Separation length scaling for dual-incident shock wave–turbulent boundary layer interactions with different shock wave distances

Abstract

In this study, the length scaling for the boundary layer separation induced by two incident shock waves is experimentally and analytically investigated. The experiments are performed in a Mach 2.73 flow. A double-wedge shock generator with two deflection angles ( $\alpha _1$ and $\alpha _2$ ) is employed to generate two incident shock waves. Two deflection angle combinations with an identical total deflection angle are adopted: ( $\alpha _1 = 7^\circ$ , $\alpha _2 = 5^\circ$ ) and ( $\alpha _1 = 5^\circ$ , $\alpha _2 = 7^\circ$ ). For each deflection angle combination, the flow features of the dual-incident shock wave–turbulent boundary layer interactions (dual-ISWTBLIs) under five shock wave distance conditions are examined via schlieren photography, wall-pressure measurements and surface oil-flow visualisation. The experimental results show that the separation point moves downstream with increasing shock wave distance ( $d$ ). For the dual-ISWTBLIs exhibiting a coupling separation state, the upstream interaction length ( $L_{int}$ ) of the separation region approximately linearly decreases with increasing $d$ , and the decrease rate of $L_{int}$ with $d$ increases with the second deflection angle under the condition of an identical total deflection angle. Based on control volume analysis of mass and momentum conservations, the relation between $L_{int}$ and $d$ is analytically determined to be approximately linear for the dual-ISWTBLIs with a coupling separation region, and the slope of the linear relation obtained analytically agrees well with that obtained experimentally. Furthermore, a prediction method for $L_{int}$ of the dual-ISWTBLIs with a coupling separation region is proposed, and the relative error of the predicted $L_{int}$ in comparison with the experimental result is $\sim$ 10 %.