A symmetry-based length model for characterizing 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 is 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) describing a physically sound two-dimensional multi-regime structure of transitional boundary layer. Previous studies showed accurate predictions, especially on the drag coefficient, by the SED-SL for airfoil flows at different subsonic Mach numbers, Reynolds numbers and angles of attack. Here, the SED-SL is extended to compute the hypersonic heat transfer 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 a proper setting of the multi-regime structure with three parameters (i.e. a transition center, an after-transition near-wall eddy length, and a transition width quantifying transition overshoot) yields an accurate description of the surface heat fluxes measured in wind tunnels. Uniformly good agreements between simulations and measurements are obtained from windward to leeward side of the cone, implying the validity of the multi-regime description of the transition independent of instability mechanisms. It is concluded that a unified description for the HBL transition of cone is found, and might offer a basis for developing a new transition model that is simultaneously of computational simplicity, sound physics and greater accuracy.