On the Validity of the Assumed Pdf Method for Modeling Binary Mixingkeaction of Evaporated Vapor in Gawliquid-droplet Turbulent Shear Flow

An investigation of the statistical description of binary mixing and/or reaction between a carrier gas and an evaporated vapor spccics 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. Jn particular, the validity and added complications of extending single-point assumed probability 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 non-weighted scalar means and variances. Comparisons with the DNS ~sults indicates that the mixture fraction Favrc moments are nearly identical to the corresponding non-weighted moments even at the mixing layer ccntedine where the rms density fluctuation is > 12% of the mean density. It is therefore considered appropriate to use Favre moments for PDF closure. A transport equation for the Favre mixture fraction variance is then presented which contains four new terms due to evaporation 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 ~ PDF which is known to represent well the DNS generated mixture fi-action statistics for single-phase mixing, is shown to be a poor representation for mixing of vapor resulting from droplet evaporation.