Computational Fluid Dynamics data for improving freeze-dryers design

Computational Fluid Dynamics (CFD) can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular data concerning the freeze-dryer chamber and the duct connecting the chamber with the condenser, with the valves and vanes eventually present are given here, and can be used to understand the behavior of the apparatus allowing an improved design. Pilot and large scale freeze-drying chambers have been considered; data of a detailed simulation of a complete pilot scale apparatus, including duct and condenser are included. Data on conductance of an empty duct with different L/D ratio, on disk valves with different geometry, and on mushroom valve are presented. Velocity, pressure, temperature and composition fields are reported on selected planes for chambers and valves. Results of dynamic simulations are also presented, to evaluate possible performance of monitoring device in the chamber. Some further data, with detailed interpretation and discussion of the presented data can be found in the related research article by Barresi et al. [1] and Marchisio et al. [2] [1] A.A. Barresi, V. Rasetto, D.L. Marchisio, Use of Computational Fluid Dynamics for improving freeze-dryers design and understanding. Part 1: modelling the lyophilisation chamber, Eur. J. Pharm. Biopharm. 129 (2018) 30–44.http://dx.doi.org/10.1016/j.ejpb.2018.05.008. [2] D.L. Marchisio, M. Galan, A.A. Barresi, Use of Computational Fluid Dynamics for improving freeze-dryers design and understanding. Part 2: condenser duct and valve modelling, Eur. J. Pharm. Biopharm. 129 (2018) 45–57.http://dx.doi.org/10.1016/j.ejpb.2018.05.003

A multienvironment conditional probability density function model for turbulent reacting flows

The multienvironment conditional probability density function (MECPDF) model was first proposed by Fox [Computational Models for Turbulent Reacting Flows (Cambridge University Press, Cambridge, 2003)] as a simple extension of multienvironment probability density function models for turbulent reacting flows. Like the conditional moment closure (CMC) and the laminar flamelet model (LFM), the MECPDF model describes the reacting scalars conditioned on the value of the mixture fraction. However, unlike CMC and LFM, the new model provides a consistent description of conditional fluctuations in both the scalar dissipation rate and the reacting scalars, and hence can be used to model partial extinction and reignition in homogeneous turbulent reacting flows. In this work, a general derivation of the MECPDF model is presented for a single reaction-progress variable using the direct quadrature method of moments. Extensions of the model to multiple reaction-progress variables and conditioning on the mixture-fraction vector are also discussed. After deriving the model, the closure assumptions are validated using direct simulations for pure diffusion of two randomly distributed, initially correlated scalar fields. Two homogeneous applications are then considered: nonreactive mixing starting from nontrivial initial conditions, and reactive mixing with partial extinction and reignition

Use of Computational Fluid Dynamics for improving freeze-dryers design and understanding. Part 1: Modelling the lyophilisation chamber

This manuscript shows how computational models, mainly based on Computational Fluid Dynamics (CFD), can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular, the freeze-dryer chamber and the duct connecting the chamber with the condenser, with the valves and vanes eventually present are analysed in this work. In Part 1, it will be shown how CFD can be employed to improve specific designs, to perform geometry optimization, to evaluate different design choices and how it is useful to evaluate the effect on product drying and batch variance. Such an approach allows an in-depth process understanding and assessment of the critical aspects of lyophilisation. This can be done by running either steady-state or transient simulations with imposed sublimation rates or with multi-scale approaches. This methodology will be demonstrated on freeze-drying equipment of different sizes, investigating the influence of the equipment geometry and shelf inter-distance. The effect of valve type (butterfly and mushroom) and shape on duct conductance and critical flow conditions will be instead investigated in Part 2

Use of Computational Fluid Dynamics for improving freeze-dryers design and process understanding. Part 2: Condenser duct and valve modelling

This manuscript shows how computational models, mainly based on Computational Fluid Dynamics (CFD), can be used to simulate different parts of an industrial freeze-drying equipment and to properly design them; in particular in this part the duct connecting the chamber with the condenser, with its valves, is considered, while the chamber design and its effect on drying kinetics have been investigated in Part 1. Such an approach allows a much deeper process understanding and assessment of the critical aspects of lyophilisation. This methodology will be demonstrated on freeze-drying equipment of different sizes, investigating influence of valve type (butterfly and mushroom) and shape on duct conductance and critical flow conditions. The role of the inlet and boundary conditions considered has been assessed, also by modelling the whole apparatus including chamber and condenser, and the influence of the duct diameter has been discussed; the results show a little dependence of the relationship between critical mass flux and chamber pressure on the duct size. Results concerning the fluid dynamics of a simple disk valve, a profiled butterfly valve and a mushroom valve installed in a medium size horizontal condenser are presented. Also in these cases the maximum allowable flow when sonic flow conditions are reached can be described by a correlation similar to that found valid for empty ducts; for the mushroom valve the parameters are dependent on the valve opening length. The possibility to use the equivalent length concept, and to extend the validity of the results obtained for empty ducts will be also discussed. Finally the presence of the inert gas modifies the conductance of the duct, reducing the maximum flow rate of water that can be removed through it before the flow is choked; this also requires a proper over-sizing of the duct (or duct-butterfly valve system)

CFD-based scale-up of hydrodynamics and mixing in bubble columns

Unsteady and three-dimensional Eulerian–Eulerian CFD simulations of bubble column reactors under operating conditions of industrial interest are discussed in this work. The flow pattern in this equipment depends strongly on the interactions between the gas and liquid phases, mainly via the drag force. In this work, a correlation for the drag force coefficient is tested and improved to consider the so-called swarm effect that modifies the drag force at high gas volume fractions. The improved swarm factor proposed in this work is the adjustment of the swarm factor proposed by Simonnet et al. (2008). This new swarm factor is suitable for very high gas volume fractions without generating stability problems, which were encountered with the original formulation. It delivers an accurate prediction of gas volume fraction and liquid velocity in a wide range of tested operating conditions. Results are validated by comparison with experimental data on bubble column reactors at different scales and for several operating conditions. Hydrodynamics is well predicted for every operating condition at different scales. Several turbulence models are tested. Finally, the contribution of Bubble Induced Turbulence (BIT), as proposed by Alméras et al. (2015), on mixing is evaluated via an analysis of the mixing time

Simulation of macromolecule self-assembly in solution: a multiscale approach

One of the most common processes to produce polymer nanoparticles is to induce self-assembly by using the solvent-displacement method, in which the polymer is dissolved in a "good" solvent and the solution is then mixed with an "anti-solvent". The polymer ability to self-assemble in solution is therefore determined by its structural and transport properties in solutions of the pure solvents and at the intermediate compositions. In this work, we focus on poly-ε-caprolactone (PCL) which is a biocompatible polymer that finds widespread application in the pharmaceutical and biomedical fields, performing simulation at three different scales using three different computational tools: full atomistic molecular dynamics (MD), population balance modeling (PBM) and computational fluid dynamics (CFD). Simulations consider PCL chains of different molecular weight in solution of pure acetone (good solvent), of pure water (anti-solvent) and their mixtures, and mixing at different rates and initial concentrations in a confined impinging jets mixer (CIJM). Our MD simulations reveal that the nano-structuring of one of the solvents in the mixture leads to an unexpected identical polymer structure irrespectively of the concentration of the two solvents. In particular, although in pure solvents the behavior of the polymer is, as expected, very different, at intermediate compositions, the PCL chain shows properties very similar to those found in pure acetone as a result of the clustering of the acetone molecules in the vicinity of the polymer chain. We derive an analytical expression to predict the polymer structural properties in solution at different solvent compositions and use it to formulate an aggregation kernel to describe the self-assembly in the CIJM via PBM and CFD. Simulations are eventually validated against experiments

A modelling and experimental study on the co-precipitation of Ni0.8Mn0.1Co0.1(OH)2 as precursor for battery cathodes

A multi-inlet vortex mixer is used to investigate the co-precipitation of Ni0.8Mn0.1Co0.1(OH)2 particles, largely employed to produce Li-ion battery cathodes. The co-precipitation process is simulated with a population balance model, adopted to describe the experimental findings and gain deeper understanding of the process. Experiments and simulations are carried out under different operating conditions to quantify the effect of mixing conditions, turbulence and feed reactant concentrations on the final characteristics of the obtained particles, such as the size distribution, structure, morphology and density. These characteristics are measured by conducting static light-scattering, FESEM and XRD analyses and are expected to have, in turn, a tremendous effect on the final electrochemical performance of the cathode. Based on the experimental and modelling observations, we discuss the role of nucleation, molecular growth and aggregation in the co–precipitation process. Eventually a possible mechanism explaining the formation of Ni0.8Mn0.1Co0.1(OH)2 particles is proposed

Mixing phenomena in circular and rectangular cross-sectional T-mixers: Experimental and numerical assessment

In the present work, the mixing performance of square and circular cross-sectional millimetre-sized T-mixers was experimentally and numerically investigated. The pure dilution of non-reacting species (blue and yellow food dyes) and the chemical reaction of two-coloured reactants (i.e., strong acid and strong base with a pH indicator) were captured experimentally by adopting a low-cost colorimetric digital image analysis technique. Turbulence was modelled by k − ε model coupled with the β-PDF approach to account for turbulence-chemistry interactions. The circular cross-sectional T-mixer showed better mixing efficiency than the square one. Moreover, an even larger mixing performances were obtained by setting unbalanced fluid flow rates. To exploit the low computational demanding k − ε model, the Cε2 parameter was tuned, showing good reliability in describing the phenomena in the mixers. Mixing time estimations were based on both time averages and instantaneous quantities, and some possible limits of the approaches commonly adopted in the literature were identified