PDF transport equations for two-phase reactive flows and sprays

For two-phase flows, single-point and single-time (probability) density functions of jointly all liquid-phase and gas-phase dependent variables are defined. Corresponding transport equations are derived in which the terms concerning the local and instantaneous interaction between the two phases are in closed form. Generally an Eulerian formulation is used which, however, can straightforwardly be rewritten in Lagrangian form. For the special case of sprays, the density function transport equations are suitably adapted. In particular, for the particle or liquid phase, Williams' Spray Equation is recovered, and for the carrier or gaseous phase a density function transport equation with an interfacial source term is derived. The statistical description of two-phase flows developed here is valid for both laminar and turbulent flows, though for the latter generally some modeling will be required. (C) 2000 by The Combustion Institute.