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2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Towards a better understanding of flows over Piano key weirs
S. Erpicum, B. Dewals, P. Archambeau, M. Pirotton HECE, ArGEnCo Department, University of Liege, Belgium
2nd Belgian Hydraulic Days – Flanders Hydraulics Research,
Antwerp – 5 October 2015
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Van Phong dam – Vietnam – Gates + PKW – 320m long - 8,700m³/s
Malarce dam PKW – France 13.8 m³/s/m with a head of 1.50m
Piano Key weir (PKW) = recent evolution of traditional labyrinth weir (Lempérière &
Ouamane, 2003)
• Decrease of sidewalls height
• Reduced footprint can be placed on the crest of gravity dams
• High hydraulic capacity
PKW : a new solution to improve the discharge capacity of existing dams
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Saint Marc dam (EDF - France)
PKW : a new solution to improve the discharge capacity of existing dams
Etroit dam (EDF - France)
How can such a structure be modeled/understood ?
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Application of composite modeling to study PKW hydraulics
Large scale
physical modeling
Development of a
simplified
numerical model
parametric
analysis
Parametric scale
models (limited
number of
parameters and
variation range)
Physical scale modeling of real projects (design validation for real cases)
Physical scale modeling to assess scale effects
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Step 1: Large scale physical modeling
≈1/10 Scale factor – Simplified sketch in a test flume – Wide range of discharge
Hydraulic behavior Control section location Importance of the inlet
cross section area
- H – Q curve - Flow types on the weir
crests - Flow characteristics on the
structure (velocity, pressure, free surface level, flow patterns)
(Machiels et al., 2011)
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Step 2: Simplified numerical modeling
1D approach – Physical processes oriented math. model – Short computation time (some seconds) – Freeware WOLF1DPKW
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Channels bottom
Free surface level in the inlet
Free surface level in the outlet
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Q - Outlet
Fr - Inlet
Fr - Outlet
(Erpicum et al., 2010)
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Comparison of the numerical results with experimental data from scale model studies
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Cw
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H/P [-]
Chatou 4 - Num
Chatou 4 - Exp
Biskra - Num
Biskra - Exp
Chatou 2 - Num
Chatou 2 - Exp
Liege (2009) - Num
Liege (2009) - Exp
Error bars = +/-10%
Step 2: Simplified numerical modeling
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Step 2: Simplified numerical modeling
1D approach – Physical processes oriented math. model – Short computation time (some seconds) – Freeware WOLF1DPKW
- H – Q curve - Mean free surface levels - Discharge repartition
- Validation regarding varied
previous scale model studies
Parametric study Identification of pertinent
range for parameters variation
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Step 3: Parametric scale models
Reduced sketch in a flume – Wide range of discharge
- H – Q curve - Systematic analysis of
parameters influence
Optimal value for Alveoli width ratio Inlet slope Overhangs position
Analytical formulation for discharge capacity
Importance of technico-economical criteria (several hydraulic optima)
(Machiels, PhD Thesis, 2012) (Machiels et al., 2014)
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Where we are today…
• Extensive experimental works (Biskra, Algeria; LNHE, France; LCH, Switzerland; UWRL, USA;
HECE, Belgium; Vietnam; …)
• Numerical studies in 1D and 3D (EDF-CIH, France; HECE, Belgium)
• Key geometric parameters … • Crest length magnification ratio L/W (Ouamane & Lempérière, 2006; Leite Ribeiro et al.,
2012)
• Weir height P, keys width ratio Wi/Wo, overhangs length ratio Bo/Bi (Machiels et al., 2011 and 2012)
• … and optimal values • L/W ≈ 5 (Lempérière, 2009 and 2011)
• P/Wu ≈ 1.33 (Machiels et al., 2014)
• Wi/Wo є [1.25 - 1.6] (Leite Ribeiro et al, 2012; Anderson & Tullis, 2013, Machiels et al., 2014)
• Bo/Bi > 1 with Bi ≠ 0 (Lempérière et al., 2011; Machiels et al., 2014)
• P/Wu = 0.5 (Machiels, 2012)
• Wi/Wo = 1 (Machiels et al., 2014)
• Bo/Bi = 1 (Machiels et al., 2014)
• Lempérière « cost efficient » design (Lempérière, 2009)
• Equations to predict H/Q curve (Leite Ribeiro et al., 2012; Machiels et al., 2014)
Hydraulic optimum
Technico-economic optimum
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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… and where we want to go
• Unified H/Q design equation
• Improvement of the geometry
• Downstream energy dissipation
• Aeration/nappe vibration
• …
2nd Belgian Hydraulic Days – FHR – 5 October 2015
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2nd Belgian Hydraulic Days – FHR – 5 October 2015
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Some thoughts / questions
• Hydraulic structures: well known, out of fashion ?
• Physical and numerical hydraulic modeling: conflict or love story?