Laminar-to-Turbulence Transition Prediction in a Hypersonic Boundary Layer using Nonlinear Non-Modal Analysis
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The prediction of laminar-to-turbulent transition in hypersonic boundary layers contributes to optimizing fuel consumption and improving aerodynamic heating predictions. Theoretically, Mack’s second mode is recognized as the primary linear instability; consequently, the transition path driven by these acoustic waves has been extensively investigated through both numerical simulations and experiments. In this study, we investigate the nonlinear amplification mechanism of this transition scenario, with a particular focus on its early stages. We employ the nonlinear non-modal analysis proposed by Pringle & Kerswell (2010) [1] and Cherubini et al. (2010) [2], which was subsequently extended to compressible flows by Huang and Hack (2020) [3]. Our numerical implementation is based on our previous work [4] concerning supersonic boundary layers. In the current simulation, the Mach number and the Reynolds number based on the Blasius length are set to M=7.0 and Re=1000, respectively. Our current simulations at Re=1000, utilizing a fine grid of 1536×256×128 points, have successfully identified the early-stage nonlinear growth of optimal perturbations associated with Mack’s second mode. Notably, despite the high-resolution 3D setup, the flow remains predominantly two-dimensional until t<400, highlighting the robust stability of Mack’s second mode at this Reynolds number. To capture the actual transition, we are extending this high-resolution analysis to higher Reynolds numbers (Re≥2000), we aim to clarify the interaction between dominant second-mode waves and non-modal streaks that triggers secondary instabilities and subsequent breakdown. This work provides a rigorous foundation for identifying energy thresholds and redefining transition mechanism in the hypersonic boundary layer.
