SPILLWAY CHUTES DESCARREGADORES DE CHEIA … chutes Descarregadores de cheia com queda guiada 2 ... Coeficiente de correção da energia cinética (coeficiente de Coriolis)

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SPILLWAY CHUTES

DESCARREGADORES DE CHEIA COM QUEDA GUIADA

Hydropower Hidroenergia

1 Hydropower, 2015/2016

Jorge Matos1 and Inês Lúcio2

[email protected] [email protected]

@ Matos and Lúcio

Hydropower, 2015/2016

Spillway chutes Descarregadores de cheia com queda guiada

2

Estimate the flow properties along the developing, clear-water flow region

@ Matos and Lúcio

mailto:[email protected]

mailto:[email protected]

21-11-2015

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Channel on the hillside (A.3), with hydraulic jump stilling basin (B.3)

Descarregador de cheias em canal de encosta (A.3), com bacia de dissipação por ressalto a jusante (B.3)

Vermiosa Dam Barragem de Vermiosa

Spillways examples Exemplos de descarregadores de cheias

Channel on the hillside Descarregador de cheias

em canal de encosta

http://www.apambiente.pt

3 @ Matos and Lúcio


Spillway over the dam (A.1), with guided fall and hydraulic jump stilling basin (B.3)

Descarregador de cheias sobre a barragem (A.1), com queda guiada e bacia de dissipação de energia (B.3)

Torrão Dam Barragem do Torrão

http://www.a-nossa-energia.edp.pt

Vídeo: https://www.youtube.com/watch?v=NQLexyMwJvE

https://www.youtube.com/watch?v=NQLexyMwJvE


@ Matos and Lúcio



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Plan

Developed section

Cross section

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Flow properties along the chute Grandezas do escoamento ao longo do descarregador

6

Hmax

Zcrest

N

Zbasin floor

Figure: In Manzanares (1980)

How to estimate h, U, H, ΔHt , Fr,.....?

t t

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21-11-2015

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Hydropower, 2015/2016 7

• Potential (irrotational) flow from the upstream end – the simplest (conservative) estimate.

• Gradually varied flow from the upstream end.

• Curves in Chow (1959) on the basis of experience, theoretical analysis and a limited amount of experimental information obtained from prototype tests.

• Development of the boundary layer from the upstream end until it reaches the free-surface, and gradually varied air-water flow calculations further downstream.

• Computational Fluid Dynamics (CFD) modelling (Flow 3D®, Open Foam®, SPH,….).

Some approaches…


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Z (ft)

U (ft s-1)

Velocity at the toe of steeply sloping spillways

under various heads, falls and slopes (1V:0.8H ~ 51° ; 1V:0.6H ~ 59°)

Figure: In Chow (1959)


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21-11-2015

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Z (ft)

U (ft s-1)

Velocity at the toe of steeply sloping spillways

under various heads, falls and slopes (1V:0.8H ~ 51° ; 1V:0.6H ~ 59°)

Figure: In Chow (1959)


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Hydropower, 2015/2016 10 @ Matos and Lúcio

But why can’t we apply the typical gradually

varied flow equations…?

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Wood (1991), “Free surface air entrainment on spillways”, in Air entrainment in free-surface flows, IAHR Hydraulic Structures Design Manual, Ed. I. R. Wood, A.A: Balmeka, Rotterdam.

Flow regions in a self-aerated flow down a spillway

Regiões do escoamento num descarregador




• The boundary layer thickness, δ, is the distance across a boundary layer from the wall to a

point where the flow velocity has essentially reached the 'free stream' velocity, Vmax. This

distance is defined normal to the wall, and the point where the flow velocity is essentially that

of the free stream is customarily defined as the point where: V = 0.99 Vmax.

• The displacement thickness, δd, is the distance by which a surface would have to be moved in

the direction perpendicular to its normal vector away from the reference plane in an inviscid

fluid stream of velocity Vmax to give the same flow rate as occurs between the surface and the

reference plane in a real fluid.

•The Energy thickness, δe, is defined as the thickness of an imaginary layer in free stream flow

which has energy equal to the loss of energy caused to actual mass flowing inside the

boundary layer.

Basic definitions

http://civildigital.com/wp-content/uploads/2013/10/boundary-layer.png

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Potential flow

Point of inception

Developing boundary layer

1 – Clear-water flow region

2 – Partially aerated flow region

3 – Fully aerated flow region

4 – Uniform flow region Photograph: J. Matos




Various formulae: Hickox (1939), Lovely (1953), Bauer (1954),

Annemuller (1958),..

Keller and Rastogui (1975, 1977) : k-ε turbulence model applied for a

wide range of flow rates, roughness and spillway slopes, for an ungated

WES crest profile

Further developments by Cain and Wood (1981), Wood (1983, 1991),

Chanson (1988, 1989, 1996),...

Location of the point of inception

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),g,k,q(fLI )tg,kg

q(f

k

L

3

I





Q ↑ → Li… ↑↓? θ ↑ → Li…↑↓? k ↑ → Li…↑↓?

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Q = 80 l/s (dc/h = 1.1) Q = 200 l/s (dc/h = 2.0)

Photograph: J. Matos Photograph: J. Matos





Q = 80 l/s (dc/h = 1.1) Q = 200 l/s (dc/h = 2.0)

Photograph: J. Matos Photograph: J. Matos

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713.0*

0796.0I Frsen6.13k

L

3*

kseng

qFr

Roughness Froude number

Li ↑ ~ q 0.713 Li ~ senθ -0.277 Li ~ k-0.07

After a multiple regression analysis of the results by Keller and Rastogui, Wood (1983) obtained:




Location and flow properties at the point of inception

713.0*

0796.0I Frsen6.13k

L

643.0*04.0

I Frsen

223.0

k

h

3*

kseng

qFr

Roughness Froude number

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Location and flow properties at the point of inception

Chanson(1996), “Air bubble entrainment in free-surface turbulent shear flows”,Academic Press.





k

L I

*Fr


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k

L I

*Fr

Attention…





Flow depth at the point of inception

*Fr

k

h I


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Flow depth at the point of inception

*Fr

k

h I


Attention…


Boundary layer development along the chute

Desenvolvimento da camada limite ao longo do descarregador

713.0*

0796.0I Frsen6.13k

L

3*

kseng

qFr

Halbronn and Bauer (1954)

Cain (1978)

Wood (1983)

10.0

11.0

k

Lsen021.0

L

( x ~ xs )

Wood (1983, 1991)

δ → y: V = 0.99 Vmax

N1

max

y

V

V

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Flow properties in the non-aerated flow region

Propriedades do escoamento na região não arejada do escoamento

1. Boundary layer thickness, δ

Data: ϴ, k, L Calculation: δ

10.0

11.0

k

Lsen021.0

L

Wood (1991)

2. Flow depth of the irrotational flow (absence of head losses)

Data: ϴ, zcrest, Hspillway (q) Calculation: hp

or 2

p

2

pcrestspillwayhg2

qcoshzzH 2

p

2

phg2

qcoshzN

3. Velocity of the irrotational flow

p

ph

qU




4. Displacement thickness

Previous calculation: δ Calculation: δd

N1d

Typically, for conventional concrete chutes, N = 6 (Chanson 1996), hence

14.0d

5. Flow depth (considering head losses)

dphh

6. Mean water velocity

h

qU

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7. Energy thickness

N3

1

N1

1Ne

Previous calculation : δ Calculation: δe

19.0e

Typically, for conventional concrete chutes, N = 6 (Chanson 1996), hence

8. Head loss

qg2

UHt

3pe

9. Total head at a given cross-section

HtNHt

10. Specific energy at a given cross-section

zHtH


Kinetic energy correction coefficient (Coriolis coefficient)

Coeficiente de correção da energia cinética (coeficiente de Coriolis)

and from the definition of the kinetic head correction coefficient, one can obtain:

N1

max

y

V

V

Considering that the velocity distribution is given by:

)h(

3N

N

h

1

U

V3

max

At the inception point:

= (N+1)3 / [ N2 (N+3) ] 𝛼 = 1.06, for N = 6.0

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31

Example of Application

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http://www.a-nossa-energia.edp.pt

Vídeo: https://www.youtube.com/watch?v=NQLexyMwJvE



@ Matos and Lúcio



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http://www.apambiente.pt/index.php?ref=77&subref=839

TORRÃO DAM

PURPOSE - Hydroelectric

LOCATION DAM

District - Porto

Municipality - Marco de Canavezes

Site - Torrão/Alpendurada

River Basin - Douro

River - Tâmega river

Concrete - Gravity dam, lightened by large hollows

Height above foundation - 69 m

Crest elevation - 69 m

Crest length - 218 m

Crest width - 8,35 m

Foundation - Granite

Volume of dam body - 224,415 x 1 000 m3

SPILLWAY RESERVOIR

Location - Dam body

Control type - Controlled

Spillway type - Over the dam

Sill elevation - 54,4 m

Sill length - 53,50 m

Number of gates - 5

Maximum discharge - 4500 m3/s

Energy dissipation - Hydraulic jump

Reservoir area - 6 500 x 1 000 m2

Gross capacity - 124 000 x 1 000 m3

Effective storage- 77 000 x 1 000 m3

Dead storage - 47 000 x 1 000 m3

Normal water level (NWL) - 65 m

Maximum flood level (MFL) - 65 m

Minimum operating level - 49 m

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Cross-section

Hmax = 60.00 Zcrest = 54.40

N=65.00

Width (B) = 53,50 m Slope (i): 1:0.70 (V:H) Maximum discharge (Qmax) = 4500 m3/s

Z = 0.00

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Documents

SPILLWAY CHUTES DESCARREGADORES DE CHEIA … chutes Descarregadores de cheia com queda guiada 2 ... Coeficiente de correção da energia cinética (coeficiente de Coriolis)