Distributed roughness-induced transition on a blunt body at Mach 6: a numerical investigation

Surface roughness significantly impacts transition to turbulence, especially over high-speed, blunt geometries where surface ablation is necessary to mitigate heat loads during atmospheric entry. Inspired by sand-grain roughness experiments performed by Hollis (2017), we perform the first direct numerical simulation of a blunt cylinder in Mach 6 cross-flow with roughness elements distributed along the entire surface. Such simulations aimed to uncover the precise means by which laminar–turbulent transition occurs given the limited measurements attainable from experiments and non-existent high-fidelity simulations. Element heights were held fixed at approximately 35 % boundary-layer thickness, while the relative phasing between streamwise rows was varied. All configurations exhibited convective instabilities in the post-shock subsonic flow driving the transition process, with the mode type being set by the roughness configuration. A fundamental sinuous streak mode dominated the aligned roughness element case, whereas both the staggered and randomly phased cases saw two-dimensional Tollmien–Schlichting (T–S) waves dominating. These instability waves, when grown to sufficient amplitude, triggered the steady streaks seeded by the underlying roughness pattern to begin forming hairpin vortices and breakdown occurred soon thereafter. The roughness arrangement was found to dramatically influence the degree to which the waves were destabilised, as well as the strength of the underlying steady streaks, thereby combining to dictate the position along the surface where laminar–turbulent transition occurred. Since exogenous forcing was not required for the T–S-dominated cases, an acoustic feedback loop is proposed in which upstream-propagating acoustic disturbances generated by turbulence in the subsonic region couple to and sustain the T–S waves.