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 threedimensional 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 shapewere 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 theory pioneered by Reshotko and Tumin [11] where the roughness-induced velocity perturbations are assumed to be proportional to roughness height. Wang and Zhong [12] studied the transient growth of a flat-plate boundary layer to small surface roughness periodic in the spanwise direction. The results showed that the assumption, the roughness-induced velocity perturbations are proportional to roughness height, is only valid when roughness height is smaller than approximately one thirty-fifth of the local boundary-layer thickness. Therefore, the transient growth theory cannot be directly applied to the transient growth induced by finite-height roughness [8–10]. Unfortunately, the roughness-induced transition in hypersonic boundary layers, especially that induced by arbitrary surface roughness, is still poorly understood due to the limitations in experimental facilities and numerical methods [13]. Marxen et al. [14] studied the effect of a two-dimensional (2-D) roughness element on the stability of a hypersonic boundary layer. They showed that in the vicinity of the separation regions located near the edges of the roughness the destabilization of a second-mode disturbance occurs for a certain frequency. Even though roughness is generally expected to lead to an early transition several past studies have shown that roughness can stabilize boundary-layer flows and delay transition in some situations. For example, Holloway and Sterrett [15] concluded from their experiments that surface roughness can delay transition when its height is less than the local boundary-layer thickness. Fujii [16] found that a wavy roughness can suppress the transition of a Mach 7.1 boundary layer. Although no physical explanation is given the repeatable results indicate that some unknown mechanisms must have been presented. Recently, Wang et al. [17] studied the response of a Mach 8 flow over a 5.3 deg half-angle wedge to wall blowing– suction and showed that the synchronization point plays a critical role in the stability of hypersonic boundary layers. The results of Wang et al. [17] indicate that the location of roughness with respect to the synchronization point might play a role in the roughness-caused second-mode destabilization [14] and transition delay [15,16]. In this Technical Note, we present our numerical simulation results on the stabilization of aMach 5.92 flow over a flat plate by 2-D finiteheight roughness. The main objective is to investigate the effect of roughness location on mode S instability. Although three-dimensional surface roughness is more relevant to the roughness-induced transition the current numerical simulations on 2-D finite-height roughness are still valuable for the effect of roughness on the stability of hypersonic boundary layers. Figure 1 shows a schematic of the problem where boundary-layer waves are excited by a blowingsuction slot near the leading edge and a finite-height roughness is put downstream of the slot. Specifically, four cases of numerical simulations are conducted with the roughness at different locations. The results show that mode S is destabilized only when the roughness element is located closely upstream of the synchronization point. When the roughness element is downstream of the synchronization Presented at the 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, Orlando, Florida, 5–8 January 2009; received 17 October 2011; revision received 13 June 2012; accepted for publication 14 June 2012; published online 21 November 2012. Copyright © 2012 by XiaowenWang. Published by the American Institute of Aeronautics andAstronautics, Inc., with permission. Copies of this papermay be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-385X/12 and $10.00 in correspondence with the CCC. *Graduate Research Assistant, Mechanical and Aerospace Engineering Department. Student Member AIAA. ResearchAssociate,Mechanical and Aerospace EngineeringDepartment. Senior Member AIAA. Professor,Mechanical andAerospace EngineeringDepartment. Associate Fellow AIAA.