Stabilization of a Mach 5.92 Boundary Layer by Two-Dimensional Finite-Height Roughness

THE performance of hypersonic transportation vehicles and reentry vehicles is significantly affected by the laminar-turbulent transition of boundary-layer flows over vehicle surfaces as transition has a first-order impact on lift, drag, stability, control, and surface heating of these vehicles. For example, the roughness-induced transition is an important consideration in the design of thermal protection systems [1,2]. For a reentry vehicle transition can lead to an increase in surface-heating rate by a factor of five or more. Hence, the understanding of transition mechanisms is critical to the development of future hypersonic vehicles [3]. The dominant mechanism in the roughness-induced transition is the transient growth associated with purely wall-normal and spanwise velocity perturbations, which finally evolve into streak-like motion. Transient growth has been studied by many researchers. Andersson et al. [4] calculated the transient growth of a flat-plate boundary layer to steady disturbances and found that the maximum transient growth scales linearly with the distance from the leading edge, which was consistent with the results of Hanifi et al. [5]. Collis and Lele [6] investigated the stationary crossflow vortices in a three-dimensional boundary layer over a swept wing due to surface roughness near the leading edge. The results showed that the initial amplitude of crossflow vortices is enhanced by convex surface curvature and strongly reduced by nonparallel flow effects. White and Ergin [7] studied the transient growth of a Blasius boundary layer generated by a spanwise array of roughness elements. The results indicated that the energy of the roughness-induced disturbances is proportional to the roughness-height-based Reynolds number. White et al. [8] further investigated the effects of the height and diameter of cylindrical roughness element on transient growth. Their results showed that the energy of transient growth is proportional to the square of the roughness-height-based Reynolds number. In addition, transient growth strongly depends on roughness diameter. Choudhari and Fischer [9,10] examined the transient growth in a laminar boundary layer due to a spanwise array of circular disks at the surface. The effects of roughness height, size, and shape were explored. Their results indicated that the energy of transient growth is consistent with the scale of White et al. [8]. One explanation to the roughness-induced transition is the transient growth