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In this thesis, two separate studies are conducted. First a semi-analytical solution in terms of quadrature-based moment method for the Conditional Moment Closure (CMC) is provided and tested with multi-step reaction source term. The chemical mechanism used in this study is adopted from [1]. The initial number of nodes selected as 10, while as the solution proceeds in time, according to magnitude of the quadrature weights, the number of nodes is reduced to 5 until wellmicromixed condition is achieved. Therefore, with the quadrature-based solution, the additional grid requirement for conditioning variable in CMC application is eliminated, for which H2 combustion calculations are performed for statistically homogeneous flow and operator-splitting is used for the solution of molecular mixing and the chemical source terms. The results are satisfied with the expected final conditions. Secondly, separate from the CMC studies mentioned above, two-phase flow simulations for a stirred-tank reactor are performed and compared with the experimental results, as an independent study. The gas-liquid simulations are performed with constant bubble-size assumption for three different stirring rates (200, 350 and 700 rpm) while five different bubble sizes are tested (0.5, 1.5, 2.5, 3.5 and 5 mm). In all cases, Eulerian two fluid model is adopted and turbulence is modeled via Large-Eddy simulation. The drag, virtual-mass and turbulence dispersion forces are included in the momentum exchange term, while stirrer motion is solved in multiple-reference frame. The simulation results of velocity profiles and gas-holdups are compared with the experimental results of [2] and it has been observed that, around the impeller average bubble size of 0.5 mm agrees better with the experimental results while above the impeller average bubble size of 1.5 mm correlates better. On the other hand, experimental and simulation velocity profiles are in good agreement.

Application of the quadrature-based conditional moment closure to hydrogen combustion and computational fluid dynamics simulations of stirred tank reactor for gas-liquid systems