Daniele Marchisio

CFD simulation of mixing and reaction: the relevance of the micro-mixing model

Abstract The aim of this work is to understand the role of the micro-mixing model in computational fluid dynamics (CFD) simulations of fast reactions. Using CFD, in fact, the reactor is modelled through a computational grid and the governing equations are discretised using numerical methods. However, the mixing phenomena that occur at scales that are smaller than the grid size remain unresolved. This means that the probability density function (PDF) of all scalars is assumed to be a delta function centred at the mean value. In order to take into account micro-mixing effects a model must be added. In this work the finite-mode PDF approach is used to predict the selectivity of a parallel reaction in a Taylor–Couette reactor working in semi-batch conditions. Experimental data are compared with model predictions in order to investigate the relevance of the micro-mixing model. The case of precipitation is also discussed.

Model-based monitoring and control of industrial freeze-drying processes: Effect of batch nonuniformity

This article deals with the monitoring and control of the freeze drying of pharmaceuticals in vials taking into account batch heterogeneity. Firstly, the problem of nonuniformity of the batch is addressed: the vials in the chamber of the freeze dryer can, in fact, exhibit different time evolutions due not only to radiation from the wall of the chamber, but also to temperature gradients on the heating shelf, vapor fluid dynamics, and nonuniform inert distribution, as it has been evidenced by means of computational fluid dynamics simulations. Then, the effect of batch heterogeneity on the performance of the monitoring and control system is discussed and a new tool is presented, based on an advanced algorithm, the Dynamic Parameters Estimation, that estimates the state of the system (product temperature and residual ice content) by using the results of the pressure rise test, coupled with a controller (LyoDriver) that changes the shelf temperature in order to maintain product temperature below the maximum allowed value while minimizing the duration of primary drying.

Multiphase reacting flows : modelling and simulation

Contents: R.O. Fox: Introduction and fundamentals of modeling approaches for polydisperse multiphase flows. - D.L. Marchisio: Quadrature method of moments for polydisperse flows. - M. Massot: Eulerian multi-fluid models for polydisperse evaporating sprays. - B.H. Hjertager: Multi-fluid CFD analysis of chemical reactors - J.J. Derksen: The lattice-Boltzmann method for multiphase fluid flow simulations and Euler-Lagrange large-eddy simulations. - J. Reveillon: Direct numerical simulation of sprays: turbulent dispersion, evaporation and combustion

Large Eddy Simulation of mixing and reaction in a Confined Impinging Jets Reactor

Abstract Confined Impinging Jets Reactors have recently found many interesting applications. Their ability to provide very efficient mixing performances is of paramount importance in the production of very fine particles. In fact, in many particle precipitation processes mixing plays a crucial role in determining the final particle size distribution and therefore the final product quality. Relevant examples are the production of polymeric nano-particles for pharmaceutical applications through solvent displacement, the production of many oxides through sol–gel processes, as well as standard reactive crystallization processes. In order to develop reliable design and scale up rules and in order to understand and master the interaction between mixing and particle formation, it is of crucial importance to resort to modeling and simulation tools. In this work mixing and reaction in these devices is studied with Computational Fluid Dynamics (CFD) by using the Large Eddy Simulation (LES) approach coupled with a subgrid-scale mixing model, to take into account the effect of molecular mixing. The performance of the model is investigated through a sensitivity analysis and eventually predictions are compared with experimental data and with simulations obtained by using the Reynolds-Averaged Navier–Stokes equations (RANS) approach.

On the use of a dual-scale model to improve understanding of a pharmaceutical freeze-drying process

The evolution of product temperature and of residual ice content in the various vials of a batch during a freeze-drying process can be significantly affected by local conditions around each vial. In fact, vapor fluid dynamics in the drying chamber determines the local pressure that, taking into account the heat flow from the shelf and, eventually, radiation from chamber surfaces, is responsible for the sublimation rate and product temperature. These issues have to be taken into account when using mathematical simulation to predict the evolution of the product as a consequence of the operating conditions (recipe design), as well as during the scale-up of a recipe obtained in a small-scale equipment to a large-scale unit. In this framework, a dual-scale model can significantly improve the understanding for pharmaceuticals freeze-drying processes: it couples a three-dimensional model, describing the fluid dynamics in the chamber, and a second mathematical model, either mono- or bi-dimensional, describing the drying of the product in each vial. Thus, it can be profitably used to gain knowledge about process dynamics, and to improve the design of the equipment, as well as the performance of the control system of the process.

Extension of the Darcy–Forchheimer Law for Shear-Thinning Fluids and Validation via Pore-Scale Flow Simulations

Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food, as well as petroleum and groundwater engineering, and in many other industrial applications. Under the majority of operating conditions typically explored, the dependence of pressure drops on flow rate is non-linear and the development of models capable of describing accurately this dependence, in conjunction with non-trivial rheological behaviors, is of paramount importance. In this work, pore-scale single-phase flow simulations conducted on synthetic two-dimensional porous media are performed via computational fluid dynamics for both Newtonian and non-Newtonian fluids and the results are used for the extension and validation of the Darcy–Forchheimer law, herein proposed for shear-thinning fluid models of Cross, Ellis and Carreau. The inertial parameter β is demonstrated to be independent of the viscous properties of the fluids. The results of flow simulations show the superposition of two contributions to pressure drops: one, strictly related to the non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic one, arising at higher Reynolds numbers, is dependent on the porous medium properties. The use of pore-scale flow simulations on limited portions of the porous medium is here proposed for the determination of the macroscale-averaged parameters (permeability K, inertial coefficient β and shift factor α), which are required for the estimation of pressure drops via the extended Darcy–Forchheimer law. The method can be applied for those fluids which would lead to critical conditions (high pressures for low permeability media and/or high flow rates) in laboratory tests.

On the role of micro- and mesomixing in a continuous Couette-type precipitator

Abstract Precipitation of barium sulphate in the annular gap of a continuous Couette reactor with two unpremixed feeds has been experimentally investigated. The experiments have been carried out in the turbulent regime with an axial Re z varying from 100 to 240; the hydrodynamics can be described with the plug flow plus dispersion model, and in the condition tested the Peclet number varied from 2 to 6. The initial supersaturation has the strongest effect on both the particle size and the crystal morphology. The average size of the crystals is also influenced in some cases by the diameter of the feed tube and by the feed velocity, indicating the relevance of mesomixing. The rotation velocity has a relatively weak effect on crystal size and CSD, but a maximum has been observed increasing the rotation velocity. The performances of the system have been predicted in the limit cases of minimum and maximum age mixedness as a function of the Peclet number.

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.

An extended and total flux normalized correlation equation for predicting single-collector efficiency.

In this study a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. The correlation equation does not exploit the additivity approach introduced by Yao et al. (1971), but includes mixed terms that account for the mutual interaction of concomitant transport mechanisms (i.e., advection, gravity and Brownian motion) and of finite size of the particles (steric effect). The correlation equation is based on a combination of Eulerian and Lagrangian simulations performed, under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a cylindrical control volume. The normalization of the deposited flux is performed accounting for all of the particles entering into the control volume through all transport mechanisms (not just the upstream convective flux as conventionally done) to provide efficiency values lower than one over a wide range of parameters. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation, valid both for point and finite-size particles, is extended to include porosity dependency and it is compared with previous models. Reduced forms are proposed by elimination of the less relevant terms.

Preparation of Poly(MePEGCA-co-HDCA) Nanoparticles with Confined Impinging Jets Reactor: Experimental and Modeling Study

In this work, the biodegradable copolymer poly(methoxypolyethyleneglycolcyanoacrylate-co-hexadecylcyanoacrylate) is used to prepare nanoparticles via solvent displacement in a confined impinging jets reactor (CIJR). For comparison, nanoparticles constituted by the homopolymer counterpart are also investigated. The CIJR is a small passive mixer in which very fast turbulent mixing of the solvent (i.e., acetone and tetrahydrofuran) and of the antisolvent (i.e., water) solutions occurs under controlled conditions. The effect of the initial copolymer concentration, solvent type, antisolvent-to-solvent ratio, and mixing rate inside the mixer on the final nanoparticle size distribution, surface properties, and morphology is investigated from the experimental point of view. The effect of some of these parameters is studied by means of a computational fluid dynamics (CFD) model, capable of quantifying the mixing conditions inside the CIJR. Results show that the CIJR can be profitably used for producing nanoparticles with controlled characteristics, that there is a clear correlation between the mixing rate calculated by CFD and the mean nanoparticle size, and therefore that CFD can be used to design, optimize, and scale-up these processes.