A global pressure relaxation for high speed laminar and turbulent flows

The applicability of the Reduced Navier-Stokes (RNS) model is extended to high supersonic flows. The steady-state primitive variable formulation of the RNS equations is employed. The discretization used is a form of flux-difference splitting. The splitting of the streamwise pressure gradient term allows for upstream elliptic influence in subsonic regions through the forward-differenced portion of this term. The finite-difference equations are solved by a streamwise marching line-relaxation procedure developed in previous work. The pressure is the relaxed variable. For some of the flows considered, all shock waves are captured using the conservation form of the governing equations. For flows at higher Mach numbers, the outer bow shock is fitted with the aid of the Rankine-Hugoniot jump conditions. This allows the computational domain to be limited to the region between the outer shock and the body. All embedded shocks in this region are captured. Flows over a number of geometries including cone, aircraft forebody, cone-cylinder-boattail, cone-cylinder-trough, cone-cylinder-cavity, cone-cylinder-flare, cone-cylinder-base, and base flow with and without a centered jet are investigated. The flow over these geometries at high Reynolds number involves strong viscous-inviscid interactions, embedded shocks and moderate to large separation regions. Laminar and turbulent flows are considered for these axisymmetric bodies. Both the Cebeci-Smith and Baldwin-Lomax turbulence models are employed for turbulent flow calculations. Supersonic and high supersonic flow solutions are obtained. Some comparisons with experimental results are made.