SPILLWAY CHUTES DESCARREGADORES DE CHEIA COM QUEDA GUIADA

Transcription

1 SPILLWAY CHUTES DESCARREGADORES DE CHEIA COM QUEDA GUIADA Hydropower Hidroenergia Jorge Matos 1 and Inês Lúcio 2 1 jorge.matos@tecnico.ulisboa.pt 2 ines.lucio@tecnico.ulisboa.pt 1 Spillway chutes Descarregadores de cheia com queda guiada Estimate the flow properties along the developing, clear-water flow region 2 1

2 Spillways examples Exemplos de descarregadores de cheias Vermiosa Dam Barragem de Vermiosa 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) Channel on the hillside Descarregador de cheias em canal de encosta 3 Spillways examples Exemplos de descarregadores de cheias Torrão Dam Barragem do Torrão 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) Vídeo: 4 2

3 Spillways examples Exemplos de descarregadores de cheias Torrão Dam Barragem do Torrão 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) Developed section Plan Cross section 5 Flow properties along the chute Grandezas do escoamento ao longo do descarregador How to estimate h, U, H, ΔHt, Fr,...? Zcrest N Hmax t t Zbasin floor Figure: In Manzanares (1980) 6 3

4 Flow properties along the chute Grandezas do escoamento ao longo do descarregador Some approaches 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,.). 7 Z (ft) Flow properties along the chute Grandezas do escoamento ao longo do descarregador 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) U (ft s -1 ) 8 4

5 Flow properties along the chute Grandezas do escoamento ao longo do descarregador Z (ft) 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) U (ft s -1 ) 9 But why can t we apply the typical gradually varied flow equations? 10 5

6 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: Balmea, Rotterdam. 11 Basic definitions The boundary layer thicness, 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 thicness, 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 thicness, δe, is defined as the thicness 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. 12 6

7 Potential flow Developing boundary layer Point of inception 1 Clear-water flow region 2 Partially aerated flow region Photograph: J. Matos 3 Fully aerated flow region 4 Uniform flow region 13 Location of the point of inception Various formulae: Hicox (1939), Lovely (1953), Bauer (1954), Annemuller (1958),.. Keller and Rastogui (1975, 1977) : -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),

8 Location of the point of inception L I L I f (q,,g, ) f (, tg) q g 3 15 Location of the point of inception Q L i? θ L i? L i? 16 8

9 Location of the point of inception Q = 80 l/s (d c /h = 1.1) Q = 200 l/s (d c /h = 2.0) Photograph: J. Matos Photograph: J. Matos 17 Location of the point of inception Q = 80 l/s (d c /h = 1.1) Q = 200 l/s (d c /h = 2.0) Photograph: J. Matos Photograph: J. Matos 18 9

10 Location of the point of inception After a multiple regression analysis of the results by Keller and Rastogui, Wood (1983) obtained: L Fr I * 13.6 sen q g sen Fr * Roughness Froude number L i ~ q L i ~ senθ L i ~ Location and flow properties at the point of inception L I hi 13.6 sen sen Fr Fr * * Fr * q g sen 3 Roughness Froude number 20 10

11 Location and flow properties at the point of inception Chanson(1996), Air bubble entrainment in free-surface turbulent shear flows,academic Press. 21 Location of the point of inception L I Fr * Chanson(1996), Air bubble entrainment in free-surface turbulent shear flows,academic Press

12 Location of the point of inception L I Attention Fr * Chanson(1996), Air bubble entrainment in free-surface turbulent shear flows,academic Press. 23 Flow depth at the point of inception h I Fr * Chanson(1996), Air bubble entrainment in free-surface turbulent shear flows,academic Press

13 Flow depth at the point of inception h I Attention Fr * Chanson(1996), Air bubble entrainment in free-surface turbulent shear flows,academic Press. 25 Boundary layer development along the chute Desenvolvimento da camada limite ao longo do descarregador Halbronn and Bauer (1954) V V LI Fr * max y 13.6 sen q 1 N g sen Fr * ( x ~ xs ) Cain (1978) Wood (1983) δ y: V = 0.99 Vmax 0.021sen L 0.11 L 0.10 Wood (1983, 1991) 26 13

14 Flow properties in the non-aerated flow region Propriedades do escoamento na região não arejada do escoamento 1. Boundary layer thicness, δ 0.021sen L Data: ϴ,, L 0.11 L 0.10 Calculation: δ Wood (1991) 2. Flow depth of the irrotational flow (absence of head losses) N z h p 2 q cos 2g h 2 p Data: ϴ, zcrest, Hspillway (q) or 3. Velocity of the irrotational flow q Up h p H spillway z crest Calculation: hp z h p 2 q cos 2g h 2 p 27 Flow properties in the non-aerated flow region Propriedades do escoamento na região não arejada do escoamento 4. Displacement thicness d 1 N Typically, for conventional concrete chutes, N = 6 (Chanson 1996), hence d Previous calculation: δ Flow depth (considering head losses) h h p d 6. Mean water velocity q U h Calculation: δd 28 14

15 Flow properties in the non-aerated flow region Propriedades do escoamento na região não arejada do escoamento 7. Energy thicness 1 1 e N 1 N 3 N Typically, for conventional concrete chutes, N = 6 (Chanson 1996), hence Previous calculation : δ 8. Head loss 3 e Up Ht 2g q 9. Total head at a given cross-section Ht N Ht 10. Specific energy at a given cross-section H Ht z e Calculation: δe 29 Kinetic energy correction coefficient (Coriolis coefficient) Coeficiente de correção da energia cinética (coeficiente de Coriolis) Considering that the velocity distribution is given by: V V max y and from the definition of the inetic head correction coefficient, one can obtain: At the inception point: 3 1 N Vmax 1 N (h ) U h N 3 = (N+1) 3 / [ N 2 (N+3) ] α = 1.06, for N =

16 Spillways examples Exemplos de descarregadores de cheias Example of Application 31 Spillways examples Exemplos de descarregadores de cheias Torrão Dam Barragem do Torrão 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) Vídeo:

17 Spillways examples Exemplos de descarregadores de cheias Torrão Dam Barragem do Torrão 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 PURPOSE - Hydroelectric LOCATION District - Porto Municipality - Marco de Canavezes Site - Torrão/Alpendurada River Basin - Douro River - Tâmega river SPILLWAY 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 m 3 /s Energy dissipation - Hydraulic jump DAM Concrete - Gravity dam, lightened by large hollows Height above foundation - 69 m Crest elevation - 69 m Crest length m Crest width - 8,35 m Foundation - Granite Volume of dam body - 224,415 x m 3 RESERVOIR Reservoir area x m 2 Gross capacity x m 3 Effective storage x m 3 Dead storage x m 3 Normal water level (NWL) - 65 m Maximum flood level (MFL) - 65 m Minimum operating level - 49 m 33 Spillways examples Exemplos de descarregadores de cheias Torrão Dam Barragem do Torrão N=65.00 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) Zcrest = Hmax = Z = 0.00 Cross-section Width (B) = 53,50 m Slope (i): 1:0.70 (V:H) Maximum discharge (Qmax) = 4500 m 3 /s 34 17