Arnaud Cockx

Reconstruction of a distribution from a finite number of its moments: A comparative study in the case of depolymerization process

Abstract The resolution of the population balance equation (PBE) using moment-based methods offers a high computational efficiency however, information on the time evolution of the probability density function (PDF) is out of reach. For this, several PDF reconstruction methods using a finite number of moments are proposed in the literature. In this contribution, three different methods (i.e. beta kernel density function based method, spline based technique and the maximum entropy based approach) are tested and compared to the analytical solution of a depolymerization process. The maximum entropy method gives the most accurate approximations using only a set of six moments. This method is combined with the quadrature method of moments (QMOM) for a simultaneous reconstruction during the PBE resolution. A three nodes and a four nodes quadrature are tested. The results show that the quality of the reconstruction is highly dependent on the accuracy of the computed moments.

A NOVEL METHODOLOGY TO MEASURE MASS TRANSFER AROUND A BUBBLE

An original approach for accurately measuring the mass transfer of a single bubble rising in a liquid is reported. The approach consists in using PLIF technique (Planar Laser Induced Fluorescence) at micro-scale to capture images of the released oxygen concentration field in the bubble wake. The applicability of the technique for determining mass transfer coefficients in different fluids (1 < Re < 100) is demonstrated and the relevance of the results is corroborated by established correlations. This direct and non-intrusive technique could be a promising tool to enrich the understanding of mass transfer phenomena.