The description of the fluid-dynamics and of mass transfer in gas-liquid systems requires the evaluation of bubble size and composition distributions, dictated by bubble breakage, coalescence and mass exchange with the liquid phase. In our previous work, gas-liquid systems were investigated by coupling CFD with mono-variate population balance equation (PBE) solved with the quadrature method of moments (QMOM). The problem is here extended to the solution of multi-variate PBE. In this work the

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... ditional Quadrature Method of Moments (CQMOM) is for the first time validated by comparison with Direct Simulation Monte Carlo (DSMC). Results, obtained from the comparison of the two methods, show that the quadrature approximation implicitly used in CQMOM for overcoming the closure problem is very accurate. CQMOM is then implemented in ANSYS/Fluent and OpenFoam and predictions are compared with experiments, resulting in very good agreement. NOMENCLATURE AND ACRONYMS G continuous rate of change of bubble size h discontinuous event for coalescence and break up L bubble size M k,l mixed moment of order k and l n number density function u L bubble velocity conditioned on size I number of oxygen moles in one bubble I mass transfer rate CFD computational fluid dynamics CQMOM conditional quadrature method of moments DQMOM direct quadrature method of moments DSMC direct simulation Monte Carlo FV finite volume ODE ordinary differential equations NDF number density function PD product difference QBMM quadrature-based moment method QMOM quadrature method of moments