Dependence of Turbulent Spot Initiation Rates on Hypersonic Boundary Layer Flow Parameters

Abstract

Boundary layer transition in hypersonic flows occurs due to non-linear breakdown of acoustic instabilities resulting in the formation of turbulent spots. While the effects of the various flow and geometrical parameters on the location of onset of transition in hypersonic flows have been studied extensively, their effects on the extent of the transition zone have received less attention. It is seen from the literature that the extent of the transition zone can be estimated if information about the initiation rates of turbulent spots, the location of onset of transition, the flow velocity and the Mach number is available. The aim of the present study is to estimate the turbulent spot initiation rates for a wide range of experimental datasets and understand their dependence on flow and geometrical parameters. This paper presents details of a systematic analysis of existing experimental hypersonic transition zone data to estimate the initiation rates of turbulent spots over smooth flat plates and right circular cones with sharp leading edges and at zero angle of attack. The uncertainties in the estimated turbulent spot initiation rates have been quantified and presented. It is observed that the turbulent spot initiation rates are a strong function of the unit Reynolds number of the flow. The edge Mach number and the wall-to-stagnation temperature ratio, and, in the case of right circular cones, the cone half-angles are also found to affect the initiation rates of turbulent spots, although to lesser extents. The physical reasoning behind the observed relationship between spot initiation rates and the flow and geometrical parameters are discussed.