A quadrature closure for the reaction-source term in conditional-moment closure

A Gaussian-quadrature closure is introduced for the conditional reaction-source term in conditional-moment closure, motivated by the desire to accurately model the dynamics of homogeneous extinction and re-ignition in turbulent non-premixed flames. A priori analysis of the quadrature model was performed using results of direct numerical simulations (DNS) of isotropic turbulence which included a mixture fraction and reaction-progress variable with a reversible chemical-source term. The DNS calculations for three Damkohler numbers, each exhibiting a different degree of extinction and all exhibiting re-ignition, were used to demonstrate the shortcomings of the Taylor-series closure. A quantitative validation was completed, and the quadrature closure showed significantly less error than the Taylor-series closures for all of the conditions considered. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.