Gauging Centrifugal Instabilities in Compressible Free-Shear Layers via Nonlinear Boundary Region Equations

Abstract

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward-facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier–Stokes equations are reduced to the nonlinear boundary region equations (BREs) in a high Reynolds number asymptotic framework, wherein the streamwise wavelength of the disturbances is assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number M∞, the shear layer thickness δ, the amplitude of the incoming disturbance A, and the relative velocity difference across the shear layer ΔV on the development of these centrifugal instabilities. Our parametric study shows that, among other things, the kinetic energy of the curved shear layer flow increases with increasing ΔV and A decreases with increasing delta. It was also found that increasing the disturbance amplitude of the incoming disturbance leads to significant growth in the mushroom-like structure’s amplitude and renders the secondary instability structures more prominent, indicating increased mixing for all Mach numbers under consideration.