The computational cost to model high Reynolds number flows of engineering interest scales poorly with problem size and is excessively expensive. This fact motivates the development of turbulence wall models to lessen the computational burden. These models aim to provide accurate wall flux quantification on computational meshes that would otherwise be unable to accurately estimate these quantities. The benefit of using such an approximation is that the height of the wall-adjacent computational elements can be increased by one to two orders of magnitude, allowing for comparable increases in stable explicit timestep. This increase in timestep is critically necessary for the large eddy simulation of high Reynolds number turbulent flows. To date, most research in the application of wall models has focused on incompressible flows or flows with very weak compressibility. Very few studies examine the applicability of wall models to flows with significant compressibility and heat transfer. The present work details the derivation of a wall model appropriate for compressible flows with heat transfer. The model framework allows for the inclusion of non-equilibrium terms in the determination of wall shear and heat transfer. The model is applied to a variety of supersonic and hypersonic flows, and is studied in both Reynolds-averaged simulations and large eddy simulations. The impact of several modeling approaches and model terms is examined. The wall-modeled calculations show excellent agreement with wall-resolved calculations and experimental data. For time accurate calculations, the use of the wall model allows for explicit timesteps more than 20 times larger than that of the wall-resolved calculation, significantly reducing both the cost of the calculation and the time required converge the solution.
University of Minnesota Ph.D. dissertation. August 2016. Major: Aerospace Engineering and Mechanics. Advisor: Graham Candler. 1 computer file (PDF); vii, 118 pages.
Development and Validation of a Turbulence Wall Model for Compressible Flows with Heat Transfer.
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