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On the numerical solution of high Mach number flows

Klothakis Angelos

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Summary

In this study the simulation and analysis of rarefied hypersonic flows is outlined. The study is divided in two parts. The first part is devoted the enhancement of the in-house academic Computational Fluid Dynamics solver Galatea to encounter such simulations is reported in this study. In case of rarefied gas flows and particularly for fluids in slip flow regime (Knudsen number greater than 0.01) the no-slip condition on solid wall surfaces is no longer valid; hence, velocity slip conditions as well as temperature jump ones have to be included instead. Furthermore, to increase accuracy at that regime the second-order accurate spatial slip model of Beskok and Karniadakis has been incorporated, which avoids the numerical difficulties, entailed by the evaluation of the second derivative of slip velocity when complex geometries along with unstructured hybrid grids are encountered. Due to oscillations that might appear, especially during the initial steps of the iterative procedure, a normalization scheme is additionally employed, to allow for the gradual increase of the corresponding slip/jump values. Galatea is validated against a benchmark test case concerning rarefied laminar flow (inside the slip flow regime) over a wing with a NACA0012 airfoil in different angles of attack. The obtained results were compared with those of obtained by the parallel open-source DSMC code SPARTA. According to this last approach, the flow domain is divided into a finite number of computational cells, while the required sample macroscopic flow properties are retrieved assuming intermolecular collisions of the simulated particles inside such cells. An excellent agreement was achieved between the results obtained by Galatea and SPARTA as well. In the second part base flows produced by the DSMC method are extensively analyzed by linear stability theory in order to recover underlying flow transition mechanisms and flow modes. It was found that in cases where oscillations where imposed or physically generated in the boundary layer, the characteristics of these oscillations are predicted accurately by linear stability analysis. Most interestingly, in one specific case, the effect of the generated perturbation is felt well outside of the boundary layer, generating oscillations of the leading-edge shock that synchronize with linear perturbations inside the boundary layer. Finally, the design methodology, simulation and analysis of a hypersonic high-altitude waverider is presented.

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