COMPREHENSIVE DEM-DPM-CFD SIMULATIONS - MODEL SYNTHESIS .

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Seventh International Conference on CFD in the Minerals and Process IndustriesCSIRO, Melbourne, Australia9-11 December 2009COMPREHENSIVE DEM-DPM-CFD SIMULATIONS MODEL SYNTHESIS, EXPERIMENTAL VALIDATION AND SCALABILITYChristoph KLOSS1, Christoph GONIVA1, Georg AICHINGER3 and Stefan PIRKER1,21Christian Doppler Laboratory on Particulate Flow Modelling2Institute of Fluid Mechanics and Heat Transferboth Johannes Kepler University, Altenbergerstr. 69, 4040 Linz, Austria3Siemens VAI Metals and Technologies, IR DR Technology, Turmstr.44, 4031 Linz, AustriaINTRODUCTIONGenerally, two modelling strategies for particle flow canbe applied. The continuum approach considers themultitude of particles as an artificial continuum and isbased on the solution of the underlying conservationequations using CFD techniques. Of course, such anapproach disregards the local behaviour of individualparticles. The so-called kinetic theory for granular flowhas been introduced and successfully applied in manycases, but as it stems from kinetic gas theory, theapplication is limited to cases where the motion of theparticles resembles the motion of molecules in a gas.However, in systems comprising particles that are evenlydistributed with the same bulk properties so that they canbe thought of as forming a continuum, such an approachcan yield results that are in qualitative agreement withexperimental data.The second modelling strategy does not rely uponcontinuum mechanics. It rather simulates the motion ofeach particle individually, with a special treatment foreventual collisions. Many such methods have beendeveloped over the years. They can be subdivided intotwo categories. The first category comprises theprobabilistic methods that are based on randomlydisplacing the particles in the simulation domain, insteadof directly resolving interparticle collisions. If theinterparticle collisions are important, but not dominant,statistical methods might be used to model their influence(Sommerfeld, 2001; Kahrimanovic et al, 2008; Kloss andPirker, 2008). The second category of discrete models isthe Discrete Element Method and its derivates. Lately, theDEM comes more and more into the focus of engineersand researchers. Being discrete in nature, it is, in principal,capable of capturing all granular physical phenomena. Onthe other hand, the DEM leads to massive CPU effortmaking it impossible to simulate large scale industrialprocesses with a straight-forward approach.Practically, none of all those granular models hasbeen proven to describe general granular flow situationswith reasonable CPU effort.Furthermore, single phase ‘dry’ granular flow rarelyoccurs. In the vast majority of natural or industrialprocesses concerning granular materials, a secondary fluidphase, such as air, is present and its effects likefluidization (aeration of particles by gas injection) play animportant role.ABSTRACTWe report on the synthesis of the Discrete ElementMethod (DEM) modelling the behaviour of granularmaterials and a finite volume model for the continuousinterstitial fluid using Computational Fluid Dynamics(CFD). DEM captures the physics of granular materialsbest but is computationally time-consuming. For thisreason, the DEM is complemented by a Discrete PhaseModel (DPM) for disperse granular flow in order toaccelerate the overall simulation. In our case, both DEMand DPM are applied within one simulation by usingspatial domain decomposition. The implementation of thecode permits fully parallel simulations for all threemodels. We demonstrate the efficiency and validity of ourapproach by three validation examples and discuss thescalability of the coupling approach.NOMENCLATURECd drag coefficientCu Cundall numberCu* modified Cundall numberd diameterfp force density the particles exert on the fluidFf sum of all forces the fluid exerts on a single particleg gravity constantp pressureu velocityΔup relative particle velocity at contact pointRep particle Reynolds numberΔxp particle overlap at contact pointSubscript indices:ffluidn normal to contact pointp particlettangential to contact pointGreek letters:volume fractiondynamic viscosityCoulomb friction coefficientdensitystress tensorangular velocityαμμcρτωCopyright 2009 CSIRO Australia1

In the following section, we give a brief overview ofour modelling approach. We then present and discuss ourtest cases before drawing final conclusions in the lastsection.Here, Ff is the force that the fluid phase exerts on theparticles, which will be described in further detail later.Other body forces like gravity, electrostatic or magneticforces are subsumed into Fb.Similar balances are necessary for the particles’angular momentum which are not stated here or the sakeof shortness.The power of the DEM lies in its ability to resolve thegranular medium at the particle scale, thus allowingrealistic contact force chains and giving rise to phenomenainduced by particle geometry combined with relativeparticle motion, such as particle segregation bypercolation. Thereby, it is able to capture manyphenomena, describe dense and dilute particulate regimes,rapid flow as well as slow flow and equilibrium states orwave propagation within the granular material.The drawback of the method is that the time-step hasto be chosen extremely small because the contact forceexhibits a very stiff behaviour. Depending on the materialproperties and the particle size the time-step size can be aslow as in the order of 10-6 sec for an accurate simulation.Thanks to advancing computational power, the DEMhas become more and more accessible lately. On actualdesktop computers, simulations of up to a million particlescan be performed. On very large clusters, the trajectoriesof hundreds of millions of particles can be computed.MODEL DESCRIPTIONSince in many cases different granular regimes occurwithin one simulation, a synthesis of individuallydedicated models is considered to be the best trade-offbetween capturing the physics and ensuring computability.The actual coupling is implemented by joining the twocommercial software packages EDEM and FLUENT byan in-house code. While the former covers the DEMmodelling, the latter describes the fluid dynamics of thecontinuous phase and the motion of particles in dilute flowregimes by means of the Discrete Phase Model.A further implementation of the coupling, using theopen-source software OpenFOAM as CFD solver and themolecular dynamics software LAMMPS (sse plimptom,1995) as DEM solver, was also developed, and is yet inbeta stadium.From a physical point of view, the coupling currentlycomprises the effect of (a) volume displacement by theparticles, (b) drag of the fluid on the particles as well as(c) Magnus force due to particle rotation.Discrete Element Method (DEM)CFD ApproachThe Discrete Element Method was introduced by Cundalland Strack (1979). In the frame of the DEM, all particlesin the computational domain are tracked in a Lagrangianway, explicitly solving each particle’s trajectory, based oncorresponding momentum balances for translational andangular accelerations. A very brief description of themethod will be provided in this section. Further details onthe contact physics and implementational issues areavailable in the literature (e.g. Campbell, 1990; Zhou etal., 1999; Mattutis et al., 2000; Bertrand et al., 2005).Generally, the particles are allowed to overlapslightly. The normal force tending to repulse the particlescan then be deduced from this spatial overlap Δxp and thenormal relative velocity at the contact point, Δun. Thesimplest example is a linear spring-dashpot model:Fn, µct,put,upFtdt c t Δ Fb FfFtFntoFt .Copyright 2009 CSIRO Australia(5)DEM-CFD interactionTo implement the coupling, the DEM solver EDEM andthe CFD solver FLUENT are being run eitherconsecutively or concurrently, each halting calculationafter a predefined number of time-steps for the purpose ofdata exchange managed by our software. This dataexchange routine consists of several steps: For each particle, the corresponding cell in the CFDgrid is determined. The volume fraction occupied by the granular phase iscalculated. Based on this information, the momentum exchangeterms between the gas phase and the particulate phasecan be evaluated.The most important contribution to particle-fluidmomentum exchange is established by means of a dragforce depending on the particle volume fraction. Certainempirical or semi-empirical approaches have beenpublished to model this force. In our coupling software(2)where Ft is the tangential force and Δup,t is the relativetangential velocity of the particles in contact. The integralterm represents an incremental spring that stores energyfrom the relative tangential motion, representing theelastic tangential deformation of the particle surfaces. Thesecond part, the dashpot, accounts for the energydissipation of the tangential contact. The magnitude of thetangential force is limited by the Coulomb frictional limit,where the particles begin to slide over each other.Subsequently, the total force acting on a particle can thenbe expressed as: (α f τ ) ρ f α f) .g(1) , αfHere, αf is the volume fraction occupied by the fluid, ρf isits density, uf its velocity, τ is the stress tensor for thefluid phase and fp represents the momentum exchangewith the particulate phase. For each cell, it is calculatedfrom the forces Ff (described in the following section) forall particles residing within this cell. If Ff comprises onlydrag force, this term is also called generalized drag.The magnitude of the tangential contact force can bewritten as:t min k t Δ tc ,0f(4)ufuf p ) 0,) (ρfp (ρ f α f tuf α f (α f tufn,p cn ΔupxFn k n ΔThe motion of the fluid phase in the presence of asecondary particulate phase is governed by a modified setof Navier-Stokes-Equations, which can be written as:(3)2

is desired to automatically switch between DEM and DPMdepending on the local particle volume fraction. In ourimplementation, a DPM parcel represents only oneparticle. Therefore, it is possible to transfer particles fromDPM to DEM without loss of information.The interaction with the fluid phase is calculated asdescribed in the section “DEM-CFD interaction” for allparticles, irrespective of whether the particle motion itselfis handled by DEM or DPM.dupufupufFdpackage, we use a model by Gidaspow (1994) combiningmodels for the dilute and dense granular regime. Thismodel is very common, but the transition between thedilute regime and the dense regime is discontinuous,which could lead to convergence problems. Therefore, inaddition to Gidaspow’s model, we alternatively make useof a drag model by Di Felice, also used by Yu et al.(2008):21p π(6) ρf ( ) Cdα f 1 χ .242,eR (1.5 log 2χ 3.7 0.65 exp upufeRρ f dp α fVALIDATION EXAMPLESIn this section, the models described are applied to threecases: First, particle rope formation and dispersionduring pneumatic conveying is focused (case I). Next, particle discharge from a hopper-standpipeconfiguration is addressed (case II). Finally, we discuss the charging of particles intoa test facility (case III).The first two cases are examined using coupled DEMCFD simulations. In the third case, all three models(DEM, DPM, and CFD) are used within one simulationFor all of the cases, spherical beads made of soda limeglass are used. The wall materials are glass and sheetmetal for case I, and Perspex for case II and III.(7)eR 4.8C d 0.63 p 10p)2 , (8)(9).μfFurther literature on similar approaches can be found inYu et al. (2008), Tsuji et al. (2008) and Kafui et al.(2002). Beside the drag force resulting from a relativevelocity between the particle and the fluid, other forcesmay be relevant too. These may stem from the pressuregradient in the flow field (pressure force), from particlerotation (Magnus force), particle acceleration (virtualmass force) or a fluid velocity gradient leading to shear(Saffman force). The force Ff exerted by the fluid phaseon a single particle is then the sum of all these forces.For the pneumatic conveying example, drag force andMagnus force are being accounted for, Ff Fd Fm. TheMagnus force formulation used is given by Lun et al.(1997). For the other validation examples, all other forcesthan the drag force can be neglected, so that Ff Fd.p Case I: Pneumatic ConveyingThe pneumatic conveying facility consists of a radial fanfollowed by a particle injector fed by a vibrator chute. Adouble–looping is placed right after the injector, providingfor the formation of a particle strand caused by centrifugalforces. The double-looping is followed by themeasurement section. The geometry of the measuringchannel is shown in Fig. 1. At these positions,measurements using a Particle Image Velocimetry (PIV)system can be conducted. The volume concentration canbe evaluated as well by digital image processing. Thistechnique has been published in detail by Kloss and Pirker(2008). For further details on the design of the pneumaticconveying facility itself, the reader is referred toKahrimanovic et al. (2008). Because air density is muchlower than particle density, forces like the Basset force orvirtual mass force can be neglected. Furthermore, theSaffman force is negligible too. On the other hand, theMagnus force is found to have an important effect on theparticle volume fraction profile. To study this effect, thesimulation was conducted with and without the Magnusforce.The simulation is carried out with an air mass-flow of0.18 kg/s and a granular mass-flow (particle diameter 0.85mm) of 0.09 kg/s, corresponding to a mass loading of 0.5.The total number of particles in the simulation is around200,000. Simular simulations with higher mass loadingshave been performed with up to 600,000 particles though.The CFD grid contained around 100,000 cells.The dedicated velocity and volume fraction profilesfor position 3 are shown in Fig. 2. “Left”, “Middle” and“Right” refer to the left, center and right sections of theprofile as marked in Fig. 1.Discrete Phase Model (DPM)The standard Lagrangian DPM is, like the DEM, based ona translational force balance that is formulated for anindividual particle.In the standard DPM, each particle represents a parcelof particles. Like DEM particles, a DPM parcel is subjectto gravity, drag force, pressure force, Magnus force,virtual mass force and Saffman force, not all of which areavailable in the commercial package FLUENT.A crucial difference to DEM is that in the frame ofDPM, interparticle collisions are neglected. Since theDPM also neglects the gas displacement by the particles,the volume fraction of the gas phase remains constant.Due to this assumptions and simplifications, the DPMis valid for dilute fluid-particle flow only.Recommendations for the applicability vary in literature.In our validation case III, the DPM is applied for parts ofthe domain where the particle volume fraction is below5%. The advantage over the DEM is however, that timesteps in the order of 10-4 sec can be used.DEM-DPM interactionFully coupled DEM-CFD simulations require a lot ofcomputational effort in terms of CPU performance andmemory requirement. If interparticle collisions can beneglected, it is permissible to use the DPM to account forthe particulate phase’s motion. The actual coupling isrealised by static domain decomposition. If a particle’strajectory traverses the predetermined boundary betweenthe DEM and the DPM domain, the particle is transferredfrom one program to the other. For future applications, itCopyright 2009 CSIRO Australia3

One can deduce from Fig. 2 that the Magnus force,stemming from particle rotation induced by collisions,especially in the double-looping, tends to dissolve theparticle strand and to even out the volume fraction profilewhile slightly decreasing the particle velocity. Generally,the particle volume fraction lowers as the particles areaccelerated by the gas phase. As the Magnus force tendsto dissolve the particle strand, the solids fraction profilesat positions 2 and 3 (not shown) are steeper than atposition 1.In Fig. 3, comparisons of measured and simulatedprofiles for position 3 are given. At position 3, theagreement of the volume fraction profiles is quite good. Atpositions 1 and 2, the experimental and numerical profilesdo show deviations. This could be due to the fact that wallroughness has not been accounted for in the simulation.Kahrimanovic et al. (2008) found out that the influence ofwall roughness may be of high importance when it comesto particle strand dispersion at a wall.Left/Middle/RightCase II: Hopper Dischargey in mFigure 1: Geometry of the double-looping and themeasurement channel, taken from Kahrimanovic et al.(2008). All values are in mm.particle volume fraction at pos. 3 from coupled DEM-CFD simulation0.14left0.12rightmiddle0.1no magnus forcewith magnus force0.08The second example is the discharge of glass beads (4 mmin diameter) from a hopper with enclosed standpipe. Thehopper is made of Perspex and exhibits a hopper angle of10 . It can thus be regarded as a mass-flow hopper. Thegeometry and a simulation snapshot are shown in Fig. 4.The evolving granular mass-flow in the simulation is0.097 kg/s.particle velocity at pos. 30.12measurementsimulation0.10.060.08y in m0.040.060.0200.0400.20.40.60.81volume fraction1.21.41.6-30.02x 10particle velocity at pos. 3 from coupled DEM-CFD simulation0.14middleno magnus forcewith magnus force0.1y in m00leftright0.12123456particle velocity in m/s78910volume fraction at pos. 30.120.080.1measurementsimulation0.060.08y in m0.040.0200.060.040246810particle velocity in m/s0.02Figure 2: Profiles of volume fraction and particle velocityfor position 3 from coupled DEM-CFD simulation,wherey is the height over the channel ground.000.20.40.60.8volume fraction11.21.4Figure 3: Comparison of the profiles of volume fractionand particle velocity from measurement and fromsimulation at position 3, where y is the height over thechannel ground.Copyright 2009 CSIRO Australia4-3x 10

Pressure of the fluid phase0-0.5simulationmeasurement-1-1.5-2-2.5Figure 4: Geometry of the hopper-standpipe combination(left, all values in mm) and simulation snapshot duringdischarge (right).-3-3.5-400.10.20.30.4z in m0.50.60.70.8Figure 6: Pressure of the fluid phase over z together withthe geometry of the hopper.with hardly any feedback influence on the particles (oneway-coupling in a physical point of view).The pressure of the fluid phase is shown in Fig. 6.Each distinct point in the figure is the pressure in onecomputational cell. The drop at z 0.4 is caused by thetransition from the hopper to the standpipe. The highervalues correspond to cells at the edge of the hopper, wherethe air is de facto at rest, whereas the lower values arereached in cells close to the standpipe. The pressurechange at z 0.47 m is caused by a change in thestandpipe’s cross-sectional area.At the end of the standpipe (corresponding to z 0.77m), ambient pressure is reached again. The pressure valuesinside the standpipe have been measured with dedicatedsensors. The good agreement with the pressure from thesimulation indicates that the flow field within thestandpipe is well reproduced by the simulation.Figure 5: Snapshot of the solids fraction in the y-z planeduring discharge (left) and flow field of the fluid phase inthe symmetry plane during discharge in m/s (right).The CFD grid size and number of particles are 25,000 and60,000, respectively. A snapshot of the particle volumefraction during discharge is shown on the left hand side ofFig. 5.It is well reported in literature (e.g. Rao and Nott, 2008)that the addition of a standpipe to a hopper may increasethe discharge flow rate. This is because the particlesflowing out of the hopper accelerate the air phase thatsurrounds them. In the absence of the standpipe, thiswould lead to a flow of surrounding air towards the fallingparticle strand in order to fulfil the mass-balance for thegas phas

comprehensive dem-dpm-cfd simulations - MODEL SYNTHESIS, EXPERIMENTAL VALIDATION AND SCALABILITY Christoph KLOSS 1 , Christoph GONIVA 1 , Georg AICHINGER 3 and Stefan PIRKER 1,2

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