Fluid-particle flows are frequently encountered in industrial facilities and especially in chemical engineering processes. In this work, we focus on fluidized beds, which involve a fluid flow passing upward through a pack of particles with such a velocity that the fluid force acting on particles is larger than their weight

Bernard, Manuel

Climent, Éric

Wachs, Anthony

English

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   Open Archive TOULOUSE Archive Ouverte (OATAO)  OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.  This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 10472 To cite this version : Bernard, Manuel and Climent, Eric and Wachs, Anthony Mesocale approach for fluidized beds. (2013) In: Euromech Colloquium 555 : Small-scale numerical methods for multi-phase flows, 28 August 2013 - 30 August 2013 (Bordeaux, France). (Unpublished) Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Mesocale approach for fluidized bedsManuel Bernard1  Eric Climent2  Anthony Wachs11 Fluid Mechanics Department, IFP Energies Nouvelles, 69360 Solaize2 Institut de Mécanique des Fluides de Toulouse, University of Toulouse - UMRCNRS 5502, 31400 Toulouse1 IntroductionFluid-particle flows are frequently encountered in industrial facilities and especially in chemical engi-neering processes. In this work, we focus on fluidized beds, which involve a fluid flow passing upwardthrough a pack of particles with such a velocity that the fluid force acting on particles is larger thantheir weight. This technology is commonly used for its high heat and mass transfer rates in Circulat-ing Fluidized Beds or Fluid Catalytic Cracking processes which are composed of millions of particlesfrom a few micrometers to some millimeters, fluidized by a liquid or a gas. In order to optimizeperformances of those engineering processes, numerical simulations of multiphase flows became indis-pensable, especially over the last 20 years with the considerable rise of computational power and theprogress in multiphase computational fluid dynamics. Depending on the length scale, there are threemain approaches to simulate the dense particulate flows in fluidized beds (see fig 1).At the micro-scale, the fluid motion equations are solved directly on a small mesh compared tothe particle diameter. Direct numerical simulation (DNS) provides precise solutions but the numberof fluid cells does not permit to simulate systems containing more than a few thousands particles ina reasonable computing time.At the macro-scale, by using Eulerian methods, the fluid and solid phases are considered as twointer-penetrating media. The mesh is then coarser than a particle diameter and simulation of largedomains, up the real size reactor, are doable. However, this length scale requires the introductionof numerous assumptions in the model to describe the evolution of the solid phase and its couplingwith the surrounding fluid. Moreover, since the solid phase is considered as a continuous media,particle trajectories are not individually treated, which is a crucial lack of information for engineeringprocesses.At an intermediate scale between the DNS and Euler-Euler methods, the fluid is solved on alarger grid than the particle diameter, as it is in the Euler-Euler methods, but as in DNS methods,the particle trajectories, including collisions, are tracked with a discrete element method (DEM). Thisapproach, commonly called discrete element method / computationnal fluid dynamics (DEM-CFD) orEuler-Lagrange method, was first introduced by Tsuji et al. [7] and Hoomans et al. [5]. This methodhas been widely developped and used since the beginning of the XXIst century (see e.g. [6, 11]).A) Micro b) Meso c) MacroFigure 1: Different length scales used for simulating fluid-particle flows12 Model equations and numerical techniques2.1 Particle trajectoriesThe translational and rotational motion of a particle i with mass mi is calculated using Newton'ssecond law of motion :midvidt= fg;i + fpp;i + ffp;i (1)Where vp and !p are the translational and rotational velocities, respectively. fg, fpp and ffp are thegravity force, the contact force and the hydrodynamic force eperienced by the particles embedded inthe fluid respectively (see subsection 2.3).The collision model used in this work is based on a soft-sphere / discrete element model, allowingcolliding particles to slightly overlap to compute the contact forces. Contact forces considered hereare a normal elastic restoring force, a normal viscous dynamic force and a tangential friction force.Particle trajectories and contacts are solved with the IFPEN granular code Grains3D [10].2.2 Fluid motionThe fluid motion is described with spatially averaged continuity and momentum balance equationsintroduced by Anderson and Jackson [2]. In this work, the B model (see [4]) formulation of the twofluid model (TFM) is used :8>><>>:@"@t+r  ("uf ) = 0; (2a)@(f"uf )@t+r  (f"uf  uf ) =  rP + Fpf +r  ("fi ) + "fg (2b)Where uf , f , P and fi are the fluid velocity, density, pressure and stress, respectively. Fpf is avolumetric force modelling the particle-fluid interaction. The fluid volume fraction " is calculatedwith respect to the number of particles in each fluid cell.Navier-Stokes equations (2) are solved using a Marchuk-Yanenko first order operator splitting fortime integration. For the space discretization, a classical finite volume / staggered grid scheme isemployed.2.3 Two-way couplingIn order to respect Newton's third law of motion, the volumetricparticles-on-fluid force, Fpf , must balance the sum of fluid-on-particleforces, ffp, in each cell :Fpf =  Pnci=1 ffp;iV(3)Figure 2: Interaction forcesThe fluid-on-particle force is obtained by integrating the total fluid stress on the boundary of eachparticle. Considering the local averaging process introduced by Anderson & Jackson [2], the fluidstress ff can be decomposed into its local mean value ff and a fluctuation term ff0. As ff =  P ij+fif ,fluid-on-particle force can be expressed as the sum of a hydrostatic contribution and a hydrodynamiccontribution. In this work, only drag and buoyancy forces are considered, hence the fluid-on-particleforce reduces to :ffp =  Vpfg + fd (4)We employ the drag force correlation suggested by Di Felice [3], which shows good predictions over alarge range of particle concentration and Reynolds number.2Figure 3: Comparison between PeliGRIFF simulation and experimental data of Alobaid et al. [1]3 Validation testsThe DEM-CFD model presented in section 2 has been implemented in the IFPEN PeliGRIFFplatform [8, 9]. Several validation tests have been performed, both in bubbling and spouting regimesas illustrated in figure 3.The C++ code PeliGRIFF is fully MPI using non blocking communication pattern and dataexchange between fluid and granular solvers has been optimized. Figure 4-a shows the evolution ofthe computing time in the different parts of the code with respect to the number of computing cores.Computing time is normalized by a full node (i.e. 16 cores) computing time.The particles and fluid cells load per core is constant in our test, thus we expect that the computingtime is constant on 32, 64 and 128 cores for a twice, 4 times and 8 times larger problem than the 16cores one. The Stokes problem solution does not scale very well due to the low fluid cells load per corebut it represents only a few percents of the total computing time (see table 4-b). However, the rest ofthe code scales very well beyond 2 full nodes and the global parallel behaviour of the implementationis deemed to be satisfactory.30000 and 120000 particles per core simulations have be performed on up to 128 cores, i.e. up to15 millions of particles, with the same good parallel behaviour. That opens the way to simulations ofseveral hundred millions of particles on a larger number of cores, which is close to some engineeringprocesses size.4 Ongoing workThe multi-scale framework we wish to build implies to transfer information from DNS at the micro-scale to the DEM-CFD model at the meso-scale. To achieve this goal, we are currently investigatingthe same system (a fluidized bed containing a few tens of thousands of particles) both by DNS andDEM-CFD simulations. Simultaneously, additional DEM-CFD simulations are performed to examinethe particles kinetic energy and collision rate evolution with respect to time, inlet velocity and bedheight.3 100 150 200 250 300 350 400 450 500 550 16  32  64  128% of a full nodeNumber of coresTotal Epsilon Stokes Grains(a)Node(s)Part 1 2 4 8Stokes 1% 2% 3% 4%Epsilon 12% 15% 15% 14%Grains 81% 80% 84% 78%(b)Figure 4: Scale-up results with constant load per core (30000 particles). (a) Time repartition evolu-tion, (b) Time repartition in percents.References[1] F. Alobaid, J. Ströhle, and B. Epple. Extended cfd/dem model for the simulation of circulating fluidizedbed. Advanced Powder Technology, 2012.[2] T.B. Anderson and R. Jackson. Fluid mechanical description of fluidized beds. equations of motion.Industrial & Engineering Chemistry Fundamentals, 6(4):527539, 1967.[3] R. Di Felice. Hydrodynamics of liquid fluidisation. Chemical engineering science, 50(8):12131245, 1995.[4] D. Gidaspow. Multiphase flow and fluidization: continuum and kinetic theory descriptions. AcademicPr, 1994.[5] BPB Hoomans, JAM Kuipers, WJ Briels, and WPM Van Swaaij. Discrete particle simulation of bubble andslug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach. Chemical EngineeringScience, 51(1):99118, 1996.[6] KD Kafui, C. Thornton, and MJ Adams. Discrete particle-continuum fluid modelling of gas-solid fluidisedbeds. Chemical Engineering Science, 57:23952410, 2002.[7] Y. Tsuji, T. Kawaguchi, and T. Tanaka. Discrete particle simulation of two-dimensional fluidized bed.Powder technology, 77(1):7987, 1993.[8] A. Wachs. A dem-dlm/fd method for direct numerical simulation of particulate flows: Sedimentation ofpolygonal isometric particles in a newtonian fluid with collisions. Computers & Fluids, 38(8):16081628,2009.[9] A. Wachs. Peligriff, a parallel dem-dlm/fd direct numerical simulation tool for 3d particulate flows. Journalof Engineering Mathematics, 71(1):131155, 2011.[10] A. Wachs, L. Girolami, G. Vinay, and G. Ferrer. Grains3d, a flexible dem approach for particles of arbitraryconvex shape-part i: Numerical model and validations. Powder Technology, 2012.[11] B.H. Xu, A.B. Yu, S.J. Chew, and P. Zulli. Numerical simulation of the gassolid flow in a bed with lateralgas blasting. Powder Technology, 109(1-3):13  26, 2000.4

Mesocale approach for fluidized beds

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Mesocale approach for fluidized beds

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