Antonio Buffo

Modeling and simulation of turbulent polydisperse gas-liquid systems via the generalized population balance equation

Abstract This article reviews the most critical issues in the simulation of turbulent polydisperse gas-liquid systems. Here the discussion is limited to bubbly flows, where the gas appears in the form of separate individual bubbles. First, the governing equations are presented with particular focus on the generalized population balance equation (GPBE). Then, the mesoscale models defining the evolution of the gas-liquid system (e.g., interface forces, mass transfer, coalescence, and breakup) are introduced and critically discussed. Particular attention is devoted to the choice of the drag model to properly simulate dense gas-liquid systems in the presence of microscale turbulence. Finally, the different solution methods, namely, Lagrangian and Eulerian, are presented and discussed. The link between mixture, two- and multi-fluid models, and the GPBE is also analyzed. Eventually, the different methodologies to account for polydispersity, with focus on Lagrangian or direct simulation Monte Carlo methods and Eulerian quadrature-based moment methods, are also presented. A number of practical examples are discussed and the review is concluded by presenting the advantages and disadvantages of the different methods and the corresponding computational costs.

Solution of bivariate population balance equations with high-order moment-conserving method of classes

Abstract In this work the high-order moment-conserving method of classes (HMMC) ( Alopaeus et al., 2006 ) is extended to solve the bivariate Population Balance Equation (PBE). The method is capable of guaranteeing the internal consistency of the discretized equations for a generic moment set, including mixed-order moments of the distribution. The construction of the product tables in the case of aggregation, breakage and convection in internal coordinate space are discussed. Eventually, several test cases are considered to assess the accuracy of the method. The application to a realistic mass transfer problems in a liquid–liquid system is preliminarily discussed. The comparison with analytical solutions of pure aggregation problems shows that the proposed method is accurate with only a limited number of categories.

Population balance model and experimental validation for reactive dissolution of particle agglomerates

Abstract We propose a population balance model coupled with a mass transfer model to simulate the simultaneous shrinkage and breakage of particles during the reactive dissolution of particle agglomerates in stirred tank. The high-order moment-conserving method of classes is adopted to solve the population balance model. In the mass transfer model, the driving force is estimated by considering the physical constraints including electroneutrality, water dissociation and dissolution equilibrium. The simulation results, including the concentration and the particle size distribution of the final products, were validated by experiments carried out in a laboratory scale stirred tank. The unknown physical parameters in the particle breakage model were fitted against the experimental data. The results underline the importance of particle breakage in the reactive dissolution modeling under the investigated operating conditions. Several daughter size distributions functions found in literature were tested. Among them, the beta distribution provides the most flexible way to describe breakage of the particle agglomerates.