Fluid Dynamics Of Gas Solid Fluidized Beds
3Fluid Dynamics of Gas – Solid Fluidized BedsGermán González Silva1, Natalia Prieto Jiménez1 and Oscar Fabio SalazarState University of CampinasBrazil1. IntroductionFluidization refers to the contact between a bed of solids and a flow of fluid. As a result, thesolid particles are transformed into a fluid-like behavior that can be used for differentpurposes. The fluidized bed reactor is one of the most important technologies for gas-solidheterogeneous operations chemical or petrochemical, considering catalytic or non catalyticprocesses (Kunii and Levenspiel 1991). The most important industrial applications includecatalytic cracking, coal combustion and biomass combustion. One of the most relevant typeof fluidized bed reactor is the ascendant flow reactor, which is also known as riser. The riserreactors consist of a tubular column in which both solid and gas flow upwards. The firstfluidized bed gas generator was developed in Germany by Fritz Winkler in the 1920s. Laterin the 1930s, the american petroleum industry started developing the fluidized bedtechnology for oil feedstock catalytic cracking, becoming the primary technology for suchapplications (Tavoulareas 1991).Inside the riser reactor, solid particles have a wide range of residence time, which is adisadvantage that reduces the overall conversion and the selectivity of the chemical reactions.For that reason it has recently grown the interest in a new type of gas-solid circulating reactorknown as downer. In this reactor the gas and the solid flow cocurrently downward, creatinghydrodynamic features comparable to a plug flow reactor and allowing a better control overthe conversion, the selectivity and the catalyst deactivation. The concept of downer reactorgas-solid appeared in the 1980s, with the first studies on the fluid dynamics of gas-solidsuspensions (Kim and Seader 1983) and with the first downer reactors for patents developedby Texaco for the FCC process (Gross Benjamin and Ramage Michael P 1981; Niccum PhillipK and Bunn Jr Dorrance P 1983). In these studies it is observed that in the downer reactor has auniform distribution of two-phase flow along the reactor, also observed that the contact time isvery low, achieving a 20% decrease in the amounts of coke produced during the FCC process.Applications, differences, advantages and disadvantages to these types of fluidized bedreactors can be found in various publications (Ancheyta 2010; Gonzalez, 2008; Yi Cheng etal. 2008; Crowe 2005; Wen-ching Yang 2003; Grace 1997; Gidaspow 1994; Geldart 1986)2. Fluidization regimes and particle classificationFluidization occurs when a gas or liquid is forced to flow vertically through a bed ofparticles at such a rate that the buoyed weight of the particles is completely supported bythe drag force imposed by the fluid.www.intechopen.com
40Advanced Fluid Dynamics2.1 Flow regimes in fluidized bedsAs the superficial gas velocity, U, is increased stepwise beyond the minimum fluidizationvelocity, it is observed different types of flow regimes. The principal ones are schematicallyshown in Figure 1. The flow regimes are listed by increasing value of U as follows: Bubble-free bed expansion Bubbling fluidization Slug flow Turbulent fluidization Fast fluidization and dense suspension upflowFig. 1. Flow regimes of gas–solid fluidization.The bubbling regime is one of the most studied flow regimes in gas-solid fluidization.Bubbles coalesce and break-up as fluid flow is increased. Finally, the bubbles becomelarge enough to occupy a substantial fraction of the cross-section of the small diametercolumns (Vejahati 2006). These large bubbles are called slug, as shown in the third columnof Figure 1.2.2 Particle classificationThe behavior of solids fluidized by gases fall into four clearly recognizable groups,characterized by density difference (ρs – ρf) and mean particle size. The features of thegroups are: powders in group A exhibit dense phase expansion after minimum fluidizationand prior to the commencement of bubbling; those in group B bubble at the minimumfluidization velocity; those in group C are difficult to fluidize at all and those in group D canwww.intechopen.com
41Fluid Dynamics of Gas – Solid Fluidized Bedsform stable spouted beds (Geldart 1973). Desirable properties of particles and gas forfluidized bed are delineated in Table 1.PropertyDesirable RangeParticle PropertiesMean diameter50 μm to 1.6 mmSize distributionNeither too narrow or too broad, e.g., 90th to 10th decile ratio 5 to 25DensityWide range of values possible, but uniform from particle to particleShapeRounded and with length to thickness ration no larger than 3Surface roughnessSmoothSurface stickinessAvoid sticky surfacesAttrition resistanceUsually strong as possibleHardnessAvoid resilience, but also excessive hardnessGas PropertiesDensityNo restriction, but higher value improves propertiesViscosityNo restrictionRelative humidityTypically 10 to 90%Table 1. Desirable properties of particles and gases for Gas-Solid fluidization (Jesse Zhu etal. 2005)3. Experimental measurement techniquesFor better understanding of these phenomena and to facilitate the solution of mathematicalmodels is necessary to make an analysis of experimental data. This experimental analysisrequires specialized measurement techniques are able to explain the flow field must also beautomated to minimize human involvement in the process of collecting data.The measurement techniques, to capture the important fluids dynamic behavior of the twophase flow, can be classified as non-intrusive (NMT) and intrusive (IMT) techniques. Theintrusive techniques are generally probes used to study local basic flow phenomena. Someof these are intended only as research instruments. The most common parameters that aremeasured with such probes are solids mass flows, radial and axial solids concentration,solids velocities, and distribution.The particles can be deposited in the measuring device reducing its performance or causingmalfunction. Besides this, the flow area reduction makes of the intrusive devices not the bestsolution. Non-intrusive techniques to characterize the flow within a fluidized bed are moredesirable because it does not disturb the flow behavior. In the Table 2 and Table 3classification techniques are included and recent successes have been achieved.www.intechopen.com
42Advanced Fluid DynamicsRef for more detailsNMTLaserDopplerAnemometry(LDA)X-ray -rayLDA is a technology used to measurevelocities of small particles in flows. Thetechnique is based on the measurement oflaser light scattered by particles that passthrough a series of interference fringes (apattern of light and dark surfaces). Thescattered laser light oscillates with a specificfrequency that is related to the velocity of theparticles.Radiographic techniques based either basedon electromagnetic radiation such as X and yrays. The transmission of X-rays or -raysthrough a heterogeneous medium isaccompanied by attenuation of the incidentradiation, and the measurement of thisattenuation provides a measure of the lineintegral of the local mass density distributionalong the path traversed by the beam(C.H. Ibsen, T. Solberg,and B.H. Hjertager 2001;Claus H. Ibsen et al. 2002;Kuan, W. Yang, andSchwarz 2007; Lu, Glass,and Easson 2009; VidarMathiesen et al. 1999;Werther, Hage, andRudnick 1996)(Franka and Heindel 2009;Newton, Fiorentino, andSmith 2001; Petritsch,Reinecke, and Mewes2000; Tapp et al. 2003; C.Wu et al. 2008; Heindel,Gray, and Jensen 2008)(Du, Warsito, and Fan2005; Kumar, Moslemian,and Milorad P. Dudukovic1995; Tan et al. 2007;Thatte et al. 2004;Veluswamy et al. 2011; H.G Wang et al. 2008)RadioactiveParticleTracking(RPT)Technique to measure velocity field andturbulent parameters of multiphase flow.This is based on the principle of tracking themotion of a single tracer particle as a markerof the solids phase. The tracer particlecontains a radioactive element emitting γrays. This radiation is received by anensemble of specific detector.(Muthanna Al-Dahhan etal. 2005; S. Bhusarapu,M.H. Al-Dahhan, andDuduković 2006; Fraguíoet al. 2009; Khanna et al.2008; Larachi et al.;Vaishali et al. 2007)ParticleImageVelocimetry(PIV)PIV measures whole velocity fields by takingtwo images shortly after each other andcalculating the distance individual particlestravelled within this time. The displacementof the particle images is measured in theplane of the image and used to determine thedisplacement of the particles(van Buijtenen et al. 2011;Fu et al. 2011; He et al.2009; Hernández-Jiménezet al.; Kashyap andGidaspow 2011; Lavermanet al. 2008; Sathe et al.2010)Table 2. Non-intrusive measurement techniques.www.intechopen.com
43Fluid Dynamics of Gas – Solid Fluidized BedsReferencesIMTMechanical method based ondetermination of momentum by meansof differential pressure measurements(Al-Hasan and Al-Qodah 2007;Bader, R., Findlay, J. andKnowlton, TM 1988; R.-C.Wang and Han 1999)Fiber OpticProbeThis technique is commonly used aseffective tools to measure the localporosity in fluidized beds.(Fischer, Peglow, and Tsotsas2011; Link et al. 2009; Meggitt2010; Zhengyang Wang et al.2009; Ye, Qi, and J. Zhu 2009;Zhou et al. 2010; Haiyan Zhu etal. 2008)CapacitanceProbeThis technique is used to measure thelocal dielectric constant of the gas-solidsuspension, which is linked to the localvolume fraction of solids(A. Collin, K.-E. Wirth, andStroeder 2009; Anne Collin,Karl‐Ernst Wirth, and Ströder2008; Demori et al. 2010; Guoand Werther 2008; Vogt et al.2005; Wiesendorf 2000)Pitot TubeTable 3. Intrusive measurement techniques.4. Computational fluid dynamics (CFD)Computational Fluid Dynamics (CFD) is a technique which uses conservation principlesand rigorous equations of fluid flow (Navier-Stokes) along with specialized turbulencemodels (k- , k- , SST among others). These models are more accurate and fundamentallymore acceptable than empirical ones. The empirical models are approximations thatassemble different phenomena to remove a number of unknown parameters. For thisreason, these models are not reliable and therefore should not be generalized.The CFD models can be divided into two groups: the Eulerian-Eulerian model in which thegas and solid phases are considered as two interpenetrating continuum flows; and theEulerian-Lagrangian model that consider the gas as a fluid phase and the solids as discretephase. The Eulerian-Lagrangian model calculates the trajectory of each individual particleusing Newton’s second law. The interaction between particles can be described by thepotential energy or the dynamic of collisions. This method has the advantage of knowingexactly the particle trajectory and the system variables. However, this requires highcomputational effort, higher yet when gas and solid velocity fields are coupled.4.1 Governing equationsGoverning equations for Eulerian-Eulerian model are here presented in tensor notation.4.1.1 Continuity equationsThe gas and solid continuity equations are represented by: g g g g vg 0 twww.intechopen.com(1)
44Advanced Fluid Dynamics s s s s vs 0 t (2)Where , and v are volume fraction, density and the vector velocity, respectively. Nomass transfer is allowed between phases.4.1.2 Momentum equationsThe gas phase momentum equation may be expressed as: g g v g g g v g vg g p g g g g vs v g t (3)p and g are fluid pressure and gravity acceleration. β is the drag coefficient between thephases g and s. The stress tensor is given by: g g g v g v g T 2 3 g g v gThe solid phase momentum equation may be written as:(4) s s vs s s vs vs sG s s s s g vg vs t T 2 s s s vs vs s s vs (5)(6)3G is the modulus of elasticity given by:G exp C G s s ,max Where s,max is the maximum solid volume fraction andtransfer proposed by Gidaspow, (1994): (7)is the interface momentum 1 g g s g vs v g 150 s 1.75 g 0.8 dp g dp2(8) s g g vs v g 2.65 3 g 0.8 CD g 4dp Where dp and CD are the particle diameter and the drag coefficient, based in the relativeReynolds number (Res) 24 1 0.15Re0.687s CD Res 0.44 Re s www.intechopen.com Res 1000 g vs v g g Res 1000(9) (10)
45Fluid Dynamics of Gas – Solid Fluidized Beds4.1.3 Energy equationThe gas and solid energy equations can be written as: C g g H g g g v g H g g g Tg Ts Tg g g H r r t tr s s H s s s vs H s s s Ts Tg Ts tWhereH Specific enthalpyT Temperatureγ Interface heat transfer coefficient: (11)(12) Nu / d p Thermal conductivity4.2 Turbulence modelsTurbulence is that state of fluid motion which is characterized by random and chaotic threedimensional vorticity. When turbulence is present, it usually dominates all other flowphenomena and results in increased energy dissipation, mixing, heat transfer, and drag. Thephysical turbulence models provide the solution the closure problem in solving Navier –Stokes equations. While there are ten unknown variables (mean pressure, three velocitycomponents, and six Reynolds stress components), there are only four equations (massbalance equation and three velocity component momentum balance equations). Thisdisparity in number between unknowns and equations make a direct solution of anyturbulent flow problem impossible in this formulation. The fundamental problem ofturbulence modeling is to relate the six Reynolds stress components to the mean flowquantities and their gradients in some physically plausible manner.The turbulence models are summarized in Table 4FamilygroupReynolds –AveragedNavier–Stokes(RANS)ModelsZero equation modelsOne equation modelsTwo equation models–ε–ωReynolds Stress Model lDynamic subgrid-scalemodelRNG – LES modelWALLE modelwww.intechopen.comDescription and advantagesThe most widely used models. Its mainadvantages are short computation time, stablecalculations and reasonable results for manyflows.Provides good predictions for all types of flows,including swirl, and separation. Longercalculation times than the RANS models.Provides excellent results for all flow systems.LES solves the Navier-Stokes equations for largescale motions of the flow models only the smallscale motions.
46Advanced Fluid DynamicsFamilygroupModelsDescription and advantagesThe difficulties associated with the use of thestandard LES models, has lead to thedevelopment of hybrid models (like that DES)that attempt to combine the best aspects ofRANS and LES methodologies in a singlesolution strategy.The most exact approach to turbulencesimulation without requiring any additionalmodeling beyond accepting the Navier–Stokesequations to describe the turbulent flowprocesses.Detached Eddy Simulation (DES)Direct Numerical Simulation (DNS)Table 4. Summary of turbulence models.4.3 System discretizationThe most important numerical methods used to approximate the partial differentialequations by a system of algebraic equations in terms of the variables at some discretelocations in space and time (called “discretization method”) are the Finite Volume (FV), theFinite Difference (FD) and the Finite Element (FE) methods. In this book, the finite volumemethod and the commercial software CFX 12.0 were chosen; the solution domain isdiscretized in a computational mesh that can be structured or unstructured.Finite volume (FV) methodThe FV discretization method is obtained by integrating the transport equation around afinite volume. The general form of transport equations is given by: t v S IIIIII(13)IVi. Transient termii. Convective termiii. Diffusive termiv. Source termThe transport equations are integrated in each computational cell using the divergencetheorem over a given time interval t: dV v dA dA S dV dtv V t t t t(14)Linearization and interpolation techniques can be clarified considering the finite volume Pshown in Figure 3.In agreement with Figure 3 notation, diffusive term can be represented as dA www.intechopen.com Awhw P W Dw P W (15)
Fluid Dynamics of Gas – Solid Fluidized Beds47Fig. 2. Gas flow over a flat solid surface (left to right) experimental picture, refined meshnear the wall and contrast between experiment and discretization.Fig. 3. Finite volume representation and notation.4.4 Source term linearizationA generic source term may be written asS PVP SC S P P(16)Where S P is the value of source term in the center of the cell P and VP is the volume ofcomputational cell centered on node P. The method to represent S P was suggested byPatankar, 1980www.intechopen.com
48 dS P *S P S * P P P d * Advanced Fluid Dynamics(17)This type of linearization is recommended since the source term decreases with increasingΦ. The source term coefficients are represented by:* dS P * SC S * P P VP d (18) dS P SP VP d (19) *4.4.1 Spatial discretizationThe most widely used in CFD is first and second order Upwind methods. In the first orderone, quantities at cell faces are determined by assuming that the cell-center values of anyfield variable represent a cell-average value and hold throughout the entire cell. The facevalue (Φw) are equal to the cell-center value of Φ in the upstream cell. v dA vw Aw W C w W (20)Where, Cw is the west face convective coefficient. Aw can be represented by:Aw MAX C w ,0 Dw(21)In the second order one, quantities at cell faces are computed using a multidimensional linearreconstruction approach (Jespersen and Barth 1989). In this approach, higher-order accuracy isachieved at cell faces through a Taylor series expansion of the cell-centered solution about thecell centroid. Thus, the face value Φw is computed using the following expression: w W WW W 32121 W WW 2(22)The east face coefficient and matrix coefficient are shown below e P W32Aw MAX C w ,0 121MAX C e ,0 Dw2(23)(24)4.4.2 Temporal discretizationTemporal discretization involves the integration of every term in the differential equationsover a time step t. A generic expression for the time evolution of a variable Φ is given by F twww.intechopen.com(25)
49Fluid Dynamics of Gas – Solid Fluidized BedsWhere the function F incorporates any spatial discretization. The first-order accuratetemporal discretization is given by n 1 n t F (26)And the second-order discretization is given by3 n 1 4 n n 1 F 2 t(27)5. Case studiesIn order to give a better introduction with regards to the simulation of fluidized beds, in thischapter there are presented three case studies that were carried out by using a CFD softwarepackage.The case studies were carried out using simulations in dynamic state. These simulationswere set up taking into account the average value of the Courant number, which isrecommended to be near 1. Besides this, it was used a constant step time, in this way waspossible to have numerical stability during the execution of each of the simulations.5.1 Cases 1 and 2Lab scale riser reactor (Samuelsberg and B. H. Hjertager 1996; V Mathiesen 2000). Riserheight, 1 m; riser diameter, 0.032 m. Experimental data and LES - Smagorinsky simulationswere compared for three velocities with initial particle bed, 5cm.5.1.1 Mesh parameters and boundary conditions Control volumes number: 100.000 x 2 mm Matrix determinant 0.5 and minimum angle 50 The boundary conditions for both cases are shown in Table 5 and Table 6.In addition, tests were made with a 500.000 control volume mesh with same blockdistribution (the description of volume distribution in the meshes, are pre
4. Computational fluid dynamics (CFD) Computational Fluid Dynamics (CFD) is a technique which uses conservation principles and rigorous equations of fluid flow (Navier-Stokes) along with specialized turbulence models (k-H, k-Z, SST among others). These models are more accura
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