# Stilling Basin of Sluice in Low Head

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Momentum equation： i j i i 1u f
i t )(
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j )]
jx¶
i jx xr¶ ¶
j ix x¶ ¶

u
u u pn n
u
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= –
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Turbulent kinetic energy equation： ( ) i ( )k k kuGn n e+ = ê ú + + –
t ki ix x¶ ¶ ë û
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(3)Turbulent kinetic energy dissipation rate equation：
1ke k
2k e
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2*( )i ( ) uC G Ce e e e en n¶ ¶ ¶ ¶ é ù(4)504Wherent is the eddy viscosity coefficient obtained through the turbulent kinetic k and theturbulent dissipation rate e ,2tkCmne= .1 1* 03(1 / )1C Ce eh h hbh–= –+，h e = Sk / ， S = (2 ) S S ij ij 1/2 ，Inthe tensor expression, i and j are used as the summation subscripts.Free water surfaceVOF method is the effective method of dealing with the complex free surface put forward byHirt and Nichols in 1981, which is widely applied in numerical simulation of tracing free surface.This method defines the fluid volume function F = F(x, y, z t , ) , which means the ratio ofvolume of fluid in computational domain. For a unit, F =1 indicates the unit is completely filledwith fluid. F = 0 indicates that the unit cell is empty, no fluid. F =1 ~ 0 indicates the unit is filledwith the fluid partly.( )i 0iF Fu

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¶ ¶(5)Grid generation, boundary condition and initial conditionGrid generationThe model region is established using AUTOCAD software, upstream section is 150 m long,downstream section is 100 m long from anti-scour trench. The numerical simulation covers theupstream river, the stilling basin, and the downstream reach.Free mesh method and structured orthogonal grid is used to computing area, and local area is ofgradient encryption. In order to control the total number of grid, the upstream channel, lockchamber and downstream river are meshed respectively. Grid number of upstream channel is about160000, total grid of downstream river is about 220000. Grid of original design lock chamber isabout 780000, and that of optimization is about 1.2 million. The calculation region and thecomputing grid are shown in Figure 2 and Figure 3.Boundary conditionsInflow boundary: based on pressure boundary, water level values on the inflow boundary mustbe given, such as design or check flood level.Outflow boundary: the pressure boundary conditions are given on the exit of the calculationregion, and the corresponding water level is set on the outflow boundary.Wall boundary: using the wall-function method.Initial conditionsSetting the initial water region and giving initial water level with hydrostatic pressure. Theinitial time step is set to 0.002s, the minimum time step is set to 0.000001s.(a) (b)Figure 2 Numerical simulation region of sluice chamber; (a)Original design; (b)Optimization scheme.(a) (b)Figure 3 Mesh of simulation region; (a)Original design; (b)Optimization scheme.505RESULTS AND DISCUSSIONDischarge capacityDischarge capability of free discharging: 5 gates are fully open.Based on physical model test data, stage-discharge relation can be expressed as
Q Z = + 62.265( 1.00)1.579According to the calculated data, stage-discharge relation can be expressed asQ Z = + 66.644( 1.00)1.533
(6)
(7)
In which Q is drainage quantity, m3 / s; Z is inland water level, m; -1.00 is slab elevation ofsluice, m.Figure 4 shows the fitting curve between calculated value and measured value. It can be seenfrom the chart that the measured values is very close to calculated values.0.00.51.01.52.02.53.03.54.04.55.00.0 200.0 400.0 600.0 800.0 1000.0Q(m3/s)Z(m)
Experimental
Calculated
Figure 4 Stage-discharge relations for free dischargingFlow patternOriginal designIt can be seen from Figure 5 that the computed flow pattern agrees very well with thatmeasured from the physical model. For a certain discharge and tailwater level, the hydraulic jumpwas entirely located in the stilling basin. Through stilling basin, the flow spread quickly withobvious phenomenon of shock wave. At the end of the stilling basin, the velocity of water flow islarge and water depth is nonuniform along transect. In check condition, current has kept its velocityhigher at the end of anti-scour trench.(a) (b)Figure 5 Flow patterns under check condition; (a) physical model; (b) mathematical model.Optimization schemeIt can be seen from Figure 6 that the submerged hydraulic jump in stilling basin agrees wellwith the measured. The strong aerated water in the foreside of the stilling basin is turbulent and thefree water surface fluctuates greatly and randomly. Hydraulic jump is occurred in the first stillingbasin completely. Then the flow enter slope section of the second stilling basin through first stillingbasin section, submerged hydraulic jump is also forced successfully. After stilling basin, the flowevenly spread. Water depth is uniform along transect and there is no obvious phenomenon of shockwave. The computed maximum vertical mean velocity at the end of anti-scour trench is lower thanthat of the original design. It is said that the energy dissipation effect is improved.506(a) (b)Figure 6 Flow patterns under check condition; (a) physical model; (b) mathematical model.VelocityThe mathematical velocity of horizontal and longitudinal profile can better reflect the flowalong stilling basin (Figure 7 and Figure 8). The velocity measuring points are about 0.1 m from theend sill elevation of the stilling basin. Due to the existence of the two stilling basins of optimization,the flow pattern in the stilling basin has stronger three-dimensional features.It can be seen from Figure 7 that the maximum velocity at the end of anti-scour trench of theoriginal design reaches 8 m/s approximately, and flow velocity distribution is nonuniform. As foroptimization, two stilling basins strengthen the water mixing obviously. After the second stillingbasin, flow velocity decreases sharply. The maximum velocity at the end of anti-scour trenchreaches 4 m/s. It also can be seen from Figure 8 that flow velocity near the slab of optimization issmaller than that of original design. It is said that two stilling basins can effectively reduce the waterflow velocity at the downstream river and make velocity distribution more uniform.(a) (b)Figure 7 Contour map of velocity distribution with plane surface; (a)Original design;(b)Optimization scheme.(a)(b)Figure 8 Contour map of velocity distribution with center section; (a)Original design;(b)Optimization scheme.Water surface profileFigure 9 and Figure 10 show the simulated and measured results of the water surface profilealong the stilling basin. The computed results are in good agreement with that of model test, itfurther illustrates the reliability of the mathematical model, and it can reflect the real flow structureand characteristics.507-5.0-2.50.02.55.0-100 -80 -60 -40 -20 0 20 40 60 80 X(m) 100Z(m)
ExperimentalCalculated
Figure 9 Water surface profile of original design under check condition-5.0-2.50.02.55.0-100 -80 -60 -40 -20 0 20 40 60 80 100 X(m)Z(m)
ExperimentalCalculated
Figure 10 Water surface profile of optimization under checkconditionEnergy loss ratioThe energy loss ratio could be expressed as follows
1 2jK = E E 100%´
(8)
1– EFrom figure (8) the specific energy at the beginning of the jump (E1), and at the end of the jump(E2)can be written as:211=H + 1 0V2E Zg– 、222 =H + 2 0V2E Zg–Under design condition, energy loss ratio of the original design and optimization is 27.4%,49.6% respectively. When under check condition, the energy dissipation ratio of the original designand optimization is 21.7%, 45.4% respectively. Energy loss ratio of the optimization is better.The distributions of the turbulent kinetic energy are shown in Figure 11 and Figure 12. It can beseen that the turbulent kinetic energy takes the maximum on the foreside of the stilling basin, andthen gradually declines along the slab of the stilling basin. Near the foreside of the stilling basin, theflow is strongly turbulent and most of the energy is dissipated. The energy dissipation is very weakat the end of the stilling basin.(a)(b)Figure 11 Distributions of turbulent kinetic energy for original design; (a)Design condition; (b)Check condition.(a)(b)Figure 12 Distributions of turbulent kinetic energy for optimization; (a)Design condition; (b)Check condition.508CONCLUSIONSThe numerical simulation is carried out for the stilling basin of low head sluice, as is in apractical project with original and optimum scheme. The characteristics of the hydraulic jump in astilling basin are studied by using RNG turbulence models of Flow-3D in this article, and thenumerical simulation results are verified by a series of model experiments. The conclusions are asfollows:(1) 3-D numerical simulations are carried out for the water flow in a stilling basin. Thecalculated results, such as discharge capacity, flow pattern, velocity, and water surface profile are ingood agreement with those obtained by experiments. It indicates that the turbulence models arevalid.(2) The energy loss ratio is calculated, and results show that two stilling basins can increase theenergy dissipation. Besides, the turbulent kinetic energy distribution is also simulated by usingturbulence mode, and simulated results agree better with the practical situation of the water flowmovement.References Katakam V. 1998. Spatial B-jump at channel enlargements with abrupt drop. Journal ofHydraulic Engineering, ASCE, 124(6). Chen J.Y. 2005. Experimental researchon enegry dissipater of diversion works in Low Head.Northwest A&F University. Xu W.L., Liao H.S. and Yang Y.Q. et al. 1996. Numerical simulation of 3-D turbulent flows ofplunge pool and energy dissipation analysis. Journal of Hydrodynamics, Ser. A, 11(5): 561-569. Lu L. and Li Y.C. 2008. Numerical simulation of turbulent free surface flow over obstruction.Journal of Hydrodynamics, 20(4): 414-423. Pan Z.L. 2008. Numerical simulationof free surface in a stilling basinof sluice. ZhejiangHydrotechnics, (11): 25-27. Chen C., Wei W.L.and Yan J.J. 2008. Two Dimensional Numerical Simulation of HydraulicJump Behind Sluice Based On Fluent. Journal of Heilong jiang Hydraulic Engineering, 34(3):17-23. Shi Z.P. 2010. Numerical simulation of energy dissipater with low-head flood dischargingstructure. Northwest A&F University. Wang Y.H. Bao Z.J. and Wang B. 2012. Three Dimensional Numerical Simulation of Flow inStilling Basin Based On Flow-3D. Engineering journal of wuhan university, 45(4): 454-457.509