Hypersonic Computational Fluid Dynamics Heat Flux Sub-Models

M4 Engineering, Inc., in conjunction with Massachusetts Institute of Technology (MIT), will develop a new turbulence modeling approach for supersonic and hypersonic flows with emphasis on heat transfer for Navy relevant applications. The new model adds a transport Partial Differential Equation (PDE) to the Spalart-Allmaras (SA) model to track eddy conductivity. This new PDE will mimic the original SA transport PDE for eddy viscosity with advection, diffusion, production and wall-destruction terms. As with SA, the eddy conductivity PDE will be built in a hierarchy of shells, starting with a base model for free shear layers, then progressing to high Reynolds number wall bounded vortical flows and finally near-wall viscous layers. The calibration of the model will rely on simplified canonical flows where the PDE can be reduced to an Ordinary Differential Equation (ODE). For more complex calibration flows, an output-based mesh adaptation process will be used to minimize numerical errors.