Three-dimensional curved shock theory

Curved shock theory is developed to characterize the flow on the downstream side of a three-dimensional shock surface. It is applied to non-symmetric, stationary, blunt-body shocks in a uniform, steady, supersonic freestream. The flow-plane-associated derivatives that are tangential and normal to the shock of pressure, density, velocity components, vorticity, and shock curvatures are presented. Relations are provided for the shock angles, flow deflection angles, intrinsic coordinates, the associated basis, pressure derivatives along these coordinates, streamline curvatures, and the reflection coefficient. A global analysis, utilizing scatterplots, is used to locate curves of sonic flow, maximum flow deflection angle, maximum vorticity, and curves for zero streamline curvature (Crocco) and zero streamwise pressure gradient (Thomas) on the back of a three-dimensional shock wave surface.