Evolution of supersonic corner vortex in a hypersonic inlet/isolator model

There are complex corner vortex flows in a rectangular hypersonic inlet/isolator. The corner vortex propagates downstream and interacts with the shocks and expansion waves in the isolator repeatedly. The supersonic corner vortex in a generic hypersonic inlet/isolator model is theoretically and numerically analyzed at a freestream Mach number of 4.92. The cross-flow topology of the corner vortex flow is found to obey Zhang's theory [Analytical analysis of subsonic and supersonic vortex formation, Acta Aerodyn. Sin. 13, 259-264 (1995)] strictly, except for the short process with the vortex core situated in a subsonic flow which is surrounded by a supersonic flow. In general, the evolution history of the corner vortex under the influence of the background waves in the hypersonic inlet/isolator model can be classified into two types, namely, from the adverse pressure gradient region to the favorable pressure gradient region and the reversed one. For type 1, the corner vortex is a one-celled vortex with the cross-sectional streamlines spiraling inwards at first. Then the Hopf bifurcation occurs and the streamlines in the outer part of the limit cycle switch to spiraling outwards, yielding a two-celled vortex. The limit cycle shrinks gradually and finally vanishes with the streamlines of the entire corner vortex spiraling outwards. For type 2, the cross-sectional streamlines of the corner vortex spiral outwards first. Then a stable limit cycle is formed, yielding a two-celled vortex. The short-lived limit cycle forces the streamlines in the corner vortex to change the spiraling trends rapidly. Although it is found in this paper that there are some defects on the theoretical proof of the limit cycle, Zhang's theory is proven useful for the prediction and qualitative analysis of the complex corner vortex in a hypersonic inlet/isolator. In addition, three conservation laws inside the limit cycle are obtained. Published by AIP Publishing.