Search

An open-source CFD software OpenFOAM® is used to simulate two multiphase stirred-tank reactors relevant to industrial processes such as slurry polymerization and fuel production. Gas-liquid simulations are first performed in a single-impeller stirred-tank reactor, studied experimentally by Ford, J. J., T. J. Heindel, T. C. Jensen, and J. B. Drake. 2008. “X-Ray Computed Tomography of a Gas-Sparged Stirred-Tank Reactor.” Chemical Engineering Science 63: 2075–85. Three impeller rotation speeds (200, 350 and 700 rpm) with three different bubble diameters (0.5, 1.5 and 2.5 mm) are investigated. Flow patterns compared qualitatively to those from experiments. Compared to the experimental data, the simulations are in relatively good agreement for gas holdup in the reactor. The second multiphase system is a multi-impeller stirred-tank reactor, studied experimentally by Shewale, S. D., and A. B. Pandit. 2006. “Studies in Multiple Impeller Agitated Gas-Liquid Contractors.” Chemical Engineering Science 61: 486–504. Gas-liquid simulations are performed at two impeller rotation speeds (3.75 and 5.08 RPS). The simulated flow patterns agree with published pictures from the experiments. Gas-liquid-solid simulations of the multi-impeller stirred-tank reactor are also carried out at impeller rotation speed 5.08 RPS. The addition of solid particles with a volume fraction characteristic of slurry reactors changes the flow pattern significantly. The bottom Rushton turbine becomes flooded, while the upper pitched-blade downflow turbines present a radial-pumping flow pattern instead of down-pumping. Nonetheless, the solid phase has a similar flow pattern to the liquid phase, indicating that the particles modify the effective density of the fluid.

Two solution algorithms are developed for the conditional moment closure (CMC) using quadrature-based moment methods (QBMM). Their primary purpose is to eliminate the necessity of the additional grid for the conditioning variable (e.g., mixture fraction). As in almost every probability-density-function (PDF)-based description, the main technical hurdle is the solution of the molecular-mixing term. Here the focus is on solving this term coupled with chemistry, as opposed to spatial transport. In the first algorithm (referred to as SA-CMC), this is done by semi-analytically solving an equation for the deviation variable of the conditional scalar mean in terms of Jacobi polynomials. The mixture-fraction space is represented by the Gauss–Lobatto quadrature rule and a β-PDF. In the second algorithm (referred to as QBMM-CMC), a closed set of differential equations is written for the joint moments of a scalar and the mixture fraction, thereby eliminating the need to assume a form for the mixture-fraction PDF. Both solution algorithms are tested for multi-step H2 combustion, and the expected results are achieved with at most six quadrature nodes. Since in the proposed algorithms the scalar mean is ensured to be constant during molecular mixing, it is further concluded that the proposed algorithms are accurate, computationally cost-effective, and straightforward alternatives for traditional CMC solution methods.

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.

The Eulerian–Eulerian two-fluid model is widely used for computational fluid dynamics simulations of gas–solid flows. For non-isothermal flows, the averaged conservation equations solved in the two-fluid model require closures for drag, gas–solid heat transfer, pseudo-turbulent velocity fluctuations and the pseudo-turbulent heat flux (PTHF). However, the pseudo-turbulence terms are usually neglected in two-fluid simulations due to the lack of accurate correlations. With the increase in computational power, closures for these terms are now available from particle-resolved direct-numerical simulation (PR-DNS). Here, the PTHF closure as well as the heat-transfer closure (i.e., the Nusselt number) extracted from PR-DNS are implemented in the two-fluid thermal energy equation in OpenFOAM. The implementation is validated by comparing the simulation results with the PR-DNS data for the temperature profiles. Based on the analysis of the thermal energy budget, the PTHF can have a significant contribution and neglecting it can lead to large errors.

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.

We present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posing fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent Eulerian statistics remains a challenge for all methods. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5396–5412, 2017

International audience; To assist industrial engine design, 3D simulations are increasingly used as they allow evaluation of a wide range of engine configurations and operating conditions and bring a comprehension of the underlying physics comple-mentary to experiments. While the gaseous flow description has reached a certain level of maturity, the multiphase flow description involving the liquid jet fuel injected into the chamber still faces some major challenges. There is a pressing need for a spray model that is time efficient and accurately describes the fuel-particle cloud dynamics downstream of the injector, which is an essential prerequisite for predictive combustion simulations. Due to the highly unsteady nature of the flow following the high-pressure injection process and the complexity of the flow regimes from separated/dense compressible phases to fully developed turbulent spray with evaporating droplets, Eulerian-Eulerian descriptions of two-phase flows are seen as very promising approaches towards realistic and predictive simulations of the mixing process. However they require some effort in terms of physical modeling and numerical analysis related to the more complex mathematical structure of the system of equations and to the unclosed terms appearing in space/time-average equations. Among the various challenges faced, one critical as-pect is to capture spray polydispersity in this framework. A review of recent developments that have permitted key advances in the spray modeling community is proposed in this paper. It is divided into four parts. First, an introduction to automotive spray modeling is provided. Then the formalisms for the description of the disperse region of an engine spray are presented with particular emphasis on the pros and cons of classical Lagrangian par-ticle methods versus Eulerian approaches. The third part presents the motivation for and the recent developments of Eulerian high-order moment methods for size polydispersion. Finally, the extension to fully two-way coupled interactions with the gas phase and the implementation of such methods for variable-geometry applications in CFD codes is described in the fourth part. Using realistic direct injection conditions computed with the IFP-C3D solver, the application and efficiency of Eulerian approaches is illustrated.

The quadrature-based semi-analytical solution for the conditional moment closure (SA-CMC) given in (A. D. Ilgun, A. Passalacqua, and R. O. Fox, “A quadrature-based conditional moment closure for mixing-sensitive reactions,” Chem. Eng. Sci., 226, 2020) eliminates the additional conditioning-space discretization in CMC applications by assuming that the mixture-fraction PDF is well represented by a β-PDF. A Gaussian quadrature provides the mixture-fraction abscissae, and the conditional scalar mean is expressed in terms of Jacobi polynomials. Here, by preserving the computational efficiency of SA-CMC, a novel quadrature-based moment method (QBMM-CMC) is developed for CMC applications, which does not assume the form of the mixture-fraction PDF. Remarkably, by solving the closed forms for the micromixing terms from CMC, exact expressions result for the mixture-fraction moments of any order. Thus, QBMM-CMC covers cases where the mixture-fraction PDF cannot be well represented by a β-PDF and can be applied to disperse multiphase flows with mass transfer (e.g., droplet evaporation). For single-phase and multiphase pure-mixing problems, the QBMM-CMC mixture-fraction moments are observed to deviate from the β-PDF. For single-phase mixing with and without dispersed-phase mass transfer, QBMM-CMC predictions for mixing-sensitive competitive-consecutive and parallel reactions are investigated parametrically.

Turbulent mixing in the confined swirling flow of a multi-inlet vortex reactor (MIVR) was investigated using planar laser induced fluorescence (PLIF). The investigated Reynolds numbers based on the bulk inlet velocity ranged from 3290 to 8225, and the Schmidt number of the passive scalar was 1250. Measurements were taken in the MIVR at three different heights (¼, ½, and ¾ planes). The mixing characteristics and performance of the MIVR were investigated using instantaneous PLIF fields and pointwise statistics such as mixture fraction mean, variance, and one-point concentration probability density function. It was found that the scalar is stretched along velocity streamlines, forming a spiral mixing pattern in the free-vortex region. In the forced-vortex region, mixing intensifies as the turbulent fluctuations increase significantly there. The mixing mechanisms in the MIVR were revealed by identifying specific segregation zones. At Re = 8225 the mixing in the free-vortex region was dominated by both large-scale structures and turbulent diffusion, while in the forced-vortex region mixing is dominated by turbulent diffusion. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2409–2419, 2017

The multi-inlet vortex reactor (MIVR) is used for flash nanoprecipitation to manufacture functional nanoparticles. A validated computational fluid dynamics model is needed for the design, scale-up, and optimization of the MIVR. Unfortunately, available Reynolds-averaged Navier-Stokes methods are unable to accurately model the highly swirling flow in the MIVR. Large-eddy simulations (LES) are also problematic, as excessively fine grids are required to accurately model this flow. These dilemmas led to the application of the dynamic delayed detached eddy simulation (DDES) method to the MIVR. In the dynamic DDES model, the eddy viscosity has a form similar to the Smagorinsky sub-grid viscosity in LES, which allows the implementation of a dynamic procedure to determine its model coefficient. Simulation results using the dynamic DDES model are found to match well with experimental data in terms of mean velocity and turbulence intensity, suggesting that the dynamic DDES model is a good option for modeling the turbulent swirling flow in the MIVR. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2570–2578, 2016

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.

A novel algorithm consisting of a quadrature-based semi-analytical solution to the conditional moment closure (CMC) is developed for mixing-sensitive reactions in turbulent flows. When applying the proposed algorithm, the additional grid in mixture-fraction phase space used in CMC codes is eliminated, and at most ten quadrature nodes are needed to model mixing-sensitive turbulent reacting flows. In this work, the mixture-fraction probability density function (PDF) is assumed to be a β-PDF, which is the weight function for the Gauss-Jacobi quadrature rule. The conditional moments of reacting species are determined from unconditional moments that are first order with respect to the species and higher order with respect to mixture fraction. Here, the focus is on the efficient treatment of the molecular-mixing step by using a semi-analytical solution in the form of a Jacobi polynomial expansion. The application of the algorithm is demonstrated considering mixing-sensitive competitive-consecutive and parallel reactions in a statistically homogeneous chemical reactor.

Buoyancy driven turbulence due to heterogeneous bubble swarms are typically encountered in bubble columns operating in the dense heterogeneous regime. The integral scales of such turbulence are much larger than single bubble produced pseudo-turbulence. Accurate computational fluid dynamics predictions in this regime require correctly formulated anisotropic turbulence models with closures accounting for buoyancy driven turbulence effects. In the current study, a Reynolds-stress transport equation is formulated for bubbly flows from a hyperbolic two-fluid model by Reynolds averaging. The unclosed terms generated due to Reynolds averaging are quantified using high grid resolution, two-fluid simulations for bubbly flows in a periodic domain. The relative importance of the unclosed terms are discussed from a modeling stand point. The turbulence statistics, length and time scales, energy spectra, mean momentum budget and the Reynolds stress budget are analyzed for different bubble void fractions. The results show that the unclosed terms generated due to the averaging of Drag is significant in the liquid phase Reynolds Stress budget. Moreover, the unclosed terms generated due to the averaging of Drag, Virtual mass and Buoyancy are significant in the gas phase Reynolds Stress budget.

Conference: 9th International Symposium on Mixing in Industrial Processes Location: Birmingham, Angleterre Date: 2017/06/25-28; International audience; Cell growth in a chemostat is a well-documented research topic. How cells uptake the avail-able substrate to gain weight and engage cell division is not generally taken into account inthe modelling bioreactors. In fact, the growth rate is related to a population doubling timewhereas the microorganisms’ growth in mass is due to the mass transfer of substrates fromthe liquid phase to the biotic phase. Clearly, growth in mass precedes growth in number.Similarly, the transport of substrates down to the cell scale precedes the mass transfer. Thisarticle’s main feature is a two-dimensional population balance model that allows to uncou-ple growth in mass and growth in number when the equilibrium between a cell populationand its environment is disrupted. The cell length and the rate of anabolism are chosen asinternal variables. It is proved that the hypothesis “growth in number = growth in mass” isvalid at steady-state or in exponential growth only. The glucose uptake is assumed drivenby two transport systems with a different affinity constant for the substrate. This combina-tion of two regulated uptake systems operating in parallel explains a 3-fold increase in theuptake following a glucose pulse, but can also predict substrate uptake rates higher thanthe maximal batch value as observed in some experiments. These features are obtainedby considering carbon fluxes in the formulation of regulation principles for uptake dynam-ics. The population balance’s implementation in a multi-compartment reactor is a naturalprospective work and allows extensions to industrial processes.

The extended quadrature method of moments (EQMOM) for the solution of population balance equations (PBE) is implemented in the open-source computational fluid dynamic (CFD) toolbox OpenFOAM as part of the OpenQBMM project. The moment inversion procedure was designed (Nguyen et al., 2016) to maximize the number of conserved moments in the transported moment set. The algorithm is implemented in a general structure to allow the addition of other kernel density functions defined on R + , and arbitrary kernels to describe physical phenomena involved in the evolution of the number density function. The implementation is verified with a set of zero-dimensional cases involving aggregation and breakage problems. Comparison to the rigorous solution of the PBE provides validation for these cases. The coupling of the EQMOM procedure with a CFD solver to address aggregation and breakage problems of non-inertial particles is validated against experimental measurements in a Taylor-Couette reactor from the literature.

An analytical framework for calculating the filtration efficiency of polydisperse aerosols in a granular bed is developed for cases where inertial impaction and interception are the principal filtration mechanisms. This framework is used to develop a model for the polydisperse single-collector efficiency from monodisperse single-collector efficiency correlations. Conceptually, the polydisperse model is developed by transforming the probability density of particle radius into a probability density of particle Stokes number that is then used to weight the monodisperse single-collector efficiency at a given Stokes number. An extension of this polydisperse filtration concept results in an analytical solution for the axial variation of polydisperse particle flux in a random three-dimensional granule configuration. In order to verify the analytical results for polydisperse particle filtration, a granule-resolved direct numerical simulation approach is coupled with Lagrangian particle tracking to simulate filtration of polydisperse aerosols in a granular bed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3594–3606, 2015

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 ...

Non-intrusive quadrature-based uncertainty quantification with reconstruction of the distribution of the system response is introduced and applied to the simulation of dense fluidized beds. This approach relies on the conditional quadrature method of moments (CQMOM) to generate a set of samples of the distribution of multiple uncertain parameters of the model. The moments of the system response are directly estimated using Gaussian quadrature formulae, and are used to reconstruct an approximate distribution of the response using extended quadrature method of moments (EQMOM). The approach is demonstrated by considering a bubbling fluidized bed with two uncertain parameters. Contour plots of the mean and standard deviation of volume fraction, phase velocity and pressure are provided. The probability distribution functions of the response are reconstructed using EQMOM with appropriate kernel density functions. The simulation results are compared to experimental data provided by the 2013 NETL small-scale challenge problem.

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 ...

International audience; 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.

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. Continuo...

This work presents an Eulerian computational fluid dynamics (CFD) model of biomass gasification for use in fluidized-bed gasifier (FBG) simulations. The physical and chemical processes of particle gasification and their interaction with the reactive gas flow are modeled within a multi-fluid framework derived from kinetic theory of granular flows. The transport equations of continuous solid phases and species mass fraction of CO, CO2, CH4, H2, H2O, O2, N2, tar, char, and ash are coupled with chemical kinetic models, which describe moisture vaporization, particle devolatilization, homogeneous volatile reaction, heterogeneous char oxidation and char gasification. Continuously variable particle density due to volatilization of lighter components and chemical reactions is implemented to account for the evolution of reacting particles' physical properties. A time-splitting method is employed for decoupling the chemical source from convection. A time-step adaption and restart procedure is implemented to provide the solution stability for strong chemical reaction and to achieve numerical solution efficiency for energy reactor simulations in the time-splitting approach. The chemical source terms based on chemical kinetics are implemented with first-order accuracy in the finite-volume framework. The CFD model is used to simulate wood gasification using air as a fluidization agent in a lab-scale FBG. The simulation results provide detailed information on the dynamic particle processes, char elutriation, and gas composition at the reactor outlet. Operating conditions of different air/biomass mass flow ratio, reactor temperature, and biomass moisture content are simulated and analyzed as to their influence on gas composition and product yields at the gasifier outlet.

Accurately predicting polydisperse bubbly flow is a nontrivial task due to the complexity of the bubble number density function (NDF) and the strong dependence of the instantaneous bubble velocity on the bubble size and shape. To describe polydisperse bubbly flow, a joint mass-velocity NDF is adopted in this work. In the absence of mass transfer between phases and coalescence or breakage, the bubble mass is a conserved quantity from which the bubble size and shape can be found given the liquid pressure and surface tension. Quadrature-based moment methods (QBMM) are applied to solve numerically the kinetic equation of the joint NDF using the extended quadrature method of moments (EQMOM) coupled with an open-source incompressible Navier–Stokes solver for the liquid phase. Transport equations for the joint mass-velocity moments are derived from a kinetic equation for the joint NDF and closure is attained using a monokinetic NDF valid in the limit of small bubble Stokes number. The integer moments with respect to mass are used to reconstruct the continuous univariate NDF with EQMOM, while the joint mass-velocity moments are used to determine the bubble velocity as a continuous function of the bubble mass. The model is first applied to simulate a quasi-2-D bubble column with different aeration profiles and a narrow bubble size distribution in order to validate the approach with experimental data from the literature. Additional cases with a wide continuous bubble size distribution are used to show the ability of the modelling approach to describe polydisperse bubbly flows.

A large eddy simulation (LES) study was performed on a turbulent incompressible wake flow in a rectangular channel. The simulation results were evaluated using particle image velocimetry (PIV) data from a previous experimental study of the same flow (Liu et al., 2013). Comparisons were made of one-point statistics as well as spatial correlations. An extensive pre-simulation study was carried out in which the effect of inlet conditions, grid resolution, time step and subgrid model was investigated and the parameters were optimized. Using the digital filter method of Klein et al. (2003), turbulent inflow velocities were generated based on velocity mean and variance obtained from the experimental data and correlation length scales. It was found that the simulation results in large parts of the domain were strongly dependent on the inlet length scales specified. With a suitable set of length scales, the inlet method was successful at providing inlet conditions that generated accurate simulation results. The very good agreement seen between experiment and simulation demonstrates LES as a method that, with carefully selected inlet conditions, not only can predict the pointwise turbulence statistics of a liquid wake flow, but also capture key features of its large-scale turbulent structures.

This work presents an Eulerian computational fluid dynamics (CFD) model of biomass gasification for use in fluidized-bed gasifier (FBG) simulations. The physical and chemical processes of particle gasification and their interaction with the reactive gas flow are modeled within a multi-fluid framework derived from kinetic theory of granular flows. The transport equations of continuous solid phases and species mass fraction of CO, CO2, CH4, H2, H2O, O2, N2, tar, char, and ash are coupled with chemical kinetic models, which describe moisture vaporization, particle devolatilization, homogeneous volatile reaction, heterogeneous char oxidation and char gasification. Continuously variable particle density due to volatilization of lighter components and chemical reactions is implemented to account for the evolution of reacting particles' physical properties. A time-splitting method is employed for decoupling the chemical source from convection. A time-step adaption and restart procedure is implemented to provide the solution stability for strong chemical reaction and to achieve numerical solution efficiency for energy reactor simulations in the time-splitting approach. The chemical source terms based on chemical kinetics are implemented with first-order accuracy in the finite-volume framework. The CFD model is used to simulate wood gasification using air as a fluidization agent in a lab-scale FBG. The simulation results provide detailed information on the dynamic particle processes, char elutriation, and gas composition at the reactor outlet. Operating conditions of different air/biomass mass flow ratio, reactor temperature, and biomass moisture content are simulated and analyzed as to their influence on gas composition and product yields at the gasifier outlet.

Combustion-based synthesis is the prominent technique for large-scale production of commercial-grade nanoparticles, such as titanium dioxide (titania or TiO 2 ). 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, TiCl 4 , 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.

Flame-based synthesis of nanoparticles is an important chemical process used for the manufacturing of metal oxide particles. In this aerosol process, nanoparticle precursors are injected into a high-temperature flame that causes precursor oxidation, nucleation, and subsequent growth of solid particles through a variety of processes. To aid computational design of the aerosol process, a large-eddy simulation (LES) based computational framework is developed here. A flamelet-based model is used to describe both combustion and precursor oxidation. The solid phase nanoparticle evolution is described using a bivariate number density function (NDF) approach. The high-dimensional NDF transport equation is solved using a novel conditional quadrature method of moments (CQMOM) approach. Particle phase processes such as collision-based aggregation, and temperature-induced sintering are included in this description. This LES framework is used to study an experimental methane/air flame that used titanium tetrachloride to generate titania particles. The simulation results show that the evolution process of titania nanoparticles is largely determined by the competition between particle aggregation and sintering at downstream locations in the reactor. It is shown that the bivariate description improves the prediction of particle size characteristics, although the large uncertainty in inflow and operating conditions prevent a full scale validation. © 2013 American Institute of Chemical Engineers AIChE J 60: 459–472, 2014

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.

Gas–particle flows are present in many industrial applications such as polymerization, fluid catalytic cracking, chemical vapor deposition, combustion and drying. Particle–particle, particle–wall and gas–particle interactions cause electrostatic charge to form on particles. The motion of charged particles creates an electric field, affecting the hydrodynamics in reactors such as polymerization fluidized beds and fluid catalytic crackers ( Hendrickson, 2006 ). In this work, a combined multi-fluid and electrostatic model previously developed in Rokkam et al. (2010) is used to simulate laboratory-scale experiments on electrostatics in gas–solid fluidized beds conducted by Sowinski et al. (2010) . The fluidized-bed experiments were operated in two flow regimes, bubbling and slug flow. Charge-to-mass ratio ( q / m ) measured in the experiments was used as an input to the computational fluid dynamic (CFD) electrostatic model. Particle-phase segregation from CFD simulations with electrostatic forces compared well with experimental measurements and observations.

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.

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 Browni...

In this work, an Euler–Euler multiphase computational fluid dynamics (CFD) model, which couples a biomass particle pyrolysis model with a multi-fluid hydrodynamics model for gas–particle flow, is used to describe a biomass pyrolysis process, and model predictions are compared to experimental data produced in a lab-scale fluidized-bed reactor. A parametric study of operating conditions was also performed. The kinetic model is based on superimposed hemicellulose, cellulose, and lignin reactions. General biomass feedstock can be represented through the initial mass composition with respect to the three components. The gas–particle flow is modeled with a multi-fluid description (gas, sand, biomass) derived from the kinetic theory of granular flows. The predicted product yields at the reactor outlet are presented and compared with the experimental measurements for both pure cellulose and red oak pyrolysis, and encouraging quantitative agreement is achieved. The model is then applied to investigate the effect of various operating conditions on the pyrolysis product yields in the reactor. Results indicate that biomass particle size and superficial gas velocity influence tar yield and residence time considerably with a fixed bed height. For the range of operating temperature studied, the model captures the trend of biomass decomposition versus temperature and shows an optimal temperature of about 500 °C for bio-oil production as reported in the literature. Different biomass feedstocks are also simulated and model shortcomings are discussed.

Large Eddy Simulations (LESs) were performed for a confined rectangular liquid jet with a co-flow and compared in detail with particle image velocimetry (PIV) measurements. A finite-volume CFD library, OpenFOAM, was used to discretize and solve the filtered Navier–Stokes equation. The effects of grid resolution, numerical schemes and subgrid models on the LES results were investigated. The second and fourth order schemes gave similar performance, while the fourth order scheme costs much more computationally. Subgrid model comparison showed that the locally dynamic procedure is necessary for complex flow simulation. Model validation was performed by comparing LES data for the point-wise velocity statistics such as the mean and the root-mean-square velocity, shear stress, correlation coefficient, velocity skewness and flatness with the PIV data. In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data. Good agreement was observed leading to the conclusion that the LES velocity field accurately captures the important characteristics of all the turbulent length scales present in the flow, from the fully resolved energy-containing eddies to the subgrid-scale dissipative eddies.

The apparent particle dispersion in a granular medium due to the combined effects of random granular arrangements and interstitial fluid flow was studied. The particle motion was a two-dimensional random walk on the transverse plane. The corresponding dispersion coefficient was found by sampling all possible trajectories with the aid of two granular media models. The theoretical results were verified by numerical simulation data obtained with commercial CFD software. Reasonably good agreement between the theory and simulation suggests that the present theory may be applied to practical granular system applications.

An iterative procedure for the solution of multi-fluid equations for gas–particle flows, with kinetic theory closures and frictional stress models for the description of the particle phase is presented and was implemented in the fully unstructured open source code OpenFOAM®, capable of using arbitrarily-shaped polyhedral cells. Improved interpolation practices have been adopted to ensure the smoothness of the solution in situations where the phase effective density presents steep gradients, aiming at reproducing the discretisation typical of the staggered grid arrangement. This was achieved including the strongly varying source terms of the momentum equation in the momentum interpolation procedure. Phase coupling was implemented using the partial elimination algorithm, which was incorporated in the improved interpolation practice. An implicit treatment for the particle pressure was implemented to ensure the robustness of the algorithm whenever the particle phase approaches the packed condition, where strong and rapidly changing stresses as a function of the dispersed phase volume fraction are present. The implemented code was tested against a number of test cases, including a bubbling fluidised bed, and results were verified against the solution provided by another solver (MFIX), or against published numerical solutions.

Bubble-column reactors are frequently employed in the biological, chemical and petrochemical industries. This paper presents a novel approach to model bubble-column flows using quadrature-based moment methods (QBMM). A fully two-way coupled flow solver is developed that solves the incompressible Navier-Stokes equation for the liquid phase and moment transport equations for the dispersed bubble phase. The moment transport equations for the dispersed bubble phase are solved using a kinetic theory approach. Contributions from the liquid-phase pressure gradient, vorticity, drag, virtual mass and gravity are accounted for in the bubble-phase force balance. The solution algorithm and coupling procedure are described in detail, and results are presented for a 2-D bubble column with two different gas flow rates (1.6 and 8.0 l/min).

In this work, an Euler–Euler multiphase CFD model is proposed for continuous fast pyrolysis of biomass in a fluidized-bed reactor. In the model, a lumped, multi-component, multi-stage kinetic model is applied to describe the pyrolysis of a biomass particle. Variable particle porosity is used to account for the evolution of the particle's physical properties. Biomass is modeled as a composite of three reference components: cellulose, hemicellulose, and lignin. Pyrolysis products are categorized into three groups: gas, tar vapor (bio-oil), and solid char. The particle kinetic processes and their interactions with the reactive gas phase are modeled with a multi-fluid description derived from the kinetic theory of granular flows. A time-splitting approach is applied to decouple the convection and reaction calculations using a synchronized time step. The CFD model is employed to study the fast pyrolysis of both cellulose and bagasse in a lab-scale fluidized-bed reactor. The dynamics, particle heating, reaction of the biomass phase, char formation, elutriation, and spatial distribution of tar and gas inside the reactor are investigated. The yields of tar, gas, and char are also discussed.

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.

Predictive device-level computational fluid dynamics (CFD) simulation of gas–solid flow is dependent on accurate models for unclosed terms that appear in the averaged equations for mass, momentum and energy conservation. In the multifluid theory, the second moment of particle velocity represents the strength of particle velocity fluctuations and is known to play an important role in the prediction of core-annular flow structure in risers (Hrenya and Sinclair, AIChEJ, 43 (4) (1994) [5]). In homogeneous suspensions the evolution of the second velocity moment is governed by the particle acceleration–velocity covariance. Therefore, fluctuations in the hydrodynamic force experienced by particles in a gas–solid flow affect the evolution of particle velocity fluctuations, which in turn can affect the mean and variance of the hydrodynamic force. This coupling has been studied in the limit of Stokes flow by Koch and co-workers using a combination of kinetic theory and multipole expansion simulations. For Reynolds numbers beyond the Stokes limit, direct numerical simulation is a promising approach to quantify this coupling. Here we present direct numerical simulation (DNS) results for the evolution of particle granular temperature and particle acceleration variance in freely evolving homogeneous gas–solid suspensions. It is found that simple extension of a class of mean particle acceleration models to their corresponding instantaneous versions does not recover the correlation of particle acceleration with particle velocity. This study motivates the development of better instantaneous particle acceleration models that are able to accurately capture the coupling between particle acceleration and velocity.

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.

For titanium dioxide (TiO2) nanoparticles manufactured in flame reactors, the precursor is injected into a pre-existing flame, exposing it to a high-temperature gas phase, leading to nucleation and particle growth. Predictive modeling of this chemical process requires simultaneous development of detailed chemical mechanisms describing gas-phase combustion and particle evolution, as well as advanced computational tools for describing the turbulent flow field and its interactions with the chemical processes. Here, a multiscale computational tool for flame-based TiO2 nanoparticle synthesis is developed and a flamelet model representing detailed chemistry for particle nucleation is proposed. The effect of different chemical mechanisms (i.e., one-step, detailed, flamelet) on the prediction of nanoparticle nucleation is investigated using a plug-flow reactor and a partially stirred tank reactor to model the flow field. These simulations demonstrate that particle nucleation occurs much later in the flame with de...

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 R u ′ ϕ ′ correlation field, there were a positive and a negative vertically oriented elliptical correlation region, which were symmetric around the basis point. The R v ′ ϕ ′ correlation region was a horizontally oriented ellipse with negative values of the correlation coefficient. The correlation field of R ϕ ′ ϕ ′ 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.

A third-order quadrature-based moment method for simulating dilute and moderately dilute fluid–particle flows has been implemented with full coupling in a computational fluid dynamics code. The solution algorithm for the particle phase uses a kinetic-based finite-volume technique to solve the velocity moment equations derived from kinetic theory. The procedure to couple the particle-phase volume-fraction and momentum equations with the Eulerian solver for the fluid phase is explained in detail. As an example application, simulations of a particle-laden vertical channel flow at fluid-phase Reynolds number 1379 and particle Stokes numbers 0.061 and 0.61 were carried out. The fluid and particle velocities, particle-phase volume fraction and granular temperature were observed to reach a steady state in the case of Stokes number 0.061, while instabilities that led to the formation of structures and initiated the particle segregation process were observed in the case with the higher Stokes number. These results are validated against results from a classical two-fluid model derived from the kinetic theory of granular flows in the small Knudsen number limit, and Euler–Lagrange simulations of the same flow.

A quadrature-based moment model is derived for moderately dense polydisperse gas-particle flows starting from the inelastic Boltzmann-Enskog kinetic equation including terms for particle acceleration (e.g., gravity and fluid drag). The derivation is carried out for the joint number density function, f(t,x,m,u), of particle mass and velocity, and thus, the model can describe the transport of polydisperse particles with size and density differences. The transport equations for the integer moments of the velocity distribution function are derived in exact form for all values of the coefficient of restitution for particle-particle collisions. For particular limiting cases, the moment model is shown to be consistent with hydrodynamic models for gas-particle flows. However, the moment model is more general than the hydrodynamic models because its derivation does not require that the particle Knudsen number (and Mach number) be small.

Fluidized-bed reactors are widely used in the biofuel industry for combustion, pyrolysis, and gasification processes. In this work, a lab-scale fluidized-bed reactor without and with side-gas injection and filled with 500–600 μm glass beads is simulated using the computational fluid dynamics (CFD) code Fluent 6.3, and the results are compared to experimental data obtained using pressure measurements and 3D X-ray computed tomography. An initial grid-dependence CFD study is carried out using 2D simulations, and it is shown that a 4-mm grid resolution is sufficient to capture the time- and spatial-averaged local gas holdup in the lab-scale reactor. Full 3D simulations are then compared with the experimental data on 2D vertical slices through the fluidized bed. Both the experiments and CFD simulations without side-gas injection show that in the cross section of the fluidized bed there are two large off-center symmetric regions in which the gas holdup is larger than in the center of the fluidized bed. The 3D simulations using the Syamlal-O'Brien and Gidaspow drag models predict well the local gas holdup variation throughout the entire fluidized bed when compared to the experimental data. In comparison, simulations with the Wen-Yu drag model generally over predict the local gas holdup. The agreement between experiments and simulations with side-gas injection is generally good, where the side-gas injection simulates the immediate volatilization of biomass. However, the effect of the side-gas injection extends further into the fluidized bed in the experiments as compared to the simulations. Overall the simulations under predict the gas dispersion rate above the side-gas injector. © 2009 American Institute of Chemical Engineers AIChE J, 2010

The direct quadrature method of moments (DQMOM) can be employed to close population balance equations (PBEs) governing a wide class of multivariate number density functions (NDFs). Such equations occur over a vast range of scientific applications, including aerosol science, kinetic theory, multiphase flows, turbulence modeling, and control theory, to name just a few. As the name implies, DQMOM uses quadrature weights and abscissas to approximate the moments of the NDF, and the number of quadrature nodes determines the accuracy of the closure. For nondegenerate univariate cases (i.e., a sufficiently smooth NDF), the N weights and N abscissas are uniquely determined by the first 2N non-negative integer moments of the NDF. Moreover, an efficient product−difference algorithm exists to compute the weights and abscissas from the moments. In contrast, for a d-dimensional NDF, a total of (1 + d)N multivariate moments are required to determine the weights and abscissas, and poor choices for the moment set can lead...