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.