Shock detachment from curved wedges by local choking: numerical verification

Abstract

Computational fluid dynamics shows that a shock wave can detach from the sharp leading edge of a curved wedge at a wedge angle smaller than the classical maximum flow deflection as well as the sonic wedge angle. This is attributed to the inability of the sonic flow, at the wedge trailing edge, to pass as much mass flow as is being admitted through the shock wave attached at the leading edge. At this condition, the flow is unsteady, causing both the sonic surface and the shock to make adjustments in their shapes and positions to achieve a steady state with mass-flow balance. As a result, the shock wave becomes detached. Time-accurate CFD calculations show the gasdynamic details of the adjustment where the flow and the detached shock assume a steady state as the mass-flow imbalance gradually decreases to zero. This mechanism of shock detachment, occurring near the leading edge, is called local choking to distinguish it from shock detachment due to global choking that occurs because of flow choking at the exit of a convergent duct and to distinguish it as well from detachment due to an excessive leading-edge deflection. The local choking mechanism has been postulated to be a cause of shock detachment from doubly curved wedges. An analysis, based on curved shock theory and confirmed by CFD, shows that local choking and shock detachment from a doubly curved leading edge are dependent on Mach number, wedge angle, wedge curvature (both streamwise and cross-stream), and wedge length.