Accurate numerical integration of β-PDF for the flamelet approach

When turbulent combustion simulations are performed using the flamelet approach, which indirectly considers the detailed chemical reaction mechanism, the probability density function (PDF) gets applied to statistical distributions for turbulent fluctuations in the mixture fraction that are modeled using the Reynolds-averaged Navier-Stokes or the large eddy simulation. In this case, the so-called “presumed PDF”-i.e., one in which the PDF is assumed and the flamelet table is constructed in advance-is generally employed, and the β-function is widely used for the PDF. This study investigated numerical integration for the equation with the β-function and examined the appropriate method. We succeeded in establishing the optimum value of the parameter for the integration interval and determining the appropriate numerical integration method.