PDF Models for Mixing in Turbulent Reactive Flows

In modeling turbulent reactive flows based on the transport equation for the joint probability density function (PDF) of velocity and composition, the change in fluid composition due to convection and reaction is treated exactly, while molecular mixing has to be modeled. A new mixing-model is proposed, which is local in composition space and which seeks to address problems encountered in flows with simultaneous mixing and reaction. In this model the change in particle composition is determined by particle interactions along the edges of a Euclidean minimum spanning tree (EMST) constructed in composition space. Results obtained for the model problem of passive scalars evolving under the influence of a mean scalar gradient in homogeneous turbulence are found to be in reasonable agreement with experimental data. A model problem for studying turbulent nonpremixed reacting flow is proposed which captures several important features of turbulent flames. The solutions to this problem are parametrized by the Damkohler number and the reaction zone thickness parameter. At sufficiently high Damkohler number there is stable reaction, but as the Damkohler number is decreased below a critical value, global extinction occurs. The range of parameter values is chosen such that the model problem reproduces important phenomena such as stable near equilibrium reaction, local extinction and global extinction. A self-similar model thermochemistry is proposed which allows access to the parameter range of interest at reasonable computational expense. Monte Carlo simulations are performed to solve for the joint PDF of velocity, turbulent frequency and composition. Results are compared for two different mixing models: the interaction by exchange with the mean (IEM) model, and the Euclidean Minimum Spanning Tree (EMST) model. For large values of the reaction zone thickness parameter it is found that the models are in good agreement with each other and also with the simpler conditional moment closure (CMC) model. However, there are significant differences between the model predictions for values of this parameter below unity. The results support the idea that the localness principle, which is the essential feature of the new EMST mixing model, provides a more physically accurate representation of mixing in such reactive flows.