Onset of separation unsteadiness in hypersonic shock boundary layer interaction on a cone-step

TL;DR

This study investigates intrinsic unsteadiness in hypersonic SBLI over a cone-step at Mach 6 in a quiet flow, combining time-resolved Schlieren, SPOD, and high-fidelity axisymmetric and 3D simulations. It delineates how unsteadiness transitions from shear-layer oscillations to large-amplitude pulsations as Re_L and geometry vary, with dominant low-frequency modes around $St\approx0.17$ at onset and $St\approx0.13$ in pulsations. SPOD and 3D simulations reveal a hydrodynamic coupling between the separation zone and bow shock, and spectral-submanifold analysis uncovers a supercritical Hopf bifurcation governing the onset of limit-cycle oscillations. The findings clarify the roles of Reynolds-number effects and contact discontinuities in cone-step SBLI, offering insights for predicting and managing unsteadiness in hypersonic configurations.

Abstract

Shock-boundary layer interactions (SBLI) on hypersonic cone step flows exhibit a range of intrinsic unsteady behaviors, from shear-layer oscillations to large-scale pulsations. This work investigates the unsteadiness in a cone-step geometry at Mach 6 under quiet flow conditions at different freestream Reynolds numbers using time-resolved Schlieren imaging and spectral proper orthogonal decomposition (SPOD). Experimental results are compared with high-fidelity axisymmetric and three-dimensional simulations. Results demonstrate regime transition in the parameter space, across the unsteadiness boundary, all the way from shear-layer breakdown to shock system oscillations and ultimately to large-amplitude pulsations. The dominant mode in the experiments and the simulations corresponds to a Strouhal number St ~ 0.17 for small oscillations reducing to St ~ 0.13 for large pulsations. A detailed description of the unsteady shock dynamics, the instability of the shear layer during onset of unsteadiness and an analysis of the nonlinear limit cycle is presented.

Figures (24)

• Figure 1: Flow configuration and features at Mach 6 flow on a cone-step, left: schematic of the cone-step geometry; right: flow field visualization using vertical density gradient.
• Figure 2: Schematic of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT)
• Figure 3: The cone-step geometric model and freestream conditions considered in the work.
• Figure 4: An overview of the experiments in geometric and freestream Reynolds number parameter space. $\theta^s_1$ and $\theta^s_2$ are the scaled angles defined in Equation \ref{['eq:thetadef']}. The color key is blue: steady, orange: oscillatory and red: pulsatory. The key for the references is: MAU60: maull1960spike, CJW62: wood1962, MH66: holden1966spike, WAM52: mair1952, SD21: sasidharan2021, TH09: hashimoto2009experimental, SA12: swantek2012heat, KSK24: Kumar_Sasidharan_Kumara_Duvvuri_2024, KW78: kenworthy1978
• Figure 5: Geometric illustration of the parameter space $\theta^{s}_1$ and $L/D$. The color key is blue: steady, orange: oscillatory and red: pulsatory. The color coding in the illustration helps interpret collated experimental data in the $L/D-\theta^{s}_1$ space.