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 beta -probability-density-function (beta -PDF) mixing model. This physical transport and subgrid joint beta -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 die 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 beta) 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 beta -PDF are presented and are found to be acceptable. A robust beta -PDF function evaluation procedure is presented that accommodates arbitrarily high beta -PDF distribution factors. This robust algorithm simply transforms the joint beta -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 functions is quantified and shown to be less accurate.