Full PDF modelling of reactive sprays via an evaporation-progress variable

For reactive two-phase flows a single probability density function (PDF) is defined for the totality of all gas-phase and liquid-phase random variable s. This single unconditional PDF - or equivalently its gas-conditional and liquid-conditional PDF together - allows a complete statistical description and hence a full modelling of reactive, laminar or turbulent, two-phase fl ows. For the special case of two-phase sprays, for both the gas phase and t he liquid phase general PDF-transport equations are given in which the term s concerning the local and instantaneous interaction between the two phases are in closed form but certain turbulence terms would require modelling. The full model is tested by numerically simulating with a particle method t wo laminar one-dimensional test cases, viz., (i), a non-reactive evaporatio n and mixing case and, (ii), a case in which evaporation of liquid fuel, mi xing of gas-phase species and gas-phase combustion take place. For - but no t limited to - the test cases, a (currently but not necessarily) one-dimens ional deterministic model based on four reduced variables - notably one of these variables describes the evaporation progress - is developed. For comb ination with the panicle method, a PDF-variant of the SIMPLE pressure-corre ction algorithm is described.