2nd International Workshop. Labyrinth and Piano Key Weirs Paris - Chatou, France November 2013

Transcription

1 2nd International Workshop on Labyrinth and Piano Key Weirs Paris - Chatou, France November 2013 Improvement of the form of labyrinth weirs Ahmed OUAMANE François LEMPERIERE Laboratory of hydraulic developments and environment University of BISKRA (ALGERIA)

2 Upstream Upstream W Downstream W Downstream Linear Weir Labyrinth Weir - The labyrinth weir is often used when the width of the weir or the maximum head is limited. - The cost of the labyrinth weir is relatively low compared to weirs with gates, this led to its use simultaneously to increase the storage and discharge capacity of the spillway.

3 The geometry in the plane of the crest of the labyrinth weir is characterized by an discontinuous centerline. This thus results in a complex flow mode (Lux III & Hinchliff, 1985), which is considered as three-dimensional.

4 Upstream Disturbance Middle Jet area Downstream 0 ld lc l c : Length of crest l d : Length of distarbance ljc: Length of middle jet Flow is characterized by the length disturbance and the length of the middle jet

5 The non-linear shape of the crest of the labyrinth weir creates a three-dimensional flow disturbed at each discontinuity of the axis of the weir. These flow conditions cause a reduction in the performance of labyrinth weir. Qc 2 3 Cm 2 3 3/ 2 n ld 2 ghcn n ( lc ld ) 2 gh 3/ 2 cn Cm: Coefficient of disturbance 2 3/ n 2gh 2 cn Qc lc (1 Cm ) l 3 C m ( l ) (l): Discharge coefficient of the disturbance flow n: Discharge coefficient of the two-dimensional flow n d The reduction of the crest length caused by the disturbance

6 The importance of the reduction of discharge coefficient is dependent on the head on the weir and the importance of the angle of the corner. (Indlekofer & Rouve ) Although the labyrinth weir has been thesubject of several applications and it has proved his efficiency, some changes in classic shape can have a positive effect on the hydraulic and economic performance.

7 The main parameter that promotes flow disturbance and therefore reduces the performance of the labyrinth weir, corresponds to the discontinuity of the weir crest. Thus, to reduce the effect of this discontinuity, a profiling of the front wall of the labyrinth weir can have a positive effect on the hydraulic efficiency. A. Labyrinth weir model with rounded front wall B. Model labyrinth weir with flat front wall

8 The comparison of results obtained on two models of weir noted that the design of a rounded shaped entrance leads to an improving the performance of about 10%. This can be explained on the one hand, by the profiled shape of entrance which facilitates the flow on either side of the front wall along the latter. On the other hand, the rounded shape eliminates the discontinuity points and thus reduces the effect of the disturbance at the top of the weir. 2.5 Trapezoidal labyrinth weir with a rounded front wall 2 Trapezoidal labyrinth weir with a flat front wall 1.5 Cw H*/P Flow coefficients according to the shape of the entrance of labyrinth weir L / W = 3.9, W / P=1

9 As reported by the literature, the labyrinth weir is an economical solution as the specific discharge is less than 50 m3/s/m. Beyond this value the labyrinth weir requires great height walls which implies a greater thickness of walls and greater reinforcement. Labyrinth spillway at Labyrinth spillway at Ute Dam, New Mexico

10 It is possible that the design of the labyrinth weir with a partial filling of the alveoli by ordinary concrete leads to a reduction of the additional cost, this implies a reduction in the free part of the wall height and thus provides a low wall thickness and therefore a small reinforcement of the structure. A B B P/5 B P a 2a 1.2P A-A W A Wt B 3P/4 B-B P Schematic of labyrinth weir with entrance profiled and alveoli partially filled

11 The experiment of two models showed that the flow over the weir partially filled alveoli and rather airy and stable for low charge, which is not the case for weirs without filling alveoli. This justifies the offset between the two curves of discharge coefficient for the range of values of the relative head H*/P < Profiled shape with a partial filling of alveoli Profiled shape without filling of alveoli Cw H*/P Discharge coefficient of labyrinth weir with profiled shape L/W = 3.9 W / P=1

12 The alveoli filling has no effect than for the low heads. For the range of values of H* / P> 2.5, the two weirs have the same hydraulic performance. So, the partial filling of the alveoli has no effect on the performance of labyrinth weir and helps to avoid the problem of aeration for low heads over the weir Trapezoidal shape with a partial filling of alveoli Trapezoidal shape without filling of alveoli Cw H*/P H/P

13 Thus, it is possible for the greater specific discharges than 50m 3 /s/ml to design the labyrinth weir with the alveoli partially filled in ordinary concrete this gives an economic structure while maintaining hydraulic performance similar to that of classical labyrinth weir without a filling of alveoli.

14 It is possible that other shape in plan can be effective as the trapezoidal and triangular shapes often used in existing dams. Thus, for practical, economic and hydraulic performance reasons, we may adopt a rectangular shape in plan with a profiled entrance and a slab of the downstream alveoli as a stairs and that of the upstream alveoli partially inclined. These structural particularities can improve the performance of labyrinth spillway and reduce the cost of construction. The choice of the rectangular shape allows vary the widths of the upstream and downstream cells to obtain a ratio of width which allows for better hydraulic efficiency and reduced cost.

15 The partial filling of alveoli upstream and downstream of ordinary concrete can reduce the thickness of the walls and the quantity of steel, because the free part of the walls is reduced. The design of the slab of the downstream alveoli as stair step, also help to dispel some of the energy. 2 Upstream 1 b a 2 Downstream w 1 B B 2P/3 1 1 P 2P/3 2 2 P Rectangular labyrinth weir with shaped entrance and a partial filling of alveoli

16 The profiled shape of the entrance and the inclination of part of the slab of the upstream alveoli can improve the flow conditions at the entrance of the labyrinth; therefore the weir becomes more efficient.

17 Often the labyrinth spillway is designed with a trapezoidal shape in plan that is repeated periodically. It is possible that the labyrinth weir take another geometric shape that can be as effective as the trapezoidal shape. The choice of a rectangular shape can be as effective of viewpoint, hydraulic and economic performance and its construction is easiest, especially when it is used as a dam weir of low height in the rivers.

18 The experiment of two models of labyrinth weirs, successively, trapezoidal and rectangular showed that the rectangular shape can be as effective as the trapezoidal shape and even more effective for the relative heads lower than 0.5, corresponding to the practical range for design weirs labyrinth. 1,6 1,4 1,2 Rectangular shape L/W=4 Trapezoidal shape L/W=4 1,0 Cw 0,8 0,6 0,4 0,2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 H*/P Discharge coefficient according to the shape of the labyrinth weir

19 Usually the labyrinth weirs are designed with vertical walls. This arrangement requires a substantial length of the side walls to achieve effective performance. This limits the application of the labyrinth weir and does not allow its installation ti on most crests of concrete dams. It is possible to reduce the length of the base of the side walls without affecting the length of the sill of labyrinth weir. This is feasible by using a part of the length of the side walls in overhang. A B B B r B P S a/2 b a b a/2 A B bp A-AA bp B-BB

20 Experimental result obtained in labyrinth weir with downstream overhang and an inclined slab showed that this weir configuration provides a better performance which can be three times that of a linear weir for medium heads Labyrinth weir with overhang Linear weir 1.2 Cw H*/P Discharge coefficients of labyrinth weir with a downstream overhang and linear weir

21 The disposition of the inclined slab between the side walls leads to reduction in the average height of the weir. Thus, the walls of the weir become less thick than the weir with horizontal slab due to the reduction of forces applied to the walls, which reduces the quantity of steel reinforcement. However, the volume of the concrete of the slab becomes larger. The use of inclined slab minimizes the effect of turbulence at the weir crest, producing a flow of the threads of liquid which are more or less regular.

22 The application of the previously mentioned improvements to the labyrinth weir can lead to a form of economic weir and of a better hydraulic performance. The piano keys weir (PK-Weir) brings all these advantages and other, Th th PK W i Thus, the PK-Weir was born

23 The Piano Key Weir can be used for new dams or existing dams that require increase in the spillway capacity and / or storage capacity. It can be placed on small sections of existing or new concrete dams and allows discharging of specific flows up to 100 m3/s/m and. multiply by at least three the discharge weir Creager (Lempérière & Ouamane, 2003). The final configuration of the PK-Weir was determined following testst onphysical models, which h helped define the geometry of the PK-Weir (Ouamane & Lempérière, 2006), which is based on: - A rectangular layout. - An inclined slab of the upstream and downstream alveoli. - A base length reduced through the use of overhang. - A reduced width of rectangular elements

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

25 Piano Keys Weir type A

26 Piano Keys Weir type B

27 PK-Weir type A The P.K.Weir type A was studied in a extensive way in 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 then downstream hangovers. The hydraulic shape of the entrance is important. For H between 3 to 5 m, the ratio N=L/W should be about 4 to 6. For smaller H, the ratio N could be more important.

28 If h is the head of water, the specific flow is close to 4hH0.5 for the heights most often used (0.25H<h<1.5H). The outflow of a traditional Creager crest is hence multiplied 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 nearly 1.8 H1.5. A saving in head of water (i.e storage) of nearly 0.5H is obtained.

29 Tests result of experiments showed that the flow is related to the head on the PK-Weir: For low and medium heads, the flow is defined by two discharging nappe, the first in the form of a jet of the bottom and the second in the form of a screen more or less thin. For the high heads the two nappes become interdependent constituting so a single nappe.

30 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 order of 1,5 times. This shows thatt the P.K.Weir can be a solution to evacuate high discharges under low heads P.K.Weir type B Creager Weir Q (l/s) 80 Increase 60 discharge Saving head ,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00 H* (cm)

31 P.K.Weir type B P.K.Weir type A P.K.Weir type B Creager Weir Q (l/s) ,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00 H* (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 model B can be a solution for large discharges.

32 2,0 18 1,8 1,6 1, 4 L/W=4 W/P=1,67 a/b=1,5 L/W=4 W/P=1,25 a/b=1,5 L/W=4 W/P=1,0 a/b=1,5 Cw 1,2 1,0 0,8 0,6 0,4 0,2 0,0 00 0,0 01 0,1 0, 0, 0, 05 0,5 06 0,6 07 0,7 H*/P Discharge coefficient according to the ratio of vertical aspect W/P The increase of the height of 25% increases the capacity of weir from 5 to 8%.

33 Q (l/s) L/W=8 P/B=0,36 a/b=1,5 L/W=6 P/B=0,36 a/b=1,5 / /, 2,0 L/W=4 P/B=0,36 a/b=1,5 0 0,0 2,0 4,0 6,0 8, 10,0 12,0 14,0 16,0 H* (cm) Cw 1,5 1,0 0,5 L/W=6 P/B=0,5 a/b=1,5 L/W=4 P/B=0,5 a/b=1,5 0,0 0,0 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 the variation of the ratio L/W has no effect on the capacity of Weir. TheincreaseoftheratioL/Wfrom4to6allowstoincreasethe capacity of weir about 10 % for the medium relative heads.

34 2,5 2,0 L/W=6 W/P=1,1 a/b=1,2 L/W=6 W/P=1,1 a/b=1,5 / /b L/W=6 W/P=1,1 a/b=0,67 Cw 1,5 1,0 0,5 0,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 H*/P Discharge coefficient according to the width of the inlet and outlet 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 additional expence.

35

36 PKWeir: Goulours Dam (EDF 2006) France