2nd International Workshop onon

Labyrinth and Piano Key Weirs Paris - Chatou, France 20-22 November 2013

Improvement of the formImprovement of the formImprovement of the formImprovement of the formof labyrinth weirsof labyrinth weirs

Ahmed OUAMANE François LEMPERIERE

L b t f h d li d l t d i tLaboratory of hydraulic developments and environment

University of BISKRA (ALGERIA)

Upstream Upstream

WW

Downstream Downstream

LinearWeir LabyrinthWeir

- The labyrinth weir is often used when the width of

LinearWeir LabyrinthWeir

ythe weir or the maximum head is limited.- The cost of the labyrinth weir is relatively lowy ycompared to weirs with gates, this led to its usesimultaneously to increase the storage andy gdischarge capacity of the spillway.

The geometry in the plane of the crest of thel b i th i i h t i d b di tilabyrinth weir is characterized by an discontinuouscenterline. This thus results in a complex flow

d (L III & Hi hliff 1985) hi h imode (Lux III & Hinchliff, 1985), which isconsidered as three-dimensional.

Upstream

Disturbance Middle�Jetarea

Downstream

0�ld�lclc: Length of crestld: Length of distarbanceljc: Length of middle jet

Flow is characterized by the length disturbance andthe length of the middle jetthe length of the middle jet

The non-linear shape of the crest of the labyrinth weir createsa three dimensional flow disturbed at each discontinuity ofa three-dimensional flow disturbed at each discontinuity ofthe axis of the weir. These flow conditions cause a reductionin the performance of labyrinth weir.in the performance of labyrinth weir.

2/32/3 2)(222 hgllhglCmQc �� �� 2)(3

23 cndcncndn hgllhglCmQc ��� ��

2 � �dmccnn lClhgQc )1(232 2/3 ��� �

The reduction of thecrest length caused bythe disturbance

Cm: Coefficient of disturbance )l(C ��Cm: Coefficient of disturbance

�(l): Discharge coefficient of the disturbance flow

�n: Discharge coefficient of the two dimensional flow

nmC ��

�n: Discharge coefficient of the two-dimensional flow

The importance of the reduction of dischargeffi i t i d d t th h d th icoefficient is dependent on the head on the weir

and the importance of the angle of the corner.( dl k f(Indlekofer & Rouve )

Al h h h l b i h i h b h bj fAlthough the labyrinth weir has been the subject ofseveral applications and it has proved his

ffi i h i l i hefficiency, some changes in classic shape canhave a positive effect on the hydraulic and

i feconomic performance.

The main parameter that promotes flowdisturbance and therefore reduces theperformance of the labyrinth weir, corresponds tothe discontinuity of the weir crest. Thus, to reducethe effect of this discontinuity, a profiling of the frontwall of the labyrinth weir can have a positive effecton the hydraulic efficiency.

A Labyrinth weir model with rounded front wall B. Model labyrinth weir with flat front wallA. Labyrinth weir model with rounded front wall y

The comparison of results obtained on two models of weir noted thatthe design of a rounded shaped entrance leads to an improving theperformance of about 10%. This can be explained on the one hand, bythe profiled shape of entrance which facilitates the flow on either side ofthe front wall along the latter. On the other hand, the rounded shapeeliminates the discontinuity points and thus reduces the effect of thedisturbance at the top of the weir.

2.5

Trapezoidal labyrinth weir with a rounded front wall

1.5

2 Trapezoidal labyrinth weir with a flat front wall

1

Cw

Flow coefficients according0.5

Flow coefficients accordingto the shape of the entranceof labyrinth weir L / W = 3.9,W / P = 1

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

H*/P

As reported by the literature, the labyrinth weir isAs reported by the literature, the labyrinth weir isan economical solution as the specific discharge isless than 50 m3/s/m. Beyond this value theless than 50 m3/s/m. Beyond this value thelabyrinth weir requires great height walls whichimplies a greater thickness of walls and greaterimplies a greater thickness of walls and greaterreinforcement.

Labyrinth spillway atLabyrinth spillway atUte Dam, New Mexico

It is possible that the design of the labyrinth weir with apartial filling of the alveoli by ordinary concrete leads to ap g y yreduction of the additional cost , this implies a reduction inthe free part of the wall height and thus provides a low wallthickness and therefore a small reinforcement of thestructure.

B

P/5

BA

a 2a

B P

1.2P a 2a

WP

BA

A-A

Schematic of labyrinthWt

3P/4

BA

B-B

Schematic of labyrinthweir with entrance profiledand alveoli partially filled

The experiment of two models showed that the flow overthe weir partially filled alveoli and rather airy and stable forp y ylow charge, which is not the case for weirs without fillingalveoli. This justifies the offset between the two curves ofdischarge coefficient for the range of values of the relativehead H*/P <0.25

2.5

3

Profiled shape without filling of alveoli

Profiled shape with a partial filling of alveoli

2

Profiled shape without filling of alveoli

1

1.5

Cw

0

0.5

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8

Discharge coefficient oflabyrinth weir with profiled

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8H*/P

shape L/W = 3.9 W / P = 1

The alveoli filling has no effect than for the low heads. Forthe range of values of H* / P> 2.5, the two weirs have theg ,same hydraulic performance. So, the partial filling of thealveoli has no effect on the performance of labyrinth weirand helps to avoid the problem of aeration for low headsover the weir.

1 6

1.8

2

Trapezoidal shape without filling of alveoliTrapezoidal shape with a partial filling of alveoli

1

1.2

1.4

1.6

Cw

0.4

0.6

0.8

1C

0

0.2

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8H*/PH /P

Thus it is possible for the greater specificThus, it is possible for the greater specificdischarges than 50m3/s/ml to design the labyrinthweir with the alveoli partially filled in ordinaryweir with the alveoli partially filled in ordinaryconcrete this gives an economic structure whilemaintaining hydraulic performance similar to that ofmaintaining hydraulic performance similar to that ofclassical labyrinth weir without a filling of alveoli.

It is possible that other shape in plan can be effectiveas the trapezoidal and triangular shapes often usedas the trapezoidal and triangular shapes often usedin existing dams. Thus, for practical, economic andhydraulic performance reasons, we may adopt ahydraulic performance reasons, we may adopt arectangular shape in plan with a profiled entranceand a slab of the downstream alveoli as a stairs andand a slab of the downstream alveoli as a stairs andthat of the upstream alveoli partially inclined. Thesestructural particularities can improve thestructural particularities can improve theperformance of labyrinth spillway and reduce thecost of construction.cost of construction.The choice of the rectangular shape allows vary thewidths of the upstream and downstream cells towidths of the upstream and downstream cells toobtain a ratio of width which allows for betterhydraulic efficiency and reduced cost.hydraulic efficiency and reduced cost.

The partial filling of alveoli upstream and downstream ofordinary concrete can reduce the thickness of the walls and theordinary concrete can reduce the thickness of the walls and thequantity of steel, because the free part of the walls is reduced.The design of the slab of the downstream alveoli as stair step,

U t 12

galso help to dispel some of the energy.

Upstream 12

Downstream 1b a w

B

2

P

B

2P/3P

B

2P/3

Rectangular labyrinth weirwith shaped entrance and

2�� 21�� 1a partial filling of alveoli

The profiled shape of the entrance and the inclination of part ofthe slab of the upstream alveoli can improve the flowthe slab of the upstream alveoli can improve the flowconditions at the entrance of the labyrinth; therefore the weirbecomes more efficient.becomes more efficient.

Often the labyrinth spillway is designed with atrapezoidal shape in plan that is repeatedperiodically. It is possible that the labyrinth weir takeanother geometric shape that can be as effective asthe trapezoidal shape. The choice of a rectangularshape can be as effective of viewpoint, hydraulic andeconomic performance and its construction iseasiest, especially when it is used as a dam weir oflow height in the rivers.

The experiment of two models of labyrinth weirs, successively,trapezoidal and rectangular showed that the rectangular shapecan be as effective as the trapezoidal shape and even moreeffective for the relative heads lower than 0.5, corresponding toth ti l f d i i l b i ththe practical range for design weirs labyrinth.

1,6l h /

1,2

1,4Rectangular�shape�L/W=4

Trapezoidal�shape�L/W=4

0,8

1,0

Cw

0,4

0,6

Discharge coefficient

0,0

0,2Discharge coefficientaccording to the shapeof the labyrinth weir

0,0 0,2 0,4 0,6 0,8 1,0

H*/P

Usually the labyrinth weirs are designed with vertical walls.This arrangement requires a substantial length of the sidewalls to achieve effective performance.This limits the application of the labyrinth weir and does notll it i t ll ti t t f t dallow its installation on most crests of concrete dams.

It is possible to reduce the length of the base of the side wallswithout affecting the length of the sill of labyrinth weirwithout affecting the length of the sill of labyrinth weir.This is feasible by using a part of the length of the side walls inoverhang.

B B

A B

B B

S

P

rB

A A

bp

B B

bp

a a/2a/2 b bA-A B-B

A B

Experimental result obtained in labyrinth weir with downstreamoverhang and an inclined slab showed that this weirconfiguration provides a better performance which can bethree times that of a linear weir for medium heads.

1 61 6

1.81.8Labyrinth weir with overhangLabyrinth weir with overhang1 6

1.8Labyrinth weir with overhang

1.21.2

1.41.4

1.61.6 Labyrinth weir with overhangLabyrinth weir with overhang

Linear weirLinear weir

1.2

1.4

1.6 Labyrinth weir with overhang

Linear weir

0.80.8

11

Cw

Cw

0.8

1

Cw

0.20.2

0.40.4

0.60.6

0.2

0.4

0.6

Discharge coefficientsof labyrinth weir with a

0000 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6

H*/PH*/P

00 0.1 0.2 0.3 0.4 0.5 0.6

H*/P

of labyrinth weir with adownstream overhangand linear weir

The disposition of the inclined slab between theside walls leads to reduction in the averageheight of the weir. Thus, the walls of the weirbecome less thick than the weir with horizontalslab due to the reduction of forces applied to thewalls, which reduces the quantity of steelreinforcement. However, the volume of theconcrete of the slab becomes larger. The use ofinclined slab minimizes the effect of turbulence atthe weir crest, producing a flow of the threads ofliquid which are more or less regular.

The application of the previously mentioned improvements tothe labyrinth weir can lead to a form of economic weir and of abetter hydraulic performance. The piano keys weir (PK-Weir)brings all these advantages and other,

Th th PK W iThus, the PK-Weir was born

The Piano Key Weir can be used for new dams orexisting dams that require increase in the spillwayg q p ycapacity and / or storage capacity. It can be placed onsmall sections of existing or new concrete dams and

.allows discharging of specific flows up to 100 m3/s/m andmultiply by at least three the discharge weir Creager(Lempérière & Ouamane, 2003).The final configuration of the PK-Weir was determinedf ll i t t h i l d l hi h h l d d fifollowing tests on physical models, which helped definethe geometry of the PK-Weir (Ouamane & Lempérière,2006) which is based on:2006), which is based on:- A rectangular layout.- An inclined slab of the upstream and downstreamAn inclined slab of the upstream and downstreamalveoli.- A base length reduced through the use of overhang.g g g- A reduced width of rectangular elements

�Many study and test were done since 2002 in university ofBiskra (Algeria) allowed to define two forms of PK-Weir, thefirst with an upstream and downstream overhangs (model A)and the second with only an upstream overhang (model B)

Piano Keys Weir Piano Keys Weir type Atype A

Piano Keys Weir type B

PK-Weir type AThe P.K.Weir type A was studied in a extensive way in2002 – 2003. Expérimental results showed that:�hangover slopes between 2/1 and 3/2�width of the inlets 1.2 times that of outlets “e”�Upstream hangovers are more efficient thendownstream hangovers.� The hydraulic shape of the entrance is important.�For “H” between 3 to 5 m, the ratio N=L/W shouldbe about 4 to 6.�For smaller “H”, the ratio N could be moreimportant.

�If “h” is the head of water, the specific flow is closeto 4hH0.5 for the heights most often used(0.25H<h<1.5H).

� The outflow of a traditional Creager crest is hencemultiplied by almost 4 when h = 0.25 H, by 3 when h= 0.4H and by 2 when h is around 0.8H.

� The increase in specific flow (in m3/s/m) is nearly1.8 H1.5. A saving in head of water (i.e storage) ofnearly 0.5H is obtained.

Tests result of experiments showed that the flow is related tothe head on the PK-Weir:the head on the PK-Weir:� For low and medium heads, the flow is defined by twodischarging nappe, the first in the form of a jet of the bottomg g jand the second in the form of a screen more or less thin.�For the high heads the two nappes become interdependent

tit ti i lconstituting so a single nappe.

The discharge of P.K.Weir is superior to that of Creager weir.�For the heads lower than the half of the height of the weir(h/P < 0,5), it is from 3,5 to 2,5 times.�For heads equal or superior to the height of the weir, it is in

d f 1 5 ti Thi h th t th P K W i border of 1,5 times. This shows that the P.K.Weir can be asolution to evacuate high discharges under low heads.

160

180P.K.Weir type B

120

140

160y

Creager Weir

S i h d

60

80

100Q (l/s)

Increasedi h

Saving head

20

40

60 discharge

00,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00

H* (cm)

P.K.Weir type B

180

PK Weir type A

120

140

160P.K.Weir�type�A

P.K.Weir�type�B

Creager�Weir

80

100

120

Q (l/s)

20

40

60Q�(l/s)

0

20

0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00H* (cm)

P.K.Weir type B allows an increase of discharge about 10 %with regard to the P K Weir type A This result shows that

H �(cm)

with regard to the P.K.Weir type A. This result shows thatmodel B can be a solution for large discharges.

1 8

2,0

L/W=4��W/P=1,67�a/b=1,5

1, 4

1,6

1,8

L/W=4��W/P=1,25�a/b=1,5

L/W=4��W/P=1,0���a/b=1,5

1,0

1,2Cw

0,4

0,6

0,8

Discharge coefficient

0,0

0,2

0 0 0 1 0 0 0 0 5 0 6 0 7

Discharge coefficientaccording to the ratio of vertical

aspect W/P0,0 0,1 0, 0, 0, 0,5 0,6 0,7

H*/P

p

The increase of the height of 25% increases the capacity ofweir from 5 to 8%.

140

160

180

L/W=8��P/B=0,36��a/b=1,5L/W=6��P/B=0,36��a/b=1,5 2,0

L/W=6��P/B=0,5��a/b=1,5

L/W=4��P/B=0,5��a/b=1,5

80

100

120

140

Q�(l/s)

/ / , / ,L/W=4��P/B=0,36��a/b=1,5

1,5

Cw

20

40

60

80

0,5

1,0

0

20

0,0 2,0 4,0 6,0 8, 10,0 12,0 14,0 16,0H*�(cm)

0,00,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

H*/P

Discharge and Discharge coefficient according to ratio L/W

For slope of aprons of the P.K.Weir type B lower than 0,5 thevariation of the ratio L/W has no effect on the capacity of Weir.p y

The increase of the ratio L/W from 4 to 6 allows to increase thecapacity of weir about 10 % for the medium relative heads.

2,5

L/W=6�W/P=1,1��a/b=1,2/ / /b

1,5

2,0L/W=6��W/P=1,1��a/b=1,5L/W=6�W/P=1,1��a/b=0,67

1,0

Cw

0,0

0,5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Discharge coefficient according to the width of the inlet and outlet

H*/P

The optimum of relative width is near a/b=1,2. It is possible for the same cost to increase the width of the inlet of 10 % and to reduce consequently the width of the outlet. This increases efficiency about 5 % without any additionalThis increases efficiency about 5 % without any additional expence.

PKWeir: Goulours Dam (EDF 2006) France