Investigation of ODE-based non-equilibrium wall shear stress models for large eddy simulation

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Dzanic, Tarik
Oefelein, Joseph
Menon, Suresh
Yeung, Pui-Kuen
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For high Reynolds number flows, wall modeling is essential for performing large eddy simulation at a reasonable computational cost. In this work, a novel low-cost ODE-based non-equilibrium wall model is introduced for wall shear stress modeling in LES. Using polynomial approximations of the pressure gradient and convective terms obtained from interpolation of the LES solution, as opposed to direct evaluation of these gradients within the wall model, the governing wall model equations reduce from coupled PDEs to uncoupled ODEs that do not require an embedded wall model grid within the LES grid. Additionally, the steady form of the wall model equations was utilized, feasible due to the spatial decoupling of the wall model equations, and the effects of the temporal evolution on the wall shear stress were modeled. The effects of polynomial degree on the accuracy of the wall shear stress predictions were explored, and an empirical lag model was built to model the unsteady effects without requiring the solution of a time-stepping problem. Wall resolved large eddy simulations of separated flow around the NASA wall mounted hump and an iced NACA 63A213 airfoil were performed and used as a reference for the comparison of the non-equilibrium wall model to a commonly used equilibrium wall model. The proposed non-equilibrium wall model was able to predict separated flow and laminar flow regions in much better agreement with the wall resolved results than the equilibrium wall model. Underpredictions in the skin friction coefficient in non-equilibrium flow regimes were reduced from 20-50% to less than 10% between the equilibrium and the non-equilibrium wall modeled approaches. Minor improvements in the pressure coefficient predictions were observed with the non-equilibrium model in the separated flow region of the iced airfoil. The results suggest that the proposed wall model can offer better predictions of separated and/or laminar flows compared to equilibrium wall models with negligible computational cost increase.
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