Interaction of Oblique Shocks and Laminar Shear Layers

Abstract

This paper examines the steady interaction of a shear layer separating two uniform supersonic streams of Mach numbers $M_1$ and $M_2$ with an oblique shock approaching from the faster stream at an incident angle ${\sigma }_i$ sufficiently small for the postshock flow to remain supersonic everywhere. The development begins by considering the related problem of oblique-shock impingement on a supersonic vortex sheet of infinitesimal thickness, for which the region of existence of regular shock refractions with downstream supersonic flow is delineated in the parametric space $(M_1,M_2,{\sigma }_i)$ . The interaction region located about the impingement point, scaling with the shear-layer thickness, is described next by integrating the Euler equations in the postshock region, formulated in characteristic form, subject to the Rankine–Hugoniot jump conditions at the shock front. The results are used to investigate the accuracy and limitations of a simplified treatment, the so-called Moeckel–Chisnell approach, commonly employed for determining the shape of the shock wave in these scenarios, which does not account for the influence of the postshock flow. It is found that, although the Moeckel–Chisnell method predicts accurately the shape of the shock front as it evolves across the shear layer, it is unable to predict the final transition to the transmitted-shock solution, which occurs beyond the edge of the shear layer. The structure of the shear layer in the far field also is addressed here for the first time, with the objective being to lay the groundwork for future studies of shock-induced ignition in supersonic fuel–air mixing layers.