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Abstract
For reactive two-phase flows a single probability density function (PDF) is defined for the totality of all gas-phase and liquid-phase random variables. This single unconditional PDF - or equivalent^ 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 flows. For the special case of two-phase sprays, for both the gas phase and the liquid phase general PDF-transport equations are given in which the terms 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 two laminar one-dimensional test cases, viz., (i), a non-reactive evaporation and mixing case and, (ii), a case in which evaporation of liquid fuel, mixing of gas-phase species and gas-phase combustion take place. For - but not limited to - the test cases, a (currently but not necessarily) one-dimensional deterministic model based on four reduced variables - notably one of these variables describes the evaporation progress - is developed. For combination with the particle method, a PDF-variant of the SIMPLE pressure-correction algorithm is described.
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