考虑惯性效应的渗流方程及相关阻力标度律

The Seepage Equation with Inertial Effects and the Scaling Law of Related Resistances

本文基于体积平均法推导得到了多孔介质中考虑惯性效应时的局部线化宏观流动方程,由此可以递推得到较大雷诺数Re时Navier-Stokes方程的解,从而避免了直接求解Navier-Stokes方程所带来的计算成本高和计算稳定性差的问题.针对正方形周期排列模型的算例表明,平均速度方向与宏观压力梯度方向并不总是一致,一般情况下,随着Re增大,二者差异也会增大.当固定平均速度方向v?时,压差阻力在较大的Re范围内存在标度律,标度指数约为3.该标度指数与弱惯性区域标度指数一致,但弱惯性区域Re范围仅为0<Re<1,而本文发现的标度律区域可宽达100.

The local linear filtration equation with inertial effects based on volume averaging is proposed in this paper to obtain the solutions of Navier-Stokes equations at relative high Re recursively.The proposed method can avoid the expensive computation cost and the poor performance of stability brought by the direct numerical solution of Navier-Stokes equations.According to the numerical simulation of periodic arrays of aligned squares,the average velocity direction is not always consistent with the macro pressure gradient direction.In general,the angle difference between the two directions will increase with Re growing.When the direction of the average velocity is fixed,there is a scaling law of the pressure resistance on a large scale,and the scale index is about 3.This scale index is consistent with the one in weak inertial regime 0<Re<1.However,in this paper,the regime with the scaling law is as wide as 100.