Nonasymptotic Theory of Unseparated Turbulent-Boundary-Layer — Shock-Wave Interactions with Application to Transonic Flows

Abstract

Shock-turbulent-boundary-layer interactions are important in the aerodynamic design of high-speed aircraft wings, and of turbine and cascade blades in turbomachinery and air-breathing-engine inlets and diffusors. Of particular importance are the features of upstream influence, boundary-layer displacement, skin friction, and incipient separation dominated by the thin interactive shear-stress disturbance layer very close to the surface. Lighthill’s pioneering study [2.1] of this region, however, takes into account only the laminar portion of the incoming turbulent-boundary-layer profile, which is inaccurate for the higher Reynolds numbers pertaining to full-scale aircraft. On the other hand, more recent work on an improved theory either has been confined to the treatment of the transonic regime by asymptotic methods [2.68, 2.69] that entail a severe limiting model of the interactive physics as Re _l → ∞, or has involved approximate double-layered models for supersonic flow [2.70–2.72] with insufficient consideration of the basic flow structure in the shear-disturbance sublayer [2.73]. Consequently, there is a need for a more general theory at ordinary practical Reynolds numbers, applicable to both transonic and supersonic flow.