A new algebraic turbulence model for simulating hypersonic boundary layer transition.*

We report a new algebraic turbulence model (SED-SL) based on a structural ensemble dynamics (SED) theory of wall turbulence (She et al., 2017). The model specifies a multi-layer profile of a stress length (SL) function (which defines the eddy viscosity) in both the streamwise and wall-normal directions, characterizing the laminar-turbulent transition on a wall. First, we report clear evidence of a successful simulation of flat-plate compressible TBLs by the SED-SL model (She et al., 2018). Then, we report further applications of the model to the hypersonic boundary layer transition on a straight cone at Mach 6. The SED-SL model predicts correctly the mean surface heat fluxes during the transition processes for all the experimental cases (Horvath, 2002), superior to other closure models. Remarkably, the transition peak and the subsequent relaxation to the fully developed turbulent flow is accurately simulated. The most important achievement is the physical interpretation of the model parameters: they specify the differentiating multi-layer structures of TBLs with well-behaved parameter variation; consequently, the model delivers high simulation accuracy for all cases, and specifies the physics of CTBL for varying flow circumstances.