Three-dimensional viscous hypersonic flows over general bodies using shock-layer and parabolized Navier-Stokes equations

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Virginia Polytechnic Institute and State University


The three-dimensional viscous hypersonic flowfield over blunted cones at large angles of attack, including crossflow separation, has been solved using both viscous shock-layer (VSL3D) and parabolized Navier-Stokes equations (PNS). The viscous shock-layer equations have been used for the solution of windward region up to the crossflow separation point and the parabolized Navier-Stokes equations have been used to complete the solution in the crossflow separated region. A fast implicit iterative technique known as the Pseudo Elimination Method (PEM) has been used to solve the PNS equations, and the computing time has been reduced by 35 percent. A computer code (VSLPNS) has been developed using this technique, and calculations were made for two test cases, which typically encompass reentry flow conditions. Case 1 considered low Mach number (10) and high Reynolds number (2 x 10⁶/foot) at moderate angle of attack (10 deg.). Case 2 considered high Mach number (25) and low Reynolds number (7,256/foot) at large angle of attack (35 deg.). The results have been compared with a complete PNS solution, and for Case 1, the aerodynamic coefficients have been compared with available experimental data. The comparisons indicate good agreement for wall pressure, both longitudinal and crossflow skin-friction coefficients and aerodynamic coefficients. The computing times required indicate that the present code obtains complete flowfield solutions in the shortest possible time thus making it (VSLPNS) an ideal tool for design analysis of lifting reentry vehicles.