自由表面旋涡数值模拟与涡、汇模型理论分析

为研究吸气旋涡的产生机理,并进行相应的理论分析,将水利和水工设备进水口前常见的自由表面旋涡现象简化为盆池自由放水模型,采用“流体体积”(VOF)方法结合RNG k-ε湍流模型模拟自由表面旋涡现象．通过数值模拟获得自由液面从纯水涡到吸气旋涡的生成与演化过程,将计算结果与理论Burgers涡模型进行对比,发现Burgers涡模型的切向速度分布方程与计算结果相符,涡量向中心聚集是导致自由液面发生凹陷并最终产生吸气旋涡现象的原因之一,同时发现Burgers涡的径向速度和轴向速度分布方程与计算结果相比存在很大差异．进一步简化模型后,剔除切向速度影响,模拟了无旋流体的排水过程．通过理论推导在球坐标系下提出“汇球面”模型,获得了较好的速度分布方程,并发现“汇”效应也是产生吸气旋涡现象的重要因素之一．

Numerical simulation of free surface vortex and theoretical analysis on vortex/sink model

To study the formulation mechanism of suction vortex and put forward some related theoretical analysis, the phenomenon of free surface vortex often observed above a drainage intake was simplified into a model of discharging sink water, which was simulated by using VOF (volume of fluid) method and RNG k-ε  turbulent model. The process of suction vortex evolving from free surface vortex was numerically simulated. By comparing the calculated results with Burgers vortex theory, it is found that the tangential velocity distribution equation in Burgers vortex model agrees with the calculation; and that vortexes gather towards the center is one of the factors that cause the free surface to depress and eventually become suction vortex. It is also found that the other two velocity distributions in Burgers vortex model, the radial and axial velocity distribution equations, in comparison with the calculation, were theoretically incorrect. To further simplify the model, ruling out tangential velocity, water discharge without vortex was simulated. To clarify the sink effect for surface depression, through theoretical deduction, based on spherical coordinate system, a kind of spherical sink model was proposed, with which a better velocity distribution equation was obtained. “Sink” effect is one of the important factors that lead to suction vortex phenomenon.