Finite rate chemistry and presumed PDF models for premixed turbulent combustion

The sensitivity of the prediction of mean reaction rates in turbulent premixed flames to presumed PDF shape is studied. Three different presumed PDF shapes are considered: (i) a beta function PDF, (ii) a twin delta function PDF, and (iii) a PDF based on unstrained laminar flame properties. The unstrained laminar flame has the same thermochemistry as the turbulent flame. Emphasis is placed on capturing the finite rate chemistry effects and obtaining a simple expression for the mean reaction rate. It is shown that, as the PDFs approach their bimodal limit, the mean reaction rate expressions obtained using the above three PDFs reduce to a common form. These expressions differ only in the numerical value of a multiplying factor. Predictions are compared with DNS data. Under the conditions of this comparison, the beta function and twin delta function PDFs lead to significant errors, while the PDF based on properties of an unstrained laminar flame gives good agreement with the DNS.