Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner (NASA technical report)
by James Edward Carter
Category: Aerodynamics, Supersonic

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite-difference method of Brailovskaya, which has the second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and the wall pressure distributions measured experimentally by Lewis, Kubota, and Lees for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner, of 6.8 x 104 and 1.5 x 105. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression-corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat-plate flow field, beginning at the leading edge. The compression-corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points. Numerical tests were performed to deduce that the magnitude of the errors introduced by the extrapolation was small. Calculations were made to show the effect of ramp angle and wall suction on the interaction flow field. The pressure distributions obtained in the present calculations, including a case of incipient separation, were plotted together by using the free-interaction scaling of Stewartson and Williams. A good correlation of the numerical results was found, but only fair agreement was found between this correlation and the universal pressure distribution found numerically by Stewartson and Williams.