Influence of geometric parameters of discrete roughness elements on hypersonic boundary layer instability

•Developing two-dimensional linear stability analysis code for wake instability.•Analyzing the influence of roughness shape and height on flow instability.•Critical height within boundary layer thickness affecting instabilities is identified.•Low-frequency instability is enhanced of as the roughness's height increases.•The most effective shape for destabilization varies with the roughness height. This study conducts a stability analysis of the hypersonic boundary layer downstream of a discrete roughness element to investigate the influence of the element's shape and height on boundary layer instability. An isolated discrete roughness element attached to a flat plate was considered, and a linear stability analysis method was employed for a two-dimensional plane perpendicular to the streamwise direction. To solve the stability problem numerically, the plane stability analysis module was developed and validated by comparison with the results of previous studies. The spatial amplification rates and N-factor envelopes were calculated for the streak mode, the primary unstable mode, for the dominant unstable frequency band. The range of the N-factor corresponding to the transition onset location was estimated by comparing the experimental data with the stability analysis results. The existence of the critical height, the minimum height at which the effect of roughness element attachment becomes apparent, was confirmed, and a trend of the increasing instability with greater element height was observed. It is also found that the dominant frequency band varies with the height, and that the upper shape effective in destabilizing flow depends on the height of the element. The two-dimensional linear stability analysis method applied in this study is expected to be useful for investigating the parameters affecting instability in practical flows, such as downstream flows of discrete roughness elements or vortex generators attached to the surface of flight vehicles.