Pressure gradient effects on wake-flow instabilities behind isolated roughness elements on re-entry capsules

Abstract

Laminar-turbulent transition caused by modal disturbance growth in the wake flow of isolated roughness elements on blunt re-entry capsules is studied numerically at typical cold hypersonic wind-tunnel conditions. Two fundamentally different heat shield shapes are considered. On the sphere-cone forebody the wake flow of the roughness is exposed to an adverse pressure gradient, whereas the spherical heat shield exhibits a strongly favorable pressure gradient. The pressure gradient effects on the development of the stationary wake flow and its modal instability characteristics are discussed for various heights and diameters of the cylindrical roughness element. Regions of increased shear develop in its wake, which persist longer in the adverse pressure gradient case. Consequently, the results of spatial two-dimensional eigenvalue analyses reveal that the unstable wake-flow region extends much further downstream and the wake-mode instabilities are considerably more amplified. The disturbance kinetic energy production terms are used to assess the contributions of the different shear-layer regions to the mode growth and its dependence on the pressure gradient.