Joint probability density function models for multiscalar turbulent mixing

Modeling multicomponent turbulent mixing is essential for simulations of turbulent combustion, which is controlled by mixing of fuel, oxidizer, combustion products, and intermediate species. One challenge is to find functions that can reproduce the joint probability density function (PDF) of scalar mixing states using only a small number of parameters. Even for mixing with only two independent scalars, several statistical distributions, including the Dirichlet, Connor-Mosimann (CM), five-parameter bivariate beta (BVB5), and statistically-most-likely distributions, have previously been proposed for this purpose, with minimal physical justification. This work uses the concept of statistical neutrality to relate these distributions to each other, relate the distributions to physical mixing configurations, and develop a systematic approach to model selection. This approach is validated by comparing the ability of these distributions to reproduce the evolution of the scalar PDF from Direct Numerical Simulations of three-component passive scalar mixing in isotropic turbulence with 11 different initial conditions that are representative of a wide range of mixing conditions of interest. The approach correctly identifies whether the Dirichlet, CM, and BVB5 distributions, which are increasingly complex bivariate generalizations of the beta distribution, can accurately model the joint PDFs, but knowledge of the mixing configuration is required to select the appropriate distribution. The statistically-most-likely distribution is generally less accurate than the appropriate bivariate beta distribution but still gives reasonable predictions and does not require knowledge of the mixing configuration, so it is a suitable model when no single mixing configuration can be identified.