两相光滑粒子流体动力学方法在动床溃坝问题中的应用

Application of two-phase smoothed particle hydrodynamics method to dam break over movable bed

光滑粒子流体动力学(SPH)方法采用离散分布的粒子作为离散工具,借助粒子和核函数将场变量及其导数以某种加权求和的方式进行计算,使得该方法更适于处理包含大位移、动边界和自由表面的问题。本文在分析动床条件下的溃坝问题时,以Drunker-Prager准则作为底床颗粒物的侵蚀启动判断条件。满足该条件而发生启动的颗粒物将以非牛顿流体的特征发生运动,即以Herschel-Bulkley-Papanastasiou模型来描述;否则,认为底床颗粒物未启动而保持静止状态。为进一步改进计算结果,采用基于体积比的两相SPH方法描述固液混合体的动力学特征,并基于固液混合颗粒流的动力学特征对混合黏度的计算进行改进。基于上述原理,分析动床条件下的溃坝问题,并将数值计算结果与已有的实验数据进行对比,证明本文提出的混合黏度计算公式改进了数值计算结果。

Smoothed particle hydrodynamics （SPH） method adopts discrete particles for discretion of computational domain, and field variables and their spatial derivatives are evaluated by summation interpolation based on particle and kernel functions, which makes this method more suitable for processing the large displacement, movable boundary, and free surface problems. In order to analyze the dam break problem over movable bed, an erosion condition based on Drunker-Prager is used. The particles satisfying this condition will move with the non-Newtonian characteristic, i.e. ,Herschel-Bulkley-Papanastasiou rheology, while the particles which do not satisfy the condition will remain still. In order to improve the results of numerical modelling further, a two-phase SPH method which is based on the ratio of volume is applied when modelling the dynamics of mixture, and the calculation of viscosity of mixture is improved based on the dynamic characters of solid-fluid mixture. A dam-break problem over movable bed is analyzed based on the model mentioned above. Numerical results are compared with the experimental data, and the comparison verifies that the proposed formula improves the results of numerical modelling.