Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

Abstract

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$ . This damping rate is found to scale as $1/L$ , leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$ , a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

Stability of hypersonic flow over a curved compression ramp

“…In fact, the optimal gain is insensitive to the forcing frequency for ω r L/U ∞ < 10 ( f < 27 kHz). Such a low-pass feature was also observed in hypersonic compression-ramp flow (Dwivedi et al 2019) and shock impingement on a supersonic boundary layer (Bugeat et al 2022). By comparing cases T77 and T75, flow separation is found to increase slightly the maximum optimal gain by a factor of 1.6, while the preferential spanwise wavelength is largely unchanged.…”

“…2019) and shock impingement on a supersonic boundary layer (Bugeat et al. 2022). By comparing cases T77 and T75, flow separation is found to increase slightly the maximum optimal gain by a factor of 1.6, while the preferential spanwise wavelength is largely unchanged.…”

Response of hypersonic compression corner flow to upstream disturbances

“…The shock-induced separated flow can support various local and global flow instabilities (Robinet 2007; Egorov, Neiland & Shvedchenko 2011; Guiho, Alizard & Robinet 2016; Sansica, Sandham & Hu 2016; Bugeat et al. 2022) that may lead to unsteadiness and a laminar‒turbulent transition. Experiments and direct numerical simulations (DNSs) with many canonical configurations (Chapman, Kuehn & Larson 1958; Ginoux 1960; Simeonides & Haase 1995; Benay et al.…”

Krylov methods for large-scale dynamical systems: Application in fluid dynamics

“…It has also been used to solve high-dimensional Ricatti equations for linear optimal control in [235], or to study the stability properties of flow governed by the compressible Navier-Stokes equations with or without shocks [94,95,226]. These include modal and non-modal stability of compressible boundary layers [49,50,117,125,218], cavities [41,247,253,277], wavepackets in jets [26,192,236], transonic buffet [75-77, 199, 200, 255], including the flow past the NASA Common Research wing Model [254,255], wakes [181] and bluff bodies [163,164,226,227].…”

“…to the size m of the Krylov subspace and the integration time τ . At least three runs were made with m ∈(50,75,100,125,150,175,200) and τ = ( T /12, T /10, T /8, T /6, T /4, T /2, T ), where T is the characteristic timescale of the instability. Two cases are considered: the two-dimensional cylinder flow at Re = 80 and the two-dimensional open cavity flow at Re = 4700.…”