0.94 2.53 2.13 1.82 1.59
0.0159 4 4.99 101.1 7.49 7.66 7.77 7.63 5.14 5.12 5.10 5.07 0.13 0.16 0.19 0.22 2.13 1.97 1.87 1.96
0.0159 4 5.01 99.82 7.35 7.49 7.55 7.48 5.23 5.20 5.17 5.13 0.24 0.27 0.30 0.33 2.37 2.19 2.10 2.14
0.0159 4 5.01 100.3 7.38 7.54 7.57 7.53 5.34 5.30 5.26 5.22 0.34 0.37 0.40 0.43 2.47 2.24 2.18 2.17
0.0159 4 5.01 100.9 7.10 7.26 7.28 7.24 5.13 5.08 5.03 4.98 0.44 0.47 0.50 0.52 2.55 2.31 2.24 2.23
0.0159 4 4.99 99.88 6.96 7.15 7.18 7.14 5.10 5.04 4.99 4.94 0.53 0.56 0.59 0.62 2.69 2.38 2.29 2.27
0.0159 4 5.02 99.59 6.96 7.17 7.24 7.18 5.19 5.14 5.11 5.08 0.64 0.67 0.70 0.73 2.84 2.49 2.36 2.41
0.0159 4 5.01 99.9 6.89 7.06 7.16 7.11 5.19 5.19 5.22 5.27 0.74 0.77 0.80 0.83 2.96 2.69 2.58 2.72
0.0159 4 5.00 100.6 6.73 6.90 7.06 7.03 5.17 5.22 5.30 5.42 0.80 0.83 0.86 0.89 3.22 2.98 2.84 3.11
0.0159 4 4.98 150.9 7.49 7.58 7.69 7.60 5.42 5.38 5.34 5.30 0.12 0.14 0.16 0.18 2.41 2.28 2.13 2.17
0.0159 4 4.98 149.9 7.42 7.55 7.60 7.42 5.53 5.47 5.41 5.35 0.23 0.25 0.27 0.28 2.64 2.41 2.28 2.41
0.0159 4 4.97 151.2 7.17 7.26 7.28 7.11 5.55 5.47 5.39 5.30 0.32 0.34 0.36 0.38 3.07 2.79 2.64 2.76
0.0159 4 5.04 149.5 6.86 7.06 7.16 6.88 5.44 5.34 5.22 5.11 0.43 0.45 0.47 0.49 3.56 2.93 2.62 2.85
0.0159 4 5.03 149.7 6.57 6.70 6.75 6.49 5.33 5.19 5.03 4.86 0.53 0.55 0.57 0.59 4.09 3.35 2.94 3.11
0.0159 4 4.98 149.8 6.67 6.80 6.83 6.57 5.55 5.33 5.09 4.83 0.63 0.65 0.67 0.69 4.45 3.40 2.87 2.86
0.0159 4 5.01 151.1 6.55 6.66 6.67 6.48 5.47 5.12 4.73 4.29 0.72 0.74 0.76 0.78 4.65 3.26 2.59 2.30
0.0159 4 5.02 199.7 7.39 7.57 7.56 7.33 5.29 5.23 5.17 5.10 0.12 0.13 0.15 0.16 2.40 2.15 2.11 2.26
0.0159 4 5.03 199.3 7.19 7.29 7.22 7.02 5.54 5.44 5.33 5.21 0.22 0.24 0.25 0.27 3.06 2.73 2.67 2.79
A
ppendix B
255
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 4 4.99 200 6.78 6.82 6.77 6.51 5.53 5.39 5.23 5.06 0.32 0.34 0.35 0.37 4.02 3.48 3.26 3.47
0.0159 4 5.00 200.3 6.58 6.59 6.46 6.23 5.66 5.46 5.26 5.04 0.42 0.43 0.45 0.46 5.44 4.46 4.19 4.23
0.0159 4 5.02 200.7 6.48 6.48 6.30 6.04 5.78 5.54 5.30 5.05 0.52 0.54 0.55 0.56 7.20 5.40 5.03 5.10
0.0159 4 10.0 75.2 9.26 9.60 9.70 9.65 4.63 4.62 4.59 4.57 0.18 0.26 0.34 0.42 2.17 2.02 1.97 1.98
0.0159 4 10.0 75.5 9.05 9.68 9.73 9.60 4.98 4.96 4.93 4.90 0.28 0.36 0.44 0.52 2.47 2.13 2.10 2.14
0.0159 4 10.0 74.6 9.03 9.55 9.64 9.51 4.87 4.84 4.81 4.78 0.39 0.47 0.55 0.63 2.41 2.13 2.08 2.12
0.0159 4 10.0 75.5 8.81 9.33 9.44 9.47 4.82 4.79 4.75 4.72 0.49 0.57 0.65 0.73 2.52 2.22 2.15 2.12
0.0159 4 10.0 75.4 8.57 9.12 9.43 9.74 4.57 4.53 4.49 4.45 0.59 0.67 0.75 0.83 2.51 2.19 2.04 1.90
0.0159 4 10.1 74.6 8.61 9.16 9.64 9.91 4.63 4.60 4.55 4.50 0.67 0.75 0.83 0.91 2.53 2.21 1.98 1.86
0.0159 4 10.0 101.1 9.07 9.46 9.76 9.47 4.90 4.87 4.84 4.81 0.16 0.22 0.28 0.34 2.41 2.19 2.04 2.15
0.0159 4 10.0 101.5 8.88 9.14 9.37 9.23 4.85 4.82 4.78 4.74 0.26 0.32 0.38 0.44 2.49 2.32 2.18 2.23
0.0159 4 10.0 100.9 8.98 9.10 9.32 9.28 5.00 4.96 4.91 4.86 0.37 0.43 0.49 0.54 2.52 2.42 2.28 2.26
0.0159 4 10.0 101.0 8.92 9.09 9.33 9.35 5.06 5.01 4.95 4.90 0.47 0.53 0.59 0.65 2.60 2.46 2.29 2.25
0.0159 4 10.0 99.8 8.54 8.83 9.09 9.18 4.83 4.77 4.73 4.70 0.57 0.63 0.69 0.75 2.71 2.48 2.30 2.24
0.0159 4 10.0 101.0 8.42 8.71 9.09 9.20 4.82 4.79 4.79 4.83 0.67 0.73 0.79 0.85 2.79 2.56 2.34 2.30
0.0159 4 10.0 100.8 8.23 8.48 8.97 9.53 4.70 4.73 4.82 5.01 0.77 0.83 0.89 0.95 2.83 2.67 2.42 2.21
0.0159 4 10.0 150 8.88 9.01 9.19 9.21 5.14 5.10 5.04 4.98 0.15 0.19 0.23 0.27 2.69 2.57 2.42 2.38
0.0159 4 10.1 149.5 8.94 9.06 9.23 9.11 5.36 5.29 5.22 5.14 0.25 0.29 0.33 0.37 2.82 2.67 2.51 2.54
0.0159 4 10.0 150.5 8.44 8.56 8.70 8.56 5.23 5.14 5.05 4.94 0.35 0.39 0.43 0.47 3.14 2.94 2.75 2.77
0.0159 4 10.0 150 8.23 8.24 8.41 8.17 5.33 5.22 5.09 4.93 0.45 0.49 0.53 0.57 3.47 3.33 3.02 3.11
0.0159 4 10.0 150.6 8.07 8.14 8.32 8.08 5.37 5.21 5.02 4.79 0.55 0.59 0.63 0.67 3.73 3.44 3.05 3.06
0.0159 4 10.0 150.5 8.00 8.04 8.22 8.03 5.43 5.18 4.87 4.49 0.65 0.69 0.73 0.77 3.90 3.50 3.00 2.83
0.0159 4 10.0 150.5 7.53 7.59 7.75 7.68 5.01 4.58 4.04 3.37 0.75 0.79 0.83 0.87 4.00 3.35 2.71 2.34
0.0159 4 10.0 150.2 7.60 7.71 7.97 7.93 5.01 4.43 3.70 2.79 0.81 0.85 0.89 0.93 3.89 3.07 2.36 1.95
0.0159 4 10.0 200.7 9.16 9.23 9.35 9.07 5.38 5.31 5.23 5.14 0.13 0.16 0.19 0.22 2.66 2.56 2.44 2.56
0.0159 4 10.1 199.7 8.46 8.50 8.59 8.30 5.31 5.20 5.07 4.93 0.23 0.26 0.29 0.32 3.21 3.06 2.87 3.00
0.0159 4 10.0 200.8 7.93 7.93 8.04 7.74 5.33 5.17 4.99 4.80 0.33 0.36 0.39 0.42 3.89 3.65 3.31 3.42
0.0159 4 10.0 201.7 7.60 7.50 7.54 7.25 5.41 5.20 4.97 4.73 0.43 0.46 0.49 0.52 4.59 4.38 3.91 3.98
256
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 4 10.0 200.7 7.66 7.55 7.59 7.31 5.74 5.49 5.23 4.97 0.54 0.57 0.59 0.62 5.25 4.89 4.28 4.30
0.0159 3 4.99 75.1 8.06 8.07 8.13 7.83 5.25 5.23 5.20 5.18 0.15 0.19 0.23 0.26 1.78 1.76 1.71 1.89
0.0159 3 5.02 75.2 7.59 7.69 7.79 7.68 5.32 5.29 5.27 5.24 0.25 0.29 0.33 0.37 2.22 2.10 2.00 2.06
0.0159 3 4.99 74.9 7.44 7.53 7.74 7.60 5.25 5.22 5.20 5.17 0.35 0.39 0.43 0.47 2.29 2.17 1.97 2.05
0.0159 3 4.99 75.0 7.35 7.53 7.70 7.55 5.21 5.18 5.14 5.11 0.45 0.49 0.53 0.57 2.34 2.13 1.96 2.05
0.0159 3 4.99 75.3 7.04 7.15 7.33 7.29 4.93 4.89 4.85 4.81 0.55 0.59 0.63 0.67 2.36 2.21 2.02 2.02
0.0159 3 4.98 75.3 7.25 7.51 7.69 7.63 5.15 5.11 5.07 5.02 0.65 0.69 0.73 0.77 2.38 2.08 1.90 1.91
0.0159 3 4.98 74.9 6.98 7.26 7.49 7.46 4.89 4.85 4.80 4.75 0.75 0.79 0.83 0.87 2.39 2.07 1.85 1.84
0.0159 3 5.03 100.9 7.59 7.68 7.79 7.56 5.20 5.17 5.14 5.11 0.13 0.16 0.19 0.22 2.11 2.01 1.91 2.06
0.0159 3 5.00 100.9 7.32 7.52 7.64 7.41 5.24 5.20 5.16 5.12 0.23 0.26 0.29 0.32 2.40 2.16 2.02 2.19
0.0159 3 5.00 100.6 7.25 7.41 7.49 7.33 5.18 5.14 5.09 5.04 0.33 0.36 0.39 0.42 2.42 2.20 2.09 2.19
0.0159 3 5.02 100.4 7.20 7.34 7.43 7.28 5.17 5.12 5.07 5.01 0.44 0.47 0.50 0.53 2.48 2.27 2.13 2.22
0.0159 3 4.98 100.5 7.27 7.44 7.50 7.36 5.35 5.30 5.24 5.19 0.54 0.57 0.59 0.62 2.61 2.33 2.22 2.31
0.0159 3 5.00 99.48 6.88 7.10 7.17 7.01 5.15 5.11 5.07 5.05 0.64 0.67 0.70 0.73 2.91 2.52 2.39 2.55
0.0159 3 5.01 99.7 6.76 7.01 7.11 7.00 5.23 5.22 5.24 5.28 0.75 0.78 0.81 0.84 3.28 2.82 2.69 2.94
0.0159 3 4.97 100.4 6.71 7.02 7.13 7.15 5.32 5.38 5.48 5.62 0.84 0.87 0.90 0.93 3.57 3.06 3.04 3.27
0.0159 3 4.98 150.3 7.49 7.61 7.68 7.44 5.40 5.35 5.30 5.25 0.12 0.14 0.16 0.18 2.38 2.21 2.10 2.28
0.0159 3 5.00 149.8 7.21 7.29 7.33 7.12 5.36 5.29 5.22 5.14 0.23 0.25 0.27 0.28 2.71 2.51 2.37 2.53
0.0159 3 5.03 149.5 7.15 7.23 7.21 7.00 5.50 5.41 5.31 5.21 0.33 0.35 0.37 0.39 3.05 2.77 2.66 2.82
0.0159 3 5.01 149.4 6.79 6.89 6.90 6.68 5.50 5.36 5.20 5.01 0.42 0.44 0.46 0.48 3.89 3.27 2.95 3.00
0.0159 3 5.00 151.2 6.57 6.67 6.68 6.41 5.43 5.13 4.76 4.32 0.52 0.54 0.56 0.58 4.42 3.25 2.61 2.40
0.0159 3 5.01 200.6 7.48 7.56 7.58 7.26 5.48 5.41 5.34 5.26 0.12 0.13 0.15 0.16 2.51 2.35 2.25 2.51
0.0159 3 5.01 199.5 6.88 6.91 6.88 6.62 5.34 5.22 5.09 4.96 0.22 0.24 0.25 0.27 3.26 2.98 2.81 3.03
0.0159 3 5.02 199.9 6.80 6.86 6.78 6.52 5.67 5.50 5.32 5.14 0.32 0.33 0.35 0.36 4.46 3.70 3.46 3.64
0.0159 3 4.99 200.5 6.58 6.63 6.51 6.22 5.80 5.59 5.36 5.14 0.42 0.43 0.45 0.46 6.39 4.81 4.37 4.63
0.0159 3 4.98 199.3 7.59 7.71 7.55 7.49 5.48 5.41 5.34 5.26 0.12 0.14 0.15 0.17 2.37 2.18 2.26 2.24
0.0159 3 5.02 200.2 7.08 7.09 7.11 6.89 5.53 5.41 5.29 5.15 0.22 0.24 0.25 0.27 3.26 3.01 2.77 2.90
0.0159 3 5.00 200.2 6.71 6.66 6.63 6.43 5.56 5.39 5.22 5.03 0.32 0.33 0.35 0.36 4.39 3.95 3.55 3.58
A
ppendix B
257
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 3 5.02 200.4 6.73 6.72 6.73 6.43 5.80 5.60 5.40 5.20 0.37 0.38 0.40 0.41 5.38 4.51 3.81 4.10
0.0159 3 10.0 75.4 9.40 9.17 9.08 9.37 4.55 4.52 4.49 4.47 0.18 0.26 0.34 0.42 2.07 2.16 2.19 2.04
0.0159 3 10.0 74.9 9.20 9.29 9.34 9.55 4.77 4.74 4.71 4.68 0.29 0.37 0.45 0.53 2.26 2.20 2.16 2.05
0.0159 3 10.0 75.2 9.20 9.29 9.37 9.63 4.84 4.81 4.77 4.74 0.38 0.46 0.54 0.62 2.30 2.24 2.18 2.05
0.0159 3 10.0 75.4 8.84 8.86 9.11 9.53 4.54 4.50 4.46 4.42 0.49 0.57 0.65 0.73 2.34 2.31 2.16 1.97
0.0159 3 10.0 75.0 8.86 9.05 9.39 9.83 4.56 4.51 4.47 4.42 0.59 0.67 0.75 0.83 2.34 2.22 2.04 1.86
0.0159 3 10.0 75.3 8.34 8.90 9.34 10.9 4.12 4.07 4.02 3.97 0.69 0.77 0.84 0.92 2.38 2.08 1.89 1.44
0.0159 3 10.0 99.96 9.18 9.37 9.43 9.41 4.99 4.96 4.92 4.88 0.16 0.22 0.28 0.34 2.39 2.27 2.22 2.21
0.0159 3 10.0 99.87 8.85 9.18 9.22 9.27 4.93 4.89 4.85 4.80 0.26 0.32 0.38 0.44 2.56 2.34 2.29 2.24
0.0159 3 10.0 99.98 8.92 9.07 9.11 9.24 4.99 4.94 4.89 4.83 0.37 0.43 0.49 0.55 2.57 2.44 2.38 2.28
0.0159 3 10.0 99.87 8.53 8.83 8.85 8.99 4.78 4.72 4.67 4.61 0.47 0.53 0.59 0.65 2.69 2.45 2.41 2.30
0.0159 3 10.0 100.6 8.58 9.07 9.11 9.23 5.04 4.98 4.94 4.91 0.57 0.63 0.69 0.75 2.84 2.46 2.41 2.33
0.0159 3 10.0 100.2 8.35 8.92 9.10 9.19 4.97 4.94 4.93 4.97 0.67 0.73 0.79 0.85 2.98 2.53 2.42 2.39
0.0159 3 10.0 100.5 8.09 8.65 8.96 9.80 4.83 4.85 4.92 5.06 0.77 0.83 0.89 0.95 3.08 2.64 2.48 2.12
0.0159 3 10.0 150.4 8.79 8.98 9.01 8.80 5.07 5.02 4.95 4.88 0.14 0.18 0.22 0.26 2.71 2.54 2.48 2.57
0.0159 3 10.0 149.5 8.78 8.98 8.94 8.77 5.29 5.21 5.13 5.04 0.24 0.28 0.32 0.36 2.88 2.66 2.63 2.69
0.0159 3 10.0 149.9 8.28 8.48 8.39 8.26 5.17 5.07 4.95 4.80 0.34 0.38 0.42 0.46 3.22 2.94 2.92 2.90
0.0159 3 10.0 150.6 7.97 8.22 8.20 8.02 5.27 5.09 4.84 4.49 0.45 0.49 0.53 0.57 3.74 3.22 3.00 2.85
0.0159 3 10.0 150.2 7.75 8.00 7.97 7.78 5.13 4.73 4.16 3.35 0.54 0.58 0.62 0.66 3.85 3.09 2.64 2.27
0.0159 3 10.0 200.9 8.51 8.41 8.32 8.31 5.20 5.12 5.02 4.92 0.13 0.16 0.19 0.22 3.03 3.06 3.06 2.97
0.0159 3 10.0 199.7 8.10 8.09 8.00 7.91 5.32 5.19 5.04 4.87 0.24 0.27 0.30 0.33 3.61 3.47 3.40 3.31
0.0159 3 10.0 199.7 7.78 7.88 7.76 7.56 5.40 5.21 5.01 4.80 0.34 0.37 0.39 0.42 4.23 3.78 3.66 3.65
0.0159 3 10.1 200.1 7.71 7.80 7.67 7.40 5.68 5.45 5.21 4.96 0.44 0.47 0.50 0.52 4.97 4.30 4.10 4.13
0.0159 3 10.0 200.3 7.64 7.73 7.60 7.29 5.80 5.55 5.28 4.99 0.52 0.55 0.58 0.61 5.49 4.62 4.35 4.40
258
Appendix B
Table B.8 - Flow boiling heat transfer coefficient experimental results with local saturation temperature Tsat = 15 oC measured at each section of the of the test section inside 15.9 mm internal diameter tube.
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 Plain tube 9.95 74.9 21.5 22.0 22.6 23.4 14.3 14.3 14.3 14.3 0.10 0.18 0.27 0.35 1.39 1.29 1.21 1.09
0.0159 Plain tube 9.98 75.1 21.7 22.2 22.5 23.3 14.1 14.1 14.1 14.1 0.16 0.24 0.33 0.41 1.32 1.23 1.19 1.08
0.0159 Plain tube 9.98 75.1 22.3 22.8 23.1 24.1 14.3 14.3 14.3 14.3 0.22 0.30 0.39 0.47 1.26 1.19 1.14 1.03
0.0159 Plain tube 10.00 75.3 22.2 22.6 22.9 23.8 14.1 14.1 14.1 14.1 0.28 0.36 0.44 0.53 1.23 1.17 1.14 1.03
0.0159 Plain tube 9.99 75.3 22.4 22.8 23.4 24.3 14.2 14.2 14.2 14.2 0.38 0.46 0.55 0.63 1.22 1.16 1.08 0.99
0.0159 Plain tube 9.99 75.2 22.3 22.9 23.7 23.9 13.9 13.9 13.9 13.9 0.47 0.56 0.64 0.72 1.19 1.12 1.03 1.00
0.0159 Plain tube 10.04 75.7 22.4 22.9 24.0 25.4 13.7 13.7 13.7 13.7 0.58 0.66 0.74 0.82 1.15 1.09 0.98 0.86
0.0159 Plain tube 9.94 74.4 22.4 22.9 23.8 24.4 13.6 13.6 13.6 13.6 0.60 0.69 0.77 0.85 1.13 1.07 0.98 0.92
0.0159 Plain tube 10.06 76.5 22.9 23.7 25.2 23.1 14.0 14.0 14.0 14.0 0.65 0.73 0.81 0.89 1.13 1.04 0.90 1.11
0.0159 Plain tube 9.99 100.1 22.0 22.3 22.6 22.7 14.8 14.8 14.8 14.8 0.10 0.16 0.23 0.29 1.39 1.32 1.28 1.25
0.0159 Plain tube 9.96 99.59 21.8 22.1 22.3 22.3 14.5 14.5 14.5 14.5 0.14 0.20 0.26 0.33 1.36 1.31 1.28 1.27
0.0159 Plain tube 9.98 100.1 21.7 21.8 22.2 22.4 14.5 14.5 14.5 14.5 0.21 0.27 0.33 0.39 1.41 1.37 1.30 1.26
0.0159 Plain tube 9.93 99.98 21.6 21.7 22.1 22.3 14.5 14.5 14.5 14.5 0.31 0.37 0.43 0.50 1.40 1.38 1.30 1.27
0.0159 Plain tube 9.88 100.8 21.6 21.7 22.2 22.4 14.5 14.5 14.5 14.5 0.41 0.47 0.53 0.59 1.39 1.36 1.28 1.24
0.0159 Plain tube 9.93 99.89 21.9 22.0 22.5 22.7 14.5 14.5 14.5 14.5 0.51 0.57 0.63 0.69 1.35 1.32 1.25 1.21
0.0159 Plain tube 9.91 99.95 21.9 22.1 22.6 22.8 14.5 14.4 14.4 14.4 0.61 0.67 0.73 0.79 1.33 1.30 1.22 1.18
0.0159 Plain tube 9.93 100.7 21.9 22.0 22.6 23.0 14.4 14.4 14.3 14.3 0.68 0.74 0.80 0.86 1.33 1.29 1.21 1.15
0.0159 Plain tube 9.97 99.65 21.7 22.0 22.7 23.9 14.2 14.1 14.1 14.1 0.75 0.81 0.87 0.93 1.32 1.28 1.17 1.02
0.0159 Plain tube 10.0 150.4 21.1 21.2 21.4 21.4 14.7 14.7 14.7 14.7 0.08 0.12 0.16 0.20 1.55 1.54 1.48 1.49
0.0159 Plain tube 9.9 150.2 21.2 21.1 21.2 21.3 14.7 14.7 14.7 14.7 0.14 0.18 0.22 0.26 1.54 1.55 1.52 1.50
0.0159 Plain tube 9.9 150.6 21.3 21.3 21.6 21.5 14.9 14.9 14.9 14.9 0.24 0.28 0.32 0.36 1.55 1.56 1.49 1.51
0.0159 Plain tube 9.9 150.1 21.5 21.5 21.7 21.6 14.9 14.9 14.9 14.9 0.34 0.38 0.42 0.46 1.52 1.51 1.46 1.48
0.0159 Plain tube 10.0 149.6 21.5 21.4 21.7 21.4 14.8 14.8 14.8 14.7 0.44 0.48 0.52 0.56 1.50 1.50 1.44 1.50
0.0159 Plain tube 10.0 149.4 21.4 21.3 21.5 21.2 14.9 14.9 14.9 14.9 0.54 0.58 0.62 0.66 1.55 1.58 1.53 1.59
0.0159 Plain tube 10.0 149.8 20.8 20.7 20.8 20.6 14.9 14.8 14.8 14.8 0.64 0.68 0.72 0.76 1.68 1.72 1.67 1.72
0.0159 Plain tube 10.0 149.6 21.3 21.0 20.9 20.8 14.9 14.8 14.8 14.8 0.74 0.78 0.82 0.86 1.56 1.61 1.64 1.66
A
ppendix B
259
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 Plain tube 10.0 150.1 20.4 20.3 20.3 20.6 14.8 14.8 14.8 14.8 0.82 0.86 0.90 0.94 1.80 1.84 1.81 1.71
0.0159 Plain tube 10.0 200 19.1 19.1 19.2 19.0 15.4 15.3 15.3 15.2 0.13 0.17 0.20 0.23 2.72 2.62 2.52 2.63
0.0159 Plain tube 10.0 200.9 18.5 18.6 18.7 18.5 15.3 15.3 15.2 15.1 0.24 0.27 0.30 0.33 3.19 3.01 2.89 2.92
0.0159 Plain tube 10.0 201.2 18.2 18.3 18.4 18.3 15.5 15.4 15.3 15.2 0.33 0.37 0.40 0.43 3.73 3.43 3.24 3.21
0.0159 Plain tube 10.0 200.7 17.9 18.1 18.1 17.9 15.5 15.4 15.3 15.2 0.44 0.47 0.50 0.53 4.23 3.73 3.56 3.66
0.0159 Plain tube 10.1 200.6 17.4 17.6 17.6 17.4 15.3 15.3 15.3 15.4 0.54 0.57 0.60 0.64 4.81 4.38 4.37 4.89
0.0159 14 10.0 75.0 20.4 20.9 21.8 21.3 14.6 14.6 14.6 14.6 0.19 0.27 0.35 0.44 1.73 1.59 1.40 1.51
0.0159 14 10.0 74.4 20.4 21.1 21.8 21.5 14.8 14.8 14.8 14.8 0.29 0.38 0.46 0.54 1.79 1.59 1.43 1.49
0.0159 14 10.0 74.9 20.4 20.9 21.8 21.6 14.7 14.7 14.7 14.7 0.39 0.47 0.55 0.64 1.77 1.62 1.40 1.46
0.0159 14 10.0 75.0 20.7 21.0 22.1 21.8 14.5 14.5 14.5 14.5 0.49 0.57 0.65 0.74 1.64 1.56 1.32 1.38
0.0159 14 10.0 75.2 21.2 21.2 22.5 22.0 14.6 14.6 14.6 14.6 0.59 0.67 0.75 0.83 1.53 1.53 1.26 1.36
0.0159 14 10.0 75.0 21.7 21.4 23.3 23.6 14.2 14.2 14.2 14.2 0.68 0.77 0.85 0.93 1.33 1.40 1.10 1.07
0.0159 14 10.1 100.1 20.3 20.7 20.9 20.5 15.0 14.9 14.9 14.9 0.17 0.23 0.29 0.35 1.90 1.75 1.68 1.79
0.0159 14 10.0 100.5 19.7 20.3 20.7 20.3 14.9 14.9 14.9 14.9 0.26 0.33 0.39 0.45 2.09 1.85 1.73 1.85
0.0159 14 10.0 101.3 20.0 20.5 20.7 20.2 14.8 14.8 14.7 14.7 0.37 0.43 0.49 0.55 1.93 1.75 1.69 1.81
0.0159 14 10.0 99.6 20.3 20.6 20.9 20.3 14.9 14.9 14.8 14.8 0.47 0.53 0.59 0.66 1.86 1.74 1.66 1.82
0.0159 14 10.0 100.9 20.2 20.4 20.8 20.2 14.8 14.8 14.7 14.7 0.56 0.62 0.69 0.75 1.84 1.79 1.66 1.82
0.0159 14 10.0 100.0 20.7 20.4 21.1 20.6 14.7 14.6 14.6 14.6 0.66 0.72 0.79 0.85 1.67 1.74 1.55 1.69
0.0159 14 10.0 99.5 21.7 20.4 21.7 21.3 14.6 14.6 14.6 14.6 0.77 0.83 0.90 0.96 1.42 1.72 1.41 1.49
0.0159 14 10.0 150.5 19.2 19.8 19.8 19.7 15.0 15.0 15.0 15.0 0.15 0.19 0.23 0.27 2.38 2.09 2.10 2.10
0.0159 14 10.0 150.2 19.0 19.5 19.4 19.4 15.0 15.0 15.0 14.9 0.25 0.29 0.33 0.37 2.50 2.21 2.28 2.23
0.0159 14 10.0 149.8 19.0 19.4 19.2 19.3 15.1 15.1 15.0 15.0 0.35 0.39 0.43 0.47 2.57 2.33 2.40 2.31
0.0159 14 10.0 150.2 18.8 19.2 19.0 19.1 15.0 14.9 14.9 14.7 0.45 0.49 0.53 0.57 2.66 2.39 2.41 2.32
0.0159 14 10.0 150.2 18.7 19.0 18.9 18.9 15.0 14.8 14.6 14.4 0.54 0.59 0.63 0.67 2.68 2.42 2.36 2.20
0.0159 14 10.0 150.7 18.3 18.6 18.6 18.6 14.6 14.3 13.9 13.3 0.65 0.69 0.73 0.77 2.73 2.36 2.12 1.87
0.0159 14 10.0 151.1 18.3 18.9 18.9 19.0 14.7 14.1 13.2 12.0 0.74 0.78 0.82 0.86 2.77 2.09 1.75 1.43
0.0159 14 10.0 149.3 17.8 18.3 18.5 18.7 13.9 12.5 10.8 8.4 0.85 0.89 0.93 0.97 2.57 1.73 1.29 0.98
0.0159 14 10.0 200.4 18.9 19.4 19.3 19.3 15.0 15.0 14.9 14.9 0.14 0.17 0.20 0.23 2.57 2.25 2.30 2.31
260
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 14 9.9 200.4 18.9 19.4 19.4 19.3 15.3 15.3 15.2 15.2 0.23 0.26 0.29 0.33 2.78 2.44 2.42 2.44
0.0159 14 10.0 200 18.3 18.8 18.8 18.7 15.1 15.0 14.9 14.9 0.34 0.37 0.41 0.44 3.06 2.65 2.63 2.62
0.0159 14 10.1 199.1 18.1 18.6 18.6 18.5 15.1 15.0 14.9 14.8 0.44 0.47 0.50 0.54 3.34 2.80 2.79 2.78
0.0159 14 10.0 200.5 18.2 18.6 18.6 18.5 15.4 15.3 15.2 15.0 0.54 0.57 0.60 0.63 3.62 3.09 2.93 2.89
0.0159 14 10.0 201.1 17.9 18.2 18.3 18.1 15.3 15.1 14.8 14.6 0.64 0.67 0.70 0.73 3.79 3.18 2.94 2.81
0.0159 14 10.0 199.9 17.8 18.1 18.2 18.1 15.2 14.9 14.5 14.0 0.73 0.77 0.80 0.83 3.84 3.09 2.69 2.46
0.0159 14 10.0 200.7 17.3 17.7 17.9 17.9 14.6 14.1 13.4 12.6 0.83 0.86 0.89 0.93 3.82 2.76 2.24 1.89
0.0159 9 9.99 75.3 21.2 21.7 22.3 23.1 14.7 14.7 14.6 14.6 0.19 0.27 0.35 0.43 1.53 1.42 1.32 1.19
0.0159 9 9.98 75.0 21.4 21.7 22.8 23.1 14.6 14.6 14.6 14.6 0.29 0.37 0.45 0.53 1.46 1.41 1.22 1.18
0.0159 9 10.03 75.2 21.4 21.6 22.9 23.1 14.6 14.6 14.5 14.5 0.39 0.47 0.55 0.64 1.46 1.43 1.20 1.17
0.0159 9 10.04 75.0 21.2 21.6 23.2 23.5 14.1 14.1 14.1 14.1 0.49 0.57 0.65 0.74 1.41 1.33 1.10 1.07
0.0159 9 9.98 74.9 21.5 22.1 23.6 24.4 14.3 14.2 14.2 14.2 0.59 0.67 0.75 0.84 1.39 1.27 1.07 0.98
0.0159 9 10.0 99.9 20.6 20.6 21.0 21.4 15.0 15.0 14.9 14.9 0.17 0.23 0.29 0.35 1.79 1.77 1.66 1.56
0.0159 9 10.0 100.1 20.8 20.5 21.0 21.2 14.9 14.9 14.9 14.8 0.27 0.33 0.39 0.45 1.70 1.77 1.63 1.58
0.0159 9 10.0 100.9 21.0 20.5 20.9 20.9 14.9 14.9 14.9 14.8 0.36 0.42 0.49 0.55 1.66 1.78 1.67 1.66
0.0159 9 10.1 100.1 20.7 20.5 20.8 20.4 14.9 14.8 14.8 14.8 0.47 0.53 0.59 0.66 1.73 1.80 1.69 1.80
0.0159 9 10.1 100.6 19.8 20.1 20.4 20.0 14.7 14.7 14.7 14.7 0.57 0.63 0.70 0.76 1.98 1.88 1.77 1.87
0.0159 9 10.0 100.6 19.2 20.0 20.6 20.2 14.6 14.6 14.6 14.5 0.67 0.73 0.79 0.85 2.19 1.85 1.67 1.79
0.0159 9 10.1 99.5 19.3 20.6 21.9 22.5 14.7 14.7 14.7 14.7 0.77 0.83 0.89 0.95 2.17 1.70 1.39 1.29
0.0159 9 10.0 150.4 19.8 19.6 19.8 20.0 15.1 15.1 15.1 15.1 0.14 0.18 0.22 0.27 2.15 2.23 2.13 2.04
0.0159 9 10.0 149.9 19.6 19.3 19.5 19.6 15.2 15.2 15.1 15.1 0.25 0.29 0.33 0.37 2.29 2.44 2.32 2.26
0.0159 9 10.0 150.4 18.7 18.8 18.9 19.0 15.0 14.9 14.9 14.9 0.35 0.39 0.44 0.48 2.68 2.63 2.54 2.42
0.0159 9 10.1 150.7 18.4 18.8 19.0 19.0 15.1 15.0 15.0 15.0 0.45 0.49 0.53 0.57 3.02 2.68 2.53 2.50
0.0159 9 10.0 149.8 18.2 18.6 18.9 18.9 15.1 15.1 15.0 15.0 0.55 0.59 0.63 0.67 3.27 2.81 2.60 2.58
0.0159 9 10.0 148.7 18.1 18.6 18.9 18.9 15.1 15.1 15.1 15.1 0.66 0.70 0.74 0.78 3.40 2.91 2.65 2.64
0.0159 9 10.0 149.5 17.9 18.4 18.5 18.6 15.1 15.1 15.1 15.1 0.75 0.79 0.83 0.87 3.53 3.01 2.93 2.84
0.0159 9 10.0 147.6 17.9 18.4 18.8 19.2 14.9 14.9 15.0 15.0 0.85 0.89 0.93 0.98 3.42 2.92 2.60 2.41
0.0159 9 10.0 200.4 19.3 19.1 19.2 19.2 15.1 15.0 15.0 15.0 0.13 0.17 0.20 0.23 2.39 2.49 2.38 2.36
A
ppendix B
261
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
h [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 9 10.0 200.8 18.9 18.8 18.9 18.9 15.2 15.1 15.1 15.0 0.23 0.26 0.30 0.33 2.70 2.75 2.67 2.59
0.0159 9 9.9 200.9 18.4 18.3 18.4 18.5 15.2 15.1 15.1 15.0 0.33 0.37 0.40 0.43 3.07 3.12 2.95 2.81
0.0159 9 9.8 202.2 17.9 17.8 18.0 18.0 15.0 15.0 14.9 14.8 0.43 0.46 0.49 0.52 3.45 3.50 3.15 3.06
0.0159 9 10.0 200.4 18.1 18.4 18.4 18.2 15.3 15.2 15.1 15.0 0.54 0.57 0.61 0.64 3.56 3.20 3.04 3.08
0.0159 9 10.0 200.6 17.9 18.2 18.2 18.0 15.2 15.1 15.0 14.8 0.63 0.67 0.70 0.73 3.71 3.26 3.15 3.16
0.0159 9 10.0 200.1 17.8 18.0 18.0 17.9 15.3 15.2 15.1 14.9 0.74 0.77 0.80 0.83 4.08 3.49 3.36 3.36
0.0159 9 9.9 199.5 17.7 18.1 18.2 18.1 15.4 15.3 15.2 15.1 0.83 0.86 0.89 0.92 4.29 3.51 3.37 3.37
0.0159 9 10.0 199.8 17.5 18.1 18.2 18.1 15.3 15.2 15.2 15.1 0.88 0.92 0.95 0.98 4.49 3.51 3.36 3.37
0.0159 4 10.1 74.8 19.6 19.8 20.3 20.6 14.7 14.7 14.7 14.7 0.19 0.27 0.35 0.44 2.05 1.96 1.80 1.70
0.0159 4 10.0 75.0 19.2 20.0 20.5 20.6 14.6 14.6 14.6 14.5 0.29 0.38 0.46 0.54 2.16 1.86 1.70 1.66
0.0159 4 10.0 75.0 19.3 20.1 20.6 20.5 14.7 14.7 14.6 14.6 0.38 0.47 0.55 0.63 2.18 1.83 1.67 1.70
0.0159 4 10.0 75.0 19.3 20.0 20.3 20.5 14.8 14.8 14.7 14.7 0.49 0.57 0.66 0.74 2.23 1.92 1.80 1.74
0.0159 4 10.0 74.7 19.0 19.8 20.1 20.2 14.6 14.6 14.5 14.5 0.59 0.67 0.76 0.84 2.27 1.91 1.81 1.76
0.0159 4 10.0 99.4 19.1 19.4 19.6 19.7 15.0 15.0 14.9 14.9 0.17 0.23 0.29 0.35 2.42 2.27 2.15 2.12
0.0159 4 10.1 100.5 18.9 19.2 19.4 19.4 14.9 14.9 14.9 14.9 0.27 0.33 0.39 0.45 2.56 2.38 2.26 2.22
0.0159 4 10.0 100.4 18.7 19.0 19.2 19.2 14.8 14.8 14.7 14.7 0.37 0.43 0.49 0.55 2.58 2.35 2.25 2.21
0.0159 4 10.0 99.8 18.7 18.9 19.2 19.3 14.8 14.8 14.8 14.7 0.47 0.53 0.59 0.66 2.60 2.44 2.27 2.20
0.0159 4 10.1 100.7 18.8 19.0 19.4 19.5 15.0 14.9 14.9 14.9 0.57 0.63 0.69 0.76 2.67 2.46 2.28 2.19
0.0159 4 10.0 99.6 18.5 18.9 19.3 19.6 14.8 14.8 14.9 15.0 0.67 0.74 0.80 0.86 2.73 2.46 2.26 2.18
0.0159 4 10.0 100.7 18.2 18.6 19.2 19.6 14.6 14.6 14.7 15.0 0.77 0.83 0.89 0.95 2.77 2.52 2.28 2.17
0.0159 4 10.1 151 18.7 19.0 19.2 19.4 15.1 15.1 15.1 15.0 0.14 0.18 0.23 0.27 2.80 2.57 2.43 2.33
0.0159 4 10.1 150.1 18.5 18.6 18.8 18.9 15.0 15.0 14.9 14.8 0.25 0.29 0.33 0.37 2.86 2.78 2.59 2.51
0.0159 4 10.0 151.5 18.5 18.7 19.0 19.0 15.3 15.2 15.2 15.1 0.35 0.39 0.43 0.47 3.13 2.90 2.66 2.61
0.0159 4 10.0 150.5 18.0 18.2 18.4 18.4 15.1 15.0 15.0 15.0 0.45 0.49 0.53 0.57 3.38 3.20 2.94 2.93
0.0159 4 10.0 149.7 18.1 18.2 18.4 18.5 15.3 15.3 15.5 15.7 0.55 0.59 0.63 0.67 3.63 3.52 3.37 3.63
0.0159 4 10.1 199.9 19.1 19.1 19.3 19.3 15.4 15.3 15.3 15.2 0.13 0.17 0.20 0.23 2.72 2.64 2.53 2.47
0.0159 4 10.0 200.9 18.4 18.5 18.6 18.6 15.2 15.1 15.1 15.0 0.23 0.26 0.29 0.33 3.11 2.99 2.81 2.79
0.0159 4 10.0 200 18.1 18.1 18.3 18.2 15.3 15.2 15.1 15.0 0.34 0.37 0.40 0.43 3.52 3.42 3.14 3.13
262
Appendix B
Twall [oC]
Twall [oC]
Twall [oC]
Twall [oC]
Tref [oC]
Tref [oC]
Tref [oC]
Tref [oC]
x [-]
x [-]
x [-]
x [-]
h [kW/m2oC]
h [kW/m2 oC]
h [kW/m2 oC]
H [kW/m2 oC]
D
[m]
y
[-]
[kW/m2]
G
[kW/m2 s] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0.0159 4 10.0 200.6 18.1 18.1 18.3 18.2 15.5 15.4 15.3 15.2 0.43 0.46 0.49 0.52 3.92 3.74 3.39 3.36
0.0159 4 10.0 199.8 17.6 17.6 17.7 17.7 15.3 15.1 15.0 14.7 0.53 0.56 0.60 0.63 4.29 4.05 3.61 3.44
0.0159 4 10.0 201.2 17.6 17.6 17.7 17.6 15.3 15.0 14.7 14.3 0.63 0.66 0.69 0.72 4.43 3.96 3.35 3.01
0.0159 3 9.99 75.6 19.8 19.7 19.7 19.8 14.8 14.8 14.7 14.7 0.19 0.27 0.35 0.44 2.00 2.02 2.02 1.96
0.0159 3 10.0 74.6 19.2 19.6 19.6 19.8 14.7 14.7 14.7 14.6 0.29 0.38 0.46 0.54 2.23 2.05 2.02 1.94
0.0159 3 10.0 75.3 19.0 19.4 19.6 19.5 14.5 14.4 14.4 14.4 0.39 0.48 0.56 0.64 2.19 2.00 1.94 1.95
0.0159 3 10.0 75.1 19.2 19.7 19.9 20.0 14.7 14.7 14.7 14.7 0.49 0.57 0.66 0.74 2.25 2.02 1.94 1.89
0.0159 3 10.0 76.0 19.0 19.5 19.8 19.9 14.7 14.6 14.6 14.6 0.58 0.67 0.75 0.83 2.32 2.07 1.96 1.89
0.0159 3 10.0 75.0 19.1 19.7 20.1 20.3 14.5 14.5 14.5 14.5 0.71 0.80 0.88 0.96 2.17 1.93 1.78 1.71
0.0159 3 10.1 100.0 19.2 19.3 19.2 19.4 14.8 14.8 14.8 14.8 0.17 0.23 0.29 0.35 2.33 2.27 2.27 2.19
0.0159 3 10.0 100.2 18.9 19.3 19.4 19.5 15.0 15.0 14.9 14.9 0.27 0.33 0.39 0.45 2.58 2.33 2.28 2.21
0.0159 3 10.0 100.9 18.7 19.0 19.2 19.4 14.9 14.9 14.9 14.9 0.36 0.43 0.49 0.55 2.62 2.41 2.32 2.22
0.0159 3 10.0 100.4 18.5 18.8 19.1 19.3 14.8 14.8 14.8 15.0 0.47 0.53 0.60 0.66 2.67 2.49 2.38 2.32
0.0159 3 10.0 99.9 18.6 19.0 19.3 19.6 15.0 15.1 15.3 15.7 0.57 0.63 0.69 0.75 2.73 2.52 2.50 2.58
0.0159 3 10.0 150.2 18.8 19.2 19.4 19.2 15.2 15.2 15.1 15.1 0.14 0.18 0.23 0.27 2.78 2.51 2.39 2.48
0.0159 3 10.0 150.1 18.1 18.5 18.7 18.6 14.9 14.9 14.8 14.8 0.25 0.29 0.33 0.37 3.20 2.81 2.61 2.64
0.0159 3 10.0 151.1 18.2 18.6 18.8 18.7 15.3 15.2 15.1 15.1 0.34 0.38 0.43 0.47 3.42 2.96 2.76 2.77
0.0159 3 10.0 150 17.9 18.3 18.4 18.4 15.2 15.1 15.0 15.0 0.45 0.49 0.53 0.57 3.76 3.21 2.97 2.92
0.0159 3 10.0 149.9 17.7 18.1 18.4 18.3 15.2 15.1 15.0 14.9 0.55 0.59 0.63 0.68 4.03 3.37 3.04 2.96
0.0159 3 10.0 149.9 17.7 18.1 18.3 18.3 15.3 15.2 15.0 14.9 0.64 0.68 0.73 0.77 4.11 3.40 3.02 2.88
0.0159 3 10.0 149.7 17.7 18.1 18.4 18.3 15.2 15.0 14.8 14.6 0.75 0.79 0.83 0.87 4.08 3.28 2.84 2.67
0.0159 3 10.0 200 19.1 19.1 19.2 19.0 15.4 15.3 15.3 15.2 0.13 0.17 0.20 0.23 2.72 2.62 2.52 2.63
0.0159 3 10.0 200.9 18.5 18.6 18.7 18.5 15.3 15.3 15.2 15.1 0.24 0.27 0.30 0.33 3.19 3.01 2.89 2.92
0.0159 3 10.0 201.2 18.2 18.3 18.4 18.3 15.5 15.4 15.3 15.2 0.33 0.37 0.40 0.43 3.73 3.43 3.24 3.21
0.0159 3 10.0 200.7 17.9 18.1 18.1 17.9 15.5 15.4 15.3 15.2 0.44 0.47 0.50 0.53 4.23 3.73 3.56 3.66
0.0159 3 10.1 200.6 17.4 17.6 17.6 17.4 15.3 15.3 15.3 15.4 0.54 0.57 0.60 0.64 4.81 4.38 4.37 4.89
0.0159 3 10.0 199.7 17.3 17.5 17.5 17.3 15.5 15.7 16.0 16.4 0.64 0.67 0.70 0.73 5.63 5.60 6.63 11.11
Publications 263
Appendix C – Publications
Personal informations:
Name:Taye Stephen Mogaji
Place and date of birth: Akure,Ondo State,Nigeria, 1974
Academic training and qualifications:
Doctor of Science in Mechanical Engineering Area of concentration;Térmicos e
fluidos., Universidade de São Paulo, São Carlos,Brazil, 2010-2014.
Master’s degree: Master of Engineering in Mechanical Engineering (building Services
Option) - The Federal University of Technology, Akure - Nigéria – 2008.
First degree:Mechanical Engineering:The Federal University of Technology Akure,
Nigeria-2002.
Given below are the journal articles produced during this study:
MOGAJI, T.S., KANIZAWA, F.T., BANDARRA FILHO, E.P. RIBATSKI, G. Experimental study of the effect of twisted-tape inserts on flow boiling heat transfer enhancement and pressure drop penalty. International Journal of Refrigeration, Vol. 36, pp. 504-515, 2013.
MOGAJI, T.S., RIBATSKI, G., Enhancement and prediction of flow boiling heat transfer inside horizontal tubes containing twisted-tape inserts. Proceedings of the 22nd International Congress of Mechanical Engineering November, Ribeirão Preto, SP, Brazil ,COBEM: ISNN 2176-5480, , p. 190-201, 2013
KANIZAWA, F.T., MOGAJI, T.S., RIBATSKI, G Evaluation of the heat transfer enhancement and pressure drop penalty during flow boiling inside tubes containing twisted-tape inserts. Applied Thermal Engineering, 2014 (accepted for publication).
MOGAJI, T.S., RIBATSKI, G. Flow boiling heat transfer enhancement inside horizontal tubes containing twisted-tape inserts. International Journal of Heat and Mass Transfer, 2014 (Under review).
MOGAJI, T.S., KANIZAWA, F.T., BANDARRA FILHO, E.P. RIBATSKI, G. Experimental study of the effect of twisted-tape inserts on flow boiling heat transfer enhancement and pressure drop penalty.Proceedings of ECI 8th International Conference on Boiling and Condensation Heat Transfer, Lausanne, Switzerland (ECI,2012), 2012.
KANIZAWA, F.T., MOGAJI, T.S., RIBATSKI, G. Estudo experimental de transferência de carlor durante escoamento bifásico de R134a em tubo com fita retorcidas. Proceedings of 3o Encontro brasileiro sobre ebulição, condensação e escoamento multifasicos. Curitiba, PR, Brazil;2012.
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