1,721,064 research outputs found
Solution of bivariate population balance equations with high-order moment-conserving method of classes
No full textIn 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
Liquid-liquid extraction in a rotating disc column: Solution of 2D population balance with HMMC
No full textIn this work mass transfer in liquid-liquid extraction is investigated with the two-dimensional high-order moment-conserving method of classes (2D-HMMC) (Buffo and Alopaeus, 2016). The solution of a realistic liquid-liquid test case, a counter-current rotating disc column (RDC) composed of three stages where the droplets exchange mass with the continuous phase, is studied. This detailed modelling approach is compared with two other possible approximated models. In the first all the droplets are assumed to have the same size and concentration, and in the second all the droplets are assumed to have the same concentration but different sizes. The results of this comparison show that the information regarding the two-dimensional droplet size-concentration distribution may be needed to properly evaluate the mass transfer rates and therefore the behaviour of the system for all the operating conditions investigated
Simulation of a reacting gas-liquid bubbly flow with CFD and PBM: Validation with experiments
No full textIn this work we use computational fluid dynamics (CFD) to simulate a reactive gas-liquid bubbly system in a rectangular bubble column, operating at low superficial velocities (i.e. homogeneous regime). The gas bubbles, injected in the column through a sparger, contain one of the reactants, namely CO2, that via mass transfer moves to the continuous liquid phase, where it reacts with NaOH. A key role is played by the bubble size distribution (BSD) and the specific surface area that define the overall mass transfer rate in the CFD model. In order to correctly predict the BSD and the polydispersity of the bubbly system the population balance equation is solved by the quadrature method of moments (QMOM), within the OpenFOAM (v. 2.2.x) two-fluid solver compressibleTwoPhaseEulerFoam. To reduce the computational time and increase stability, a second-order operator-splitting technique for the solution of the chemically reactive species is also implemented, allowing to solve the different processes involved with their own time-scale. To our knowledge this is the first time that QMOM is employed for the simulation of a real reactive bubbly system and predictions are validated against experiments
ON THE IMPLEMENTATION OF MOMENT TRANSPORT EQUATIONS IN OPENFOAM TO PRESERVE CONSERVATION, BOUNDEDNESS AND REALIZABILITY
Full text linkDifferent industrial scale multiphase systems can be successfully described by considering their polydispersity (e.g. particle/droplet/bubble size and velocity distributions) and phase coupling issues are properly overcome only by considering the evolution in space and time of such distributions, dictated by the so-called Generalized Population Balance Equation (GPBE). A computationally efficient approach for solving the GPBE is represented by the quadrature-based moment methods, where the evolution of the entire particle/droplet/bubble population is recovered by tracking some specific moments of the distribution and the quadrature approximation is used to solve the "closure problem" typical of moment-based methods. In this contribution some crucial computational and numerical details concerning the implementation of these methods into the opensource Computational Fluid Dynamics (CFD) code OpenFOAM are discussed. These aspects are in fact very often overlooked, resulting in implementations that do not satisfy the properties of conservation, realizability and boundedness. These constraints have to be satisfied in a consistent way, with respect to what done with the other conserved transported variables (e.g. volume fraction of the disperse phase) also when higher-order discretization schemes are used. These issues are illustrated on examples taken on our work on the simulation of fluid-fluid multiphase system
Molecular Drivers of Self-Assembly in RNA-Loaded lipid nanoparticles Revealed by Coarse-Grained simulations
Full text linkThe development of lipid nanoparticles (LNPs) has revolutionised RNA-based biopharmaceuticals, enabling efficient delivery of mRNA for therapeutic applications. LNPs consist of an ionisable lipid, a neutral phospholipid, cholesterol, and a PEG-ylated lipid (PL). The mixing of an aqueous solution containing mRNA with an ethanol solution containing the lipids leads to the spontaneous formation of mRNA-LNP complexes. However, the mechanisms underlying this process and the behaviour of each component under variable conditions remain partially unclear. Coarse-grained molecular dynamics was here employed to simulate the formation of RNA-loaded LNPs under various conditions, with a specific focus on ethanol. Following exposure to a polar solvent, non-polar forces prevailed, and lipids formed spherical aggregates. Due to Coulombic and hydrophilic interactions, aggregates settled on mRNA surface until they completely cover it. Finally, lipids rearranged depending on their affinity with the surrounding environment. The variation in the ethanol content did not affect the behaviour of lipids, except for the PL: when ethanol was added, the PL tended to migrate toward the inner region of the LNPs. The decrease in PLs on the external surface of LNPs could decrease their ability to regulate particle aggregation, leading to the formation of larger particles at higher ethanol content. Furthermore, higher ethanol fractions resulted in larger, less ordered nanoparticles. Together, these two phenomena could explain the experimental evidence of larger particle produced at higher ethanol content. These findings provide a detailed molecular understanding of LNP self-assembly, offering pivotal insights for designing more stable lipidic carriers for RNA encapsulation
On the implementation of moment transport equations in OpenFOAM: Boundedness and realizability
No full textIn this contribution some crucial numerical aspects concerning the implementation of quadrature-based moment methods (QBMM) into the open-source Computational Fluid Dynamics (CFD) code OpenFOAM are discussed. As well-known QBMM are based on the simple idea of solving a kinetic master equation, not in terms of the underlying number density function (NDF), but in terms of the moments of the NDF itself, via moment transport equations. These numerical aspects are in fact very often overlooked, resulting in implementations that do not satisfy the properties of boundedness and realizability for the moments of the NDF. Boundedness is an important property (i.e., moments of the NDF have to be bounded between some minimal and maximum values), that in turn depends on the initial and boundary conditions. Boundedness can be guaranteed by using a consistent approach with respect to the constraints imposed on the transport variables, such as dispersed phase volume fraction. Realizability is instead related to the existence of an underlying NDF that corresponds to a specific moment set. It is well-known that time and spatial discretization schemes can corrupt a moment set unless they are specifically designed to preserve realizability. One popular choice is to use ad-hoc pseudo high-order schemes to ensure realizable moment set is obtained. In this work, moment transport equations are implemented in the CFD code OpenFOAM using a similar form proposed by Weller (2002) for preserving the boundedness of the volume fraction, together with the numerical schemes of Vikas et al. (2011) for ensuring moment realizability. The effectiveness of such implementation is illustrated on two simple examples, taken from our work on the simulation of fluid-fluid multiphase systems
SIMULATION OF A REACTIVE GAS-LIQUID SYSTEM WITH QUADRATURE-BASED MOMENTS METHOD
Full text linkThe description of the interaction between fluid dynamics and fast chemical reactions in gas-liquid systems is complicated by the fact that the gas phase is poly-dispersed, namely it is constituted by bubbles characterized by a distribution of velocity, size and composition values. Phase coupling can be successfully described only if the modeling approach acknowledges the existence of this distribution, whose evolution in space and time is governed by the so-called Generalized Population Balance Equation (GPBE). A computationally efficient approach for solving the GPBE is represented by the Quadrature-Based Moment Methods (QBMM), where the evolution of the entire bubble population is recovered by tracking some specific moments of the distribution. In the present work, one of these methods, the Conditional Quadrature Method of Moments (CQMOM) has been implemented in the OpenFOAM two-fluid solver compressibleTwoPhaseEulerFoam , to simulate a chemically reacting gas-liquid system. To reduce the computational time and increase stability, a second-order operator-splitting technique for the solution of the chemically reacting species was also implemented, allowing to solve the different processes involved with their own time-scale. This modeling approach is here validated by comparing predictions with experiments, for the chemical absorption of CO 2 in NaOH solution, performed in a rectangular bubble colum
Multi-dimensional population balance models for the simulation of turbulent gas-liquid system
No full textA novel simplified multivariate PBE solution method for mass transfer problems
No full textInterphase mass transfer estimation may require not only the accurate knowledge of the interfacial area, which depends on the information about the size of each dispersed element, but also on the driving force, that can be different if the elements of the disperse phase have different chemical composition. To take into account such polydispersity, bivariate (or multivariate) population balance model (PBM) are formulated according to physical phenomena occurring in the investigated mass transfer problem. This often includes aggregation, breakage, advection, mass transfer of the chemical species and chemical reactions of the transferring components. In this work we propose a novel and simplified method to solve the bivariate/multivariate population balance equation for a mass transfer problem, based on the high-order moment-conserving method of classes (HMMC) (Alopaeus et al., 2006). The proposed method is based on the idea of deriving additional material balance equations for the concentration of droplets belonging to each size class, reducing significantly the total number of unknown variables with respect to true bivariate/multivariate method of classes. This modeling approach is compared with two other possible solution methods for a test case in which mass transfer and chemical reactions occur in a system with two immiscible liquid phases. In the first the traditional approach is used, where a single material balance is formulated for the disperse phase along with PBM, while in the second a true bivariate/multivariate solution method is used. The results of this comparison show that the proposed method is robust and accurate, capable of properly describing the multidimensional droplet size-composition distribution needed to evaluate the mass transfer rates, in a fraction of computational time compared with more accurate methods
Investigation of mass transfer in poly-disperse gas-liquid systems by using multi-variate population balance models and CFD
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