Scalar-dissipation modeling for passive and active scalars: A priori study using direct numerical simulation

Abstract

Transitional databases from direct numerical simulation (DNS) of three-dimensional mixing layers for single-phase flows and two-phase flows with evaporation are analyzed and used to examine the typical hypothesis that the scalar-dissipation probability distribution function (PDF) may be modeled as a Gaussian. The databases encompass a singlecomponent fuel and four multicomponent fuels, two initial Reynolds numbers ( Re), two mass loadings for two-phase flows and two free-stream gas temperatures. Using the DNS-calculated moments of the scalar-dissipation PDF, it is shown, consistent with existing experimental information on single-phase flows, that the Gaussian is a modest approximation of the DNS-extracted PDF, particularly poor in the range of the high scalar-dissipation values, which are significant for turbulent reaction rate modeling in non-premixed flows using flamelet models. With the same DNS-calculated moments of the scalar-dissipation PDF and making a change of variables, a model of this PDF is proposed in the form of the β-PDF which is shown to approximate much better the DNS-extracted PDF, particularly in the regime of the high scalar-dissipation values. Several types of statistical measures are calculated over the ensemble of the 14 databases. For each statistical measure, the proposed β-PDF model is shown to be superior to the Gaussian in approximating the DNS-extracted PDF. Additionally, the agreement between the DNS-extracted PDF and the β-PDF even improves when the comparison is performed for higher initial- Re layers, whereas the comparison with the Gaussian is independent of the initial Re values. For two-phase flows, the comparison between the DNS-extracted PDF and the β-PDF also improves with increasing free-stream gas temperature and mass loading. The higher fidelity approximation of the DNS-extracted PDF by the β-PDF with increasing Re, gas temperature and mass loading bodes well for turbulent reaction rate modeling.