On the unsteadiness of shock–laminar boundary layer interactions of hypersonic flows over a double cone

Abstract

Unsteadiness of axisymmetric shock-dominated hypersonic laminar separated flow over a double cone is studied for the first time using a combination of time accurate Direct Simulation Monte Carlo (DSMC) calculations, linear global instability analysis, and momentum potential theory (MPT). Close to steady state linear analysis reveals the spatial structure of the underlying temporally stable global modes. At all Reynolds numbers examined, the amplitude functions demonstrate the strong coupling between the separated flow region at the cone junction with the entire shock system, including pressure and temperature waves generated behind the shock and spatially amplified Kelvin-Helmholtz waves. In addition, as the Reynolds number is increased, temporally damped harmonic shock oscillations and multiple-reflected λ-shock patterns emerge in the eigenfunctions. Application of the MPT (valid for both linear and nonlinear signals) to the highest Reynolds number DSMC results shows that large acoustic and thermal potential variations exist in the vicinity of the separation shock, the λ-shock patterns, and the shear layers. It is further shown that the motion of the bow shock system is highly affected by non-uniformities in the acoustic field. At the highest Reynolds number considered here, the unsteadiness is characterized by Strouhal numbers in the shear layer and bow-shock regions and is found to be in qualitative agreement with earlier experimental and numerical work.