叶栅内非定常不可压流动的数值模拟

基于SMAC(Simplified Marker and Cell)方法推导出直接求解二维非定常、不可压N-S方程的隐式数值方法.求解的基本方程是任意曲线坐标系中以逆变速度为变量的N-S方程和椭圆型的压力Poisson方程.采用该方法,对二维叶栅非定常分离流场进行了数值模拟,叶栅表面压力的计算结果与试验结果相比比较吻合,从而验证了这种方法的可靠性.同时对叶栅非定常流场的流场结构和流动机理做了初步的探讨.在均匀来流和定常边界条件下,叶栅内部流动表现出强烈的非定常性;在小冲角和高雷诺数时,叶栅尾部产生类似卡门涡街的周期性流动.

NUMERICAL SIMULATION OF UNSTEADY INCOMPRESSIBLE FLOWS THROUGH A CASCADE

An implicit finite-difference method based on the SMAC (Simplified Marker and Cell) scheme for directly solving incompressible unsteady N-S equations is developed. The method is based on the contravariant velocities and the elliptical Poisson pressure equations in general curvilinear coordinates. Numerical results for two-dimensional unsteady separated flows through a cascade are shown. The computed results of the surface pressure coefficient are in satisfactory agreement with the experimental data. The structure of flow fields and the mechanism of unsteady flows are investigated preliminarily. The numerical results indicate that the flows are strong unsteady flows, though the inlet velocity is mean and the boundary conditions are steady. When the angle of attack is small and the Reynolds number is high, periodic fluctuating flow similar to the Kármán vortex street is formed at the trailing edge.