PDF transport equations for two-phase reactive flows and sprays

For two-phase flows, single-point and single-time (probability) density fun ctions of jointly all liquid-phase and gas-phase dependent variables are de fined. Corresponding transport equations are derived in which the terms con cerning the local and instantaneous interaction between the two phases are in closed form. Generally an Eulerian formulation is used which, however, c an straightforwardly be rewritten in Lagrangian form. For the special case of sprays, the density function transport equations are suitably adapted. I n particular, for the particle or liquid phase, Williams' Spray Equation is recovered, and for the carrier or gaseous phase a density function transpo rt equation with an interfacial source term is derived. The statistical des cription of two-phase flows developed here is valid for both laminar and tu rbulent flows, though for the latter generally some modeling will be requir ed. (C) 2000 by The Combustion Institute.