In this work the effect of isolated surface roughness on the behaviour of a hypersonic boundary layer is investigated, with a particular focus on the effect of the three-dimensional roughness shape on the instability of the roughness wake and the subsequent transition process. The analysis is performed computationally using direct numerical simulations, which solve the compressible Navier-Stokes equations, and a new code, developed in the scope of the current work, to analyse the linear stability of these equations. The full three-stage roughness-induced transition process has been investigated: firstly, the receptivity process and generation of boundary layer instabilities from freestream disturbances; secondly, the generation of a roughness wake and its initial linear instability; and finally the non-linear breakdown to turbulence of the roughness wake. In particular the effect of the three-dimensional roughness shape on these processes has been studied, looking at the roughness height, frontal profile, planform shape and upward/downward ramps. Also the effect of freestream disturbance amplitude andwall cooling has been investigated. It has been found that the roughness height and frontal profile have a large influence on the stability characteristics of the resulting wake and the subsequent transition. The roughness planform shape has a marginal effect, although cylindrical and diamond-shaped elements yield more unstable wakes than a square roughness element. Bi-local stability analysis can be used in most cases to predict the most unstable wake mode, but it under-predicts the instability growth rates due to non-parallel effects. The roughness shape has been observed to affect the transition onset location. The criteria commonly used to predict roughness-induced transition, do not take into account the three-dimensional shape, and an alternative transition prediction, based on the amplitude of the roughness-induced streamwise streak, is considered.
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