基于湍流自旋理论的二维方腔旋转流动的数值模拟

Numerical Simulation of Two Dimensional Rotating Flow In Square Cavity Based on Spin Model of Turbulence

基于湍流自旋理论对旋转方腔内不可压流体的流动进行了二维数值模拟,用有限容积法在交叉网格上对控制方程进行离散,采用SIMPLEC算法进行计算,对流项的离散方面采用了延迟修正的QUICK格式,最后采用二维的TDMA算法进行迭代求解,并对边界条件处理采用了Block块技术.同时与经典理论即Navier-Stokes(N-S)方程的模拟情况做了比较.得出下列结论:N-S方程表明方腔旋转时内部流体只会作刚体旋转;而自旋模型表明该类流动具有不平凡性和不稳定性:即流体的内聚力不足以使流体跟随固体边界作刚体运动,旋转边界必然在流体中诱导出小尺度耗散涡旋,这些小尺度涡旋在固壁附近组织出正负相间的拓扑缺陷(涡旋场强),这一流体定向奇性会与速度场耦合,并容易形成复杂的大尺度的涡旋运动.

Two-dimensional numerical simulation based on the spin model of turbulence was carried out for the incompressible fluid flow in square cavity.The discrete representation of the general form was obtained at staggered grid with the Finite Volume Method.The calulation was done using the SIMPLEC algorithm.The discrete schemes of convective term were dealt with deferred correction method of quadratic upwind interpolation of convective kinematics.two-dimensional TDMA was used to get the iteration solve,and boundary condition was delt with by the method of Block finally.And comparing with that of classical theory—the Navier-Stokes（N-S） equations,the following conclusions are got that,according to the N-S equations,the inner fluid just rotates as a rigid body with the rotating square cavity,but the spin model of turbulence predicts such a flow has nontrivial property and instability,namely,the cohesion of fluid is not so strong to make the fluid rotate as a rigid body with the solid boundary,namely,the rotating boundary must induce microscale dissipative eddy in fluid,such eddy evolves unsteady,and organizes topological defects（vortex intensity） chequered with positive and negative space near the solid wall,and these orientation singularities in fluid are sensitive to velocity disturbance which is ubiquitous in real flow,and can stimulate the amplification of disturbance to large scale vortex motion.