The extended IEM mixing model in the framework of the composition PDF approach: applications to diesel spray combustion

Abstract

In the first part of this paper (which is a modified version of Sabel'nikov and Gorokhovski [1, 2]), the IEM/LMSE micro-mixing model is further developed to account for the entire range of mixing frequencies in the engineering computation of turbulent reacting flow, based on the composition PDF method. This new model comprises of two simple ideas: (i) the temporal evolution of the mixing frequency is described in the framework of a log-normal stochastic process, according to Pope and Chen's approach (Physics of Fluids, 1990, 2, 1437–1449); and (ii) at the given frequency, the mixing is viewed as stochastic relaxation to the scalar conditional on this frequency. The Fokker-Planck equation for the joint PDF of scalar and mixing frequency is derived and numerically solved for the simple case of statistically homogeneous flow. The computed marginal scalar PDFs exhibited the relaxation of the initial shape of the PDF alongside with the scalar fluctuation's decay. For intermediate decay times, this relaxation is in qualitatively good agreement with DNS. The second part of this paper includes examples of application. Using the stochastic particles method of Pope (e.g. Progress in Energy and Combustion Science, 1985, 11, 119–192), this model was implemented into the computation of an auto-ignition process and soot formation in diesel-like conditions. Here mixing in the presence of vaporized droplets was simulated in terms of a Partially Stirred Reactor stochastic model (PaSR). Comparing with IDEA experimental data, it is shown that the prediction of ignition delay, scalar variance and soot concentrations can be improved using the extended IEM model.