Multi-Environment Probability Density Function Method for Modeling Turbulent Combustion Using Detailed Chemistry

One of the most important issues to address in turbulent combustion calculations is the intense nonlinear interaction between fluid mixing and finite-rate chemistry. In combustion processes which are characterized by fast chemistry, use of the flamelet model (Peter, 1984) or conditional moment closure (CMC) (Bilger, 1993) based on a conserved scalar is known to be quite accurate in making qualitative as well as quantitative predictions. However, these methods may not be viable in slow chemistry regimes such as the formation and destruction of NOx. The flamelet model requires the specification of a scalar dissipation rate and assumes the shape of the PDF at the sub-grid level. The first-order CMC model ignores any fluctuations about the conditional mean. The transported PDF method (Pope, 1985), on the other hand, computes the joint PDF in terms of a set of delta-functions. The principal advantage of the method is that the chemical reaction appears in closed form in the PDF equations. As a consequence, realistic combustion chemistry can be incorporated without the need for closure approximations pertaining to reaction. Therefore, PDF methods are able to accurately describe turbulent-chemistry interactions in turbulent flames. Other processes – notably molecular diffusion – have to be modeled. The transport joint PDF equation is multi-dimensional and cannot be solved using Eulerian grid techniques. Recent PDF calculations using particle based Monte-Carlo schemes with realistic chemistry show good agreement with experimental results (Tang et al., 2000; Xu and Pope, 2000; Lindstedt et al., 2000; Raman et al., 2004). However, the handling of a large number of Lagrangian particles along with detailed chemistry can be computationally prohibitive in practical flow configurations.