State space sensitivity to a prescribed probability density function shape in coal combustion systems: joint β-PDF versus clipped Gaussian PDF

The turbulent transport of three coal off-gas mixture fractions is coupled to a prescribed joint //-probability- density-function (//-PDF) mixing model. This physical transport and subgrid joint //-PDF mixing model is used to explore the incorporation of coal off-gas compositional disparities between the devolatilization and the char oxidation regime in detailed pulverized-coal combustion simulations. A simulation study of the University of Utah pulverized-coal research furnace is presented to evaluate the sensitivity of different mixing model assumptions. These simulation studies indicate that using a variable composition to characterize the process of coal combustion does not appreciably change the predicted gas-phase temperature field. Moreover, neglecting fluctuations in the char off-gas stream was found to change gas-phase temperature predictions by approximately 15%. State space variable sensitivity to the assumed shape of the PDF (clipped Gaussian vs. joint //) is presented. Simulation results indicate differences in temperature profiles of as much as 20% depending on the chosen shape of the PDF. Integration accuracy issues for the joint //-PDF arc presented and are found to be acceptable. A robust //-PDF function evaluation procedure is presented that accommodates arbitrarily high //-PDF distribution factors. This robust algorithm simply transforms the joint //-PDF function evaluation into a logarithmic form. The assumption that a joint PDF, as rigorously required within a prescribed subgrid mixing model, can be written as the product of N - 1 statistically independent probability density (unctions is quantified and shown to be less accurate.