Numerical investigation of hypersonic step-flows

Hypersonic aerospace vehicles are exposed to extreme flight conditions with heavy contour loads during their mission. Especially at ridges and sharp corners, the wall heat flux and pressure may cause serious damage to the body. Sometimes, the surface material cannot resist the high loading and fails completely. In this work the laminar hypersonic flow over forward and backward facing steps is investigated by CFD techniques and the results are compared with experimental data. The selected flow conditions correspond to cold hypersonic flow according to the availability of experimental data. The Navier-Stokes equations in the high temperature gas approximation of a thermally perfect gas in local equilibrium serve as the model for the physical problem. A multiblock finite-volume method is used to discretize consistently all spatial derivatives appearing in the balance equations. A second order in space Godunov-type method is utilized for the non-diffusive part of the governing equations whereas centered differences are used for the diffusive part. Time integration is performed by a second order implicit scheme. In each time step, the resulting nonlinear system of equations is solved by Newton's method employing a relaxation scheme based on conjugate gradients for the linear equation system. The results obtained permit a close insight into the physics of the flow problems under consideration and by this provide valuable information for construction concepts of hypersonic vehicles. Besides a careful comparison of the numerical results with experimental data, numerical aspects like the grid influence are addressed. Received 9 November 1998 / Accepted 2 December 1999