Effects of Expansion Corner on Linear and Non-Linear Three-Dimensional Boundary Layer Stability

The transition of hypersonic boundary layers remains a significant unresolved challenge in fluid mechanics, particularly regarding the influence of expansion corners on three-dimensional boundary layer instability. The present work investigates a hypersonic swept wing configuration with an expansion corner using linear stability theory (LST) and direct numerical simulations (DNSs). A high-order shock-fitting method provides the laminar base flow for sweep angles of 30∘, 45∘ and 60∘ and expansion corner angles of 0∘, 3∘ and 6∘. As the sweep and expansion angles increase, both the favourable pressure gradient and crossflow intensity are strengthened. LST reveals that, while the expansion corner suppresses disturbance growth locally, it promotes the development of subharmonic modes downstream, with the dominant spanwise wavelength doubling across the corner. Crossflow instability intensifies with increasing sweep and expansion angles. DNSs accounting for non-parallel effects confirm a sharp reduction in growth rate at the corner itself, while upstream and downstream trends remain consistent with LST predictions. Nonlinear simulations with finite-amplitude perturbations show saturated crossflow vortex structures. The subharmonic mode develops into mushroom-shaped vortices distinct from those in conventional studies. The expansion corner weakens the vortex intensity for both spanwise wavelengths, exerting a complex effect on the transition process.