Formulation of a two-phase filtered density function approach for large eddy simulation

摘要

Two-phase velocity-scalar filtered density function (FDF) methods have recently been extended for large eddy simulation (LES) of separated two-phase flows [1]. Several terms in the two-phase FDF transport equation are unclosed and must be modeled for practical application of the two-phase FDF theory. Some terms, such as conditional dissipation in momentum, scalar, and momentum-scalar phase spaces are analogous to those in the single-phase velocity-scalar FDF formulation for which closures are readily available. Phase-coupling and interphase conversion terms, however, which are unique to the two-phase FDF formulation are unclosed and must be modeled. There are, then, three distinct types of unclosed terms in the two-phase FDF formulation: conditional dissipation terms, phase-coupling terms and interphase conversion terms. In this study, the mathematical formulation of this approach is presented and conditional dissipation, phase-coupling and interphase conversion terms are identified and their connection to standard LES closures identified.