A massively parallel CFD/DEM approach for reactive gas-solid flows in complex geometries using unstructured meshes

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A massively parallel CFD/DEM approach for reactive gas-solid flows in complex geometries using unstructured

meshes

Yann Dufresne, Vincent Moureau, Ghislain Lartigue, Olivier Simonin

To cite this version:

Yann Dufresne, Vincent Moureau, Ghislain Lartigue, Olivier Simonin. A massively parallel CFD/DEM approach for reactive gas-solid flows in complex geometries using unstructured meshes. Computers and Fluids, Elsevier, 2020, 198, pp.104402. �10.1016/j.compfluid.2019.104402�. �hal-02390009�

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To cite this version:

Dufresne, Yann and Moureau, Vincent and Lartigue, Ghislain and Simonin, Olivier A massively parallel CFD/DEM approach for reactive gas-solid flows in complex geometries using unstructured meshes. (2020) Computers and Fluids, 198.

104402. ISSN 0045-7930 Official URL:

https://doi.org/10.1016/j.compfluid.2019.104402

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A massively parallel CFD/DEM approach for reactive gas-solid flows in complex geometries using unstructured meshes

Yann Dufresne^a,∗, Vincent Moureau^a, Ghislain Lartigue^a, Olivier Simonin^b

aCORIA-UMR6614, Normandie Université, CNRS, INSA and UniRouen, Rouen, 760 0 0, France

bInstitut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, Toulouse, France

a b s t r a c t

Despite havingbeen thoroughlydescribed invarious simple configurations,the study ofgas-fluidized systemsinaCFD/DEM(DiscreteElementMethod)formalismbecomeschallengingasthecomputational domainsizeandcomplexityrise.Forawhile,attentionhasbeendrawntothedesignofphysicalmodels forfluid-particlesinteractions,butarecentchallengefornumericaltoolshasbeentotakeadvantagefrom theincreasingpowerofdistributedmemorymachines,inordertosimulaterealisticindustrialsystems.

Furthermore, unstructuredmeshes areappealing fortheir abilityto describecomplex geometriesand toperformlocal refinements,butleadtosignificantcoding effortinvolvingsophisticatedalgorithm.In aattemptto design anumericaltool abletocope withtheselimitations, the methodologypresented hereproposesan efficient non-blockingalgorithmformassive parallelism management,as wellas an exhaustivecontactschemetodealwitharbitrarilycomplexgeometries,alltobeoperatedonunstructured meshes.Theaimistwo-fold:(i)To assistlargerscalecodesintheirendeavortoclosethesolidstress tensorforexample,(ii)topavethewayforcomplexindustrial-scalesystemsmodelingusingDEM.The methodologyissuccessfullyappliedtoapilot-scalefluidizedbedgathering9.6Msphericalparticlesand enablestoreachinterestingphysicaltimesusingreasonablecomputationalresources.

1. Introduction

InFluidizedBedReactors(FBR), thefluidization regimeoccurs whenthe fluidthat passesthrough thegranularmaterialexceeds the minimum fluidization velocity.In thisregime, the drag force appliedtothesolidgrainscounterbalancesgravity,whichleadsto astrongmixingofthefluidandsolidphases.Thismixingensures efficientheatandmasstransfersacrossthereactorandminimizes temperature and species concentration gradients in the fluidized region. These propertiesare particularly beneficial inthe field of metallurgy, energy and chemical industry for instance, in large scaleoperationssuchaschemicalsynthesis,coatingordrying[1]. Low-temperature combustionwithhighconversionefficiencyand

Nomenclature for non-obvious or recurrent abbreviations (by order of appearance in the text): DEM, Discrete Element Method; ELGRP, Mesh element Group; PTGRP, Particle Group; INTCOMM, Internal Communicator; EXTCOMM, External Commu- nicator; MPI, Message Passing Interface; PTEXTCOMM, Particle External Communi- cator; PGTS, Particle Group To Send; VR , Voronoi Region; F, E,V, boundary Face, Edge, Vertex; BFG, Boundary Face Group; BSBFG, Bounding Sphere of Boundary Face Group; BSF, Bounding Sphere of Face.

∗ Corresponding author.

E-mail addresses: yann.dufresne@insa-rouen.fr, yann.dufresne@coria.fr

lowpollutantemissionssuch asnitrogenoxidesisone ofthenu- merousachievementofFBR.Inthepast,alackofunderstandingof thecomplex dynamicbehavior of such deviceshas beenpointed out[2]asoneofthecauseoftheseveredifficultiesintheirdesign andscale-up [3]. Thus, much time and resource is spent on the buildingofpreliminarytestsonpilot-scale reactors thatwilllead tothe design ofthe final industrial-scalereactor by the meanof empiricalprocesses[4].

ComputationalFluidDynamics(CFD)hasalreadycontributedto theunderstandingofmanyelementaryphysicalprinciplethrough numerousstudiesonvarioussystemsizes,rangingfromthestudy ofheatandmasstransferattheparticlescale[5]tothemodeling ofcompleteindustrialunits[6].Theprimedifficultyresidesinthe largespectrumoflengthandinvolvedtimescales.Indeed,evenin industrialscalesystemswheretheratioofthereactorsize tothe solid particle diameter is very large, the fluidization regime fea- tures macroscopicstructures such asrecirculations, particle clus- ters and gas bubbles of which dynamics prediction strongly de- pendson themicroscopic descriptionof particlecontacts,inpar- ticular.

Today,themost promisingframework forthe modeling ofin- dustrialunitsremains theTwoFluidModel(TFM)alsoreferred to asEuler-Euler method,in which itis assumed that both the gas

andthe particle phase are inter-penetratingcontinua [6]. Its un- derlyingassumptionistheexistenceofaseparationofscales:the sizeoftheaveragingregionismuchlargerthantheparticlescale.

Thisclass of methods is computationally effectivebut theestab- lishmentofan accurate continuousdescription ofthe solidphase ischallenginganditsformulationrequiressemi-empiricalclosures anddetailedvalidations.Ontheother hand,theDiscreteElement Method(DEM)alsoreferred toasdiscreteparticlemethodallows for a more detailed description of particle-particle and particle- wall interactions. This deterministic approach finds its origins in the molecular dynamics methods initiated by Alder and Wain- wright[7]and hasbeen benefiting fromits advances eversince.

InCFD/DEM,orEuler-Lagrangemethods,thegasphaseisstillcon- sideredcontinuousanditstime evolutionisobtainedfromaclas- sicalCFD-typeEuleriancode,buttheparticlesaredescribedindi- vidually assuming that their motion obeys Newton’s second law of motion, which is solved using standard schemes for ordinary differentialequations.Thislevelofmodelingdesignatedasmeso- scalestillrequiresclosuresfordrag,collisionandotherforcesasa CFDgridcell typically containsup toa few tensofparticles, but itsadvantageslieinitsabilitytoaccountfortheparticle-walland particle-particleinteractionsinamorerealisticmannerthanEuler- Eulermethods.

Forthe time being, apartfromtheclosures stillneededwhen usingCFD/DEM, two mainfactors limit its utilizationforrealistic industrialsystemstudy:i) Thesolving ofthemomentumbalance foreach particle gives rise to substantial costs that can only be overcomeby themeanofoptimizedparallelismmanagement and ii) industrialsystemgeometries areoftencomposed ofcylindrical andirregularpartsthat preventtheuseofconventionalCartesian meshes and necessitate a proper methodology to treat particle- wall contacts. Reaching sufficient computational performances in CFD/DEMsimulations servestwo purposes:thefirst istodevelop closurelaws which can represent the effective averaged interac- tionsinthelargerscalemodelssuchasTFM,andthesecondisto pavethewayforpilot andindustrial scale systemsimulations in thelongrun.

Many open-source or commercialCFD/DEM packageshave al- readyshowngoodcapabilitiesforsimulatingsuchsystemsormore complex ones. Among them, one can cite NGA [8] and MFIX- DEM[9]parallelsolverswhichare bothcapabletosimulatereac- tiveflows basedonCartesianmeshes. Othercodes relyingonun- structured meshesare built based on the coupling ofone solver dedicatedtothefluid phaseandanothertothesolid phase,such as OpenFoam®+LIGGGHTS® [10] and Fluent®+EDEM CFD® [11]. This study presents the design of a massively parallel code for simulatingbothphasesonunstructuredmeshes.Concerningcom- plex geometries, contrary to the algorithm suggested by Lin and Canny[12]implementedinthepopularI-Collide[13]collisionde- tectionpackage, the methodproposed inthiswork is ableto re- turn the measure of a particle penetration depth into the wall, whilebeingsimplerthantheVoronoi-clipalgorithm[14],whichis designedforarbitrarycomplex3D polyhedracollisions.Thiscode canalsoworkinreactingconditions.

AnapproachcombiningDEMtorepresentthesolidphasewith Large-EddySimulation (LES)equations solved on an Eulerianun- structured grid forthe fluid phase hasbeen implemented inthe finite-volume code YALES2 [15], a LES and DNS (Direct Numeri- cal Simulation) solver based on unstructured meshes. This code solvesthelow-MachnumberNavier-Stokesequationsforturbulent reactiveflows usinga time-staggeredprojection methodfor con- stant[16]orvariabledensityflows[17].

There isabundantliteratureonthesubjectofthedifferentex- istingmodels fordrag[18],collisionforce[19]andother closures thatmaybeusedforturbulenceorheat transfermodeling.These discussionsdon’tfallwithinthescopeofthiswork,whichfocuses

onamethodologyforperformanceincrease.Thus,onlyelementary modelsareusedinthepresentwork.Furthermore,asheattransfer neitherplays asignificant rolein codeperformancesnorinvolves extra specific numericalmethodology, our attentionturns to the studyofanisothermalgas-soliddensefluidizedbedexperimented attheUniversityofBirmingham[20].

In this context, this paper is organized in seven parts. The Euler–Lagrange formalism is first describedfor both the gaseous andtheparticle phaseinSection 2.Some noteworthyfeatures of theYALES2codearethenbrieflyintroducedinSection3.Thepur- poseofSection4istopresentanefficientalgorithmforparallelism management.Then,aviablemannertotreatsphericalparticlecon- tactswitharbitrarycomplexgeometriesispresentedinSection5. The main caseunderstudyis describedinSection 6. Finally,the performancesofthecodearemeasuredinSection7.Usefulabbre- viationscanbefoundinfootnote¹.

2. TheEuler–Lagrangeformalism

This section exposes themain models andnumerics used for solvingthelow-MachnumberNavier–Stokesequationsderivedfor granularflows inaLESframework.Then, adescriptionoftheclo- suresandnumericsforsolidphasemodelingispresented.Thecou- plingbetweenthephasesisprovidedintheAppendixA,including theinterpolation/projectiontechniqueandthedescriptionoffilter- ingstepssuitedforunstructuredmeshes.

2.1. Gasphasemodeling

The LES governing equations for granular flows are obtained from the filtering of the unsteady, low-Mach number Navier–

Stokesequations,takingthelocalfluidandsolidfractionsintoac- count. Further details concerning the volume filtering operations canbe foundin[21].Thegoverningequationsformassconserva- tion,momentumtransport,sensibleenthalpytransportandspecies transportfinallyread:

∂∂^t(ερ^¯)⁺∇·(ερ^¯u˜)^{=0, (1)}

∂∂^t(ερ^¯u˜)⁺∇·(ερ^¯u˜u˜)⁼⁻∇^P¯+∇·(ετ^¯)⁺ερ^¯g+F_p→f, (2)

∂∂^t ερ^¯˜hs

+∇· ερ^¯u˜˜hs

=∇^·μ^t

Prt∇^h˜s

+dP0

dt +∇^· ελ∇^T

+εω^˙T+Qp→f, (3)

∂∂^t ερ^¯Yk

+∇· ερ^¯u˜Yk

=∇^· μ^t

Sc_k,t∇^Yk

+∇^·

ερ^¯Dk∇^Yk

+εω^˙k. (4)

u,ρ^,μ^{,P, hs,P}0,T, λ^,Dk,Y_k,ε ^{are thegas velocity, density,dy-}

namic viscosity, dynamic pressure, sensible enthalpy, thermody- namicpressure,temperature,thermalconductivity,diffusioncoef- ficient,mass fractionofspeciesk,andfluid fraction,respectively.

ω˙kis the chemical source termand ˙ω^T the enthalpy source term.

Theturbulentvariablesnotedμ^t,PrtandSck,tarethegasturbulent viscosity,turbulentPrandtlnumberandturbulentSchmidtnumber ofspeciesk.Theviscousstraintensorτ¯ ^{iscalculatedas:}

τ¯⁼(μ⁺μ^t) ∇^u˜+∇^u˜T−2₃(∇^·u˜)I

, (5)

whereIistheidentitytensor.F_p→f andQ_p→f arethemomentum sourcetermandtheheatsourceduetothecouplingwithparticles,

respectively.Thereisnospeciestransferbetweengasandparticles.

Details concerning the computationof theseterms can be found intheAppendixA.Theseequationsaresupplementedbytheideal gasEquation-Of-State(EOS):

P₀=ρ¯^{r˜T with ˜r}=

k∈S

RYk

W_k, (6)

with r being the ideal gas mass constant, R being the ideal gas constant, W_k themolarmass ofspeciesk,andSbeingtheset of species.

Forthesake ofclarity,thefluid filteredquantitiesu˜,ρ¯,P¯,h˜s, T,Y_k,τ¯, ˜r,F_p→f andQ_p→f willbe writtenu,ρ^{,P,hs,T, Y}k,τ^,r,

F_p→fandQ_p→finthefollowingsections.

Eqs. (2)–(4) are integrated using an explicit variable density solverprovidingafullymass,momentumandenthalpyconserving timeadvancement.

2.2. Particlephasemodeling

The translational motion of a particle’s center of gravity and itsrotationalmotionaroundthecenterofgravitycanbefullyde- scribed by the following system of equations given by Newton’s second law, assuming spherical and constant mass particle with highsolid/gasdensityratio:

mp

dup

dt =FD+FG+FP+FC with dxp

dt =up, (7)

Ip

dωp

dt =MD+MC, (8)

wheremp,up, xp,Ip andω^{p are theparticle mass,velocity, posi-}

tion,momentofinertiaandangularvelocity, FD isthedragforce, F_G=mpg is the gravity force and F_P=−Vp∇^P@p is the pressure gradient force. In the last term, Vp is the particle’s volume and

∇^P@p is the local pressure gradient interpolatedat the centerof the particle. As in many dense gas-fluidized bed cases, a soft- sphere model[22]is employed,inwhichparticles areallowed to overlapotherparticlesorwallsinacontrolledmanner.Aresulting contact force F_C accounting forparticle-particle andparticle-wall repulsion isthus addedinthe momentumbalance ofeach parti- cle.MC isthetorqueofthecontactforceF_CandMD isthetorque offluiddragforces.Theparticletemperatureevolutionisgivenby:

mpC_p,pdTp

dt =QF, (9)

whereCp,pandTp aretheparticlemassheatcapacityandtemper- ature,andQ_Fistheheatfluxexchangedwiththefluid.

The source terms for particles F_D and MD are calculated us- ing a combination ofthe Ergun [23] andWen andYu [24] drag laws,andaclosurefromtheworkofDennis[25],respectively.The closuresused forthe computationofQF won’tbe detailedinthis study,whichfocusesonanisothermalapplication.Therelationbe- tweenF_D,F_P andF_p→f,betweenQ_F andQ_p→f,aswell asdetails concerningtheinterpolationkernelsaregivenintheAppendixA.

Asecond-orderexplicitRunge-Kutta(RK2)algorithmisusedto advancetheparticles intime.Theuseofasoft-spheremodelde- mandsthat^tp<T_C,where^tpistheparticletimestepandT_Cis acontacttimedescribedinSection2.2.1.Inthiswork,^tp=T_C/10 wasconsidered,toensureareasonableprecision.

2.2.1. Modelingofcollisions

Thetotal collisionforceFC actingon particleaiscomputedas the sum of all pair-wise forces f^col_b→a exerted by the Np particles andNwwallsincontact.Asparticlesandwallsaretreatedsimilarly

Fig. 1. Soft sphere representation of two particles undergoing collision.

duringcollisions,thebindexreferstoboth:

FC=

Np+Nw

b=1

f^col_b→a with f^col_b→a=f^col_n,b→a+f_t^col_,b→a. (10)

Here a linear-spring/dashpot [22] model is used along witha simpleCoulombslidingmodelaccountingforthe normal

f^col_n,b→a

and tangential

f_t,b→^col _a

components of the contact force, respec- tively,asintheworkofCapecelatro[21].Foroneparticle(orwall) bactingonaparticlea:

f^col_n,b→a=

−knδabn_ab−2γ^nMabu_ab,n

0 and

f^col_t,b→a=

−μ^tan||^fcoln,b→a||^tab if δab>0,

0 else. (11)

Fig.1showsarepresentationoftwocollidingparticles.knisthe normalspringstiffness,γ^{nisthenormaldampingparameter,and} μtan isthe friction coefficient. The termδab=r_a+r_b−||^xb−x_a||

isdefinedasthe overlapbetweenthe a andb entities expressed usingeach particleradius rp andcenter coordinates xp. The sys- tem effective mass M_ab is expressed as M_ab=(¹/m_a+1/m_b)^−1. The unit normalvector n_ab from particlea towards entityb and aunittangentialvectort_abaredefinedusingparticles’relativepo- sitionandvelocity.n_abandt_abarecalculatedasfollows:

nab= xb−xa

||^xb−xa|| ^and

t_ab=

_u

ab−u_ab,n

||^uab−u_ab,n|| ^if ||^uab−u_ab,n||^>0,

0 else. (12)

The relative velocity of the collidingsystem atthe contactpoint u_abiswritten:

u_ab=(^ua−ub)⁺(^raω^a+rbωb)^∧nab. (13) Itsnormalcomponentisthengivenbyu_ab,n=(^uab·n_ab)ⁿab.

Using Newton’s third law yields an analytical expression for the system’s natural frequency ω0=

kn/M_ab and the contact time[26]:

TC= π ω²0−γn²

∝

mp

kn

. (14)