21-11-2015
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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
21-11-2015
2
Hydropower, 2015/2016
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
4 Hydropower, 2015/2016
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
Spillways examples Exemplos de descarregadores de cheias
@ Matos and Lúcio
21-11-2015
3
5 Hydropower, 2015/2016
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
Spillways examples Exemplos de descarregadores de cheias
Plan
Developed section
Cross section
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Hydropower, 2015/2016
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…
Flow properties along the chute Grandezas do escoamento ao longo do descarregador
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Hydropower, 2015/2016 8
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)
Flow properties along the chute Grandezas do escoamento ao longo do descarregador
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21-11-2015
5
Hydropower, 2015/2016 9
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)
Flow properties along the chute Grandezas do escoamento ao longo do descarregador
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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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Hydropower, 2015/2016 11 @ Matos and Lúcio
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
Hydropower, 2015/2016 12 @ Matos and Lúcio
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
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Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
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
Hydropower, 2015/2016 14 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
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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Hydropower, 2015/2016 15 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
),g,k,q(fLI )tg,kg
q(f
k
L
3
I
Hydropower, 2015/2016 16 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
Q ↑ → Li… ↑↓? θ ↑ → Li…↑↓? k ↑ → Li…↑↓?
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Hydropower, 2015/2016 17 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
Q = 80 l/s (dc/h = 1.1) Q = 200 l/s (dc/h = 2.0)
Photograph: J. Matos Photograph: J. Matos
Hydropower, 2015/2016 18 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
Q = 80 l/s (dc/h = 1.1) Q = 200 l/s (dc/h = 2.0)
Photograph: J. Matos Photograph: J. Matos
21-11-2015
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Hydropower, 2015/2016 19 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
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:
Hydropower, 2015/2016 20 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
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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Hydropower, 2015/2016 21 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location and flow properties at the point of inception
Chanson(1996), “Air bubble entrainment in free-surface turbulent shear flows”,Academic Press.
Hydropower, 2015/2016 22 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
k
L I
*Fr
Chanson(1996), “Air bubble entrainment in free-surface turbulent shear flows”,Academic Press.
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Hydropower, 2015/2016 23 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Location of the point of inception
k
L I
*Fr
Attention…
Chanson(1996), “Air bubble entrainment in free-surface turbulent shear flows”,Academic Press.
Hydropower, 2015/2016 24 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Flow depth at the point of inception
*Fr
k
h I
Chanson(1996), “Air bubble entrainment in free-surface turbulent shear flows”,Academic Press.
21-11-2015
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Hydropower, 2015/2016 25 @ Matos and Lúcio
Flow regions in a self-aerated flow down a spillway
Regiões do escoamento num descarregador
Flow depth at the point of inception
*Fr
k
h I
Chanson(1996), “Air bubble entrainment in free-surface turbulent shear flows”,Academic Press.
Attention…
Hydropower, 2015/2016 26 @ Matos and Lúcio
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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Hydropower, 2015/2016 27 @ Matos and Lúcio
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
Hydropower, 2015/2016 28 @ Matos and Lúcio
Flow properties in the non-aerated flow region
Propriedades do escoamento na região não arejada do escoamento
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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Hydropower, 2015/2016 29 @ Matos and Lúcio
Flow properties in the non-aerated flow region
Propriedades do escoamento na região não arejada do escoamento
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
Hydropower, 2015/2016 30 @ Matos and Lúcio
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
21-11-2015
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Hydropower, 2015/2016
Spillways examples Exemplos de descarregadores de cheias
31
Example of Application
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32 Hydropower, 2015/2016
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
Spillways examples Exemplos de descarregadores de cheias
@ Matos and Lúcio
21-11-2015
17
33 Hydropower, 2015/2016
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
Spillways examples Exemplos de descarregadores de cheias
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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34 Hydropower, 2015/2016
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
Spillways examples Exemplos de descarregadores de cheias
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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