Formulation Of A Two-phase Filtered Density
Function Approach For Large Eddy Simulation
Author(s)
M. D. Carrara & P. E. DesJardin
Abstract
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 b e modeled. There are, then, th ree d istin ct types o f unclo sed terms in th e
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 .
1 Two-phase FDF transport equation
Two-phase probability density function (PDF) methods have recently been formulated
and successfully applied for dispersed/continuum phase flows [2, 3, 4].
Probability density function methods are based on defining a suitable set of flow
realizations over which the PDF may be defined in the ensemble statistics context
and therefore in practice are devoid of any spatial information about the two-phase
flow. That is to say, turbulent flow field information in the PDF approach must
be given in the time-averaged or RANS context, and consequently coupling to a
RANS calculation for the carrier gas field is common [4, 2]. Filtered density func-
Keywords
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