Heat transfer in flowing packed beds

HEAT

TRANSFER

IN FLOWING

PACKED

BEDS

A 0 0 DENLOYEt and J S M BOTTERILL Department of Chemical Engmeermg, Uluverslty of Bammgham, Blrmmgham BlS 2TT, England (Receaved 15 September 1976, accepted 1 November 1976) Abstract-Heat transfer coefficleots were determmed between a small exposed heat transfer surface and a flowmg bed of parkles The experunents were camed out wnth a range of parUes of dtierent properties and of mean sue between 160 and 2370 m, usmg Aa, Freon, Hehum and Argon as the “stagnant” gas medmm Particle residence

tunes at the transfer surface ranged between 1 and 10 set The results fitted closely the predictions of a modtied version of the “Mlckley” packet model with the lnclus~onof an addltional resistance to heat transfer at the transfer surface

INTRODUCTION

In the earlier experrments[l], a flowmg packed bed was used to model the heat transfer behavlonr of a freely tlmd~cd bed of pticles Thus, by controlhng the downward rate of flow of the bed past a small exposed heat transfer surface It was possible to regulate the residence tune of the bed mate& adjacent to the transfer surface Those expenments showed that partlclelsurface contacts were only of an intermittent character In this extension of the work, a particular Interest was the behavlour of systems with beds of large mean particle dmmeter (-1 mm) when the interphase gas convective becomes of comparable component of heat transfer magnitude or larger than the particle convective component [2] Imtmlly, it had been hoped that the flowmg packed bed could then be operated agamst a controlled counter current flow of gas circulated upwards through the bed to cover a correspondmg range of fluid-bed operatmg cond&ons However, tis was not found to be possible The counter current gas flow markedly miluenced the pticle flow behavlour, the bed voidage changed and it was not possible to measure the gas flow rate, bed voidage nor pmcle residence tune as accurately as was necessary Nevertheless, the results obtamed when the flowmg packed bed was operated with “stagnant” gas atmospheres were of interest 111themselves m that they afforded further tests of a modtied packet model of heat transfer and It 1s the purpose of this paper to report them A model for the prediction of the interphase gas convective component of bed to surface heat transfer and Its comparison with packed and quescent bed results IS reported separately[3]

replaced by a fresh packet of particles from the bulk of the bed This IS parallelled m the flowmg packed bed experunent by the Bow of a “packet of particles” across the small exposed heat transfer surface with which it 1s m contact for a residence tuue t They assumed that the thermal properties of the packets were the same as those of the quiescent bed, and denved the followmg expression for the local mstantaneous heat transfer coefficient, hL,

where Ae, pe are the effective thermal conductivity and density of the packets respectively, and C,,, IS the specdic heat of the solid A defect of Mtckley’s model IS the assumption that “packets” of par&les m contact with the heat transfer surface are homogeneous and have undorm thermal propeties Baskakov et al [f&8] mtroduced an additional contact reststance, R,, to allow for the effect of the resistance to heat transfer m the region of Increased voldage adJacent to the surface, m series with the thermal LS mderesistance of the packets, R. Tlus reslstauce pendent of tuue to a first approximation Gelperm et al [9, lo] developed tlus approach further and derived expressions for the overall heat transfer coefficient Thus, assuming that close to the heat transfer surface, where the mean voldage 1s increased to E, and the thermal resistance IS R,, the temperature drops from T, at the wall surface to T, at a distance of d/2 from the surface, Gelpenn ef al [lo] denved the followmg expresston for the heat transfer coefficient, h

TEE BEAT TRANSFERMODEL Mickley and Tnlhngl41 were the first to appreciate the role of the caculatmg particles in the transfer of heat between a flu&zed bed and surface and the unsteady state nature of the process Mlckley and Favbanks[5] later developed a model m which a group of pticles, or “packet”, was considered to be m contact vvlth the heat transfer surface for a short residence tune, f, then to be tPresent address Umverslty of Ife, Ile-Ee, Oyo State, Nlgena CES Vol 32, No 5-A

h=$[l-&ln(l+?)]

(2)

where

Ths assumes that the temperature at the mterface, T,, IS a constant and t 1s the mean residence time of the particles 461

442

A

0

0

DENLOYE and J S M BOTTERILL

at the heat transfer surface If the regon of Increased voldage 1s hmlted to about half a particle hameter from the surface and the heat transfer through thrs regon 1s solely by steady state conduction, the resistance, R,, IS given by

R, = dl2he,

(3)

where Ae, IS the effective thermal conduchvlty m the near wall region We followed Kunu et al [ 1l-131 m deriving an estimate of he and Ae, PLOwINGPACMEDBEDCOLUMN The flowmg packed bed column (Fig 1) has been described m detad by Desal[l4] and Denloye[15] The vertical column was of rectangular cross-section (51 mm x 25 mm) and deslgned to operate at stats pressures up to 1 13 MN/m* Two perspex windows m its walls permitted visual observation and the measurement of the velocity of the flowing solids adjacent to the wall A two-stage bucket conveyor was used to transfer the solids collectmg at the base of the column back to a hopper above It The heater consisted essentially of a 2060n, 25 W, 29 mm x 10 mm x 2 mm soldenng iron element Thts was embedded w&m a block of copper to provided an essentially isothermal surface In these expenments, the heater was supported by a horizontal 3 mm diameter stainless steel tube, and was set m the middle of the column A variable d c power supply to the heat was used, and the power was measured by an ammeter and voltmeter Iron-Constantan thermocouples, 0 254 mm m diameter were used m all measurements of temperature The thermoelectnc e m f was measured by a Tmsley precision vernier potentiometer The particle residence time at the heat transfer surface was estimated by setting a replica heater at the surface sf the perspex wmdow and measuring the tune taken for the particles to flow down the surface of that replica heater A magmfymg glass was used to md visual observation of the particles The lower limit of the residence time that could be accurately determined by this method was approximately one second

Fig

1

heat

transfer

2

solrds

flow

3

gas

L

bucket

5

hopper

surface control

valve

Inlet lift

1 Flowmg packed bed apparatus

RFSULTS AND DJSCUSSlON The flowmg packed bed coefficient, h, 1s given by

to

surface

heat

transfer

Q it = A,dt,,, where Q 1s the heat flow across the transfer surface of known area A, and dt,,, IS a suitable mean temperature tierence The anthmetlc mean of the temperature dfierence between the bed and the transfer surface was used because of the small vanatlon m the temperature dtierence (
Sand

Coal ash Soda glass

Mean size (Fm) 160 340 620 160 590 1020t 1020$ 2370 420 415

t400-3300 pm range $600-1400 pm range

Consistent with predlctlons of simple models and earlier experunents[2], the coefficient of heat transfer between the flowing packed bed and the immersed heater was found to increase with decrease m the particle residence time The rate of increase was greater with beds of smaller particles, all generally convergmg with mcreasmg particle residence tune (Fig 2) The heat transfer coefficient approached hmltmg maximum values wth decreasing particle residence time Static pressure had little effect on the measured heat transfer coefficient (Fig 3), an increase from 0 1 to 0 93 MN/m’ increasing the coefficient by less than 10% with a bed of sand of mean diameter 590 Frn This 1s of the order of increase m gas thermal conductlvlty with pressure predicted by the correlation of Lenolr, Junk and Commgs [ 161 and the bed to surface transfer coefficient 1s sensitive to the gas thermal conductlvlty (see Fig 5 for experiments with tierent gases) The pressure effect seemed to be independent of both particle size and particle residence time As expected[2], the physical property that has the greatest effect on the rate of heat transfer IS particle size Figure 2 compares the heat transfer coefficient obtained with three sEes of sand at atmosphenc pressure An

463

Heat transfer m flowmg packed beds

2370/m I

I

2

I

I

III1

5

r, set

Fig 2 Effect of particle residence time on bed to surface heat expenmeots at atmosphenc pressure, mean transfer, w/sand partlcle diameters X, 160pm, 0, 590pm. A, 2370pm

than those of narrower dlstrtbution and further dlustrates the importance of particle packmg adJacent to the surface from whch the overall particle size effect results[2] The effect of the mtersltml gas on the rate of heat transfer 1s shown m Fig 5 where the maximum heat transfer coefficient at a parkle residence time of 1 set for 1020 pm sand 1s plotted agamst the gas thermal conductivity This mdlcates that the heat transfer coefficient IS heat capacity of the proportional to k,073 The volumetic gas had no apparent effect on the rate of heat transfer over tests m which the static pressure was mcreased up to 9 atm and smular coefficients were obtamed with CO2 and Argon although the heat capacity of CO2 IS approaching twice that of Argon at atmospherrc pressure but they have slmllar thermal conductlvltles (Fig 5)

Fig 3 Effect of particle residence tune on bed to surface heat transfer,au/sandexperunents,meanparticledmmeter590Frn Cl, 0 1 MN/m*, 0, 0 93 MN/m’ mcrease m mean particle size from 160 to 2370 pm reduced the maxunum heat transfer coefficient from 460 to 120 W/m’ “C Figure 4 presents results for two cuts of sand (Table 1) of the same diameter (based on the surface to volume ratlo) but of dtierent size range It can be seen that the coefficients obtamed with the sand of wider size dntnbution were, on average, 10% higher than those with the narrower distnbution This lends confirmation to the fact that beds of wider size &stnbution pack more closely

Y “E

200

I

I

I

Illlll 01

001 kg, W/m”C

Fig 5 Effect of gas thermal conductwty on the maxlmum bed to surface heat transfer coefficient, sand 600-14OOrm size range

Expenmental results obtamed with au at atmospheric pressure as the atmosphere were correlated by a plot of Nusselt number (effectively hd) agamst r/d2 m Figs 6 and 7 Such a correlation IS expected to hold from a srmple paticle replacement model[I7, 181 However, It can be seen from the k/Copper expenmental results (Fig 6), for example, that the “two-particle” model[ 181 overpredicts the coefficient Introduction of a gas gap of thickness equal to 10% of the particle diameter reduces the discrepancy at short residence tunes but increases it at longer ones For a umform surface renewal of particles, the hkldey and Frurbank’s model[S] predicts that

‘z -c

3 t

5

7

9

hd

=

(%!$‘)03 (_$-”’

set

Fig 4 Effect of particle resldence tune on bed to surface heat transfer, &sand experunents. at atmospheric pressure mean particle size 1020~ X, size range 4W-3Hw)~m, A, SIZCrange 60&1400 *m

To apply thus, It IS necessary to know the mean voidage of the flowmg bed m order to estunate Ae and pe However, It was not possible to do this for the flowmg bed condltmn

A 0 0 DENLOYE and J S M BOWERILL

Fig 6 Comparison between Aowmg packed bed to surface coefficients and predlctlons of various models, au/copper experiments at atmospheric pressure 2 Partlcle Model (no gas gap), -, (10% d gas gap), --, Mlckley’s Model - -, No Rw, -----, Rw = d/2Ae, 1, 160 pm, 2, 340 Frn, 3, 620 pm, A, 620 pm, 0, 340pm, X, 160pm

t/d2

.

s/m2

FIN 7 Companson between flowmg packed bed to surface coefficientsand predlctlonsof Mckley model, au/sand No Rw, ----, Inclusive Rw, 1, 16Opm. 2, expenments at atmosphenc pressure Mmkley’s Packet model -, 590pm, 3, 1020pm, 4,237O pm X, 160pm, 0, 590wrn, A, 600-1400pm, Cl, 2370 pm so the static packed bed value was used and the value of he was then estimated from the relatlonshlps developed by Kunn et al 111-131 The resulting predIctions of the packet model for the Au/Copper and h/Sand systems are also aven on FQS 6 and 7 They, too, overestiate the experlmental results but that sunple model, as &scussed above, makes no allowance for the addItional resistance to heat transfer m the region of increased voldage directly adJacent to the heat transfer surface Using the estimate mven by eqn (3) for the wall resistance, expression (2) can be used to make a revised estimate havmg estnnated Ae, followmg Kunu and Snuth[l3] It can be seen (Figs 6 and 7) that agreement between the expenmental results and the mod&d model takmg mto account the wall resistance IS close

The packet model predicts that there should be increase m the heat transfer coefficient with increase m pressure because of the consequent mcrease m gas density (and hence m the volumetic heat capacity of the gas) and, more important quantltatlvely, because of the increase m the gas thermal conductivity which amounts to about 10% over the expenmental range of 0 1-O 93 MN/m*[l6] The model predicts an increase of 5% for this expenmental range which compares reasonably well with the 7% increase observed for a comparable 5% increase m gas conductlvlty aione (Fig 5) The maximum value of the flowing bed coefficient was correlated by plottmg the correspondmg Nusselt number, (h,,djkp), agamst the Archunedes number which 1s a combmatlon of the drag coefficient and particle Reynolds

Heat transfer m flowmg packed beds

465

50

2

t IO 5

Fig 8 Correlaaon

of maxunum flowmg bed to surface coefficients agamst Archunedes number Copper/Au A, 160 Pm, a, 340, v, 620 Sand/Au A, 160 pm, 0,590, V, 1020, Cl, 2370 Soda-glass/Au 0,415 Frn D , Sand (590, 0, Sand (1020~m)/Carbon I)loxlde, x, Sand (6001020, 2370 pm)lFreon, CI , Sand (1020~m)/Argon, 1400 *m)/Hehum

number correspondmg to the bed flow condlfions (Fig 8) This relates h,, to the physical properties of the sohds and to the thermal and physical properties of the gas The correlation can be expressed by the followmg relationship h d = 1 283~~0 162 msx for k,

lV
106

CONCLUSIONS

The flowmg packed bed to surface heat transfer coefficient increases with decreasing particle residence tune, wth decreasmg particle size, and with mcreasmg gas thermal conductivity The results were adequately interpreted by a modified version of the Mckley and Fmbanks model[S] which additional wall heat transfer incorporated an resistance [ lo] A correlation was estabhshed between the heat transfer coefficient to the flowmg packed bed and the system’s physical propeties and operatmg conditions Acknowledgements-The authors gratefully acknowledge support @venfortJusworkbytheSRC andoneofus(AOOD)ls mdebted to the Nlgenan Government for a research scholarstip NOTATION

area of heat transfer surface, m* spectic heat of sohd material, J/kg”C particle diameter, m mean temperature dtierence, “C acceleration due to gravity, mlsec? bed to surface heat transfer coefficient, W/m* “C maxnnum flowing packed bed to surface heat transfer coefficient W/m* “C local instantaneous ‘heat transfer coefficient, W/m* “C thermal conductivity of gas, Wlm”C net heat supplied to the heat transfer surface, W thermal resistance of the “packet” of particles “contact” and resistance respectively, mz OC/W

I T,, T,

residence tune, set temperature at mterface tively, o

and at the wall respec-

Greek svmbols bed voldage voldage close to a wall surface effective packet thermal conductivity, W/m “C effective thermal conductivity near wall gas vlscoslty, Ns/m2 density of gas and solid respectively, kg/m3 effective density of “packets” of particles, kg/m3 Archimedes number [gd’ps(ps - p,)]/pl

111 Bottertll J S M and Desm M , Powder Technology 1972 6 231

121 Botterdl J S M , I&Id-Bed Heat Transfer Academic Press, London 1975 [31 Botterdl 1 S M and Denloye

A 0 0 , Heat Transfer to a Packed or Qurescent Fluuiued Bed, to be pubhshed [41 Mlckley H S and Trdlmg C A, Ind Engng Chew 1949 41 1135 [51 Mazkley H S and Fmbanks D F , A I Ch E J 1955 1 374 WI Berg B V and Baskakov A P , Khrm Prom I%1 43 439 171 Baskakov A P , Inch Fiz Zh Akad Nauk Belonrssk 1%3 6 20

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S M,ButtM

H D.CamG

L andRedlshK

A,

m Drmkenburg. Intematwnal Symposrum on Fbudrzatron. p 442 Netherlands Umverslty Press, Amsterdam 1%7