Stochastic multiple mapping conditioning for a piloted, turbulent jet diffusion flame

Abstract

A stochastic implementation of the multiple mapping conditioning (MMC) approach has been applied to a turbulent jet diffusion flame (Sandia Flame D). This implementation combines the advantages of the basic concepts of a mapping closure methodology with a probability density approach. A single reference variable has been chosen. Its evolution is described by a Markov process and then mapped to the mixture fraction space. Scalar micro-mixing is modelled by a modified “interaction by exchange with the mean” (IEM) mixing model where the particles mix with their -in reference space- conditionally averaged means. The formulation of the closure leads to localness of mixing in mixture fraction space and consequently improved localness in composition space. Results for mixture fraction and reactive species are in good agreement with the experimental data. The MMC methodology allows for the introduction of an additional “minor dissipation time scale” that controls the fluctuations around the conditional mean. A sensitivity analysis based on the conditional temperature fluctuations as a function of this time scale does not endorse earlier estimates for its modelling, but only relatively large dissipation time scales of the order of the integral turbulence time scale yield acceptable levels of conditional fluctuations that agree with experiments. With the choice of a suitable dissipation time scale, MMC-IEM thus provides a simple mixing model that is capable of capturing extinction phenomena, and it gives improved predictions over conventional PDF predictions using simple IEM mixing models.