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 and k–e turbulent 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 and k–e equations. The algebraic equations of momentum equations and k–e equa-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.

Key words: Hollow-jet valve, Simplified marker and cell(SMAC) method Contravariant velocity, Total variation dimsinishing(TVD), Unsteady incompressible flows