Transitional shock wave boundary layer interaction over a flexible panel

Abstract

A three-dimensional transitional shock boundary layer interaction (SWBLI) over a finite-span flexible panel is investigated by performing direct numerical simulations (DNS). The laminar inflow is at Mach 2, on which an oblique shock of turn angle 5.62∘ is imposed. The shock impinges at the mid-chord length of the panel, giving rise to flow separation due to the induced adverse pressure gradient. The flow separation leads to streamline curvature in the laminar boundary layer, initiating a centrifugal instability similar to Görtler instability; where the nominally two-dimensional and steady SWBLI becomes three-dimensional and unsteady at a critical Reynolds number. The flow transition is characterized by the presence of counter-rotating streamwise-oriented Görtler-like vortices, engendering spanwise undulations for increasing Görtler number. The transitional SWBLI is analyzed over both the rigid and flexible panels by performing proper orthogonal decomposition (POD) in order to examine the onset of transition as well as the modal response of the flexible panel. The presence of flexible panel promotes flow transition, resulting in lower values of the critical Reynolds and Görtler numbers. Furthermore, at a post-critical Reynolds number, the interaction results in increased turbulence levels and exchange of energy at the low and high wavenumber modes.