Hypersonic attachment-line instabilities with large sweep Mach numbers

TL;DR

This paper investigates hypersonic attachment-line instabilities over highly swept flows at large sweep Mach numbers, revealing the dominant modes and their influence on transition, with implications for flow stability analysis.

Contribution

It introduces high-fidelity base flow calculations using shock-fitting methods and identifies the inviscid nature of attachment-line modes at hypersonic speeds, highlighting the importance of external flow effects.

Findings

Attachment-line mode dominates transition at sweep Mach numbers above 5.

Inviscid flow outside the boundary layer significantly influences instability.

Leading-edge curvature affects mode stability differently for various spanwise wave numbers.

Abstract

This study aims to shed light on hypersonic attachment-line instabilities with large sweep Mach numbers. Highly swept flows over a cold cylinder that give rise to large sweep Mach numbers are studied. High fidelity base flows are obtained by solving full Navier-Stokes equations with a high-order shock-fitting method. Using local and global stability theories, an attachment-line mode is found to be dominant for the laminar-turbulent transition along the leading edge that agrees well with experimental observations Gaillard1999. The behavior of this mode explains the reason why the transition occurs earlier as the sweep Mach number is above 5. Also, this attachment-line mode is absent if the base flow is calculated with boundary-layer assumptions, indicating that the influence of inviscid flow outside the boundary layer can not be ignored as is normally done. It is clearly demonstrated that the global modes display the features of both attachment-line modes, as in sweep Hiemenz flow, and cross-flow-like modes further downstream along the surface. In contrast to incompressible flows, the mode is shown to be of inviscid nature. Moreover, the leading-edge curvature has a destabilizing effect on the attachment-line mode for large spanwise wave numbers but a stabilizing effect for small spanwise wave numbers.