Constant Density Approximations for the Flow Behind Axisymmetric Shock Waves

The incompressible rotational flow equations are used to obtain solutions for the flow behind axisymmetric shock waves with conic longitudinal sections. The nonlinear part of the term due to rotation is retained in the analysis. Numerical results for standoff distance and stagnation point velocity gradient are presented for the case in which the shock wave is a paraboloid, a sphere, or an oblate or prolate ellipsoid. A similarity parameter is proposed which correlates approximately the flow behind geometrically similar shock waves at different free-stream conditions.