Effects of Small Leading-Edge Bluntness on High-Speed Boundary-Layer Instabilities on Flat Plates

Abstract

A numerical investigation of the effect of small leading-edge bluntness on the linear stability regime in high-speed boundary layers for flat plates was carried out using linear stability theory. While it is known that increasing leading-edge bluntness leads to stabilization of the linear instability, it is not completely understood when leading-edge bluntness effects become relevant; in other words, for which leading-edge radii the primary instability regime is affected for flat plates at higher Mach numbers. For the so-called “sharp” geometries, it is assumed that the influence of the nose radius on stability and transition is negligible. For cones, it is generally accepted that nose radii resulting in Reynolds numbers (based on nose radius) smaller than 1000 can be considered sharp. However, no clear guidelines supported by numerical or experimental data exist to conclusively determine what constitutes a sharp leading edge for a flat plate. In this work, bluntness effects are assessed by considering the influence of the leading-edge radius on the linear stability characteristics for high-speed flat-plate boundary layers. It was found from linear stability calculations that surprisingly small leading-edge radii have significant effects on the critical Reynolds number and spatial amplification rates, thus resulting in substantially reduced maximum -factors.