2D and 3D Stability of Cavity Flows in High Mach Number Regimes

Abstract

The stability characteristics of an open cavity flow at very high Mach number are examined with BiGlobal stability analysis based on the eigenvalues of the linearized Navier-Stokes equations. During linearization, all possible first-order terms are retained without any approximation, with particular emphasis on extracting the effects of compressibility on the flowfield. The method leverages sparse linear algebra and the implicitly restarted shift-invert Arnoldi algorithm to extract eigenvalues of practical physical consequence. The stability dynamics of cavity flows at four Mach numbers between 1.4 and 4 are considered at a Reynolds number of 502. The basic states are obtained through Large Eddy Simulation (LES). Frequency results from the stability analysis show good agreement when compared to the theoretical values using Rossiter’s formula. An examination of the stability modes reveals that the shear layer is increasingly decoupled from the cavity as the Mach number is increased. Additionally, the outer lobes of the Rossiter modes are observed to get stretched and tilted in the direction of the freestream. Future efforts will extend the present analysis to examine current and potential cavity flame holder configurations, which often have downstream walls inclined to the vertical.