Implicit Numerical Scheme Based on SMAC Method for Computing Unsteady Incompressible Turbulent Flows

摘要

An implicit numerical scheme was developed based on the simplified marker and cell (SMAC) method for computing the three-dimensional (3-D) unsteady incompressible turbulence Reynolds- averaging equations in general curvilinear coordinates. The governing equations included the Reynolds averaged momentum equations with contravariant velocities as the unknown variables, pressure Poisson equation and k εε ? turbulent model equations. The governing equations were discretized in 3-D MAC staggered grid. To improve the numerical stability of the implicit SMAC scheme, the higher-order high resolution Chakravarthy-Osher TVD scheme was used to discretize the convective terms in momentum equations and k εε ? equations. The algebraic equations of momentum equations and k εε ? equations were solved by CTDMA method. The algebraic Poisson equations were solved by the Tschebyscheff SLOR method with alternating computational directions. The unsteady flows through a simplified cascade made up of NACA65-410 blade at high Reynolds numbers were simulated with the code written by the first author. The numerical results of the surface pressure coefficient were in satisfactory agreement with the experimental data. The numerical results indicate that the Reynolds number and the angle of attack were two primary factors which affected the unsteady characteristics of the flows.