Campus Units

Chemical and Biological Engineering, Mechanical Engineering

Document Type


Research Focus Area

Computational Fluid Dynamics

Publication Version

Accepted Manuscript

Publication Date


Journal or Book Title

Chemical Engineering Science

First Page





A novel algorithm consisting of a quadrature-based semi-analytical solution to the conditional moment closure (CMC) is developed for mixing-sensitive reactions in turbulent flows. When applying the proposed algorithm, the additional grid in mixture-fraction phase space used in CMC codes is eliminated, and at most ten quadrature nodes are needed to model mixing-sensitive turbulent reacting flows. In this work, the mixture-fraction probability density function (PDF) is assumed to be a β-PDF, which is the weight function for the Gauss-Jacobi quadrature rule. The conditional moments of reacting species are determined from unconditional moments that are first order with respect to the species and higher order with respect to mixture fraction. Here, the focus is on the efficient treatment of the molecular-mixing step by using a semi-analytical solution in the form of a Jacobi polynomial expansion. The application of the algorithm is demonstrated considering mixing-sensitive competitive-consecutive and parallel reactions in a statistically homogeneous chemical reactor.


This is a manuscript of an article published as Ilgun, A. D., A. Passalacqua, and R. O. Fox. "A quadrature-based conditional moment closure for mixing-sensitive reactions." Chemical Engineering Science (2020): 115831. DOI: 10.1016/j.ces.2020.115831. Posted with permission.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

Elsevier Ltd.



File Format


Published Version