一种考虑流体状态方程的土体CFD-DEM耦合数值方法

Coupled CFD-DEM method for soils incorporating equation of state for liquid

在离散元(DEM)商业软件PFC2D的基础上,通过将描述流体体变–压力非线性关系的Tait状态方程(EOS)引入计算流体动力学(CFD),建立模拟弱可压缩流体的CFD-DEM耦合计算模块。首先,推导CFD-DEM的控制方程:包括流体–颗粒相互作用力方程、流体运动方程、Tait状态方程和颗粒运动方程。接着,通过PFC2D自定义FISH语言和C++语言将离散化的CFD-DEM控制方程嵌入商业软件PFC2D中。最后,通过单颗粒水下自由沉降运动和一维单面排水固结试验的模拟验证该耦合模块的可行性。模拟结果表明单颗粒自由沉降速度和Stokes理论解接近,一维单面排水固结试验中孔压消散和固结度随着无因次时间因数Tv的变化均与太沙基固结理论符合较好。从而使得用离散元法全耦合分析土体不排水条件下的力学特性成为可能。

The Tait equation of state for liquid is implemented into the N-S equations-based computational fluid dynamics(CFD). This method is then coupled with the distinct element method(DEM) so as to establish CFD-DEM codes to simulate the porous media with weakly compressive fluid. Firstly, the governing equations for the coupled CFD-DEM method are introduced, including equations for fluid-particle interaction forces, N-S equations, Tait equation of state for liquid and motion equations for particle system. Then, a coupled CFD-DEM scheme is implemented into the DEM commercial software PFC2D. Finally, two benchmarking examples, namely, single particle free settling and one-dimensional consolidation, are used to validate the coupled CFD-DEM method. The results show that in the CFD-DEM simulations the free settling velocity of single particle meets the Stokes' s solution, and the excess pore pressure and degree of consolidation at different values of Tv are close to those of the Terzaghi's consolidation theory.