Epstein N., Grace J.R. Spouted and Spout-Fluid Beds: Fundamentals and Applications

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Heat and mass transfer 167

Table 9.3. Correlations of heat transfer from wall or submerged vertical tube to spouted beds.

Author Correlation

Malek and Lu

= 0.54





0.52





0.45





0.08





0.17

(9.25)

Uemaki and Kugo

= 13.0





0.10





0.46





−0.42





0.2

(

1 − ε

)

(9.26)

Chatterjee et al.

= 0.42





1.16





0.89





0.24





0.08

for Ud

ρ/μ < 4.0 (9.27)

Chatterjee et al.

= 0.6





0.39





0.72





0.12

for Ud

ρ/μ > 4.0 (9.28)

Macchi et al.

= 0.0196 Ar

0.36



(

1−ε

)



0.28

in the spout at r/R = 0 (9.29)

Macchi et al.

= 0.009 Ar

0.35



(

1−ε

)



0.38

in the annulus at r/R = 0.59 (9.30)

400

300

SPOUT-FLUID BED

FLUIDIZED BED

SPOUTED BED

200

100

0.1 0.2 0.3 0.4

0.5

, cm

dp, mm

, W/m

Figure 9.1. Effect of particle diameter on wall-to-bed heat transfer coefﬁcient for three possible

modes of contact in the same setup.

Can. J. Chem. Eng., 61 (1983), 390–397. Copyright

C

2009 by Can. Soc. Chem, Eng. Reprinted with permission of John Wiley & Sons, Inc.

and Kugo

proposed a somewhat different correlation, Eq. (9.26). The term ε in the

latter equation is an overall spouted bed voidage, calculated from the total volume of the

spouted bed.

For spout-ﬂuid beds, Chatterjee et al.

developed Eqs. (9.27) and (9.28). Comparison

of their results for three gas-solids contacting modes is shown in Figure 9.1.

168 Andrzej Kmiec and Sebastian Englart

9.3.3 Theoretical model

Epstein and Mathur

1,2

developed a theoretical model based on the analysis of heat

transfer from a cylindrical wall to a moving bed of sand by Brinn et al.

For solids in

the annulus of a spouted bed, they adopted a two-dimensional penetration model after

Higbie.

Neglecting axial conduction relative to transverse conduction, the solution in

terms of the surface-mean coefﬁcient h

over heated length Z was

= 1.129(v

/Z )

1/2

. (9.31)

The proposed model was found to be in qualitative agreement with experiment by Epstein

and Mathur,

1,2

and later by Freitas and Freire.

Its accuracy depends to a large extent

on correct evaluation of the annulus parameters in Eq. (9.31).

9.4 Between submerged object and bed

The next mode of heat transfer can be realized by the use of heating or cooling elements

submerged in the bed. This method of heat transmission is especially useful for chemical

reactors.

9.4.1 Transfer mechanisms

As for moving beds, there are two parallel heat transfer mechanisms involved: (1) forced

gas convection past the submerged object (a pipe or a coil), and (2) particle convective

heat transferred through unsteady state conduction to the particles in contact with the

surface of a heater, followed by absorption of that heat by the bulk of the bed. The

contact time of particles with the heating surface is one of the main governing factors.

The gas convective heat transfer coefﬁcient, h

, is based on the heat exchanged with

the gas percolating along the surface in the interstitial voids between the particles.

9.4.2 Experimental ﬁndings

Extensive research work in this area was carried out by Zabrodsky and Mikhalik

and

Klimenko et al.

toward the end of the 1960s, and more recently by Macchi et al.

Investigations by Macchi et al.

of heat transfer from a vertical tube submerged in a

spouted bed showed that h

reaches a maximum at the spout axis and monotonically

decreases toward the column wall, as illustrated in Figure 9.2. The decrease was largest

at the spout–annulus boundary. Most of the effects of different parameters could be

explained by the ﬂow patterns of the gas, although particle convection still contributed,

to some extent, to the heat transfer. The radial proﬁle of vertical gas velocity ﬂattens

out progressively with elevation, as more and more gas moves from the spout into the

annulus.

2,3,37

Local heat transfer coefﬁcients obtained by Klimenko et al.,

as well

as by Macchi et al.,

are consistent with this gas velocity trend. Separate correlations

Heat and mass transfer 169

210

190

170

150

130

0 0.1 0.2 0.3

, W/m

C°

0.4 0.5 0.6 0.7 0.8 0.9

1.0

r/R

U/U

= 1.1

U/U

= 1.3

U/U

= 1.5

Figure 9.2. Effect of superﬁcial gas velocity on radial proﬁles of h

for spouting of glass

particles (d

= 1.6 mm, H = 0.27 m, z = 0.21 m, D

= 0.019 m, D = 0.0127 m).

Can. J. Chem.

Eng., 77 (1999), 45–53. Copyright

C

2009 by Can. Soc. Chem. Eng. Reprinted with permission

of John Wiley & Sons, Inc.

were developed by Macchi et al.

for heat transfer coefﬁcients in the spout and in

the annulus, assuming that gas convection is the predominant mode of heat transfer,

but without neglecting particle convection. By least squares ﬁtting of their data, they

generated Eqs. (9.29) and (9.30) in Table 9.3.

9.5 Temperature uniformity

Temperature distribution within the spouted bed is of great importance in some processes,

such as coffee or barley roasting.

14,58

To control the product quality, it is desirable to

model the temperature and moisture proﬁles of the grain during roasting.

9.5.1 Within individual particles

A number of models are available in the literature for the drying of cereal grains,

according to Robbins and Fryer,

who considered two alternatives:

Model 1 – lumped temperature, where the temperature of the grain, T, is assumed

uniform, so the heat balance becomes

= h

a(T

− T ), (9.32)

where T = T

at t = 0.

170 Andrzej Kmiec and Sebastian Englart

Model 2 – distributed temperature, where the temperature is a function of position

within the grain:

∂T

∂t

=∇(λ

∇T ) (9.33)

with the boundary condition

∂T

∂r

= h

− T

) (9.34)

and initial condition T = T

at t = 0.

Robbins and Fryer

analyzed both temperature and moisture distributions in the grain

numerically, where Eq. (9.3) was used to calculate h

in the boundary condition.

9.5.2 Between spout and annulus

Kmiec

and Englart et al.

analyzed heat transfer between spout and annulus by writing

separate differential equations for the hot spout and the cold annular regions and solving

them numerically. The difference at each level between the axially falling bulk temper-

ature of the spout and the axially-rising bulk temperature of the annulus is the driving

force for heat transfer between the two zones, exclusive of particle convection.

Chapter-speciﬁc nomenclature

a speciﬁc surface area of grain, m

mass ratio of solute to solution, kg/kg

Gu Gukhman number, (T

− T

)/T

ﬂuid-to-particle heat transfer coefﬁcient, W/m

wall-to-bed heat transfer coefﬁcient, W/m

surface-to-bed heat transfer coefﬁcient, W/m

gas mass ﬂow rate, kg/s

mass ﬂow rate of the liquid, kg/s

mass ﬂow rate of the solution, kg/s

Re Reynolds number, d

Uρ/μ

Reynolds number, d

ρ/μ

particle radius, m

uniform bed temperature outside thermal boundary layer at wall, K

bulk bed solids temperature, K

at t = 0, K

exit gas temperature, K

inlet gas temperature, K

wet bulb temperature, K

wall temperature, K

mass of bed, kg

Heat and mass transfer 171

mass ﬂow rate of solids, kg/s

w bed width, m

s slot width, m

Greek letters

T

logarithmic mean temperature driving force, K

φ particle shape f actor (reciprocal of sphericity), φ ≥ 1

Subscripts

b bulk

g gas

s solids, surface

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Heat and mass transfer 173

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174 Andrzej Kmiec and Sebastian Englart

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10 Powder–particle spouted beds

Toshifumi Ishikura and Hiroshi Nagashima

This chapter is a systematic summary of the characteristics and applications of spouted

beds, called powder–particle spouted beds (PPSBs), consisting of ﬁne powders contacted

with coarse particles. The main aspect of conventional spouting that is relevant to PPSBs

is the ﬁnal elutriation of the dried or partially dried ﬁnes, often produced by attrition,

from a coarse particle bed.

Figure 10.1 shows the operating conditions of several kinds of ﬂuidization for particles

of density 2500 kg/m

, according to Geldart’s classiﬁcation,

indicating also the ﬁne

particle size and gas velocity ranges in four reported studies of PPSBs. The two solid

lines show the superﬁcial gas velocity at minimum ﬂuidization ( U

) and the terminal

velocity of a single particle (U

). In a PPSB, as one of the operating conditions, the gas

velocity is determined by the diameter and density of the coarse particles and is usually

greater than U

of the ﬁne powders, so the ﬁnes are elutriated from the coarse particle

bed.

10.1 Description of powder–particle spouted beds

Conceptual illustrations of a PPSB are shown in Figure 10.2. Group D particles in

Geldart’s classiﬁcation usually act as the coarse par ticles and Group A, B, or C particles

as the ﬁne powders. As shown in Figure 10.2a, for a Group C–D particle system, the

coarse particles in the bed are ﬁrst spouted and raw powders (ﬁne particles) in a dry

or partially dried state are then continuously fed to the bottom of the spouted bed

with spouting gas. Because the coarse particle movement is very vigorous in the bed,

agglomerates of ﬁnes can be readily broken up. The ﬁne powders, which adhere to

the surface of the coarse particles, are eventually elutriated from the bed based on the

difference in the terminal velocity of the ﬁne and coarse particles, and are collected

by bag ﬁlters. For the Group C–D particle system, agglomerating powders should be

pneumatically conveyed into the column by the spouting gas. Freitas and Freire

pointed

out that one advantage of bottom feeding over top or side feeding is its axial symmetry,

helping to maintain spouting stability, which is useful for scaleup, especially if thermal

or concentration gradients are present. However, particle attrition is greater with bottom

feeding than with top or side f eeding.

Spouted and Spout-Fluid Beds: Fundamentals and Applications, eds. Norman Epstein and John R. Grace.

Published by Cambridge University Press.



Cambridge University Press 2011.

176 Toshifumi Ishikura and Hiroshi Nagashima

–1

–2

–1

Powder-particle spouted bed

Circulating

fluidized bed

Conventional

spouted

bed

Fluid

bed

Teeter

bed

particles

cohesive

= 2500 kg/m

m = 1.8 × 10

–5

Pa s

r = 1.2 kg/m

aeratable

Particle size, d

, μm

Gas velocity, U, m/s

spoutable

sandlike

Figure 10.1. Operating conditions for spouting and several kinds of ﬂuidization: 1: Xu et al.,

bottom feeding of ﬁnes; 2: Ishikura et al.,

top feeding; 3: Zhu et al.,

bottom feeding;

4: Ishikura et al.,

top feeding.

Product powder

(fine particles)

Bag filter

Particles and powder

(coarse particles and fine particles)

Powder

(fine particles)

Cyclone

Spouted

bed

Spouted

zone

Disengagement

zone

Spouted

bed

Freeboard zone (TDH)

Gas

Raw powder

(fine particles)

Gas

(a) (b)

Figure 10.2. Schematic diagram of a powder–particle spouted bed (PPSB). (a) Group C–D

particle system, bottom feeding of ﬁnes; (b) Group B–D particle system, top feeding of solids.

On the other hand, as shown in Figure 10.2b, for a Group B–D particle system,

the mixture of ﬁne and coarse particles, introduced at the top of the bed through the

screw feeder, is blown up to the freeboard above the top of the spout by the spouting

gas. Some ﬁnes are elutriated out of the column and collected by a cyclone, whereas

others fall back either into the discharge pipe or onto the surface of the spouted bed