A CFD Model for Fluid Dynamics in a Gas-fluidised Bed

CHEM. RES CHINESE U. 2004, 20(4),483--488A CFD Model for Fluid Dynamics in a Gas-fluidised BedZHANG Kail,2.and Stefano Brandani21. State Key Laboratory of Heavy Oil Processing, Faculty of Chemical Science& engineeringUniversity of Petroleum, Beijing 102249, P. R. China;2. Centre for CO Technology, Department of Chemical engineeringUniversity College London, London WClE TJE, UKReceived June 3, 2004uid momentumpredict the gas-fluidised bed behaviour. Additional terms are included in both the fluid and the particle momentum balance equations to take into account the effect of the dispersed solid phase This model has beenextended to two-dimensional formulations and has been implemented in the commercial code CFX 4.3. Themodel correctly simulates the homogeneous fluidisation of Geldart Group a and the bubbling fluidisation ofKeywords Gas-solid fluidised beds, Modified particle bed model, Hydrodynamics, CFD simulationArticle|D1005-9040(2004)-04-483-06Introductiontwo items solid phase pressure lJ and solGas-solid fluidised beds are widely used in stress.3)in the solid momentum equationsmany chemical processes and power stations. OverThe classic one-dimensional particle-bed modelthe past decades, scientists and engineers have con- (PBM)developed by Foscolo and Gibilaroldhasducted an enormous amount of research, both ex- been used to investigate the fluid dynamic stabilityperimentally and theoretically, to understand the of fluidised suspensions based upon the criterion offluidisation phenomenon, in which solid particles Wallis (63. The model was first used numerically toacquire fluid-like properties as a result of being lev- follow the development of imposed concentrationitated by fluid flow. A realistic model of gas-flu- perturbations in gas- and liquid-fluidised bedsidised beds must capture the effects of hydrody- showing the return to the homogeneous state fornamics, heat transfer, and reaction kinetics. Most stable systems, and the growth of disturbance ammodels of these reactors have been based on empiri- plitudes toward full shocks in the cases of instabilical correlations because of the complex phenomena ty. It was also used to study the evolved shocksbetween gas and solid phases. More recently, com- by means of the jump conditions, which were theputational models have also been developed. Such consequence of mass and momentum conservationComputational Fluid Dynamics( CFD )models for across a discontinuity, thereby representing neces-gas-fluidised beds derived from the conservation sary conditions for its existence L6, ?.Later,Chenlaws for mass, momentum, energy and species are et al. 8. 9)extended it to two-dimensional formationcommonly divided into the Eulerian-Lagrangian based on the primary force acting on a fluidisedmodel and the Eulerian- Eulerian model. The La- particle in both axial and lateral directions, andgrangian approach, describing the gas phase as a then used this model to depict the fluidisation qualcontinuum and the solid phase at a particle level, is ity in either a gas-or liquid-fluidised system. Howtoo complicated to be applied to an engineering in- ever, the classical PBM ignores the particle-particlestallation at present. The Eulerian approach, con- interaction effects on the gas momentum balancesidering both gas and solid phases to be continuous Recently, we proposed a modified PBM consideringand fully interpenetrating, has been recently uti- the effect of the dispersed solid phase on both fluidzed in industry to support engineering design. and中国煤化工 uationsHowever, there is still no consensus concerningCNMHGM was applied toSupported by EU Commission(No, ENK5-CT2000-00314)Towhomcorrespondenceshouldbeaddressed.E-mail:kaizhang@bjpell.edu.cn484CHEM. RES. CHINESE Uvo!.20investigating the hydrodynamics in gas-solid fluFn=C3(-B)/-c1idised beds within a commercial code CFX 4.3The homogeneous fluidisation of Geldart Group Aand the bubbling fluidisation of Geldart Group BtA8-.2-42+(-6)g(3were simulated in a gas-solid bedLateral component, Fsx is described asMathematical ModelF. -C. 3eP v-V).I(u=,212-1.8_Hydrodynamic models of fluidisation adopt theon and Newton's second law. The(4)classic PBM was developed on the basis of primary where u and v are velocities in the axial and lateralfluid-particle interaction forces, which may be con-sidered alone to support a fluidised particle under directions, respectivelysteady-state equilibrium conditions, together witI2. 2 Gas-phase Force Compeparticle-phase elasticity, which provides a forceAxial component, Fn, is described asproportional to void fraction gradient and so comes34(x-a1)·|(cn-t,into play under non-equilibrium conditions ti. Thepresent model was modified based upon the considd[(E-E)-2(5)eration of the effect of the dispersed solid phase onon and lateral component, Fox, is describedboth the fluid and the particle momentum balanceequations Cio). The equations, describing gas and Fa=-c. 3e,P-U.).1(u-u)solid flow in a cold fluidised bed, are given below.1 Mass Balance EquationsThe accumulation of mass in each phase is balThe drag coefficient Cp may be expressed byanced by the convective mass fluxes (i gas, the empirical Dallavalle relation:olid )Cb=(0.63+n)/a+V·(Ea;)=0where e is the volume fraction t is the time and u wherethe velocity vector. For the investigations de-evodscribed in this paper, mass exchange between thephases is not considered.Eqs.(1)-(6)fully describe the general sys2 Momentum Equationstem. It is noteworthy that the only empirical inputAccording to Newton s second law, the is the single unhindered-particle drag-coefficient Cpchange of momentum for each phase equalizes the in Eq(7)net force on a domain. The forces in a fluidised bed Simulation Methodlude inter-phase drag force, body force, staticA commercial CFD code, CFX 4. 3 from aEApressure force, and fluid-dynamic elasticity. The Technology, UK, was used to solve the aboveother forces, such as added mass effect, lift force, governing equations. In the momentum equations,and Basset force, can be negligible. Accordingly, the interphase drag and particle-phase clasticityhe momentum equations for each phase are given force terms were calculated by invoking user-deas i=gas, solid)tfined Fortran subroutines and the other items wereu.V)u=F2+F+F+F.(2) obtained directly using Command file. Each term inthe governing equations is discretised in space bywhere Fa, Fb, F, and F represent inter-phase drag using the second-order centred differencing apartforce, body force, static pressure force, and fluid- from the advection terms, which were obtained bydynamic elasticity force, respectively. According to using the rhie-chow interpolation formula. Rhienecessary that all net primary forces, F, need to chequerboard oscillations of pressure on the co-a athe closure principles of governing equations, it is Chow algorithm is an effective method to preverbe derived from basic variables, i.e., volume frac- cated中国煤化工 ty-pressure coution E, pressure P, and velocity vector ui2 I Particle-phase Force ComponentsCNMHGnOf CFX 4.3,aAxial component, F., is described asprocedure has been implemented. Different differNo 4ZHANG Kai et alencing methods were used to treat the advection However, this procedure is based on a point relaxterms: central differencing scheme for gas or solid ation technique without linearization, which cannotvolume fraction, upwind differencing scheme for be employed directly in CFX 4.3. Thus, we pro-the shared pressure field, and hybrid differencing posed a parallel method which is to rebuild excessTo resolve the algebraic equations derived by the corresponding momentum equations p>ction toscheme for all velocity componentssolid concentration together with a correntegrating transport equations over control vol- Test Casesumes, iterations were performed at two levels inSimulations reported here relate to a rectangu-CFX 4.3. An inner iteration is used for the spatial lahose dimensions in 2-Dcoupling for each variable and an outer iteration for wide and 0.5 m high. The lateral walls were treat-he coupling between variables, However, the ed as the free slip boundary conditions for bothtreatment of pressure is slightly different from the phases. Dirichlet boundary and pressure boundaryabove description. SIMPLEC algorithm( 3,a modconditions were respectively employed at the botfied version of SIMPLE (semi-implicit method for tom of the bed and the top of the freeboardpressure-linked equations)algorithmC143, was Im- Table 1 gives the physical properties of gas andplemented to deal with the velocity-pressure cou- particles and the uniform gas inlet velocity usedpling. Under-relaxation factors in the outer iteraAccording to GeldartLie, alumina particles be-tion were between 0. 6 and 0. 7 for all variables ex- long to Group a and sand particles belong to Groupcept that it is 1.0 for pressure. The linear equation B. The initial conditions specify the concentrationfor each variable was solved by Block Stone's of solids in the bed, and the fluid flow through thebed. a settled bed was considered 0. 3 m deep, andThe lower void fraction limit is usually a seri- solid volume fraction was defined as 0. 55. The uni-ous problem in the application of CFD software form gas inlet velocity through the bed was fixedpackages to two- and three-dimensional fluid-parti- only in the vertical direction. Pressure profile wascle systems. In order to resolve this problem, Gi-calculated by the hydrostatic bed height in thebook lis])added a solid phase pressure term in thedense phase, whilst a constant pressure,i. e.ambient atmosphere, was set in the upper section, orsolid momentum equations. Gidaspowl1sJdeclaredfreeboard. The mesh used in the simulation wasas:This term becomes of numerical significance 100X 40. Here, 100 is in the axial direction and 40only when the void fractions go below the minimumin the lateral direction. Time step was 1.0 xfluidisation void fraction. It also helps to make thesystem numerically stable, because it converts the 10-sTable 1 Physical properties of gas and parimaginary characteristics into real values.For some calculations, it was necessary to adMateriDensity/ Viscosity/ Diameter/ Inlet velocity/kg·m-)(kg·m-1·-1)m(m·8-1)just this stress to prevent the void fraction from Air18×10-5reaching impossibly low values. "Massoudi et al. Alumina150060x10-·0.00354compared nine empirical relations for the modulus Sand2500of elasticity. They calculated two formulations un-With the PBM the transition between homeder the same conditions and found that the results, neous and bubbling fluidisation was predicted by843N/m?and-5.06X10 N/m, were orders comparing the propagation velocities of kinematicof magnitude apart. It is clear that the additional and dynamic one-dimensional waves through thesolid phase pressure can prevent solid concentration fluidised bed. a kinematic wave is a velocity dis-exceeding the maximum value, but the parameters turbance caused by an increase of the superficialin this term depend strongly upon the gas-solid gas velocity, which moves up in the bed. Dynamicsystem used. This implies that a straightforward waves, on the, other hand, occur when a net forceand general method is necessary to avoid solid con- on acentration exceeding its physical limitation.中国煤化工 y a concentra-A skilful approach proposed by Chen et al. [. 9]thrYHCN MH Go this criterionwas to adjust the particle pressure in each gridwhen the dynamic wave velocity is greater thancording to the particle-particle contact forces. that of the kinematic wave, a stable, homogeneous486CHEM. RES. CHINESE U.Vol 20fluidisation occurs. On the contrary, an unstable, small voids were placed uniformly across the baseheterogeneous fluidisation occurs. We worked out of the bed. As shown in Fig. 1, the imposed voidsthat the air-alumina fluidised bed was a homoge- simply detached from the base of the bed, lost theirneous system and the air-sand fluidised bed was a sharp boundaries, rose through the bed as"mushheterogeneous system under the operation condi- room-shaped parvoids", and penetrated the bedtions usedsurface, causing very little disruption t thereafter1 Homogeneous System(Case 1)the bed returned to the homogeneous state.At the beginning of the simulation, three0.30.300.00.10.2=0.28t=0.6st=1.0器=1.6·t=Fig. 1 Homogeneous system (air-alumina particlesColour code scale for the solid volume fraction2 Heterogeneous System(Case 2)rose independently. The bed surface rose smoothlyFig. 2 shows the instantaneous solid volume at first and then displayed a degree of disruptionfraction in the 2-D rectangular gas-fluidised bedAfter about 0.6s, the initial voids broke at theSimilar to the homogeneous system, three surface and their effect on the bed dynamics wassmall voids were placed uniformly across the base totally lost. Subsequently, the bubbling fluidisaof the bed at the beginning. A little while later, tion matured through the bedthe voids developed into nearly symmetric bubblesThe instantaneous porosity contours and gasand another three voids appeared above the bed velocity vectors are given in Fig 3. It can be seenbottom. Then, the voids in the upper region rose that the gas velocity inside the voids was muchand merged randomly while the voids at the bottom faster than the uniform air inlet velocity or average4·g·0.6【a0.3250中国煤化工t=1.0:1.5CNMHGFlg.2 Heterogeneous system (air-sand particles).Colour code scale for the aolid volume fraction, the unit for time as secondNo 4ZHANG Kai et al487air velocity in the bed, and the ascending of the Conclusionvoids was greater than the gas velocity in the emul-A modified particle bed model was employedsion phase around them. A considerable amount of to investigate the hydrodynamics in gas-solid flugas thus took its way right through the bubbleidised beds with commercial CFD softwareCFX4.3. A straightforward method has been developed to avoid the solid volume fraction exceeding the physical limitation, which is to rebuild excess solid concentration together with a correctionto the corresponding momentum equations. Themodel correctly predicts the homogeneous fluidisa-tion of Geldart Group A, and the bubbling fluiation of Geldart group B in a two-dimensionalFig 3. Instantaneous porosity contours and gasNotationveloclty vectors(air-sand particles)Ca=Particle drag forceFig. 4 depicts the porosity contours and soliddp=Particle diameter,mIt is cleF=Net forNpattern with the uniform gas inlet can be regardedg=Acceleration due to gravity, m/s 2as an overall double-cell circulation pattern accom-p=Pressure drop, N/m2panied by randomly small local circulations asR,= Reynolds numbershown in Fig. 5. This process mainly involves thatt=Time,su=Velocity vector, m/su=velocity in the axial direction, m/su=Velocity in the lateral direction, m/sLateral distz=Axial distance,ml到e=Volume fractionp=Density, kg/mu=viscosity, Ns/m2t=1.0st=2,0tt=3,0SubscriptFig 4 Instantaneous porosity contours and solidvelocity vectors(air-sand particles).s=solidr=Lateral directiong=Axial directionReferences[1] Massoudi M., Rajagopal K.AIChE,J,,1992,38,471[2] Needham D. J, Merkin J. H, J. Fiuid Mech., 1983131,427[3] Christie L, Ganser G, H, Sanz-Serna J. M.,J. Comput.FIg 5 Solid circulaton pattern.[4] Foscolo P. U, Gibilaro L, Chem. Eng. Sci., 1987.(1)bubbles entraining particles rose along the be[5] Wallis G. B,, Onr-dimensionai Two-phase Flow,McGrawcentreline and broke on the bed interface :(2)theHill, New York, 1969particles entrained in the void wake were thrown [61中国煤化工ng.Sci.,19,49,randomly and then concentrated near the wall,(3)these particles eventually fell near the wall and [1]CNMHGU,“a,,cMmrent back above the distributor[8] Chen Z, Gibilaro L. G, Foscolo P. U, Ind. Eng. CheI.Res.,199,38(3),610CHEM. RES CHINESE UVol 20[9] Chen Z, Gibilaro L. G, Jand N, Comput. Chem. Eng2003,27(3),681[13] van Doormal J. P, Raithby G. D,NHeat Tran[10] Zhang K, Brandani S, Yates J ., Publication of Fluid.Particle Interactions Conference W, August 25-30, 2002[14] Patankar S, V, Numerical Heat Transfer and Fluid FlowBarga, Italy[11] Gibilaro L. G,, Fluidization Dynamics, Butterworth Heine- [15] Gidaspow D, Multiphase Flow and Fluidization, Academicann, London, 2001[12] AEA Technology plc.. CFX4 3 User Manuals, Harwell[16] Geldart D, Powder Technology, 1973,7,275中国煤化工CNMHG