Solution of population balance equation using quadrature method of moments with an adjustable factor

For description of dispersed phases in many practical applications, population balance equations (PBE) of entities under investigation are coupled with the thermo-fluid dynamics of the surrounding fluid. Hence, solution of PBE needs to be implemented in a computational fluid dynamics (CFD) code, which leads to additional computational cost. The excess computational demand has limited the applicability of numerical techniques such as class method (CM) or Monte Carlo method (MCM). Although quadrature method of moments (QMOM) and direct quadrature method of moments (DQMOM) have been shown to be accurate and computationally efficient when used with CFD codes, numerical difficulties can arise for cases where there is a large variation of moments. To circumvent this problem, the standard QMOM was modified by incorporating an adjustable factor, which allows the moments of size distribution to be adjusted, in order to improve the accuracy or reduce CPU time. The performance of this method for solving PBE has been evaluated by case studies involving pure aggregation and breakage, agglomeration and breakup, as well as particle growth, which have analytical solutions or exact solutions from CM or finite element method (FEM). The results demonstrate that the modified QMOM is capable of achieving high accuracy at a low CPU cost if an appropriate adjustable factor is chosen. An interesting feature is that different adjustable factors can be assigned to different processes depending on the balance between accuracy requirement and CPU cost.