Sébastien Erpicum (ULg) gaat dieper in op de methodes (schaalmodellen, 1D-numerieke modellering) die gebruikt kunnen worden om stroming over een Piano Key Weir beter te begrijpen en op de stand van zaken wat betreft dit onderzoek binnen de onderzoeksgroep

1. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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

2. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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

3. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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 ?

4. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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

5. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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)

6. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
Step 2: Simplified numerical modeling
1D approach – Physical processes oriented math. model – Short
computation time (some seconds) – Freeware WOLF1DPKW
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Elevation[m]
x [m]
Channelsbottom
Freesurfacelevel in the inlet
Freesurfacelevel in the outlet
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Fr[-]
Q[m³/s]
x [m]
Q - Inlet
Q - Outlet
Fr - Inlet
Fr - Outlet
(Erpicum et al., 2010)

7. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
Comparison of the numerical results with experimental data from scale model studies
0.0
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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

8. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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

9. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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)

10. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
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

11. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
… and where we want to go
• Unified H/Q design equation
• Improvement of the geometry
• Downstream energy dissipation
• Aeration/nappe vibration
• …

12. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be

13. 2nd Belgian Hydraulic Days – FHR – 5 October 2015
http://www.hece.ulg.ac.be
Some thoughts / questions
• Hydraulic structures: well known, out of fashion ?
• Physical and numerical hydraulic modeling: conflict or love
story?