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HANOI 28 November 2012
Piano Key weirs and Labyrinth weirs
Research and Applications in France and in Vietnam
mhotakhanh@yahoo.com
1. General
A well known solution : the labyrinth spillway
Example of the Song Mong spillway in Vietnam
A PKW is a particular labyrinth weir with rectangular alveoli in plan view (origin
of its name), with generally upstream and downstream cantilevers in order to
lengthen the overflowed lateral walls compared to the base.
As the labyrinth weirs, the PKW allows increasing the specific discharge for a
given nappe depth (higher spillway capacity) or reducing this nappe depth for a
specific discharge (higher reservoir capacity without heightening the dam).
A new solution: the Piano Key Weir (PKW)
Definition and characteristics
Advantages of the PKW
The PKW can be placed on the thin crest of gravity dams, this placement being
rarely possible with traditional labyrinth weirs.
For equivalent geometrical features, the capacity of a PKW is generally a bit
higher than the capacity of a labyrinth weir.
The PKW can adopt several different shapes and provides consequently more
flexibility for the designs.
Different shapes (types) of PKW
Different PKW types can be adopted following
the site conditions, the particular requirements of
the design and the constraints of construction.
The different cross-sections on the right side
suggest some solutions but many other
alternatives are possible.
It can be noticed that the PKWs without
overhang are rectangular labyrinths in plan
form, with sloped or stepped bottoms (type D
and E), which can be economically placed in a
low barrage or a side spillway (in place of some
gates) as indicated below. ↓
Fundamental
parameters
of PKW
The PKW is defined
by many parameters
but its capacity can
be easily
approximated :
- by using some
standard shapes as
indicated in the next
slide,
- by comparison
with an existing
PKW,
- by utilization of
some specialized
softwares.
Standard Model of PKW Type A (proposed by Hydrocoop)
This model can be adopted for a first approximation and adjusted later by numerical or
physical models.
The «Standard shape» is function of a simple parameter Pm
n ≈ 5, q ≈ 4.3H √Pm
n = L/W, (L: developed length and W: total width of the weir ) Cross section: 1-1 (Outlet)
q = specific discharge
H = nappe depth
1 2
1 2 Pm 0.8 Pm
3.6 Pm
1.8 Pm
Cross section: 2-2 (Inlet)
2. Rating curves of PKW for free flows
Rating curves for low nappe depths (HCMUT)
For P.K.W type A with n=4 → q4 = 5.6 H1.22
For P.K.W type A with n=5 → q5 = 6.4 H1.28
For P.K.W type A with n=7 → q7 = 8.7 H1.15
For a linear Creager weir → qCreager= 2.15 H1.50
• For low nappe depths, the specific discharges of PKW and labyrinth depend mainly on
the values of n (q = αn H1.5β, with α>1 and β<1).
•The ratios of qPKW/qCreager vary with n (hereunder from 2.4 to 3.5, for H= 1.5m)
Rating curves for medium and high nappe depths (HCMUT)
The rating curves are quasi linear in the range of the measures.
For a same value of H, the values of q increase with n.
y = 4.32x + 1.28
R2 = 0.987
y = 3,94x - 2,34R² = 0,991
y = 3,81x - 4,27R² = 0,998
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8 9 10 11 12
q (m
3/s
.m)
H√Pm
n = 5.5
n = 5.0
n = 4.0
3. Some PKWs in France and in Vietnam
Utilization of PKWs on existing dams in France
for increasing the spillway capacity (about 10 PKWs up to now)
Physical model of the Goulours Dam (France)
The first video shows the model of a PKW added on the crest of the Goulours
dam, located in a narrow valley, in order to increase the capacity of the existing
spillway.
The second video shows the simulation of the passage of floating debris (logs)
on the PKW.
PKWs under design or construction in Vietnam
Dakmi 2 2
Ngan Truoi
Vinh Son 3
Dak Rong 3
Van Phong
An example of combination
of gated spillway and PKW
(Type A) for a low barrage.
Van Phong : Plan view and cross-sections (gate and PKW)
Van Phong : Hydraulic Model tests Tests for free and submerged flows
Van Phong : Construction of the PKW (Type A) Excavation, formworks, scaffoldings and reinforcement
Xuân Minh
4. Utilization of PKW for low barrage
A programme of research between
EDF-CIH (France) and HCMUT (Vietnam)
PKW with overhangs (Types A to C) have important advantages compared
with the traditional Creager weirs, as already indicated.
However one drawback of this type of weir is to require, in some cases, more
qualified manpower, more scaffoldings, formworks and reinforcement for the
construction of the thin cantilevered parts.
In the cases of low barrages (run-of-river schemes) or side spillways, there are
no more constraints regarding the PKW footprint, and then no need for
overhanging structures. PKW Types D and E, even if slightly less hydraulically
efficient, are very cost-effective solutions in comparison with PKW Types A to C
or traditional labyrinth weirs thanks to construction delay and ease.
Taking into account this advantage, a study program for different types of PKW
and labyrinth weirs was consequently performed by EDF-CIH and the HCMUT
to provide further information concerning the hydraulic and cost/structural
characteristics of the PKW without overhang (Type D) and to compare these
with the other types of weirs. The hydraulic study is based on both physical and
numerical models.
Programme of research concerning 3 types of labyrinth weirs
(PKW type A, PKW type D and Rectangular labyrinth weir)
with physical and numerical (Flow-3D) models
• Determination of q= f(H0) for free flows.
• Determination of q= f(Hu, Hd) for submerged flows.
• Structural analysis of the weirs (on going, to be completed).
• Comparison of cost and delay of construction (on going, to be completed).
PKW type D PKW type A Rectangular Labyrinth weir
Photos of the 3 physical models
(1) PKW Type A (2) PKW Type D (3) Rectangular labyrinth weir
(1)
(2)
(2)
(3)
(3)
4.1. Free flow tests
Photos of the tests for:
PKW type A (1),
PKW type D (2)
R.L weir (3)
(HCMUT Hydraulic Lab)
1
2
3
Comparison of physical
and numerical models
Example for the PKW Type D
and for the free flow.
(Good agreement between the 2
models)
0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
40,00
45,00
50,00
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00
q (
m3/s
.m)
H0 (m)
Rating curves for the 3 different types of weirs (free flow)
The rating curves of the labyrinth
weirs are quasi linear for :
0.50< H0/P0< 2.
qA is max and qD is min, qL is
intermediate. qE (not tested) is
probably the same than qL.
The ratios of the specific discharges
q for the different types of labyrinth
weirs are not constant but decrease as
H0 increases (for H0=P0 for example,
the ratio qA/qL is only = 1.08).
The ratios of the specific discharges
for qA and qCreager are :
qA/qCreager = 2.25 for H0/P0 =0.5
qA/qCreager = 1.44 for H0/P0 =1
qA/qCreager = 1.22 for H0/P0 =1.5
qA/qCreager ≈ 1.0 for H0/P0 =2
Creager
PKW Type A (R2 = 0.998) Labyrinth (R2 = 0.999)
PKW Type D (R2 = 0.997)
0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
40,00
45,00
50,00
0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00
q (
m3/s
.m)
Ho(m)
Free flow
4.2. Submerged flow tests
Photos of the tests for:
PKW Type A (1),
PKW Type D (2)
R.L weir (3)
(HCMUT Hydraulic Lab)
1
2
3
Numerical models (Flow-3D) for PKW Types A & D and R.L weirs
with submerged flows (analysis by EDF-CIH)
Submerged Flow tests with the numerical model qs/qf versus Hd/Hu for different H0
The different curves are represented for each value of H0 in the following figures. They
are distinct and consequently they depend a bit on the values of H0, in particular for the
labyrinth weir (on the right) which presents a larger variation compared with the PKW
Type A (on the left).
Submerged Flow tests with the physical model
qs/qf versus Hd/Hu for different q
The physical model confirms the outcomes provided by the numerical model, the curves
being established for different values of q. It can be noticed in particular the larger
dispersion of the curves for the labyrinth weir.
0
0,2
0,4
0,6
0,8
1
0 0,2 0,4 0,6 0,8 1
qs/q
f
Hd/Hu
PKW Type A
0
0,2
0,4
0,6
0,8
1
0 0,2 0,4 0,6 0,8 1
qs/q
f
Hd/Hu
Labyrinth weir
Submerged flow tests : qs/qf versus Hd/Hu for
PKW Types A & D and R.L weir (with a «mean curve» for each weir)
Results of numerical models Results of physical models
0
0,2
0,4
0,6
0,8
1
0 0,2 0,4 0,6 0,8 1
qs.W
s/q
fWf
Hd/Hu
Submerged flows Comparaison of different types of weirs by the Chatou Hyd. Lab (France)
• Good agreement between the outcomes of the Chatou and HCMUT Laboratories.
• The decrease of the ratio (qs/qf) versus (Hd/Hu) is the most sensitive for the sharp-
crested linear and the Creager weirs and the least sensitive for the thick–crested
linear weir (qf being lower for this weir). The PKWs provide then the most efficient
results.
A possible alternative for low barrages : PKW type D or type E
Initial design PKW Type A (outlet)
New alternatives PKW Type D
• To simplify the construction.
• To reduce the delay of construction.
•To lower the cost.
5. PKW and Stepped Spillways
Combination of PKW and stepped spillways (HCMUT)
Tests in the HCMUT Hydraulic Laboratory in order to study the dissipation of the energy
at the toe of the dam downstream a Creager weir and a PKW. The downstream face of
the spillway is smooth, or with regular steps 2D and 3D. Steps-2D Regular steps-3D Steps with baffles-3D
PKW + 2D-Stepped spillway Regular 3D-steps 3D-steps with baffles
PKW + 2D-Stepped spillway Regular 3D-steps 3s with baffles
Determination of the scour at the toe of the dam
Longitudinal profile of scour hole at center line of channel
PK weir with smooth spillway
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
0 10 20 30 40 50 60 70 80 90 10
0
11
0
12
0
13
0
14
0
15
0
16
0
17
0
18
0
19
0
20
0
L(cm)
h(cm
)
37.75-
smooth
spillway
36.70-
smooth
spillway
35.00-
smooth
spillway
34.20-
smooth
spillway
Conclusion
The PKW is a new type of labyrinth weir - with their own advantages plus the
possibility to be placed easily on the crest of gravity dams - which is very
promising and has known a rapid and important development during these
last years.
For new dams, the PKW can sometimes replace totally or partially gated
spillway with the advantages of lower costs, more safety and less
maintenance. The utilization of PKW type D (or type E) is probably the most
interesting for low barrages.
The combinations of PKW with gated spillway and/or PKW with stepped
spillway are probably the best solutions for gravity dams.
There are several types of PKW with the possibility of selecting the most
adapted to the conditions of the site, the requirements of the design and the
constraints of construction. An optimal alternative has to take into account
the hydraulic and structural aspects of the problem.
The PKW depends on many parameters but a first approach can be easily
obtained by using the outcomes of the recent R&D on PKW, in particular the
existing numerical models already valided by the physical models.
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