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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]

Improving the efficiency of the production of uniformly sized functional nanoparticles for pharmaceutical and agricultural applications has been a problem of great interest. The macroscale multi-inlet vortex Reactor (macro-MIVR) could potentially be used for this purpose due to its ability to achieve the rapid mixing necessary for the flash nanoprecipitation nanoparticle fabrication technique. In the presented work, the coherent structures, a key contributor to the turbulent mixing, were investigated for the turbulent swirling flow within the MIVR. The two-point spatial correlations of velocity and concentration fluctuations at various basepoints were measured from instantaneous velocity and concentration fields obtained using simultaneous stereoscopic particle image velocimetry and planar laser-induced fluorescence. The basepoint locations were chosen as the middle and at the edge of the partially mixed concentration spiral arms. The correlations were found to be elliptical in shape, inclined, and peaked at the basepoints. A region near the basepoint was positively correlated and was surrounded by negatively correlated regions. Autocorrelations of concentration were also elliptical and curved toward the center of the reactor. The linear stochastic estimation was used to interpret the coherent structure features that would result in the observed spatial correlations. The linear stochastic estimates of the velocity fields were computed directly from the cross correlations of the tangential velocity fluctuations with the concentration fluctuations. The estimated conditional velocity fields revealed obliquely oriented counter-rotating vortical structures that stir the fluid from high-concentration regions to low-concentration regions, and the orientation of these vortical structures depended on the local concentration gradient. [ABSTRACT FROM AUTHOR]

Modeling particle-laden turbulent flows at high volume fractions requires accounting for the coupling between phases. The latter is often a sensitive point, and proper closure of the exchange and production terms due to the presence of particles is not straightforward. In the present work, a Lagrangian probability-density-function model developed for homogeneous cluster-induced turbulence is extended to a channel flow. The key features are consistent two-way coupling and the decomposition of the particle velocity into spatially correlated and uncorrelated components, which is crucial for dense flows and which allows dealing with collisions from a statistical point of view. A numerical scheme for the coupled solution of the stochastic differential equations for the particles and a Reynolds-stress model for the fluid is developed. Tests with tracer particles without two-way coupling are done to assess the validity and the consistency of the numerical scheme. Finally, two sets of numerical simulations with particles with different diameters in a turbulent channel flow at a shear Reynolds of R e τ = 300 are reported. The effect of two-way coupling by varying the mass loading of the dispersed phase in the mass-loading range φ = 0–2 is analyzed, and the results are compared to previous Eulerian–Lagrangian and Eulerian–Eulerian direct-numerical simulation (DNS) studies. Mean velocities and turbulent kinetic energy show good agreement with DNS, especially regarding the trend with respect to mass loading. Consistent with prior work, increased mass loading causes a drastic reduction of turbulent kinetic energy in the range φ = 0–2. [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]

In the context of modeling turbulent scalar mixing using probability density function (PDF) methods, the treatment of molecular mixing is of paramount importance. The conditional moment closure (CMC) offers a high-fidelity description for molecular mixing in nonpremixed flows. Recent work has demonstrated that first-order CMC can be implemented numerically using the moments of the conditioning variable and first-order joint moments of the scalar of interest. When solving the CMC using, for example, quadrature-based moment methods (QBMM), a functional form must be chosen for the conditional scalar dissipation rate (CSDR) of the conditioning variable. In prior work, the CSDR was chosen to produce a β-PDF for the conditioning variable (mixture fraction) at steady state. This choice has the advantage that the system of moment equations used in QBMM-CMC can be written in closed form. In this work, an alternative choice for the CSDR is investigated, namely, the amplitude mapping closure (AMC). With the AMC, the moment equations can be closed using the quadrature method of moments incorporated into a realizable ordinary differential equation solver. Results are compared with the β-CSDR closure for binary, passive scalar mixing in homogeneous single- and disperse-phase turbulent flows. It is also demonstrated that the moment formulation of CMC provides a straightforward method for modeling the effect of differential diffusion in the context of CMC. [ABSTRACT FROM AUTHOR]

Starting from a generalized population balance equation and the Boltzmann–Enskog collision model for hard spheres, a kinetic theory model for polydisperse gas–particle flows is presented. Here, polydispersity results from spherical particles with the same material density but different diameters. The particle size distribution (PSD) of the particles is allowed to evolve in space and time due to physical processes such as mixing. In order to treat a continuous PSD, the particle-phase model is formulated in terms of the moments of the PSD, and velocity moments conditioned on the particle size. Velocity moments up to second order are included, resulting in transport equations for the mass, momentum and granular temperature, all conditioned on the particle size. In the numerical implementation, the PSD is represented using quadrature-based moment methods (QBMM). With QBMM, a continuous PSD can be treated using a relatively small number of moments as compared to class or sectional methods. Here, a realizable numerical algorithm for solving the moment system in a finite-volume code is proposed, valid for dilute systems wherein frictional forces are negligible. The ability of the proposed model to describe polydisperse gas–particle systems is demonstrated using cluster-induced turbulence and riser flow. Unlabelled Image • A novel moment-based polydisperse kinetic theory was proposed. • A realizable numerical algorithm based on QBMM was developed to solve the moment transport equations. • The ability of the proposed model is demonstrated using cluster-induced turbulence and riser flow. [ABSTRACT FROM AUTHOR]

The conditional velocity time averages (⟨Ui|ξ⟩) and conditional mixture fraction time averages (⟨Φ|ωi⟩) were computed based on the Eulerian approach from the experimental data measured in a macroscale multi-inlet vortex chemical reactor. The conditioning events were determined by equally sized intervals of the sample space variable for the mixture fraction (ξ) and the velocity vector (ωi). The experimental data, which consisted of instantaneous velocities and concentration fields for two Reynolds numbers (Re = 3250 and 8125), were acquired using the simultaneous stereoscopic particle image velocimetry (stereo-PIV) and planar laser induced fluorescence techniques. Two mathematical models, the linear approximation and probability density function (PDF) gradient diffusion, were validated by experimental results. The results of the velocity conditioned on the mixture fraction demonstrated that the linear model works well in a low turbulence region away from the reactor center. Near the reactor center, high velocity gradients coupled with low concentration gradients reduce the accuracy of the linear model predictions. Nevertheless, an excellent agreement was found for the conditional events within ±2Φrms (mixture fraction root mean square). Due to lower concentration gradient in the tangential direction, the linear model better predicted the tangential velocity component for all locations investigated. The PDF model with an isotropic turbulent diffusivity performed inadequately for the tangential and axial velocity components. A modified version of the PDF model that considers the three components of the turbulent diffusivity produced a better agreement with the experimental data especially in the spiral arms regions of significant concentration gradients. Furthermore, the mixture fraction conditioned on the velocity vector components showed a more linear behavior near the reactor center, where the PDF of the mixture fraction is a Gaussian distribution. As the concentration gradients became prominent away from the reactor, ⟨Φ|ωi⟩ also deviated from the linear pattern. This was especially remarkable for the mixture fraction conditioned on the tangential velocity. The overall prediction of ⟨Φ|ωi⟩ improves at higher Reynolds number as the fluid mixing is enhanced. [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]

The conditional quadrature method of moments (CQMOM) was introduced by Yuan and Fox (2011) [4] to reconstruct a velocity distribution function (VDF) from a finite set of its integer moments. The reconstructed VDF takes the form of a sum of weighted Dirac delta functions in velocity phase space, and provides a closure for the spatial flux term in the corresponding kinetic equation. The CQMOM closure for the flux leads to a weakly hyperbolic system of moment equations. In subsequent work by Chalons et al. (2010) [8] , the Dirac delta functions were replaced by Gaussian distributions, which make the moment system hyperbolic but at the added cost of dealing with continuous distributions. Here, a hyperbolic version of CQMOM is proposed that uses weighted Dirac delta functions. While the moment set employed for multi-Gaussian and conditional HyQMOM (CHyQMOM) are equivalent, the latter is able to access all of moment space whereas the former cannot (e.g. arbitrary values of the fourth-order velocity moment in 1-D phase space with two nodes). By making use of the properties of CHyQMOM in 2-D phase space, it is possible to control a symmetrical subset of the optimal moments from Fox (2009) [24] . Furthermore, the moment sets for 2-D problems are smaller for CHyQMOM than in the original CQMOM thanks to a judicious choice of the velocity abscissas in phase space. [ABSTRACT FROM AUTHOR]

Many fluid–particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are close-packed as well as very dilute regions where particle–particle collisions are rare. Thus, in order to simulate such fluid–particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in the flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas–particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid–particle flows. [ABSTRACT FROM AUTHOR]

The dynamics of cavitation bubbles are important in many flows, but their small sizes and high number densities often preclude direct numerical simulation. We present a computational model that averages their effect on the flow over larger spatiotemporal scales. The model is based on solving a generalized population balance equation (PBE) for nonlinear bubble dynamics and explicitly represents the evolving probability density of bubble radii and radial velocities. Conditional quadrature-based moment methods (QBMMs) are adapted to solve this PBE. A one-way-coupled bubble dynamics problem demonstrates the efficacy of different QBMMs for the evolving bubble statistics. Results show that enforcing hyperbolicity during moment inversion (CHyQMOM) provides comparable model-form accuracy to the traditional conditional method of moments and decreases computational costs by about ten times for a broad range of test cases. The CHyQMOM-based computational model is implemented in MFC, an open-source multi-phase and high-order-accurate flow solver. We assess the effect of the model and its parameters on a two-way coupled bubble screen flow problem. • A fully-coupled sub-grid method for flowing cavitating bubbles. • Method for representing, for the first time, statistics in the bubble dynamics. • State-of-the-art moment methods: CHyQMOM, CQMOM, and Gaussian tested and analyzed. • For the statistics of cavitating bubbles, CHyQMOM outperforms CQMOM and Gaussian. • Method implemented in open-solver MFC and tested on fully-coupled bubbly flows. [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]

The generation of nanostructured particles in high-temperature flames is important both for the control of emissions from combustion devices and for the synthesis of high-value chemicals for a variety of applications. The physiochemical processes that lead to the production of fine particles in turbulent flames are highly sensitive to the flow physics and, in particular, the history of thermochemical compositions and turbulent features they encounter. Consequently, it is possible to change the characteristic size, structure, composition, and yield of the fine particles by altering the flow configuration. This review describes the complex multiscale interactions among turbulent fluid flow, gas-phase chemical reactions, and solid-phase particle evolution. The focus is on modeling the generation of soot particles, an unwanted pollutant from automobile and aircraft engines, as well as metal oxides, a class of high-value chemicals sought for specialized applications, including emissions control. Issues arising due to the numerical methods used to approximate the particle number density function, the modeling of turbulence-chemistry interactions, and model validation are also discussed. [ABSTRACT FROM AUTHOR]

There was also an error in Table V. Table V appears correct below: TABLE V. First-order temporal discretization (Euler scheme). Publisher's Note: "A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime" [Phys. [Extracted from the article]

Flame synthesis represents a viable technique for large-scale production of titanium dioxide (TiO2) nanoparticles. A key ingredient in the modeling of this process is the description of the chemical kinetics, which include Ti oxidation, hydrocarbon fuel combustion, and chlorination. While detailed chemical mechanisms have been developed for predicting TiO2 nanoparticle properties by West et al. (e.g., Combust. Flame 2009, 156, 1764), their use in turbulent reacting flow simulations is limited to very simple configurations or requires significant modeling assumptions to bring their computational cost down to an acceptable level. In this work, a reduced kinetic scheme describing the oxidation of TiCl4 in a methane flame is derived from and validated against the predictions of a detailed mechanism from the literature. The reduction procedure uses graph-based methods for unimportant kinetic pathways elimination and quasi-steady-state species selection. Reduction targets are chosen in accordance with previous modeling results that showed the importance of temperature and overall concentration of titanium-containing species in both nucleation and surface growth rates. The resulting reduced scheme is thoroughly evaluated over a wide range of conditions relevant to flame-based synthesis, and the capability of the reduced model to adequately capture the process dynamics at a much lower computational cost is demonstrated. [ABSTRACT FROM AUTHOR]

The design and scale-up of fluidized-bed reactors is an important step to commercialize viable conversion pathways (such as fast pyrolysis) for biomass into hydrocarbon intermediates and fuels that lead to "drop-in" replacements for jet fuel, diesel, gasoline, and other petroleum-based products. Detailed information about the particle size distribution (PSD) and particle density evolution throughout the fluidized-bed reactor can play a critical role in determining in situ catalyst selectivity, intermediate components, and reactor performance. This work presents an Euler-Euler computational fluid dynamics (CFD) model applied to biomass thermochemical conversion for use in fluidized-bed reactor simulations. The complex chemical and physical processes of particle devolatilization and their interaction with the reacting gas environment are described within a multifluid framework based on the kinetic theory of granular flows. The direct quadrature method of moments is used to describe the biomass PSD. Continuously varying particle density due to mass evolving to the gas flow was applied to describe the evolution of particles' physical properties. The global kinetic model is based on superimposed hemicellulose, cellulose, and lignin reactants. The calculations of the stiff chemical source terms and convection are decoupled using a time-splitting method. The CFD model is applied to simulate the fast pyrolysis of red oak in a laboratory-scale fluidized-bed reactor and validated against experimental data. The simulated product yields at the reactor outlet are presented and compared with monodisperse results and the experimental measurements. It is demonstrated that our current CFD model is able to predict in detail the dynamic particle processes, mixing and segregation, char particle elutriation, and produced gas composition at the reactor outlet needed to optimize the reactor operating conditions. [ABSTRACT FROM AUTHOR]

A technique for visualizing and quantifying reactive mixing for laminar and turbulent flow in a microscale chemical reactor using confocal-based microscopic laser induced fluorescence (confocal μ-LIF) was demonstrated in a microscale multi-inlet vortex nanoprecipitation reactor. Unlike passive scalar μ-LIF, the reactive μ-LIF technique is able to visualize and quantify micromixing effects. The confocal imaging results indicated that the flow in the reactor was laminar and steady for inlet Reynolds numbers of 10, 53, and 93. Mixing and reaction were incomplete at each of these Reynolds numbers. The results also suggested that although mixing by diffusion was enhanced near the midplane of the reactor at Rej = 53 and 93 due to very thin bands of acidic and basic fluid forming as the fluid spiraled towards the center of the reactor, near the top, and bottom walls of the reactor, the lower velocities due to fluid friction with the walls hindered the formation of these thin bands, and, thus, resulted in large regions of unmixed and unreacted fluid. At Rej = 240, the flow was turbulent and unsteady. The mixing and reaction processes were still found to be incomplete even at this highest Reynolds number. At the reactor midplane, the flow images at Rej = 240 showed unmixed base fluid near the center of the reactor, suggesting that just as in the Rej = 53 and 93 cases, lower velocities near the top and bottom walls of the reactor hinder the mixing and rection of the acidic and basic streams. Ensemble averages of line-scan profiles for the Rej = 240 were then calculated to provide statistical quantification of the microscale mixing in the reactor. These results further demonstrate that even at this highest Reynolds number investigated, mixing and reaction are incomplete. Visualization and quantification of micromixing using this reactive μ-LIF technique can prove useful in the validation of computational fluid dynamics models of micromixing within microscale chemical reactors. [ABSTRACT FROM AUTHOR]

Aggregation of colloidal particles under shear is studied in model systems using a Langevin dynamics model with an improved interparticle interaction potential. In the absence of shear, aggregates that form are characterized by compact structure at small scales and ramified structure at larger scales. This confirms the structural crossover mechanism previously suggested by Sorensen and coworkers, that colloidal aggregation occurs due to monomer addition at small scales and due to cluster-cluster aggregation at large scales. The fractal dimension of nonsheared aggregates is scale-dependent. Smaller aggregates have a higher fractal dimension than larger ones, but the radius of gyration where this crossover occurs is independent of potential well depth for sufficiently deep wells. When these aggregates are subjected to shear they become anisotropic and form extended cigar-like structures. The size of sheared anisotropic aggregates in the direction perpendicular to the shear flow is limited by shear-induced breakage because the shear force dominates interparticle attraction for sufficiently large aggregates. Anisotropic aggregates are not completely characterized by a single radius of gyration, but rather by an inertia ellipsoid. Consequently the fractal dimension is no longer an adequate metric to properly characterize them, and to identify changes in their structure from their nonsheared isotropic counterparts. We introduce a new compactness-anisotropy analysis that characterizes the structure of anisotropic aggregates and allows us to distinguish between aggregates from sheared and nonsheared systems. Finally, using the ratio of interparticle force to the shear force fpot,sh we are able to characterize different outcomes of sheared aggregation as a function of dimensionless well depth and Péclet number. [ABSTRACT FROM AUTHOR]

A coarse-graining (CG) approach is developed to infer mesoscale interaction potentials in aggregating systems, resulting in an improved potential of mean force for Langevin dynamics (LD) and Brownian dynamics (BD) simulations. Starting from the evolution equation for the solute pair correlation function, this semi-analytical CG approach identifies accurate modeling of the relative acceleration between solute particles in a solvent bath as a reliable route to predicting the time-evolving structural properties of nonequilibrium aggregating systems. Noting that the solute–solvent pair correlation function attains a steady state rapidly as compared to characteristic aggregation time scales, this CG approach derives the effective relative acceleration between a pair of solute particles in the presence of this steady solute–solvent pair correlation by formally integrating the solvent force on each solute particle. This results in an improved potential of mean force that explicitly depends on the solute–solute and solute–solvent pair potentials, with the capability of representing both solvophilic and solvophobic interactions that give rise to solvation forces. This approach overcomes the difficulty in specifying the LD/BD potential of mean force in aggregating systems where the solute pair correlation function evolves in time, and the Kirkwood formula U(r) = −kBT ln g(r) that is applicable in equilibrium diffusion problems cannot be used. LD simulations are compared to molecular dynamics (MD) simulations for a model colloidal system interacting with Lennard-Jones pair potentials to develop and validate the improved potential of mean force. LD simulations using the improved potential of mean force predict a solute pair correlation function that is in excellent match with MD in all aggregation regimes, whereas using the unmodified MD solute–solute pair potential in LD results in a poor match in the reaction-limited aggregation regime. The improved potential also dramatically improves the predicted extent of aggregation and evolution of cluster size distributions that exhibit the same self-similar scaling found in MD. This technique of coarse-graining MD potentials to obtain an improved potential of mean force can be applied in a general multiscale framework for nonequilibrium systems where the evolution of aggregate structure is important. [ABSTRACT FROM AUTHOR]

Multiphase flows occurring in nature and in technological applications are often turbulent. The large range of length scales and timescales in turbulent multiphase flows makes direct numerical simulation of the microscale governing equations intractable for many applications. In this article we review a systematic approach for developing large-eddy-simulation (LES) tools for dispersed multiphase flows starting from the microscale model. A key intermediate step is the mesoscopic model for the dispersed phase, formulated in terms of kinetic equations, that contains the physical models for the flow. Owing to the phase-space variables, direct solution of the mesoscopic model is usually intractable, and additional mathematical approximations are introduced to arrive at a macroscopic model. We show that self-conditioned LES models can be derived for both the mesoscopic and macroscopic models, but the former is preferred to ensure consistency and physical accuracy. The principal difficulties and open challenges in closing the LES model equations are highlighted. [ABSTRACT FROM AUTHOR]

Electrostatic charges in gas-solid fluidized beds are known to influence the bed dynamics, bubble shape and size, particle agglomeration, segregation and entrainment. In practice, accumulation of electrostatic charges in fluidized beds can lead to operational issues. The present work focuses on the modeling of electrostatics in gas-solid fluidized beds. The particles are assumed to carry a prescribed size-dependent charge, and charge generation and dissipation are not modeled. To consider the effects of bi-polar charging the polarity of the charge carried by fine particles is taken opposite to that of coarse particles. The magnitude of particle charges is approximated to realistic charges reported in the literature. The principal objective is to develop a multi-fluid Euler-Euler model that can describe electrostatic forces on charged particles in gas-solid fluidized beds. The multi-fluid model is solved in a commercial CFD code (ANSYS Fluent 6.3) and uses the kinetic theory of granular flow for calculating solids pressure and viscosity. The electric field, generated by the presence of charged particles, is solved for at every time step in the time-dependent simulation. The electrostatic forces, proportional to the gradient of the electric field and the particle charge, lead to charge-dependent forces on the particles. The electrostatic model has been developed and applied to a two-dimensional fluidized bed. Charge-dependent segregation is found to vary with the polarity and magnitude of the charge on the solid phase as a function of the particle size. [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]

A model study has been conducted for Flash Nanoprecipitation(FNP)a novel approach to produce functional nanoparticles. A population balance equation with the FNP kinetics has been integrated into a computational fluid dynamics (CFD) simulation of a custom-designed microscale multi-inlet vortex reactor (MIVR) to yield conditions comparable to the real experimental settings. In coping with the complicated aggregation model in the CFD code, a new numerical approach, the conditional quadrature method of moments (CQMOM), has been proposed, which is capable of solving the multivariate system efficiently and accurately. It is shown that the FNP process is highly influenced by mixing effects in the microreactor, and thus coupling CFD with the kinetics model is essential in obtaining valid comparisons with 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]

Attempts to combine the generalized IEM (GIEM) model with the mapping closure to model the molecular mixing terms in the probability distribution function balance equation. Assumption of a linear relationship between the rates of change of the reactive scalars and an inert scalar during the mixing step.

Droplet dispersion in liquid–liquid systems is a crucial step in many unit operations throughout the chemical, food, and pharmaceutic industries, where improper operation causes billions of dollars of loss annually. A theoretical background for the description of droplet breakup has been established, but many assumptions are still unconfirmed by experimental observations. In this investigation, a von Kármán swirling flow device was used to produce homogeneous, low-intensity turbulence suitable for carrying out droplet breakage experiments using optical image analysis. Individual droplets of known, adjustable, and repeatable sizes were introduced into an isotropic turbulent flow field providing novel control over two of the most important factors impacting droplet breakage: turbulence dissipation rate and parent droplet size. Introducing droplets one at a time, large data sets were gathered using canola, safflower, and sesame oils for the droplet phase and water as the continuous phase. Automated image analysis was used to determine breakage time, breakage probability, and child droplet size distribution for various turbulence intensities. Breakage time and breakage probability were observed to increase with increasing parent droplet size, consistent with the classic and widely used Coulaloglou–Tavlarides breakage model (C–T model). The shape of the child drop size distribution function was found to depend upon the size of the parent droplet. [ABSTRACT FROM AUTHOR]

Mass production of functional nanoparticles may be realized through flash nanoprecipiation in microscale reactors such as the multi-inlet vortex reactor (MIVR). A comprehensive understanding of mixing in the MIVR is required for process control and reactor design. Mixing in the MIVR is studied using a technique coupling laser induced fluorescence with confocal laser scanning microscopy. It is shown to provide meaningful qualitative and statistical data of the scalar field for analysis and comparison with numerical simulations. Data were collected for four flow rates, showing that mixing is incomplete even at the highest flow rate. [ABSTRACT FROM AUTHOR]

• 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]

Abstract: Simultaneous measurements of velocity and concentration using stereoscopic particle image velocimetry (stereo-PIV) and planar laser-induced fluorescence (PLIF) were used to investigate the mixing performance of a scaled-up multi-inlet vortex reactor (MIVR). Data were collected in three measurement planes located at different heights from the reactor bottom (¼, ½, and ¾ of the reactor height) for Reynolds numbers of 3250 and 8125 based on the reactor inlet velocity and hydraulic diameter. The collected data were analyzed to determine turbulent flow statistics such as turbulent viscosity, turbulent diffusivity, and turbulent Schmidt number. When analyzed across 16 different azimuth angles and radial positions (r) normalized by the reactor radius (Ro), the turbulent viscosity was found to be nearly axisymmetric. In the free-vortex region (r/Ro > 0.2), the turbulent viscosity results were nearly constant. Near the center of the reactor in the forced-vortex region (r/Ro < 0.1), the turbulent viscosity significantly increased, with peak values occurring near the center. The turbulent viscosity and Reynolds shear stress were highest near the reactor exit at the ¾ plane. The dominance of high turbulent fluxes and low concentration gradients near the reactor center led to high turbulent diffusivity. Away from the center, the turbulent diffusivity was reduced because of large concentration gradients and low turbulence intensity in the spiral arm region. The turbulent Schmidt numbers were also found to correlate with concentration gradients. The turbulent Schmidt number values were found to vary from 0.1 to 1.2. The highest spatial variation in Sct was observed in the spiral arms region, where the concentration gradients are also the highest. This spatial variation in Schmidt number contrasts with the common assumption of constant Sct in Reynolds-averaged CFD models.Graphical abstract: A typical stereo-PIV/PLIF simultaneous instantaneous measurement for Re = 8125. The color and vectors represent the instantaneous mixture fraction and in-plane velocity field, respectively. (a) ¼ Plane. (b) ½ Plane. (c) ¾ Plane. [ABSTRACT FROM AUTHOR]

Velocity fluctuations in the carrier phase and dispersed phase of a dispersed multiphase flow are studied using particle-resolved direct numerical simulation. The simulations correspond to a statistically homogeneous problem with an imposed mean pressure gradient and are presented for Rem=20 and a wide range of dispersed phase volume fractions 0.1≤ϕ≤0.4 and density ratios of the dispersed phase to the carrier phase 0.001≤ρp/ρf≤1000. The velocity fluctuations in the fluid and dispersed phase at the statistically stationary state are quantified by the turbulent kinetic energy (TKE) and granular temperature, respectively. It is found that the granular temperature increases with a decrease in the density ratio and then reaches an asymptotic value. The qualitative trend of the behavior is explained by the added mass effect, but the value of the coefficient that yields quantitative agreement is non-physical. It is also shown that the TKE has a similar dependence on the density ratio for all volume fractions studied here other than ϕ=0.1. The anomalous behavior for ϕ=0.1 is hypothesized to arise from the interaction of particle wakes at higher volume fractions. The study of mixture kinetic energy for different cases indicates that low-density ratio cases are less efficient in extracting energy from mean flow to fluctuations. [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]

In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity. The exact Reynoldsaveraged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian-Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption. [ABSTRACT FROM AUTHOR]

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian-Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocity fluctuations into spatially correlated and uncorrelated components, used to define the components of the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, "Numerical study of collisional particle dynamics in cluster-induced turbulence," J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocity fluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics. [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]

The microscale multi-inlet vortex reactor (MIVR) has been developed for use in flash nanoprecipitation, a technique to generate functional nanoparticles. A scaled-up MIVR is motivated by the desire for a higher output of nanoparticles than the microscale reactor can provide. As the first step of this scaling process, the flow characteristics in a macro-scale MIVR have been investigated by stereoscopic particle image velocimetry. The studied Reynolds numbers based on the inlet geometry range from 3290 to 8225, resulting in a turbulent swirling flow within the reactor. The flow in the mixing chamber is found to be unstable with a wandering vortex center. The vortex wandering is constrained to a small area near the center of the reactor and has little effect on the mean velocity field. However, the measured turbulence kinetic energy and Reynolds stresses are found to be sensitive to the vortex wandering. The flow characteristics of the macro-scale MIVR are compared with the microscale MIVR in terms of swirl ratio and micromixing time. It is found that the swirl ratio and micromixing time of the flow increases as the MIVR is scaled up, indicating a flow with stronger swirl yet less mixing effectiveness in the scaled-up reactor. [ABSTRACT FROM AUTHOR]

Highlights: [•] A large eddy simulation is performed on a turbulent confined wake flow. [•] Presimulations were performed to optimize inlet conditions and subgrid model. [•] The simulation is validated against particle image velocimetry data. [•] Detailed comparisons of one-point statistics as well as spatial correlations were made. [•] With carefully selected inlet conditions, the simulation showed very good agreement with the experiment. [Copyright &y& Elsevier]

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]

The microscale multi-inlet vortex reactor (MIVR) is designed for use in Flash NanoPrecipitation (FNP), a promising technique for producing nanoparticles within small particle size distribution. Fluid mixing is crucial in the FNP process, and due to mixing's strong dependence upon fluid kinematics, investigating velocity and turbulence within the reactor is crucial to optimizing reactor design. To this end, microscopic particle image velocimetry has been used to investigate flow within the MIVR. Three Reynolds numbers are studied, namely, Rej = 53, 93 and 240. At Rej = 53, the flow is laminar and steady. Due to the strong viscous effects at this Reynolds number, distinct flow patterns are observed at different distances from the reactor top and bottom walls. The viscous effects also retard the tangential motions within the reactor, resulting in a weaker vortex than appears at the higher Reynolds numbers. As the Reynolds number is increased to 93, the flow becomes more homogeneous over the depth of the reactor due to weaker viscous effects, yet the flow is still steady. The diminishing effects of viscosity also result in a stronger vortex. At the highest Reynolds number investigated, the flow is turbulent. Turbulent statistics including tangential and radial velocity fluctuations and Reynolds shear stresses are analyzed for this case in addition to the mean velocity field. The tangential motions of the flow are strongest at Rej = 240. Both the tangential and radial velocity fluctuations increase as the flow spirals toward the center of the reactor. The magnitudes of the tangential and radial velocity fluctuations are similar, suggesting that the turbulence is locally isotropic. [ABSTRACT FROM AUTHOR]

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: Gas-particle and other dispersed-phase flows can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). However, computing the dispersed velocity is a challenging task due to the large number of independent variables. A level set approach for computing dilute non-collisional fluid-particle flows is presented. We will consider the sprays governed by the Williams kinetic equation subject to initial distributions away from equilibrium of the form . The dispersed velocity is described as the zero level set of a smooth function, which satisfies a transport equation. This together with the density weight recovers the particle distribution at any time. Moments of any desired order can be evaluated by a quadrature formula involving the level set function and the density weight. It is shown that the method can successfully handle highly non-equilibrium flows (e.g. impinging particle jets, jet crossing, particle rebound off walls, finite Stokes number flows). [ABSTRACT FROM AUTHOR]

Experimental results for conditional statistics in a confined turbulent wake were compared to the linear model and the transported probability density function (PDF) model for predicting the velocity conditioned on scalar mixture fraction and to a linear model for predicting the scalar mixture fraction conditioned on velocity. For velocity conditioned on scalar mixture fraction, the linear model was found to accurately predict the conditional transverse velocity, but for the conditional streamwise velocity, agreement between the experiments and the linear model was poor. The transverse conditional velocity was accurately predicted by the transported PDF model, but for the streamwise conditional velocity, a modified transported PDF model that incorporated two components of the scalar diffusivity tensor had to be used. Finally, it was found that a linear model for predicting the fluctuating scalar conditioned on velocity performed poorly due to the strongly non-Gaussian scalar PDF at the downstream locations investigated. [ABSTRACT FROM AUTHOR]

Abstract: Mean-field population balance equations are used to describe the evolution of particle size distributions in a wide variety of systems undergoing simultaneous aggregation and breakage. In this paper we develop a population balance that includes aggregation combined with collision-induced particle breakage for arbitrary fragment distribution functions, provided that this distribution function depends only on the total mass of the particles undergoing a collision. We then develop a specific distribution function for arbitrary two-body collisions by postulating that each collision produces a transition-state aggregate having the morphology of a linear polymer. The behavior of the resulting equation is then analyzed for the case in which the collision kernel is a constant, and partial analytical solutions are derived and compared to corresponding Monte-Carlo simulation results. The computer simulations are then used to validate a proposed scaling law for the steady-state particle size distribution. Lastly, the behavior of the aggregation with collision-induced-breakage population balance equation is compared and contrasted with the behavior of an analogous aggregation with linear-breakage population balance equation. [Copyright &y& Elsevier]

Reactive flow simulations using large-eddy simulations (LES) require modelling of sub-filter fluctuations. Although conserved scalars like mixture fraction can be represented using a beta-function, the reactive scalar probability density function (PDF) does not follow an universal shape. A one-point one-time joint composition PDF transport equation can be used to describe the evolution of the scalar PDF. The high-dimensional nature of this PDF transport equation requires the use of a statistical ensemble of notional particles and is directly coupled to the LES flow solver. However, the large grid sizes used in LES simulations will make such Lagrangian simulations computationally intractable. Here we propose the use of a Eulerian version of the transported-PDF scheme for simulating turbulent reactive flows. The direct quadrature method of moments (DQMOM) uses scalar-type equations with appropriate source terms to evolve the sub-filter PDF in terms of a finite number of delta-functions. Each delta-peak is characterized by a location and weight that are obtained from individual transport equations. To illustrate the feasibility of the scheme, we compare the model against a particle-based Lagrangian scheme and a presumed PDF model for the evolution of the mixture fraction PDF. All these models are applied to an experimental bluff-body flame and the simulated scalar and flow fields are compared with experimental data. The DQMOM model results show good agreement with the experimental data as well as the other sub-filter models used. [ABSTRACT FROM AUTHOR]