A comparison of large Eddy simulations with a standard k–ε Reynolds-averaged Navier–Stokes model for the prediction of a fully developed turbulent flow over a matrix of cubes

Abstract A fully developed turbulent flow over a matrix of cubes has been studied using the large Eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) [more specifically, the standard k – e model] approaches. The numerical method used in LES of an incompressible fluid flow was a second-order accurate, fully conservative discretization scheme. This scheme was used in conjunction with a dynamic semi-coarsening multigrid method applied on a staggered grid as proposed originally by Ham et al. (Proceedings of the Seventh Annual Conference of the Computational Fluid Dynamics Society of Canada, Halifax, Nova Scotia, Canada, 1999; J. Comput. Phys. 177 (2002) 117). The effects of the unresolved subgrid scales in LES are modeled using three different subgrid-scale models: namely, the standard Smagorinsky model; the dynamic model with time-averaging procedure (DMT); and, the localized dynamic model (LDM). To reduce the computational time, LES calculations were conducted on a Linux-based PC cluster using the message passing interface library. RANS calculations were performed using the STREAM code of Lien and Leschziner (Comp. Meth. Appl. Mech. Eng. 114 (1994) 123). The Reynolds number for the present flow simulations, based on the mean bulk velocity and the cube height, was 3800 which is in accordance with the experimental data of Meinders (Ph.D. Thesis, Faculty of Applied Sciences, Delft University of Technology, Delft, Netherlands, 1998). A comparison of predicted model results for mean flow and turbulence with the corresponding experimental data showed that both the LES and RANS approaches were able to predict the main characteristics of the mean flow in the array of cubes reasonably well. LES, particularly when used with LDM, was found to perform much better than RANS in terms of its predictions of the spanwise mean velocity and Reynolds stresses. Flow structures in the proximity of a cube, such as separation at the sharp leading top and side edges of the cube, recirculation in front of the cube, and the arch-type vortex in the wake are captured by both the LES and RANS approaches. However, LES was found to give a better overall quantitative agreement with the experimental data than RANS.

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