Heat transfer to liquid fluidized beds in annuli

Chemical Engineering and Processing, 31 (1992) 363-375

Heat transfer

to liquid fluidized

M. Jamialahmadi,

H. Miiller-Steinhagen,

Department of Chemical and Materials Engineering,

363

beds in annuli B. Stellingwerf

The University of Auckland. Auckland (New Zealand)

and B. Robson Alcoa of Australia Ltd., Kwinana, W.A. (Australia) (Received

March

24, 1992; in final form May 20, 1992)

Abstract Heat transfer coefficients to a liquid/solid tluidized bed in an annulus have been measured. Water and Bayer liquor have been used as liquids, while glass spheres and two types of steel cylinders have been used as solid particles. The possible operating parameters, heat flux, flow velocity and bulk temperature, have been varied over a wide range. The measurements with water are compared with the predictions of 13 correlations from the literature. The formation of sodium aluminium silicate on the heat transfer surface was studied for the fluidized bed section and

for plain annular flow.

Tntroduction Severe heat exchanger fouling is a major problem in many chemical and mineral processing industries. The related overdesign and/or the frequent cleaning cycles control the economy of the whole process because of equipment cost, long downtime, energy losses and costs for cleaning chemicals. A typical example of such rapid fouling is the deposition of sodium aluminium silicate (De-Silication Product, DSP) in the heat exchangers of the Bayer process, where cleaning cycles as frequent as every 5-20 days are common. Several methods have been developed during the past years to reduce the formation of deposits in heat exchangers by chemical or mechanical means [ 11. One of the most promising concepts is the fluidized bed heat exchanger. which is described in detail by Kollbach [2, 31. Mechanically and chemically inert particles are fluidized by the fouling liquid. Owing to the slightly abrasive action of the particles, any deposits that may form on the heat transfer surfaces are immediately removed. Commercial scale fluidized bed heat exchangers are manufactured and marketed by Dorr-Oliver Deutschland and ESKLA BV [4]. The increased turbulence caused by the fluidized particles also increases the heat transfer coefficient from the heated surface to the fluid. While there have been several investigations onto heat transfer for solid-liquid fluidized beds in circular tubes, no information was found for the annular space between two concentric tubes. Since this flow geometry is quite common, for

0255-2701/92,‘%5.00

example in double pipe heat exchanger or in fouling monitoring systems, investigations for this system have been performed.

Experimental Test rig Figure 1 shows the test apparatus used for the present investigations. The liquid flows in a closed loop consisting of temperature controlled storage tank, pump and test section. The flow velocity of the liquid was measured with calibrated orifice plates. The fluid temperature was measured by thermocouples located in mixing chambers, before and after each of the two

:

:

I :

It : :

Drain

Fig. 1. Schematic

diagram

0

of test apparatus.

1992 -

Elsevier Sequoia. All rights reserved

364

parallel test sections. The pressure inside the rig could be adjusted by connecting the supply tank to pressurized air. The complete rig was made from stainless steel. The fluidized bed test section was designed to accommodate the most commonly used fouling monitoring system, namely the heating rod initially designed and developed by Heat Transfer Research Inc. (HTRI) as Portable Fouling Research Unit (PFRU) [5]. The complete unit shown in Fig. 2 consists of an electrically heated cylindrical heating rod made of stainless steel, which is mounted concentrically within the surrounding pipe. The dimensions of the test sections are: diameter of heating rod annular gap length of heating rod length

of heated

section

10.67 mm 14.73 mm 400 mm 100 mm

The flow channel expands above the heated section to decrease the flow velocity and restrict particle carry over. The local surface temperature of the heater is measured using four thermocouples, which are installed just below the heat transfer surface. The ratio between the distance of the thermocouples from the surface and the thermal conductivity of the heating rod material (s/J,,,) was determined by calibration measurements using a Wilson plot technique. The surface temperature of the heater can be calculated using this ratio, the heat flux and the thermocouple temperature.

Tw= Tth- 4(s/Av> A part of the pipe surrounding the heating rod was made of glass to allow examination of the effect of heat flux, bulk temperature, flow velocity and particle type on the appearance of the fluidized bed and on the formation of vapour bubbles, at least for the measurements with pure water. The liquids used in the present investigation were pure water and spent Bayer liquor supplied by an Alcoa of Australia Ltd. refinery. Bayer liquor is a concentrated caustic soda solution with

TABLE

4 (mm)

A

3.06 2.0 1.96

7900 2500 7900

Fig. 2. Schematic

chamber

diagram

of fluidized

bed

test section.

&Pk

Material

0.45 0.41 0.40

steel glass steel

(2)

Preliminary experiments have been performed with a perspex test section to find a suitable design and to determine the relationship between bed voidage and superficial flow velocity. Experimental

procedure

and data reduction

Flow velocity and heat flux were varied while the bulk temperature was kept constant. All measurements were taken after the system had reached steady state conditions. The runs were started with the highest heat flux to eliminate hysteresis effects due to bubble site activation. The experiments were carried out in an arbitrary sequence and some runs were repeated to check the reproducibility of the experiments, which proved to be satisfactory. Calibration experiments have been carried out without fluidized particles to check the agreement between the experimental convective heat transfer coefficients and the predictions of the Gnielinski equation (61. The local heat transfer coefficients are defined as:

range of the experimental parameters covered in investigation is shown in Table 2. All experimental are tabulated in the Appendix, Tables Al-A12. important parameter for the characterization of

TABLE

\

(km-‘)

d,=dpfi

2. Range

Flow velocity Heat flux density Bulk temperature System pressure Particles mixing

of particles

considerable amounts of dissolved alumina, silica and various organic components. Three types of particles have been used in the present investigations, as shown in Table 1. The equivalent diameter of the particles, which is required for the calculations discussed in the section entitled correlation of data has been calculated from

The this data An section

1. Properties

of parameters O.lms’l
Z

365

fluidized eqn.

beds

is the bed voidage,

which

is defined

in

(4)

VF

HTED,,~- 4 VP HTTD,,~

E==-C=

For a given number of particles, therefore, only the bed height has to be measured to determine the voidage.

Results Measurements with pure water Injluence of heat J%X Figure 3 shows the heat transfer coefficient as a function of the heat flux for the three different particle types under investigation. For comparison, the results for the empty test section are included. All experiments have been performed for a flow velocity of 0.3 m s ’ and a bulk temperature of 95 “C. One can clearly distinguish between two regimes of heat transfer, depending on the effect of heat flux on the heat transfer coefficient. In the convective heat transfer regime, the heat transfer coefficient is independent of the heat flux, while it increases strongly with heat flux for the subcooled nucleate boiling regime. It is obvious, that the convective heat transfer coefficients of the fluid&d bed are considerably higher than the values for single phase annular flow. Furthermore, the convective heat transfer coefficients increase with increasing mass of the individual particles: from the glass spheres via the small steel cylinders to the large steel cylinders. However, all curves seem to converge into a single line for fully developed subcooled boiling. Figure 4 shows the test section during an experiment where bubble formation occurred at the heat transfer surface. It has been observed that the growing bubbles moved the fluidized particles away from the heat transfer surface towards

Fig. 4. Fluidized

bed during

boiling

experiment.

the opposite pipe wall. This mechanism reduced the effect of the particles on the mixing of the sublayer and explains why heat transfer for high heat fluxes is controlled only by the growth and detachment mechanisms of the bubbles. Injuence of Jaw velocity For fully developed subcooled flow boiling, heat transfer coefficients with and without particles are almost identical and independent of the flow velocity. This is demonstrated in Fig. 5, which shows the experimental results for a heat flux of 400 000 W m ‘. The minor deviations between the data are most likely due to experimental uncertainties.

W/m2K 20.000 E .a, .u ?= 8 0

10.000

5 ‘-,

$ F c Y + ‘;;

3.ooc

10

20

Heat

50

Flux

100

I 200

” = 30 cm/s T,, = 95°C p = 1.2 bor 500

nnn

I

m

;yjw’

5.000

I”

3

0.2

0.1

1,000

kW,‘m2

Fig. 3. Heat transfer coefficient as a function of the heat flux.

Flow

0.3

Velocity

Fig. 5. Heat transfer coefficient as a function for fully developed subcooled boiling.

05

0.7 4s

of the flow velocity,

366 20,000 W/m’K

‘; .%

.u

i

10.000 1

r

/

*

I

:_~ez*o.;; p$Jq 0.1

02

Flow

0.3

0.5

0.7

1.0

cm/s

Velocity

Fig. 6. Convective heat transfer coefficient as a function of the flow velocity.

For the convective heat transfer regime, the effect of flow velocity on the heat transfer coefficient is shown in Fig. 6. While the heat transfer coefficients for the empty annular section increase with increasing flow velocity to the power of about 0.85, the heat transfer coefficients for the fluidized bed decrease slightly with increasing flow velocity over the range 0.2 m s-’ < u < 0.5 m s ‘. The local values in this region depend on particle material, but also on the mass of particles which was added to the test section, as shown in Fig. 7. If the flow velocity is low, the particles form a fixed bed below the heated part of the test section. The heat transfer coefficients are low, corresponding to the convective heat transfer coefficients for this velocity. Once a certain flow velocity is exceeded, the particles become fluidized and increase heat transfer in the test section. The fluidized bed reaches the thermocouple cross section for lower velocities, and creates a more pronounced plateau region, if more particles have been added to the

4,000 0.3

0.4 Flow

0.5 Velocity

0.6

test section. If the flow velocity is larger than the terminal flow velocity of the particles [7], particle carry over occurs and the heat transfer coefficient decreases to the convective heat transfer coefficient for this velocity. As shown in Figs. 3 and 6, the convective heat transfer coefficient for the fluidized bed increases with increasing mass of the individual particles. For identical flow velocities, the convective heat transfer coefficients for the fluidized bed are always considerably higher than the convective heat transfer coefficients for the empty test section. However, experiments with plastic fluidized particles (pP = 1370 kg mm3 and pp = 1760 kg m-‘) in a circulating fluidized bed demonstrated that the heat transfer coefficient of the pure fluid remains unchanged if the fluidized particles have a density similar to that of the carrier liquid [8]. Infiruence of bed porosity The porosity of the fluidized bed depends on the flow velocity, size and material of the particles and on the physical properties of the fluid. Figure 8 shows the appearance of the test section for experiments with high, medium and low voidage, all for the 2.5 mm stainless steel spheres. From the pilot experiments it was found that the annular gap has an effect on the porosity of the fluidized glass spheres, while the much heavier steel particles are not affected. Figure 9 shows the heat transfer coefficients for the two steel particles as a function of the heat flux, for three different porosities. The convective heat transfer coefficients increase with decreasing bed porosity. For the same heat flux and bed porosity. the heat transfer coefficients for the larger particles are higher than those for the smaller particles. This effect is more pronounced for the measurements with high porosity and decreases with decreasing porosity. It is, therefore, not possible to correlate the heat transfer cokfficients solely using the bed porosity.

07 cm/s

Fig. 7. Effect of flow velocity on convective heat transfer coefficient for different amounts of particles.

Fig. 8. Appearance of test section for different voidages.

367 is almost independent of the flow velocity. If the values of the heat transfer coefficients at Tb = 95 ‘C are compared with the corresponding values for pure water in Fig. 6, it is found that the heat transfer coefficients for the liquor are considerably lower than those for pure water and that the fluidization occurs for lower flow velocities. This effect is attributed to the different physical properties of the liquor. The major effect of increasing the bulk temperature is a reduction of the viscosity. As can be seen in Fig. 10, this moves the quidization heat transfer coefficient to higher flow velocities and higher values. Forced convective and subcooled flow boiling heat transfer coefficients for annular flow of Bayer liquor without particles have been investigated in Ref. 9. If the appropriate physical properties are used, convective heat transfer coefficients predicted using the Gnielinski equation [5] are in excellent agreement with the measured data. coefficient

8,000

5

IO

20 Heat

50

100

200

Flux

500

I.000

kW/m’

Fig. 9. Heat transfer coefficient as a function of heat flux for various bed porosities.

Measurements with Bayer liquor Bayer liquor is used to dissolve aluminium oxide from bauxite. It is a complex mixture of concentrated caustic soda with considerable amounts of dissolved aluminium oxide, silica and various organic components. The physical properties of Bayer liquor vary greatly with temperature and composition. To investigate if the results for pure water could be applied for more complex process fluids, a series of experiments with 100 g of the large steel particles in the test section have been performed. These particles provided the highest heat transfer coefficient for pure water. Since Bayer liquor is not a clear liquid, no visual observations could be made. For safety reasons (pH z 14), the glass section has been replaced by a stainless steel section. Figure 10 shows the effect of flow velocity and bulk temperature on the heat transfer coefficients for Bayer liquor. As for the measurements with pure water, a region is observed where the convective heat transfer

Fouling experiments Two preliminary experiments have been performed to compare the performance of the fluidized bed test section with that of the parallel empty test section with identical geometry. Figure 11 shows that the heat transfer coefficient in the empty test section drops rapidly within the first 300 minutes of the experiment, due to the formation of sodium aluminium silicate on the heat transfer surface. The fluidized bed test section, which was installed in parallel, indicated hardly any foulingrelated drop in heat transfer. This result was confirmed by visual inspection of the two heaters, after the experiment: Fig. 12 shows that the heating rod installed in the fluidized bed was essentially clean and shiny, while the other heating rod was covered with tough, adherent silica scale which had to be removed mechanically. A close-up of the deposit is shown in Fig. 13. An attempt

W/m2K 8.000

7

Tb=

3

Tb=

3

Tb=

5 :E

b Tt,=

z:

7,500

: 0

7.000

b % c

6.500

z + Particle diameter

properties 2.5

mm

s

6,000

2 500

Flow

Velocity

cm/s

Fig. 10. Effect of flow velocity and bulk temperature on the heat transfer coefficients for Bayer liquor.

1,000 Time

1,500

2 min

Fig. 11. Heat transfer fouling in the fluidized bed section and in the empty test section.

368

W/m2K

0

2,000

1,000

3.000

4,000

Time

Fig. 12. Appearance of the two test heaters after the fouling experiment. Upper heater was installed in the fluidized bed, lower heater

was installed

Fig. 13. Deposit

Fig. 14. Heat transfer parallel heaters.

5,000

6. 00 min.

u&Ticienl

as a function

of time for two

in the empty test section.

formed

at the

heal

transfer

surface.

to remove the deposit by installing the fouled heater in the fluidized bed did not show any beneficial results within two days of operation. The results of the second fouling experiment are shown in Fig. 14. Again, we observe a relatively steep drop in heat transfer followed by a more gradual continuous decrease for the heater without particles. The heat transfer coefficient for the fluidized bed is initially constant (first 1 500 minutes) and decreases slowly up to about 3 000 minutes. After this time, the heat transfer coefficient dropped by approximately 2 000 W mm2 K-’ and then increased again to the value it would have reached if no drop had occurred. Again, the heat transfer surface of the fluidized bed heat exchanger was found essentially free of deposit, after the experiment. This indicates, that the drop in heat transfer was rather caused by changes in the hydrodynamic conditions than by the formation of deposits. It was also found that the stainless steel wire mesh installed to retain the particles at the bottom of the test section was severely fouled

Fig. 15. Fouled

flow distribution

mesh.

(see Fig. IS) and may have caused maldistribution of flow past the heated section. Considerably more experiments to assess the fouling performance of the fluidized bed are at present being undertaken.

Correlation

of data

A considerable number of correlations exist for the prediction of heat transfer coefficients in liquid fluidized bed, most of them compiled in Ref. 10. Generally, these correlations can be presented in the following form ‘ed( 1 - E)~ with

(6)

369

pr=t+-%F AF

The coefficients suggested by the various authors are given in Table 3 together with the range of applicability. The following two parameters are also used: (9) and Ar = g43(P, -

convective single phase flow, the variation between the predictions of the various authors is quite considerable. For all three particle types under investigation, the best agreement between measured and predicted values was obtained with the correlations suggested by Allen ef al. [ 181 and by Wehrmann and Mersmann 1201. The Kollbach correlation consistently provided values lower than the measured data, as predicted by the author [lo]. The fact that about half of the investigated correlations predicts the measured heat transfer coefficients reasonably well supports the validity of the measured data.

PF>

PF’F2

Conh.e3ions

has been shown in a previous paper [7] that the correlation of Hirata and Bulos [ll] in conjunction with the Richardson-Zaki model [ 121 predicts the bed voidage E in annuli with a standard deviation of only 6%. Figures 16(a-c) show a comparison between the measured and calculated heat transfer coefficients for the three different particle types used in this investigation. While all correlations predict a considerable increase in heat transfer above the values for forced It

TABLE 3. Coefficients for equation

(4)

Reference

NO.

I.

Ruckenstein

and Shorr

2.

Hamilton

3.

Tripathi

4.

Brea and Hamilton

5.

Richardson,

6.

Allen, Fukuda,

[ 131

[ 141 [IS]

and Pandey

z

a

b

0.067 0.326 3.38

0.33 0.33 0.33

-0.237 0.423 0.565

0.0173

0.31

0.73

et al.

er al.

[ 171

8.

Wehrmilnn

e

d 0 0 0

0 0 0.57 -0.19

-1.6

[ 181

et al.

[ 191

Re,Ar OS8z 0.09 Re,Ar-058 < 0.09 18 < Re, < 1251

0

40 < Re, i 1000

0.52 0.33

0.55 0.62

0.15 0

0 -1

0.45 0.38

0 0

1.85 11.8

0.33 0.33 0.14

0.52 0.52 0.48

0.2 0.2 0.38

-0.04 0 0

0.52 0.48 0.56

0 0 0

0.5 0.5 0.5 0.37

0.70 0.50 0.629 *

0 0 0 0

-1 -1 0 0

0.20 0.33 0.375 0.725

Re,+ < 30 Re,+ < 30 0 *0.0325 Re, + 1.19 Re,043

0

0.145

0

0.2 0.725

9. 10.

Schiitt [21] Kahn, Juma, ef al. [22]

0.148 0.2895 0.4114 *

11.

Midoux, Wild, et al. [23]

0.177

0.41

0.71

0

12. 13.

Kollbach [IO] Carlson and Richardson

0.116 *

0.5 0.37

0.7 *

0 0

and Mersmann

[20]

16

-

-

*equal to * on same line.

[24]

-1

Range investigated by the author

0 0 0.546

0.943 0.67

1.823 Kahn, Richardson,

c

Additional characteristic numbers

[ 161

Romani

I.

Heat transfer coefficients to an annular fluidized bed. are considerably higher than the single phase convective heat transfer coefficients, as long as the proper flow conditions are maintained. For flow velocities below and above a certain critical region, the heat transfer coefficients drop back to the corresponding forced convection values of the single phase liquid flow. The correlations suggested by Allen er al. [ 181 and by Wehrmann and Mersmann [20] can be used to predict

l
-0.7,

(_-> 5+11.E

*0.0325 Re, + 1.88 Re Po.43

30 < Re+ < 40000

(5):

_I Tb

=

(1982)

\

(6)

water

Schutt

g.pc

p= 1.2 bar 0.6

0.4

0.8

Porosity

Porosity 10

2 Flow

Fig.

16 (a).

Comparison

16 cm/s

Velocity

of measured

and predicted

24 Flow

heat transfer

coefficients

10

5

Velocity

for liquid

24

15 cm/s

fluidized

beds. Glass

particles.

20.000 W/m=K 2 16$00 .% g al 8 12.000 b “G 6

8.000

k z a, I

4.000

0

0.2

04

PoPo6sity

1

0.8

02

04

0.6

0.8

1

Porosity I

I

Flow

Fig.

16 (b).

2

Velocity

Comparison

10

30

20

of measured

5 Flow

cm/s50

and predicted

heat transfer

25

15

coefficients

for liquid

fluidized

beds.

50

35 cm/s

Velocity

1.6 x 1.6 mm steel cylinders

20.000 W/m2K 2 .?

16.000

g a, $ 12.000 5 ‘t; 5

8.000

k z u

I

0.2

04

0.6 Porosity 10

Flow

Fig.

20

1 I

08 30

40

Velocity

16 (c). Comparison

and predicted

0 02

0.4

I

heat transfer

0.6 Porosity 10

50 cm/s

of measured

4.000

Flow

coefficients

Velocity

for liquid

20

0.8

1

I 30

40

50 cm/s

fluidized

beds. 2.5 x 2.5 mm steel cylinders.

371

the heat transfer coefficients for annular solid/liquid flow at higher bed porosities. Heat transfer fouling from dissolved silica is greatly reduced in the fluidized bed due to the abrasive action of the particles and the improved mixing of the thermal sublayer. However, close control of operating conditions may be required to avoid maldistribution of particles and excessive deposition in other parts of the equipment.

P

pk th W

References 1 H. M. Mtiller-Steinhagen, 2

Acknowledgements The authors are indebted to Alcoa of Australia Ltd. for supporting this research project and to the Institut fiir Verfahrenstechnik, University of Aachen, for supplying the various particles.

3

4

5

Nomenclature

6

Ar a-e

7

L, 4 4 H

g A4 Nu

Pr P L

Ret,+ s T z’ V z

Archimedes number exponents in eqn. (5) heat capacity, J kg-’ K-’ hydraulic diameter, m equivalent particle diameter, m particle diameter, m bed height, m acceleration due to gravity, mss2 mass, kg Nusselt number Prandtl number pressure, kPa heat flux, W rnp2 Reynolds number defined in eqn. (8) Reynolds number defined in eqn. (9) distance between thermocouple location heat transfer surface temperature, “C flow velocity, m s ’ volume, m3 constant in eqn. (5)

Greek letters heat transfer a

& i, P v P

coefficient, W m ’ Km’ voidage thermal conductivity, W mm’ K ’ dynamic viscosity, kg mm’ SS’ kinematic viscosity, m2 s- ’ density, kg mm3

8

9

10

11 12 13

and

14 15 16 17

18

19

20

Subscripts/superscripts

b F L

bulk fluid liquid

particle packed bed thermocouple wall

21

Mitigation of heat exchanger fouling: Trends and Technologies (keynote lecture) Proc. 4th Australasian Heat and Mass Tramfer Conf., Christchurch, 1989, pp. 25-43. R, Rautenbach and J. Kollbach, New dcvclopmcnts in fluidized bed heat transfer for preventing fouling, Swiss Chem. 8 (1986) 41-55. J. Kollbach, W. Dahm and R. Rautenbach, Continuous cleaning of heat exchangers with recirculating fluidized bed, Heat Transfer Eng., 8 (1987) 2632. D. G. Klarcn. The fluid bed heat exchanger: Principles and modes of operation and heat transfer results under severe fouling conditions, Fouling PYPY. Res. Dig., 5 (1983). P. Fischer, J. W. Suitor and R. B. Rrtter, Fouling measurement techniques. Chem. Eng. Progr., 71 (1975) 67-12. V. Gnielinski, Warmeiibertragung in Rohren, VDI-Wiirmeatlas, VDI-Vcrlag, Dusseldorf, 5th edn., 1986. M. Jamialahmadi and H. Miiller-Steinhagen. Bed voidage in annular solid-liquid fluidised beds. Chem Eng. Process., 31 (1992) 221-227. H. Schmidtke, Belagbildung und W&ueiibertragung in &em Zwangsumlaufverdampfer mit zirkulierenden Partikeln, VDZ Fortschrittsberichte, 3 ( 1989). M. Jamialahmadi and H. M. Miiller-Stkinhagen, Convective and subcooled boiling heat transfer to BAYER process liquor, Light Metals, (1992) 141-150. J. S. Kollbach, Entwicklung eines Verdampferverfahrens mit Wirbelschicht- Warmeaustauscher zum Eindampfen krustenbildender Abwlsser, Ph.D. Thesis, University of Aachen. Germany, 1987. A. Hiram and F. B. Bulos, Predicting bed voidage in solid-liquid fluidization, J. Chem. Eng. of Japan, 23 (1990) 5999604. J. F. Richardson and W. N. Zaki, Sedimentation and Fluidization, Trans. Inst. Chem. Eng. 32 (1954) 35-53. E. Ruckenstein and V. Shorr, Despre transferul de caldura dintre un strat fluidizat cu lichid si peretelevasului care-1 contine, Studii cercetari fiz, Akad. rep. populurr Romine, Vol. IO (1959). W. Hamilton, A correlation for heat transfer in liquid tluidized beds. Can. J. Chem. Eng. 48 (1970) 52-56. G. Trip&hi and G. N. Pandey, Heat transfer in liquid fluidized beds, Indian J. Technol., 8 (1970) 285-289. F. M. Brea and W. Hamilton, Heat transfer in liquid Ruidized beds, Trans. Insm. Chem. Engrs. 49 (1971) 196-203. J. F. Richardson, M. N. Romani and K. J. Shakiri, Heat transfer from immersed surfaces in liquid fluidized beds, Chew Eng. SC. 31 (1976) 619-624. C. A. Allen, 0. Fukuda, E. S. Grimmett and R. E. McAtee, Liquid fluidized bed heat exchangers horizontal configuration experiments and data correlations. 12th Intersociety Energy Concersion Eng. Cotzfi (1977). Preprints pp. 824-831. A. R. Kahn, J. F. Richardson and K. J. Shakiri, Heat transfer between o Jluidized bed and a small immersed surface, Cambridge University Press, Cambridge! 1978, pp. 351-356. M. Wehrmann and A. Mersmann, Warrneiibertragung in fliissigkeitsdurchstriimten Fest- und FlieBbetten, Chem. Eng. Techn. MS 940/81 (1981). U. Schiitt, Warmeiibertragung in der Fliissigkeitswirbelschicht nut senkrechten Rohren, Wiss. Zeitung der Techn. Hochschule Magdeburg 26, ( 1982) 71-74.

372 22 A. R. Kahn, A. K. A. Juma and F. Richardson, Heat transfer from a plane surface to liquids and liquid-solid fluidized beds, Chem. Eng. SC. 38, (1983) 2053-2066. 23 N. Midoux, G. Wild, M. Purwasamita, J. C. Charpentier and H. Martin, Zum Fliissigkeitsinhalt und zum Warmeiiber-

gang in Rieselbettreaktoren bei hoher Wechselwirkung des Gases und der Fliissigkeit, Chem. Eng. Techn. 2 (1986) 142143. 24 J. M. Coulson and J. F. Richardson, Chemical Engineering Vol. 2. Pergamon Press, Oxford, 3rd edn., 1985, pp. 250-255.

Appendix Experimental TABLE Al.

results Experiments

Heat flux (W m

*)

without

particles;

water, T,, = 75 “C, p = 1S bar

Heat transfer v=O.lSms

TABLE A2. Experiments *)

with steel cylinders, Heat transfer v=O.S6ms-’ E = 0.97 M,=50g

320000 240000 200000 160000 120000 100000 80000 60000 40000 20000 10000

’

6970 5585 4286 3584 2909 2362 2064 1926 1891 1814 1760 1554

320000 240000 200000 160000 120000 100000 80000 60000 40000 20000 10000

Heat flux (W m

coefficient (W mm2 K- ‘) at

10392 10122 9606 9477 9258 8992 8827 8650 8383 8088 8079 8032

0.30 m s-’

0.50ms~’

0.90ms-’

7557 6155 4724

8262 6885 5609 5362 5313 5247 5192 543x 5344 5108 4991 4927

9736 9527 8987 8944 8708 8519 8359 8245 8142 7912 7819 7991

3499 3415 3406 3387 3382 3349 3386 3470

d, = 3.1 mm; water,

rr, = 75 “C, p =

coefficient (W m-* K-‘)

I.5 bar

at

0.50ms-’ 0.94 1oog

0.40ms-’ 0.89 15og

0.30ms-’ 0.79 300 g

0.18m s-’ 0.66 500 g

11829 11395 10984 10866 10713 10092 9822 9835 9961 9465 9307 9786

12448 12069 11628 11438 11205 10802 10479 10386 10223 9915 9443 9313

15547 15388 14621 14113 13805 13259 13188 12627 12165 12415 12272 11969

17265 16606 16101 I5367 14880 14292 13891 13379 13259 12915 11578 12485

373 TABLE Heat

A3.

Experiments

flux (W m

without

*)

particles; Heat

water, transfer

T,, = 85 “C, p = 1.5 bar coefficient

(W m

v=O.l5ms-’ 400000 320000 240000 200000

8315 5129 4339 3543 2787 2392 2080 2037 2030 2010 1997

100000 80000 60000 40000 20000 10000

TABLE Heat

A4.

Experiments

with

steel cylinders, Heat

flux (W mm*)

coefficient

v =0.56ms-’ E = 0.97 A4,=5og 400000 320000 240000 200000 160000 120000 100000 80000 60000 40000 20000 10000

TABLE Heat

11502 10952 10664 10258 10044 9618 9615 9518 9317 9180 8566 9022

A5.

Experiments

flux (W mm2)

without

particles; Heat v=0.15ms-1

400000 320000 240000 200000 160000 120000 100000 80000 60000 40000 20000

11054 8534 6514 5476 4429 3400 2954 2484 2127 2077 2077 2141

water, transfer

‘) at

0.3Oms~

osoms-1

0.90ms-’

8660 7090 5476 4784 4001 3553 3541 3516 3491 3491 3556 3595

8809 7370 6046 5695 5638 5538 5488 5436 5365 5310 5287 5229

10273 10133 9758 9550 9369 9122 9095 8997 8985 8737 9306 10959

d, = 3.1 mm; water,

transfer

’ K

Tb = 85 “C, p = 1.5 bar

(W m _ * K

‘) at

0.50ms-’ 0.94 100 g

0.40 m s 0.89 15og

12210 12016 11593 11375 10883 10686 10404 10250 10036 9860 9299 9190

12896 12469 12133 I2054 11772 11344 10933 10905 10970 10170 10482 10229

Tb = 95 “C, coefficient

’

0.30m 0.79 300 g 16004 15166 15015 14967 14413 13846 13903 13389 13024 12667 14374 14650

s-’

O.l8ms-’ 0.66 500 g 17843 16178 16580 16051 15400 14703 14567 14063 13947 12604 12118 11815

p = 1.5bar

( W m- ’ K - ‘) at 0.30ms-’

0.50m

10413 8478 6475 5559 4663 3824 3695 3647 3609 3577 3589 3462

10327 8593 6977 6260 5829 5724 5654 5584 5541 5534 5419 5591

s-’

0.90ms-’ 11212 10369 9923 9805 9644 9299 9186 8987 8973 8619 8397 8388

374

TABLE A6. Experiments T,=95”C,p=lSbar

with steel cylinders,

Heat flux (W m-*)

Heat transfer ”

480000 400000 240000 200000 160000 120000

100000 80000 60000 40000 20000 10000

TABLE A7. Experiments

=0.50ms-’

coefficient ( W m _ ’ K _ ‘) at 0.9Onls~

1.20ms-’

15452

16327 14553 12887 12339 12104 11911 I1458 11385 11231 10989 10884 10597 11892

13796 11887 9771 6977 6260 5829 5724 5654 5584 5541 5534 5419 5591

13433 11550 9923 9805 9644 9299 9186 8987 8973 8619 8397 8388

with steel cylinders,

Heat flux (Wtn2)

Heat transfer L’

=0.56ms-'

400000 320000 240000 200000 160000 120000 80000 60000 40000 20000 10000

Heat flux (W mm*)

without

particles;

480000 400000 320000 240000 160000 120000

60000 40000 20000 10000

coefficient (W mm2 K-‘)

0.30 m s -

_

15000 11992 9085 7480 6135 4830 4322 397 1 3482 2936 2238 2226

15170 11981 9176 7793 6766 6000 5514 4836 4135 3412 3210 3092

0.30 m s 0.79 300 g

’

O.l8ms-’ 0.66 500 g

16728 16156 15742 15228 14738 14257 13947 13717 13432 13001 13372 12201

18392 17964 17195 16543 16102 15053 14975 14534 13973 12839 12211 11903

0.50ms-

0.90ms-’

17424 14562 11967 9724 8659 7950 6943 6264 5689 5351 5312 5409 5635

17772 15867 13754 12116 11235 10348 9375 9107 8955 8859 8504 8861 9057

p = 1.2 bat

coefficient (W m-a K

_

’

13581 13139 12440 12406 12136 11629 11329 11135 10838

10479 10297 10272 9746 9224

water, Tb = 95 “C,

at 0.40 m s 0.89 150g

12899 12277 12113 11796 11500 11025

Heat transfer o=0.20ms-’

T, = 95 “C, p = 1.5 bar

0.94 1oog

12317 11303 10911 10650 10521 10212 10035 9809 9595 9682 9192 9725

100000

de = 3.1 mm; water,

0.50ms-'

I: = 0.97 M,=5Og

TABLE A8. Experiments

d, = 3.1 mm; water,

’

‘) at 0.40 In s

14373 11453 8780 8086 7535 6628 5947 5311 4635 4351 4299 4376

’

375 TABLE A9. Experiments T,,=95”C,p=1,2bar Heat

flux (W m

2,

with

Heat

glass

spheres,

transfer

TABLE Heat

0.23 m s0.94

19594 16427 13309 10378 9181 8120 7578 7632 7449 7390 7166 7489 6993

AIO.

Experiments

with

19139 15193 12575 9.519 827 1 7075 6265 5967 5818 5747 6080 6634 6432

18365 15565 12499 9943 8544 7457 6579 6311 5984 6017 5767 5716 5400

transfer

coefficient

Heat

19141 17181 15064 14458 13884 13781 13344 12902 12519 12536 11921 11849 11641

Al 1. Experiments

flux (W m-‘)

with

steel cylinders, Heat

M, = 300 g 480000 400000 320000 240000 200000 160000 120000 100000 80000 60000 40000 20000

10000

lXY93 17136 16152 15265 14804 14287 13611 13575 13426 12664 11967 11079 11781

Experiments with/without r,, = 110 “C, p = 2 bar

flux (W m - ‘)

Heat transfer u = 0.50 m s-’ E= Mp=

400000 320000 240000 200000 160000 120000 100000 80000 60000 40000 20000 10000

8469 7304 6390 5658 5172 4478 4048 3564 3339 3269 3259 3165

steel cylinders,

coefficient

0.48 m s-j 0.95 100 g

9428 8637 7332 6809 6216 5492 5415 5374 5335 5273 5237 5150

11661 9750 8556 8054 7331 7003 6828 6706 6521 6378 6429 6220

‘)

at

’

0.30 m s-’ 0.86

0.40 m s 0.95

300 g

200 g

75 g

75 g

19009 16487 14514 13937 13498 13301 12680 12331 12081 11962 11571 11821 12014

18157 15435 13819 12234 11531 11516 10865 10684 10382 10351 10061 10209 8787

18024 14948 12479 10166 9529 8915 8593 8553 8309 8302 8029 8396 9066

17468 15191 13467 11648 11118 10518 9777 9542 9351 9128 8771 8804 8711

coefficient

(W mm2 K- ‘) at

0.90 m s-’

0.23ms-’ 0.79

water,

de = 3.1 mm

r,, = 95 “C, p = 1.2 bar

(W m -’ K-

d, = 3.1 mm;

transfer

1: =0.30ms-’ E = 0.79

Heat

d, = 1.96 mm; water,

M,=400g

TABLE

TABLE A12. Bayer Liquor,

0_30ms0.96 20 g

L’=O.l8ms-’ E-0.71

480000 400000 320000 240000 200000 160000 120000 100000 80000 60000 40000 20000 10000

I

30g

steel cylinders, Heat

flux (Wm-‘)

water,

( W ni - * K - ‘) at

coefficient

o=O.l6ms-’ E = 0.85 M,=70g 480000 400000 320000 240000 200000 160000 120000 100000 80000 60000 40000 20000 10000

d, = 2 mm;

0.50 In s 0.98

r, = 95 “C, p = 1.2 bar

(W t-r-* Km’) 0.40 m s _ 0.88 180g 17557 15372 14023 13299 13142 13828 12686 12244 11926 11768 11437 11926 11551

’

at 0.50ms-’ 0.95 18Og

0.50ms-’ 0.95

17038 14782 13319 12339 11697 11303 10724 10659 10351 10020 9958 10030 9898

16545 14496 12415 11135 10800 10194 9816 9560 9594 9081 9111 9167 9218

80 g

’