Influence of computational drop representation in LES of a droplet-laden mixing layer

Abstract

The objective of this work is to quantify the in uence of the number of computational drops and grid spacing on the accuracy of predicted ow statistics and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provides minimal error in ow prediction. For this purpose, Large Eddy Simulation (LES) of a mixing layer with evaporating drops has been performed using the dynamic Smagorinsky model and employing various numbers of computational drops. The LES were performed by reducing the number of physical drops by a factor varying from 8 to 128 to obtain the ensemble of computational drops, and by utilizing either a coarse or ane grid. A set ofrst order, second order and drop statistics are extracted from LES predictions and are compared to results obtained byltering a Direct Numerical Simulation (DNS) database. First order statistics such as Favre averaged streamwise velocity, Favre averaged vapor mass fraction, and the drop streamwise velocity are predicted accurately independent of the number of computational drops and grid spacing. Second order ow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor ux are predicted accurately by thene mesh LES only whenQ U is less than 32 and by the coarse mesh LES reasonably accurately for allQ U values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must be kept approximately the same as in the DNS. Multiphase turbulent ows are encountered in many practical applications including turbine engines or natural phenomena involving particle dispersion. Numerical computations of multiphase turbulent ows are important because they provide a cheaper alternative to performing experiments during an engine design process or because they can provide predictions of naturally occurring situations which one may wish to avoid. The most accurate method of numerically simulating the ow is based on Direct Numerical Simulation (DNS) of the governing equations in which all scales of the ow responsible for the overwhelming amount of dissipation are resolved. DNS, however, requires high computational cost and cannot be used in engineering design applications where iterations among several design conditions are necessary or utilized for predicting natural phenomena where spatial scales are very large. Large Eddy Simulation (LES) provides a cheaper alternative to numerically simulate multiphase turbulent ows, although it has modeling requirements which do not exist in DNS. In LES only the energy-containing large scales, which are of engineering interest, are resolved and the more universal small scales are modeled thereby minimizing computational costs. The LES equations are obtained byltering the governing equations. The eect of theltered small-scale motion on resolved large scale motion appears as Subgrid-Scale (SGS) terms in the LES equation and it depends on the unresolved or "sub-grid" oweld which is unavailable; thus, these terms must be modeled. This modeling is typically done through representing the subgrid scale terms as functions of the large scale oweld. Another approximation that is often employed in LES of multiphase turbulent ows is the computational