Linear and Nonlinear Flow Analysis of Elements of a Supersonic Inlet

Abstract

Boundary layer development in a supersonic inlet is studied, focusing on the flow over the compression ramp and the ramp–isolator junction. Two designs of the junction, a backward-facing step (BFS) and a backward-facing notch (BFN), are first evaluated to identify three linear frequency bands (high, medium, and low) of the shear layer instabilities. Compared with BFS, the laminar flow and linear instabilities of BFN are largely insensitive to the incoming boundary layer thickness and show relatively weaker low-frequency unsteadiness. Subsequent linear analysis of the combined ramp and BFN junction identifies a two-dimensional Kelvin–Helmholtz (K-H) instability within the ramp separation, the spectral signature of which extends further downstream. Corresponding large-eddy simulation (LES) predicts transition over the ramp and a turbulized boundary layer at the BFN junction. Modal analysis of LES shows that transition is primarily driven by the breakdown of Görtler vortices due to secondary instabilities, which are tailored by the two-dimensional K-H mode of the ramp separation. The linear analysis provides a reasonable estimate of the pre-transition LES spectrum. The topology of the BFN junction includes streamwise vortices within the turbulent separation bubble, and low-frequency convecting structures further downstream. Statistical parameters from LES indicate strong non-equilibrium effects in the boundary layer post-transition.