Multivariate population balance for turbulent gas-liquid flows

This dissertation focuses on the development of computational tools capable of predicting the complex fluid dynamics behavior of industrial scale gas-liquid systems. In the past, the description of such systems for design purposes was performed through the use of correlations, formulated by means of very expensive experimental campaigns. The limits of this approach can be overcome by the use of modern simulation tools, such as Computational Fluid Dynamics (CFD). However the momentum and mass transfer description of gas-liquid systems is characterized by the intrinsic poly-dispersity of the gas phase, namely the different dispersed bubbles are usually distributed over a certain range of size, velocity and chemical composition values. Then a proper methodology must be applied to tackle this issue: Population Balance Modeling (PBM), originally formulated for crystallization problems, can be successfully adopted to describe any generic dispersed system in which the combination of different phenomena (i.e., physical space advection, diffusion, aggregation, breakage, growth, nucleation) determines the state of the dispersed system. All these considerations explain the interest of the multiphase flow community in efficient coupled PBM-CFD methods, especially when such methodologies are employed to investigate large scale systems with complex phenomena involved, such as mass transfer and chemical reactions. Moreover, the knowledge of more than one property of the disperse phase can be required to properly describe the problem (i.e., multivariate description instead of monovariate), as in the case of reacting multiphase systems, and this fact represents a challenge from the modeling point of view. At this point, it is very important to reduce the computational costs introduced by the Population Balance Equation (PBE), by recurring to approximate but reliable methods. In this sense, it is also recent the formulation of Quadrature-Based Moments Methods (QBMM) for particulate flows, a class of solution methods particularly suitable for the purposes of this work. Therefore in this dissertation the issues related to the application of these methods for the description of industrial scale bubble columns and aerated stirred tank reactors will be discussed. In the first part of this work, the derivation of PBE and the Eulerian-Eulerian methodology for gas-liquid systems is shown, especially concerning the description of the mass transfer problem in air-water system, in which the information on the bubble size distribution is needed to estimate the interfacial area and the distribution of bubble composition may be required to calculate the local mass transfer driving force. Moreover the QBMM solution methods, both for monovariate and multivariate cases, are here presented and discussed in detail. In the second part, a preliminary study of QBMM stability and accuracy for simplified zero-dimensional systems is performed through comparison with accurate PBE solution methods, then the implementation is verified through the simulation of one and two-dimensional systems in order to point out the numerical issues than may arise when physical space advection is considered. Eventually, the simulation of realistic gas-liquid systems (i.e., a stirred tank reactor and a bubble column), for which experimental data are available relating to the local bubble size distribution (BSD) and mass transfer, are performed for validation purposes. The shown results prove the effectiveness of the proposed PBM-CFD approach: in general a very good agreement with the experimental data is observed with a reasonable computational costs.