An evaluation of beta PDF integration using the density-weighted PDF and the un-weighted PDF

In many turbulent combustion models, the mean values of scalars are often calculated by integrating the product of the scalar profile and the probability density function (PDF) over mixture fraction space. For the integration, researchers used the weighted and the un-weighted PDF interchangeably depending on their preference. For both PDFs, a β-function is normally presumed. However, a recent study by Liu et al. [Internat. J. Therm. Sci. 41 …