Effect of particle loading on heat transfer enhancement in a gas-solid suspension cross flow

ISSN 1009 - 3095 Joumal of Zhejiang Uhiversity SCIENCE V.3 No.4 P.381- 386 Sep. -Oct. ,2002http ://www. periodicals. com. cn ; http ://www. zju. edu. an/Englishhttp ://www. zjupress. oom ; http //ib. zju. edu. on/ eindex. htm ;jzu_ s@mail. hz. zi. cn381Effect of particle loading on heat transfer enhancementin a gas-solid suspension cross flowZHOU Jin-sonS周劲松广, LUO Zhong- yang骆仲泱), GAO Xian{高翔)NI Ming-jiang倪明江),CEN Ke-fe( 岑可法)( Clean Energy and Environment Engineering Key Lab of Ministry of EducationInstitute. for Thermal Power Engineering , Zhejiang University , Hangshou 310027 , China )E mail : zhoujs@ cmee. zju. edu. cnReceived Nov.26 , 2001 ; revision accepted Jan.25 ,2002 .Abstract : Heat transfer between gas solid multiphase flow and tubes occurs in many industry processes , suchas circulating fluidized bed process , pneumatic conveying prooess，chemical process , drying process，etc. Thispaper focuses on the influence of the presence of particles on the heat transfer between a tube and gas- solid sus-pension.' The presence of particles causes positive enhancement of heat transfer in the case of high solid loadingratio ,but heat transfer reduction has been found for in the case of very low solid loading ratio( M, of less than0.05 kg/kg). A useful correlation incorporating solid loading ratio , particle size and flow Reynolds numberwas derived from experimental data. In addition , the k-ε two- equation model and the Fluctuation Spectrum-Random- Trajectory Model( FSRT Model ) are used to simulate the flow field and heat transfer of the gas-phase and the solid- phase , respectively. Through coupling of the two phases the model can predict the localand total heat transfer characteristics of tube in gas-solid cross flow. For the total heat transfer enhancementdue to particles loading the model predictions agreed well with experimental data.Key words : Multiphase flow , Heat transfer , Particle loadingDocument code: ACLC number: TP124INTRODUCTIONidized bed( George et al. , 1982 ; Wood et al.，1980 ). Most of these studies showed that theThe heat transfer characteristics of gas-solid solid loading ratio could alter the heat transfertwo-phase flow are of great interest in many in- between tubes and solid suspensions in the splashdustrial processes , such as circulating fluidized zone and dilute region.bed process ，pneumatic conveying process ,However, it is difficult to research experi-chemical process ，drying process , etc. Interest mentally this heat transfer mechanism because ofin the influence of particles in solid suspension on imprecise measurement of the solid loading ratioconvective heat transfer has increased since the in circulating fluidized bed. So several researchers1950s. The heattransfer problem in the studied the effct of solid particles on heat trans-pipelines of pneumatic conveying systems was in-fer of tube in gas-solid cross flow by controllingvestigated in numerous experimental studies more precisely the solid loading ratio. The heat( Farbor et al , 1957 ; Wilkinson et al.，1967 ) transfer characteristics in suspension crosS flowand theoretical studies( Michaelides , 1986 ; Kuo was studied experimentally by Woodcock et al.etal. , 1988 ;Han et al. , 1991 ). The mecha- ( 1966 ) for an in-line tube bank where the solidnism of heat transfer enhancement due to parti- loading ratio was in the range of 2 to 8cles had been studied ( Kurosaki et al. , 1990 ; ( kg/kg ), and bv_ Murrav et al. ( 1991 ) for aYoshida et al. , 1990 ) for the case of impinging stage中国煤化工urray( 1994a b)in-jet flows. The influence of particles on heat vestisY片C N M H G associated with thetransfer for the case of a tube or tube bank in enhancement ot convectuve heat transfer over thecross flow had been investigated primarily in the front of a tube in a particulate cross flow. Unfor-dilute region of fluidized bed or circulating flu- tunately , there is little research work for numeri-Projea， National Natural Science Foumdation for Distinguished Young Scholars( No. 50025618 )382ZHOU Jinsong , LUO Zhongyang et al.cal simulation especially dealing with the total collisions can be neglected. With these assump-heat transfer characteristics of a tube in a particu-tions , the particle motion equation is :late two- phase flow，especially the numericalM,1. dVpV-V(v_- v,)+M,g,simulation.: CDPgApIn this work , the heat transfer enhancement(2)for a gas-particle cross flow around a tube waswhere Vp is the instantaneous velocity of particlestudied experimentally and theoretically. A mod-phase, Vg is that of gas- phase，which can beel was developed to simulate this enhancementseparated into mean velocity Vg and fluctuatingwith the coupling of the gas phase and solidphase and particle to -wall conduction. In addi-velocity V g , that is :tion , the numerical simulation results were alsoVg= Vg+V'g(3 )compared with the experimental data.The fluctuating velocity of the gas phase canbe simulated by a random Fourier series :NUMERICAL PROCEDUREug= R1Umco iwt - R2af ),(4)T his section summarizes the main features ofv'g = 2R3V.co io,t - R4a"' ),the numerical procedure developed to calculatewhere R1 and R2 are random values with Gaus-the flow and heat transfer of the particulate two-sian distribution , w; is the turbulent fluctuatingphase cross flow.' The two equation k-ε Modeland the Fluctuation- Spectrum- Random- Trajecto-frequency , a; and a;" are the fluctuating initialry Model( FSRT Model ) were used to simulatephase angles , and Umi and Vmi are the ampli-the flow and heat transfer of gas phase and solid-tudes determined by the turbulent fluctuatingphase respectively.spectrum.For steady , two-dimensional ，incompress-The drag coefficient Cp in a turbulent flow isible , constant property , turbulent flow the basic obtained from the following expression( Fan etequations can be written in the following generalal. , 1987 ):form :Cp=4( 1+0.19Rel:.62 )aφ)Rep最(pUφ)+}yρVψ)= (Axaφ1+0.095( firRep )],(5 ))+Sp+S%,(1)Moreover , the particle trajectory can be ob-where φ is a universal parameter ( standing fortained by solving the following equations :u ,V ,k ,ε ,etc. ) ,I$ is the relevant coefficientxp=xp+( up+ up )Dt/2，of turbulent diffusion , Sψ is the source term andyp=yx+( vp+ Vw )t/2.(6)Sp is the particulate source term which representsthe net flux of u ,乙,k ,ε ,etc. into the fluidFig.1 is a sketch of a single partice imping-ing on and rebounding from the surface of aphase due to the particle fluid interaction.The Lagrangian treatment of the particulatetube. For determining the position of impact ,a .phase combined with the Eulerian approach forsmall region around the tube of thickness δb isthe fluid has been used by many researchers , es-proposed to be set to 0. 005D ( Schuh et al. ,pecially by Schuh et al. ( 1989 ) for the numerical1989 ), where D is the diameter of the tube.calculation of particle laden gas flows past tubes.When the particle first approached the surface ,In this paper，the Fluctuating -Spectrum- Ran-the solution alonrithm. is uInaware of its presencedom- Trajectory model ( FSRT model ) proposed and中国煤化工ss the surface. Whenby Cen et al. ( 1992 )is used to consider the ef- thisYHC N M H Greturned to its previ-fect of turbulence on particle dispersion.ous position , the step size is decreased by a factorFor the particle trajectory calculation , partic- of 2 ,and calculating is retried. This procedure isularly for the analysis of dilute particle-laden repeated until the particle falls into the δb region.flows, it was. assumed that effects of virtual Assuming that the velocity of the particle remainsmass , Bas死帮瑪nd Magnus forces and particle constant within δb , the velocity and direction ofEffect of particle loading on heat transfer enhancement383the rebounding particle can be obtained by the Fig. 2.following formulas|V21=( 1.0- 0.02108a1 + 0.0001417a} )Draft fan|Vp1ISeperator/1 + ctg2 a2ComputerN 1 +ctg2a1 '7 HopperData logger。Feedera2 =Test tube0.95 + 0.00055a1ctgl (1.0- 0.02108a1 +0.0001417a7)|ctga2 ]，Blower(7)where Vpl and Vp are the velocities of the parti-Fig.2 Schematic of the experimental facilitycle before and after collision with the tube , a1and a2 are angles of collision and rebounding , re-Air was drawn into a 200 X 200 mm pipelinewhere the flow rate was monitored by a swingspectively.type air meter. The solid particles used in thisinvestigation were ash with mean diameter of 65micron and sands with mean diameterof 120 mi-cron and 328 micron respectively.. The particleswere introduced into the main flow using a rotaryTube surfacevalve rotation rate controlled by an electric mo-Particletor. The solid loading ratio could be up to4.5 kgper kg air. A cyclone was used to separate thesolid particles from the air and return them to astorage hopper connected to the feeder. The total .heat transfer rate was measured using an electri-Fig. 1 A particle impinging on and rebounding fromcally heated probe.the tubeThe heat conduction between impacting par-RESULTS AND DISCUSSIONticles and a tube wall was studied by Sun et al.( 1988 ) who found that the total energy exIt is well known that the solid loading ratio ischange on impinging could be given byone of the main factors that have great influenceon the heat transfer between surface and suspen-Am( Tw-T。)rt.)1/29c(ρ,CpK,)I/2+(ρwCpKw)z'. (8) sion. Fig.3 shows the effect of the solid loadingratio( where M。<0.05 kg/ kg ) for particle sizewhere tc is the contact time ,( Tw- Tp )is the of63 pum , 150 pum and 385 μrm. Fig. 4 showsinitial temperature difference between the particle the effect of the solid loading ratio( where 0.05and the wall , C is the thermal capacity and K is < M。< <2.5 kg/kg) for particle size of 63 μrmthe thermal conductivity , Acmex is the maximum and 385 pm. Heat transfer was evidently en-contact area , Amx=0.87πr2 , re is the contacthanced with increasing solid loading ratio , butradius. Subscripts p and w refer to the particlethe presence of solid particles reduced instead ofand tube wall.enhanced the heat transfer in the range of very中国煤化bour. M。< 0. 015EXPERIMENTAL FACILITIES AND PROCE-kg/lto that of suspensionheat:FYHC N M H Gurberet al. ,1957 ).DURESIt is possible that the presence of particles in agas flow reduces the level of turbulence as a resultThe heat transfer measurements were carried of eddy- particle interactions( Hetsroni , 1989 ).out in a closed-loop circulating wind tunnel with Analysis of this negative effect ( Gao et al. ,a partice描d separation system as shown in 1996 ) using particle critical value θ showed that384ZHOU Jinsong , LUO Zhongyang et al.this negative effect was mainly due to turbulence pation is increased ，compared to single phasesuppression by particles , with consequent lower-flow ,by a ratioof( 1+ M_/p。)2. ( The relax-ing of the heat transfer rate.ation time , τ , can be written as d3p/18vp ;the characteristic time scale for the eddies，Te ,istheir characteristic size divided by characteristicvelocity , l/ ug'. ) For larger particles with t>1.05。τe , Owen( 1969 ) suggested that the turbulentfluctuations in the presence of the particles should中decrease as( 1 + MJ/p; τ/te) 12. Therefore ,●d,=0.385mm: i.◆d,=0.150mmheat transfer reduction due to turbulence sup-" d,-0.063mmpression increases for larger particles. All of the0.950 0.005 0.01 0.0150.02 0.025 0.03 0.035 0.04M. (kg/kg)above factors induce the trend of increasing enhancement of heat transfer with decrease in par-ticle size.Fig.3 Variation in Nusselt number with the solid load-1.4ing ratio( where M,< 0. 05 kg/kg )Re=12 000, M.-1.0 kg/kg1.33.5， 1.22.51.10 50 100150 200 250 300 350H d,=0.064mmd, (um)0.51.5Fig.5 Variation in Nusselt number with particle sizeReynolds number is also one of the factorsFig.4 Variation in Nusselt number with the solid load-ing ratio( where 0.05< M,<2.5 kg/kg)which influence the heat transfer enhancement.In Fig. 6 , the effect of varying Reynolds numberFig.5 shows the effect of particle size on1.Nusselt number for a Reynolds number ofd,=0. 064 mm, M.=0.6 kg/kg12 000 and a solid loading ratioof 1.0 kg/kg. Itcan be seen that the enhancement increases with是1.35reducing particle size. The smaller the particlesare , the larger the number of particles in a unitvolume are for the same solid loading ratio. Thusthe heat transfer enhancement from the reductionin the boundary layer thickness becomes large as40008000 12000 1 600020000the number of particles passing through theRboundary layer increases. As mentioned in Mur-ry( 1994a ), the thermal response time of smallFig.中国煤化工er with fIow Reynoldsparticles becomes shorter than that of large parti-cles. Thus the suspension will have higher ther-YHCNMHGmal capacity for small particles and more stored is examimed tor the partucle size of 64 pum andthermal energy is transported out of the heated solid loading ratiof0.6 kg/kg. In this case ,afluid zone by rebounding particles. For very trend of increasing enhancement with decreasingsmall particles 。where τ《τe , Owen( 1969 )Reynolds number can be found. According to thesuggestedPth秘the rate of turbulent energy dissi-changes in the boundary layer characteristics inEffect of particle loading on heat transfer enhancement385the presence of particles ，the boundary layer cal heat transfer characteristics of the tube in sus-around the tube is thinner for higher Reynolds pension cross flow.The result can be seen innumber and the residence time of particles pass- Fig. 9 for a Reynolds number of 13 400 and par-ing through the boundary layer is smaller than ticle size of 64 μm.' The curves shown are forthat for lower flow Reynolds number. Hence ，solid loading ratioof0 ,1.0 and 2.0( kg/kg),heat transfer enhancement reduces for high respectively. As shown in Fig.9 ,a trend of lo-Reynolds number with reducing disturbance of cal heat transfer enhancement can be identified.particles. .The largest enhancement can be found at theThe effect of main factors，such as solid front point and the second largest at the rearloading ratio ，particle size and flow Reynoldsnumber , have been investigated above. Experi-mental data yielded the following useful correla-0.1tion for the heat transfer of a tube in suspensioncross flow :0.01 tNusNe=1+4.1Re 0,31dp0.23M0:2, (9)0.001where Re= 3000- 20 000 ,dp=64 - 328 pm，0.0001204060 80 100120 140160180 200M,=0.05- 2.5 kg/kg.d(um)After flow field and temperature field havebeen calculated by SIMPLE scheme , particletrajectories and temperature can be calculatedFig.7 The predicted effect of particle size on the levelof the particle' s influence on the thermal bound-with the flow field and temperature field andary layer over the front of the tubethen particle source terms can be obtained. Nu-merical simulation results are outputted after the0.9coupling of the flow phase and solid phase.0.8-Fig.7 and Fig. 8 show the predicted effectsof particle size and Reynolds number on the ther-0.6-mal boundary layer , respectively. The modified0.5-thermal effectiveness factor ，ηt ，defined by0.4Murry( 1994a ) can indicate the influence of a0.particle on the thermal boundary layer ，is also0.26 5000 10000 15000 20000 25000used in our present study ，can be written as(TT。)( Tw-T。), where Tpmaxrepresentsthe maximum particle temperature reached onFig.8 The predicted effect of flow Reynolds number onpassing through the thermal boundary layer. Butthe level of the particle' s influence on the ther-in Murry' s study ,the thermal response time wasmal boundary layer over the front of the tubeconstant while a particle traveled through thethermal boundary layer. It may induce some er-100rors in predicting this influence. In our present又80三9公investigation , the change in the particles temper-E 70[-ature and velocity was directly obtained by inte-三60grating the particle motion and energy equation8using the fourth- order Runge- Kutta scheme. It40|中国煤化工was found that the level of the partice' s influ-ence reduces dramatically with increasing particleMHCNMHG°160180size and flow Reynolds number. This may ex-plain why there is little heat transfer enhance-ment for large particles size and high ReynoldsFig.9 The predicted local heat transfer factor of a tubein a suspension cross flow( Re= 13 400 ,dp=number.0.064mm )The磊凉憝据al model can also predict the lo-386ZHOU Jinsong , LUO Zhongyang et al.point of the tube( where φ is equal to0 and 180 Farbar ,L ,Morley ,M. J. ,1957. Heat Transfer to flow-degrees , respectively ). But there was little localing gas-solid mixtures in a circular tube. Ind. Engng .Chem. ,4% 7 ):1143- 1150.enhancement at the point of φ= 125一145 de-Gao ,X. ,Shen ,L. C. ,Luo,Z.Y. ,et al.，1996. Efectgrees.' This result is in good agreement with theof ash particle in flue gases on heat transfer of surper-experimental result of Murry( 1994b ).heater and eonomizers. Power Engineering ,16( 5):8The total heat transfer enhancement with in--14( in Chinese).creasing solid loading ratio was also predicted by George,S. E ,GraceJ. R. ,1982. Heat transfer to hori.zontal tubes in the freeboard region of a gas fluidized bedthe numerical model , as shown in Fig. 10. Acombustor. AIChEJ. ,28 5 ):759- 765.trend of increasing enhancement with increasingHan,K. E. ,Sung ,H. J. ,ChungM. K. ,1991. Analysissolid loading ratio in the simulated results couldof heat transfer in a pipe carrying two phase gas particlebe found，although the predicted increase insuspension. Int. J. Heat Mass Transfer ,31( 1 ): 69Nusselt number was smaller than that in the pre-- 78.Hetsroni , G. , 1989. Particles- turbulence interaction. Int .sent experimental data.J. Multiphase Flow ,15( 5 ):735 - 746.Kuo,J. T. and Chiou,C. H. ,1988. Momentum and heattransfer of gas-solids suspensions in vertical pipes.35AIChE Symp. Ser. ,84 :207- 211.Kurosaki, Y. , Satoh, I.，Kameoka, Y.，Annmo, Y.，是2.51990. Mechanisms of heat transfer enhancement around是2the stagnation point of an impinging air jet laden withRe=13400, d,0.064mmsolid particles. Proc. of the Ninth Int. Heat Transfer1.5- predicted curve: experimenal dataConf. ,4 :99- 104.Michaelides, E. E. ，1986. Heat transfer in particulate0.5~.0 1.5 2.0 2.5flows. Int. J. Heat Mass Transfer ，29( 2 ):M, (kg/kg)265 - 273.Murray ,D. B. , Fitzpatrick ,J A. , 1991. Heat Transferin a staggered tube array for a gas- solid suspension flow.Fig.10 Predicted increase in Nusselt number comparedTrans. ASMEJ. Heat Transfer ,113 :865 - 873.with that in the experimental data( Re= 13，Murray ,D. B.，1994a. Local enhancement of heat transfer400 ,dp= 0.064 mm )in a particulate cross flow一I Heat transfer mechanisms.Int. J. Multiphase Flow ,20( 3 ):493 - 504.CONCLUSIONSMurray ,D. B.，1994b. Local enhancement of heat transfern a particulate cross flow- -II Experimental data andpredicted trends. Int. J. Multiphase Florw , 20( 3 ):Investigation of the effect of solid particles on505 - 573.the heat transfer characteristic of a tube in sus-Owen, P. R.，1969. Pneumatic transport. J. FluidMech. ,39 407 - 432.pension cross flow yielded a useful crrelationin. Shuh,M. J. ,Schuler,c. A. ,HumphreyJ. A. c..corporating solid loading ratio , particle size and1989. Numerical Calculation of particle laden gas flowflow Reynolds number. Heat transfer reductionpast tubes. AIChEJ. ,35( 3 ) :466 - 480.has been found for very low solid loading ratio Sun,J. ,Chen, M. M.，1988. A theoretical analysis of( M。< 0. 05 kg/kg ). The local heat transferheat transfer due to particle impact. Int. J. Heat MassTransfer ,31 969 - 975.characteristics around the tube were successfullyWilkinson ,G. T. ,Norman,J. R. ,1967. Heat transfer topredicted by the present numerical model. Fora suspension of solids in a gas. Trans. Instn. Chem.total heat transfer enhancement due to particlesEngrs. ,45 314- 318.the model have been shown to give good agree-Wood ,R. T. ,Kuwata ,M. ,Staub,F. W. , 1980. Heatment between predictions and experimental data.transfer to horizontal tube banks in the splash zone of afluidized bed of large paricles. In : Fluidization ( Edit-References中国煤化工M. )Plm Pes,Cen,K. F. , Fan.J. R. , 1992. Prospects of applying woC NMH G. ,1966. Gassolid suS-computer- aided testing( CAT ) to designing and testingTHnedie. Proc. of Instn.boilers, Proc. of the Int. Power Engineering Conf. ,Mech. Engrs. ,181 :17- 33.p.39 - 45.FanJ. R. ,Cen,K. F. ,1987. Effects of turbulent fluctu-Yoshida, H. , Suenaga, K. , Echigo, R.，1990. Turbu-lence structure and heat transfer of a two dimensionalation and frequency spectrum on the drag coefficient of aimpinging jet with gas- solid suspensions. Int. J.spherigelrwiele in gas-solid flow. 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