Distributed Roughness-Induced Transition on a Blunt Body at Mach 6: a Numerical Investigation

TL;DR

This paper addresses laminar-turbulent transition over a hypersonic blunt body with fully distributed surface roughness at Mach 6 by performing the first direct numerical simulations of a cylinder with sinusoidal roughness along the entire surface. By varying the spanwise phasing of roughness rows, the study reveals that the roughness pattern selects distinct instability modes (varicose vs sinuous T-S-like waves) and governs the transition location, with a downstream breakdown into hairpin vortices observed across configurations. Linear stability analyses on mean-roughness-affected flows corroborate the DNS findings for certain patterns and expose limitations of purely transient-growth explanations, while an upstream acoustic-feedback mechanism is proposed to explain sustained LTT in some cases. The results show that distributed roughness can dramatically alter instability dynamics and that random phasing generally yields intermediate behavior between aligned and staggered patterns, offering new physical insights and potential guidance for TPS roughness design and predictive transition tools.

Abstract

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 (DNS) 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 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 2D 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 LTT occurred. Finally, exogeneous forcing was not required for the T-S dominated cases as the acoustics generated by the turbulence in the subsonic flow excited T-S waves on the other side - a feedback mechanism hitherto unknown.

Figures (20)

• Figure 1: Schematic of cylinder geometry and roughness configurations. Only 9 out of 220 roughness element rows in the streamwise direction are shown for clarity.
• Figure 2: Contour plots of time-averaged, streamwise mass flux, $\rho U$, obtained from the DNS each roughness configuration. Angle from stagnation, $\Theta$, increases from top to bottom, and is constant for each row. Contour levels are the same for all plots.
• Figure 3: Wall-normal integrated spanwise harmonics of time-averaged streamwise mass-flux (see eq. \ref{['eq:integral_rhoU_fourier']}) at select planes for staggered (left), random (middle), and aligned (right) roughness configurations.
• Figure 4: Development of DNS time-averaged flow field in terms of (a) $99.5\%h_{0,\infty}$ boundary layer thickness, similarity variable transformed profiles of normalised (b) streamwise velocity and (c) temperature. Line colours denoting roughness pattern in (a) are maintained in (b) and (c).
• Figure 5: Development of normalised DNS streamwise velocity streak amplitude in terms of (a) angle from stagnation point, (b) wall-normal profiles and (c) $\eta=0.1$ mm plane just above roughness for staggered (top), random (middle), and aligned (bottom) configurations. Line colours denoting roughness configuration in (a) are maintained in (b).