Piomelli, Ugo

Models for Large Eddy Simulations of Turbulent Channel Flows Including Transpiration

[PhD thesis]. Stanford University

Ferziger, Joel; Moin, Parviz (supervisors)

1988

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- Abstract
An investigation of models for the large eddy simulation of turbulent channel flow is presented. The results of a direct simulation of ReT = 180 turbulent channel flow are used to guide the choice of consistent combinations of filter and subgrid scale Reynolds stress models. It is found that model and filter must carry the same length scale information. Using consistent combinations such as the cutoff filter with the Smagorinsky model or the Gaussian filter with the mixed Smagorinsky-scale similarity model in numerical simulations yields more accurate results than those obtained with other combinations at R er = 180 and at Rer = 640. Comparison of the one-dimensional spectra with those obtained from direct simulations shows that the prediction of even the smallest structures admitted by the grid is very accurate.

Approximate boundary conditions which model the wall layer and thus allow use of LES with much coarser grids have also been developed and tested. The shifted boundary condition that requires the wall stress to be in phase with the velocity in the logarithmic region at some distance downstream has good correlation with the “exact” wall stress. A new model that correlates the fluctuating wall stress with the normal velocity component is proposed. This model, which simulates the effect of the low speed fluid ejected from the wall region, also correlates well with the “exact” wall stress. Both the shifted and ejection models are used in large eddy simulations of turbulent channel flow at Rer = 640 and R er — 4700 and compared with the results of a large eddy simulation in which the wall layer is resolved and with experimental results. The ejection model gives very accurate results even when very coarse grids are used. The results of simulations of channel flow with uniform transpiration at the walls are also presented. A simulation which resolves the wall layer gives good agreement with the experimental data, and highlights the effect of transpiration on the wall layer dynamics. Use of modified forms of the law of the wall in the shifted and ejection models lead to very accurate prediction of the mean velocity profile, friction coefficient and turbulence intensities. Using the mixed model-Gaussian filter combination in conjunction with accurate wall layer models, large savings can be achieved, in terms of CPU time, over standard LES in which the wall layer is resolved, and even more over direct simulations. Prediction of first- and second-order quantities is accurate, and the cost of computations required for convergence of the statistical results is reduced by 85% over simulations in which the wall layer is resolved and over 97% over direct simulations.