Further Developments of the Extended Quadrature Method of Moments To Solve Population Balance Equations

Abstract

Developing numerical methods to solve polydispersed flows using a Population Balance Equation (PBE) is an active research topic with wide engineering applications. The Extended Quadrature Method of Moments (EQMOM) approximates the number density as a positive mixture of Kernel Density Functions (KDFs) that allows physical source terms in the PBEs to compute continuous or point-wise form according to the moments. The moment-inversion procedure used in EQMOM has limitations such as the inability to calculate certain roots even if it is defined, absence of consistent result when multiple roots exist or when the roots are nearly equal. To address these limitations, the study proposes a modification of the moment-inversion procedure to solve the PBE based on the proposed Halley-Ridder (H-R) method. Although there is no significant improvement in the extent of variability relative to the mean of the tested shape parameter cr values, an increase in the number of floating point operations (FLOPS) is observed which the proposed algorithm responds in limitations mentioned above. The total number of FLOPS for all the kernels used for the approximation increased by around 30%. This is an improvement towards the development of a more reliable and robust moment-inversion procedure.