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The effect of electrostatic forces on the dispersion of small like-charged inertial particles transported by a homogeneous isotropic turbulent flow is analysed by means of direct numerical simulations coupled with the Lagrangian tracking of charged particles. The results show that particle dispersion decreases for increasing charge. Since turbulent particle dispersion is related to the intensity of particle agitation and to the Lagrangian particle integral time scale, we analyse the effects of electrostatic forces on these two quantities. Particle agitation decreases for increasing particle charge. In fact, particle kinetic energy is not directly modified by electrostatic forces, which are conservative, it is rather the particle entrainment by fluid turbulence that is modified. To support this claim, one shows that the fluid–particle velocity covariance is destructed by electrostatic forces, a destruction can be predicted by drawing an analogy between inter-particle collisions and Coulomb collisions. As expected, electrostatic forces decorrelate particle velocities leading to a decrease of the Lagrangian particle integral time scale. Finally, one shows that the analogy with inter-particle collisions allows us to predict the reduction of particle dispersion.

International audience; Introducing liquid fuel inside an aeronautical combustion chamber is associated with several complex phenomena like droplet dispersion by turbulence, spray evaporation and combustion. In order to study experimentally the spray behaviour, under non-reactive and reactive conditions, Mie scattering images provided by the PROMETHEE-LACOM test rig have been processed. However, the transition between a 3D flow in the combustion chamber to a 2D planar Mie scattering images leads to some errors. The present paper focuses on the evaluation of these errors and the influence on the droplet spatial distribution. Results show that the droplet distribution remains practically the same between the 3D-2D transition. Moreover, the restriction error decreases when droplet density number increases and the projection error increases when droplet density number increases.

International audience; A new experimental setup PROMETHEE has been built to study spray combustion. The design corresponds to a square-duct channel with a bluff body spanning over the entire width of the channel. Turbulent flow circulates around the obstacle and liquid fuel is injected at the rear of the bodyvthrough a flat-fan nozzle. The two-dimensional configuration has been chosen to facilitate the optical measurements, and the operating conditions partially reproduce those encountered inside a turboreactor. A procedure based on Mie scattering images is proposed to characterize the interdroplet distance to the nearest neighbor and to describe the spray spatial distribution. Such a procedure could benefit spray combustion modeling, providing a more precise length scale. First, the droplet spatial distribution under reacting conditions was investigated with respect to the interdroplet distance and the spatial distribution law at six locations downstream from the bluff body for the PROMETHEE experiments. For the distribution law, comparisons between the experimental, theoretical uniform, and uniformly random distributions, and numerical results from an in-house Monte-Carlo solver show that the distribution is close to the uniformly random one and that the interdroplet distance and its standard deviation evolve linearly with respect to the inverse of the density number square root. In addition, the numerical approach was used to estimate the projection and restriction errors associated with the interdroplet distance. Second, the procedure has been assessed through six Direct Numerical Simulation—Direct Particle Simulation (DNS/DPS) isotropic homogeneous turbulent simulations to highlight the clustering effects on the dimensionless mean and standard deviation of the nearest-neighbor interdroplet distance when decreasing the Stokes number. The results show that the droplet distribution is similar to the uniformly random distribution when the particle Stokes number is high enough while the mean (standard deviation) decreases (increases) with the reduction of the Stokes number due to the clustering effect. Such an observation demonstrates that preferential segregation is probably not important in the present experimental data.

International audience; Powder discharging from a silo provokes an emission of dust. To understand and prevent this source of danger,3D simulations of a silo dischargewere performed using an Euler-Euler approach. The impact of the coupling between the flow inside the silo and the granular jet in free-fall is analyzed. Results show that the solid mass flow rate is correctly predicted and that gas back-flowing at the hopper exhaust appears responsible for the formation of a fluctuating and radially expanding jet. However, the radial expansion of the free-falling jet is underestimated. Stochastic fluctuations of the particles velocity at the hopper exhaust are introduced to evaluate their effect onthe downstream development of the free-falling jet. These fluctuations are found capable of generating a development of the jet similar to that observed experimentally. This suggests that the granular flow conditions at the hopper exhaust are responsible for the further dispersion of powder.

International audience; The numerical simulations on the large-scale fluidized beds still remain challenging due to the computational limitation and experimental validation. In the present work, a CFD study of a large-scale fluidized bed is investigated using the NEPTUNE_CFD code based on an Eulerian n-fluid modeling approach. A SubGrid Scale (SGS) drag model based on the filtered approach is used to take into account the effect of very small solid structures unresolved with the coarse mesh. The numerical results are compared with the experimental data carried out in a pilot-scale fluidized bed unit and provided by Particulate Solid Research Inc (PSRI). By applying the SGS drag model without any specific or empirical tuning, mesh-independent numerical results are obtained. The flow regimes inside the fluidized bed are well predicted for all the superficial gas velocities studied here. The bed density profiles and the solid entrainment fluxes are also in good agreement with the experimental measurement.  The large-scale fluidized bed simulations are validated against PSRI experiments for different flow regimes from turbulent to fast fluidization.  A SGS drag model based on the filtered approach is using without any specific or empirical tuning which shows certain universality.  The gas-solid flows inside the fluidized bed with different gas velocities are characterized.  The validation in this study is a critical step toward industrial-scale fluidized bed simulations. Gas-solid fluidized bed simulations using the filtered approach: Validation against pilot-scale experiments Abstract The numerical simulations on the large-scale fluidized beds still remain challenging due to the computational limitation and experimental validation. In the present work, a CFD study of a large-scale fluidized bed is investigated using the NEPTUNE CFD code based on an Eulerian n-fluid modeling approach. A SubGrid Scale (SGS) drag model based on the filtered approach is used to take into account the effect of very small solid structures unresolved with the coarse mesh. The numerical results are compared with the experimental data carried out in a pilot-scale fluidized bed unit and provided by Particulate Solid Research Inc (PSRI). By applying the SGS drag model without any specific or empirical tuning, mesh-independent numerical results are obtained. The flow regimes inside the fluidized bed are well predicted for all the superficial gas velocities studied here. The bed density profiles and the solid entrainment fluxes are also in good agreement with the experimental measurement.

International audience; For the last 30 years, experimental and modeling studies have been carried out on fluidized bed reactors from laboratory up to industrial scales. The application of developed models for predictive simulations has however been strongly limited by the available computational power and the capability of computational fluid dynamics software to handle large enough simulations. In recent years, both aspects have made significant advances and we thus now demonstrate the feasibility of a massively parallel simulation, on whole supercomputers using NEPTUNE_CFD, of an industrial-scale polydispersed fluidized-bed reactor. This simulation of an olefin polymerization reactor makes use of an unsteady Eulerianmulti-fluid approach and relies on a billion cellsmeshing. This is a worldwide premiere as the obtained accuracy is yet unmatched for such a large-scale system. The interest of this work is two-fold. In terms of High Performance Computation (HPC), all steps of setting-up the simulation, running it with NEPTUNE_CFD, and post-processing results induce multiple challenges due to the scale of the simulation. The simulation ran using 1260 up to 36,000 cores on supercomputers, used 15 millions of CPU hours and generated 200 TB of rawdata for a simulated physical time of 25s. This article details the methodology applied to handle this simulation, and also focuses on computation performances in terms of profiling, code efficiency and partitioning method suitability. Though being by itself interesting, the HPC challenge is not the only goal of this work as performing this highly-resolved simulation will benefit chemical engineering and CFD communities.Indeed, this computation enables the possibility to account, in a realistic way, for complex flows in an industrial-scale reactor. The predicted behavior is described, and results are post-processed to develop sub-grid models. These will allow for lower-cost simulations with coarser meshes while still encompassing local phenomenon.

We use Particle-Resolved (Direct Numerical) Simulation (PR-DNS or PRS) to investigate momentum and heat transfer in the incompressible flow of a Newtonian fluid through a fixed bed of mono-disperse spheres. We perform a set of simulations with various porosities ranging from 0.5 to 0.9 , Reynolds numbers ranging from 18 to 72 and Prandtl numbers ranging from 1 to 5 and analyze computed results. All cases are hence in the moderately convection dominated thermal regimes, i.e., Peclet numbers from 18 to 360 . We locally average fluid flow data around particles using different filters centered at each particle mass center and we study the effect of the mathematical form of the filter as well as of the filter support size on the particle Nusselt number distribution. While both mathematical form and support size have a limited effect on the average particle Nusselt number, the width of the distribution, i.e., the standard deviation, is strongly influenced by the filter support size. This observation has important consequences for the derivation of new transfer coefficient models that incorporate information about the actual particle microstructure and attempt to estimate the transfer coefficient fluctuations for a given average local porosity.

A predictive modelling for the simulation of bioreactors must account for both the biological and hydrodynamics complexities. Population balance models (PBM) are the best approach to conjointly describe these complexities, by accounting for the adaptation of inner metabolism for microorganisms that travel in a large-scale heterogeneous bioreactor. While being accurate for solving the PBM, the Class and Monte-Carlo methods are expensive in terms of calculation and memory use. Here, we apply Methods of Moments to solve a population balance equation describing the dynamic adaptation of a biological population to its environment. The use of quadrature methods (Maximum Entropy, QMOM or EQMOM) is required for a good integration of the metabolic behavior over the population. We then compare the accuracy provided by these methods against the class method which serves as a reference. We found that the use of 5 moments to describe a distribution of growth-rate over the population gives satisfactory accuracy against a simulation with a hundred classes. Thus, all methods of moments allow a significant decrease of memory usage in simulations. In terms of stability, QMOM and EQMOM performed far better than the Maximum Entropy method. The much lower memory impact of the methods of moments offers promising perspectives for the coupling of biological models with a fine hydrodynamics depiction.

International audience; The main objective of this work is to study the effects of distance-dependent interactions in turbulent gas-particle flows using an Euler–Lagrange simulation approach. The turbulent gas flow is accounted for via Direct Numerical Simulation to the Kolmogorov scale using a spectral method to solve the Navier–Stokes equations in a cubic computational domain with tri-periodic boundary conditions. This flow simulation is coupled (one-way) with a Lagrangian particle phase solver that performs particle trajectory tracking. Electrostatic forces can be calculated using two different approaches. Firstly, the direct method consists of a sum of all inter-particle interactions for all the particles of the computational domain and their periodic images. However, this purely Lagrangian approach is computationally costly for a large number of particles, therefore another approximative approach is considered. According to it, one can estimate the short-range interactions via a sum of inter-particle interactions within a cut-off distance and the long-range ones via a sum of particle interactions with clusters of particles that, from a distance greater than the cut-off, are “seen” as one pseudo-particle. This method is then adjusted in order to accommodate periodic boundary conditions, which are not trivial in the case of electrostatic interactions as periodicity entails an infinite number of periodic domain images that has to be truncated to a finite number. Simulations are then performed by varying the properties of the particles in terms of diameter, density (Stokes number) and charge (electrostatic Stokes number). Finally, a statistical analysis is performed in order to investigate how the dynamics of the turbulent gas-particle flow are affected by distance-dependent particle–particle interactions, namely electrostatic forces.

International audience; We numerically investigated the transport, deformation and buckling events of an isolated elastic fiber in Taylor-Green vortices and studied the dynamics of long filaments in homogeneous isotropic turbulence. The fiber is modelled by an assembly of spherical beads. The contact between beads enforces the inextensibility of the filament while bending is accounted for by the Gears Bead Model (GBM) proposed by Delmotte et al. (2015). In the cellular Taylor-Green flow, the buckling probability is a function of a dimensionless number, called Sperm number, which is a balance between the compression rate of the flow and the elastic response of the filament. The shapes of the filament and its ability to buckle have been successfully validated through comparisons with experiments from the work by Quennouz et al. (2015). The deformation statistics of long flexible fibers in sustained homogeneous isotropic turbulence were analyzed for various flow and fiber material conditions. Two regimes have been identified depending on the ratio of fiber length to persistence length which is a measure of turbulent forcing to flexibility. The numerical results are in good agreement with existing experimental data (C. Brouzet et al., Phys. Rev. Lett. 112, 074501 (2014)) validating the assumptions of our model for the configurations we investigated.

International audience; Multiphase pipelineflows are widely used in the oil and gas industry to transport solid-liquid or gas-solid mix-tures. Erosion caused by the impact of solid particles is a major challenge for equipment maintenance and safety,especially in complex geometries such as elbows. In this work, a CFD study on wall erosion in a 90° standardelbow has been performed using a multi-fluid approach, also called Euler/Euler, for poly-dispersedfluid-particleflows. A model is used for the erosion prediction taking into account particle turbulent kinetic energy obtainedfrom the Euler-Euler approach. A good agreement with experiments is observed. The effects of wall roughnessand solid massflow rate on the erosion rate are also investigated. For a certain amount of sand passing throughthe pipe elbow, there exists a solid massflow rate for which the particle impact damage is most dramatic.

International audience; In this paper, reactive unsteady three-dimensional numerical simulations of a chemical looping combustion (CLC) unit are presented. The configuration is a 120-kW pilot plant working with perovskite, CaMn0.9Mg0.1O3d, as the selected oxygen carrier. Numerical simulations were performed using NEPTUNE_CFD code in the frame of an Euler-Euler approach by computing both gas and solid phases in an Eulerian technique, accounting for specific closures in order to model the interphase mass, and momentum and energy transfers. Heterogeneous reduction and oxidation (gas–solid) reactions were modeled by means of a grain model to account for the competing mechanisms of the chemical reaction onto the grain surface, the gaseous diffusion through the product layer around the grain, and the external transfer through the gas mixture surrounding the particle. Results from numerical simulations were assessed against experimental measurements and analyzed in order to acquire insight on the local behavior of reactive gas-particle flow in the CLC system. The theoretical/numerical tool developed in this work can be used for the design upgrade of crucial parts of the system in the stage of scaling-up from pilot to industrial plants.

International audience; The paper presents numerical simulations of particle-laden fully developed turbulent channel flows performed in a stochastic Lagrangian framework. The particle inertia is large in order to neglect the effect of the turbulent gas motion on the particle dispersion. In contrast the inter-particle collisions are important and accounted for by using Direct Simulation Monte-Carlo (DSMC) method. The comparison of the Monte-Carlo results with those obtained by Discrete Particle Simulation (DPS) shows that the stochastic collisions algorithm is able to predict accurately the particle statistics (number density, mean velocity, second- and third-order velocity moments) in the core flow. More, the paper analyses the number sections needed for accurate predictions. In the very near-wall region, the Monte-Carlo simulation fails to account for the wall shelter effect due to the wall-normal unbalanced inter-particle collisions influence induced by the presence of the wall. Then, the paper shows that DSMC permits to assess the closure approximations required in moment approach. In particular, the DSMC results are compared with the corresponding moment closure assumptions for the third-order correlations of particle velocity, the correlations between the drag force and the velocity and the inter-particle collision terms. It is shown that at the opposite of the standard DSMC, the moment approach can predict the wall shelter effect. Finally, a model for the mean transverse force is proposed for taking into account wall shelter effect in DSMC.

International audience; During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finite size particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta-function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.

International audience; Population Balance Models have a wide range of applications in many industrial fields as they allow accounting for heterogeneity among properties which are crucial for some system modelling. They actually describe the evolution of a Number Density Function (NDF) using a Population Balance Equation (PBE). For instance, they are applied to gas–liquid columns or stirred reactors, aerosol technology, crystallisation processes, fine particles or biological systems. There is a significant interest for fast, stable and accurate numerical methods in order to solve for PBEs, a class of such methods actually does not solve directly the NDF but resolves their moments. These methods of moments, and in particular quadrature-based methods of moments, have been successfully applied to a variety of systems. Point-wise values of the NDF are sometimes required but are not directly accessible from the moments. To address these issues, the Extended Quadrature Method of Moments (EQMOM) has been developed in the past few years and approximates the NDF, from its moments, as a convex mixture of Kernel Density Functions (KDFs) of the same parametric family. In the present work EQMOM is further developed on two aspects. The main one is a significant improvement of the core iterative procedure of that method, the corresponding reduction of its computational cost is estimated to range from 60% up to 95%. The second aspect is an extension of EQMOM to two new KDFs used for the approximation, the Weibull and the Laplace kernels. All MATLAB source codes used for this article are provided with this article.

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.

This study deals with mathematical modeling and numerical simulations of reactive multiphase flows in dense fluidized beds. These flows involve complex physical mechanisms related to the coupling between the bed hydrodynamic and the reactions,which are still poorly understood. In this context, numerical simulations can provide explanatory access to the underlying physics taking place in the reactor, thus supplementing the experimental results. The present contribution focuses on the natural gas combustion in a dense fluidized bed reactor, for which experimental results are available from the literature (Dounit, 2001; Dounit et al., 2001, 2008). In their experiments, the authors pointed out the essential role played by the particle projection zone, above the bed surface, in the global thermal efficiency of the reactor operating at relatively low temperatures (600°C–800°C). In the present study, this point is further investigated by analyzing the results obtained by the numerical simulations. The unsteady 3D numerical simulations were performed using NEPTUNE_CFD code which is based on an Euler–Euler approach; the latter computes both the gas and the particulate phases in an Eulerian framework, accounting for specific closures modeling the interphase momentum and energy transfers. Time-averaged quantities were then computed and compared with the available experimental measurements. Numerical results (especially the gas temperature) were found to be very sensitive to the mesh refinement for the selected operating point. A further analysis at mesoscopic and macroscopic scales was carried out. This analysis pointed out the crucial role of the toroidal loop, which extends from the bed, close to the ejection zone, to the freeboard, on the fuel conversion. In numerical simulations, this loop must be accurately reproduced in order to provide reliable combustion predictions.

In chemical engineering applications, it is not uncommon to encounter reactors featuring rotating parts. As these rotating parts are present in order to enhance processes such as chemical reactions and/or ensure homogeneity, it is essential to take them into account to perform predictive numerical simulations. This aspect can be particularly challenging, even more so when complex industrial geometries are to be treated. In this paper a numerical methodology for simulating unsteady granular flow in rotating geometries is presented. The method is based on splitting the domain into static and rotating parts. The information between rotating and static parts is passed by a non-conformal mesh matching technique. The presented methodology is validated numerically by comparing its results with other conventional methods. The method is then applied to an industrial scale problem. The applicability of the method and the way it may be used to investigate complex flow is demonstrated. Therefore this approach enables to consider the full geometry of complex reactors. It opens the door to further investigation, optimization and design of industrial scale chemical processes.

This study addresses the modeling of the denebulization (i.e., the removal of droplets) of warm fogs (T ≥ 0°C) by hygroscopic salt microparticles from the initial seeding at the top of the fog layer to the fall of the rain droplets on the ground. Two main phenomena can occur: condensation of water vapor on salted droplets and the concomitant evaporation of fog droplets, and coalescence between the salted droplets and the fog droplets. Three salts have been investigated: NaCl, CaCl2, and KCl. Based on the conservation equations, the modeling approach (1D) considers the hygroscopicity of the salts through the water activity in the aqueous solution and the coalescence induced by gravity and turbulence. From this study, NaCl is the most efficient salt in the tested operating conditions. Actually, this result can be explained by the strong hygroscopicity of this salt in very dilute solutions. From the calculations, 15 kg of NaCl particles of 6.7-μm diameter can dissipate a typical fog layer of 40 m in height within less than 17 min over 0.25 km2. According to the calculations, a fog layer of 100 m in height can be denebulized within 45 min. The contribution of the coalescence induced by gravity and by turbulence seems to have a negligible effect on the final horizontal visibility, the condensation/evaporation phenomena being preponderant for these operating conditions.

The consequences of substrate concentration heterogeneities at the cell level, on the behavior of microbial populations have been identified some years ago. However, subgrid effects are rarely considered in bioreactor modelling. In this paper, this central issue is investigated with Direct Numerical Simulations (DNS) coupled with Lagrangian particle tracking and scalar field calculations in the case of statistically steady homogeneous and isotropic turbulence. From these calculations, the exact distribution of substrate uptake rates of a microorganism population is calculated and compared, favorably, to analytical solutions. A metabolic model considering anabolism, oxidative catabolism and dissimilation is invoked to quantify the consequences in terms of overall reaction rates at the population scale. It is shown that imperfect mixing reduces the growth rate and increases the by-product formation while leaving the total uptake rate unchanged. This work provides a rational explanation, based on physical consideration, for the loss in biomass productivity and the increase of by-product formation in imperfectly mixed bioreactors.

International audience; 3D numerical simulations of dense pressurized fluidized bed are presented. The numerical prediction of the mean vertical solid velocity are compared with experimental data obtained from Positron Emission Particle Tracking. The results show that in the core of the reactor the numerical simulations are in accordance with the experimental data. The time-averaged particle velocity field exhibits a large-scale toroidal (donut shape) circulation loop. Two families of boundary conditions for the solid phase are used: rough wall boundary conditions (Johnson and Jackson, 1987 and No-slip) and smooth wall boundary conditions (Sakiz and Simonin, 1999 and Free-slip). Rough wall boundary conditions may lead to larger values of bed height with flat smooth wall boundary conditions and are in better agreement with the experimental data in the near-wall region. No-slip or Johnson and Jackson׳s wall boundary conditions, with sufficiently large value of the specularity coefficient (ϕ≥0.1)(ϕ≥0.1), lead to two counter rotating macroscopic toroidal loops whereas with smooth wall boundary conditions only one large macroscopic loop is observed. The effect of the particle-particle restitution coefficient on the dynamic behaviour of fluidized bed is analysed. Decreasing the restitution coefficient tends to increase the formation of bubbles and, consequently, to reduce the bed expansion.

International audience; The aim of the paper is to introduce and validate a Monte-Carlo algorithm for the prediction of an ensemble of colliding solid particles, or coalescing liquid droplets, suspended in a turbulent gas flow predicted by Reynolds Averaged Navier Stokes approach (RANS). The new algorithm is based on the direct discretization of the collision/coalescence kernel derived in the framework of a joint fluid–particle pdf approach proposed by Simonin et al. (2002). This approach allows to take into account correlations between colliding inertial particle velocities induced by their interaction with the fluid turbulence. Validation is performed by comparing the Monte-Carlo predictions with deterministic simulations of discrete solid particles coupled with Direct Numerical Simulation (DPS/DNS), or Large Eddy Simulation (DPS/LES), where the collision/coalescence effects are treated in a deterministic way. Five cases are investigated: elastic monodisperse particles, non-elastic monodisperse particles, binary mixture of elastic particles and binary mixture of elastic settling particles in turbulent flow and finally coalescing droplets. The predictions using the new Monte-Carlo algorithm are in much better agreement with DPS/DNS results than the ones using the standard algorithm.

The purpose of the study is the modeling of the denebulization of fogs by micronic hygroscopic particles from the initial seeding to the fall of the rain droplets on the ground. The microparticles generated by flares are made of hygroscopic salts. Three stages occur: first, the condensation of water vapor on solid particles, this is the deliquescent stage which is very fast and can be ignored by the model, then the stage of condensation of water vapor on liquid salted particles / evaporation of fog droplets and finally the coalescence stage when the liquid salted particles diameter become large enough. Three different salts have been tested: NaCl, CaCl2 and KCl. The 1-D modeling approach studied considers the conservation equations (salt mass, water mass, salted droplets number density, fog droplets number density), the hygroscopicity of the salts through the water activity in the aqueous solution and the coalescence induced by gravity. The model reveals that NaCl is the most efficient salt because of its stronger hygroscopicity at high dilution rates although CaCl2 is the more hygroscopic at low dilution rates. A cloud of NaCl particles of 9 μm diameter initially generated over a height of about 7 m with a number density of 12 cm−3 allows to completely dissipates a typical fog layer of 40 m within less than 13 mn. This means that 10 kg of NaCl particles could be able to clear such a fog over 13.25 ha. The model shows that a layer of 100 m can be cleared within 29 mn. From the calculations, the contribution of the coalescence to the denebulization process is less than 1%, phenomena of condensation / evaporation are preponderant for these operating conditions.

International audience; Deposition of inertial solid particles transported by turbulent flows is modelled in a framework of a statistical approach based on the particle velocity Probability Density Function (PDF). The particle-turbulence interaction term is closed in the kinetic equation by a model widely inspired from the famous BGK model of the kinetic theory of rarefied gases. A Gauss-Hermite Lattice Boltzmann model is used to solve the closed kinetic equation involving the turbulence effect. The Lattice Boltzmann model is used for the case of the deposition of inertial particles transported by a homogeneous isotropic turbulent flows. Even if the carrier phase is homogeneous and isotropic, the presence of the wall coupled with particle-turbulence interactions leads to inhomogeneous particle distribution and non-equilibrium particle fluctuating motion. Despite these complexities the predictions of the Lattice Boltzmann model are in very good accordance with random-walk simulations. More specifically the mean particle velocity, the r.m.s. particle velocity and the deposition rate are all well predicted by the proposed Lattice Boltzmann model.

The paper deals with the Euler-Euler numerical simulation of an experimental study (Ansart et al., 2009 [1]) of freely falling granular jet for investigating the dispersion of dust. The configuration is a bunker, where quasi-static particulate flow takes place, and a free-fall chamber. As a first step, a frictional viscosity model developed by Srivastava and Sundaresan (2003) [2] is implemented to take into account the frictional effects occurring in the quasi-static particulate flows. Without the frictional model for the viscosity, the numerical simulations overpredict the solid mass flow rate at the outlet of the bunker. When using the frictional viscosity, the solid mass flow rate is in better accordance with the experimental value. However, the solid velocity is overestimated in numerical simulations.

QC 20191128

International audience; The paper deals with gas-solid turbulent flows carrying non-spherical particles. The main objective of the present paper is to compute the hydrodynamics forces on non-spherical particles as a function of the particle orientation, for different particle shapes and a large range of particle Reynolds number. Two Direct Numerical Simulations at the scale of the particle are used, i.e. a body-fitted approach and a viscous penalty approach, in the case of a uniform flow with a single ellipsoidal particle. Results are compared with several correlations from the literature and a new proposal for the drag coefficient is given. The study is then extended to the case of a lattice of non-spherical particles to measure the pressure drop and to connect it with the drag coefficient.

Euler–Euler two-phase model simulations are usually performed with mesh sizes larger than the small-scale structure size of gas–solid flows in industrial fluidised beds because of computational resource limitation. Thus, these simulations do not fully account for the particle segregation effect at the small scale and this causes poor prediction of bed hydrodynamics. An appropriate modelling approach accounting for the influence of unresolved structures needs to be proposed for practical simulations. For this purpose, computational grids are refined to a cell size of a few particle diameters to obtain mesh-independent results requiring up to 17 million cells in a 3D periodic circulating fluidised bed. These mesh-independent results are filtered by volume averaging and used to perform a priori analyses on the filtered phase balance equations. Results show that filtered momentum equations can be used for practical simulations but must take account of a drift velocity due to the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and particle sub-grid stresses due to the filtering of the non-linear convection term. This paper proposes models for sub-grid drift velocity and particle sub-grid stresses and assesses these models by a priori tests.

International audience; Gas-particle flows in vertical risers are involved in many industrial scale fluidized bed applications such as catalytic cracking, fossil or biomass combustion. Risers flows are often simulated by two-fluid model equations coupled with closures developed in the frame the kinetic theory of granular media. However, two-fluid model discretized over coarse mesh with respect to particle clustering size are performed for large units because of limited computational resources. Now, it is well established that meso-scales cancelled out by coarse mesh simulations have dramatic effect on overall behaviour of flows. This study proposed a sub-grid modeling approach for effective drag force and particle stresses which accounts for the effects of unresolved structures on the resolved flows.

International audience; In most modelling works on bioreactors, the substrate assimilation is computed from the volume average concentration. The possible occurrence of a competition between the transport of substrate towards the cell and the assimilation at the cell level is generally overlooked. In order to examine the consequences of such a competition, a diffusion equation for the substrate is coupled with a specific boundary condition defining the uptake rate at the cell-liquid interface. Two assimilation laws are investigated, whereas the concentration far from the cell is varied in order to mimic concentration fluctuations. Both steady and unsteady conditions are investigated. The actual uptake rate computed from the interfacial concentration is compared to the time-averaged uptake rate based on the mean far-field concentration. Whatever the assimilation law, it is found that the uptake rate can be correlated to the mean far-field concentration, but the actual values of the parameters are affected in case of transport limitation. Moreover, the structure of the far-field signal influences the substrate assimilation by the microorganism, and the mean interfacial uptake rate depends on the ratio between the characteristic time of the signal and the diffusional time scale, as well as on the amplitude of the fluctuations around the mean far-field concentration in substrate. The present work enlightens some experimental results and helps in understanding the differences between the concentration measured and that present in the microenvironment of the cells. (C) 2012 Elsevier Ltd. All rights reserved.

Dispersion of particles in a turbulent wall-bounded flow is crucial in many practical applications. For numerical simulation of particle-laden turbulent flow various approaches are available. Among these, LES is perhaps the most promising because its computational cost is lower than that of DNS and its predictive capability is much higher than Reynolds-Averaged Navier-Stokes methods especially in case of particles-turbulence interaction in boundary layers. Various subgrid models are available which have proved their validity for several types of flow. However, the treatment of particles in LES is still a relatively new topic with open questions regarding e.g. Sub-Grid Scales (SGS) effects on particle behavior and the modeling of particle-particle, particle-fluid or particle-wall interactions. To address these issues, an international collaborative benchmark test has been proposed as part of the activity of the COST Action P20 LESAID. The objective is to gather a large database of results obtained with different numerical methods, SGS models and physical models in order to resolve questions about the validity of these models. In this paper the first statistics of the benchmark for a base Eulerian-Lagrangian simulation of particle-laden channel flow, are presented. The specific simulation parameters have been chosen also to allow estimate of the quality of the LES results upon comparison with available DNS results (Marchioli et al., 2008) for the same test case. The groups participating in the benchmark are: UUD-UPI (Marchioli, Soldati, Salvetti); TUE (Kuerten); IMFT-ASU (Konan, Fede, Simonin, Squires); TUM (Gobert, Manhart); TUK-TUD (Jaszczur, Portela). Results provided by each group refer to a statistically stationary situation in which the particle concentration has reached a steady state. The time taken to reach steady concentration is very long (up to 2⋅104 in wall units (Marchioli et al., 2008)) thus making the required computational effort quite high even for a LES-based calculation.

The purpose of the paper is the deposition on the wall of inertial solid particles suspended in turbulent flow. The modeling of such a system is based on a statistical description using a Probability Density Function. In the PDF transport equation, an original model proposed Aguinaga et al. (2009) is used to close the term representing the fluid-particle interactions. The resulting kinetic equation may be difficult to solve especially in the case of the particle response time is smaller than the integral time scale of the turbulence. In the present paper, the Lattice Boltzmann Method is used in order to overcome such numerical problems. The accuracy of the method and its ability to solve the two-phase kinetic equation is analyzed in the simple case of inertial particles in homogeneous isotropic turbulence for which Lagrangian random walk simulation results are available. The results from LBM are in accordance with the random walk simulations.

Three dimensional unsteady numerical simulations of dense pressurized polydisperse fluidized bed have been carried out. The geometry is a medium-scale industrial pilot for ethylene polymerization. The numerical simulation have been performed with a polydisperse collision model. The consistency of the polydisperse model predictions with the monodisperse ones is shown. The results show that the pressure distribution and the mean vertical gas velocity are not modified by polydispersion of the solid phase. In contrast, the solid particle species are not identically distributed in the fluidized bed indicating the presence of particle segregation.Copyright © 2011 by ASME

A comparative parameter study is performed in order to analyze the influence of turbulence on the rate of droplet coalescence. Therefore, Direct Numerical Simulations (DNS) of the fluid turbulence are coupled with a Lagrangian tracking of the particle phase (DPS) accounting for collisions leading to coalescence and to a broad droplet size distribution. In addition the accuracy of stochastic collision models is evaluated by comparison of Monte-Carlo predictions with the obtained results from the DNS/DPS simulations and statistical collision models are evaluated.

Preferential concentration of solid inertial colliding particles suspended in homogeneous isotropic turbulence is numerically investigated using Direct Numerical Simulation (DNS) coupled with Discrete Particle Simulation (DPS). The results show that the preferential concentration is decreasing when the collision frequency increases. This effect is found enhanced for non-elastic particle-particle collisions.

International audience; Eulerian two-fluid approach is generally used to simulate gas-solid flows in industrial fluidized beds. Because of limitation of computational resources, simulations of large vessels are usually performed using too coarse mesh to capture the influence of the fine flow scales which can play an important role in the dynamic behaviour of the beds. In particular, neglecting the particle segregation effect at small scale leads to an inadequate modelling of the mean interfacial momentum transfer between phases. Then, an appropriate modelling approach which accounts for influences of unresolved structures has to be proposed for "coarse simulations". For this purpose, computational grids are refined to get mesh-independent results for a dense and a periodic circulating fluidized beds in which statistical quantities do not change with further mesh refinement. These mesh-independent results are filtered by volume averaging and then used to perform a priori analysis on the filtered drag term. Results show that filtered momentum equation can be computed on "coarse simulations" but must take into account the particle to fluid drift velocity due to the subgrid correlation between the local fluid velocity and the local particle volume fraction. In the present paper we propose a model, for subgrid the drift velocity, written in terms of the difference between the averaged of gas velocity weighted by solid volume fraction and the averaged of gas velocity weighted by gas volume fraction. We use a systematic procedure to provide constitutive closures for the subgrid drift velocity and the closure depends of both the filtered solid volume fraction and a characteristic filter size.

The present paper is dedicated to numerical and experimental study of the hydrodynamic of a non-reactive isothermal pressurized fluidized bed. Experimental data have been obtained using PEPT technique allowing to track a particle trajectory inside a dense fluidized bed. A specific post-processing approach has been developed to compute the Eulerian time-averaged particle velocity field. The comparison with 3-dimensional numerical model predictions shows a good agreement in the core of the fluidized bed. In contrast, in the near wall region the numerical model overestimate the downward particle velocity. The modification of particle phase wall boundary condition improves the numerical predictions.

In this study, mono-disperse flows in squared risers conducted with A and B-type particles were simulated by Eulerian n-fluid 3D unsteady code. Two transport equations developed in the frame of kinetic theory of granular media supplemented by the interstitial fluid effect and the interaction with the turbulence (Balzer et al., 1996) are resolved to model the effect of velocity fluctuations and inter-particle collisions on the dispersed phase hydrodynamic. The studied flow geometries are three-dimensional vertical cold channels excluding cyclone, tampon and returning pipe of a typical circulating fluidized bed. For both type of particles, parametric studies were carried out to determine influences of boundary conditions, physical parameters and turbulence modeling. The grid dependency was analyzed with mesh refinement in horizontal and axial directions. For B-type particles, the results are in good qualitative agreement with the experiments and numerical predictions are slightly improved by the mesh refinement. On the contrary, the simulations with A-type particles show a less satisfactory agreement with available measurements and are highly sensitive to mesh refinement. Further studies are carried out to improve the A-type particles by modeling subgrid-scale effects in the frame of large-eddy simulation approach.

To analyze in detail the coalescence mechanisms and validate modeling approaches, deterministic Lagrangian simulations of droplet trajectories (DPS) coupled with Direct Numerical Simulations (DNS) of a Homogeneous Isotropic Turbulence (HIT) are performed. The influence of the colliding particle velocity correlations induced by the fluid turbulence on the rate of droplet coalescence is investigated for different particle inertia. The results are compared to predictions using the Direct Quadrature Method of Moments (DQMOM) accounting for coalescence. The particle diameter distribution is written as a summation of Dirac functions. This allows to derive Eulerian transport equations for the dispersed phase statistics, which account for coalescence and conserve the low-order moments of the particle size distribution. The collision terms are modeled applying the molecular chaos assumption in order to account for coalescence. Particle size distributions and moments obtained from DQMOM are compared to those of the DNS/DPS simulations in function of particle inertia.Copyright © 2009 by ASME

The general purpose of this paper is the modeling of particle-turbulence interaction and particle-particle collisions taking place in dilute gas-solid flows. Direct numerical simulation of a homogeneous isotropic turbulence coupled with discrete particle simulation have been carried out with a model taking into account the effect of the film drainage between colliding particles. The results show that, depending on the particle Stokes number, the particle kinetic energy is strongly modified by the fluid drainage effect. In the frame of the joint fluid-particle approach, taking into account the correlations induced by the turbulence on the colliding velocities, a model has been derived and compared with the DNS results.Copyright © 2009 by ASME

A time driven Lagrangian particle detection algorithm for a poly-dispersed mixture of particles is developed and validated. The advantage of this algorithm is the possibility to treat a distribution of particle diameters. We are especially interested in the collision treatment of poly-dispersed particle mixtures and coalescence. Particle pairs are found by applying the overlap criteria and additionally another second criterion, which allows a substantial increase of the time step without limiting the algorithm’s accuracy. The algorithm, which is developed here, is validated with test cases by comparison with predictions of the kinetic theory of rarefied gases. They are applied to dry granular flows. The algorithm accuracy is determined with respect to time step criteria, for both dilute and dense systems.Copyright © 2008 by ASME

The purpose of the paper is to introduce the formalism of the joint fluid-particle PDF approach for polydisperse gas-particle flow and to focus on the derivation of the collision terms. The originality of this work is that our model takes into account the correlation between colliding particles and also the effect of a large drift. A discussion is performed on the model.Copyright © 2006 by ASME

This paper introduce a model for the kinetic stress transfer by collision in binary mixture of inelastic particles. The derived model is based on a perturbated two-Maxwellian approach allowing to described non-equilibrium particulate flows. The model is validated by comparison with numerical results carried out using a deterministic Discrete Particle Simulation (DPS).Copyright © 2005 by ASME

The general purpose of this paper is the modelling of particle-particle interactions in binary mixture of particles suspended in turbulent flows. The model predictions are compared with statistics issued from Large Eddy Simulation of an homogeneous isotropic gas coupled with Discrete Particle Simulation of a non-settling mixture.Copyright © 2003 by ASME

The purpose of this paper is the modelling of particle-particle collisions by Stochastic Lagrangian approach in gas-solid turbulent shear flows. A generalized Monte Carlo algorithm is introduced which takes into account the correlation between the colliding particles. Particle-particle and fluid-particle velocity correlations from Stochastic Lagrangian simulations are compared with results from Deterministic Particles Simulation coupled with Large Eddy Simulation of a gas turbulent shear flow (DPS/LES), and with predictions computed in the frame of the moment method using separate transport equation for the fluid and particle velocity correlations.Copyright © 2003 by ASME

This paper is dedicated to Lagrangian approach for modelling particle-particle interactions in gas-solid turbulent flows. This approach is based on a joint fluid-particle pdf equation solved using Monte Carlo method which has been developed to take into account the correlation between colliding particles induced by the fluid. The modification of the turbulence by the particles is not included in the simulations. The Lagrangian results are presented in comparison with LES simulations (Lavieville et al., 1995) and continuum model.Copyright © 2002 by ASME