A DNS evaluation of mixing and evaporation models for TPDF modelling of nonpremixed spray flames

Abstract

Abstract In the present work, nonpremixed temporally evolving planar spray jet flames are simulated using both direct numerical simulation (DNS) and the composition transported probability density function (TPDF) method. The objective is to assess the performance of various mixing and evaporation source term distribution models which are required to close the PDF transport equation in spray flames. Quantities which would normally be provided to the TPDF solver by spray models and turbulence models are provided from the DNS: the mean flow velocity, turbulent diffusivity, mixing frequency, and cell-mean evaporation source term. Two cases with different Damkohler numbers ( Da ) are considered. The low Da case ( Da -) features extinction followed by reignition while extinction in the high Da case ( Da +) is insignificant. The TPDF modelling considers two mixing models: interaction by exchange with the mean (IEM) and Euclidean minimum spanning trees (EMST). Three models for distribution of the evaporation source terms are considered: EQUAL which distributes them in proportion to notional particles’ mass weight, NEW which creates new particles of pure fuel, and SAT which distributes the sources preferentially to notional particles close to saturation. It is found that the IEM model overpredicts the extinction when used with any evaporation model for both Da - and Da + cases. The EMST model captures well the trend for extinction and reignition for the Da - case when it is coupled with the EQUAL evaporation model, but it overpredicts the extinction when coupled with the NEW or SAT evaporation model. For the Da + case, all evaporation models reasonably capture the flame dynamics when coupled with EMST. The flame temperature in the mixture fraction space was examined to further assess the model performance. In general the EMST model results in narrow PDFs with little conditional fluctuation, while the IEM model produces bimodal PDFs with burning and partial extinction branches.