A frequency domain analysis of compressible linearized Navier-Stokes equations in a hypersonic compression ramp flow

Abstract

We utilize the frequency response analysis of the linearized Navier-Stokes equations to quantify amplification of exogenous disturbances in a hypersonic flow over a compression ramp. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks. Our analysis of the laminar shock/boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific span-wise wavelength. These streaks are associated with heat flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favorably with observations from two different hypersonic compression ramp experiments. Furthermore, we utilize the dominant response to analyze the physical effects in the linearized dynamical system responsible for amplification of disturbances. We show that flow compressibility that arises from base flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Both these effects contribute to the appearance of temperature streaks observed in experiments and are critically important for the development of control-oriented models for transition to turbulence in hypersonic flows.