Simulation of hydraulic jump characteristics of triangular bed based on WCSPH method

Hydraulic jump is a hydraulic phenomenon in open channel flow.In hydraulic conservancy projects,the severe scouring and erosion of the downstream riverbed are primarily induced by the violent turbulence of the downstream flow,thus establishing a corrugated bed in the stilling basin to develop hydraulic jump can improve the energy dissipation effect and reduce the damage to the buildings.At present,the research on the corrugated bed is mainly based on the experimental results and grid method of triangular corrugated bed.However,there are few systematic studies on the hydraulic jump characteristics of the triangular corrugated bed using WCSPH(Weakly Compressible Smoothed Particle Hydrodynamics) method.Exploring the hydraulic jump characteristics of the triangular corrugated bed has certain significance for the construction of the stilling basin. The open source code SPHYSICS_2D is used to perform numerical calculations.A push plate is used to provide stable flow and the upstream water depth is used to control the flow.Numerical simulations (the particle distance dx=0.005 m) were carried out on 20 groups cases with the ratio of wavelength to wave height (S/t) of 1,2,3,4,and 5 and Fr of 1.68,2.47,4.45,and 6.08,then the hydraulic jump characteristics,such as flow pattern,velocity distribution,conjugate depth and energy dissipation rate on the triangular corrugated bed,are analyzed in details. The comparison between the simulation and experimental results shows that the numerical simulation results is in accordance with the experimental results.A downstream flow is developed at the gate and the surface of the water flow,a part of the flow back is formed at the bottom of the triangular corrugated bed due to the obstruction of the main flow area.The flow makes a violent whirl motion on the surface rolling zone and the triangular corrugated bed increases the boundary layer and roughness contributing to the formation of a vortex.Compared with the experimental results,the errors of the simulated and experimental values of the conjugate depth of the five waveforms are 1.50%,1.96%,2.68%,067% and 0.08%,respectively.Compared with the smooth bed,the energy dissipation rates of the five waveforms are increased by 47.53%,44.33%,48.52%,41.18% and 37.41%,respectively.Among them,the energy dissipation effect of the waveform S/t=3 is better than that of other corrugated bed,and the energy dissipation rate is the largest with the same Fr,that is,the energy dissipation effect is the best.On the best triangular corrugated bed (S/t=3) with Fr=1.68,2.47,4.45,6.08,the conjugate depth is reduced by 10.55%,14.12%,15.81% and 16.09%,respectively,while the energy dissipation rate is increased by 84.91%,48.58%,35.42% and 32.20%,respectively,compared with the one on the smoothed bed. The WCSPH method can better simulate the hydraulic jump characteristics of the triangular corrugated bed.Compared with the smooth bed,the hydraulic jump length and conjugate depth of the triangular corrugated bed have been reduced,and the energy dissipation effect is better than that of the smooth bed.The surface on the triangular corrugated bed will exhibit a clockwise vortex,and the size of the vortex will gradually decrease with the direction of the water flow.In the hydraulic jump section,the middle velocity is higher and the surface velocity is smaller;in the open channel section,the bottom velocity is smaller and the surface velocity is larger.Therefore,the triangular corrugated bed can increase energy dissipation and improve energy dissipation rate.Meanwhile,with an analysis of the hydraulic jump characteristics of different cases indicates that the best triangular corrugated bed is S/t=3,and its conjugate depth is 14.15% less than the average of the smooth bed,and increases with the increase of Fr;the energy rate is 48.52% higher than that of the smooth bed,and decreases with the increase of Fr.

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