Accurately predicting hypersonic transitional flow on cone via a symmetry approach

Abstract

A new algebraic transition model is proposed based on a Structural Ensemble Dynamics (SED) theory of wall turbulence, for accurately predicting the hypersonic flow heat transfer on cone. The model defines the eddy viscosity in terms of a two-dimensional multi-regime distribution of a Stress Length (SL) function, and hence is named as SED-SL. This paper presents clear evidence of precise predictions of transition onset location and peak heat flux of a wide range of hypersonic Transitional Boundary Layers (TrBL) around straight cone at zero incidence, to an unprecedented accuracy as validated by over 70 measurements for varying five crucial influential factors (Mach number, temperature ratio, cone half angle, nose Reynolds number and noise level). The results demonstrate the universality of the postulated multi-regime similarity structure, in characterizing not only the spatial non-uniform distribution of the eddy viscosity in hypersonic TrBL on cone, but also the dependence of the transition onset location on the five influential factors. The latter yields a novel correlation formula for transition center Reynolds number which takes similar functional form as the SL function within the symmetry approach. It is concluded that the SED-SL model simulates TrBL around cone with uniformly high accuracy, and then points out to an optimistic alternative way to construct hypersonic transition model.