Search

The current state-of-the-art for computational modeling of polydisperse multiphase flows is reviewed and future research directions are discussed. Physics-based computational models at three distinct levels of abstraction: the microscale, mesoscale and macroscale; are discussed and compared. Special emphasis is placed on the relationship between the models at different scales and on how information from the finer scales is used to provide closures at the coarser scales. For disperse multiphase flows, it is argued that the passage from a direct-numerical simulation at the microscale to the kinetic description at the mesoscale is the crucial step for ensuring the validity of the macroscale model. In particular, the passage from the microscale to the mesoscale requires physics-based closures, while the passage from the mesoscale to the macroscale requires mathematical closures. The choices made in the physical and mathematical closures of the spatial fluxes and coupling terms will determine whether the Eulerian model is well-posed. In addition, the use of quadrature-based moment methods for polydisperse particles is presented as an efficient macroscale closure when dealing with a distribution of particle sizes. Examples of monodisperse and polydisperse multiphase flows are provided for cases where the fluid phase is compressible (high speed) and incompressible (low speed). [Display omitted] • Kinetic-based modeling of polydisperse multiphase flows is reviewed. • A multiscale modeling framework consisting of micro-, meso- and macroscale models is proposed. • The links between the micro- and mesoscale and the meso- and macroscale models are described using gas–particle flow. • The importance of verifying that the model is well-posed as each scale is emphasized. • The multiscale modeling approach is shown to reproduce the correct physics over a wide range of parameters. [ABSTRACT FROM AUTHOR]

Hyperbolic conservation equations for polydisperse, high-speed, compressible, fluid–particle flows with added mass and fluid-phase pseudoturbulence are derived. First, the kinetic-based model for monodisperse particles that accounts for collisional and frictional pressure, as well as added mass and internal energy, is reviewed. Then, a kinetic-based model for polydisperse particles is formulated in terms of the moments of the particle size distribution, and velocity moments conditioned on the particle mass or size. Transport equations for velocity moments up to second order (or total kinetic energy) are closed using the hyperbolic quadrature method of moments. In the numerical implementation for the spatial fluxes and source terms, the particle mass distribution is treated using the generalized quadrature method of moments and the size-conditioned moments are found with the conditional quadrature method of moments. Example results for spatially 1-D test cases demonstrate the ability of the polydisperse model to capture a wide range of particle-size-dependent multiphase flow physics. [Display omitted] • A kinetic model for polydisperse particles that includes added mass and particle–fluid–particle stresses is formulated. • Kinetic-based model is coupled to modified Euler equations for high-speed fluid flow, and includes pseudo-turbulent kinetic energy. • For collisional flows, moment equations for particle phase are derived and closed using quadrature-based moment methods. • Macroscale model is well-posed and solved numerically using standard solvers for hyperbolic conservation laws. • Using numerical examples, polydisperse model reproduces the correct physics over a wide range of volume fractions. [ABSTRACT FROM AUTHOR]

The main goal of this work is to explore the closures used in two-fluid models to represent the interphase forces between particles and high-speed flows. To this aim, a hyperbolic two-fluid model for high-speed, monodisperse, gas–particle flow is employed to study the interaction of a thin, moderately dense (volume fraction α p < 0. 2) particle curtain impacted by an incident shock with Mach number M s. Mimicking the experimental setup, the numerical setup consists of a one-dimensional shock tube with a thin particle curtain in the driven section. This allows to validate the two-fluid model against recent experimental campaigns exploring a wide range of particle diameters, material densities, volume fractions, curtain widths and shock speeds. In general, the two-fluid model allows to reproduce the experimental data where the highest discrepancy is obtained in the configurations with the smallest M s. Attention is drawn to the particle-Mach-number (M p) dependence of the drag and added-mass coefficients, which have not yet been explored extensively in the literature. Also, the two-fluid model based on kinetic theory includes a particle pressure accounting for particle–fluid–particle (pfp) interactions. Thus, a parametric study is presented to evaluate the impact of the drag coefficient, the added-mass coefficient, and the magnitude of the pfp pressure. The complete drag model accounting for particle Reynolds number R e p , M p and α p is more accurate than previous drag models depending only on R e p and α p. Due the high particle-to-gas density ratio, the added-mass model has only a minor impact on the results. The magnitude of the pfp pressure has a significant impact on the spread of the curtain due to the high slip velocity. [Display omitted] • Assessment of a hyperbolic compressible two-fluid model is presented using experimental data for shock–particle interactions. • Drag modeling with Mach dependency is taken from very recent simulation data and compared to existing model without Mach effects. • Added-mass modeling from the two-fluid model is also explored. • The pfp pressure term arising from kinetic theory in the two-fluid model ensures hyperbolicity and has a visible effect on the curtain dynamics. [ABSTRACT FROM AUTHOR]

A computational model for the simulation of the particle-size evolution of nanoparticles in mixing-controlled processes is presented. This model accounts for the effect of molecular mixing on particle-size evolution when mixing time scales are smaller than the phase-space time scales. The approach is formulated by deriving evolution equations for the moments of joint mixture fraction-size moments PDF, and closing such moment equations using the conditional quadrature method of moments. A test case consisting of a mixing-dependent aggregation problem in a multi-inlet vortex reactor is considered. The results accounting for the correlation between mixture fraction and size moments are compared against those computed neglecting such correlation to demonstrate its impact on the model predictions. The average particle volumes are different in the order of 10 4 mm 3 at the reactor exit under the studied conditions. • Model for nanoparticle size evolution under mixing limited conditions. • Quadrature-based solution approach. • Application to a multi-inlet vortex reactor. [ABSTRACT FROM AUTHOR]

Modeling the oxidation of soot particles in flames is a challenging topic both from a chemical point of view and regarding the statistical treatment of the evolution of the soot number density function (NDF). The method of moments is widely-used for the statistical modeling of aerosol dynamics in various applications, and a number of different moment methods have been established and successfully applied to the modeling of soot formation and growth. However, a shortcoming of existing moment methods is the lack of an accurate, numerically robust, and computationally efficient way to treat soot oxidation, especially regarding the prediction of the particle number density. In this work, the recently developed Extended Quadrature Method of Moments (EQMOM) is integrated with a physico-chemical soot model and combined with a treatment for particle removal by oxidation. This leads to a modeling framework for the simulation of coupled inception, growth, coagulation, and oxidation of soot in flames. In EQMOM, the moment equations are closed by reconstructing the soot NDF with a superposition of continuous kernel functions. Various standard distribution functions can be used as kernel functions, and the algorithm has been implemented here using gamma and lognormal distributions. It is shown that and discussed why gamma distributions are more suitable as kernel functions than lognormal distributions in order to accurately predict soot oxidation. The integrated model is validated by comparisons with analytical solutions for the NDF, results from Monte Carlo simulations of soot formation and oxidation in flames, and experimental data. [ABSTRACT FROM AUTHOR]

The quadrature method of moments (QMOM) for a one-dimensional (1-D) population balance equation was introduced by R. McGraw (Aerosol Science and Technology, 27 , 255-265, 1997) to close the moment source terms. QMOM is defined based on the properties of the monic orthogonal polynomials Q i of degrees i = 0 , 1 , ... , n that are uniquely defined by the set of 2 n moments up to order 2 n − 1. The moment of order 2 n is fixed to the boundary of moment space such that the distribution function is approximated by a sum of n Dirac delta functions. Using the recursion coefficients of the orthogonal polynomials for i > n ≥ 1 , the generalized quadrature method of moments (GQMOM) extends the quadrature representation to a sum of N > n terms using the same moments as QMOM. In doing so, the known moments are preserved and higher-order moments correspond to a distribution function in the interior of moment space. Here, GQMOM closures for distributions on R , R + , and (0 , 1) are defined and analyzed. Generally speaking, GQMOM provides a more accurate moment closure than QMOM without increasing the number of moments and at nearly the same computational cost. • GQMOM improves the performance and accuracy of QMOM by allowing for an arbitrary number of quadrature nodes. • GQMOM requires only one additional moment compared to QMOM with nearly the same computational cost. • GQMOM uses the same moments as EQMOM but is more accurate and easier to implement. • GQMOM can solve population balance equations for which QMOM and EQMOM have difficulties. [ABSTRACT FROM AUTHOR]

Abstract: Electrostatics plays an important role in gas–solid polymerization fluidized-bed reactors. Agglomeration of polymer particles can occur due to either electrostatic and/or thermal effects, and can lead to reactor operability problems if not properly mitigated. In this work a first-principles electrostatic model is developed and coupled with a multi-fluid computational fluid dynamic (CFD) model to understand the effect of electrostatics on the bulk polymer, polymer fines, and catalyst particles. The multi-phase CFD model for gas–solid flow is based on the kinetic theory of granular flows and the frictional theory. The electrostatic model is developed based on a fixed, size-dependent charge for each type of particle (catalyst, polymer fines and polymer). The combined CFD model is first verified using simple test cases and then applied to a pilot-plant-scale polymerization fluidized-bed reactor. The multi-phase CFD model is applied to reproduce qualitative trends in particle segregation and entrainment due to electrostatic charges observed in experiments. [ABSTRACT FROM AUTHOR]

Abstract: In many industrial-scale fluidized-bed reactors, particle mixing and segregation play an important role in determining reactor performance. Detailed information about the particle size distribution (PSD) throughout the bed at different operating conditions is crucial for design and scale up of practical systems. In this work, a multi-fluid model based on the Euler–Euler approach and the direct quadrature method of moments (DQMOM) is used to describe particle segregation, and the model predictions are validated with available experimental and simulation data. For binary mixtures, multi-fluid simulations are compared with digital image analysis experiments for beds of glass beads. By properly defining the solid–solid drag force, the multi-fluid model can reproduce the segregation rate found experimentally for different flow conditions with binary mixtures. Segregation phenomena in gas–solid fluidized beds with a continuous PSD are also investigated. Here, the multi-fluid simulations are compared with discrete particle simulations (DPS). Using the moments of the PSD from DPS, the weights and abscissas used in DQMOM are initialized in the multi-fluid model. The segregation rate and the local moments of the PSD predicted by the multi-fluid model are compared to the DPS results. The dependence of the results on the number of DQMOM nodes is also investigated. [Copyright &y& Elsevier]

Linear stability analysis is performed for the two-dimensional, two-fluid model for gas–liquid flow applied in our previous computational study of bubble columns [Monahan, S.M., Vitankar, V.S., Fox, R.O., 2005. CFD predictions for flow-regime transitions in bubble columns. A.I.Ch.E. Journal 51, 1897–1923]. The growth rate and the velocity of propagation for a small-amplitude disturbance wave are shown to be highly dependent on the wave number, the direction of propagation, and the two-fluid model parameters. Two types of vertical instabilities are identified: one corresponding to the classical analysis of Jackson [1963. The mechanics of fluidized beds. I: the stability of the state of uniform fluidization. Transactions of the Institution of Chemical Engineers 41, 13–21] for the one-dimensional model, and the other due to a second pair of roots to the characteristic equation of the linearized two-dimensional model. Numerical simulations keeping one type or the other of the roots stable (or unstable) show distinctly different dynamics and suggest that large-scale instabilities seen experimentally may be associated with the second type of instability. The latter leads to instability in the horizontal velocities and is associated with a positive lift coefficient in flows without mean shear in the presence of isotropic bubble–bubble interactions (i.e., “bubble pressure”). This instability is thus different than previously reported instabilities due to negative lift or cooperative/hindered rise. [Copyright &y& Elsevier]

Abstract: The implementation of a population balance equation (PBE) in computational fluid dynamics (CFD) represents a crucial element in the simulation of multiphase flows. Some of the available methods, such as classes methods (CM) and Monte Carlo (MC) methods, are computationally expensive and simulation of real cases of practical interest requires intractable CPU times. On the other hand, other methods such as the method of moments (MOM) are computationally affordable but have proven to be inaccurate for a number of cases. In recent work a new closure, the quadrature method of moments (QMOM), has been introduced, applied and validated. In our earlier work, QMOM was shown to be an efficient and accurate method for tracking the moments of the particle size distribution (PSD) in a CFD simulation. However, QMOM presents two main disadvantages: (i) if applied to multi-variate distributions it loses simplicity and efficiency, and (ii) by tracking only the moments of the PSD, it does not represent realistically polydisperse systems with strong coupling between the internal coordinates and phase velocities. In order to address these issues, in this work the direct quadrature method of moments (DQMOM) is formulated, validated, and tested. DQMOM is based on the idea of tracking directly the variables appearing in the quadrature approximation, rather than tracking the moments of the PSD. Nevertheless, for monovariate cases we show that QMOM and DQMOM yield identical results. In addition, we show how it is possible to extend the DQMOM to multivariate cases and some of relevant theoretical and numerical issues are discussed. These issues are discussed in the present work for homogeneous and one-dimensional flows. References to recent CFD applications of DQMOM to multiphase flows are provided as further proof of the utility of the method. [Copyright &y& Elsevier]

A hybrid finite-volume (FV)/transported probability density function (PDF) method is used for the simulation of a partially premixed flame with detailed chemistry. The FV code is implemented to handle detailed chemistry implicitly with no subgrid closure. A partially premixed methane–air flame is simulated to illustrate the need for closure. The PDF scheme is then substituted to handle the species transport using a subgrid mixing model. The algorithmic modifications to the PDF code are discussed in the context of a generalized structured grid solution technique. A multi-step particle transport algorithm is used to eliminate grid dependence of the time step. A detailed chemistry mechanism (GRI-2.11) is handled using in situ adaptive tabulation. It is shown that with simple modifications, the Interaction by Exchange with the Mean mixing model is able to predict the flame quite accurately. Mean profiles and conditional means obtained using the 49-species GRI-2.11 and 53-species GRI-3.0 mechanisms and the 16-species Augmented Reduced Mechanism are compared with the experimental data from the Sandia D flame. It is shown that with the mixing model, good agreement with the experimental data is achieved. Also the effect of the value of the mechanical-to-scalar time-scale ratio used in the mixing model is analyzed. The effect of the model constants in the dissipation equation for the turbulence model and the effect of radiation on flame predictions are also discussed. [Copyright &y& Elsevier]

Reactive precipitation involves four fundamental processes: mixing-limited reaction, nucleation, growth, and aggregation. A novel algorithm, in situ adaptive tabulation (ISAT), has been implemented in a code for micromixing simulations, which is often applied together with computational fluid dynamics (CFD), using full probability density function (PDF) methods to incorporate these fundamental processes in the formation of nano-particles by reactive precipitation in a plug-flow reactor. The quadrature method of moments is applied to solve population balance equations for turbulent aggregation of the growing particles. The various performance issues (error control, accuracy, number of records, speed-up) for ISAT are discussed. Based on a large number of simulations, an error tolerance of 10−4–10−5 is found to be satisfactory for carrying out time-evolving full PDF simulations of nano-particle formation by reactive precipitation. Our results show that CFD simulation of reactive precipitation requires a much smaller computational effort when the ISAT algorithm is implemented than when direct integration is used. Finally, the effects of initial species concentrations, micromixing time, and turbulent shear rate on the reactive precipitation of barium sulfate are studied. [Copyright &y& Elsevier]

• Rigorous derivation of the volume-filtered compressible equations for two-phase flows. • Evaluate unclosed terms via a posteriori filtering of particle-resolved simulations. • Propose a transport equation for PTKE and closure model for the dissipation rate. • Grid convergence of the Euler-Lagrange framework is demonstrated on compressible flow. • The model captures pseudo-turbulent Reynolds stresses independently of the drag law. In this work, we present a rigorous derivation of the volume-filtered viscous compressible Navier–Stokes equations for disperse two-phase flows. Compared to incompressible flows, many new unclosed terms appear. These terms are quantified via a posteriori filtering of two-dimensional direct simulations of shock-particle interactions. We demonstrate that the pseudo-turbulent kinetic energy (PTKE) systematically acts to reduce the local gas-phase pressure and consequently increase the local Mach number. Its magnitude varies with volume fraction and filter size, which can be characterized using a Knudsen number based on the filter size and inter-particle spacing. A transport equation for PTKE is derived and closure models are proposed to accurately capture its evolution. The resulting set of volume-filtered equations are implemented within a high-order Eulerian–Lagrangian framework. An interphase coupling strategy consistent with the volume filtered formulation is employed to ensure grid convergence. Finally PTKE obtained from the volume-filtered Eulerian–Lagrangian simulations are compared to a series of two- and three-dimensional direct simulations of shocks passing through stationary particles. [ABSTRACT FROM AUTHOR]

Highlights • A transitional delayed detached eddy simulation model was developed for use in microscale vortex reactors. • Simulation results were compared to microscopic particle image velocimetry and laser induced fluorescence experiments. • Excellent agreement was observed between simulation and experiment. • The model accurately simulated both the laminar and turbulent flow regimes in the reactor. Abstract The objective of the presented work is to verify a delayed detached eddy simulation (DDES) model for simulating transitional swirling flow in a micro-scale multi-inlet vortex reactor (MIVR). The DDES model is a k- ω based turbulence model with a low Reynolds number correction applied to the standard k- ω model such that the Reynolds-averaged Navier-Stokes (RANS) component of the DDES model is able to account for low Reynolds number flow. By limiting the dissipation rate in the k-equation, the large-eddy simulation (LES) part of the DDES model behaves similarly to a one-equation sub-grid model. The turbulent Reynolds number is redefined to represent both modeled and resolved turbulence level so that underestimation of the RANS length scale in the LES range can be reduced. Applying the DDES model to simulate both laminar and transitional flow in the micro-scale MIVR produces an accurate prediction of mean velocity and turbulent intensity compared with experimental data. It is demonstrated that the proposed DDES model is capable of simulating transitional flow in the complex geometry of the micro-scale MIVR. These simulation results also help to understand the flow and mixing patterns in the micro-scale MIVR and provide guidances to optimize the reactor for the application of producing functional nanoparticles. [ABSTRACT FROM AUTHOR]

Large eddy simulation of the passive scalar transport in a high Schmidt number turbulent confined wake flow has been performed. The results are evaluated by comparison to particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) data, including point-wise data as well as spatial correlations. In the LES simulations, the gradient diffusion hypothesis is used to close the transport equation for the passive scalar. Different discretization schemes are investigated in order to determine the best choice for ensuring boundedness of the passive scalar and to accurately predict the mixing rate. The simulation results compare well to experimental data, demonstrating that the transport mechanisms in this high Schmidt number turbulent flow are well predicted by the LES method. Two-point spatial correlations of passive scalar with velocity predicted by the simulation show good agreement with the experimental results, indicating that the turbulent coherent structures of the flow are reproduced by the simulation. [ABSTRACT FROM AUTHOR]

Abstract: Combustion-based synthesis is the prominent technique for large-scale production of commercial-grade nanoparticles, such as titanium dioxide (titania or TiO2). Both time and economic constraints have led to an increase in the sophistication of the models for such chemical processes. State-of-the-art models for combustion-based nanoparticle synthesis incorporate highly detailed gas-phase kinetic models to describe the effects of the complex chemical reactions on particle formation and growth. Accurate models for particle evolution must be coupled with the detailed gas-phase kinetics in order to predict the particle properties. In this work, a bivariate population balance model for titania nanoparticle produced in flame reactors is used to investigate the role of gas-phase and surface chemistry in the determination of particle properties. The model considers all relevant particle evolution events including nucleation, surface growth, aggregation and sintering. In order to focus on the relative importance of the gas-phase mechanism, the flow field is modeled using a simple multi-environment plug-flow reactor model. Both one-step and detailed chemistry for Ti oxidation from the precursor, TiCl4, are compared for two different flame configurations. The simulation results demonstrate the importance of the location of nuclei formation in the flame, which depends strongly on the gas-phase and surface growth kinetic models, and their effect on the final product properties. These results suggest that detailed gas-phase chemical kinetics combined with a detailed surface growth model are required to accurately describe the combustion-based synthesis of nanoparticles. [Copyright &y& Elsevier]

Abstract: To evaluate the quality of mixedness in particulate systems, either through experiments or with CFD simulations, proper quantification methods are necessary. Two analysis tools are presented here that allow for quantitative assessment of the mixedness of binary particulate systems when its internal structure is known, either through experimental tomographic techniques or through numerical simulations; they are a newly-defined Particle Segregation Number (PSN) and the Cube Analysis (CA). The study has been conducted using simulated material distributions in a 3D cylindrical vessel which approximates a collapsed fluidized bed. The particle distribution is denoted in terms of volume concentration per voxel (i.e., a 3D pixel). The results show that the PSN and CA measures are independent of particle size, material densities, and overall volume fraction, which is not true for other available segregation measures, and can therefore be used over a wide range of operating conditions to assess and compare particulate mixing. Furthermore, it was found that using these methods allows for capturing even small changes in the overall bed segregation condition. [Copyright &y& Elsevier]

Abstract: In this work, we present a multiscale computational model for flame synthesis of TiO2 nanoparticles in a turbulent flame reactor. The model is based on large-eddy simulation (LES) methodology in conjunction with detailed gas-phase chemical kinetics to accurately model the highly complicated combustion and nucleation processes in a turbulent flame. A flamelet-based model is used to model turbulence–chemistry interactions. In particular, the transformation of TiCl4 to the solid primary nucleating TiO2 nanoparticles is represented using an unsteady kinetic model considering 30 species and 69 reactions in order to accurately describe the important event of nanoparticle formation. The evolution of the TiO2 number density function is tracked using the quadrature method of moments (QMOM). For validation purposes, the detailed computational model is compared against experimental data and reasonable agreement is obtained. [Copyright &y& Elsevier]

Abstract: A consistent hybrid large-eddy simulation/filtered-density-function approach (LES-FDF) is formulated for variable-density low-Mach-number flows. The LES-FDF approach has been proposed as a suitable method for finite-rate-chemistry-based predictive modeling of turbulent reactive flows. Due to the large computational grid associated with LES, use of Lagrangian schemes is numerically expensive. In this work, a highly efficient parallel Lagrangian implementation is used for the simulation of a nonpremixed flame. This bluff-body-stabilized flame is characterized by complex flow fields that interact strongly with the combustion mechanism. A LES grid size of 1 million computational cells and roughly 15 million notional particles is used to simulate a time-accurate variable-density flow. The hybrid approach predicts the time-averaged velocity and root mean square (RMS) velocity components quite accurately. Species profiles including hydroxyl radical compare well with experimental data. Consistency and accuracy are established by comparing particle and Eulerian density, mixture fraction, and RMS mixture fraction fields. Scalar FDFs at select locations are shown to be well approximated by the presumed beta function used in typical combustion LES. [Copyright &y& Elsevier]

• Pyrolysis of beech wood particles in a bubbling fluidized bed was investigated. • Effect of beech wood particle shape on their pyrolysis conversion was studied. • A high-precision scale was used to measure the beech wood mass evolution. • Pyrolysis time is proportional to the particles heat transfer characteristic length. • A simple shrinking model proposed can properly predict the effect of particle shape. The effect of biomass particle shape on the conversion of beech wood during pyrolysis in a bubbling fluidized bed (BFB) was experimentally quantified. A lab-scale BFB installed on a high-precision scale was used to characterize the mass loss of the biomass particles immersed in the bed. The scale could monitor the mass loss of the beech wood particles while moving freely inside the bed, which was operated at 2.5 times the minimum fluidization velocity of the bed material employed. The tests were performed at 500 and 600 °C using beech wood particles of the same mass, but different in shape. All particles used were cylindrical in shape, with the same mass, and differing in their aspect ratio, analyzing particles from typical biomass chips to standard biomass pellets. The experimental results indicate that the velocity of pyrolysis for the different particles is proportional to the characteristic heat transfer length of the particles, with pyrolysis times ranging from 27 to 53 s for a bed temperature of 600 °C and from 43 to 85 s for a bed temperature of 500 °C. The minimum pyrolysis time was obtained for particles with a diameter of 20 mm and a length of 2 mm pyrolyzing in a bed at 600 °C, whereas the maximum pyrolysis time corresponds to particles of 10 mm in diameter and 8 mm in length converting in a bed at 500 °C. Estimations of the conversion time obtained from a Shrinking Unreacted Particle Model (SUPM), assuming a constant density and reducing volume of biomass during conversion, and a Uniform Conversion Model (UCM), considering uniform volume and decreasing density of biomass along the conversion process, were compared to experimental measurements of the conversion time. Qualitative agreement was found between the experimental values and the predictions of the conversion time from the simplified models, obtaining in all cases conversion times proportional to the characteristic length of heat transfer of each particle shape. [ABSTRACT FROM AUTHOR]

• An effectiveness factor model (EFM) is developed from MGM for slurry polyolefin reactions. • The concentration gradient inside macroparticles is modeled by an effectiveness factor. • The effect of catalyst characteristics and temperature on the growth of macro- and micro- particles are investigated. • The EFM can produce similar results as the MGM with a much lower computation cost when α i ,mp < 2.0. The multigrain model (MGM) is the most widely used single-particle model, giving a detailed description of phenomena during olefin polymerization. However, the detailed modeling of the diffusion–reaction process inside the catalyst particles requires solving a large number of ordinary differential equations, which is unsuitable for coupling with multiphase CFD tools. That is the reason why the current CFD simulation studies of olefin polymerization reactors rarely consider intraparticle transport. To fill this gap, an effectiveness factor model (EFM) is developed from MGM for slurry olefin polymerizations. It maintains the multilevel framework of MGM and is suitable for use in multiphase CFD simulations. The MGM and EFM are first implemented into OpenFOAM. Moreover, the EFM has been validated by comparison with literature data. Detailed comparisons between MGM and EFM show that the EFM can produce similar results as the MGM with a much lower computation cost for olefin slurry polymerization when α i ,mp < 2.0. [ABSTRACT FROM AUTHOR]

Abstract: Due to its renewable characteristics, biomass is potentially important to energy conversion processes. Fluidized beds are involved in many processes related to energy conversion of biomass. Hence, detailed insight on the hydrodynamics of biomass fluidized beds is crucial for successful energy conversion as well as to better design and scale-up of fluidized bed reactors. The present work focuses on modeling the mixing and segregation behavior of biomass mixtures in a fluidized bed. Different effects, such as mixture composition, particle size, and superficial gas velocity, on the mixing and segregation are simulated and the results are compared to measurements obtained using X-ray computed tomography. Furthermore, side injection of biomass particles into a fluidized bed is also studied and compared with visual observations. A comparison between the numerical simulations and measurements shows good agreement. [Copyright &y& Elsevier]

Abstract: This work focuses on the prediction of the turbulent flow in a three-dimensionial Confined Impinging Jets Reactor with a cylindrical reaction chamber by using Large Eddy Simulation. Three-dimensional unsteady simulations with different sub-grid scale models, numerical schemes and boundary conditions were performed for various flow rates, covering different flow regimes. First, a qualitative analysis of the flow field was carried out and then predictions of the mean and fluctuating velocities were compared with micro Particle Image Velocimetry data. Good agreement was found both for the mean velocity components and the fluctuations. For low to moderate Reynolds numbers the sub-grid scale model was found not to be very relevant, since small scales are of less importance, as long as scalar transport and chemical reaction are not in play. An important finding is the good prediction of the high velocity fluctuations detected in particular at higher Reynolds number due to the natural instability of the system, strongly enforced by the jets unsteadiness. [Copyright &y& Elsevier]

Abstract: A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system was employed to investigate the turbulent mixing in a confined liquid-phase rectangular-wake flow with a Reynolds number based on hydraulic diameter of 37,500 and a Schmidt number of 1250. The simultaneous velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schimdt number. The streamwise and transverse turbulent fluxes were found to be of the same magnitude. The turbulent flux vector was not aligned with the mean concentration gradient. The turbulent Schimdt number was about 0.8. The spatial correlations of turbulent fluxes and concentration fluctuations were evaluated. In the correlation field, there were a positive and a negative vertically oriented elliptical correlation region, which were symmetric around the basis point. The correlation region was a horizontally oriented ellipse with negative values of the correlation coefficient. The correlation field of was also an ellipse with a horizontal major axis. The behavior of large-scale structures in both the velocity and concentration field was studied using linear stochastic estimation with a defined event of concentration fluctuation. Vortex streets were observed in the estimated velocity fields. The streamwise growth of the structure size increased linearly initially but then grew more slowly. [Copyright &y& Elsevier]

Abstract: Rapid precipitation of both organic and inorganic compounds at high supersaturation requires homogenous mixing to control the particle size distribution. We present the design and characterization of a new multi-inlet vortex mixer (MIVM). The four-stream MIVM allows control of both the supersaturation and the final solvent quality by varying stream velocities. The design also enables the separation of reactive components prior to mixing. Finally, the design enables mixing of streams of unequal volumetric flows, which is not possible with alternate confined impinging jet mixing geometries. We characterize the mixing performance of the MIVM using competitive fast reactions (the so-called “Bourne reactions”). Adequate micromixing is obtained with a suitably defined Reynolds number when . The experimental results are compared to computational fluid dynamics (CFD) simulations of the fluid mechanics and parallel reactions in the MIVM. Excellent correspondence is found between the simulation and the experimental results with no adjustable parameters. The CFD simulations provide a powerful tool for the optimization of these complex mixing geometries. [Copyright &y& Elsevier]

Abstract: Liquid-phase turbulent transport in a confined rectangular wake was investigated for a Reynolds number of 37,500 based on bulk velocity and the hydraulic diameter of the test section and a Schmidt number of 1250 using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). The velocity and concentration field data were analyzed for flow statistics such as the mean velocity, Reynolds stresses, turbulent kinetic energy, turbulent dissipation rate, mixture-fraction mean, mixture-fraction variance and one-point composition probability density functions (PDF). Computational fluid dynamics (CFD) models, including a two-layer – turbulence model, a scalar gradient-diffusion model and a scalar dissipation rate model were validated against PIV and PLIF data collected at six downstream locations. Low-Reynolds-number effects on turbulent transport were taken into consideration through the mechanical-to-scalar time-scale ratio. The experimental and computational results were found to be in satisfactory agreement. [Copyright &y& Elsevier]

Abstract: The simulation of soot formation in turbulent diffusion flames is carried out within a CFD code, by coupling kinetics and fluid dynamics computations with the solution of the population balance equation via the Direct Quadrature Method of Moments, a novel and efficient approach based on a quadrature approximation of the size distribution of soot particles. A turbulent non-premixed ethylene–air flame is used as the test case for validation of the model. Simplified kinetic expressions are employed for modelling nucleation, molecular growth and oxidation of particles, along with a Brownian aggregation kernel. A recently proposed approach for modelling the evolution of fractal dimension is used with a monovariate population balance to predict the morphological properties of aggregates. [Copyright &y& Elsevier]