Multi-scale study of the transitional shock-wave boundary layer interaction in hypersonic flow

Abstract

A high-fidelity simulation of the massively separated shock/ transitional boundary layer interaction caused by a 15-degrees axisymmetrical compression ramp is performed at a free stream Mach number of 6 and a transitional Reynolds number. The chosen configuration yields a strongly multiscale dynamics of the flow as the separated region oscillates at low-frequency, and high-frequency transitional instabilities are triggered by the injection of a generic noise at the inlet of the simulation. The simulation is post-processed using Proper Orthogonal Decomposition to extract the large scale low-frequency dynamics of the recirculation region. The bubble dynamics from the simulation is then compared to the results of a global linear stability analysis about the mean flow. A critical interpretation of the eigenspectrum of the linearized Navier-Stokes operator is presented. The recirculation region dynamics is found to be dominated by two coexisting modes, a quasi-steady one that expresses itself mainly in the reattachment region and that is caused by the interaction of two self-sustained instabilities, and an unsteady one linked with the separation shock-wave and the mixing layer. The unsteady mode is driven by a feedback loop in the recirculation region, which may also be relevant for other unsteady shock-motion already documented for shock-wave/turbulent boundary layer interaction. The impact of the large-scale dynamics on the transitional one is then assessed through the numerical filtering of those low wavenumber modes; they are found to have no impact on the transitional dynamics.

Transition to turbulence in hypersonic flow over a compression ramp due to intrinsic instability

“…2009; Lugrin et al. 2021 a ). Both stationary and oscillatory global modes were revealed using GSA (see, e.g.…”

“…It is interesting to note that self-excited instability is ubiquitous in separated flows involving SWBLI. Examples are compression-ramp flow (Egorov, Neiland & Shredchenko 2011;Sidharth et al 2017), shock impingement on a flat plate (Robinet 2007;Nichols et al 2017), double-wedge flow (Sidharth et al 2018), double-cone flow (Hao et al 2022) and flow over a hollow cylinder/flare (Brown et al 2009;Lugrin et al 2021a). Both stationary and oscillatory global modes were revealed using GSA (see, e.g.…”

Transitional shockwave/boundary layer interaction experiments in the R2Ch blowdown wind tunnel

“…The region of positive heat flux variation at reattachment is followed by a region of negative variation on the edge of the flare. Hildebrand et al (2018); Lugrin et al (2021a) showed in their numerical work that global unstable modes in the recirculation region of transitional hypersonic SBLI could lead to such an alternate pattern in the streamwise direction. Neither Görtler instabilities nor other convective mechanisms such as unveiled by Dwivedi et al (2019) display such streamwise pattern.…”

“…Either there is not any low-frequency separated region motion or a very low amplitude one. The SBLI unsteadiness is also known to have a negligible impact on the transition process in noisy environment (Lugrin et al, 2021a).…”

Special issue on the fluid mechanics of hypersonic flight

“…Finally, contributions to this volume employed state-of-the-art numerical simulations of the compressible Navier-Stokes equations to characterize hypersonic flows in both canonical and applied configurations. Lugrin, Beneddine, Garnier and Bur [36] perform large-scale simulations and linear stability analyses of M ∞ = 6 flow on a hollow cylinder/flare configuration for which experimental data are available. Wall-resolved large Eddy simulations were used to resolve transitional flow features, followed by data-driven and operator-driven [60] analyses of the results, respectively, employing Spectral POD [56,64] and mean flow stability analysis [3].…”