Degree Type


Date of Award


Degree Name

Master of Science


Chemical and Biological Engineering


Chemical Engineering

First Advisor

Rodney O. Fox

Second Advisor

Alberto . Passalacqua


In this study, a solution algorithm for the Conditional Moment Closure (CMC) is provided by using Conditional Quadrature Method of Moment (CQMOM). In CMC applications, the reactive scalars are conditioned on the conserved scalars such as mixture fraction. Unlike in Reynolds averaged reactive scalar transport equations, in CMC equations, conditioning on conserved scalar allows to write the chemical source term in a closed form. However, the closed chemical source term comes with a cost of increased dimensionality with an additional grid that must be generated for the conditioning variable. By using QBMM, the necessity of an additional grid was circumvented as the mixture fraction moments are calculated through Gauss-Lobatto quadrature rule.

Additionally, a semi-analytical solution for the molecular mixing term of CMC equation is written in terms of Jacobi polynomials and the resulting solution is tested against two test cases: (i) pure mixing and (ii) mixing sensitive reactions for statistically homogeneous flows.

In every test cases, it is concluded that, the proposed solution algorithm is an accurate, alternative solution technique for CMC application and since operator splitting is used, the extension of the current algorithm to spatially inhomogeneous flows is straightforward.

Copyright Owner

Aziz Dogan Ilgun



File Format


File Size

65 pages