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.

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

“…The relatively short optimal optimization length is consistent with the findings of Theiss et al 17,18 for the laminar wake flow development behind an isolated roughness element on the forebody of the HLB capsule. The authors have shown that due to the strongly favorable pressure gradient, 44 the laminar wake flow experiences growth and decay of the streak amplitude (and also modal disturbance growth) only within a few roughness diameters downstream of the element. Although not shown here, choosing G out E as objective function, the boundary layer on both capsule forebodies undergoes optimal non-modal disturbance growth within 30-40 boundary-layer thicknesses depending on the angular coordinate, which is about fifteen times shorter in comparison to the findings of Reshotko & Tumin 11 for flat plate flows.…”

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

“…The relatively short optimal optimization length is consistent with the findings of Theiss et al [17,18] for the laminar wake flow development behind an isolated roughness element on the forebody of the HLB capsule. The authors have shown that, due to the strongly favorable pressure gradient [44], the laminar wake flow experiences growth and decay of the streak amplitude (and also modal disturbance growth) only within a few roughness diameters downstream of the element. Although not shown here, choosing J out E as the objective function, the boundary layer on both capsule forebodies undergoes optimal nonmodal disturbance growth within 30-40 boundary-layer thicknesses depending on the angular coordinate, which is about 15 times shorter in comparison to the findings of Reshotko and Tumin [11] for flat plate flows.…”