State-Of-The-Art Review of CFD of Gas-solid Systems

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STATE-OF-THE-ART REVIEW O F COMPUTATIONAL FLU IDDYN AM ICS MODELING FOR FLUID-SOLIDS SYSTE MS

Robert W. Lyczkowski, Jacques X. Bouillard, Jainmin Ding+, Shen-Lin Chang,and Steven LottesARGONNE NATIONAL LABORATORYEnergy System s Division+Energy Technolog y Division9700 South Cass AvenueArgonne, IL60439-4815 USA

andSteve W. BurgeBABCOCK & WILCOXAlliance Research Center1662 Beeson StreetAlliance, OH44601-2196

Manuscript for an Invited Paper Subm itted toInternational Sympo sium on Parallel Com putingin Multiphase Flow Systems Simulations1994 Winter Annual M eetingAmerican Society of Mechanical EngineersNovember 6-1 1,1 99 4Chicago, Illinois

May 12,1994


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DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.


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STATE-OF-THE-ART REVIEW OF COMPUTATIONAL FLUIDDYNAMICS MODELING FOR FLUID-SOLIDS SYSTEMS*

Robert W. Lyczkowski, Jacques X. Bouillard, Jianmin Ding+,Shen-Lin Chang, and Steven LottesEnergy Systems Division

Argonne National LaboratoryArgonne, Illinois

Steve W. BurgeBabcock & Wilcox

Alliance Research CenterAlliance, Ohio

ABSTRACTAs the result of 15 years of research (50 taff years of effort)Argonne National Laboratory (ANL). hrough its involvementin fluidized-bed combustion, magnetohydrodynamics, and avariety of environmental programs, has produced extensivecomputational fluid dynamics (CFD ) software and models topredict the multiphase hydrodynamic and reactive behavior offfuid-solids motions and interactions in complex fluidized-bedreactors (FBRs) and slurry systems. This has resulted in theFLUFIX, IRF, and SLUFDC comp uter programs.These programs are based on fluid-solids hydrodynamicmodels and can predict information important to the designerof atmospheric or pressurized bubbling and circulating FBR,fluid catalytic cracking (FCC) and slurry units to guaranteeoptimum efficiency with minimum release of pollutants intothe environment. This atter issue will become of paramountimportance with the enactment of the Clean Air ActAmendment (CAAA) of 1995. Solids motion is also the key tounderstanding erosion processes. Erosion rates in FBR s andpneumatic and slurry components are computed by ANL'sEROSION code to predict the potential m etal wastage of FBRwalls, intemals, feed distributors, and cyclones.Only the FLUFIX nd IRF odes will be reviewed in th e papertogether with highlights of the validations because of lengthlimitations. It is envisioned that one day, these codes with

user-friendly pre- an d p ost-processor software and tailored form as s i v e l y p a r a l l e l m u l t i p r o ces s o r s h a r ed m em o r y

'Present Address:Energy Technology DivisionArgonne National LaboratoryArgonne, Illinois* Work supported by U.S. Department of Energy, AssistantSecretary for Fossil Energy, under Contract W-3 1-109-ENG-38.

computational platforms will be used by industry anresearchers to assist in reducing and/or eliminating thenvironmental and economic barr iers which l imit fulconsideration of coal, s hale and biomass as energy sources, tretain energy security, and to remediate waste and ecologicaproblems.

NOMENCLATURETransport coefficients (see Eq. 15)Drag coefficient (seeEq. )Compaction modulusParticle diameter, mAccelerat ion due to gravity in the x, y, anz-directions, = g,,gy,g,, m/s2Solids elastic modulus for phase k (Gf 0). PaUnity tensorCharacteristic length or mean free path, mMolecular weight, kg/molMass source for phase k, kgl(rn3.s)Pressure, PaUniversal gas constant in the ideal gas lawJ/(mol.K)Flow resistance coefficients for flow in the X-, yand z-directions, = R,, R , R ,Reynolds NumberSource termVelocity of phase k, m/s

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w

LettersFluid-par t icle f r ict ion (drag) coeff icients forhydrodynamic models A and B, respectively,kg/( m3-s)Volume porositySurface p ermeabilities in the x-, y-, and z-directions,= Yx9Yy*YzVolume fraction of phase k,Ef = 1 - E,, q = ECompaction gas volume fractionA parameter used to select the hydrodynamic modelfor phase kBulk viscosity of phase k. P e sMicroscopic viscosity of phase k, Pa-sMicroscopic density of phase k, kg/m3Macroscopic density of phase k, = EkPk.Viscous stress of phase k,PaDependent solut ion var iable (see Eq. 15) orsphericity (also called shape factor) of solidsDependent solution variable (see Eq. 15)

SubscriptsABEFNPQSWbefi, kP4SW

Hydrodynamic model AC o n t r o l v o l u m e i n b ack of volume P orhydrodynamic mode l BControl volume east of volume PControl volume in front of volume PControl volume north of volume PControl volume of interestSubscript used to denote quantities at the center ofmain control volumes (see Eq. 15)Control volume south pf volume PControl volume w est of volume PBack faceEast faceFluid phase or front facePhase i or k (i = f,g, k = f,g)ParticleSubscript used to denote quantities on the faces of amain or momentum control volume (see Eq. 15)Solids phase or south facewest face

0peratorsV . DivergenceV Gradient

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1. INTRODUCTIONSolids motion (and the associated bed dynamics involvingbubble evolution and pressure fluctuations) is the key tounderstanding the transport processes in fluidized-bed reactors(FBRs). Fluidized-bed reactors are used industrially, but scale-up and erosion of in-bed tubes and other components is stillhampering the comm ercialization of the FBR technology.Despite its importance, the exact mechanisms of scale-up anderosion in fluidized beds are poorly understood. Many modelshave been proposed for studying hydrodynamic phenomena influidized-bed reactors. Most of them are one- O r two-dimensional models. The one-dimensional models, whichinclude chemical reaction and pollutant formulation, relyheavily on simplifying assumptions.Over the last 15 years, two- and three-dimensional modelsfor gas-solids flow have been developed with a constanmicroscopic solids viscosity at IIT (Illinois Institute ofTechnology) (Gidaspow, 1986; Gidaspow and D ing, 1990) andat B & W (Babcock t Wilcox) (Burge, 1991) and with akinetic theory model for hydrodynamics and erosion at ANL(Argonne National Laboratory) (Ding and Lyczkowski, 1992)Applicat ion of these m od els to s tudying gas-solidsfluidization phenomena has been successfully carried outComparisons between computed results and experimental datahave shown the significance of and necessity for three-dimensional models of hydrodynamics and erosion inbubbling fluidized beds (Ding and Lyczkowski, 1992). Todate, no other published three-dimensional two-phase flowmodels have been used to simulate fluidized beds, to ouknowledge. One reason has been extensive computing runtime.FLUFIX (Lyczkowski and Bouillard, 1992). ANL.'s flagshipcode, incorporated into the F ORC E2 (Burge, 1991) computecode, is a two- or three-dimensional transient Eulerian finitedifference an d finite-control-volume fluid flow and heat anmass transfer solver for gas-solids systems writ ten inCartesian and cylindrical coordinates. FLUFIX, like all ourcodes, is written in a modular form and uses the implicimultifield (IMF) numerical technique of Harlow and Amsden(1975) . Computed are sol ids loading, gas and solidvelocities, pressure, and temperatures. Applications arbubbling and circulating atmospheric and pressurized fluidizebed reactors, i.e. combustors, gasifiers, and FCC reactorsPredicted are bubble formation, bed frequencies, and solidrecirculation.SLUFIX (Lyczkowski and W ang, 1992) is a two- or threedimensional, Eulerian, finite-difference and finite-controlvolume fluid flow and heat and mass transfer solver foNewtonian and non-Newtonian l iquid-solids systemsApplications are slurry transport and atomization anliquefaction reactors. Predicted a re solids loadings, liquid ansolids velocities, pressure, mixture viscosity and shear rateand temperature.EROSION (Lyczkowski et al., 1990, 1992) is a two- anthree-dimensional finite-difference solver used to predicerosion rates of components in contact with fluid-solidsystems. It inco rpor ates Finnie's, Neilson-Gilchrist's anANL's monolayer energy dissipat ion erosion modelsPredicted are lifetimes of heat exchanger tubes, waterwasurfaces, internals, distributors, and baffles. Recom mendedthe use of FLUFIX or SLUFIX for inputs.

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The FLUFIX and EROSION codes were extensively developedduring a four year cooperative R&D venture, "Erosion of FBCHeat Transfer Tubes." Industrial participants in th e R&Dventure were ABB Combustion Engineering, Babcock &Wilcox, U.S. Department of Energy (DOE) MorgantownEnergy Technology Center, Electric Power Research Institute,Foster Wheeler Development Corp., S tate of Illinois Centerfor Research in Coal, ASEA Babcock PFBC (now dissolved),and Tennessee Valley Authority. Late joining mem bers addedwere British Coal Corporation (UK) and CISE (Milan, Italy).

A number of variants of the FLUFIX pilot code have beendeveloped which address gas-solids and wall-soliddwall-gasheat transfer, multiple solids phases, multiple gas specieschemically react ive f lows, l iquid-solids and gas-solidselectrodynamics and magnetics, kinetic theory of granularflow, and three-phase, gad liqui dsol ids. Further developmentof the codes continues and will incorporate boundary-fittedcoordinates and finite element methods.A multiphase reacting flow computer code developed by ateam of Argonne National Laboratory (ANL)nd U niversity ofI l l ino is a t Ch icago is capab le o f p red ic t ing f lowcharacteristics and combustion processes in a reacting flow fora number of gaseous species and particleddroplets of varioussizes. One unique feature of the computer code is an integralreaction submodel which provides the integral reacting flow(IRF) computer code much improved numerical stability andconvergence behavior in combustion calculations (Chang andLottes, 1993). The computer co de has been used in variousengineering applications including coal-fired combustors ormagnetohydrodynamic (MHD) power generation (Lottes andChang, 1992), air-breathing jet engines (Zhou and Chiu,1983). and diesel engines (Chang and Wang, 1987), andval ida ted par t ia lly by com par in g ca lcu la tions wi thexperimental measurements. In this paper, discussion willfocus on the simulation of a multiphase reacting flow in anMHD combustor.Coal-fired MHD power generation which deals with anelectrically conducting flow in the presence of a magnetic fieldcan attain higher overall efficiency and produce less pollutantscomp ared to a conven tional power plant. The U.S. D epartme ntof Energy has been sponsoring a proof-of-concept programtoward the commercialization of MHD power generation sinceearly 1980. As a part of the team in the program, ANL used theintegral reacting flow (IRF) computer code to investigate themultiphase flow characteristics in a prototypical 50 M W tMHD power train system (Chang et al., 1993). Among themost important considerations for the MHD technology arethe attainment of high temperature from multi-stage coal-firedcombustion and of high electric conductivity by injecting aseed material, i.e., potassium, into the combustion flow.

ANL's computer simulation was found useful in resolving som ecritical technical issues in the development of the MHDtechnology, such as oxygen jet penetration, combustionefficiency, seed particle evaporation, seed vapor mixing, andparticle wall deposition.Extensive validation of ANL's multiphase, hydrodynamic,and reactive fluid-solids flow codes and models has been ma deove r the past 15 years; this is one of ANL's particularstrengths in the area of reactive fluids-solid flow analyses.State-of-the-art multiphase laser velocimetry, gammametry,nuclear magnetic resonance (NMR) and ultra soundtomographic imaging techniques have been used to develop

the data used in validation and calib ration. Som e of thesevalidations are discussed in this paper for the F LU FK and IRFcodes.All of the above codes have been developed for CRAYs u p e r co m p u t e r s , I B M m a i n f r am e co m p u t e rs , V A Xm i n i co m p u t e r s , p e r s o n a l co m p u t e r s , an d h i g h - en dworkstations, such as IBM RISC, SUN, and Silicon Graphics.These computational fluid dynamic softwares are also beingupgraded to utilize massively parallel processors, such as theANL IBM SP-1, and multigrid convergence accelerationtechniques. In this paper, a proposed strategy for this effort isbriefly discussed.Argonne National Laboratory continues to work withindustry in applying these computer programs to a broadspectrum of problems. The FLUFIX and EROSION codes havebeen used extensively to study hydrodynamics and erosion inatmospheric and pressurized bubbling (dense) and circulating(turbulent) fluidized bed combustors, e.g. B ritish Co alCorporation, Babcock & Wilcox R&D. ABB CombustionEnginee ring, and Ahlstrom Pyropower, Inc. Currently,discussions are underway with a number of organizations toutilize the codes to analyze FCC and FBC reactors, e.g. UOP,Chevron Research & Technology, Dow Corning Corporationand E.I. du Pont de Nemours & Co., Inc.2. FLUFIX HYDRODYNAMIC MODELSTh e hydrodynamic approach to fluidization which wa sstarted by Davidson (1961) is the basis for the modelsimplemented in FLUFIX, which is incorporated into FORCE2A ll the solid particles having identical densities and diametersform a continuum. The fluid and solids phases are then treatedas interpenetrat ing f luids in an Euler ian formulat ionConservation of mass and momentum are then applied to eachphase (a total of two or more) to derive the hydrodynamicmodel. Both single and multiple particle phases have beensimulated with this approach (Gidaspow, 1986). The currenFORC E2 model considers only two phases: one fluid phasewhich can be a gas or liquid and one solids phase. T h ecapabilities of several computer codes utilizing this approachwere reviewed by Smoo t (1984) and Gidaspo w (1986). Wo rk aANL sing the FLUF IXMO D2 computer code (Lyczkowski andBouillard, 1992) to mod el IIT's sm all-scale thin "twodimensional" fluidized bed has provided partial validation othe hydrodynamic model.Two hydrodynamic models, called Models A and B byLyczkowski and Bouillard (1992) have been implemented inFOR CEZ They are extensions of the models developed byLyczkowski et al. (1990, 1992) for the FLUFIX code. Themodels have been extended in FORCE2 to include: (1) threedimensiona l Cartesian and cylindrical geom etry; (2) volumporosities and surface permeabilities to account for volume andsurface obstructions in the flow field, and (3) distributeresisance to account for pressure drops caused by bafflesdistributor plates, and large tube bundles. The hydrodynamimodels of fluidization uses the principles of conservation omass, mom entum, and energy. Th e continuity equations andthe separated phase momentum equations for threedimensional, transient, and isothermal two-phase flow argiven below.

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Continuity equations For E > 0 . 8 ,

where pk = &kPk is the ma croscopic de nsity, the subscript kdenotes the phase (Le.. k = f for the fluid phase and k = s forthe solids phase), Ek is the phase. volume fraction, are th esurface permeabilities, yvis the volume porosity, and vk is thephase velocity vector.

where

c d = 0.44,or Rep > 1O00, (9 )Momentum equations

The particle sphericity (also called shape factor), is definedas the ratio of the actual surface area of the particle to thesurface area of a spherical particle of diameter dp.The solids elastic modules, G,, is used to calculate thenormal component of the solids stress through the relation

G,VE. Th e primary computa tional function of the solids stressterm is to keep the bed from compacting below the defluidizedof packed bed state. Any solids s tress model thataccomplishes this is adequate. Here we use

where(3)

andGs=Goexp [-C(E - E)] (11

as discussed by Lyczkow ski and Bouillard (1992). In thispaper we use c = 600, E* = 0.376 used by Lyczkowski andBouillard (1992). c = 500, E * =0.422 were used byGidaspow and Syam lal (1985). Go has been taken as 1.0Pa.The three resistance coefficients, Ri, i = x,y,z, are input tothe models and can be replaced with correlations.The gas density is determined by the ideal gas law,

(4)k = % k - Kk3Kk is the bulk viscosity for phase k. The parameter, Ck, is usedto select the hydrodynamic model according to model A ormodel B. For model A, l&,,=for both the fluid and thesolids phase. For model B, cf = 1 / ~nd c , = 0, w h er eE = E f-Standard correlations are used to evaluate the fluid-particlefriction (drag). However, the drag coefficients PM (M =A orB) depend on the model selected. According to Lyczkowskiand Bouillard (1992), the relation between PA and f l ~s

- M PPg---RTwhereM is the average molecular weight, T is the absolutetemperature, and E s the universal gas constant. For the fluidphase, the solids elastic modulus, Gf,s se t to zero.To solve the three-dimensional equations of fluid-solidsflow given above, we need appropriate initial conditions andboundary conditions for the two phase velocities, the fluidphase pressure, and the porosity. The initial conditionsdepend upon the problem investigated. The inlet conditionare usually given. For example, the porosity is set to 1 wherparticle-free fluid enters the system. The boundary conditionat planes of symm etry deman d zero normal gradient of alvariables.At an impenetrable solid wall, the fluid phase velocities inthe three normal and tangential directions are se t to zero. Thno-slip condition cannot always be applied to the solidphase. Since the particle diameter is usually larger than thlength scale of surface roughness of the rigid wall, th

PA is obtained from the Ergun equation (Ergun, 1952) forE 5 0.8 and from Wen and Yu's (1966) correlation forE >0.8. These expressions may be summarized as follows:

For E S 0.8.

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particles may partially slip at the wall.velocity is given by This mean slip

where the E direction is norma l to the wall. The slipparameter, L, is taken to be the mean distance betweenparticles. In FORCE2 and FLUFIX/MO D2, the mean free pathis determined byL =dpW(6 f i e S )

Also the mean free path can be derived directly from kinetictheory of granular flow (Ding and Lyczkowski, 1992).

3. FORCE2 CODE SUMMARYThe partial differential equations with appropriate initial andboundary conditions described in the preceding section aresolved by FORCE2 using the finite-difference method. Th efinite-difference equations are derived by dividing the flowdomain into a collect ion of control volumes and thenintegrating the governing momentum and continuity equationsove r these volumes. This results in a set of coupled, non-linear equations describing the velocities, void fractions, andpressures within the volumes.The f low (o r computat ional) domain is divided into acollection of cells or control volumes in a Cartesiancoordinate system. Scalar quantities such as pressure and voidfraction are calculated at the cen ters of these volumes denotedMain Control Volumes. Fluid and solids velocities arecalculated on the Main Volume faces utilizing a second set ofcontrol volumes that are "staggered" with respect to the MainVolumes. Th is second set of volumes connect the centers ofthe Main Volumes and are called Momentum Control Volumes.The collect ion of Main and Momentum Volumes is theconventional "staggered" mesh used in most finite-differenceformulations (Patankar, 1980). A general finite-differencetransport equation (representing conservation of mass ormomentum) may then be derived using the general controlvolume arrangement as

where $p an d yp are dependent solution variables, aq isthetransport coefficients on face q of control volume P,a, = E a q + b, + Sp, S, is a source of $p , Sp is a positivecoefficient for a source of $p, and b, is a positive coefficientlinking the two dependent variables qP an d vp. Details aboutthis equation can be found in Patankar's book (1980) or th eFORC E2 documentation (Burge, 1991).For transient simulations, the implicit multifield (IMF)technique (Harlow and Amsden, 1975) is used in FORCE2 andis based primarily on the IMF scheme as implemented inFLUFIXfMOD2. The solution procedure is based on adjusting

zaq$Q ae$E + aw$W an$N + as6S + a#F + ab$B,

the node pressure until fluid phase mass is conserved. Somekey features of the method include: ( I ) cell-by-cell solution,(2) simultaneous solution for velocities on the cell faces,(3) explicit formulation for conve ction and diffusion, and(4) implicit formulation for solids stresses.

For steady-state simulations, because the finite-differenceform of the momentum and continuity equations are verynonlinear, an iterative solution procedure is required. Theapproach is to construct sets of linear equations by evaluatingthe velocity, void fraction, etc., coefficients based on assumedor trial operating conditions. The resulting h e a r equationsare solved using matrix methods and their solutions used toestimate new operating conditions. This sequence is continueduntil the equation residuals are small indicating that anacceptable solution has been achieved. Th e nonlinear natureof the governing equations also requires that the solution beadvanced slowly. A key element of the solution scheme is theadjustment of the flow field pressure to conserve mass in eachcomputational cell. The iterative procedure is based onconserving mass once a solution is achieved. The solutionprocedure is a modified version of SIM PLER (Patankar, 1980developed by Schnipke (1986).4. VALIDATION OF FORCE2Validation of FORCE2 was identified as a key step inmaking the computer program a useful tool for industry andwas, therefore, initiated a s part the in-kind w ork for theCooperative R&D Venture described in the AcknowledgmentsSection. Although FORCE2 is fundamentaIly based and,therefore, could be applied to both atmospheric and pressurizedbubbling and circulating fluidized beds and liquid-solidsfluidized beds and slurries, the current effort focused onvalidation for atmospheric bubbling gas-solids fluidized beds.Three sources of data were selected to validate FORCE2. Inthe following simulations, the solids viscosity is assumed tobe 0.1 Pas (1.0 poise) except when it is zero (inviscidsolution).

4.1. FLUFIX and t h e FLUFIX Standard ProblemA standard problem has been formulated by ANL(Lyczkowski and Bouillard, 1992) from tests conducted at IIT(Bouillard et al., 1989) on a thin " two-dime nsional" fluidizedbed with an immersed obstacle located above an inlet air jetThis fluidized bed was 40 x 3.81 cm in cross-section with acentral jet velocity of 5.78 mls. The jet inlet width wa1.27 cm. A rectangular obstacle (9.74 X 2.54 cm) w aplaced approximately 9.74 cm above the jet. The bed materiawas glass beads having a particle diameter of 500pm anddensity of 2.5 x lo3 kg/m3. The ini t id bed height wa29.9 cm. Time-average d porosities were obtained usingCs-137 gamma-ray source and detected with an ionizationgauge.The FORCE2 and FLUFM/MOD2 gr id s tructure werdeveloped by assuming a symmetry plane through the centrajet. As a result, only half of the bed is modeled. The FOR CEnodal structure, which was identical to that used iFLUFIXh4OD2, is depicted in Fig. 1. The predicted gas voifractions from FLUF IX/MOD2 and FORCE2 and the measuretime-averaged void fractions at 1 0c m and 1 7c m from th

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center of the jet are respectively shown in Figs. 2 and 3.Instantaneous gas void fractions predicted by FLUFWMOD2and FORCE in the node above the inlet jet are shown inFig. 4. The predicted results of FORCE2 reasonably agreewith the measured data and agree well with the predicted resultsof FLUFIXIMOD2. The agreement with the experimental datais promising and indicates that this fundamentally-basedmodel does simulate the major hydrodynamic features of thebed.

4.2. CAPTF Three-Dimensional Fluidized B edA 30.5 x 30.5-cm square fluidized bed with two rows oftubes was tested in the Computer-Aided- Particle TrackingFacility (CAPTF) at the University of Illinois at Urbana-Cham paign (UIUC) (Podolski et al., 1991). The bed materialwas glass beads with a mean particle diameter of 513pm and a

density of 2.5 x lo3 kg /m 3. The init ial bed height was40.6 cm. Immersed tubes having an outer diameter of5.08 cm w ere used. The bed was fluidized with a superficial airvelocity of 52cmls. In FORCE2 model, the circular tubeswe re replaced by rectangular-shaped tubes, as depicted inF i g . 5 .The FORCE2 nodal structure used to simulate the bed isshown in Fig. 5. The bed is modeled in three dimensions witha total of approximately 1134 control volumes. Th eapproximate locations of the pressure measurements (numbers1-10 for the elevations and planes A, B, C) are also shown inFig. 5. Figures 6 and 7 show the comparisons betweenmeasured and FORCE2 predicted power spectral densities of thepressure fluctuations located at A-10 and B-6, respectively.The frequencies of the maximum predicted power spectra atthese locations approximately agree with the measured data.Neither the data nor FORCE2 indicate pronounced three-dimen sional effects. Th e measured and predicted powerspectrum at various elevations did not vary significantly fromplane to plane (Burge, 1991). Based on these predictions,FORCE2 provided a reasonable simulation of the 3-D CAPTFtube bundle.

4.3.A series of pressure fluctuation and erosion tests wereconducted by the Foster Wheeler Development Corporation(FWDC ) o n a two-row tube bundle in a bubbling fluidized bed(Podolski et al., 1991). Pressure fluctuation data collectedduring testing of the 76.2cm deep (called the half-depthbundle) bed we re used for the validation study here. Th e meanparticle dia meter was 150 0 pm. The particle density was1.28 x lo3 kg/m 3. The initial bed height was 40.64 cm.The inlet air fluidizing velocity was 121.9 cm/s.In the FORCE2 model, quarter-symmetry is assumed at themid-width and mid-depth of the bed. Th e nodal structure isshown in Fig. 8. The computed pressure time series of1100 points were used to determine the power spectraldensities. Com puted and meas ured power spectral of pressurefluctuations a t locations A-2 and B-2 are shown in Figs. 9 and10, respectively.The predicted and the measured major frequencies comparefavorably. Predicted and measured maximum powers occur in

different planes, a s shown in Fig. 11.three-dimensional effects in the bed. This indicates the

5 . INTEGRAL REACTING FLOW (IRF) COMPUTERCODE MODELSAND SUMMARY

5.1. Formulation of t h e C o d eThe IRF code is for transient and steady-state analyses.Since MHD flow is a steady-state phenomenon, only thesteady-state ve rsion of the code will be discussed here. Thecode employs the Eulerian approach for both gas and particlephases. General conservation laws, expressed by elliptic-typepartial differential equations, are used in conjunction with rateequations governing the mass, momentum, enthalpy, speciesturbulent kinetic energy, and turbulent dissipation for gaseousspec ies and solid particleddroplets in a multiphase reactingflow. Some complex phenomena in the flow are modeled bysimplified phenom enological submodels. The se submod elsinclude integral reaction, two-parameter turbulence, particleevaporation, and interfacial drag and heat transfer submodels.The integral reaction submodel converts rates of reaction heatrelease, consumption of fuel, and formation of products fromreaction tim e scale to flow-time scale. Th e turbulencesubmodel is the standard k-e model (Patankar, 1980), butmodified to account for the effects of the solid phase. Theevaporation submodel treats particle evaporation and sizechange over a spectrum of particle size. The interfacialsubmodel uses empirical correlations to calculate interfacialmomentum and energy transfer.The governing equations for gas species are the ellipticpartial diffe rentia l equations of fluid mechanics, includingconservation of momentum, energy, and mass, with separateequations for chemical species conservation and turbulence.These equations contain source and sink terms for interphaseexchang e rates, the effect of reaction, etc. For convenience ofnumerical formulation the governing equations for gas phaseare pu t in a common form:

(16)

in which i is the dumm y index indicating a summ ation from 1to 2, 8 is the gas phase volume fraction, r is the effectivediffusivity, 5 is a general gas flow variable, representing ascalar , velocity components U1 r Uz, fuel, inert, or seedvapor species Yf,,Yg or Y,,, richness 2, enthalpy h, turbulenkinetic energy k, or turbulent dissipation rate E. A richnesequation which eliminates the source term in the transporequations to enhance numerical stability replaces the oxidizespecies equation.The solid phase transport equations include equations opar t icle number densi ty (n), velocities (Us,l, U . 4 andtemperature (TJ for variou s particle sizes. For each particlsize group, the convective and diffusive flux terms ar

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expressed as:

When 6 = 1, Eq. 17 is a num ber density equation; when 6 =Us,,or Us,2, Eq . 17 is a particle momentum equation; and when5 = T,, Eq. 17 is a particle energy equation. The source termof the particle number density equation accounts for particleevaporation, while the diffu sion term acco unts for particledispersion due to interaction with the turbulence of the gasphase. The interactions between phases are included in thesource terms for both gas and particle phases. For example, amomentum sink in gas flow accounting for particle drag effectsis also a momentum source for the solid flow.Source terms and effective diffusion coefficients of th etransport equations for both gas and solid phase flow variablesare calculated using empirical correlations in submodels. Forthe source terms of the t ransport equat ions of fuelconcentration and enthalpy, an integral reaction submodel isused to determine fuel consumption and heat release rates. Forseed vapor concentration and particle number density, aparticle evaporation submodel is used to determine particleevaporation and size dispersion rates. For gas and solidvelocities, correlations of interfacial drag force are used todetermine momentum exchanged between p h e s . For gasenthalpy and solid temperature, correlations of interfacial heattransfer are used to determine energy exchange betweenphases. For the effective diffusion coefficients of al l transportequations, a subm odel is used to determine turbulent diffusivityfor both gas and solid phasesThe governing non-linear partial differential equations.Eqs. 16 and 17, are solved numerically. A staggered gridsystem was used for the numerical calculation, with the gasvelocity components stored on the cell surfaces and all otherphysical quantities stored at the nodal points of each cell (orscalar cell). Th e governing equations are transformed intoalgebraic equations by integrating over the computational cellwhich achieves conservation of flow properties independent ofgrid size. Patankar's (1980) SIMPLER numerical algorithm ismodified to solve the discrete equations. These algebraicequations are solved using a line-by-line sweep in the primaryflow direction to avoid numerical asymmetry. Particles ar eallowed to deposit on the walls by extrapolating the particlevelocity to the walls. A momentum wall function is used tobridge the near wall boundary layer.6. VALIDATION OF IR F

6.1. Numerical ConveraenceThe integral reacting flow computer code described abovewas used to simulate a reacting flow with vaporizing particlesin an MHD combustor. Th e combustor was represented by asimple rectangular box consisting of four side walls withoxidizer injectors on two opposing walls and two openings fo rflow inlet and exit as shown in Fig. 12. Also in Fig. 12 is atwo-dimensional grid defined on a cross-sectional area in themiddle of the combustor away from the v iscous effects near the

7

front and back walls. The grid system consists of a horizontalx- (or Xi-)xis and a vertical y- (o r X2-) xis an d its origin isse t at the lower left comer. Evenly spaced grid points aredefined for th e y-axis and variably spaced grid points aredefined for the x-axis. Dense grid points are selected near thejet opening w here large flow property gradients are expected.Determining the minimum amount of computat ionalresources necessary to obtain good quality computationalresults with a relatively high confidence is a necessary step tocontrol costs and allow a thorough parametric study to be donefor a multiphase combustion flow simulation. A convergenceand grid sensitivity study was conducted for MHD flowcalculations to identify convergence levels for both gas an dparticle phases in which com puted variables have converged tofour or more decimal digits, to identify a level of gridrefinement in which computed variables change little uponfurther grid refinement, and to identify a number of particlesize groups in which computed particle variables change littleupon further refinement of particle size space. Resu lts of thesensitivity study indicate that if the average local massresidual is 9 orders of magnitude smaller than the inlet flowrate (or a convergence level of 9). the com bustion calculationhas converged to a minimum of four decimal digits over all ofthe grid points for all major variables. All calculations in th efollowing discussion achieve the convergence level of 9 orabove. Furthennore, the sensitivity study shows that a 54 by32 grid and 5 particle size groups are required to obtain aconvergent so lu t ion for a combus t ing f low wi th pa r t i c l eevaporation in the MHD combustor. Such a calculation takesabout 2000 CPU seconds on a CRAYlxMP supercomputer.6.2. ComDarison of IRF with Measurements

Parametric studies were performed to investigate theeffect of seed particle size and oxidizer injection angle oncombustion efficiency, particle wall deposition, seed particleevaporation rate, and seed vapor distribution in the combustor.Common flow properties used in the parametric calculationsare listed in Table I.

TABLE I COMMON FLOW PROPERTIESINAN MHD

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Multiphase flow patterns for various oxidizer jet angles werecomputed and compared. Oxidizer jet an gle was found to have agreat effect on combustion performance as well as particleevaporation. Predicted flow patterns of a co-flow injection (jetangle smaller than 90 degrees) case contrast sharply withthose of counter-flow injection uet angle larger than 90degrees). For co-flow injection the oxidizer jets do notpenetrate significantly into the main flow, but rather arerapidly turned into the downstream forming a thick highgradient region near the walls. This flow configuration createsa nearly pure diffusion flame with a relatively low rate ofmixing and combustion compared to the counter-flow degreeinjection case. The change of flow patterns greatly affects thecombustion performance, especial ly , the uniformity oftemperature profile at the exit plane, which has great influenceon the seed particle vaporization and vapor dispersion. Alarge increase in combustion eff iciency and par t iclevaporization occurs when going from co-flow injection tocounter-flow injection. The angle for the highest combustionefficiency and the most effective particle vaporization andvapor dispersion is approximately 130 degrees.Particle and gas flow patterns are significantly different inthe vortex area as shown in Fig. 13. Velocity differencebetween gas and particles (or slip velocity) diminishes asparticles move downstream in the combustor. The smaller theparticle the smaller the slip velocity. For particles smallerthan 5 pm. slip velocity is negligible and particle temperaturereac hes boiling temperature alm ost instantaneously. So meparticles are trapped and deposited on the wall near theupstream edg e of the oxidizer je t slots (Fig. 14a). Seed vaporis formed mainly in the central portion of the combustor andgradually diffused to the side walls as the gas flows downstream(Fig. 14b). Large particles (larger than 34 microns in diameter)can escape the combustor before complete vapor izat ion(Fig. 15).Design verification tests of the TRW's 50 MWt combustorwere performed in the DOE'S Component Development andIntegration Facility (CDIF) in Butte Montana. Test resultsshowed that (1) oxidizer injection angle is set at 135 degreesfor maximum MHD performance, (2) growth of particledeposition was found in the second stage combustor, and (3)higher seed injection rate (70% more than design value) wasrequired to achieve the design MHD performance (Braswell etal., 1993). The oxidizer injec tion angle agrees with thetheoretical prediction in the previo us discussion. Th eobserved locations of particle deposition growth are in thepredicted area as shown in Fig. 14a. The incompletevaporization of the seed particles (Fig. 15)and the highlynon-uniform seed vapor distributions (Fig. 14b) appears tolower the overall performance of the MHD power generationand results in a required higher seed injection rates used in thetesting to boost MHD channel performance for the CDIF ests.7 . MASSIVELY PARALLEL MULTIGRIDSTRATEGYIn this section, we outline the strategy to solve themultiphase Navier-Stokes equations using massively parallelmultigrid algorithms. Perfo rma nce of the order of 2500Mflops were reported for massively parallel computationalfluid dynamics (CED) ingle-phase multigrid algorithms using

8

a SUPRENUM type of architecture with a successive overrelaxation (SOR) auss-Seidel smoother (A lef, 1991). T ests ofthe parallel multigrid versions of the algorithm will beperformed on Argonne National Laboratory IBM SP-1 parallelcomputer facility to test the performance of the proposedalgorithms. The Fortran parallel langu age used in this workwill be the portable parallel virtual machine (PVM) (Begueline t al., 1991). and the P4 (Butler and Lush, 1992). These twolanguages are very similar and are chosen because mostsoftware developers use either or both language. Let us firstreview the basic principles involved in multigrid techniquesand then the parallel computing techniques.7.1. The Multiarid ConceptThe concept of the multigrid technique can be explained asfollows. Consider a set of linear finite-difference equations,

fo r a general elliptic operator L , where W is the solutionvector. Any iterative procedure such as Gauss-Seidel or Jacobiconverges rapidly for the first few iterations and very slowlythereafter. A Fourier analysis of the error-reduction processshows that these conventional iterative procedures are mostefficient in smoothing out errors of wavelengths comparableto the mesh size, but are inefficient in annihilating low-frequency components. The multigrid technique is based onthe premise that each frequency range of error must besmoothed on the grid where it is most suitable to do so.Consequently, the multigrid technique cycles between coarseand fine grids until all frequency components are appropriatelysmoothed.The multigrid method cycles between a hierarchy ofcomputational grids D k with corresponding functions W k ,that ask decreases, Dk ecome s coarser. By doubling the meshsize in each direction (see Fig. 16, which shows the fullcoarsening technique) several levels of coarse grids aregenerated. In the full approxima tion storage PAS) procedure(Brandt, 1984), the solution is initialized on the finest grid M.When the relaxation procedure (iteration) fails to smooth theresiduals at the desired theoretical rate on the finest grid M. theiterations are stopped on grid M and the residuals (FM LM#= R M ;w M s an approximation to W M ) are transferred to thenext coarser grid (restriction). On he coarser grid D"', theequation solved is

k = 1, 2, ..., M. The step size on D k is hk and hk+l = 1/2hk, SO

where Lk-' is the ope rator on grid Dk-', nd I!-' is the operatorto restrict (project) the k variables on grid k-1, Rk-l isrestricte d to grid k-2 and a solutio n of Eq. 19 is sought on gridk-2. Wh en an accurate solution of Eq. 19 is obtained, thechange from the previous value &-* Zf'wfu is prolongated(bilinear interpolation) to grid k. The correction to wk is then

ROBERTLYCZKOWSKI


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The iterations on each grid k are continued until the requiredconvergence criterion lekl I sk is met, at which time th esolution vector is transferred to th e next finer level ( e k is thetolerance level allowed on grid k). When the finest level issolved to the desired accuracy, the overall solution cycle isterminated.Such multigrid algorithms have been successively used byVanka (1986) and Bouillard and Beny (1992) in the solution ofNavier-Stokes equations for single-phase fluid flows on serialmachines. Essentially, the technique consists in solving themomentum equations and adjusting the pressures and velocitiesto satisfy the continuity equations. Th e multigrid version ofthe s ingle-phase algor i thm was recently extended byThompson e t a l . ( 1992) fo r para l le l shared-memorycomputers. A nearly linear speed-up scaling relationship wasachieved as the number of processors was increased. Similarwork has also been performed by Alef (1991). The proposedmul t ig r id s t r a tegy would con s is t in adop t ing theprolongations and restrictions of Eqs. 19 and 20 to the fluidcontinuity equation residuais of the two-phase Navier-Stokesequation solver discussed above.7.2. The Parallel Multiarid StrateayIn a parallel algorithm, the total number of computationalcells is decomposed into patches that are assigned to eachcomputer. This is represented in Fig. 17. In a shared-me moryarchitecture, all the computational cells reside in a commonmemory. It is important that common data not be updated bytwo processors at the same time. T o avoid this conflict,special software systems called monitors have been created.The monitor guarantees that the initialization is performedbefore contention for the share data begins and that only oneof the operations may be performed at only one time. Fordetailed presentation on monitors (see Boyle et al., 1987).Such a principle was recently used by Thompson et al. (1992)to solve a multigrid single-phase flow problem on a smallnumb er of processors (15-20). Speed-up factors of the order of15 were achieved on a moderate number of processors (20processors on the Sequent Symmetry). This leads us toconclude that about one order of m agnitude speed-up could begained by using multigrid techniques and another order ofmagnitude could be gained using a moderate number ofprocessors. This could result in two orders of magnitude speed-up and gigaflop performance using only a moderate number ofprocessors. T o avoid data dependencies between theprocessors, a Jacobi smoother will be used in the multigridtechnique. Since the use of the parallel programming language(PVM and P4) proposed in this project is transportable todistributed-memory parallel processors, the same FORTRANcode could easily be extended to be used on the distributedmassively parallel processors such as the Intel touchtonedelta.8. CONCLUSIONSApplications of FLUFM as incorporated into FORCE2 inatmospheric gas-solids fluidized beds have been successfullycarried out, as demo nstrated in this paper. Favorab lecomparisons with data have been shown and indicate that themodels and modeling approach are sound. Many features, suc h

as three dimensions, variable control volume size, flowresistance coefficients, and volume porosities and surfacepemeabilities, needed to model industrial-scale fluidized beds,have been implemented in FORCEZ. With our three-dimensional hydrodynamic computer code FORCE2, it is nowpossible to better model complex large-scale fluid-solidssystems. including atmospheric and pressurized bubbling andcirculating fluidized bed combustors gasifiers and incinerators,and slurries for many industrial applications.The integral reacting flow (IRF) computer cod e was used tosimulate multiphase reacting flow in a TRW 50 MWt MHDsecond stage combustor. Th e simulation predicts the effects ofcombustor operation parameters on combustion efficiency,particle wall deposition, seed particle evaporation, and vapordispersion characteristics in the combustor, which arecrucially important to the performance of the overall MHDpower generation. The predictions are in good agreement withtest results.An advanced multigrid, multiphase Navier-Stokes equationsolver s trategy for using massively paral lel computerarchitectures is proposed on distributed multi-instructionmultidata (MIMD) shared-memory.Such parallel multigrid compu ter programs d o not presentlyexist and the development of such numerical solver would helpbridge this gap. The use of the proposed massively parallelmultigrid strategies could help reduce the excessive computerrunning time, typically from hours or days to few minutes, andthus bring routine design calculations of fluid-solids hardwarein the practical realm of the engineer or the scientist.ACKNOWLEDGMENTThis study was supported under the Cooperative R&DVenture "Erosion of FBC Heat Transfer Tubes," ContractW-31109-ENG-38. Members are the U.S.Department of EnergyMorgantown Energy Technology Center; Electric PowerResearch Institute; Statg-of Illino is Center fo r Research onSulfur in Coal; Foster Wheeler Development Corp.; ASEABabcock PFBC; ABB Combustion Engineer ing, Inc.;Tennessee Valley Authority; British CoalForporation; CISE-+Tecnologie Innovative; and Argonne National Laboratory.This work was also supported by U.S. Department oEnergy, Assistant Secretary for Fossil Energy, under ContracW-31-109-ENG-38. Information provided by TRW, Inc. igreatly appreciated.

" _ ^ -I_-~.

REFERENCESAlef, M., 1991, "Co ncep ts for Eff icient Mult igr iImplementation on Suprenum-like Architectures," ParalleComputing, 17: pp. 1-16.Beguelin, A., Dongarra, J., Manchek, R., and Sunderam, V.1991, "A User's Guide to P VM Parallel Virtual Machine," OakRidge National Laboratory Report ORNL/TM-11826, OaRidge, TN.Bouillard, J.X., Lyc zkow ski, R.W., and Gidaspow, D.1989, "Porosity Distributions in a Fluidized Bed With aImmersed O bstacle," AZChE Journal, 35. pp. 908-922.Bouillard, J.X., and Berry, G.F., 1992, "Performa nce ofMulti-Grid-Three-Dimensional MHD Generator CalculatioProcedure," International Journal of Heat and Mass Transfe35(9): pp. 2219-2332 .

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Boyle, J., Butler, R., Disz, T., and Glickfeld, B., 1987.Portable P rog ra m for Parallel Processors, Holt, Rinehart andWinston Inc., NY.Brandt. A., 1984, "M ultig rid Techniques: Guide withApplications to Fluid Dynamics," Von Karman Institute.Lecture Series.Braswell, R., Koyama. T., McAllister, M., Myrick, S., andPote, B., 19 93, "50 MWt Pro to typ ica l Combus to rPerformance," Proceedings of 31 st Symposium of EngineeringA s p e c t s o f M a g n e t o h y d r o d y n a m i c s . Whitef ish, MT,

Burge, S.W., 1991, "FORCE 2: A Multidimensional FlowProgram for Gas-Solids Flow Theory Guide and User's Guide,"Babcock & Wilcox Company, Research & DevelopmentDivision Repo rt, RDD:49 1 1- 10-01102, All iance, Ohio.Reprinted as DOWMC/24193-3503/4.Butler, R., and Lusk, E., "User 's Guid e to the P4Programming System," Argonne National Laboratory ReportANL-92/17, Argonne. IL.Chang, S.L., and Wang, .S., 1987, "Therm al Radiation andSpray Group Combustion in Diesel Engines," ASME WinterAnnual Meeting, Boston, MA , HTD-81:25-34.Chang, S.L. and Lottes, S.A., 1993, "Integral Com bustionSimulation of a Turbulent Reacting Flow in a Channel withCross-Stream Injection," Numerical Heat Transfer Part A.Chang. S.L., Lottes, S.A., Bouillard, J.X., and Petrick M.,1993, "Study of M ulti-Phase F low Characteristics in an MHDPowe r Train," Proceedings of 31st Symposium of EngineeringAspects of MHD,Whitefish, MT, pp. Vb.2.1-12.Davidson, J.F., 1961, "Sym posium o n Fluidization -Discussion," Transactions of the Institution of the ChemicalEngineers, 39, pp. 230-232.Ding, J., and Lyczkowski, R.W., 992, "Three-DimensionalKinetic Theory Modeling of Hydrodynamics and Erosion inFluidized Beds," Powder Technology, 73(2), pp. 127-138.Ergun, S., 1952, "Fluid Flow through Packed Columns,"Chem Eng. Prog., 48, pp. 89-94.Gidaspow, D., 1986, "Hydrodyn amics of Fluidization andHeat Transfer: Supercomputer Modeling," Applied MechanicsReviews, 39(1), pp. 1-23.Gidaspow, D., and Ding, J., 1990, "Predictive Models forCirculating Fluidized Bed Com bustors: Three-Dim ensionalCode," DOE Repor t , DOEIPCl89769-1 , (NTIS no .DE900 10842).Gidaspow, D., and Syam lal, M., 1985, "Solids-Gas Flow,"presented at AZChE 1985 Annual Meeting, Chicago, IL,Nov. 10-15, 1985, paper no. 74e.Harlow, F.H., and Am sden, A.A., 1975, "Nu me ricalCalculation of Multiphase Fluid Flow," Journal ComputationalPhysics , 17, pp. 19-52.Lottes, S.A., and Ch ang , S.L., 1992, "Pa rticle-J etIn terac t ions in an MHD Second Stage Combus to r ,"Proceedings of 30th Symposium of Engineering Aspects ofMHD, altimore, MD, pp. VI.4.1-12.Lyczkow ski, R.W., Bo uillar d, J.X., G idaspow, D., a ndBerry, G.F., 1990, "Com puter Mod eling of Erosion i nFluidized Beds," Argonne National Laboratory Report,ANUESDKM-1, Argonne, IL.Lyczkowski, R.W., Bouillard, J.X., olga, S.M., andChang, S.L., 1992, "User's Manual for EROS IONIMOD l: AComputer Program for Fluid-Solids Erosion," Argonne

pp. 11.1.1-17.

24(1), pp. 25-43.

National Laboratory Report, Argonne, IL. Reprinted asLyczkowski, R.W., and Bouillard, J.X., 1992, "UserManual for FLUF WM ODZ : A Compu ter Program for FluidSolids Hydrodynamics," Argonne National Laboratory Report

Argonne, IL. Reprinted as D OUMU 24193-3501.Lyczk owski, R.W., and Wang, C.S., 1992, "Hydrod ynam iModeling and Analysis of Two-Phase Non-NewtonianCoaWater Slurr ies ," Powder Technology, 69, pp. 285-294.Pata nka r, S.W., 198 0. Numerical Heat Transfer and FluidFlow, Hemisphere Publishing, Washington, DC.Pod olski, W.F., Lyc zkow ski, R.W., Montrone , E.,Drennen, J., Ai, Y.H., and Chao, B.T., 1991, "A Study oParameters Influencing Metal Wastage in Fluidized BedCombustors," Proceedings of the 11th (1991) InternationaConference on Fluidized Bed Combustion, E.J. Anthony, edAmerican Society of Mechanical Engineers, Vol. 2, pp. 6096 1 8 .Schnipke, B.J., 1986, "A Streamline Upwind Finite ElemenMethod fo r Lamina r and Turbul ent Flow," Ph.D. ThesisUniversity of Virginia.Smoot, L.D., 1984, "Mode ling of Coal-CombustioProcesses," Progress, Energy and Combustion Science, 10Thom pson, C.P., Cow ell, W.R., and Leaf, G.K., 992, "Othe Parallelization of an Adaptive Multigrid Algorithm forClass of Flow Problems," Parallel Computing, 18, pp. 449466 .Van ka, S.P., 1986 , "Blo ck-Im plicit Mu ltigrid Solution oNavier-Stokes Equations in Primitive Variables," JournaComputational Physics, 65, pp. 138-158.W en, C.Y., and Yu, C.H., 1966, "Me chanic s oFluidization," AIChE Symp. Ser., (ed. B.S. Lee), 62, p. 100112, American Institute of Chemical Engineers, NY.Zho u, X.Q., and Chiu , H., 1983, "Spray Group CombustioProcesses in Air Breathing Propulsion Combustors," Pape

AIAA-83- 1323, AIAAISAEIASME, 19th Joint PropulsioConference, Seattle,WA.

DOE IMU2 4 193-3500.

pp. 229-272.

Thewbmitted manuscript has teen authoredby a contractor of the U.S. Governmentunder contract No. W-31-104ENG-38.Accordingly. the U. S. Government retains anonexclusive. royalty-free license to publishor reproduce the published form of thiscontribution, or allow others to do 90. forU.S. Government purposes.

10 ROBERT LYCZKOWSKI


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AI R OUTL-7

Blocked Cells.No S l i p Boundary -C o n d i c i o n (Obrcacle)

No Slfp loundary(U11') I

,iI

IFluidizing N r1nl.t . - - -

FIGURE1. FORCE2 NODAL STRUCTURE USED FOR THESOLUTIONOFTHE STANDARD PROBLEM

'.'c0.9

0.8x$ 0.70a

c-0.6

05

0.4

m0.3 10 20 30 40 50Bed Height (m )

OataF-UFIX

FORCE2

8-...........-

FIGURE2. PREDICTED AND MEASUREDTIME-AVERAGED BED POROSITIES 10cm FROMTHE CENTEROF THEJET, INVISCID SOLUTION (j.~s 0)

1.1

1

0.9

FLUFIX

FORCE2............

10 10 M 30 40 50 60Bed Height (an)

FIGURE3. PREDICTED AND MEASURED TIME-AVERAGED BED POROSITIES 17an FROM THE CENTEROFTHEJET, INVISCIDSOLUTION (J& =0)



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O t0.3 I

FORCE2

0 0.2 0.4 0.6 0.a 1 1.2Time (sec)

FIGURE4. INSTANTANEOUS GAS VOID FRACTIONPREDICTED BY FLUFIX AND FORCE2 IN THE NODEABOVE THE JET, VISCOUS SOLUTION (pS=.0.1 Pa-s)

0.06 7J

0 . e

0.04

0.03

0.01

0.01

0.00

Location A-10rrns=0.08255

-

0 1 2 3 4 3 6 7 8 s l O l l t 2Ffrquency, n. Ht

FIGURE5. FORCE2NODAL STRUCTURE USED TOMODEL THE30.5 x 30.5-m SQUARE FLUIDIZED-BED

TUBE BUNDLE TESTED IN THECAPTF

FIGURE6. PREDICTED (LOWER) AND MEASURED(UPPER)POWERSPECTRAL DENSITIESOFTHEPRESSURE FLUCTUATIONSIN THE30.5 x 30.5-u-nSQUARE CAPTF TUBE BUNDLE, LOCATION A-10

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afmQ

CI

Y

P 0 . 05 'c0.Q

Q

rmr=0.26860.W

--

0.003

FIGURE8. FORCE2 NODAL STRUCTURE USED TOMODELTHEFWDC HALF-DEPTH TUBE BUNDLE

FIGURE7. PREDICTED(LOWER) AND MEASURED(UPPER)POWER SPECTRAL DENSITIESOF THEPRESSURE FLUCTUATIONSINTHE30.5 x 30.5-cm

SQUARECAPTF TUBE BUNDLE, LOCATION56

O.CQ25

O.cQo5

Frequency (Hz)

FIGURE 9. PREDICTED AND MEASUREDPOWERSPECTRAL DENSITIES OFM E PRESSUREFLUCTUATIONSIN THE FWDCHALF-DEPTH TUBEBUNDLE, LOCATIONA-2



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O i l0.0015

v

0 0 1 2 3 4 5 6 7 8 9 1 0 1 1 12Frequency (Hz)

FIGURE10. PREDICTED AND MEASURED POWERSPECTRAL DENSITIESOFTHE PRESSUREFLUCTUATIONSINTHE FWDCHALF-DEPTH TUBEBUNDLE, LOCATION5 2 .

0.003

0.0025

- 0.0020IEug 0.0015i-Y

I ............

Frequency (Hz)

FlGURE11. PREDICTED AND MEASURED POWERSPECTRAL DENSITIES OF THE PRESSUREBUNDLE, LOCATIONSC-2 (PREDICTED)AND LOCATIONSFLUCTUATIONSINTHE FWDCHALF-DEPTHTUBEA-2 AND E2 (MEASURED)

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FIGURE 12. AN MHD COMBUSTOR AND A 54BY32GRID

FIGURE13.COMPARISONOFGAS AND PrnncLEFLOW PATERNS

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FIGURE 14. CHARACTERISTICS OF SEED PARTICLEEVAPORATION IN THE MHD COMBUSTOR FIGURE 16. RELATIONSHIPS BETWEEN DIFFERENTMULTIGRID LEVELS

FIGURE15.CENTERUNE P m n c ENUMBERDENSITYIN THE MHD COMBUSTORFOR VARIOUSSIZES FIGURE 17. DOMAIN SPUlTNG IN BOTHDIRECTIONS(TWO IMENSIONS), EACH DOMAINISASSIGNED TO APROCESSOR

State-Of-The-Art Review of CFD of Gas-solid Systems

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