Shock and shear layer interaction in a confined supersonic cavity flow

Abstract

The impinging shock of varying strengths on the free shear layer in a confined supersonic cavity flow is studied numerically using the detached-eddy simulation. The resulting spatiotemporal variations are analyzed between the different cases using unsteady statistics, $x-t$ diagrams, spectral analysis, and modal decomposition. A cavity of length to depth ratio $[L/D]=2$ at a freestream Mach number of $M_\infty = 1.71$ is considered to be in a confined passage. Impinging shock strength is controlled by changing the ramp angle ($\theta$) on the top-wall. The static pressure ratio across the impinging shock ($p_2/p_1$) is used to quantify the impinging shock strength. Five different impinging shock strengths are studied by changing the pressure ratio: $1.0,1.2,1.5,1.7$ and $2.0$. As the pressure ratio increases from 1.0 to 2.0, the cavity wall experiences a maximum pressure of 25% due to shock loading. At [$p_2/p_1]=1.5$, fundamental fluidic mode or Rossiter's frequency corresponding to $n=1$ mode vanishes whereas frequencies correspond to higher modes ($n=2$ and $4$) resonate. Wavefronts interaction from the longitudinal reflections inside the cavity with the transverse disturbances from the shock-shear layer interactions is identified to drive the strong resonant behavior. Due to Mach-reflections inside the confined passage at $[p_2/p_1]=2.0$, shock-cavity resonance is lost. Based on the present findings, an idea to use a shock-laden confined cavity flow in an enclosed supersonic wall-jet configuration as passive flow control or a fluidic device is also demonstrated.