Study on Stabilization and Destabilization Effect of a Smooth Hump in Hypersonic Boundary Layers by PSE

Abstract

Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied. Parabolized stability equations (PSE) is employed to analyze the linear evolution of mode S over a hump in Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier-Stokes (PNS) equations. Hump with height smaller than local boundary layer thickness is used. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect of hump located at upstream and downstream of synchronization point are confirmed. Results of parametric studies to examine the effect of hump height, location, etc. are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers. Nomenclature b = hump half width c = phase speed f = physical frequency F = non-dimensional frequency h = hump height L = streamwise distance from leading dege to hump center location M = Mach number N = N-factor R = Reynolds number based on boundary layer length scale Re = unit Reynolds number Re L = Reynolds number based on L δ = boundary layer length scale θ c = cone half angle ω = angular frequency

Second Mode Suppression in Hypersonic Boundary Layer by Roughness: Design and Experiments

“…All results are consistent with the initial finding that 2-D roughness elements can damp 2-D disturbances and have shown the importance of roughness locations and synchronization locations. In 2013, Park and Park [20] performed a theoretical parabolized stability equations (PSE) study of a smooth hump on a hypersonic flat plate to investigate the importance of the synchronization location as Fong et al discovered [21]. They found the stabilization effect of the hump on convective instability is possible and confirmed the idea of the importance of the roughness location and the synchronization point.…”

Nonlinear resonance of low- and high-frequency waves in a cooled hypersonic boundary-layer

“…From the broken line, we can observe that at x * = x * tr. , the maximum N-factor is 5.2, which is a reasonable value for a predictive threshold of the transition onset in conventional tunnels (Fujii 2006, Park and Park 2013, Mortensen 2018. The frequency of the critical mode is approximately 420 kHz, which almost falls in the frequency range of the dominant surface-pressure fluctuations (figure 3) and is also close to one of the fundamental waves giving peak bicoherence (figure 5 (a) and (b)).…”

“…In particular, the latter is known as an efficient tool for studying the effects of nonparallelism and weak non-linearity with low computational cost. Using PSEs, several authors (Chang et al 2019, Park and Park 2013, Pruett and Chang 1995 have investigated transition mechanisms in hypersonic boundary layers on conical geometries. To our knowledge, however, the only study to focus on interactions in LHFWs was that of Chen et al (2017).…”

“…To examine the accuracy of the present code, comparisons were made against other linear PSE and DNS studies by Park and Park (2013), Pruett and Chang (1995). For the former, figure 7(a) illustrates N-factors of axisymmetric Mack's second modes in an axisymmetric conical boundary layer.…”