Curved aerodynamic shock waves

1AbstractCurved shock theory (CST) has been extended to apply to axisymmetric shocks in non-uniform flow. A general formula has been derived for the vorticity jump across a doubly curved shock in non-uniform flow. Influence coefficient forms of equations for the gradients and vorticity show the effect of changing pre-shock conditions. CST has been applied to a series of simple shock flows and to the orientation of the sonic surface at the rear face of a doubly curved shock. This orientation is significant in determining the occurrence of embedded shocks in the post-shock flow. Application of CST to curved, concave, normal shocks allowed the derivation of an explicit relationship between the shock's curvature and the length of down-shock subsonic flow. Investigations of conical flows by analysis, CFD and experiment all failed to demonstrate the existence of regular reflection of shocks at the centre line of axisymmetric flows. An analytically predicted conical shock, on the calculated streamline, does not extend all the way to the centre line but terminates in Mach reflection. It appears that the existence of an analytical Taylor-Mccoll (T-M) solution is not in itself a guarantee of the physical existence of a conical flow in all cases. The T-M equations predict the existence of an axisymmetric centered compression fan, analogous to the Prandtl-Meyer fan in planar flow. A free-standing conical shock is located downstream of the compression fan. Both features have been shown to exist by CFD as well as experiment. Busemann flow is the only flow where these wave structures can exist; it is possible to reflect an incident, centered compression as a conical shock. Discovery of an inflection point on the Busemann streamline has an important implication to spontaneous starting of Busemann intakes. Three types of flow can exist behind a doubly curved concave shock; characterized by the orientation of the sonic surface which, in turn, is determined by the pre-shock Mach number and the shock curvatures ratio. Shapes of special axial shock surfaces, with straight post shock streamlines (Crocco shocks), or vanishing streamwise pressure gradient (Thomas shocks) and shocks with specific sound reflectivity (zero, if desired), have been calculated and illustrated. Boundary layer generated noise abatement is a possibility. Local flow choking, near the leading edge, leads to shock detachment from a curved wedge with such detachment depending on freestream Mach number, the wedge2angle, the wedge curvature and the wedge length. These are new criteria for shock detachment with analogies extending to the transition from regular to Mach reflection of shock waves.