A Symmetry-Based Length Model For Describing The Hypersonic Boundary Layer Transition On A Slender Cone At Moderate Incidence

Abstract The hypersonic boundary layer (HBL) transition on a slender cone at moderate incidence has been studied via a symmetry-based length model: the SED-SL model. The SED-SL specifies an analytic stress length function (which defines the eddy viscosity) parameterizing a two-dimensional multi-regime structure characterizing the laminar-turbulence transition. Previous studies show accurate predictions by the SED-SL for airfoil flows at different subsonic Mach numbers, Reynolds numbers and angles of attack, especially for the drag coefficient achieving a small error of a few counts. Here, we report a successful extension for computing transitional flows on a 7° half-angle straight cone at Mach numbers 6 and 7 and angles of attack from 0° to 6°. It is shown that, by properly setting the multi-regime HBL structure with only three physical parameters (i.e. a transition center location, a turbulent HBL near-wall eddy length, and a transition width coefficient quantifying overshoot strength), the SED-SL is able to predict correctly the heat flux distribution on the whole cone surface, with great accuracy compared with wind tunnel data. The good predictions cover a range of flow parameters and persist in different instability mechanisms (which vary from the windward to the leeward sides of the cone). We conclude that a unified transition model is found for describing the transitional HBLs, with the potential to lead a new generation of turbulence model that is simultaneously of computation simplicity, sound physics and greater accuracy.