Numerical Solution of Two-Dimensional Turbulent Blunt Body Flows with an Impinging Shock

Abstract

AN implicit finite-difference method has been developed to compute two-dimensional, turbulent, blunt-body flows with an impinging shock wave. The complete timeaveraged Navier-Stokes equations are solved with algebraic eddy viscosity and turbulent Prandtl number models employed for shear stress and heat flux. The irregular-shaped bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied. A Type III turbulent shock interference flowfield has been computed and the numerical results compare favorably with existing experimental data. Contents The problem of shock interference heating arising from an extraneous shock wave impinging on a blunt body has been studied extensively during the past several years. In the Type III interference pattern, as described by Edney,l a shear layer originates at the intersection of the impinging shock and bow shock and interacts with the wall boundary layer. It has been shown1;2 that the heat transfer is strongly dependent on whether the shear layer is laminar, transitional, or turbulent. A method for computing laminar shock interference flowfields has been developed previously and applied to both two-dimensional3'4 and three-dimensional5 configurations. This method numerically computes the entire shock layer flowfield using the standard, unsplit, MacCormack finitedifference scheme6 to solve the complete set of compressible Navier-Stokes equations. In order to calculate turbulent shock interference flowfields, a turbulence model was added to the method. Unfortunately, this explicit method suffers from the fact that the allowable time step is proportional to the square of the grid spacing in viscous regions. In order to overcome this step size limitation, an implicit, noniterative, approximate-factorization, finite-difference scheme developed by Lindemuth and Killeen,7 McDonald and Briley,8 and Beam and Warming9 is used in the present study to solve the complete time-averaged Navier-Stokes equations. Although this scheme increases the computation time per step over that of the previous explicit scheme by a factor of 1.8 for turbulent calculations, it permits a time step that is many times greater than the explicit time step when fine meshes are