Stochastic Modeling of Partially Stirred Reactors

Modeling of Partially-Stirred-Reactors (PaSR) by stochastic simulation is carried out for investigating the influence of unmixedness on thermo-chemical properties. First, the joint scalar probability density function (pdf) of the PaSR is derived using a control volume analysis to provide theory for development of stochastic simulation procedures. Second, through numerical exploration and analysis, an improved stochastic algorithm is developed to eliminate the dependence of solution on time step. The limitations on age distribution from the stochastic simulation are identified. For nonpremixed combustion with either the modified Curl's mixing model or the Linear-Mean-Square-Estimation (LMSE) mixing model, analytic expressions are derived for the unmixedness in terms of residence time and mixing frequency. Numerical simulations have been performed revealing that the unmixed nature has profound influence on ignition delay and NO formation in PaSR with hydrogen combustion. The performance of recently developed reduced chemistry for hydrogen combustion is evaluated by comparisons with detailed chemistry. The predicted NO formation is found sensitive to mixing model.