Bubble size distribution modeling in stirred gas–liquid reactors with QMOM augmented by a new correction algorithm

Local gas hold‐up and bubbles size distributions have been modeled and validated against experimental data in a stirred gas–liquid reactor, considering two different spargers. An Eulerian multifluid approach coupled with a population balance model (PBM) has been employed to describe the evolution of the bubble size distribution due to break‐up and coalescence. The PBM has been solved by resorting to the quadrature method of moments, implemented through user defined functions in the commercial computational fluid dynamics code Fluent v. 6.2. To overcome divergence issues caused by moments corruption, due to numerical problems, a correction scheme for the moments has been implemented; simulation results prove that it plays a crucial role for the stability and the accuracy of the overall approach. Very good agreements between experimental data and simulations predictions are obtained, for a unique set of break‐up and coalescence kinetic constants, in a wide range of operating conditions. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

New quadrature‐based moment method for the mixing of inert polydisperse fluidized powders in commercial CFD codes

To describe the behavior of polydisperse multiphase systems in an Eulerian framework, we solved the population balance equation (PBE), letting it account only for particle size dependencies. To integrate the PBE within a commercial computational fluid dynamics code, we formulated and implemented a novel version of the quadrature method of moments (QMOM). This no longer assumes that the particles move with the same velocity, allowing the latter to be size‐dependent. To verify and test the model, we simulated the mixing of inert polydisperse fluidized suspensions initially segregated, validating the results experimentally. Because the accuracy of QMOM increases with the number of moments tracked, we ran three classes of simulations, preserving the first four, six, and eight integer moments of the particle density function. We found that in some cases the numerics corrupts the higher‐order moments and a corrective algorithm, designed to restore the validity of the moment set, has to be implemented. © 2012 American Institute of Chemical Engineers AIChE J, 58: 3054–3069, 2012     

Automatic differentiation‐based quadrature method of moments for solving population balance equations

The quadrature method of moments (QMOM) is a promising tool for the solution of population balance equations. QMOM requires solving differential algebraic equations (DAEs) consisting of ordinary differential equations related to the evolution of moments and nonlinear algebraic equations resulting from the quadrature approximation of moments. The available techniques for QMOM are computationally expensive and are able to solve for only a few moments due to numerical robustness deficiencies. In this article, the use of automatic differentiation (AD) is proposed for solution of DAEs arising in QMOM. In the proposed method, the variables of interest are approximated using high‐order Taylor series. The use of AD and Taylor series gives rise to algebraic equations, which can be solved sequentially to obtain high‐fidelity solution of the DAEs. Benchmark examples involving different mechanisms are used to demonstrate the superior accuracy, computational advantage, and robustness of AD‐QMOM over the existing state‐of‐the‐art technique, that is, DAE‐QMOM. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

基于微分代数积分矩量法的聚并器超细颗粒聚团研究

研究聚并器内布朗聚团和湍流聚团引起超细颗粒聚团,特别考虑颗粒之间近程力（范德华引力、静电斥力）和颗粒与气体之间的流体力学作用力对颗粒聚团的影响。基于FLUENT软件UDF功能自定义聚团核,考虑颗粒之间近程力和流体力学作用力对聚并率的影响,引入碰撞效率α对聚团核进行修正,得到修正湍流聚并模型并将该模型与理想湍流聚并模型进行比较。应用群体平衡模型（population balance model,PBM）耦合CFD对颗粒聚团过程进行数值模拟,并采用微分代数积分矩量法（DAE-QMOM）求解群体平衡方程。结果表明：理想湍流聚并模型与实验结果误差为8.92%,而修正改进的湍流聚团模型与实验结果误差仅为3.35%,更加符合实际情况;微分代数积分矩量法具有较高的效率,而且误差较小,相比PD积分矩量法有明显的优势,稳定性也比较突出。     

Nanoparticle formation through solid‐fed flame synthesis: Experiment and modeling

The preparation of silica nanoparticles through solid‐fed flame synthesis was investigated experimentally and theoretically. Monodispersed submicrometer‐ and micrometer‐sized silica powders were selected as solid precursors for feeding into a flame reactor. The effects of flame temperature, residence time, and precursor particle size were investigated systematically. Silica nanoparticles were formed by the nucleation, coagulation, and surface growth of the generated silica vapors due to the solid precursor evaporation. Numerical modeling was conducted to describe the mechanism of nanoparticle formation. Evaporation of the initial silica particles was considered in the modeling, accounting for its size evolution. Simultaneous mass transfer modeling due to the silica evaporation was solved in combination with a general dynamics equation solution. The modeling and experimental results were in agreement. Both results showed that the methane flow rate, carrier gas flow rate, and initial particle size influenced the effectiveness of nanoparticle formation in solid‐fed flame synthesis. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

A first principles approach to identifying polymers for use in two‐phase partitioning bioreactors

BACKGROUND: Two‐phase partitioning bioreactors (TPPBs) employ an immiscible phase to partition toxic substrates/products to/away from cells to reduce cytotoxicity and improve bioprocess performance. Initially, immiscible organic solvents were used as the sequestering phase, and their selection included consideration of solute–solvent affinity, which can be predicted through first principles consideration of solute activity and phase equilibrium thermodynamics. Polymers can replace organic solvents in such systems, however, their selection has largely been via heuristic means, and a more fundamental approach is necessary for future success in rational polymer identification. RESULTS: Material properties (polymer crystallinity, solubility parameter, and glass transition temperature T_g) were examined across several polymers and polyaromatic hydrocarbons as target solutes. All were shown to influence solute–polymer affinity. CONCLUSION: This first attempt at identifying physical/chemical properties that affect solute–polymer partitioning has been able to demonstrate some clear trends, and has allowed us to formulate a polymer selection guide, based on first principles, to facilitate the selection of solute–polymer pairs for solid–liquid TPPB applications. Copyright © 2012 Society of Chemical Industry