Development of a hybrid DSMC/CFD method for hypersonic boundary layer flow over discrete surface roughness
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This work is focused on the development of a hybrid DSMC/CFD solver to examine hypersonic boundary layer flow over discrete surface roughness. The purpose of these investigations is to identify and quantify the non-equilibrium effects that influence the roughness-induced disturbance field and surface quantities of interest for engineering applications. To this end, a new hybrid framework is developed for high-fidelity hybrid solutions involving five-species air hypersonic boundary layer flow applications. A novel approach is developed for DSMC particle generation at a hybrid interface for gas mixtures with internal degrees of freedom. The appropriate velocity distribution function is formulated in the framework of Generalized Chapman-Enskog Theory, and includes contributions from species mass diffusion, shear stress and heat fluxes (both translational and internal) on the perturbation of the equilibrium distribution function. This formulation introduces new breakdown parameters for use in hybrid DSMC/CFD applications, and the new sampling algorithm allows for the generation of DSMC internal energies from the appropriate non-equilibrium distribution for the first time in the literature. The contribution of the internal heat fluxes to the overall perturbation is found to be of the same order as the stress tensor components, underscoring the importance of DSMC particle generation from the Generalized Chapman-Enskog distribution. A detailed comparison of the transport coefficients is made between the DSMC and CFD solvers, and a general best-fit approach is developed for the consistent treatment of diffusion, viscosity and thermal conductivity for a five-species air gas mixture. The DSMC VHS/VSS model parameters are calibrated through an iterative fitting approach using the Nelder-Mead Simplex Algorithm. The VSS model is found to provide the best fit (within 5% over the temperature range) to the transport models used in the CFD solver. The best-fit five-species air parameters are provided for general use by the DSMC community, either for hybrid applications or to provide improved consistency in general DSMC/CFD applications. This hybrid approach has been applied to examine hypersonic boundary layer flow over discrete surface roughness for a variety of roughness geometries and flow conditions. An (asymmetric) elongated hump geometry and (symmetric) diamond shaped roughness geometry are examined at high and low altitude conditions. Detailed comparisons among the hybrid solution and the CFD no-slip and slip wall solutions were made to examine the differences in surface heating, translational/vibrational non-equilibrium in the flow near the roughness, and the vortex structures in the wake through the Q-criterion. In all cases examined, the hybrid solution predicts a lower peak surface heating to the roughness compared to either CFD solution, and a higher peak surface heating in the wake due to vortex heating. The observed differences in vortex heating are a result of the predicted vortex structures which are highlighted using the Q-criterion. The disturbance field modeled by the hybrid solution organizes into a system of streamwise-oriented vortices which are slightly stronger and have a greater spanwise extent compared to the CFD solutions. As a general trend, it was observed that these differences in the predicted heating by the hybrid and CFD solutions increase with increasing Knudsen number. This trend is found for both peak heating values on the roughness and in the wake.