COMPUTATION OF UNSTEADY INCOMPRESSIBLE VISCOUS FLOWS AROUND A CASCADE BY USING AN IMPLICIT SMAC SCHEME

摘要

To numerical simulate the unsteady incompressible viscous flows around a cascade, the incompressible Navier-Stokes equations of contravariant velocities as unknown values and the elliptic pressure Poisson equation in general curvilinear coordinatess are solved by an implicit finite-difference scheme developed based on the SMAC (simplified marker and cell) method. The governing equations were discretized in the MAC staggered grid. In this scheme, with application of the Crank-Nicholson scheme, the unsteady flows were calculated iteratively by the Newton method at each time step, and the pressure Poisson equation was solved by the Tschebyscheff SLOR method with alternative direction. 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 governing equations. Numerical results for two-dimensional flows through a cascade at high Reynolds numbers are shown. Some computed results of the surface pressure coefficient are 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.