Explicitly-filtered LES for the grid-spacing-independent and discretization-order-independent prediction of a conserved scalar

Abstract

The previously proposed methodology of Explicitly Filtered Large Eddy Simulation (EFLES) predicts velocity fields that are grid-spacing and discretization-order independent for single-phase, and for two-phase compressible flows. In the current study, EFLES is tested for determining the predictability of a passive scalar evolution in turbulent flows, and the EFLES results are also compared to equivalent ones obtained with conventional Large Eddy Simulation (LES). A single Direct Numerical Simulation (DNS) realization of a temporal mixing layer is conducted with an initial Reynolds number of 1800. After an initial transient, the mixing-layer momentum thickness grows linearly with time. The DNS is continued during the linear growth period and until the momentum thickness Reynolds number reaches 6405. The filtered and coarsened DNS (FDNS) database is considered the template to be reached by LES or EFLES. Both LES and EFLES are conducted using the dynamic Smagorinsky model. Three grids – coarse, medium and fine – and three discretization orders – fourth, sixth and eighth – are used for each LES and EFLES. In contrast to conventional LES where the grid spacing and the filter width are proportionally related, in EFLES the filter width is set beforehand and independent of the grid spacing. The criteria for comparing LES and EFLES results to the FDNS encompass both averages and second-order quantities that characterize the passive scalar behavior. Homogeneous plane averages combined with time averaging past the time when the mixing layer becomes turbulent, enabled the computation of smooth statistics for comparison between FDNS and LES or EFLES. It is found that the conventional LES results are not predictive in that refining the grid or increasing the discretization order, or both, does not lead to coincidence of the results. In contrast, refining the grid past the medium spacing for the sixth- and eighth-order discretizations leads to the EFLES results collapsing on a single curve. Thus, the medium grid spacing and sixth discretization order is the most computationally economic predictive simulation. Based on these findings, EFLES computations, the predictions of which are unaffected by numerical errors, are recommended for model validation with experimental data.

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