Partially stirred reactor: study of the sensitivity of the Monte-Carlo simulation to the number of stochastic particles with the use of a semi-analytic, steady-state, solution to the pdf equation

The development of low pollutant emission hydrocarbon fuel engines requires well adapted turbulent combustion models. Partially Stirred Reactor (PaSR) models have been developed to deal with pollutant formation. These models are essentially based on the application of a stochastic Monte-Carlo process to determine the solution of the transport equation for the joint probability density function (pdf) for all reactive species. In this work the semi-analytic, steady-state, solution of the transport equation of the pdf of a single reacting scalar, whose chemistry is described by an Arrhenius law and by employing the Interaction by Exchange with the Mean micro-mixing model, within a PaSR is presented. The overall characteristics of this solution are discussed, with emphasis on the role played by the ratios between the residence time and the micro-mixing and chemical times, respectively. Then, a comparison is made between this solution and a numerical solution of the PaSR model equations using a Monte-Carlo technique. This comparison evidences the number of particles required for an accurate numerical computation, which is a function of the aforementioned ratios.