Computation of Unsteady Incompressible Turbulent Flow by Using an Implicit SMAC Method

Abstract

An implicit numerical method is developed based on the simplified marker and cell (SMAC) method to solve the 3-D unsteady incompressible turbulence Reynolds-averaging equations in general curvilinear coordinates. The governing equations include the Reynolds averaged momentum equations with contravariant velocities as the unknown variables, pressure Poisson equation and k - ε turbulent model equations. The governing equations are 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 is used to discretize the convective terms in momentum equations and k - ε equations. The algebraic equations of momentum equations and k - ε equations are solved by CTDMA method. The algebraic Poisson equations are solved by the Tschebyscheff SLOR method with alternating computational directions. The unsteady flows in a simplified hollow-jet valve are simulated with the code written by the first author. The computational results are in satisfactory agreement with the experimental photographs.