Heat Transfer in Gas-Solid Fluidized Beds

MAGNETIC FIELD ASSISTED FLUIDIZATION - A UNIFIED APPROACH Part 3: Heat Transfer in Gas-Solid Fluidized Beds - a critical re-evaluation of the results

Jordan Hristov Department of Chemical Engineering University of Chemical Technology and Metallurgy 1756 Sofia, 8K1. Ochridsky sir., Bulgaria, E-mail: [email protected]

CONTENTS 1. INTRODUCTION 2. EXPERIMENTAL CONDITIONS REVISITING 2.1. Magnetization modes applied - a systematization 2.2. Magnetic fields applied 2.2.1. Axial fields 2.2.2. Transverse fields 2.3. Gas-solid systems and temperature ranges 3. OVERALL THERMAL BED BEHAVIOUR 3.1. Axial temperature distribution 3.1.1. Magnetization FIRST mode 3.1.2. On-Off magnetization mode 3.1.3. Effects of the field intensity and the radial position of measurements 3.2. Radial temperature profiles (Magnetization FIRST mode) 3.2.1. Experiments in axial fields 3.2.2. Experiments in transverse fields 3.2.3. Comments on the temperature profiles 3.3. Effective thermal conductivity 3.4. Comments on the overall bed thermal behaviour 3.4.1. Stabilized beds (Magnetization FIRST mode) 3.4.2. Fluidized bed (Magnetization FIRST Mode) 3.4.3. On-Off magnetization effects 4. GAS-TO-PARTICLES HEAT TRANSFER 5. BED-TO-IMMERSED SURFACE HEAT TRANSFER

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Magnetic Field Assisted FluidizalionA Unified Approach-Part 3

5.1 Major Experiments Performed 5.1.1. Particles used and other conditions 5.1.2. Heat Transfer Probes 5.1.3. Magnetization modes applied 5.1.4. Regimes created 5.2. Pure ferromagnetic particles - Major experimental findings 5.2.1. Magnetization FIRST mode - total heat transfer coefficients 5.2.1.1. Vertical surfaces in beds subjected to axial fields 5.2.1. 2. Horizontal tubes in beds subjected to axial fields 5.2.1. 3. Vertical probes in beds subjected to transverse fields 5.2.1. 4. Spherical probes in beds subjected to transverse fields 5.2.2. Magnetization LAST - total heat transfer coefficients 5.2.2. /. Beds subjected to axial fields 5.2.2.2. Beds subjected to transverse fields 5.2.3. On-Off magnetization mode - total heat transfer coefficients 5.2.4. Reconstruction of the experimental conditions (pure ferromagnetic beds)- total heat transfer coefficients 5.2.4.1. Comments on the data before the further analysis 5.2.4.2. Reconstruction of the phase diagrams - Magnetization FIRST and LAST 5.2.4.3. On-Off magnetization mode - optimal conditions 5.2.4.4. Maximum Total Heat Transfer Coefficients - comments 5.2.4.5. Maximum Total Heat Transfer Coefficients - comments on AlQodah's results 5.2.5. Maximum (Total) Heat Transfer Coefficients - data correlations 5.2.5. l.Nusselt number relationships 5.2.5.2. ColburnjH factor correlations 5.3. Local heat transfer coefficients between a bed and an immersed horizontal probe 5.3.1 Re-construction of the experimental conditions 5.3.1.1. The effect of the angular position on the value ofmaxhw 5.3.1.2. The effect of the regime on the value ofmaxhw 5.3.2 Data correlations for local values of maxhw 5.3.3 Short comments on the local heat transfer coefficients 5.4. Admixture Beds - Major Experimental Findings 5.4.1.Magnetization FIRST mode - total heat transfer coefficients 5.4.2. On-Off magnetization mode applied on admixture beds

230

.tonkin llrislov

Reviews in Chemical Engineering

5.4.3. Maximum Heat Transfer Coefficients in admixture beds- data correlations 5.4.3.1.Magnetization FIRST- data correlations for maxh„ • Colburnjh factor • Ni4sselt number correlations 6. DISCUSSION 6.1. A backward glance on the problems reviewed 6.2.Trends - temporal and permanent 6.3. Potential problems 6.4. Final remarks ACKNOWLEDGMENTS NOMENCLATURE REFERENCES SUMMARY The third part of the series concerning the magnetic field assisted fluidization focuses the attention on the heat transfer phenomena. The discussion covers the gas-fluidized beds only. In contrast to the hydrodynamic problems the heat transfer problems (temperature distribution in both the axial and radial directions as well as gas-to-particles and bed-to immersed surface heat transfer) have paid little more attention. The paper made an attempt to re-examine the data concerning the heat transfer phenomena in gas-fluidized beds of ferromagnetic particles controlled by external magnetic field. Data from various sources have been collected and re-evaluated critically from a unified point of view.

1. INTRODUCTION The third part of the series considers the heat transfer phenomena in magnetically controlled gas-fluidized beds. Unfortunately, no published papers exist on the problem in liquid-solid and gas-liquid- solid systems. The analysis of the data available in the literature will be done on the basis of the hydrodynamic results commented widely in the first part of the series (Hristov, 2002) and the recent comments of (Hristov, 2000a,b). The analysis will be done on the basis of the well-established results in the field of nonmagnetic fluidized beds for better elucidation of the problems.

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Magnetic Fielt!/tssisletl Fluitlizalioit.4 Unified Approach-Part 3

It is well known that (Zabrodsky, 1976; Botterill, 1975) the hydrodynamic conditions (the particle motions and the bubble formation) affect significantly gas-to-particle and bed-to-surface heat transfer as well as the temperature distributions across the bed. An external magnetic field allows easy control of the particle mobility (Hristov, 2002) due to: • Particle immobilization in fixed bed structures: MSB (Magn. FIRST) or a Frozen bed (Magn. LAST or the pulsed field magnetization mode). • Reduced particle mobility due to particle aggregation in a fluidized state inspite the magnetization mode. • Reduced bubble formation and appearance. The discussion developed here tends to clarify the results from a position allowing clear identification of the magnetic field effects on the heat transfer. The main topics are: • Magnetization modes and magnetic fields applied. • Particulate materials employed in the studies. • Overall thermal bed behaviour in different regimes including both the axial and the radial temperature distribution and the effective thermal conductivity. • Gas-to-particle heat transfer. • Immersed surface-to-fluidized bed heat transfer. • Data correlations. The data treatment and the phenomena interpretations in magnetically assisted fluidized beds follow the approach established in (Hristov, 2002). Moreover, the situation in the area of the heat transfer is not so clear due to the absence of systematized data treatment and analysis. Most of the studies commented here have been performed without clear identifications of the hydrodynamic conditions. In order to re-evaluate the results several experimental conditions were re-constructed in order to arrange an almost complete relationship between the hydrodynamics and the heat transfer results. All the knowledge available on the fluidized bed hydrodynamics (with and without magnetic fields) was applied for these reconstructions and regime identifications.

2. EXPERIMENTAL CONDITIONS REVISITING 2.1. Magnetization modes applied - a systematization Knowledge of the hydrodynamics of magnetically controlled gasfluidized beds indicates that the system would exhibit different regimes with

232


Ifrixitn·

different bed thermal properties. The modes considering the field action require special attention due to their important effects on the heat transfer phenomena. The magnetization FIRST and the Magnetization LAST modes (Hristov, 2002) have been successfully applied for heat transfer experiments. Especially for the purposes of the heat transfer Kamholtz (1979) and Levenspiel and Kamholtz (1980) have invented a third magnetization mode of an intermittent field action. Hristov (2002) commented on the same magnetization mode briefly. The idea is shown schematically in Fig. la. The

ON

U. U.

H

(a)

OF

Ο

τ

τ

Fig. 1: Field ON- Field OFF ("On-Off") magnetization mode. Schematic descriptions of the magnetic field pulses employed in various studies. Present author viewpoint (I Iristov, 2000a). By courtesy of Thermal Science. a) Rectangular pulses in accordance with the mode definition invented by Kamholtz (1979) and Levenspiel and Kamholtz (1981). b) On-Off mode created by a pulsed sinusoidal field employed in (Bologa and Syutkin, 1976;Stepanchuk, 1981,1982,1984)

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Magnetic Field Assisted FluidcatinnA Unified Approach-Part ί

external magnetic field is applied as pulses termed "field-on" and "field-off' periods respectively. As commented in (Hristov, 2002) the principal goal of the inventors was to permit a short time (during the OFF-period) particle mixing without bubbling. The main results claimed by Kamholtz (1979) and Levenspiel and Kamholtz (1981) are addressed to the significant decrease of the axial temperature gradients. The deep analysis of the studies carried out by different research groups gave a surpassing result. The investigators in the Luikov Inst. of Heat Mass Transfer (Minsk, Belarus) have used the pulsed field magnetization widely for bed-to-surface heat transfer experiments Zabrosky and Tambovtsev, 1976; Stepanchuk, 1981, 1982, 1984). Zabrodsky and Tambovtsev (1976) have conceived the technique four years earlier, in 1976. In fact, the investigators in Minsk (Zabrosky and Tambovtsev, 1976; Stepanchuk, 1981, 1982, 1984) did not use the terminology of Kamholtz and Levenspiel, but termed the technique as "a magnetization by a pulsed magnetic field". The analysis of their results demonstrates that the "ONOFF" field magnetization (a term defined in Hristov, 2000a and Hristov, 2002) has a modification that follows from the possibility to use an alternating current with an industrial frequency. Figure Ib shows that "ONOFF' magnetization may be created if a half of the alternating current is eliminated (by a diode for example). The term "semi-sinusoidal pulses" is used here. In this case the lengths of both periods are equal. Table 1 summarizes literature data on "ON-OFF' mode. The data were collected in order to compare the conditions employed by different research groups. The duration of the "On" and the "Off' periods as well as the frequency, f, of the field pulses were calculated on the basis of various nonsystematized data sources (see the last columns of Table 1). The arrangement of these results in accordance with a third magnetization mode, that may be assumed as a fast and intermittent version of the Magnetization LAST (see comments further), permits a unified approach in the analysis of the heat transfer in magnetically controlled fluidized beds. The last review of Saxena et al. (1994) does not consider the pulsed field magnetization in such manner. The recent discussion (Hristov, 2000a, 2002) gave a more unified picture of the results. The analysis of the advantages (or disadvantages) of all three magnetization modes under various experimental situation will be developed in the present review.

234


.hinbin

Table 1 Summarized literature data on "On-Off" magnetization mode. The present author did the calculations. In all cases magnetic fields with axial orientations have been applied. Reference

Stepanchuk (1981)

Field Frequency applied (Hz (F«B-1)

r„, sec

Type A

0.116 0.083

3 6

r «r« sec

0.116 0.083

V r_

1 1

Data source Original Present work paper Figs.3,4 Figs. 37a,b Fig.4

(1982)

Fig.32a

(1984) Stepanchuk (1982) Stepanchuk (1984)

Stepanchuk (1984) Stepanchuk (1984) Zabrodsky ATambovtsev (1976)

Kamholtz (1979) Levenspid& Kamholtz (1981)

Type B

SO

Type A 2 4 6 8 10 Type 10 A 10 10 Type A f«.= l f»,= 15 Type A 2 5 7 10-15 6-20 25 33 Type B 40 50 Type A 0.031

0.01

0.01

1

0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.03 0.01 0.01 0.01

0.49 0.24 0.156 0.115 0.09 0.09 0.08 0.07 0.99 0.056 0.49 0.19 0.132 0.09-0.056 0.0156-0.04 0.03 0.0203 0.012 0.01 2

49 24 15.6 11.5 9 9 8 7 99 5.66

0.012 0.01 30

9-5.6 15.66-4 3 2.03 1 1 0.066

Figs. 1 -2 Fig.30 FigJla Fig.4 Fig.37a

Fig.4 in

Fig.37a

Fig.3

Fig.37b

Fig.3

Fig.30

Fig.4

Fig.31b

Example Fig.6 1 Table 2

2.2. Magnetic fields applied 2.2.1. Axial fields The analysis done recently (Hristov, 2000a, 2002 shows that the field orientation and homogeneity have significant effects on the fluidization. The application of axially oriented magnetic fields (generated by solenoids or

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Magnetic Field Assisted FluidizationA Unified Approach-Part 3

short coils) dominates: Kamholtz (1979); Levenspiel and Kamholtz (1981); Stepanchuk (1981,1982,1984); Bologa and Syutkin (1976); Amaldos, 1986; Arnaldos et al. (1986, 1987); Neff and Rubinsky (1983); Ganzha and Saxena (1998a); Qian and Saxena (1993); Dolidovich et al. (1998); Saxena and Dewan (1996)). Most of them have been generated by short solenoids and Heimholte pairs. Table 2 summarizes some details available in the literature in order to clarify this side of the heat transfer studies carried out. Details are available in Parti (Hristov, 2002). It should be noted that in the dominating situations the problems of the field homogeneity and the field orientation have not been considered (except in the works of Saxena and co-workers (Ganzha and Saxena (1998a), Qian and Saxena (1993), Dolidovich et al. (1998), Saxena and Dewan (1996)).

2.2.2. Transverse fields The only study of Bologa and Syutkin (1976) (among the pioneering works) contains a brief remark on the transverse field effect on the wall-tobed heat transfer over 25 years. The two recent papers of Al-Qodah et al. (2000, 2001) described the bed behaviour in a transverse field in accordance to the point of view and symbols employed by Penchev and Hristov (1990b) (magnetization FIRST mode) and Hristov (1998) (magnetization FIRST and LAST modes). The magnetic system of Al-Qodah is based on an electromagnet having a cast L on yoke and poles formed as parts of cylindrical surfaces. As mentioned :n Parti (Hristov, 2002) such a system has serious disadvantages due to the enormous weight and a small working volume. For example the diameter of the gap is 95 mm (Al-Qodah and AlHassan, 2000) while the whole height of the poles is 200 mm. Thus, the working volume is less than 2. 10"3 m3 while the weight of the electromagnets is about 40 kg.

2.3. Gas-solid systems and temperature ranges Most of the experiments have been performed with: • •

•

Iron powders: Bologa and Syutkin (1976). Iron shots: Bologa and Syutkin, (1976, Neff and Rubinsky (1983), Ganzha and Saxena (1998a), Qian and Saxena (1993), Dolidovich et al (1998), Saxena and Dewan, 1996). Magnetite: Zabrodsky and Tambovtsev (1976), Stepanchuk (1984).

236

Jordan //m/MV


Table 2 Magnetic fields applied - some details Reference

DC, mm

Magnetic system

Mode

Field

Amaldos (1986) Amaldos« «I (1986,1987) Zabrodsky& Tambovtsev (1976)

70

Solenoid

FIRST LAST

Axial (DC) Hmax -4 kA/m

LAST

Axial, Hmax - 40 kA/rn (AC) (industrial frequency SO Hz) Axial, Hmax = 40 kA/m (see Table 1)

Bologaft Syutkin(1976)

78

Bologa& Syutldn(1976)

78

Neff& Rubinsky (1983) GanzhaA Saxeoa (1998a) Qian& Saxena(1993) Dolidovicfaet al. (1998) Saxena &Dewan (19%) Kambhohz (1979) Lcvenspiel& Kambholtz (1981) Stepanchuk (1981)

88.9

Stepanchuk (1982) Stepanchuk (1984)

Ds = 120mm Ls =245mm

92

102

Solenoid (undefined construction) Some tentative details are available in [18](Ds=180mm; Ls=unknown Electromagnet (undefined construction) Solenoid (undefined construction) Solenoid Ds~90 Ls=105 Heimholte pair

101.6

Heimholte pair

FIRST

101.6

Hehnholtzpair

FIRST

101.6

Hehnholtzpair

FIRST

50.8

Undefined magnetic system

On-Off

Axial (Pulsed) H= 40.317 kAAn (see Table I)

93

Undefined solenoid Ds~200mm Ls = 180mm (tentative) Undefined solenoid

On-Off

Axial, Hmax = 80 kA/m

On-Off

Axial, Hmax = 80 kA/m

Undefined solenoid

FIRST

Axial (AC) (industrial frequency SO Hz) Axial (Pulsed) (see Table 1) (see Table!) Transverse (DC) Bmax = 200 mT

93

On-Off

FIRST

FIRST LAST

Transverse (AC) (industrial frequency SO Hz) Bmax =16 mT Axial (AC) (industrial frequency SO Hz) Bmax = 10.9 mT Axial (DC) Bmax=4mT

FIRST

Axial (DC) Axial (DC) Hmax=15kA/m Axial (DQ Hmax=20kA/m Axial (DC) Hmax=20kA/m

FIRST

On-Off AlQodahet al. (2000) (2001)

70

h,„=100mm

Electromagnet with a cast iron yoke Magnetic system height =200 mm

FIRST LAST

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Vol. 19, No. 3. 2003

•

Nickel-kieselguhr catalyst (Kamholtz (1979 and Levenspiel and Kamholtz(1981) • Nickel: Kamholtz (1979), Levenspiel and Kamholtz (1981), Amaldos (1986), Arnaldos et al (1986,1987). • Ammonia catalyst: Zrunchev (1975), Zrunchev and Popova (1984a, 1984b). • Iron-Sand admixtures: (Arnaldos (1986), Arnaldos et al (1986,1987),Ganzha and Saxena (1998a), Qian and Saxena (1998), Dolidovich et al (1998), Saxena and Dewan (1996) • Nickel-Sand admixtures: Arnaldos (1986), Arnaldos et al (1986,1987). • Magnetite covered by zeolite and activated carbon (AI Qodah et al. 2000,2001; AI Qodah and AI Hassan, 2000). In all the cases the fluidizing gas is air except for the two cases of exothermic gas reactions in stoichiometric gas admixtures: Kamholtz (1979), Levenspiel and Kamholtz (1981), Zrunchev (1975), Zrunchev and Popova (1984a, 19840). The temperature range does not exceed 100°C (Table 4) except for several cases of exothermic chemical reactions (Kamholtz (1979), Levenspiel and Kamholtz (1981), Zrunchev (1975), Zrunchev and Popova (1984a, 1984b)) (see Table 4 below). In all the cases the bed temperature is significantly lower than the particle material Curie point (see Table 3). The thermal conditions will be discussed further in any particular case. Table 3 Currie points of some particulate materials used in the experiments Material

Curie point, K

Data Source

Iron

1043

Amaldos (1986)

Nickel

631

Amaldos (1986) Liemelzs and Morgan (1 977) Liemelzs and Aleman (1973) Bozort(1951)]

Magnetite

848

Arnaldos (1986) Selwood(1956)

Ammonia catalyst GK-1 (Russia) as an example

238

793 (non-reduced)

Vissokov & Ivanov (1975)

Jordan Hristov

Rwiews in Chemical Engineering

3. OVERALL THERMAL BED BEHAVIOUR 3.1. Axial temperature distribution 5.7.7. Magnetization FIRST mode The axial temperature differences along the bed length have been reported non-systematically by several authors. In 1975 Zrunchev (1975) has reported that a significant temperature difference across the magnetically stabilized bed exists if the ratio L/Dc > 6 (Fig. 2a). A similar curve (Fig.2b) has been published 10 years later by Zrunchev and Popova (1984a), but with the limiting ratio L/Dc > 4. The results of Zrunchev and Popova (1984b) demonstrate a significant temperature difference across the bed (Fig. 3a). Furthermore, the redrawing of the original Fig.3a in a more informative form (Fig. 3b) makes it possible to establish that the results in Fig. 2ba and Fig. 3 are similar. On the other hand the lines in Fig. 3b indicate that the field intensity slightly affects the temperature difference across the bed. In all three cases there is no heating device immersed in the bed (see Table 4). A preliminary heating of the gas flow has performed all these experiments. No data are available about the column wall insulation in these studies. In 1986 Arnaldos (1986) has reported systematic results on the heat transfer in magnetically controlled bed with an immersed electric heater (Fig. 4). The axial temperature distributions in three regimes are shown in Fig. 5. All the measurements of Amaldos (1986) have been performed in a plane oriented normally with respect to the heater plane (see inset). The axial temperature profiles in fixed and the stabilized bed are similar, while in the fluidized bed the temperature differences are approximately 10 times smaller. Kamholtz (1979), Levenspiel and Kamholtz (1981) have reported similar results as a comparative example concerning "On-OfP magnetization mode (see below the white labels in Fig. 6). More valuable information may be obtained if all the data available are recalculated by a unified approach. In order to compare the axial temperature gradients the results shown on Figs. 2-6 were treated in the present work with a digitizer and were calculated as: gradT a = — AL

(la)

or

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l W. 19, No. 3. 2003

Λ fagnetic Field Assisted FluidizationA Unified Approach-Part 3

>

60

' 0°

30

Ο

4

I

L

8

_L_ De Fig. 2: Zrunchev's results on axial temperature difference across the bed. A relationship between ΔΤ and the dimensionless bed height L/Oc. Axial field applied. a) Results from (Zrunchev, 1975). Conditions are summarized in Table 4. Pressure of 10 Μ Pa. The present author adds the dashed lines. b) Data of Zrunchev and Popova from (Zrunchev and Popova, 1984a). Pressure of 30 Mpa.

240

Jordan Hristov


10

D° •«fr υ

I

eg

υ Ω •O Ο

υ

σ>

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I1

c

CO CO

l

υ

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Vol. 19. Ν ο. 3.2003


(A)

Copper bar (D29) Thermocouple Elect, heater Teflon (B) insulation Thermocouple

Stainless steel pipe

Copper sphere

(C) Cartridge heater

4b

Fig. 4: Two examples of electric heaters used in the experiments: a) Axial field: Arnaldos' experimental set-up (schematically). Adapted from Arnaldos (1986). By courtesy of J. Arnaldos b) Transverse fields: Experimental set-up of Al-Qodah et al. (2000, 2001) 1- gas phase inlet; 2- polyethylene particles; 3-flanges; 4-supporting grid; 5-heater; 6-magnetic particles; 7- magnetic systems 8- column; 9-manometer; measuring orifice; gas suction Insets: A - magnetic system Al-Qodah et al. (2000, 2001); B circular plate heater (Al-Qodah et al. (2000); C - spherical heater (Al-Qodah etal. (2001)

242


Jordan Uristov

150_ r,mm

Fe (450-500μιη)

(a)

07.5 • 21.5

»its 100

100

Ε

E

// 50

50

NJ (250-400|im)

Ο

50

100

150

200

250

20

60

T,°C

100

140

T,°C

150

150

100

100

Ε 50

50

Ν» (2ΚΜΟΟμπι) MSB H=2000Av/m

20

100

60 Τ. °C

140

20

tfl (250-400μπι) MSB H=4000Av/m

100

60

140

Τ. °C

Fig. 5: Arnaldos' data on the axial temperature distributions (Arnaldos, 1986) in an axial magnetic field. Experimental conditions are available in Table 3 and Table 4. By courtesy of J. Arnaldos. a) Fixed bed c) Stabilized bed (MSB) b) Fluidized bed. d) Stabilized bed (MSB)

243

Vol. 19, No. 3, 2003


43 «N

«o

s

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a

S

o

vt

Π

Sax

00 ίβ ffi

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Is 'χ

ε 'S 3l hi

•n

a| 3 l

1!

1 ""·

°

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CH

\O

^^ c^

OO

c

20

30

mm

b) Examples of radial temperature profiles in different bed regimes. Adapted from Arnaldos, (1986). See also Fig. 7 of Arnaldos et al (1987) and Fig.8 of Casal and Amaldos (1991). Measuring plane orientation normal to the heater plane. By courtesy of J. Arnaldos.

ii) A circular plate heater (inset B in Fig. 4b) placed at the column wall and a temperature measurements at different distances in the bulk of the bed - a non-symmetrically placed heater

254

Jordan Hrislov

Reviews in Chemical En,

70 FIXED BED

60

40

+, 0,· Fe tt, ·,Δ,Α Ni L=90mm Ar=20mm A j

30

MSB

50

ο ι"

!3

20 f f /

fe

10 ^^^

°0

Cl Ι ΙΙΠΙ7Ι rLUIUIZ.1

BED

Λ

1

1

1

1

1

1

2 3 H.kA/m

4

5

Fig. 12: Field intensity effect on the radial temperature gradients. Data obtained by a re-calculation of Arnaldos's results (Arnaldos, 1986). Original data from Figs. IV- 11, 12,15, 16 of Arnaldos (1986). Present work- data from Figs. 9,10,1 la (Note: AH the data correspond to γ = 90° except Ο (γ = 45°))

The temperature profiles measured by Al-Qodah et al. (2000) (by means of a circular plate heater) along the column radius are shown in Fig. 14,a, b. The plots indicate that the bed temperature inside the particle bed varies in a range of 30- 55°C, but the stronger gradients exist near the column wall. In the other hand, the temperature at the bed centreline is about 30°C.

255


100

200

L, mm Fig. 13: Length effects on the radial temperature gradients in beds stabilized by axial magnetic fields. Re-calculation of the data presented in Figs. 9-11. Present author data treatment. From Hristov (2000a).

The temperature profiles obtained with both magnetization modes demonstrate similar behaviour, and a strong influence of the bed regimes and the magnetization mode (an analysis done here and not existing in the original papers): • Magnetization FIRST. The curves 1 and 4 in Fig. 14-a, c correspond to the fixed bed regimes (see the reconstructions of the experiments in Fig. 36-a. The temperature profiles for a fixed bed and MSB (line 2 -Fig. 14a and Line 5-Fig. 14c) resemble those of the initial fixed bed. The facts confirm qualitatively the results reported by Arnaldos (1986) (see Fig. 9)

256

Jonhm Hrislov


Table 6 Keys and conditions to data presented in Fig. 13. Regime

Measuring direction

Material

Symbol

Original paper Amaldos(1986) Fig.rV-2

y.de« Fixed bed Η-ΟΑΛη

90

Fluidizedbed H=OA/m

90

MSB H=2kA/m

45

Iron

MSB H=4kA/in MSB H=2kA/m MSB H=4kA/m Semistabilized bed (Fluidizedbed at H=2kA/m Semistabilized bed (Fluidizedbed at H=4kA/m

45

Iron

90

Nickel

Data Source

Nickel

Present work Fig.9a

Ο Fig.IV-4

Iron

•

α • Δ

90

Fig.IV-12

Fig.lla

Fig.rV-11

Fig.lla

Fig.IV-8

~

Fig.rV-7

Fig.9b

A 90

Iron

90

Nickel

Fig.IV-14

+ FJg.IV-13

#

and those summarized in Fig. 8. Unfortunately, the use of a point heat source (in contrast to Amaldos set-up in Fig. 4) does not allow the measurement of the length effect on the radial temperature distribution. Magnetization LAST. According to Al-Qodah et al. (2001) the larger temperature gradients in the range of 87-1130 °C/m correspond to the transition state between the fluidized and the stabilized bed regime. However, the reconstruction of the experimental conditions (see further Fig. 36-b) shows that all the curves shown in Fig. 14-d correspond to the fluidized bed regime. The only temperature profile corresponding to a frozen bed regime is the curve 3 in Fig. 14-b. Despite these disagreements (between the explanations of Al-Qodah and the facts) the temperature profiles show two facts emerging when a point heat sources is used:

257


Vol. 19, No. 3, 2003

0

1

2

3

4

Distance from the wall (cm)

0

1

2

3

4

Distance from the wall (cm)

100

-0.85

-0.35

0.15

0.65

-0.85

-0.35

0.15

0.65

r/R (-) r/R (-) Fig. 14: Radial temperature profiles generated by a non-symmetrical heater placed at the column wall in beds stabilized by a transverse magnetic field (Al-Qodah, 2000,2001). For all the data the measuring position is 0.06 m above the supporting grid. The dashed lines (added by the present author) indicate the column axis. Particles 900 μιη. Umfo = 0.574 m/s. The numbers of the curves are added by the present author. a) Magnetization FIRST mode. Effect of the gas velocity at Β = 22 mT. (Al-Qodah, 2000). b) Magnetization LAST mode. Effect of field induction at U = 0.70 m/s,, i.e. V/Vmfo = 1.219 (Al-Qodah, 2000). c) Magnetization FIRST mode. Temperature profiles measured with a spherical heater probe placed at the bed center. B= 20 mT. (Al-Qodah, 2001). d) Magnetization LAST mode. Temperature profiles measured with a spherical heater probe placed at the bed center. (AlQodah, 2001).

258

Jordan Hrislm·

Review's in Chemical Engineering

1. Point heat source at the bed centerline. The radial temperature gradient increases as the particle mobility is reduced due to the increased filed intensity (Fig. 14-d and the locations of the points in Fig. 36-b). 2. Point heat source at the column -wall. The situation is similar and clearer from a physical point of view. The lower temperature gradient (curve 3 in Fig. 14-b) corresponds to the fluidized bed regime, while the slope of the temperature profile increases, as the particle mobility is decreased (curves 2 and 1 in Fig. 14-b). 3.2.3. Comments on the temperature profiles The radial temperature profiles (Figs. 9b,c) demonstrate clearly that radial temperature gradients in MSB are lower than those demonstrated by an ordinary fixed bed (Fig. 9a) of the same paniculate material. The potential reason should be attributed to the increased bed porosity and the increased gas convection inside the bed. It should take into account that the measuring device (the thermometer) measures the temperature of the gas only. The effect of the plane of measurements on the slope of the radial temperature profiles (Fig. 10a,b, c) is a special feature of the experiments of Amaldos, due to the non-symmetrical shape of the heater. This should be easily checked by measurements in beds heated by immersed cylindrical (or spherical) body. The experiments of AI-Qodah et αϊ. (2001) are close to that situation. However, not enough reliable information exists in the literature. The length effects on the radial temperature profile detected here on the basis of Arnaldos' results is an indicator that such investigations should be done in more precise experiments. The "fresh" results of Al-Qodah et al. (2000,2001) are in fact old, wellknown results. There is no new information about the effect of the bed structure imposed by the transverse field on the data. Really, the plots of the data resemble those reported by Arnaldos (1986) and Neff and Rubinsky (1983) (discussed widely here) despite that the fact the probe designs are quite different. It is clear that new independent and more accurate experiments (performed by other investigators) should be done in order to clarify the field orientation effect on the temperature profiles. 3.3. Effective thermal conductivity -Amaldos (1986) and Amaldos et al. (1987) The temperature distribution inside the bed and the heat transfer rate are strongly affected by the bed effective thermal conductivity, Kb. The

259


Vol. 19. No. 3, 2003

coefficient Kb has been calculated on the basis of a mathematical model in a general form:

Κκ

- + —— + -

U

P

3ΤΓ ~

(2)

C

The contribution of the vertical conduction has been neglected due to the superimposed effect of the convection. On the other hand, due to geometrical structure and symmetry the equation (2) has been expressed as

ι

(3)

It has been assumed that the heating surface (see Fig. 4a) is continuous over the X-Z plane (the heat flux has been assumed perpendicular to that plane, on its two surfaces).

(a)

(b)

Fig. 15: Elements of the model formulation. a) Definition of the boundary conditions (Fig. IV-19 of Arnaldos (1986). See also Fig. 9 of Arnaldos et al. (1987). b) Discretization of the bed -Fig. 1V-20 of Arnaldos (1986).

260

Jordan Urislov


The inlet gas temperature has been assumed as room temperature, therefore T - T0 at z = Z0

(4a)

The boundary conditions for any quadrant of the bed cross-section are shown in Fig. 15a. The heat convection between the bed and the environment has been described as

(4b) Further, it has been assumed that there is no heat flux through the vertical plane perpendicular to the heating system (see Fig. 15a): — = 0 a t e = 90° ΟΘ

(5)

On the other hand, at θ = 0 the boundary conditions have been written as ΒΎ

Qr

SKb

(6)

The last boundary condition has been established for r = 0 (under the assumption that there are no variations of T with Θ, so

du

SKi

(7)

The model has been solved numerically by an implicit procedure and a system discretization (ΔΘ-5 0 , Ar = 4375 mm, Δζ = 05 mm ) (Fig. 15 b). The temperature profiles obtained by the model are shown in Fig. 16. To obtain the optimum values of Kb an objective function has been defined in order to obtain minimized differences between the measured and the calculated values of T. The optimization has been achieved through the minimization of the parameter

261

Magnetic FielJ Assisied FluidizationA Unified Approach-Part 3

Ιοί 19, Ν ο. 3,2003

T

F- —

exp-Tcal

Π:

The variations of Kb with H are shown in Fig. 17.

Ni 250-400 μπι H=2000Av/m • experimental - model 150

L=120mm

- (a)

50 100

L=90mm

25 0

100

L=60mm

25 100

L=30mm

I -I---

25

i i I

I

I

I

I

j

I

35

35

r, mm Fig. 16: Radial temperature profiles in MSB - a validation of the model (Amaldos, 1986) a) Nickel particles bed (Fig. IV-23 of Arnaldos (1986). See also Fig. 2 of Arnaldos et al (1987).

262

Jordan llrislar


Ni 420-500 urn H=4000Av/m • experimental — model

150

L=120mm

.1.

50 100

Ο 0

L=90mm

25

100

L=60mm

25 100

L=30mm

25

35 Fig. 16: cont.

0

35

Γ

ι ΙΤΙΓΓΙ

b) Iron particle bed (Fig. IV-24 of Amaldos (1986).

3.4. Comments on the overall bed thermal behaviour The data re-examined in the previous points demonstrate several major thermal properties of gas fluidized beds of magnetizable particles that are induced by the magnetic field applied. 3.4.1. Stabilized beds (Magnetization FIRST mode) • First of all, the stabilized bed demonstrates significant axial temperature gradients (Table 4 and Figs. 3b, 8,11,13).

263

Magnetic Field Assisled FluidizationA Unified Approach-Part 3

1000

2000

3000

4000

H,Av/m Fig. 17:

• •

• •

Variations of the effective thermal conductivity with the field intensity - (Arnaldos (1986) See also Fig. 11 of Arnaldos et al. (1987) and Fig. 10 of Casal and Arnaldos (1991).

Second, the axial temperature profiles are strongly affected by the radial position of measurement (Fig.8). Generally the axial temperature gradients decrease toward the column wall (Fig.8) and approach values demonstrated by the fluidized beds unaffected by any field action. Third, the stabilized bed demonstrates a significant field effect on the axial temperature profiles (Figs. 7,1 la, 12). Fourth, the radial temperature profiles (Arnaldos' results) and the calculated radial gradients also exhibit field effects (Fig. 12) as well as significant length effects (Fig. 13).

AH these properties resemble those exhibited by the conventional packed bed (Aerov and Todes, 1968); Willhite et al., 1962). They support the

264

Jordan Hriatov


opinion that the magnetically stabilized bed is a packed bed without particle motions. All the effects mentioned above may be explained by the particle arrangement along the field lines. It should note again, that all the data mentioned above have been obtained in axial magnetic field. The simultaneous action of the fluid flow and field forms a packed bed with anisotropic structures (Hristov, 1996, 2002) situated between two limiting particle arrangements: i) an ordinary packed bed with isotropic properties (before the onset of MSB) and ii) a bed consisting of streamlined aggregates and channels dividing them (just before the breakdown of MSB). The significant field effect on the radial temperature gradients may be attributed to the decreased lateral thermal conductivity of the bed parallel to the development of the anisotropy of the bed structure. For example, the second limiting particle arrangement may be considered as a bundle of "bars" with significant gas gaps between them. Such a system demonstrates significant lateral gradients. This mechanistic interpretation could explain the field effect on the radial temperature distribution. Furthermore, in all the experiments mentioned, a radial adiabaticity has not been created. Thus, the radial heat conduction has not been eliminated as in well-designed special experiments (Beveridge et α/., 1977). The axial length effect on the radial temperature profiles (the experiments of Arnaldos) resembles that existing in conventionally packed beds (see for example Willhite et al., 1962; Li and Finlayson, 1977). As discussed by Li and Finlayson (1977), most of the data is obtained in Graetz-type experiments. In a packed bed the entry length effect (Graetz heat transfer problem) is much less likely to exist. Arnaldos' results (see the slope of the radial temperature profile at different axial position) indicate that the effective thermal conductivity K b depends on the length. This conclusion has not been stated by Amaldos, because his model is more simplified. *yp

On the other hand, if q (q = K b — ) is a constant along the bed, the 9r increase of — in any direction indicates that Kb decreases in a way 9r consistent qualitatively with the results obtained with non-magnetic packed beds (Li and Finlayson, 1977). No explanations are available in the literature, but the data in Fig. 17 indicate that Arnaldos's model assumption of the homogeneity of the bed structure is an oversimplification. A model assuming

265

Vol. 19, No. 3. 2003

Magnetic Field Assisted Fluidi:ationA Unified Approach-Part 3

an anisotropy of the thermal conductivity of MSB has not yet been developed. However, Arnaldos' results (see Fig. 17) show that at zero field intensity the thermal conductivities of the stabilized and the ordinary packed beds are different, but become almost equal under the action of high field intensities. From the point of view of the existing particle arrangements in the bed such behaviour is strange. First of all, it is impossible to create, at H-0, simultaneously a fixed bed or MSB (the possible bed regimes are a fixed bed or a fluidized bed - Hristov, 1996, 2002). Second, at high intensities the bed may be fixed or stabilized. Third, the model does not concern the gas velocity effect on the particle arrangement in MSB. Fourth, the gas-particle heat transfer effect on the effective value of Kb is not considered (Aerov and Todes (1968), Willhite et al (1862), Li and Finlayson (1977). The comments on the model are not a critique, since Arnaldos's contributions in the studies of MSB are significant. However, they focus the attention on the fact that the assumption of the bed homogeneity imposed by the concepts of Rosensweig (1979a, 1980) and Rosensweig et al. (1981) does not work (Hristov, 2002). 3.4.2. Fluidized bed (Magnetization FIRST Mode) Any particle motions available in the bed due to the fluidizing gas significantly reduce both the axial (Fig. Sb, 8, Table 4) and the radial (Figs, lib, 12, 13) temperature gradients. The magnetic field effect on fluidized particles (a semi-stabilized bed in accordance with Arnaldos) may be associated with the reduced particle mobility. The reduced contribution of the particle convection leads to greater radial (Fig. lib, 12, 13) and axial gradients with respect to the case of a non-magnetic fluidized bed (Zabrodsky, 1966; Botterill, 1975). 3.4.3 On-Off magnetization effects The intermittent magnetization with the On-Off mode may be considered as an alternative solution avoiding the significant temperature gradients in MSB. The results summarized in Table 5 and those plotted in Figs. 6 and 8 clearly demonstrate that the On-Off technique reduces significantly the axial temperature gradients. Moreover, the data of Kamholtz (1979) and Kamholtz and Levenspiel (1981) (Table I and II in these papers - not shown here) show that there are no length effects on the axial temperature profiles (see Arnaldos data - Fig. 5 too). Unfortunately, no data are available on the effect of that magnetization mode on the radial profile

266

JnrJan l Irisluv


The data re-examined here indicate that much future work should be done for better investigation of the overall thermal behaviour of gas-fluidized magnetically controlled beds. Moreover, the fluidized system offers a wide area of application of various magnetization (or fluidization) modes that may enhance the thermal properties of such beds.

4. GAS-TO-PARTICLES HEAT TRANSFER One of the inherent properties of fluidized beds is the high rate of heat transfer between the bed and the fluidizing medium. In the case of magnetically controlled beds the problems is of great importance due to its applications in mass transfer operations. From a chemical engineering point of view the devices with MSB usually operate as fixed bed reactors (Rosensweig, 1979b). Usually a steady-state (Willhite et al, 1962; Gnielski, 1987) of the heat balance (at constant bed temperature and gas flow) across the bed is employed to obtain the heat transfer coefficients. Unfortunately no information exists about the experiments performed in MSB. Since 1979, (Lucchessi et al, 1979) only the data presented in Fig. 18 has circulated through all the published papers (Rosensweig et al, 1981; Casal and Arnaldos, 1991; Liu et al, 1991; Saxena eat al., 1994). In accordance with the researchers from EXXON the data in Fig. 18 correspond to MSB obtained with Magnetization FIRST Mode (Lucchesi et al, 1979; Rosensweig et al., 1981). It is clear that the correlated data curves intersect at the Reynolds number corresponding to the onset of the stabilized bed (the point of minimum fluidization in accordance to that research group (see comments of Hristov, 2001). Moreover, they claim that (on the basis of results represented by the Nusselt number) the structure of MSB is more effective than that in a packed bed for promoting gas-solids contacting. In accordance with the comments in Lucchesi et al., 1979 and Rosensweig et al., 1981, the Nusselt number is proportional to the square of the Reynolds number. However, no additional correlations have been published since 1979. The other modes of magnetization have not been employed for such heat transfer measurements, so further work is needed to recognize their effects on the gas-particle heat transfer phenomena.

267

Vol. /V. No. 3. 2003

0.05

Magnetic field Assisted FluidizationA Unified Approach-Part 3

MSB

0.02 ai ω

111 03 to

0.01 0.005 0.002

0.001 Fig. 18:

FIXED BED

MINIMUM FLUID1ZATION

2 5 10 20 REYNOLDS NUMBER, NRe

50

Comparison of gas-solids heat transfer in magnetically stabilized and fixed beds. Adapted from Lucchessi et al (1979) and Rosensweig et al (1981). The same figure has also been published by Saxena et al. (1994), Sonolikar (1989), Casal and Arnaldos (1991) and Liu et al. (1991).

5. BED-TO-IMMERSED SURFACE HEAT TRANSFER The heat transfer exchange with an immersed surface is the second important problem considered by many investigators. In order to clarify the contributions and the main results the analysis will be done in accordance with the already defined magnetization modes. It has already been widely discussed that the magnetically controlled magnetizable bed exhibits different behaviours as a result of the simultaneous action of both the field and the fluid flow. This reflects directly on the bed thermal characteristics as mentioned in the previous part of the present work. Now, the heat transfer to an immersed surface is the focus of the commentary. The re-examination of the data done here was provoked by the fact that most of the investigators (whose results are discussed in that point) focussed

268

Jordan llrixlor

Re\-iews in Chemical Engineering

on heat transfer results, but not on the hydrodynamic effects on them. Most of the basic results on the heat transfer in magnetically controlled fluidized beds (Zabrodsky and Tambovtsev, 1976; Neff and Rubinsky, 1983) have been obtained without taking into consideration the differences in the bed behaviour in the various regimes. The review of Saxena et al. (1994) does not give answers to these problems. The reason for the discrepancies in the results is due to different bed hydrodynamics interpretations and the clear identification of the regime available under the simultaneous action of both the gas flow and the external magnetic field. The successful combination of the already available results on the heat transfer (Saxena et al, 1994; Bologa and Syutkin, 1976; Arnaldos, 1986, Amaldos et al, 1986, 1987; Neff and Rubinsky, 1983; Qian and Saxena, 1993; Saxena and Dewan, 1996; Dolidovich et al, 1998; Ganzha and Saxena, 1998a;) and the recent results on bed hydrodynamics (Hristov, 1996, 1998) (see also comments in Hristov, 1999, 2000ab, 2002) allow a re-examination of the results. The hydrodynamics effects on both the maximum and the minimum wall-to bed heat transfer coefficients have been discussed in order to clarify the results obtained by various research groups.

5.1 Major Experiments Performed The experiments carried out by different authors are summarized in Table 7. Some detailed conditions concerning the On-Off magnetization mode were already presented in Table 1. The details will be discussed separately. The experiments discussed hereafter have been obtained with magnetizable solids. There are unique experiments performed (Lucchessi et al., 1979) and Rosensweig et al., 1981) as a simulation of the heat transfer in MSB. A sublimation of naphthalene wall has been employed under simulative (mass transfer) experiment (in the range of 19 ^

•s

J2 C>

^

υ

•o

(§

's

• »i OO

1 e

ε

K)

i» ll z c oc oc-

s Cu

i r>

rts

vO OO

o

m

S

a

'-5

ΓΙ «Λ»

r—

t- —

Η ,ο 8

u s .s | | | 4^ I

271

l'ol. 19, No. 3. 2003


and Dewan, 1996; Ganzha and Saxena, 1998a; Dolidovich et al, 1998). In some particular cases nickel (Arnaldos, 1986, Arnaldos et al, 1986,1987) and magnetite (Zabrodsky and Tambovtsev, 1976; Stepanchuk, 1981, 1984) are used. This allows easy comparative calculations in order to establish common tendencies of the results re-examined in the present discussion. Some results obtained with pure ferromagnetic particles were discussed in (Hristov, 2000a, 2000b). • Beds of admixture of magnetic and non-magnetic particles (Zabrodsky and Tambovtsev, 1976; Arnaldos, 1986, Arnaldos et al, 1986,1987; Saxena et al, 1994). The discussion of the results obtained with such admixtures will be developed in the present paper in accordance with all the three magnetization modes defined (I Irislov. 2002) • Magnetic particle covered by activated carbon or zeolites (AI-Qodah et al., 2000,2001; Al-Qodah and Al-Hassan, 2000).

5.1.2. Heat Transfer Probes In all the studies electrically heated probes with a constant heat flux q have been employed. There are only a few experiments with vertical surfaces: • Vertical plate probes (Zabrodsky and Tanbovtsev, 1976; Stepanchuk, 1981, 1982,1984; Neff and Rubinsky, 1983). • A vertical cylinder (Bologa and Syutkin, 1976). • Multiple tubes heat transfer probe has been applied by Arnaldos (1986), Arnaldos et al. (1986,1987), Casal and Arnaldos (1991). • Vertical circular plate placed at the column wall (Al-Qodah et al., 2000). • Spherical heater (Al-Qodah et al., 2001). These probes permit the average heat transfer coefficient, hw to be determined only. Saxena and co-workers (Qian and Saxena, 1993; Saxena et al, 1994; Saxena and Dewan, 1996; Ganzha and Saxena, 1998a; Dolidovich et al, 1998) have applied a horizontal tube probe described by Brich et al. (1997) for total and local measurements of the heat transfer coefficients. Two approaches for measurement of the in probe surface temperature Tw have been applied. The first approach is to measure directly Tw by thermocouples (Neff and Rubinsky, 1983; AI-Qodah et al., 2000, 2001; AlQodah and Al-Hassan, 2000). The second and more popular approach is to constitute the probe as an arm of a Whitstone electric bridge (Zabrodky and

272

.Ionian Hristov


Tambovtsev, 1976; Bologa and Syutkin, 1976; Qian and Saxena, 1993;Saxena et al, 1994; Saxena and Dewan, 1996; Ganzha and Saxena, 1998a; Dolidovich et al, 1998). This permits easy establishment of a constant probe surface temperature and easy control of the heat flux q (Ganzha and Saxena, 1998a). The overall heat transfer coefficient is defined by hw = q(Tw-Tb)-'

(8)

5.7.3. Magnetization modes applied The magnetization mode and some details are summarized in Tables 1, 2 and 7. The application of axial magnetic field generated by solenoids (Zabrodsky and Tambovtsev, 1976; Bologa and Syutkin, 1976; Amaldos, 1986, Arnaldos et al, 1986,1987; Neff and Rubinsky, 1983) and Heimholte pairs (Qian and Saxena, 1993; Saxena and Dewan, 1996;Dolidovich et al, 1998) dominates. Bologa and Syutkin (1976) and Al-Qodah's group (Al-Qodah et al., 2000, 2001; Al-Qodah and AI-Hassan, 2000) have applied transverse fields only. AH these studies have been performed with both classical modes Magnetization FIRST or LAST. The studies performed in Minsk's Institute of Heat Mass Transfer form a special group of investigations - all of them have been carried out in accordance with the On-Off magnetization mode. 5.1.4. Regimes created The bed descriptions reported in the works reviewed follow two conflicting bed interpretations discussed widely in Part 1 (Hristov, 2002). They will be noted briefly for clarity of the further discussion: • The earlier studies (Zabrodsky and Tambovtsev, 1976; Bologa and Syutkin, 1976; Neff and Rubinsky, 1983) follow the description in accordance with the classical postulations in fluidization. In accordance with these authors the stabilized bed is a transitional state between the initial fixed bed and the fluidization onset. The fluidization starts at its breakdown and the onset of unrestricted particle motions (velocity, Umf) (Hristov, 1996; Hristov, 2000a, 2002). • The studies of Saxena's group follow Rosensweig's interpretation (Rosensweig, 1979a, 1979b, 1980; Rosensweig et al, 1981), i.e. the onset of MSB at a velocity close to Umfo is assumed as the fluidization onset. Amaldos (1986), Arnaldos et al (1986,1987) and Casal and Amaldos (1991) have accepted the same concept. 273

l'ol. 19. No. 3, 2003


•

The recent results of the group of AI-Qodah are arranged in accordance with the bed behaviour interpretation given by Penchev and Hristov (1990a,b) and Hristov (2002) The results published cover the fixed bed, stabilized bed and fluidized bed regimes in accordance with the Magnetization FIRST and LAST modes. The differences in bed descriptions will be taken into consideration during the reexamination of the results. The phenomena analysis and the reconstructions of the experimental situations will follow the first point of view consistent with the classic fluidization results on hydrodynamics (Kunii and Levenspiel, 1991) and fluidized bed heat transfer (Zabrodsky, 1966; Botterill, 1975). Special attention will be paid to the On-Off mode considered as a fast modification of the LAST magnetization mode (see the description of Scenarios in Part 1). The discussion in the present paper is the first heat transfer performance of that mode from a new point of view (the first systematized review).

5.2. Pure ferromagnetic particles - Major experimental findings 5.2.7. Magnetization FIRST mode - total heat transfer coefficients 5.2. 1. 1. Vertical surfaces in beds subjected to axial fields The first results reported by Bologa and Syutkin (1976) are shown in Fig. 19. The plot indicates that the heat transfer coefficients have maxima. Similar results have been reported by Neff and Rubinsky (1983) (Fig. 20a), Arnaldos (1986), Amaldos et al. (1986,1987), Casal and Arnaldos (1991) (Fig. 21). Arnaldos (1986) and Arnaldos et al. (1986, 1987) have developed data correlation with the help of the Chilton-Colburn jh factor (1933) in the form suggested by Gupta and Thodos (1963) j h f(e)=f(Re)

(9)

The relationship developed is

V K e mf

274

Jordan Hristov


0.4

0.6

0.8

1.0

1.2

U, m/s Fig. 19: Bed-to-surface heat transfer coefficients. Data of Bologa and Syutkin (1976). Magnetization FIRST Mode with an axial field. A vertical cylinder as a probe. Iron powder, 250-500μπι. hbo= 130 mm; Dc= 78 mm. Effect of the field intensity on the heat transfer coefficient. Magnetic field induction (mT): Lines: 1-5; 2-6.16; 3-0; 4-7.46; 5-8.6; 6-9.25; 7-10.9; 8-3.25

where Jo = Jmfo

at u= u

mfo - the onset of MSB

Ko = 0.2 and K,= 1 for MSB regime

and Jo ~ Jmf

at

U= Umf (the onset of fluidization, Umb -a symbol used by

Arnaldos in the original equation) KO = 2 and KI= 2 for a fluidized bed (a "semi-stabilized" in accordance with Arnaldos' terminology)

275

l'ol. 19. No. 3, 2003


lN3IOIdd300 M3JSNVHL

σ>

s° 1V3H

276


Jordan Hrislov

125

100

H • • • ® ο

Av/m 0 1000 2000 3000 4000

Η 75 CM

50

25

0.1

0.2

0.3

0.4

0.5

U, m/s Fig. 21: Bed-to-surface heat transfer coefficients. Arnaldos' results: Arnaldos(1986), Amaldos et al (1987, Casal and Arnaldos (1991). Adapted from Amaldos (1986). By courtesy of J. Arnaldos. See details in Tables 2 and 7. Magnetization FIRST mode. (I -fixed bed; II- stabilized bed; III-fluidized bed). The present author adds the arrows.

Here a (dimensionless) and b (m/A) are constants: For Iron a= 40 and b= 0.037 m/A, while for Nickel: a= 46.24, b= 0.0243 m/A) (Amaldos, 1986) Figure 22 shows a three-dimensional diagram jh = f (Re/Remf, H) (Arnaldos, 1986).

277


Vol. 19. No. 3, 2003

Re/Remf

Η (Mm)

Fig. 22: jh factor as a function of the Re/Remf and the field intensity. Steel particles, 420-500 urn. Note: Remf corresponds to Umf0 in accordance to the terminology accepted here. Data available in Amaldos (1986, Arnaldos et al (1986, 1987). By courtesy of J. Arnaldos (Arnaldos, 1986)

5.2.1. 2. Horizontal tubes in beds subjected to axial fields The group of Saxena (Qian and Saxena, 1993; Saxena and Dewan, 1996; Ganzha and Saxena, 1998a, Dolidovich et al., 1998,) has carried out experiments with that magnetization mode only and a horizontal immersed cylindrical probe. The plots are shown in Fig. 23. The shapes of the curves resemble those obtained by Bologa and Syutkin (1976) (Fig.l8a) and Neff and Rubinsky (1983) (Fig.l9a) and Arnaldos (1986).

278

JorJan l {r ist m·


320 300 CM'

280

" H=0 • H=1.842A/m 0 H=2.575A/m • H=3.302A/m « H=4.048A/m • H=5.662A/m

260 240 220 0.8

1.2

1.6

2.0

2.4

2.8

3.2

Dg, m/S Fig. 23:

Bed-to-surface heat transfer coefficients with an immersed horizontal tube as a heat transfer probe. Magnetization FIRST mode with an axial field. Results of Ganzha and Saxena (1998a). Iron shot-air (see details in Tables 2 and 7).

5.2.7. 3. Vertical probes in beds subjected to transverse fields The first results reported by Bologa and Syutkin (1976) are shown in Fig. 24a. The plots practically do not exhibit sharp maxima like those in axial fields (Fig.l8b). Moreover, the values obtained in a transverse field are twice lower that those in an axial field. No explanations exist in the original paper. The recent results of Al-Qodah (Al-Qodah et al, 2000, 2001) (see Fig. 24b) practically repeat those reported by Arnaldos (see carefully Fig. 21) in axial fields and do not confirm the results of Bologa Syutkin (1976). Moreover, these results are extremely high, thus provoking a special discussion (see further) on the data correctness. 5.2.7. 4. Spherical probes in beds subjected to transverse fields The only study of Al-Qodah et al. (2001) reports data addressed to the application on a spherical probe. The results represented as Nu = f (Re) relationships are shown in Fig. 25. According to Al-Qodah et al. (2001) the sharp increases of the values of Nu occur at two points: • at U>Ue due to the increased bed porosity, • beyond Umf due to the onset of intensive particle mixing.

279

Vol. 19, No. 3, 2003

ί


400

200

0.1

0.3

0.6

0.7

0.5 U, mls

0.8

0.7

0.9

0.9

Ug (m/s)

Fig. 24:

280

Bed-to-surface heat transfer coefficients in beds subjected to transverse fields. Magnetization FIRST Mode. a) Data of Bologa and Syutkin (1976). Vertical cylinder as a probe. A simultaneous effect of the field induction and the particle diameter on the heat transfer coefficient. Vertical cylinder as a probe. 1)^= 320 mm; Dc= 78 mm. Iron powder; Lines: 1- (0-40 μιη); 2- (40-60μιη); 3-(60-90μπι); 4- (90-140 μηι). Field induction, B (mT): · - 12; Ο - 16. b) Al-Qodah et al. (2000). Wall-to-bed heat transfer coefficients (total) measured by a vertical circular plate probe placed at the column wall (position 5 in Fig. 4b). Particles 900 μηι. U m f 0 = 0.574 m/s


JorJun Hrislov

15-

B•

•

13-

τ * !

•

11-

X *

X

X

9"

•

W

*

*

^P

7-

X

i

Φ Β= 0(m T) • B=12(mT) AB=20(mT) • B=30(mT) xB=40(mT)

5-

ι 29

34

39

44

49

54

59

64

69

74

Re(-) Fig. 25: Al-Qodah et al. (2001).)· Wall-to-bed heat transfer coefficients (total) measured by a spherical probe immersed in the bed. Source: Fig.7 of the original paper. Air-fluidized magnetic particles covered by carbon (Pe3OJAC, 900 μηι - see Table 7).

No marks showing these transitions points have been reported in the original paper (see comments on the reconstructed experimental situations). The particle diameter effect on Nu investigated by Al-Qodah et al. (2001) (Fig. 8 in the original paper - not shown here) confirms the classical results of non-magnetic beds (Botterill, 1975), i.e. finer particles exhibit higher heat transfer coefficients. 5.2.2. Magnetization LAST- total heat transfer coefficients 5.2.2.1. Beds subjected to axial fields The experiments carried out with that mode have been obtained with vertical heating surfaces by Neff and Rubinsky (1983) (Fig.l9b), Arnaldos, 1986), Arnaldos et al. (1986,1987, Casal and Arnaldos (1991)- Fig. 26. Generally, the field intensity reduces the heat transfer coefficients despite the gas velocity. The higher values of hw correspond to higher gas velocities and the non-magnetized fluidized beds exhibit the maximum heat transfer

281

Magnetic Field Assisled FluidizationA Unified Approach-Part 3

I'of. 19, No. 3, 2003

400

Fe (420-500μπι)

• 1.10 »1.20 β 1.31 • 1.42

300

ΐ 200

100

1000

2000

3000

4000

H,kA/m Fig. 26:

Bed-to-surface heat transfer coefficients with vertical multitube heater. Magnetization LAST mode with an axial magnetic field. Arnaldos' results: Arnaldos (1986), Arnaldos et al (1086), Casal and Arnaldos (1991). Adapted from Arnaldos (1986). By courtesy of J. Arnaldos. See details in Tables 2 and 7.

coefficients. Other authors have not performed experiments with that mode with steady magnetic fields. A special case ofthat mode is the application of an alternating magnetic field (f=50Hz). The results are shown in Fig. 27. 5.2.2.2. Beds subjected to transverse fields Data according to this magnetization mode have been reported by AIQodah et al. (2000,2001) only (Fig.28a, b). The plots resemble those of Arnaldos (Fig.26) and Neff and Rubinsky (Fig. 20b). According to these authors the value of Nu decreases drastically at the onset of the frozen bed (they used the term "stabilized bed"). They attributed the changes to the

282

Jordan llrislov


400 CM

300

Increasing U

200 0 8.0816.172425 H.kA/m Fig. 27:

Bed-to-surface coefficients as a function of the field intensity of an alternating (time varying field of f = 50 Hz) axial magnetic field. Classified with the Magnetization LAST mode. Adapted from Zabrodsky and Tambovtsev (1976). (Original source - Fig. 3 of that paper). Lines: 1- U= 0.39 m/s; 2-U= 0.5 m/s; 3- U= 0.66 m/s; The arrow was added by the present author.

increased bed porosity (parallel to the increased gas velocity). Al-Qodah et α/.(2001) derived an empirical relationship corresponding to the stabilized bed (i.e. the frozen bed regime): -0.092

Nu-LOSRe0·52

(Π)

in the range of 47.3 < Re< 71pCpR j*—

(12b)

in accordance with the theory of the h- calorimetry (in the Russian literature the term is a- calorimetry) (Kondratiev, 1954). All the symbols represent the properties of the steel sphere (see further Table 8). The approximate calculations of the Biot number, Bi, (by means of the data shown in Fig. 33c) give variations of Bi with the frequency and the gas velocity (lines 2-3) in the range of 0.033 to 0.047. On the other hand, the fourfold increase of the field intensity (line 4) and the change of the type of the magnetization pulse from rectangular to semi-sinusoidal give Bi in the range 0.013 - 0.033. Unfortunately, no data concerning Bi are available in Stepanchuk (1984). The conclusions are tentative due to the readings of the graphs reported by Stepanchuk (1984). The above estimations were done in the present paper by means of the temperature response curves constructed for spheres in Geiger and Poirier (1973) (Fig. 9.13 in that reference at r/R=0). However, all the information presented in Fig. 33 indicates that the corresponding Fourier number varies in the range of 10 to 50. Generally, the results shown in Figs. 30-33 indicate that the increase of the frequency at H= const, or vice versa leads to the deceleration of the particles that reflects in the bed temperature field and bed-to-surface heat transfer. The increase of the fluidizing gas flowrate eliminates these effects slightly due to the increasing gas and particle convection effects.

288

Jordan llrisiov


520 f INCREASING

480 440 400 -(a) 10 14 18 22 H.kA/m f INCREASING

400 CM

300 (b) 200 0 a081&172425 H, kA/m Fig. 32:

Simultaneous effect of the field intensity and the frequency of magnetization on the heat transfer coefficient with the On-Off magnetization mode at a fixed gas flow rate. (Details in Tables 1,2 and 7). a) Stepanchuk (1982). U= 0.68 m/s. Rectangular pulses (Fig.la): 1- non-magnetized bed; 2- f = 3Hz; 3- f = 6 Hz; 4- f = 8Hz; 5- f =12Hz and 6 - f =22 Hz. Original Fig. 4 of Stepanchuk (1982). b) Zabrodsky and Tambovtsev (1976). U= 0.66 m/s. Line 1- preliminary magnetized particles in a steady field, but under the fluidization H=0; Rectangular pulses (Fig.la), f (Hz): 2- 2; 3-5; 4- 7; 5- from 10 to 15; 6- 20; 7-25; 8-33; Semi- sinusoidal pulses (Fig.lb), 9 - f= 40 Hz; 10-50 Hz. Original Fig. 3b of Zabrodsky and Tambovtsev (1976).

289


Vol. 19, No. 3,2003

140

(a)

120 100 OT ί 80

60 40 20 0 200 400 ΘΟΟ 800 t, °C 20 40

0.6 0.8 U, m/s Fig. 33: Results of Stepanchuk (1984) from cooling of steel sphere (Details in Tables 1,2 and 7) with the On-Off mode. a) Rate of temperature decrease. U= 0.614 m/s. Effect of the type magnetization pulses. Lines, 1- Semi- sinusoidal pulses (Fig.lb), f=50 Hz, H= 20 kA/m; Rectangular pulses (Fig.la), H= 80 kA/m: 2- f= 6 Hz; 3- f= 3 Hz. Non-magnetized bed line 4. Original Fig. 2 of Stepanchuk (1984). b) Semi-logarithmic plots demonstrating a regular regime of heat transfer between the sphere and the bed. U= 0.614 m/s. Lines like in Fig 3 la. Original Fig. 2 of Stepanchuk (1984). c) Variations of the heat transfer coefficient with the gas velocity. Effects of the type of magnetization pulses Lines: 1- Nonmagnetized bed; Rectangular pulses (Fig. I a), H= 20 kA/m: 2f= 6 Hz; 3- f= 3 Hz. Semi- sinusoidal pulses (Fig.lb), f=50 Hz, H= 80 kA/m.

-2.0

290

Jordan Hristov


5.2.4. Reconstruction of the experimental conditions (pure ferromagnetic beds)- total heat transfer coefficients 5.2.4.1. Comments on the data before thefurther analysis The data reviewed above strongly indicated that the hydrodynamics conditions have not been reported correctly in all the studies. The classification of the results in accordance with the three magnetization modes discussed here requires a correlation with the existing bed regimes (corresponding to the modes). Thus, the further analysis needs (see Figs. 12) detailed reconstructions of the experimental situations on the basis of the data available. 5.2.4.2. Reconstruction of the phase diagrams - Magnetization FIRST and LAST The results on wall-to-bed heat transfer coefficients will be discussed here from the point of view of the hydrodynamic results obtained in the last decade of the century (Penchev and Hristov, 1990a, 1990b; Hristov, 1998; Hristov, 1999; Hristov, 2002) and the well-established facts (Rosensweig, 1979a, 1979b, 1980; Rosensweig et al, 1981). The authors whose papers are mentioned here did not apply the separation of the modes (except Arnaldos). This hinders the direct comparison of the results. Because of that, in the present papers a reconstruction of the experimental situations is performed. In all the experiments discussed here iron shot, iron powders, steel and nickel particles as well as magnetic cores covered by a non-magnetic layers have been used as magnetizable particulate materials (see Table 7). This permits easy comparison on their thermal and magnetic properties. However, the particle sizes cover a wide range of diameters: fine particles (Bologa and Syutkin (1976) - a transverse field), moderate sand like particles (Bologa and Syutkin, 1976; Arnaldos, 1986,; Arnaldos et al, 1986,1987; Casal and Arnaldos, 1991) and coarse particles (Qian and Saxena, 1993; Dewan and Saxena, 1996, Ganzha and Saxena, 1998a, 1998b; Dolidovich et al, 1998; AlQodah et al., 2000, 2001: Al-Qodah and Al-Hassan, 2000 ). The particles cover the entire Geldart's diagram (Geldart, 1973). •

Reconstructions of experiments in axial fields - Magnetisation FIRST mode Figures 34a-d show reconstructed experimental situations. The phase diagram of Bologa and Syutkin (1976) (Fig. 34a) was reconstructed on the values of Umf0 calculated by relationships available in Kunii and

291

/«/. 19. No. 3. 2003


210

U.m/s .80

1.00

1.20

1.40

FLUIDIZED BED Fig. 34: Reconstructed phase diagrams - Magnetization FIRST mode. a) Data of Bologa and Syutkin (1976) in an axial field hw = f (U, H) - the upper part of the diagram (see Fig. 19). The reconstructed phase diagram U = f (H) - the lower part of the figure. See also Hristov (2000a, b).

292


.Ionian llristin·

U.m/s 10

1.1

FLUIDIZED BED

Umf Fi«. 34: cont. b) Data of Neff and Rubinsky (1983) (see Fig. 20). hw = f (U, H) the upper part of the diagram. The reconstructed phase diagram - U = f (H) the lower part of the figure. The line of Umf was calculated by Umf = 0.844 + 9.76. ΙΟ"3. Β (a rearranged equation (3) of Neff and Rubinsky (1983). See also Hristov (2000a,b). Note: the labels in circles correspond to the maximum of hw in the regime of MSB - the identification was done by the present author. 1- weak fields; 2 -strong fields.

293

Vol. 19, No. 3, 2003


Levenspiel (1991). Moreover, the description given by Bologa and Syutkin (1976) indicates that all the experiments correspond to the fluidized bed state. Because of that the trend of Umfo and Umf curves is tentative. The experimental situations of Neff and Rubinsky (1983) (Fig. 34b), Ganzha and Saxena (1998a) (Fig.34c) and Arnaldos (1986) (Fig.34d) were re-constructed in a similar way. In contrast to the paper of Bologa and Syutkin (1976), in these papers data about Umfo and Umf are available.

320 300 280 260

240 22ι

1.2

1.6

2.0

2.4

2.8

3.2

FIXED BED MSB

Umfo

~\ Umf

POINTS QFMAxhw \

Fig. 34: cont. c) Data of Ganzha and Saxena (1998a) (see Fig.23). hw = f (U, H) - the upper part of the diagram. The reconstructed phase diagram - U = f (H) the lower part of the figure. See also Hristov (2000a,b). Note: The data concerning the lines of Umfo and Umf were found out from various figures available in Ganzha and Saxena (1998a)

294


Jordan Hrislov

125 1

100

-o

Ni (250·400μπι)

2-1000 3-2000 4-3000 5-4000

75 l 50

25

0.1

Π

3

0.2

0.4

0.5 U, m/s

E FIXED

±

BED

; MSB POINTS OFMAxhw

8

Umf (Ue1)

b (Umfh)

Fig. 34: cont. d) Data of Arnaldos (1986).

295

Vol. 19. No. 3, 2003


All the four reconstructed situations indicate that the maxima reported in these studies belong to the fluidized bed regimes. Moreover, the detailed analysis permits to detect the values of hw in the regime of MSB (see below). • Reconstructions of experiments in axial fields - Magnetisation LAST mode The experimental situation of Neff and Rubinsky (1983) corresponding to the magnetization LAST mode is shown in Fig. 35. The whole knowledge on the bed behaviour available with that magnetization mode was applied (Hristov, 1998, 1999, 2002). The reconstructed data confirm again that the maximum heat transfer coefficients belong to the zones with negligible effects of the field applied. The reconstructions of the experiments of Amaldos are similar and are not illustrated here. • Reconstructions of experiments in transverse fields - Magnetisation FIRST mode In contrast to the well defined conditions in axial field, the study of Bologa and Syutkin (1976) does not allow a reconstruction of the experiments, so no comments are possible on the behaviour of the heat transfer curves in Fig. 24a. The recent results of Al-Qodah (Al-Qodah et al., 2000, 2001; Al-Qodah and Al-Hassan, 2000) permit re-design of the phase diagrams. The plots in Fig. 36-a indicate that the points corresponding to the maxhw belong to fluidization regimes with intensive particle motions and a minimum effect of the field intensity. The results repeat those obtained by Arnaldos (1986), Neff and Rubinsky (1986) and the group of Saxena (Saxena et al. 1994). No comments exist on field orientation effects on the heat transfer coefficient. • Reconstructions of experiments in transverse fields - Magnetisation LAST mode The experiments performed by Al-Quoda et al. are reconstructed in Fig. 36b. The data point associated with numbers (corresponding to the velocity profiles in Fig. 14) clearly indicate that the increased field intensity lead to reduced values of the heat transfer coefficient. No new results exist in comparison to those reported by Neff and Rubinsky (1983) and Arnaldos (1986). There are no explanations-in the original works why the change of the field direction does not affect the results as well as why the plots in Fig. 24b and Fig. 28a are as if copied from the papers of Arnaldos and Neff and Rubinsky.

296


Jordan Hristov

350

10 Umfo

1.0 (0

20

30

40 B(Gauss)

STATIC (UNFLUIDIZED) BEB

FROZEN BED

E Z)

Fig. 35:

-ORDINARY "Hstr ' -BUBBLING BED BUBBLING AND STRINGS 1.5

Hfr

A reconstructed phase diagram - Magnetization LAST mode. Data of Neff and Rubinsky (1983) (see Fig.20b). hw = f (U, H) - the upper part of the diagram. The reconstructed phase diagram - U = f (H) the lower part of the figure. The lines of Hstr and Hfr were estimated approximately on the basis of the experience reported in (Hristov, 1998,2000a). See also Hristov (2000b).

5.2.4.3. Όη-Offmagnetization mode - optimal conditions The optimal conditions with that mode of magnetization are shown in Fig.37. The plots were recovered from Stepanchuk (1984) and the present author added the lower parts. They show that the maximum value of hw depends both on the ON period length and the frequency of magnetization.

297

Vol. 19, No. 3, 2003

Magnetic Field Assisted FluiJizationA Unified Approach-Part 3

2000 γ.

1800- 1400-

MSB

-

Ug (m/s)

Slugging

CQ

bed

60J Fig. 36:

298

Reconstructed experimental situations of Al-Qodah. The. labels with the regime, abbreviations and the points of max //IK are added here. a) Magnetization FIRST mode. Upper diagram: The data plotted on Fig. 24b. The dashed lines (added here) mark the transitions from MSB into the fluidized bed regimes. Bottom diagram: A phase diagram adapted from Al-Qodah et al. (2000a). The points 4 and the numbers correspond to lines on Fig. 14-a and Fig. 14-c.


Jordan Hrislov

* Ug=0.60 (m/s) A Ug=0.65 (m/s) X Ug=0.70 (m/s) • Ujj=0.75 (m/s)

Homogeneous flnidizfttion of strings

Frozen bed

0.5 10 Fig. 36: cont.

20

30

40

50

60

70

80

B(mT)

b) Magnetization LAST mode. Upper diagram: The data plotted on Fig. 28a. The dashed lines (added here) show the boundaries of the bed regimes. Bottom diagram: A phase diagram adapted from AI-Qodah et al. (2000a). The points 4 and the numbers correspond to lines on Fig. 14-b and Fig. 14-d.

299


ί'ιιΐ. 19. No. 3. 2003

500

500

400

400

CM

CM

300

300

. 200 S 100

- 200 5 ·*= 100

ι ι

24168101214

0.01 002 0.03 Ton, S

II

0.001

10

0.002

.0 20 • I

£

0.003

30

0.004

40

Fig. 37:

f Hz

I

50 Optimal conditions with On-Off magnetization modes. MagnetiteAir (see Table 1). Data of Stepanchuk (1984). Original Figs. 3 and 4 of Stepanchuk (1984). The original data are redrawn (the lines corresponding to the pure magnetic particles only) as the upper parts of the figures. The present author on the basis of the data summarized in Table 1 designed the lower parts. a) hwas function of the ON period length (TO,,) at f= 10 Hz. b) hw as a function of the frequency of magnetization at τοη = 0.01

s.

The curve in Fig.37a exhibit a maximum in a narrow range of rm = 0.0150.02 s at f= 10 Hz, while at τοη = 0.01 s (Fig. 37b), the maximum corresponds to frequency band of 4.5 - 8 Hz. The lower parts of both figures indicate that the maxima of hw may be obtained in the range of -2S- = g_ jg approximately. No additional data are ••on

available for better elucidation of the problem. Despite that, the plot shows that the main idea of the On-Off mode (formulated by Kamholtz and

300

.Jordan llrislov


Levenspiel (1981) is satisfied. The frequency band (Fig.37b) corresponding to hw covers the natural bubble frequency (NBF) commented in (Hristov, 1999, 2002) and illustrated by the results of Jovanovich et al. (1984, 1987). In this case the intermittent magnetization suppresses the bubble formation (the Off period is too short) and only particle mixing are possible. The deviation toward lower frequency of magnetization (at fixed ON period length- Fig.37b) or shorter ON period at a fixed frequency allow bubble formation in the bed and a gas bypass that decreases the heat transfer coefficient. On the other hand the increase of the ON period length (Fig. 37a) or the frequency of magnetization (at τοη = const) makes the bed more difficult for fluidization. The latter opinion is based on the fact that such conditions do not permit particle mixing and the bed behaves like MSB (Magnetization FIRST) or a frozen bed (Magnetization LAST) (Hristov, 1998, 1999, 2002). The fixed bed behaviour exhibited by both regimes leads to significant temperature gradients (the data were commented earlier). The field intensity effect on the heat transfer coefficient with On-OfF mode is the same as in the other two modes created by steady state or timevarying fields. In all cases the increasing field intensity aggregates the particles and decreases their mobility. The range of the intensities depends on the properties of the particles used (Hristov, 1998,1999,2000a, 2002).

•

5.2.4.4. Maximum Total Heat Transfer Coefficients - comments Magnetization FIRST mode - a stabilized bed The maximum heat transfer coefficients (maxh„) are shown in Figs 38a,b. The values were extracted from various original plots by digitizing (see the figure captions) and by means of the reconstructed phase diagram. Both figures show that the curve ofmaxhw corresponding to the stabilized bed regime has two branches as a function of the field intensity. No comments exist in the published studies. The possible explanation may employ the fact that the increasing branch corresponds to the increasing bed porosity and the increasing gas convection effect on the value of max//,. As already mentioned, the stabilized bed has a fixed beds structure affected by the field applied, so the decreasing branch may be attributed to the anisotropy of the particle arrangement along the field lines (axial field only applied) and the channels dividing the particle aggregates. In this case the gas bypass through the channels decreases the heat transfer. The situations with the two types of the probe surface - a vertical probe

301


Vol. 19, No. 3. 2003

(Fig. 38a) and a horizontal tube (Fig. 38b) are similar. Therefore, the bed expansion has a limit separating the well-expanded bed and the anisotropic structure with channels. However, the expansion of a particular system (particles-field orientation-field intensity) depends on many factors. No data considering the heat transfer from that point of view are available in the literature. Magnetization FIRST mode - a fluidized bed The data available about maxhw in the fluidized bed regimes indicate that there are concurrent actions of the fluid flow and the magnetic field. The field aggregates the particles (i.e. enlarge the size of the fluidized

550 FLUIDIZED

500

*

400

ARNALDOS (iron) \ (1986)

CM

§300

Ί

NEFF & RUBINSKY (1983)

\, BOLOGA&SYUTKIN (1976)

200 MSB ARNALDOS (Ni) (1986)

100 >

FLUIDIZED BED FLUIDIZED

1

2

3

4

5

8

H.kMn Fig. 38:

302

Maximum heat transfer coefficients (total values). Data corresponding to the Magnetization FIRST mode. Present author data treatment. a) Maximum hw obtained with vertical heat transfer probes. Sources: Figs.IV-28,,IV-29 of Arnaldos (1986), Fig.2 of Neff and Rubinsky (1983), Fig. 2 of Bologa and Syutkin (1976).


JorJan Hristav

620 -

(b)

580

^fr*~A DOLIDOVICH ET AL. (1 998) ^^^T (FLUID.BED)

γ·

αρ=1511μπι

540 500 N

QIAN & SAXENA (1993)

460

7 420 *
The strange fact is that the values of the heat transfer coefficients are approximately 2 or 3 times greater those of the previous work reviewed. Al-Qodah et al. (2000) attributed these extreme values of h to the increased bed porosity with both magnetization modes (Fig. 39). However, the bed height presented in Fig. 39-b (magnetization LAST) corresponds to the "homogeneous fluidization of strings" and the frozen bed (Hristov, 1998) (see Parti (Hristov, 2002). The bed-collapsing branch of the curve is omitted. These comments are important in order to arrange a correct reconstruction of the experimental situation (see Fig. 36-b) The reconstruction of the experimental situations shown in Figs. 36-a,b attempts to elucidate the origin of these results. As mentioned earlier, the points corresponding to the maxhw (Magnetization FIRST) belong to fluidization regimes with intensive particle motions and a minimum effect of the field intensity. The results repeat those obtained by Arnaldos (1986), Neff and Rubinsky (1986) and the group of Saxena (Saxena et al. 1994). Therefore, no new information is obtained, except the fact that the values of the heat transfer coefficients are extremely high. Such extreme values of h are always attributed to fine particle beds (Botterill, 1975). AH the experiments of Al-Qodah have been performed with 0.9 mm particles (close to the situations of Ganzha nd Saxena (1998a) (Fig. 23 of the present paper, for example). Moreover, the maximum values of h corresponding to fixed bed structures: MSB (Fig. 24-b and Fig. 36-a) and a frozen bed (Fig. 28-a and Fig. 36-b) are in the range of 400- 600 W/m2.K.

306

Revien-s in Chemical Engineering

Jordan Urislvv

0.21 CO

E σ> Φ

I

0.19

(a)

• B=0 m T. Increasing flow • * · B=0 m T. Increasing flow • H 8=45 m T. Increasing flow • «-8=45 m T. Increasing flow

0.17: :-

K - K - X - JK--*-·*·*'*

0.15

Fixed bed

MSB

"§ CD

0.11

Ue

0.09 Ο 0.1 02 03 0.4 05 OS 0.7 Ου 05 W 1.1

Ug (m/s) 0.13 0.12fr Fluidization ^ 0.126 of strings *§, 0.124 £ 0.122 .σ> 0.12 χ 0.11fr •σ 0.116 00 °·114' 0.112 0.11 0.108 0 10 20 30

40

50

60

70

B(mT) Fig. 39:

Bed expansion curves. Particles 900 μπι. Umfo = 0.574 m/s. ht« = 100mm a) Magnetization FIRST mode. The labels " Fixed bed", "MSB" and "Ue" are added by the present author. b) Magnetization LAST. The dashed lines (added by the present author) mark the onset of the frozen bed. See for example Fig. 36b. The labels " Fluidization of strings "and "Frozen bed" are added by the present author.

307

/'«/. /V. /V«. 3. 2003

Magnetic Field Assisted Fluidi:ationA Unified Approach-Part 3

The values correspond to those exhibited by all the beds commented upon in the present review but in the absence of a magnetic field. Moreover, they are 150 % higher then reported by Bologa and Syutkin (1976) (Fig. 24-a). Furthermore, the heat transfer coefficients measured for free bubbling beds (all the values at B=0) are 3-4 times greater then those shown on Figs 19- 32. A) >n-iiysis of the experiments The heat transfer coefficients are defined as: i) Total heat transfer coefficient (Al-Qodah et al. 2000) hw -- ^r

ΑΗ-ΔΤ

(Al)

and ii) a local heat transfer coefficient (Al-Qodah, 2001)

(A2) where Ts is the heater surface temperature and Tb is the bed temperature. There are three principal differences between the experiments of AlQodah and those reviewed here (see the data collected in Table 7): 1. !!?? The heater probes are not immersed in the bed, but are placed at the column wall at 60 mm above the grid (see position 5 in Fig. 4-b). 2. !!?? In contrast to the definitions (Eq.Al and Eq.A2) the experiments utilized thermocouples readouts of the temperature differences between heater and the inlet gas temperature (17 C°) (Al-Qodah et α/, 2001). The value of ΔΤ* in Eq. (Al) is the thermocouple readout (Al-Qodah et al., 2000). Moreover, Eq. (A2) uses the bed temperature Tb as in all the studies reviewed (Eq. 9), but information of such measurements does not exist in the papers of Al-Qodah (see table 7). 3. The data concerning the temperature profiles (Fig. 14) indicate that the surface temperature heater probe depends on the gas flow rate. Thus, in contrast to the experiments of Bologa and Syutkin (1976), Zabrodsky and Tambovtsev (1976) as well as all the studies carried out by the group of Saxena (see the data collected in Table 7) the probe temperature is not constant.

308

Jordan Hrislov


B) Analysis of the extreme values of the wall-to-bed heat transfer coefficients We take into account that the particles used are composites (magnetic core and a non-magnetic layer on it). Thus, the values of h exhibited by the composite particles should be between those exhibited by the pure metal and the material of the coatings. Botterill (1975) (Chapter 5) compared heat transfer coefficients obtained in a broad range of particle diameters and material properties. For example, Fig. 5.8 of Botterill (1975) indicates that the peak values of h for air fluidized copper particles of 150 μιη are about 700 W/m2.K and less then 400 W/m2.K for particle bed of 625 μιη. The same graph demonstrates that sand particles of 1020 μιη (close to the size used by Al-Qodah) exhibit peak values of h less than 400 W/m2.K. A careful look at the graphs of Al-Qodah shows that beds in the absence of a field demonstrate extreme values of the wall-to-bed heat transfer coefficients that are not consistent with those of the literature. What is the reason for that? The simple explanation of Al-Qodah et al. (2000, 2001) that the fact may be attributed to the increased bed porosity (MSB and frozen bed) should be accepted with caution because the particle convection does not exist in these regimes and the gas convection effects cannot explain everything. Three test procedures may be performed for validation of the results. They use values obtained with the non-magnetized beds only, since in only these situations the comparison is available. Test 1. The data presented in Fig. 28 are obtained with a heat probe of Q = 5 W and a surface area of 6.605. Iff4 m2. This leads to a heat flux density q = 7570.02 W/m2. The value of h = 1600 W/m2.K (non-magnetized bed in Fig. 28- a ) gives a temperature difference (between probe surface and the bed) of 4.73°C. The same test with the data in Fig. 28-b gives values of 4.73°C (at U= 0.6 m./s) and 7.57 °C (at U= 0.6 m/s). The plots in Fig. 14 show that the minimum temperature (at the centre of the bed) is about 30 °C. Taking into account that Eq. (Al) uses the temperature difference between the probe surface and that of the inlet gas (17°C) the temperature at the probe surface should varies between 21.73 and 24.57°C. The data in Fig. 28 show 200 % higher values of the wall temperature. Thus, the bed temperature is higher than that of the heater that is a surprise.. Let us assume that that measurements of Al-Qodah are correct and the temperature difference is measured with respect to 17 °C. The assumption

309

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Magnetic Field Assisted FliiidizationA Unified Approach-Part 3

gives a surface temperature of the probe of 21.73 °C that contradicts the data shown in Fig. 14-a. On the other hand, if we assume (on the basis of the plots in Fig. 14-a) an average temperature difference of about 15 °C between the wall (the probe surface) and the bulk of the bed (assumed as 30 °C) the corresponding value of h is h = 343.17 W/m2.K. The value is approximately 4.5 times lower that those reported by Al-Qodah, but is consistent with all the previous works available in the literature. Test 2. The assumption of an average temperature difference of about 15 °C done in Testl and a values of h from 1000 to 1600 W/m2.K gives heat flux densities from 15. 103 to 24. 103 W/m2 . The range corresponds to a probe power of 9.90 W and 15.85 W. The results are approximately 3 times higher that the data reported by Al-Qodah (see Table 7). Test 3. The temperature difference of 15 °C (at 30 °C at the center of the bed) is lower value that can be evaluated from the plots in Fig. 14. In the case of a circular plate probe (Q=5 W) the probe surface temperatures will be approximately 34.73 °C (at h= 1600 W/m2.K) and 37.57 °C (at h = 1000 W/m2.K ). The values are close but less than the lower limit of wall temperatures plotted in Fig. 14-a, b. The same tests cannot be performed with the results obtained with a spherical probe (Q= 3.5 W) (Al-Qodah et. al., 2001) because data concerning non-magnetized beds are not available. C) Conclusions on the heat transfer coefficients and final comments on AI-Qodah's results The tests carried out here employed different versions and assumptions in order to elucidate the reason for such extreme values of the heat transfer coefficients. The data of Al Qodah should be accepted with caution. The equation for the determination of h is so simple that incorrect experimental design (and measurements) only might lead to the inconsistent results noted above. The use of the gas inlet temperature as a reference value instead of the bed temperature is a strange experimental step unknown in the literature published. The studies of Al-Qodah et al. (2000, 2001) show that the transverse field is in the focus of the investigators. However, the results should be assumed as an attempt to study a new situation rather than as reliable data. These results

310

.Ionian Hrislav


will not be discussed or treated further in the present paper. New experiments, performed by independent research groups, are needed to evaluate the heat transfer characteristics of beds controlled by a transverse magnetic field. 5.2.5. Maximum (Total) Heat Transfer Coefficients - data correlations 5.2.5. l.Nusselt number relationships The data available indicate that the magnetic field permits easy control of bed-to-surface heat transfer. Unfortunately the lack of complete data hinders a unified approach for data correlations. For example Saxena et al. have correlated the data by the relationship (Ganzha et al (1982)) based on the mechanistic theory of Ganzha (1992) for large particle fluidized beds:

Nu = 8.95(1 - e)

+

C.Re°* Pra43(l - E)ai3V0*

(13)

where C is related to the powder classification of Saxena and Ganzha (1980). It was demonstrated by Saxena et al. (1994), Saxena and Dewan (1996), Ganzha and Saxena (1998a), that for stabilized beds C = 0.085, while for fluidized beds C = 0.17 (Saxena et al, 1994; Ganzha and Saxena, 1998). The analysis of Ganzha (1992) shows that the coefficient 8.95 of first term of Eq.13 may be replaced by 8.5 kCT, where kgp is

3 . 4 - +0.94

The final equation employed in (Saxena et al, 1994; Saxena and Dewan, 1996; Ganzha and Saxena, 1998a) is Nu =8.5kgp(l - ε) + CRe0·8 Pr°'43(l - z)°-m^s

(15)

However, in order to overcome the problem with reliable data on ε variations in MSB regime a simplified form has been proposed (Ganzha and Saxena, 1998a):

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Magnetic FieldAssistedFluidizationA Unified Approach-Part 3

(16) developed for air-iron and air-iron/sand systems. The studies reviewed in the present paper have a common disadvantage; i.e. the lack of data considering the ε variations in the frames of the heat transfer experiments carried out. In order to overcome the problem the data summarized are correlated by the relationship

Nu

-k

- = A 0 .Re in So g

(17)

(18)

The term S0 contributes simultaneously the particle size effect (via the Archimedes number) and the field effect by the dimensionless field intensity H/MS (introduced by Hristov (1996); see also Hristov, 2002). The proposed equation is an alternative version between the correlations available for nonmagnetic fluidized beds (Zabrodsky, 1966; Botterill, 1975) (in this case the last term is equal to 1) and the situation of a deficiency of data from the experiments reviewed. The data considered for correlation corresponds to the fluidized regime only. In order to eliminate the deficiency of data concerning the thermophysical properties of the gas and the particles used in the particular experiments the results were correlated with the data summarized in Table 8. The experiments performed with steel and iron particles have been correlated only due to reliable data on the heat transfer coefficients available in the referred papers. The data plotted in Fig.40 and the established coefficients demonstrate two tendencies. The better results were obtained with the data of Bologa and Syutkin (1976) obtained in an axial field. The ratio (Nu/S0) decreases with the increase of the Reynolds number, but the higher values of (Nu/S0) correspond to finer particles that confirm the well-known results. The variations with Re (i.e. the decreasing tendency) demonstrate by an implicit manner the field effect on the heat transfer coefficient. The higher field intensities need higher gas velocities (Re respectively), but lead to lower heat transfer coefficients due to the particle aggregation. The same tendency is

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exhibited by the results of Neff and Rubinsky (1983) and those of Arnaldos (1986) and Amaldos et al. (1986,1987). Remember that all these data have been obtained with vertical heat transfer probes. On the other hand, just the opposite tendency is exhibited by the results of Saxena's group (Ganzha and Saxena,1998a; Dolidovich et al, 1998) obtained by a horizontal cylindrical probe. In fact, the simultaneous effects of field and the gas velocity on (Nu/So) are hardly detectable in these results. The plot of Eq. (16) on the same figure demonstrates a very simplified correlation that does not take into consideration the field effects. The similarity between the plots of Dolidovich's results (Dolidovich et al., 1998) presented by both 1

H --

is practically equal to 1

within the field intensity range employed. The situation in Ganzha and Saxena (1998a) is similar (see Table 7 for the range of H and Table 8 for the value of Ms).

5.2.5.2. Colburnjh factor correlations The correlations of the Colbum factor were developed here for the maximum heat transfer coefficients, maxhm in contrast to Arnaldos relationships that cover the entire velocity ranges of the corresponding regimes. 2

The jh factor jh -St.Pr3 =f(Re) was calculated here for all the data available. The plots are shown in Fig. 41. In contrast to the previous correlations by Eq. (17) all the data exhibit similar behaviours. In order to avoid the deficiency of data concerning the bed porosity the following relationship was employed for data correlations jh=B0Ren

(19)

The coefficients established for some of the data reviewed are summarized in Table 9. The expression of the data in the form

Mir" JhO

(20)

I KeO

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3 2 1 0.8

0.6 0.4 0.2 ΐ

0.1 0.08 0.06 0.04

0.02 0.01

1

4

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40 60 100

200

400

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gives a common relationship for all the results ,-1.298

(21) JhO

at R2 = 0.830 Here, jho and Re0 correspond to maxhw at H=0 in all the cases. The plots of the data and Eq. (21) are shown in Fig. 42a The relationship (21) does not include explicitly the field intensity effect and it is valid in ranges of data summarized here. All the data referred here indicate two general results: 1) The increased magnetic field intensity (Magn. FIRST) shifts the point of maxh„ toward the range of higher velocities (with respect to the case of H=0)

316

Jordan Urislov


Table 9 Coefficients of Eq. (17) and (19) and key to Fig. 34. Additional information is available in Table 7. Mat. Key Equation (19) and Equation (17) particle size, dp (μη): n Ao m R' Bo -0.586 0.887 1.23 -0.836 Bologa and Fe ·- (160-200); 239.6 Syutkin A -(200-250); (1976) • -(250-325); axial field Bologa and Fe 57.042 -1.488 0.985 Δ- (0-90 ) Syutkin (1976) transverse field ! ! ! Neff and Fe 0-727 Rubinsky (1983) axial field t Amaldos Fe 312.23 -0.124 0.827 ! θ -460 (1986) axial field 29.76 0.642 26.30 -2.42 Amaldos Ni -02 + -325 (1986) axial field Dolidovich Fe 192.22 0.078 0.864 25.03 -0.922 G,#-1511 2 et al. (1998) axial field 21.93 -0.72 Qian and Fe 0.27 0.511 24.3 «-733 Saxena (1993) -1.022 55.56 -0.02 0.055 13.8 Ganzha and Fe Δ -1086 Saxena (1998a) axial field ! The data do not allow a correct correlation due to the practically equal values of U corresponding to various max hw (See for example Fig.20,34a-top)

Exp. Points

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(22)

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L ε μ0 ρ


dimensionless axial position C - bed voidage - magnetic permeability of the vacuum, H/m - density, kg/m3 D

τ«, - length of the magnetization period, s Ton - length of the mixing period, s θ - angular co-ordinate, deg Subscripts Exp. - experimental Calc.- calculated g - gas p - particle Abbreviations MSB- magnetically stabilized bed

ACKNOWLEDGMENTS The author wishes to express his appreciation to the following people who in various ways supported the preparations of the heat transfer review: • Prof. J. Arnaldos (Dept. Chem. Eng., UPC, Barcelona, Spain) for his significant contribution on the problems and the opportunity to use his results published in papers and especially in his Ph.D. thesis. • Prof. S. Oka (InstVINCA, Belgrade, Yugoslavia) for his support in starting a series of review papers (Hristov, 1998, 2000a) on the problems discussed here. • Prof. Iztok Golobic (University of Ljubljana, Slovenia) for the opportunity to publish the first re-examination of the heat transfer results (Hristov, 2000b). • Prof. K. Maglic ((InstVlNCA, Belgrade, Yugoslavia) for the valuable support of reference data on the properties of the participate materails commented in the review.

349

Vol. 19. No. 3. 2003


•

Prof. Bo Leckner (Chalmers, Sweden), Dr. T. Panidis (Univercity of Patras, Greece), Dr. M. Yarvined (Univ. Helsinki, Finland), Prof. B. Rubinsky (Univ. of California, Berkeley, USA), Prof. S. Saxena ( Iniv.of Illinois at Chicago, USA) for the help in the paper collection from various sources. • Prof. S. Alekseenko and Prof. P. Kuibin , both from Inst. Thermophysics, RAS, Novosibirsk, Russia for the efforts to discover the papers published in Russia.

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.Ionian UriMov


Botterill JSM (1975) Fluid-bed Heat Transfer, Academic press, London. Bozorth RM (1951) Ferromagnetism Van Nostrand. Amsterdam. Brich MA Ganzha VL, Saxena SC (1997) On the Design of Heat-Transfer Probes, Int. Comm. Heat Mass Transfer 24 : 151-159. Casal J, Arnaldos J (1991) Heat and Mass Transfer in Magnetized Fluidized Beds, Trends in Heat, Mass and Momentum Transfer, 1: 153-166. Colburn AP (1933) Trans.Am.Inst.Chem. Eng, 29: 174 (cited through Gupta and Thodos (1963). Dolidovich AF, Ganzha VL, Saxena SC, Rahman SH (1998) The magnetic Field Effect on the Particle Behaviour and the Heat Transfer Between an Immersed Horizontal Tube and a Gas magnetofluidized Bed, in: FLUIDIZATIONIX. Pp.453-460. Ganzha VL (1992) Heat and Mass Transfer in Dispersed Media with Twophase Flow. D.Sc. Thesis . Luikov Inst. Heat Mass Transfer (ITMO). Minsk, Belarus. Ganzha VL, Saxena SC (1998a) Heat-transfer Characteristics of Magnetofluidized Beds of Pure and Admixtures Magnetic and Nonmagnetic Particles, Int. J. Heat Mass Transfer 41 :209-218. Ganzha VL, Saxena SC (1998b) Heat-transfer Rate Variations from the Surface of a heat transfer probe in a magnetofluidized bed, Int. J. Heat Mass Transfer 41:203-208. Ganzha VL, Upadyay SN, Saxena SC (1982) A mechanistic theory for the heat transfer between fluidized beds of large particles and immersed surfaces, IntJ. Heat Mass Transfer 25: 1531-1540. Geiger GH, Porier DR (1973) Transport Phenomena in Metallurgy, AddisonWesley, Reading. Pp.298-300. Geldart D (1973) Types of Gas Fluidization, Powder Technology 7 : 285292. Gnielinski V (1987) Heat transfer under one-phase convection (Fixed beds) , in : Heat Exchanger Design Handbook , v. 2. Russian translations, Petukhov B, Shikov V. (eds) v l Pp 259-261. Gupta AS, Thodos G (1963) Direct analogy between mass and heat transfer to beds of spheres, AIChEJ9(6) : 751-754. Hristov JY (1996) Fluidization of ferromagnetic particles in a magnetic field. Part 1: The effect of the field lines orientation on bed stability. Powder Technology, 87:59-66.

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