On the validity of the assumed probability density function method for modeling binary mixing/reaction of evaporated vapor in gas/liquid-droplet turbulent shear flow

Abstract

An investigation of the statistical description of binary mixing and/or reaction between a carrier gas and an evaporated vapor species in two-phase gas-liquid turbulent flows is performed through both theoretical analysis and comparisons with results from direct numerical simulations (DNS) of a two-phase mixing layer. In particular, the validity and added complications of extending single-point assumed probabolity density function (PDF) methods to two-phase flows involving evaporating droplets as sources of vapor are addressed. Noting that Favre density-weighted averaging is the most convenient form for moment transport equations for these flows, algebraic relationships are derived for the ratios of the Favre and nonweighted scalar means and variances. Comparisons with the DNS results indicate that the mixing layer centerline where the root mean square (rms) density fluctuation is >12% of the mean density. It is therefore considered appropriate to use Favre moments for the nonweighted PDF closure. A transport equation for effects. The DNS results indicate that one of these terms due to scalar-source correlations is predominantly responsible for scalar variance production, whereas the remaining three terms are of negligible magnitude. Finally, the β PDF, which is known to represent well the DNS generated mixture fraction statistics for single-phase mixing, is shown to be a poor representation for mixing of vapor resulting from droplet evaporation.