Abstract
The aim of this work is to propose a new wall model for separated flows which is combined with large eddy simulation (LES) of the flow field in the whole domain. The model is designed to give reasonably good results for engineering applications where the grid resolution is generally coarse. Since in practical applications a geometry can share body fitted and immersed boundaries, two different methodologies are introduced, one for body fitted grids, and one designed for immersed boundaries. The starting point of the models is the well known equilibrium stress model. The model for body fitted grid uses the dynamic evaluation of the von Kármán constant κ of Cabot and Moin (Flow, Turbulence and Combustion, 2000, 63, pp. 269–291) in a new fashion to modify the computation of shear velocity which is needed for evaluation of the wall shear stress and the near-wall velocity gradients based on the law of the wall to obtain strain rate tensors. The wall layer model for immersed boundaries is an extension of the work of Roman et al. (Physics of Fluids, 2009, 21, p. 101701) and uses a criteria based on the sign of the pressure gradient, instead of one based on the friction velocity at the projection point, to construct the velocity under an adverse pressure gradient and where the near-wall computational node is in the log region, in order to capture flow separation. The performance of the models is tested over two well-studied geometries, the isolated two-dimensional hill and the periodic two-dimensional hill, respectively. Sensitivity analysis of the models is also performed. Overall, the models are able to predict the first and second order statistics in a reasonable way, including the position and extension of the downward separation region.
Highlights
Wall bounded turbulent flows, especially at high Reynolds numbers, require a high resolution near the wall, because of the need to solve the thin viscous sub-layer [1,2,3]
In the dynamic Smagorinsky model proposed by Germano et al [24], the coefficient is calculated b larger than the grid dynamically by defining an additional test filter with a width ∆
In Cabot and Moin [8] the use of dynamic κ was justified by the fact that their wall model (TBLE) would carry shear stress both in the Reynolds Averaged Navier-Stokes (RANS) eddy viscosity and the RANS convective terms, they needed a reduced RANS eddy viscosity, and by using the dynamic κ which had the values less than the von Kármán constant, and reduced the shear stress
Summary
Especially at high Reynolds numbers, require a high resolution near the wall, because of the need to solve the thin viscous sub-layer [1,2,3]. Posa and Balaras [16] proposed a new near-wall reconstruction model to account for the lack of resolution and provided correct wall shear stress and hydrodynamic forces They used a zonal approach (TLM), boundary layer equations with a finer grid in the near-wall region (called in this case the full boundary layer FBL) and LES in the outer region. They validated their model to simulate flow around a cylinder and a sphere.
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