Linear modal global instabilities of hypersonic flow over an inclined cone

Abstract

A systematic parametric study is presented on the modal global linear instability of Mach 6 boundary-layer flow over an inclined cone at 6 degree angle of attack under typical wind-tunnel conditions. The analysis is performed using the spatial BiGlobal theory. Results reveal two classes of global instabilities in the outboard region away from the leeward plane: high-frequency (hundreds of kHz) second mode instabilities and low-frequency (tens of kHz) crossflow instabilities. In the global eigenvalue spectra of the second mode instability, two distinct branches of significantly unstable modes are identified, namely an approximately continuous spectrum (branch S) and a few discrete points (branch D). The branch D modes peak at the windward centerline while branch S modes lie at a certain distance away from the windward meridian. The global stability characteristics of the crossflow instability over a conical configuration are uncovered for the first time. In the global eigenvalue spectra of the crossflow instability, many unstable modes emerge and form a complex pattern, with the most amplified frequency of around 30 kHz. The unstable crossflow modes are mainly distributed on the leeward side and wave angles obviously increase towards the leeward centerline. The peak growth rates are slightly smaller than those of second modes, and yet the most amplified frequency varies rather mildly along the streamwise direction so that they may achieve larger integrated growth rates than second modes do.