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Heat Transfer in Fluid beds

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Special Topic <strong>in</strong> ME6204 Convective <strong>Heat</strong><strong>Transfer</strong>:<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong>ized Beds-An OverviewProfessor A. S. MujumdarME Department, NUS, 2010


ContentsIntroductionParticle CharacterizationFlow past spheres, non-spheres<strong>Heat</strong> transfer from spheres under large Re range<strong>Fluid</strong> Beds – Concept and modificationsGeldart’s Classification<strong>Heat</strong> <strong>Transfer</strong>Bed to Immersed Surface <strong>Heat</strong> <strong>Transfer</strong> – CorrelationsSample CalculationsFB Dry<strong>in</strong>g – Plug flow vs Well-mixed<strong>Fluid</strong> be combustion (Simple Model)Example of <strong>Fluid</strong> Bed CalculationClos<strong>in</strong>g Remarks


Introduction• fluidized bed describes a f<strong>in</strong>ely granulated layer of solid material (referred to as “themass”) that is loosened by fluid flow<strong>in</strong>g through to such an extent that the particlesof solid material are free to move to a certa<strong>in</strong> degree• It is called “fluidized” because the solid material takes on properties similar to thoseof a fluid (liquid)• <strong>Fluid</strong>ized <strong>beds</strong> are used widely <strong>in</strong> eng<strong>in</strong>eer<strong>in</strong>g for applications such as combustion,reactors, dry<strong>in</strong>g, gasification of coal/biomass, thermal treatments of metal andpowder coat<strong>in</strong>g, granulation, heat transfer etc ……• Gas-solid fluidized systems are characterized by temperature uniformity and highheat transfer coefficients, due to the <strong>in</strong>tense mixture of the solid material by thepresence of gas bubbles• Liquid- solid fluidized <strong>beds</strong> have also been used for wide applications• <strong>Heat</strong> transfer <strong>in</strong> fluid <strong>beds</strong> can be from <strong>Fluid</strong> – Particle, Particle – <strong>Fluid</strong>, Wall – <strong>Fluid</strong>and to immersed surfaces, if any- care needed <strong>in</strong> calculation method used!


Particle CharacterizationParticle SizeVolume Diameter (d V )Surface Diameter (d S )Surface-Volume Diameter (d SV )Sieve DiameterStokes Diameter (d st )Free Fall<strong>in</strong>g DiameterDrag DiameterProjected Area DiameterFeret DiameterMart<strong>in</strong> Diameter ….etcd v = 6V 1⁄3pπ d S = S 1⁄2pπ d S v = 6V pS p= d v 3d s2d st =18μU tρ p −ρ s gCommonly used for applications <strong>in</strong> packed and fluid bedV P – Volume of the particle; S P – Surface area of the particle;U t – term<strong>in</strong>al settl<strong>in</strong>g velocity of the particle


Particle Characterization contd……ShapeSphereCyl<strong>in</strong>der with length (l y ) equal todiameter (d y )Cyl<strong>in</strong>der d y ≠ l yR<strong>in</strong>g with outside diameter of d o , and<strong>in</strong>side diameter of d iMixed sizesEquivalent particle diameter, d p = d sv = 6/a sd p = diameter of sphered p = d y , the diameter of cyl<strong>in</strong>der6d yd p = 4 + 2 d y ⁄ l yd p = 1.5(d o − d i )1d p =∑ix i ⁄ d pi Irregular shapes with ф = 0.5 to 0.7 d ;p = ф d vd v ≈ d ATable: Suggested equivalent particle diameters for catalysts <strong>in</strong> catalytic reactor application


Particle Characterization contd……Particle ShapeSphericity (ф)Circularity (⊄)Surface area of volume equivalent sphereф=Surface area of particleCircumference of a circle hav<strong>in</strong>g samecross − sectional area as the particle⊄=Actual Perim eter of the cross −sectionOperational Sphericity and CircularityHeywood Shape FactorParticle Densityk= V pd a3d a =4A p ⁄ πd a – Projected area diameter; A P – Projected area; V p – Volume of particle


Methods for Direct CharacterizationSieve AnalysisIn U.S. – Taylor sieve size and U.S. Sieve sizeIn Europe – British standard and German DIN sieve sizeMesh Number – number of parallel wires per <strong>in</strong>chImag<strong>in</strong>g Techniques: Direct measurements us<strong>in</strong>g enlarged photographic or electronic imagesof microscopeOptical microscope (1µm to 150 µm)Scann<strong>in</strong>g electron microscope (SEM, 5µm to 0.01 µm)Transmission electron microscope (TEM , 5µm to 0.01 µm)Gravity and Centrifugal SedimentationCharacterization by ElutriationCascade Impaction TechniqueResistivity and Optical Zone Sens<strong>in</strong>g TechniquesCoulter Counter


Particle size ranges for various methodsParticle siz<strong>in</strong>g methodSiev<strong>in</strong>gDryWetMicroscopic exam<strong>in</strong>ationOpticalElectronicZone Sens<strong>in</strong>gResistivityOpticalElutriationLam<strong>in</strong>ar FlowCycloneGravity SedimentationPipette and hydrometerPhotoext<strong>in</strong>ctionX-rayApplicable particlesize (mm)>102 – 5001.0 – 1000.01 – 5000.6 – 12001.0 – 8003 – 758 – 501 – 1000.5 – 1000.1 – 130Measured DimensionSieve diameterLength, Projected AreaStatistical diameterVolumeStokes diameterStokes diameter


Mechanical Properties of ParticlesHardgrove Gr<strong>in</strong>dability Index (HGI)Higher the HGI higher the gr<strong>in</strong>dability of materialAttrition IndexImportant <strong>in</strong> fluidization, can affect entra<strong>in</strong>ment and elutriationSolids impaction on plateAbrasiveness Indexfactor used to determ<strong>in</strong>e the effective rate of wear of theaforementioned consumablesErosiveness Index


Dimensionless numbersDimensionless numbers of <strong>in</strong>terestSignificanceFor FB <strong>Heat</strong> <strong>Transfer</strong>


Flow passed over a s<strong>in</strong>gle particleParticle Drag CoefficientRatio of force on the particle and the fluid dynamicpressure caused by the fluid times the projectedarea of the particleC D =(1 2Stokes LawDrag force resist<strong>in</strong>g very slow steady relative motion between arigid particle (sphere) of diameter d P and a fluid of <strong>in</strong>f<strong>in</strong>ite extent ofviscosity µ isTotal drag force resist<strong>in</strong>g motionWhere u r is the relative velocityF⁄ )ρ f U r 2 A P F = 1 2 C Dρ f U r 2 A PDrag Coefficient C D is a function of particle’s Reynolds numberThis is known as the stokes law and is valid ma<strong>in</strong>ly forU rA PFThis also hold true up towith some error


Flow passed over a s<strong>in</strong>gle particleThree different regimes based on the magnitude of Re PFor the Stokes Regime0.3 < (Re) PThe Intermediate Regime C D = ff[Re P ] 0.3 < (Re) P < 500Dallavalle (1948)Schiller & Naumann 1933The Newton’s Law Regime (Re) P > 500C D = 0.44


Drag coefficient for different shapesDrag Coefficient aga<strong>in</strong>st Reynolds Number (Re)


Particle fall<strong>in</strong>g under gravity through a fluidThe general force act<strong>in</strong>g on particle are gravity, buoyancy, dragGravity - Buoyancy - Drag = Acceleration FlowFor spherical particle (for acceleration = 0)F bNowSo equation becomesU t is called as term<strong>in</strong>al settl<strong>in</strong>g velocity of the particleOn solv<strong>in</strong>g for C D


Particle fall<strong>in</strong>g under gravity through a fluidFor Stokes law RegimeHenceIn stokes law regime the term<strong>in</strong>al settl<strong>in</strong>g velocity is proportional to the squere of theparticle diameterIn the Newton’s Law RegimeC D = 0.44In the Newton’s law regime the term<strong>in</strong>al settl<strong>in</strong>g velocity is proportional to the squareroot of particle diameter and <strong>in</strong>dependent of viscocity


Multiple particle systemThe motion of each particle is affected by the presence of othersSimple analysis for the fluid particle <strong>in</strong>teraction is not valid but can be adopted tomodel the multiple particle systemFor suspension of particles the stokes law is assumed to apply but an effectivesuspension viscosity and effective average suspension density is assumedEffective suspension viscosity µ e = µ / f(ε)Average suspension density = ρ ave = ε ρ f + (1-ε) ρ Pwhere ε is the voidage or volume fraction occupied by fluidFor suspension of particles the drag coefficient <strong>in</strong> stokes law regime becomeswhereAnd U r is the relative velocity of particle


Multiple particle systemUnder term<strong>in</strong>al velocity condition for a particle fall<strong>in</strong>g under gravity <strong>in</strong> a suspension theforce balanceSubstitut<strong>in</strong>g µ e and ρ aveU rel,t is known as the particle settl<strong>in</strong>g velocity <strong>in</strong> presence of other particles or H<strong>in</strong>deredSettl<strong>in</strong>g Velocity


Multiple particle systemf(ε) was shown theoretically by E<strong>in</strong>ste<strong>in</strong> to beFor uniform sphere form<strong>in</strong>g a suspension of solid column fraction less than 0.1Or (1-ε) < 0.1,Richardson and Zaki have given the values of f(ε)for stokes regime to beFor Newton’s Regime


Characterization of Multiple Particle SystemDifferent def<strong>in</strong>itions of average particle diameterArithmetic Meandd̅aaaa = ∑ ii nn iidd pppp∑ ii nn iiSurface Meandd̅ss = ∑ nn 2ii iidd pppp∑ ii nn iiVolume Mean33dd̅vv = ∑ nn iidd pppp∑ ii nn iiiiVolume Surface Meandd̅vvvv = ∑ nn 3ii iidd pppp∑2ii nn ii dd ppppWeight Meandd̅ww = vv ii dd ppppii= ∑ nn 4ii iidd pppp∑3ii nn ii dd ppppWherevv ii =nn 3iidd pppp∑3ii nn ii dd ppppLength Meandd̅ll = ∑ nn 2ii iidd pppp∑i<strong>in</strong>n ii dd pppp


<strong>Fluid</strong> Beds - Basics<strong>Fluid</strong>ized <strong>beds</strong>: Particlesuspended <strong>in</strong> an upward gasstream


Pressure drop <strong>in</strong> fixed <strong>beds</strong>Pressure drop through packed bed / fixed bed of uniformsized solids is correlated by Ergun equationIt has two factors, viscous force and the k<strong>in</strong>etic energy forceAt low Reynolds number only viscous losses predom<strong>in</strong>ateAt high Reynolds number only k<strong>in</strong>etic energy losses need to be considered


Pressure drop & M<strong>in</strong>imum <strong>Fluid</strong>ization VelocityAt the onset of fluidization, the gravity force on the particles <strong>in</strong> the bed must bebalanced by the drag, buoyancy, and pressure forces.


Pressure drop & M<strong>in</strong>imum <strong>Fluid</strong>ization VelocityThe u mf , the superficial velocity at m<strong>in</strong>imum fluidiz<strong>in</strong>g condition is found by us<strong>in</strong>gexpression for ∆p/LIn a simplified formFor small particles (Re P < 20)Or


Pressure drop & M<strong>in</strong>imum <strong>Fluid</strong>ization Velocityfor larger particles the simplified form isorWen and Yu have found for variety of systemsfor small particles the simplified form isandFor larger particles (Re P > 20)For whole range of Reynolds number


Geldart’s ClassificationA: Aeratable (U mb > U mf ) Material has significant deaeration time (FCC Catalyst)B: Bubbles Above (U mb = U mf ) 500 micron sandC: Cohesive (Flour, Fly Ash)D: Spoutable (wheat, 2000 micron polyethylene pellets)


Geldart’s Classification contd…GroupABCDCharacteristics and Properties• Good fluidization quality, aeratable, easily fluidized, smooth at lowvelocity and bubbl<strong>in</strong>g at higher velocity and slug at high velocity, bedexpands, Good solids mix<strong>in</strong>g• Small mean particle size, low density, typically 30< d p


Geldart’s Classification contd…


Geldart’s Classification contd…


<strong>Fluid</strong>ization RegimesVelocity Increas<strong>in</strong>g


<strong>Fluid</strong>ization Regimes: DescriptionVelocity range Regime <strong>Fluid</strong>ization Features and Appearance0 ≤ U ≤ U mf Fixed Bed Particles are quiescent; gas flows through <strong>in</strong>tersticesU mf ≤ U ≤ U mbParticulateRegimeBed expands smoothly and homogeneously with small-scale particlemotion; bed surface is well def<strong>in</strong>edU mb ≤ U ≤ U ms Bubbl<strong>in</strong>g Regime Gas bubbles form above distributor, coalesce and grow; gas bubblespromote solids mix<strong>in</strong>g dur<strong>in</strong>g rise to surface and breakthroughU ms ≤ U ≤ U C Slug flow Regime Bubble size approaches bed cross section; bed surface rises and fallswith regular frequency with correspond<strong>in</strong>g pressure fluctuationU C ≤ U ≤ U kTransition toturbulent<strong>Fluid</strong>izationPressure fluctuation decrease gradually until turbulent fluidizationregime is reachedU k ≤ U ≤ U tr Turbulent Regime Small gas voids and particle clusters and streamers dart to and fro;bed surface is diffused and difficult to dist<strong>in</strong>guishU ≥ U tr Fast <strong>Fluid</strong>ization Particles are transported out of the bed and need to be replaced andrecycled; normally has a dense phase region at bottom coexist<strong>in</strong>gwith a dilute phase region on top; no bed surfaceU » U trPneumaticConvey<strong>in</strong>gUsually a once-through operation; all particles fed are transportedout <strong>in</strong> dilute phase with concentration vary<strong>in</strong>g along the columnheight; no bed surface


<strong>Fluid</strong>ization Regimes: DescriptionTransition between regimesEquations have been published for transition l<strong>in</strong>esbetween various regimes. This map can be used toidentify the type of flow regime that will exist for agiven particle under specific flow conditions.Smooth or particulate fluidizationBubbl<strong>in</strong>g or aggregative fluidizationSlugg<strong>in</strong>g criteria


Design of distributor <strong>in</strong> fluidized <strong>beds</strong>• Uniform gas sparg<strong>in</strong>g is govern by the effective design of gas distributionsystem and is very important to have uniform heat transfer• Parameter affect<strong>in</strong>g performance of Gas distribution system comprise of;Gas Sparger geometryGas chamber geometryPressure drop across the gas distribution system• A good distributor should;Obta<strong>in</strong> a spatially uniform gas distribution, without stagnant zonesPrevent solids loss by leakageM<strong>in</strong>imize solid erosionAvoid chok<strong>in</strong>g of the distributorHave a def<strong>in</strong>ite and non-chang<strong>in</strong>g (with time) pressure drop for the gas


Design of distributor <strong>in</strong> fluidized <strong>beds</strong>Pressure Drop across the DistributorThe pressure drop across the distributor ΔPd is used as the criterion fordesign, and ΔPd, values vary<strong>in</strong>g from 0.01 to 1.0 times the pressure dropacross the bed ΔPb have been suggested.Siegel (1986):ΔPd/ΔPb = 0.14 - 0.22 [Galileo number (1 - 10,000)]Kunii & Levenspiel (1991):ΔPd/ΔPb = 0.1 – 0.3Siegel, M. H., Merchuk, J.C., Schugerl, K., 1986. Air-Lift Reactor Analysis: Interrelationships between Riser,Downcomer and Gas-Liquid Separator Behavior, <strong>in</strong>clud<strong>in</strong>g Gas Recirculation Effects. AIChE Journal 32(10),1585-1595Kunni, D., Levenspiel, O., 1991. <strong>Fluid</strong>ization Eng<strong>in</strong>eer<strong>in</strong>g, 2 nd Ed., Butterworth-He<strong>in</strong>emann, Boston.


Design of distributor <strong>in</strong> fluidized <strong>beds</strong>Nozzle Position (Litz, 1972)Side entry:H = 0.2D + 0.5D noz, when D noz> D 100H = , when D noz< D 100Bottom entry:18D noz( D − )H = 3D noz> D 36D noz, whenH = 100D noz, when D noz< D 36Where, D - diameter of gas distribution chamberD noz - diameter of the nozzleH - distance between the nozzle centerl<strong>in</strong>e and thedistributor plate Litz, W. J., 1972. Design of gas distributors. Chemical Eng<strong>in</strong>eer<strong>in</strong>g 13, 162-166.


Different types of fluid <strong>beds</strong> / modifications


ExampleA packed bed is composed of cubes 0.02 m on a side. The bulk densityof the packed bed, with air, is 980 kg/m 3 . The density of the solid cubes is1500 kg/m 3 .• Calculate the void fraction (ε) of the bed.• Calculate the effective diameter (D p ) where D p is the diameter of a spherehav<strong>in</strong>g the equivalent volume.• Determ<strong>in</strong>e the sphericity of the cubes.• Estimate the m<strong>in</strong>imum fluidization velocity us<strong>in</strong>g water at 38 C and a towerdiameter of 0.15 m.VoidFractionWe know:Vbed= Vfluid+ VsolidsandWbed= Wfluid+ WsolidsρbedVbed= ρfluidVfluid+ ρsolidsVsolidsρsolidsVsolids>> ρfluidVfluid


Examplecontd…..0.3515009801133=−=−=−=≅∴mkgmkgVVVandVVsolidsbed<strong>beds</strong>olidsbedbed<strong>beds</strong>olidssolidsbedbedρρερρερρ( ) mDDDadiameterEffectiveppp0.02560.0263333=∴==ππ( )0.816666 3131=⎟⎠⎞⎜⎝⎛==ΦππaaSphericitys( )( )2223249599.803994315001.75150 1smkgsmmkgmkguDDugMimimum <strong>Fluid</strong>ization Velocityfmfpsmfmfpsmfffp=⎟∗⎠⎞⎜⎝⎛−⎥⎥⎦⎤⎢⎢⎣⎡+Φ−Φ=−ρµεερρρ


Examplecontd…..( )2225323323109.7480.4450.0250.819941.751.750.445141mfmfmfpsmffmfmfsusmkgumkgDu∗×=∗∗∗∗=Φ∗=∴=Φερεε( )( ) ( )( ) ( ) ( )smusmkgusmkgusmkgusmkgmum skgcpDumfmfmfmfmfmfpsmfmf0.07149591597109.748015970.4450.0250.810.0010.6930.445115011502222222522322322=−∗+∗×=∗=∗∗⎟∗⎠⎞⎜⎝⎛∗∗−∗=Φ∗−∗εµε


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> fixed and <strong>Fluid</strong>ized <strong>beds</strong>• Ma<strong>in</strong> advantage of fluidized <strong>beds</strong> is the extremely large area of solid surfaceexposed to the fluidiz<strong>in</strong>g media• High solid surface area greatly facilitates solid-to-gas heat transfer• Because of the solids mix<strong>in</strong>g generated with<strong>in</strong> the bulk of a bubbl<strong>in</strong>g gasfluidized bed, temperature gradients are reduced to negligible proportions• High rates of heat transfer are obta<strong>in</strong>able between the fluidiz<strong>in</strong>g solids andthe immersed transfer surfaceParticle-to-gas heat transferBed-to-surface heat transferUse of immersed surfaces


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> Fixed Beds<strong>Heat</strong> transfer <strong>in</strong> fixed bed consists of follow<strong>in</strong>g mechanisms(1) conduction heat transfer between particles,(2) convective heat transfer between particles and fluid,(3) <strong>in</strong>teraction of both (1) and (2),(4) Radiative heat transfer between particles and the flow<strong>in</strong>g gas(5) <strong>Heat</strong> transfer between bed wall and bed particles(1) Particle to fluid heat transfer<strong>Heat</strong> transfer to s<strong>in</strong>gle particle can be expressed as<strong>Heat</strong> transfer coefficient can be evaluated as(2) <strong>Heat</strong> transfer through wall (one dimensional model)For homogeneous model, temperature of fluid and of bed are assumed identicalforand


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> Fixed Beds(3) <strong>Heat</strong> transfer through wall (two dimensional model)For homogeneous model,temperature of fluid and of bed are assumed identicalforand(4) Effective radial thermal conductivityforand


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong><strong>Heat</strong> transfer <strong>in</strong> a bubbl<strong>in</strong>g fluidized bed• Gas to particle heat transfer coefficients are typically small, of the order of 5 - 20 W/m 2 K• However, because of the very large heat transfer surface area provided by a mass of smallparticles, the heat transfer between gas and particles is rarely limit<strong>in</strong>g <strong>in</strong> fluid bed heattransfer• One of the most commonly used correlations for gas-particle heat transfer coefficient is thatof Kunii and Levenspiel (only for low particle Reynolds numbers)for• Gas to particle heat transfer is relevant where a hot fluidized bed is fluidized by cold gas• While follow<strong>in</strong>g are the correlation suggested based on experimental data *forfor*Chen, J.C., <strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> handbook of fluidization and fluid systems, 2003


Analysis of Gas-particle heat transferThe energy balance across the element givesIntegrat<strong>in</strong>g with boundary conditions T g = T g0 at L = 0


Analysis of Gas-particle heat transferThe distance L n , <strong>in</strong> which the gas-to-particle temperature falls by a factorIs given by,The distance over which the temperature distance is reduced to half its <strong>in</strong>itial value,L 0.5 is then


Analysis of Gas-particle heat transferA bed of 450µm particles is operat<strong>in</strong>g at 150˚C. The temperature and superficial velocityof the <strong>in</strong>com<strong>in</strong>g gas are 550˚C and 0.4 m/s, respectively. Approximately how far willthe <strong>in</strong>com<strong>in</strong>g gas have penetrated <strong>in</strong>to the bed before it is cooled to 350˚CGas physical properties can be estimated at average temperature over the specifiedrange. In this particular case the average temperature is 450 ˚C. Hence the physicalproperties of airGas velocity at 450˚C for an <strong>in</strong>let velocity of 0.4m/s at 550˚C will be 0.35m/s


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Bed to surface heat transferIn a bubbl<strong>in</strong>g fluidized bed the coefficient of heat transfer between bed and immersedsurfaces (vertical bed walls or tubes) can be considered to be made up of three additivecomponentsThe particle convective component h cp , which is dependent upon heat transferthrough particle exchange between the bulk of the bed and the region adjacent tothe transfer surface (heat transfer due to the motion of packets of solids carry<strong>in</strong>g heatto and from the surface)The <strong>in</strong>terphase gas convective component h gc , by which heat transfer betweenparticle and surface is augmented by <strong>in</strong>terphase gas convective heat transferThe radiant component of heat transfer h rThus,Approximate rangeof significance40µm 1mm > 800 µm and athigher staticpressureHigher temperatures(> 900 K) anddifference


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Particle convective heat transferOn a volumetric basis the solids <strong>in</strong> the fluidized bed have about one thousand times theheat capacity of the gas and so, s<strong>in</strong>ce the solids are cont<strong>in</strong>uously circulat<strong>in</strong>g with<strong>in</strong> thebed, they transport the heat around the bed. For heat transfer between the bed and asurface the limit<strong>in</strong>g factor is the gas conductivity, s<strong>in</strong>ce all the heat must be transferredthrough a gas film between the particles and the surface<strong>Heat</strong> transfer from bed particles to an immersed surface


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Particle convective heat transferThe particle-to-surface contact area is too small to allow significant heat transfer.Factors affect<strong>in</strong>g the gas film thickness or the gas conductivity will therefore <strong>in</strong>fluencethe heat transfer under particle convective conditions.Decreas<strong>in</strong>g particle size, for example, decreases the mean gas film thickness and soimproves h pc . However, reduc<strong>in</strong>g particle size <strong>in</strong>to the Group C range will reduceparticle mobility and so reduce particle convective heat transfer. Increas<strong>in</strong>g gastemperature <strong>in</strong>creases gas conductivity and so improves h pc .Particle convective heat transfer is dom<strong>in</strong>ant <strong>in</strong> Group A and B powders. Increas<strong>in</strong>ggas velocity beyond m<strong>in</strong>imum fluidization improves particle circulation and so<strong>in</strong>creases particle convective heat transfer.The heat transfer coefficient <strong>in</strong>creases with fluidiz<strong>in</strong>g velocity up to a broad maximumh max and then decl<strong>in</strong>es as the heat transfer surface becomes blanketed by bubbles.


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Bed to surface heat transferRange of fluidized bed-to-surface heat transfer coefficients


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Bed to surface heat transferEffect of fluidiz<strong>in</strong>g gas velocity on bed – surface heat transfer coefficient


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Particle convective heat transferThe maximum <strong>in</strong> h pc occurs relatively closer to U mf for Group B and D powderss<strong>in</strong>ce these powders give rise to bubbles at U mf and the size of these bubbles<strong>in</strong>crease with <strong>in</strong>creas<strong>in</strong>g gas velocityGroup A powders exhibit a non-bubbl<strong>in</strong>g fluidization between U mf and U mb andachieve a maximum stable bubble size.Zabrodsky (1966) has given correlation for h max for group B particlesKhan (1978) has given correlation for h max for group A particles


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Gas convective heat transferGas convective heat transfer is not important <strong>in</strong> Group A and B powders where the flow of<strong>in</strong>terstitial gas is lam<strong>in</strong>ar but becomes significant <strong>in</strong> Group D powders, which fluidize athigher velocities and give rise to transitional or turbulent flow of <strong>in</strong>terstitial gasIn gas convective heat transfer the gas specific heat capacity is important as the gastransports the heat around.Gas specific heat capacity <strong>in</strong>creases with <strong>in</strong>creas<strong>in</strong>g pressure and <strong>in</strong> conditions where gasconvective heat transfer is dom<strong>in</strong>ant, <strong>in</strong>creas<strong>in</strong>g operat<strong>in</strong>g pressure gives rise to an improvedheat transfer coefficient h gc .Baskakov and Suprun (1972) has given correlation for h gcwhere U m is the superficial velocity correspond<strong>in</strong>g to the maximum overall bed heat transfercoefficient


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Gas convective heat transfer to immersed surfacesSeveral approaches have been used to estimate h cThe most common approach assigns thermal resistance to a gaseous boundary layer at theheat transfer surface, the enhancement of heat transfer is then attributed to the scour<strong>in</strong>gaction of the solid particles on the gas film, decreas<strong>in</strong>g the effective film thicknessLava’s correlation (1952) for vertical surfaces, for larger particles, isWender and Cooper’s correlation (1958) for vertical tubes,forWhereWhere r is the radial position of the heat transfer tube and R b is the radius of the bed


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Gas convective heat transfer to immersed surfacesVreedenberg’s correlation (1958) for horizontal tubes,andforforWhere


<strong>Heat</strong> <strong>Transfer</strong> <strong>in</strong> <strong>Fluid</strong> <strong>beds</strong>Radiative heat transferFor temperatures beyond 600 o C radiative heat transfer plays an <strong>in</strong>creas<strong>in</strong>g roleand must be accounted for <strong>in</strong> calculationsFor rule of thumb estimate, the radiative heat transfer component can beestimated us<strong>in</strong>g absolute temperatures and an adaptation of the stefen -Boltzman equation <strong>in</strong> the formwhere ε r is the reduced emissivity to take <strong>in</strong>to account the different emissivity properties ofsurface ε s and bed ε b and is given byAn alternative correlation given by Panov et al. (1978) for approximate estimate is


Application of <strong>Fluid</strong>ized BedsPhysicalIndustrial ProcessesChemicalDom<strong>in</strong>at<strong>in</strong>gMechanism<strong>Heat</strong> and/ormass transferbetweengas/particles<strong>Heat</strong> and/or masstransfer betweenparticle/particleor particle/surface<strong>Heat</strong> transferbetweenbed/surfaceGas/gas reactions<strong>in</strong> which solid actsas catalyst or aheat s<strong>in</strong>kGas/solid reactions<strong>in</strong> which solids aretransformedApplications• Solids Dry<strong>in</strong>g• Absorption ofsolvents• Cool<strong>in</strong>g offertilizer prills• Food Freez<strong>in</strong>g• Plastic coat<strong>in</strong>g ofsurfaces• Coat<strong>in</strong>g ofpharmaceutical tablets• Granulation• Mix<strong>in</strong>g of solids• Dust Filtration• <strong>Heat</strong> treatment oftextile fibres,wires, rubber,glass, metalcomponents• Constanttemperature baths• Oil crack<strong>in</strong>g,reform<strong>in</strong>gmanufactur<strong>in</strong>g of• Acrylonitrile• Phthalic Anhydride• Polyethylene• Chlor<strong>in</strong>atedhydrocarbons• Coal combustion• Coal gasification• Roast<strong>in</strong>g of nickel andz<strong>in</strong>c sulphides• Inc<strong>in</strong>eration of liquidand solid waste• Catalyst Regeneration• Decomposition oflimestone


Applications<strong>Fluid</strong>ized bed dry<strong>in</strong>g<strong>Fluid</strong>iz<strong>in</strong>g with hot air is an attractive means for dry<strong>in</strong>g many moist powders andgranular productsThe technique has been used <strong>in</strong>dustrially for dry<strong>in</strong>g crushed m<strong>in</strong>erals, sand,polymers, fertilizers, pharmaceuticals, crystall<strong>in</strong>e materials and many otherproducts.The ma<strong>in</strong> reason for its popularity isEfficient gas-solids contact<strong>in</strong>g leads to compact units and relatively low capital costcomb<strong>in</strong>ed with high thermal efficiencyVery high heat and mass transfer and hence reduced dry<strong>in</strong>g timesThe absense of mov<strong>in</strong>g parts, low ma<strong>in</strong>tenance cost and possibility of us<strong>in</strong>gcont<strong>in</strong>uous modeThe ma<strong>in</strong> limitation is the material to be dried should be fluidizable and shouldhave narrow particle size distribution


<strong>Fluid</strong>ized Bed Dry<strong>in</strong>gWell mixed fluid bed dryer• common FBD used <strong>in</strong> <strong>in</strong>dustry.• bed temperature uniform, equal to theproduct and exhaust gas temperatures.• particle residence time distribution iswide• wide range of product moisture content.• feed is cont<strong>in</strong>uously charged <strong>in</strong>to FB ofrelatively dry particles, this enhancesfluidization quality.• a series of well-mixed cont<strong>in</strong>uous dryersmay be used with variable operat<strong>in</strong>gparameters.


<strong>Fluid</strong>ized Bed Dry<strong>in</strong>gPlug flow fluid bed dryer• vertical baffles are <strong>in</strong>serted tocreate a narrow particle flow path.• narrow particle residence timedistribution.• nearly equal residence time for allparticles regardless of their size• uniform product moisture content.• length-to-width ratio from 5:1 to30:1.• <strong>in</strong>let region may be agitated orapply back-mix<strong>in</strong>g, or use a flashdryer to remove the surfacemoisture.


<strong>Fluid</strong>ized Bed Dry<strong>in</strong>gDifferent designs of fluid bed dryers


<strong>Fluid</strong>ized bed combustion boilersAtmospheric <strong>Fluid</strong>ized Bed Combustion (AFBC) Boiler• Most common FBC boiler that uses preheated atmospheric air as fluidization andcombustion air


<strong>Fluid</strong>ized bed combustion boilersPressurized <strong>Fluid</strong>ized Bed Combustion (PFBC) Boiler• Compressor supplies the forced draft and combustor is a pressure vessel• Used for cogeneration or comb<strong>in</strong>ed cycle power generation


<strong>Fluid</strong>ized bed combustion boilersCirculat<strong>in</strong>g <strong>Fluid</strong>ized Bed Combustion units• A “Circulat<strong>in</strong>g <strong>Fluid</strong>ized Bed Boiler” commonlyabbreviated as CFB is a device for generat<strong>in</strong>gsteam by burn<strong>in</strong>g fossil fuels (coal) <strong>in</strong> a furnaceoperated under a special hydrodynamicsconditions.• Bed material is heated upto the ignitiontemperature of the coal with the help of naturalgas burner. Coal and limestone are <strong>in</strong>jected at thebottom of the combustor.• Total air required for combustion is split <strong>in</strong> toprimary air and secondary air.• Circulat<strong>in</strong>g solids are transported <strong>in</strong> the combustorat a velocity exceed<strong>in</strong>g the term<strong>in</strong>al velocity ofaverage particles.• Recirculation of solids creat<strong>in</strong>g uniformity <strong>in</strong> thetemperature makes the combustor as an efficientcombustion system


Key References• Yang, W.C.; Handbook of <strong>Fluid</strong>ization and <strong>Fluid</strong> –Particle Systems, Marcel Dekker, USA,2003• Kunni, D.; Levenspiel, O. <strong>Fluid</strong>ization Eng<strong>in</strong>eer<strong>in</strong>g, 1969• Geldrt, D. Gas <strong>Fluid</strong>ization Technology, John Willey and sons, USA, 1969• Mujumdar, A.S. Handbook of Industrial Dry<strong>in</strong>g, 3rd Ed; CRC Press: Boca Raton, FL,2006• Botterill, J.S.M., <strong>Fluid</strong>-Bed heat transfer, 1975.• http://www.erpt.org/012Q/rhod-00.htm• http://www.dct.tudelft.nl/race/research/staff/vanommen/<strong>in</strong>dex.html

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