(143d) Solution of Population Balance Equations by the FCMOM for in-Homogeneous Systems

In recent years, considerable attention has been paid to a specific subject in the area of Population Balance Equations (PBE), namely the development of numerical solution techniques based on the method of moments which demand a small computational effort (i.e. QMOM, DQMOM, FCMOM). Such a requirement is important in the perspective of coupling the PBE with the transport equations (mass, momentum, energy and species) of the fluid and particulate phases. The FCMOM (Finite size domain Complete set of trial functions Method Of Moments) was presented and validated for monovariate PBE in homogeneous conditions by [1] and extended to bivariate PBE by [2]. Some advantages of the FCMOM are the following: 1) it provides accurate values both for the moments and for the reconstructed particle size distribution (or for the reconstructed bivariate particle distribution function); 2) it is computationally efficient; 3) the internal variables always assume finite values and the domains of the internal variables are clearly defined within boundaries, thus assuring that the values assumed by the internal variables are always realistic (this is relevant above all in multivariate applications). The goals of the present work are two. The first one is to validate the FCMOM in the solution of monovariate PBE for in-homogeneous systems. The FCMOM methodology is applied to a general monovariate PBE, neglecting the source terms (due to particle growth, nucleation, aggregation, breakage, etc.); in fact, the treatment of the source terms in the FCMOM framework was already considered by [1]. The second goal is to demonstrate how the FCMOM methodology can be used to predict polydispersed particulate flows in CFD applications.

[1] M. Strumendo, H. Arastoopour, Chem. Eng. Sci. 60/10 (2008) 2624-2640. [2] M. Strumendo, H. Arastoopour, Ind. Eng. Chem. Res. 48/1 (2009) 262-273.