Abstract
An implicit numerical method is developed based on the simplified marker and cell(SMAC)method to solve the 3D unsteady incompressible turbulence Reynolds-averaging equa- tions in general curvilinear coordinates.The governing equa- tions include the Reynolds averaged momentum equations with contravariant velocities as the unknown variables,pressure Poisson equation andκ-eturbulent model equations.The gov- erning equations are discretized in 3D MAC staggered grid.To improve the numerical stability of the implicit SMAC scheme, the higher-order high resolution Chakravarthy-Osher total variation diminishing(TVD)scheme is used to discretize the convective terms in momentum equations andκ-eequations. The algebraic equations of momentum equations andκ-eequa- tions are solved by cyclic tridiagonal matrix algorithm (CTDMA)method.The algebraic Poisson equations are solved by the Tschebyscheff successive linear over relaxation(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.
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