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

-0.2

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Channels bottom

Free surface level in the inlet

Free surface level in the outlet

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Fr [-

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³/s]

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Q - Outlet

Fr - Inlet

Fr - Outlet

(Erpicum et al., 2010)

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Comparison of the numerical results with experimental data from scale model studies

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Cw

[-]

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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Some thoughts / questions

• Hydraulic structures: well known, out of fashion ?

• Physical and numerical hydraulic modeling: conflict or love story?