A term-by-term direct numerical simulation validation study of the multi-environment conditional probability-density-function model for turbulent reacting flows

The multi-environment conditional probability-density-function (MECPDF) approach for modeling extinction and re-ignition in turbulent nonpremixed reacting flows is analyzed. A unique derivation of the model is given, which makes use of numerical Gaussian quadrature in addition to physical assumptions. The new derivation offers insight into the physical meaning of model terms and offers a more rigorous method for model validation. The assumptions required to close the dissipation terms are validated term by term using data from direct numerical simulations of an inert and a reacting scalar in decaying isotropic turbulence. Results show convergence of the numerical quadrature with an increasing number of quadrature points. Also, good agreement is shown for the physical model assumptions required to close the mixed dissipation and the progress-variable dissipation terms. The MECPDF method is also demonstrated to offer the flexibility to incorporate either micromixing or otherwise more sophisticated models fo...