HEAT AND MASS TRANSFER TO PARTICLES IN FLUIDIZED BED

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1 IEA Technicl Meeting, Skive, Denmrk, October 2017 HEAT AND MASS TRANSFER TO PARTICLES IN FLUIDIZED BED Bo Leckner Avelningen för Energiteknik Chlmers University of Technology Göteborg, Sween 1

2 CORRELATIONS: SINGLE PHASE FLOW Reltionships for single sphericl prticles in single phse flow hve been etermine by Frössling (1938), Rnz Mrshll (1952), Rowe (1965) Nu =2+0.69Re 0.5 Pr 0.33 Sh =2+0.69Re 0.5 Sc 0.33 Gs conuction n gs convection terms, relte to the prticle imeter, re nlogous for het n mss trnsfer in this cse. Contribution from rition hs to be e in the het trnsfer cse. Het trnsfer Nu =h /k Pr= c p /k Mss trnsfer Sh = /D Sc= /D 2

3 HEAT AND MASS TRANSFER BETWEEN THE GAS AND ACTIVE PARTICLES IN THE BED Gs psses through the spce between the prticles with velocity u mf /ε i Two lrge ctive prticles surroune by smller inert prticles in be with fluiiztion velocity u. 3

4 APPLICATIONS Vrious chemicl engineering processes in fluiize be, e.g. in fuel conversion Drying n pyrolysis of fuel prticles Combustion of chr 4

5 CORRELATIONS: FLUIDIZED BED There re mny correltions giving ifferent results hving similr structure (Shown for het trnsfer (Nu) but nlogous for mss trnsfer (Sh)) n Nu const const(re / ) Pr, mf mf where or n Nu const ( / ) i i m where Nu h / k n g ( ) / 0.33 Nu h / k Re u / c g, mf mf g 3 2 i c i g i g s g Trnsformtions Nu Nu / i i Re Re / imf, mf, i 0.5 Re imf, /( ) 5

6 Bskkov Plchonok s pproch: HEAT AND MASS TRANSFER INTERPOLATED BETWEEN = i n >> i Sh 1 or Nu 1 is the low limit = i Sh i, or Nu i, is the lrge limit >> i Sh i or Nu i re in between the limits The interpoltion formule: Nu Nu i Sh i, 1 i, i Sh Nu Nu Sh Sh i, 1 i, ( / ) i ( / ) i n m Nusselt or Sherwoo number, Nu, Sh Mss n het trnsfer coefficients relte to be prticles Shi or Nui Nu, =i Nu, >>i Sh, =i Sh, >>i chimees number, Thin lines / i = Thick full lines --- Sh Thick she lines---nu chimees number 6

7 THE i = LIMIT = i ----Plchonok's correltion + Turton n Levenspiel * Bskkov et l. (10-->6) o Plchonok n Tmrin Scott et l.(2-->6) = i, Plchonok's correltion * Bskkov et l. + Hsiung n Thoos Plchonok n Tmrin Nu 1 Sh fit to t in the limit = i (Plchonok et l., 1992) Nu 1 = i 0.39 Pr 0.33 Sh 1 =2ε mf i 0.39 Sc

8 THE LARGE ACTIVE PARTICLE LIMIT >> i Trnsfer to lrge, fixe, n roune object in fluiize be, Bskkov (1973), Nu i, Pr Sh i, Sc The mss (n het) trnsfer coefficient goes to symptotic vlues s Limiting mss trnsfer coefficient m/s Lines ccoring to Bskkov. o symptotic vlue: Prins igrm x limiting vlue of -->infinity: Prins correltion Lrge prticle symptote ccoring to Bskkov 0.5 tmes the bove h symptot, W/m 2 K o Prins het trnsfer t, --> infinity ----Lrge-prticle limit, Bskkov (t from Prins 1987) x x

9 AVAILABLE HEAT TRANSFER CORRELATIONS Scott et l Tsuk n Horio, 1992 Prins, 1987 Bbos 1985 Shh, 1983 Plchonok n Tmrin,

10 HT: Scott et l. 2004; Nu 2 1.0Re ( ) mf, i Scott's t (moifie) Lines for / i =1, 2 n 2.75 (thick--within rnge, thin--extrpolte) Nu i

11 HT: Brbos et l., 1995; Nui,mx 5.33 ( ) 0.09 i 0.25 Brbos et l. t Lines for = (thick--within rnge, thin--extrpolte) o(upper) extpolte for = i o(lower) extrpolte for =0.08 m Nu i

12 HT: Tsuk n Horio, 1992: Nu ( / ) ; Nu ( PrRe )( / ) ,mx i i,mx mf i Tsuk n Horio's t Lines for = (thick--within rnge, thin--extrpolte) o(upper) extrpolte for = i o(lower) extrpolte for =0.08 m Nu i

13 HT: Prins, 1987; Nui,mx ( ) where n 0.105( ) n i i Prins't Lines for = (thick--within rnge, thin--extrpolte) o(upper) extpolte for = i o(lower) extrpolte for =0.08 m Nu i

14 HT:Plchonok n Tmrin, 1983; Nui,mx 0.41 ( ) ( ) 0.3 i 0.2 i Plchonok n Tmrin's t Lines for = , thick lines within rnge, thin--extrpolte Nu i

15 HT: Shh, 1983; Nu Nu i,mx i,mx c i p Re opt ( ) ( ) for cpi i Re opt ( ) for Shh's t Lines for = within rnge o (upper) = i o (lower) =0.08 m Nu i

16 OVERVIEW OF THE PUBLISHED HEAT TRANSFER DATA Scott's t (moifie) Lines for / =1, 2 n 2.75 i (thick--within rnge, thin--extrpolte) Nu i

17 Fit of het trnsfer t Nu Nu ( Nu Nu )( / ) i i, 1 i, i

18 SELECTED MASS TRANSFER CORRELATIONS Scl 2007 Hyhurst n Prmr 2002 Prins

19 MT: Prins 1987; m 1 m 1 Re mf mf, i Shi Sc ( ( i / ) ) mf mf m n u ( i / ) Re mf, i mf i / Prins' correltion Lines for =2, 4, 8, 10, 14, 20 mm T= K, eps=0.4 Sh i = i 0.5 Sh ( lrge)

20 MT: Scl, 2007; ,.. Scl's t re * mesure =4.6 mm green * mesure i =0.55 mm o correltion =0.2; 1; 4.6; 8.2 mm within rnge + correltion =20 mm, > outsie rnge = i (extrpolte) Sh i 0.5*Sh (lrge ) 10-1 Dt: T= K ensity 2500 kg/m 3 D= * (T/273) 1.75 m 2 /s (Sc=2.5) eps=

21 OVERVIEW OF THE MASS TRANSFER CORRELATIONS 21

22 Prins =2; 4; 10 mm Scl =2.5; 4; 10 mm Scl's conitions COMPARISON PRINS SCALA Scl s conitions in both correltions Prins conitions in both correltions Prins =2; 4; 10 mm Scl =2.5; 4; 10 mm Prins' conitions Sh i Sh i Quntity Scl Prins Temperture, K Be prticle ensity, kg/m Voige, Diffusivity, m 2 /s T T Sc

23 Fit of mss trnsfer t Sh Sh ( Sh Sh )( / ) i i, 1 i, i 1.0 T= 723 K Density 2650 kg/m 3 Diffusivity for oxygen in ir i =1.0 mm Prins c b e Sh i 10-1 i =0.1 mm Scl 10-2 Prins f Scl Active prticle size mm 23

24 CONCLUSIONS The greement between vilble correltions on het n mss trnsfer to ctive prticles in fluiize bes is not extremely high. However, the t in the mesure rnges re t lest within the limits of the Bskkov Plchonok pproch. Therefore, n estimte of coefficients is obtine by Nu Nu ( Nu Nu )( / ) i i, 1 i, i Sh Sh ( Sh Sh )( / ) i i, 1 i, i A seemingly more ccurte estimtion woul be given by the correltion of choice, pplie within its mesure rnge. It ws shown tht most correltions (exception Prins for mss trnsfer) give erroneous vlues when extrpolte to lrge ctive prticles Also, espite the imensionless representtion, the correltions epen on the properties of the mei, e.g. the Schmit number in the cse of mss trnsfer. 24

25 Appenix: HEAT TRANSFER TO AN ACTIVE PARTICLE () IN A BED OF INERT PARTICLES (i): Moel free correltions Some vilble correltions: Tmrin et l. (1982) Tmrin et l. (1985) Shh (1983) Cobbinh et l. (1984) Prins (1985) Brbos et l. (1993) Scott et l. (2004), Collier et l. (2004) (Cmbrige) Nui 5 ( ) i Nui,mx 0.41 ( ) ( ) Nu Nu mx mx i i c p Re opt ( ) ( ) for Reopt 170 cpi i Re opt ( ) for Reopt 170 i Nu,mx ( ) i n Nui,mx ( ) where n 0.105( ) Nu mx Nu c 0.61 ( ) ( ) c i pi. i 0.17 i p, g g 2 1.0Re ( ) mf, i i 25

26 References Aerov ME, Toes OM, Hyrulic n Therml Funmentls on the Opertion of Apprtus with Sttic n Fluiize Prticle Be (In Russin), Chimi, Leningr, (1968). Aveesin MM, Dvison JF, Combustion of crbon prticles in fluiize be, Trns. Inst. Chem. Eng., 51, , Brbos AL, Steinmetz D., Angelino H, Het trnsfer roun sphericl probes t high tempertures in fluiize be, pp , Fluiiztion VIII, Es J F Lrge n C Lguérie, Engineering Fountion Bskkov AP, Berg BV, Vitt OK, Filippovsky NF, Kirkosyn VA, Golobin JM, Mskev VK, Het trnsfer to objects immerse in fluiize bes, Power Technology 8 (1973) Bskkov AP, Filippovskii NF, Munts VA, Ashikhmin AA, Temperture of prticles hete in fluiize be of inert mteril, Journl of Engineering Physics 52, , Frössling, N. (1938) The evportion of flling rops [in Germn], Gerlns Beiträge zur Geophysik, 52, Hsiung TH, Thoos G, Mss trnsfer in gs fluiize bes: mesurements of ctul riving forces, Chem Engn Sci 32, (1977). Plchonok GI, Tmrin AI, Stuy of het exchnge between moel prticle n fluiize be (Trnslte), pp , J. Eng Phys Plchonok GI, Doliovich AF, Anersson S, Leckner B, Clcultion of true het n mss trnsfer coefficients between prticles n fluiize be, Fluiiztion VII, Engineering Fountion, Prins W, Fluiize be combustion of single crbon prticle, Thesis, Twente University, Rnz, WE., Mrshll Jr., WR., Evportion from rops, Chem. Engn. Progress, 48, (prt I) n (prt II) , (1952). Scl F, Mss trnsfer roun freely moving ctive prticles in the ense phse of gs fluiize be of inert prticles, Chem. Eng. Sci., 62, 4159, Shh M, Generlize preiction of mximum het trnsfer to single cyliners n spheres in gs fluiize be, Het Trnsfer Engn. 4, , Tsuk M, Horio M, Mximum het trnsfer coefficient for n immerse boy in bubbling fluiize be, In Eng Chen Res 31, , Turton R, Colkyn M, Levenspiel O, Het trnsfer from fluiize bes to immerse fine wires, Power Technology 53,

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