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Development of a mobilization technique for fibrous materials
POWDER TECHNOLOGY ELSEVIER
Powder Technology 85 (1995) 105-114
Development of a mobilization technique for fibrous materials Robert Legros "'*, Roland Cliff b, C. Alan Millington ~ • Department of Chemical Engineering, Ecole Polytechnique de Montreal, 2900 Edouard Montpetit, Montreal, Que. H3C 3A7, Canada b Centre for Environmental Strategy, University of Surrey, Guildford, Surrey GU2 5XH, UK ¢ Department of Chemical and Process Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK Received 30 June 1994; revised 11 May 1995
Abstract The 'mobilization' of a fibrous material, cut lamina tobacco particles, has been achieved in a novel contacting device which uses high velocity gas jets to create a well-defined solids flow pattern. Conventional technologies, such as fluidized and spouted beds, are incapable of maintaining such a material in a 'mobilized state' because of its entangled nature. Mobilization of tobacco particles in the device results mainly from momentum transfer from the gas jets to the bed. The maximum bed pressure drop is below that calculated to support the bed weight due to the contribution of the inlet momentum flux of the mobilizing gas jets. The maximum mobilizing flowrate at incipient mobilization can be predicted from a force balance model on the plug of fibrous particles. Keywords: Fibrous particles; Momentum transfer; Gas jets; Mobilization
1. Introduction Processing vegetable products in fluidized beds is beset by a number of problems, the most obvious being the unconventional nature of the solids with respect to fluidization itself. The materials are often easily degradable due to their biological nature. A few examples of such applications include drying of foodstuffsuch as grains [ 1 ], wheat [2], piece-form fruits and vegetables [3] and rice [4], thermal processing and cooling of cans [5 ] and food cooking using beds of salt or sugar [ 6]. The vegetable product chosen for this work, cut lamina tobacco, is a good example of an unconventional material treated in fluidized beds. Cut lamina tobacco is the main constituent in the cigarette-making process and is obtained at the end of the primary process which includes several steps, including high moisture conditioning, blending, cutting, drying, cooling and mixing, before going to the seeondary process, which is the actual cigarette making. The pitch of the cutting process is variable and in the case of 25 cuts/inch, as for the materials used in this work, the resulting fibrous particles are approximately 0.2 mm thick (the leaf thickness), I mm wide (the pitch of the cutting stage), with lengths varying between 0.5 and 10 cm. Because of folding during the blending stage, the particles are twisted along their long dimension and also have a number of 'kinks' or 'knees', * Corresponding author. 0032-5910/95/509.50 © 1995 Elsevier Science S.A. All fights reserved SSDIOO32-5910(95)O3014-Z
the resulting product being a mass of entangled fibres. The tobacco reaches this stage with a moisture content around 16% dry basis. In principle, the operations between the size reduction step and the beginning of the secondary process could be carried out continuously in fluidized beds. Successful attempts to fluidize fibrous entangled materials have yet to be found in the literature. The design of a suecessful distributor required a trial and error process, testing different possible configurations before a design suitable for tobacco processing could be established. Conventional spouted beds and slotted spouted beds with tangential entry failed to mobilize the entangled material. Severe channelling or excessively violent particle motions were observed in these configurations. This paper presents the development of a mobilizing device for processing cut lamina tobacco particles. This device will contribute to introducing a new type of particulate matter, fibres, into the fluidization field.
2. Experimental materials and procedure 2.1. Physical properties of cut lamina tobacco The material constituting 'Blend 72' was taken from the primary process, just after the cutting machines, dried in rotary dryers and stored. Tobacco, being a biological material, has physical properties which are difficult to quantify exactly
106
R. Legros et al. / Powder Technology 85 (1995) 105-114
Table 1 Physical properties of cut lamina tobacco (Blend 72)
the literature or provided by B.A.T. Group Research and Development Centre.
Properties
Values
Particle density (kg/m3) Particle shape (-)
t~=665(1 + W) parallelepiped: cross-section= 0.2 mm × 1 mm length = L-- 5-100 mm
Particle size (m) (equivalent sphere diameter)
dp= (6-~V)I/3= 7.3 X 10-3LI/3
Sphericity (-)
ff, ffi ~
2.2. Physical description of the mobilized bed distributor
sp
The mobile bed distributor developed in the course of this work is derived from the spout-fluid bed concept and is shown schematically in Fig. 1. The spout-fluidization technique was first introduced by Chatterjee [7]. It was a new contacting device, offering some characteristics of both fluidization and spouting techniques. The distributor has a square configuration with the four walls inclined at 30 ° to the vertical. The lower section is 5 cm square, while the upper section is 15 cm square. The inclined surfaces contain a number of orifices positioned in three horizontal rows, flae lowest row being at the junction of the base and the inclined wall. Each row contains 12 orifices of 4 mm in diameter (3 per side). Each orifice was profiled as illustrated in Fig. 2(a) which also shows details on the spacing of the orifices on one wall of the distributor. The lower section of the distributor contains a single orifice (7 or 10 m m in diameter) positioned on the central vertical axis. The airflow is introduced as two independently controlled and metered supplies from the same centrifugal fan. Because cut lamina tobacco particles cannot be spouted or fluidized, a special vocabulary was needed in order to describe these two gas supplies. The fluidization flow, provided by the high velocity jets from the wall nozzles, was termed the mobilizing flow. It serves two purposes in this device, to loosen and partially disentangle the bed material and to force the tobacco particles towards the central
= 0.0691L I/3
pressure taps tar moblllslng orifices
accelerating orifice
accelerating flow
Fig. 1. Mobilizing device for tobacco particles.
as they are subject to variations from one batch to another. The values given in Table I represent typical values found in
orificeprofilefor 30 cm distributor 4 mm
6mmCF7"A#F7 30 cm
•
X orifice profilefor 15 cm distributor
•
3.5 cm
~
o
o
4mm
-I~
6 mm ~ - - - ~
~1-
0
~'2mm
4 5 ~ 0 "~
I
X
0
~
~-o
I
6.5 cm
im
0,2 : X a o
Ca)
-" 5 c m
-"
Fig. 2. Details of the orificespacing for (a) 15 cm square distributor;(b) 30 cm square distributor.
(b)
R. Legros et al. ~Powder Technology 85 (1995) 105-114
upwards moving region. In other words, it mobilizes the bed material. The spouting flow, provided by the single orifice on the lower section of the distributor, was named the accelerating flow. Its purpose is to promote overall circulation of the bed material, by accelerating the particles in the upwards direction.
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2.3. Experimental set up and procedure .e_
The mobile bed distributor was placed below a 1 m high plexiglass column of square section. A cyclone was located downstream of the column to collect any entrained materials. The bed pressure gradients were measured with three pressure taps located on one of the four sloping walls as shown in Fig. 1. An additional pressure tap located at the top of the plexiglass column allowed the measurement of the overall bed pressure drop, which was measured between the lower bed pressure tap and the column pressure tap. All differential pressure measurements were made using a micro-manometer from Furnace Control Equipment, with an accuracy of 0.5 mm of water. Pressure fluctuations were not important during mobilization of the bed; dampening resulting from the pressure tap connections, which consisted of plastic tubing of 3 mm in diameter and approximately 1 m length, was sufficient to obtain steady pressure drop measurements. A typical experiment carried out to observe incipient mobilization conditions began by placing a load of fresh tobacco particles at about 15% moisture content within the distributor, continued by adjusting the accelerating flowrate to the desired value, and then proceeded by increasing the mobilization flowrate while recording the bed pressure drop until mobilization of the bed was achieved. No systematic means of loading the bed was employed during the experiments.
2.4. Qualitative observations of mobile bed operation Qualitative observations of the behaviour of fibrous materials during mobilization were made. The 15 cm square device was loaded with either 50 or 100 g of tobacco, the 100 g charge occupied the entire distributor volume. Increasing the charge by utilizing part of the plexiglass column resulted in unstable operation. By independent control of the mobilizing and accelerating flows, conditions for stable mobilization of the tobacco were investigated.
2.4.1. No accelerating flow When the mobilizing flow is started, the bed moves away from the inclined walls of the distributor. The material is compressed and a cavity appears in the lower region adjacent to the lower orifices. As the flow is increased, the upper bed surface becomes domed and the bed lifts. Suddenly, the surface of the bed breaks and motion is apparent from the central vertical axis towards the walls. At this point, the entire bed becomes mobile, with a rolling circulating pattern. Gas and solids together move upwards in the central core near the bed axis, while solids move outwards in the freeboard and then
750 O
: Start up conditions
[]
: M i n i m u m mobilisntion conditions
~,
: F a s t mebilisntion conditions
O
. . . .
0
I
50
. . . .
I
. . . .
100
I
150
,
,
,
,
I
,
,
,
,
200
250
,
,
,
300
Accelerating flowrate (l/min I
Fig. 3. Phase diagram for mobilizationof tobacco particles (bed load= 100 g).
downwards along the inclined walls. With increasing gas flow, the motion becomes more violent, until eventually the rolling mobilization is disrupted and the charge is transported out of the column. Once mobilization is established, it is possible to reduce the gas flow below the level required to induce the initial motion, without losing circulation. The solid motion suggests that the fibres are largely disentangled.
2.4.2. Both mobilizing and accelerating flows Stable mobilization is possible over a range of flows when mobilizing and accelerating flows are used in combination. The behaviour of the bed is the same as that observed without accelerating flow. The mobilizing flow needed to initiate motion is dependent upon the accelerating flowrate. The relationship between mobilizing and accelerating flowrates at minimum incipient mobilization is also dependent upon the orifice size of the accelerating nozzle. As the orifice size is reduced (from 10 to 7 mm in diameter), the dependence upon the magnitude of the accelerating flow becomes more important. Fig. 3 shows the range of stable mobilization for a bed mass of 100 g and an accelerating flow nozzle of 7 mm in diameter. Start up represents the conditions where the rolling motion of the bed starts, as distinct from minimum mobilization conditions which correspond to the minimum flow conditions to maintain motion. The fast mobilization regime corresponds to excessive entrainment of the bed material. Tobacco particle size analyses before and after 10 rain of mobilization at M-- 1050 l/rain, A = 501/min, with dn= 7 mm and initial bed inventory = 100 g, showed that breakage of particles was minimal. Some dust particles and small sections of lamina were collected in the cyclone, but this material amounted to less than 2% of the initial bed inventory.
2.5. Scale up of the mobile bed The effect of scale up on the mobilizing operation was also examined qualitatively at this stage of the development. The
R. Legros et al. / Powder Technology 85 (1995) 105-114
108
larger scale distributor was geometrically equivalent to the 15 cm distributor, with a 30 cm square top section and a 5 cm square bottom section. Details of the profile and spacing of the mobilization orifices are given in Fig. 2(b). The number of rows of mobilizing orifices was increased to 4, containing, from the lower to the upper row respectively, 2, 3, 3 and 5 orifices of 4 mm diameter. The orifices were not profiled in this distributor in order to investigate the effect on the mobilization behaviour. No scale-up criterion was used and this configuration, which was found by trial and error, gave the best results. The lower section still contained a single accelerating nozzle. A 1 m high column was fitted on top of the distributor. Both distributor and column were of plexiglass to permit visual observations. The behaviour of cut lamina tobacco in the larger distributor was similar to that observed in the smaller distributor. However, the accelerating flow had a noticeably smaller effect upon the mobilizing flowrate necessary to initiate mobilization. In general, operation remained stable at the larger scale. However the maximum bed load that could be mobilized, approximately 500 g, was below that corresponding to the volume of a full distributor. This therefore suggests the existence of a limit in the possible scale-up of a mobile bed distributor.
3. The onset of mobilization
The mechanisms involved during the onset of mobilization of a bed of cut lamina tobacco can be better described with the help of a plot of the bed pressure drop as a function of mobilizing gas flowrate. Such curves were obtained for several bed loads in the 30 cm distributor, and Fig. 4 shows a typical behaviour. The following sequence of events is observed as the mobilizing flowrate is increased. No accelerating flow was used during these experiments; its effect will be seen later.
B
2
"D
tion
Q m
Mobillsing flowrate Fig. 4. Typical pressure drop vs. mobiliNng llowrate curves.
(i) For small mobilizing flowrates, the tobacco behaves as a packed bed, with the pressure drop steadily increasing as the airflow is increased. (ii) The lower region of the bed starts to move away from the walls and a cavity appears. The compressed layers above the cavity act as a higher resistance medium and the pressure drop continues to rise along A-B. (iii) At point B, the bed is supported by the action of the gas flow and the bed starts to expand, causing the pressure drop to fall after this point. This leads to the existence of a peak in the bed pressure drop curve. (iv) After point B, the relationship between pressure drop and mobilizing flow is dependent upon the fibre length of the tobacco or in other words, upon the self-cohesion of the bed. It was observed that for short fibre tobacco, the mobilizing jets push the particles out of their way and start behaving like free jets, thereby diminishing the interaction between the gas and solids. With long fibre tobacco, the particles are entangled and the jets only penetrate to short distances before losing their identity. (v) At a certain mobilizing flowrate, corresponding to point C in Fig. 4, the pressure drop suddenly falls over a very short time interval and the bed becomes mobile. This sharp switch in bed behaviour occurs suddenly and corresponds to a discontinuity in the relationship between bed pressure drop and mobilizing flow. The value of the mobilizing flowrate at point C, called the incipient mobilization flowrate, is very dependent upon the bed history and is not exactly reproducible. (vi) Once the bed is mobilized, the pressure drop remains substantially constant for further increase of mobilizing flow. The excess flow results in more violent bed action and higher bed expansion, without significant effect on the pressure drop. (vii) When the mobilizing flow is decreased, the bed remains mobilized until point C' which corresponds to a lower value of mobilizing flow than point C. This value is called the minimum mobilizing flowrate. The bed pressure drop curve beyond this point depends on the manner in which the mobilization stops. The bed material may collapse in an orderly fashion into a packed bed with no channel. In this case, the bed pressure drop increases sharply as mobilization is lost and then decreases smoothly with reducing mobilizing flow (path C'B'A). More frequently, the bed may collapse in such way that a preferential channel still exists. The pressure drop then remains at a low value, since most of the airflow passes through the channel and decreases slowly with decreasing mobilizing flow (path C'B"A). If mobilization is restarted after the formation of such a channel, the pressure drop does not return to the original path ABC but remains approximately constant up to the point of incipient mobilization. Fig. 5 shows the actual pressure drop as a function of the mobilizing flowrate in the 30 cm square model without accelerating flow.
R. Legros et al. / Powder Technology 85 (1995) 105-114 200
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existence of E when the bed is in a mobilized state. The existence of entrainment from high velocity jets in a fluidized bed was also noted by Kvasha [ 8 ] in what he describes as the injected bed. He noted that this entrained gas flow was restricted to the periphery of the bed, within a ring of thickness 25-30 mm, and reported that the entrained gas flow can be up to 13 times the injected flow. Some tracer experiments were also carried out with a bed below the point of incipient mobilization. In this case, the tracer gas was found mainly in the top sampling stream, thereby showing an upwards flow of gas. Therefore entrainment of gas from the freeboard, leading to downward flow near the walls of the distributor, is only present once the bed is mobilized.
400 g
:450g
100
500
1000
1500
2000
2500
3000
109
3500
Mobili$1ng flowrate (llmin) Fig. 5. B e d pressure d r o p m e a s u r e m e n t d u r i n g onset o f mobilization.
4. G a s f l o w p a t t e r n i n m o b i l i z e d
beds
Visual observations through the plexiglass walls of the distributor suggested that the particles were being entrained downwards by a flow of gas, since the particle velocity was much higher than expected if driven by gravity alone. The existence of this entrained gas flow was verified in several ways. The rolling action observed during mobilization was inferred to result from an entrained gas flow, hereafter referred as E, pulling the particles downwards along the distributor walls. Therefore if E is responsible for the stability of mobilization, inhibition of E would result in destabilization of the rolling mobilized flow. Square masks, which consisted of a 15 cm × 15 cm plate (the internal dimensions of the plexiglass column) with a central square hole of different sizes, were constructed. The masks, with different open areas, were lowered down inside the 15 cm square side perspex column towards a mobilized bed. At a certain height, the system became unstable, with the bed suddenly lifting up to the top of the column. The height at which mobilization is disrupted was a function of the open area of the mask. The hypothesis advanced at this stage was that, with E interrupted by the mask, the tobacco particles were no longer entrained downwards at the walls, so that the entire bed moved upwards. A tracer experiment was performed to confirm the existence of E. Five small holes, 3 mm in diameter, were made on one side of the distributor. Helium tracer was injected through the central hole, at a very low flowrate, so that any gas flowing along the walls would immediately entrain the tracer. Gas was sampled from the other four holes, which were located at a distance of 2.5 cm up, down, right and left from the central hole, at a constant volumetric flowrate with a vacuum pump. The relative concentrations of helium in the four streams were determined and it was observed that the gas stream sampled from the bottom point contained more helium than the gas stream from the top point. Therefore the gas near the wall is flowing downwards, which proves the
5. M o d e l l i n g
of incipient mobilization
From the observations of the incipient mobilization conditions, it is possible to identify two predominant events in the bed pressure drop-mobilizing flowrate curve: the peak pressure drop and the incipient mobilization point. For design purposes, these values are of most interest. It was also seen that the onset of mobilization depends upon the bed history and the properties of the tobacco (cohesion of the bed). These variables were difficult to control, particularly for the tobacco properties which changed from one batch to another. It was therefore decided to consider only the case of long fibre tobacco and the first cycle of mobilization, since this combination gave the largest peak pressure drop and the maximum mobilizing flowrate at the point of incipient mobilization. These values can then be considered as the maximum peak pressure drop and the maximum incipient mobilization flowrate.
5.1. Peak pressure drop conditions Before point B in Fig. 4, the plug of tobacco was seen to behave as a packed bed with the bed pressure drop steadily rising with increasing mobilizing flowrate. Assuming that the mobilizing gas jets lose their momentum in a very short distahoe, allowing the airflow to become uniformly distributed over the bed cross-section, the pressure gradient through the bed at any height can be expressed by Ergun's equation:
-dP=Au + BU2
(I)
dr
where U is the superficialgas velocityat height y, and A and B are empirical coefficients.Conditions in the bed below point B can be represented as in Fig. 6. The flowrate in each region is considered to be the sum of the totalgas flow entering below itslower boundary:
Q,=(--~-~t + Q,_ , \ntoud]
(2)
R. Legroset al./ PowderTechnology85(1995)105-114
110
Yi
y
~;~,~,~q,~ ,\ u(y)
BQ2n a)2] } Fei=f((AQi)-l-[(b_l_2yta
,~t,t~i,/~ /
dy
dy
(10)
Yi - l
one obtains:
zone 3,,~
8Q,~ F p i = A Q i ( Y i - - Y i - 1 ) -~" -
ZONOt~
[
1
1 ]
X b+2yi-ltana
where n~ represents the number of mobilizing jets entering the t~hregion. The airflow is assumed to be uniformly distributed so that the velocity at height y is given by:
-
Q, ( b + 2 y tan a) 2
(3)
The pressure drop through each region i can then be obtained by integrating Eq. ( 1) from Yi- 1 to y:
Y~
-AP'= I [AUi(y) +BU~(y) ] dy
(4)
Solving Eq. (4) with Ui given by Eq. (3), one obtains:
]
+ BQ~i F" 1 1 ] 6tan al(b+2yi_~ tan a) 3 (b+2y~tan a ) i (5) The total bed pressure drop is then obtained by adding the contributions fiat'~ APto~ = ~APi
(6)
The total force on the plug of tobacco due to the pressure drop can be calculated from Eq. (1). The force per unit volume of bed is given by the pressure gradient: dF dV
dP dy
(7)
Therefore, using Eq. (1) with: dV= ( b + 2 y tan a) 2 dy
(11)
Fptot= EFpi
(12)
The upward force due to the gas jets can be calculated, assuming that each jet transfers all its momentum. The force transmitted to the plug of tobacco is therefore equal to the momentum flux carried by the jet at the vena contracta section, where the gas is no longer accelerated. Therefore, each mobilizing jet exerts an upward force on the tobacco plug equal to:
FM1= [pu~¢Sv¢] sin a
(13)
where
Yi--I
_Api=AQI I 1 i 2tan a b+2y~-l tan a b+2y~tan
b+2yitanot
The total pressure force, Fvtot is obtained by adding the contributions Fpi:
Fig. 6. Plugof tobaccoat the pointof peakpressuredrop.
U,(y)
-
2tan a
(M/n) svo
Uvc= ~
(14)
The cross-sectional area at the vena contracta, Sv¢, can be calculated from the orifice discharge coefficient, which is obtained empirically from the pressure drop-flowrate curve measured in the empty distributor, since:
ave
Ccm~ ~m
"ffd2m
where Sm= 4
(15)
Substituting Eqs. (14) and ( 15 ) into Eq. (13), and for n jets: 4pM2 sin a
FMI ---- Ccmn2Trd2m
(16)
The momentum flux carded by the gas leaving through the top section of the bed, assuming uniform gas distribution, is:
FM2=pU~S~
M where Uc = ~ A Sc = ~
(17)
Therefore: (8) FM2= pM~
(18)
one obtains for the total force:
H
Fp=J[AU(y) +BU2(y) ] ( b + 2 y tan a) 2 dy
(9)
0 The velocity U is different for different sections of the bed. Therefore, substituting Eq. (3) into Eq. (9):
From a momentum balance on the plug of tobacco as represented in Fig. 6, one obtains for the upward force Fy: Fy= [FM,--FM2]
+Fp
(19)
Substituting Eqs. (16) and (18) into Eq. (19), one obtains:
R. Legros et al. ~Powder Technology 85 (1995) 105-114
4pM 2 sin a
Fy(g)
.
pM 2 . . . . .
[ CcmnTFd2m ] [~] .
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(20)
At the point of peak pressure drop, the weight of the bed is entirely supported. Thus: Fy(M) = mg
.
111
~,
0
: experiments
Q. 150 f,
--
:
. ~
(21) 100
From Eqs. (20) and (21), it is possible to calculate the mobilizing flowrate necessary to support a bed of cut lamina tobacco, provided the resistance of the bed as expressed by the coefficients A and B are known. These coefficients were obtained from packed bed experiments. It was found that A and B can be calculated from:
[
0
(1 - ~)2
A = 25440 ~
(22)
(l-e) B = 12740 - 7 - -
(23)
for the range of e > 80%. The voidage e was determined from the measured bulk density PB with the tobacco moisture content W as: Pb = Pp( I - e)
Q.
(24)
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500
200 300 400 Tobacco load (g) Fig. 7. Comparisonbetweenmodel predictionsand experimentalpeak pressure drop measurementsfor differentbed loads. 100
increase in the momentum transfer from the mobilizing jets. From a momentum balance around the plug of tobacco, a similar result to Eq. (20) is obtained, with the upward force equal to the weight of the bed:
with 4pM2 sin a pp= 665(1 +IV)
(25)
Therefore, to estimate the point of 'peak pressure drop' of a bed of cut lamina tobacco of bulk density ~, and moisture content W, the procedure is as follows: (i) Calculate the bed voidage from Eqs. (24) and (25). (ii) Calculate the coefficientsA and B from Eqs. (22) and (23). (iii) Plot the ratio Fy(M)/mg as a function of M, with Fy(M) calculated from Eq. (20). (iv) Determine the value of M for which value
Fy(M) /mg = 1. (v) Calculate the Aptot~ for the value of M found in Eq. (4), from Eq. (5). The coefficients A and B, calculated from Eqs. (22) and (23) respectively, for the conditions Pb = 95 kg/m 3 and W= 16%, were A = 5 7 0 and B=2330. The ratio (Fy(M)/mg) was calculated from F,q. (20) for different bed loads. The points of 'peak pressure drop' were then compared to the measured values in Fig. 7. The close agreement between expected and actual values suggests that the procedure is valid to predict the value of the 'peak pressure drop'.
6. I n c i p i e n t m o b i l i z a t i o n c o n d i t i o n s
For long fibre tobacco, it was observed that the entire bed is supported by the gas flow at the point of 'peak pressure drop'. The bed is then lifted away from the walls of the distributor. From point B (see Fig. 4) to point C, the fall in the bed pressure drop is therefore compensated by the
momentum] [momentum]
-I-
-rag
Fp
•0
[pressure]
f]uxin J-L f,uxout/+Lfor
in/-[w°ight] (26)
Therefore the force due to the pressure drop, from the point of 'peak pressure drop' to the point of incipient mobilization, can be calculated from: J - 4 sin a Fp = D'lg -- ~ I / z L " C - ~ m
11 ~¢'J
( 27 )
It was noted above that, in the mobilized state, the gas flow pattern shows a region of downward flow near the walls of the distributor. This downward flow is due to the entrainment of gas by the mobilizing jets, which behave essentially as free jets when the bed is mobilized. Before mobilization, this downward flow of gas is not present. Therefore, corresponding to the sudden transition in gas flow pattern at the point of incipient mobilization, a certain discontinuity must exist. Examining Eq. (27), it is clear that at a certain value of mobilizing flowrate, the momentum transfer from the jets becomes sufficient to support the weight of the bed. At this point the pressure gradient through the bed becomes zero. Any further increase of the mobilizing flow would result in an unstable situation, since the momentum dissipation from the jets has become greater than the weight of the bed. The jets then start entraining gas from the freeboard and are able to do so since the pressure drop has become zero. Once the mobilizing jets have started entraining gas downwards, the
112
R. Legros et al. /Powder Technology 85 (1995) 105-114
3.~00
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i
. . . .
i
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i
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i
ues. The close agreement suggests that Eq. (29) is valid and can be used to predict Mi.m..
. . . .
0 3000
15 cm
[dmbu'°rl I
0
tO
7. Influence of accelerating flow on mobilization
. . . .
2000
t~
._~ 1500 O
E ._ ._~
i
/
I I
- -
0
:
experiments
1000 30 cm distributor
¢J
_c
: model
s00
200
100
300
400
500
Tobacco load (g)
Fig. 8. Comparisonbetween predicted and measured maximum incipient mobilizingflowratesfor differentbed loadswithoutacceleratingflow.
plug of tobacco is subject to a new distribution of forces and the bed is mobilized. Therefore from Eq. (27), the point of incipient mobilization can be predicted as the point where Fp = 0. ThUS:
,Ma[ 4 sin a 1 p /'C-~m--~d2 d2]=mg
(28)
or
Mim--
o~ 4 s i m g
1
(29)
Eq. (29) can be used to predict the maximum of the range of conditions corresponding to incipient mobilization, since it was derived assuming the entire bed to be supported by the gas jets. From visual observations through the perspex distributor walls, it was noted that this complete support of the bed was only possible in the case of long fibre tobacco or small bed load, in which case the bed displays great cohesion so that, before mobilization, the tobacco behaves as a single plug. In most cases, especially in the larger scale model (30 cm square), the plug of tobacco was not completely lifted away from the walls due to either the weaker self-cohesion of the bed observed for shorter fibre tobacco, or the larger bed load. The mobilization started at lower mobilizing flowrates in these cases. This can be explained by the fact that a part of the bed weight is still supported by the distributor walls, thereby requiring lower mobilizing flowrate to fulfill the requirement expressed by Eq. (29), since the effective weight to be supported is lower. Nevertheless, Eq. (29) was compared to the maximum incipient mobilization flowrates that were obtained in the small and large beds for different masses. Fig. 8 compares the experimental and calculated val-
It was seen above that a bed of cut lamina tobacco cannot be mobilized solely by the action of the accelerating flow. However, the circulation of the bed was much improved when the accelerating flow was present. It was also noted that the mobilizing flow necessary to initiate mobilization is dependent upon the accelerating gas flowrate. A first attempt to model the influence of the accelerating flow at the point of incipient mobilization was presented by Legros et al. [9]. The model was based on a force balance leading to calculation of an internal normal stress distribution along the central plane of the bed. The criterion for incipient mobilization was that the bed becomes mobilized once the tension in its upper layer exceeds a certain value. This limiting value was then used to obtain a relationship between mobilizing flow, M, and accelerating flow, A, at the point of incipient mobilization. The model predicted quite well the influence of the accelerating flow in the small 15 cm distributor using a 7 mm diameter accelerating nozzle. For larger accelerating nozzles, the influence of A upon M at incipient mobilization becomes weaker; the model does not predict this behaviour. For the 30 cm model, the predictions were even less reliable: the model predicted a stronger influence of the accelerating flow on the mobilizing flow needed at incipient mobilization, while in fact the opposite behaviour was observed. Therefore, because of several inconsistencies between the predictions and the actual observations, the force distribution model was rejected. Its derivation was nevertheless useful since it provided the first indication of a possible downward flow of gas along the distributor walls which was demonstrated subsequently. A simpler approach was then used to predict the influence of the accelerating flow. Considering Eq. (29), which was used to predict the point of incipient mobilization, and adding the contribution of the accelerating flow to the momentum flux in and out, one obtains:
4pM 2 sin a 4pA2 p(M+A) 2 +- -I-Fp-mg=O Ccmnlrd2m Ccalrd~ d~
(30)
where C~a is the discharge coefficient of the accelerating nozzle. A similar approach was recently used to take into account the contribution of atomizing air in a spouted bed coating process. Choi and Meisen [ 10] added the momentum of the atomizing air to the spouting air and found that the minimum spouting velocity of a shallow spouted bed could be predicted from this simple model. At the point of incipient mobilization, the bed pressure drop is assumed to be zero. Eq. (30) then gives a relationship between M and A which, after algebraic manipulation, can be written:
R. Legros et al. / Powder Technology 85 (1995) 105-114 3500
. . . .
i . . . .
.g~-
t . . . .
Model (equation
--
Experimental data
(31))
3ooo
O
: da=10mrn, 400g
O
: da = 7ram, 400g
A
: da=10mm , 200g : da = 7ram, 200g
2500 20001
V
v '~
1500
: da=10mm, 100g : da= 7mm, 100g
1000
: da=10mm, 50g
._Q. 5oo~ : da= 7mm, 50g o|1 0
i
, 50
, , , , 100
, , , 150
Accelerating flowrate (I/mini
2O0
Fig. 9. Comparisonbetweenmodelpredictionsand experimentalincipient mobilizingflowratesfor differentbed loads as a functionof accelerating flowrateand nozzlediameter(top: 30 cm distributor;bottom:15 cmdistributor).
,M21- 4 sin a p
reaches a value greater than rm = 0.6. However, the agreement observed between the model and the actual results confirmed that the mobilization of a fibrous materials is a 'momentum controlled' process and this is a significant result for further development of the mobilization concept.
8. Conclusions
•
e, l¢
113
1 P 2A [-C-~m--~-~2m ~ ] - ' M [ ~ ' ¢ ] + [ "4pA2
mg]=0
(31)
LCo,,~'~
Eq. (31 ) predicts the correct trends observed from the experimental data, i.e. a larger influence of A in the smaller scale model than in the large one, for identical accelerating nozzle diameter, and a greater influence of A in terms of flowrate as da is reduced. These characteristics of Eq. (31) are shown in Fig. 9. Fig. 9 also compares the predictions from Eq. (31) and actual measurements obtained in both 15 and 30 cm distributors. In general, the model predicts adequately the observed behaviour except for large accelerating flowrate and small accelerating nozzle diameter. In these cases, much lower mobilizing flowrates are predicted at incipient mobilization than are actually required. The observations showed that the value of M does not continuously decrease with increasing A, as predicted by Eq. (31 ), but in fact reaches a constant value. At this point, the mobilizing flowrate at incipient mobilization is no longer dependent upon the accelerating flowrate. This is due to the smaller contribution of the accelerating jet in the momentum balance. At high accelerating jet inlet momentum, the tobacco is pushed out of the jet path and the jet interaction with the solid is reduced. Therefore, the simplistic assumption of instantaneous transfer of momentum from the gas jet to the solids is no longer valid for the accelerating jet at this point. The model seems to deviate largely from the actual measurements when the ratio rm = (accelerating jet momentum/total jet momentum) or:
I
4/:lA2
A simple momentum balance has led to the derivation of a model capable of predicting adequately the two engineering parameters important for the design of a mobilized bed process unit: the peak pressure drop and the maximum incipient mobilizing flowrate. The model also describes the influence of the accelerating flow and gives good predictions of the effects of the accelerating nozzle diameter upon the relationship between M and A at incipient mobilization. However, the model is inconsistent for large accelerating flow, because the assumption of uniform flow above the tobacco plug is too simplistic. This assumption is reasonable when only mobilizing flow is present or at low accelerating flow, since the jets in those cases lose their identity before reaching the surface of the plug. Further development of the model should therefore take into account the fact that the momentum flux carried by the outgoing gas is larger than calculated by assuming uniformly distributed flow above the bed. Determination of the gas flow pattern showed the existence of a downward flow near the distributor walls due to entrainment into the jets. Because of this recirculation of gas, the gas phase can be regarded as perfectly mixed. The particular 'rolling action' of a mobilized bed permitted the same assumption to be made concerning the solid phase. The heat and mass transfer characteristics of the mobilized bed are presented elsewhere [ 11,12]. 9. List of symbols A
B
c~a Ccm d~ d¢ dm d~ F
F~
]
C c a q'/'d~a J
rm-- r4pMZ sin_o(.] = M 2 sin
L C¢~'a~m J
L
A2Ccm?ld2ra
aCca~
(32)
m
M n
coefficient in Ergun's Eq. (1) (kg/m 3 s) or accelerating volumetric flowrate (m3/s) coefficient in Ergun's Eq. ( 1) (kg/m 4) accelerating orifice discharge coefficient (-) mobilizing orifice discharge coefficient (-) accelerating orifice diameter (m) column diameter (m) mobilizing orifice diameter (m) tobacco particle diameter based on sphere of equivalent volume (m) force (N) momentum flux carried by the mobilizing gas flow (N) force due to pressure gradient (N) upwards force from momentum balance (N) length of tobacco particle (m) mass of tobacco (kg) mobilizing flowrate (m3/s) number of mobilizing orifices (-)
114
P Qi
R. Legros et al. /Powder Technology 85 (1995) 105-114
pressure (Pa) volumetric flowrate in each zone of the distributor (m3/s)
rm Sc Sm Sp Svc X y U Uc uv¢ V Vp W
ratio of accelerating jet to mobilizing jet momentums (-) column cross-sectional area (m 2) orifice cross-sectional area (m 2) surface area of a tobacco particle (m 2) vena contracta cross-sectional area (m 2) katharometer' s reading (1/min) upwards vertical distance from the base of the distributor (m) superficial gas velocity (m/s) superficial velocity based on column crosssectional area (m/s) gas velocity based on vena contracta crosssectional area (m/s) bed volume (m 3) tobacco particle volume (m 3) moisture content (kg H20 / kg dry tobacco)
Greek letters bed voidage (-) p gas density (kg/m 3)
Pp
r~
xp
particle density (kg/m 3) ratio of column diameter to orifice diameter (-) particle sphericity (-)
References [ 1] V. Vanecek, M. Markvart and R. Drbohlav, Fluidized Bed Drying, Leonard Hill, London, 1966. [2] H.A. Becker and H.R. Sallans, Chem. Eng. Sci., 13 (1960) 97. [3] D.F. Farkas, M.E. Lazar and T.A. Butterworth, Food Technol., 23 (1969) 1457. [4] R.L. Roberts, R.A. Carlson and D.F. Farkas, J. Food Sci., 44 (1979) 248. [5] G.M. Piggott, Food Proc., 24 (1963) 79. [6] G.F. Sachsel, FoodProc., 24 (1963) 77. [7] A. Chatterjee, Ind. Eng. Chem. Proc. Des. Dev., 9 (1970) 340. [8] V.B. Kvasha, in J.F. Davidson, R. Clift and D. Harrison (eds.), Fluidization, Academic Press, London, UK, 1985, p. 675. [9] R. Legros, C.A. Millington and R. Clift, in K. Ostergaard and A. Serensen (eds.), Fluidization V, Engineering Foundation, New York, 1986, p. 225. [10] M. Choi and A. Meisen, CJChE, 70 (1992) 916. [ l 1 ] R. Legros, Ph.D. Dissertation, University of Surrey, UK (1987). [ 12] R. Legros, C.A. Millington and R. Clift, Drying Technol., 12 (1994) 517.
Powder Technology 85 (1995) 105-114
Development of a mobilization technique for fibrous materials Robert Legros "'*, Roland Cliff b, C. Alan Millington ~ • Department of Chemical Engineering, Ecole Polytechnique de Montreal, 2900 Edouard Montpetit, Montreal, Que. H3C 3A7, Canada b Centre for Environmental Strategy, University of Surrey, Guildford, Surrey GU2 5XH, UK ¢ Department of Chemical and Process Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK Received 30 June 1994; revised 11 May 1995
Abstract The 'mobilization' of a fibrous material, cut lamina tobacco particles, has been achieved in a novel contacting device which uses high velocity gas jets to create a well-defined solids flow pattern. Conventional technologies, such as fluidized and spouted beds, are incapable of maintaining such a material in a 'mobilized state' because of its entangled nature. Mobilization of tobacco particles in the device results mainly from momentum transfer from the gas jets to the bed. The maximum bed pressure drop is below that calculated to support the bed weight due to the contribution of the inlet momentum flux of the mobilizing gas jets. The maximum mobilizing flowrate at incipient mobilization can be predicted from a force balance model on the plug of fibrous particles. Keywords: Fibrous particles; Momentum transfer; Gas jets; Mobilization
1. Introduction Processing vegetable products in fluidized beds is beset by a number of problems, the most obvious being the unconventional nature of the solids with respect to fluidization itself. The materials are often easily degradable due to their biological nature. A few examples of such applications include drying of foodstuffsuch as grains [ 1 ], wheat [2], piece-form fruits and vegetables [3] and rice [4], thermal processing and cooling of cans [5 ] and food cooking using beds of salt or sugar [ 6]. The vegetable product chosen for this work, cut lamina tobacco, is a good example of an unconventional material treated in fluidized beds. Cut lamina tobacco is the main constituent in the cigarette-making process and is obtained at the end of the primary process which includes several steps, including high moisture conditioning, blending, cutting, drying, cooling and mixing, before going to the seeondary process, which is the actual cigarette making. The pitch of the cutting process is variable and in the case of 25 cuts/inch, as for the materials used in this work, the resulting fibrous particles are approximately 0.2 mm thick (the leaf thickness), I mm wide (the pitch of the cutting stage), with lengths varying between 0.5 and 10 cm. Because of folding during the blending stage, the particles are twisted along their long dimension and also have a number of 'kinks' or 'knees', * Corresponding author. 0032-5910/95/509.50 © 1995 Elsevier Science S.A. All fights reserved SSDIOO32-5910(95)O3014-Z
the resulting product being a mass of entangled fibres. The tobacco reaches this stage with a moisture content around 16% dry basis. In principle, the operations between the size reduction step and the beginning of the secondary process could be carried out continuously in fluidized beds. Successful attempts to fluidize fibrous entangled materials have yet to be found in the literature. The design of a suecessful distributor required a trial and error process, testing different possible configurations before a design suitable for tobacco processing could be established. Conventional spouted beds and slotted spouted beds with tangential entry failed to mobilize the entangled material. Severe channelling or excessively violent particle motions were observed in these configurations. This paper presents the development of a mobilizing device for processing cut lamina tobacco particles. This device will contribute to introducing a new type of particulate matter, fibres, into the fluidization field.
2. Experimental materials and procedure 2.1. Physical properties of cut lamina tobacco The material constituting 'Blend 72' was taken from the primary process, just after the cutting machines, dried in rotary dryers and stored. Tobacco, being a biological material, has physical properties which are difficult to quantify exactly
106
R. Legros et al. / Powder Technology 85 (1995) 105-114
Table 1 Physical properties of cut lamina tobacco (Blend 72)
the literature or provided by B.A.T. Group Research and Development Centre.
Properties
Values
Particle density (kg/m3) Particle shape (-)
t~=665(1 + W) parallelepiped: cross-section= 0.2 mm × 1 mm length = L-- 5-100 mm
Particle size (m) (equivalent sphere diameter)
dp= (6-~V)I/3= 7.3 X 10-3LI/3
Sphericity (-)
ff, ffi ~
2.2. Physical description of the mobilized bed distributor
sp
The mobile bed distributor developed in the course of this work is derived from the spout-fluid bed concept and is shown schematically in Fig. 1. The spout-fluidization technique was first introduced by Chatterjee [7]. It was a new contacting device, offering some characteristics of both fluidization and spouting techniques. The distributor has a square configuration with the four walls inclined at 30 ° to the vertical. The lower section is 5 cm square, while the upper section is 15 cm square. The inclined surfaces contain a number of orifices positioned in three horizontal rows, flae lowest row being at the junction of the base and the inclined wall. Each row contains 12 orifices of 4 mm in diameter (3 per side). Each orifice was profiled as illustrated in Fig. 2(a) which also shows details on the spacing of the orifices on one wall of the distributor. The lower section of the distributor contains a single orifice (7 or 10 m m in diameter) positioned on the central vertical axis. The airflow is introduced as two independently controlled and metered supplies from the same centrifugal fan. Because cut lamina tobacco particles cannot be spouted or fluidized, a special vocabulary was needed in order to describe these two gas supplies. The fluidization flow, provided by the high velocity jets from the wall nozzles, was termed the mobilizing flow. It serves two purposes in this device, to loosen and partially disentangle the bed material and to force the tobacco particles towards the central
= 0.0691L I/3
pressure taps tar moblllslng orifices
accelerating orifice
accelerating flow
Fig. 1. Mobilizing device for tobacco particles.
as they are subject to variations from one batch to another. The values given in Table I represent typical values found in
orificeprofilefor 30 cm distributor 4 mm
6mmCF7"A#F7 30 cm
•
X orifice profilefor 15 cm distributor
•
3.5 cm
~
o
o
4mm
-I~
6 mm ~ - - - ~
~1-
0
~'2mm
4 5 ~ 0 "~
I
X
0
~
~-o
I
6.5 cm
im
0,2 : X a o
Ca)
-" 5 c m
-"
Fig. 2. Details of the orificespacing for (a) 15 cm square distributor;(b) 30 cm square distributor.
(b)
R. Legros et al. ~Powder Technology 85 (1995) 105-114
upwards moving region. In other words, it mobilizes the bed material. The spouting flow, provided by the single orifice on the lower section of the distributor, was named the accelerating flow. Its purpose is to promote overall circulation of the bed material, by accelerating the particles in the upwards direction.
.
.
.
.
107
i
.
.
.
.
i
.
.
.
.
i
.
.
.
.
i
.
.
.
.
i
.
I
,
.
.
.
1250
E
t A
2.3. Experimental set up and procedure .e_
The mobile bed distributor was placed below a 1 m high plexiglass column of square section. A cyclone was located downstream of the column to collect any entrained materials. The bed pressure gradients were measured with three pressure taps located on one of the four sloping walls as shown in Fig. 1. An additional pressure tap located at the top of the plexiglass column allowed the measurement of the overall bed pressure drop, which was measured between the lower bed pressure tap and the column pressure tap. All differential pressure measurements were made using a micro-manometer from Furnace Control Equipment, with an accuracy of 0.5 mm of water. Pressure fluctuations were not important during mobilization of the bed; dampening resulting from the pressure tap connections, which consisted of plastic tubing of 3 mm in diameter and approximately 1 m length, was sufficient to obtain steady pressure drop measurements. A typical experiment carried out to observe incipient mobilization conditions began by placing a load of fresh tobacco particles at about 15% moisture content within the distributor, continued by adjusting the accelerating flowrate to the desired value, and then proceeded by increasing the mobilization flowrate while recording the bed pressure drop until mobilization of the bed was achieved. No systematic means of loading the bed was employed during the experiments.
2.4. Qualitative observations of mobile bed operation Qualitative observations of the behaviour of fibrous materials during mobilization were made. The 15 cm square device was loaded with either 50 or 100 g of tobacco, the 100 g charge occupied the entire distributor volume. Increasing the charge by utilizing part of the plexiglass column resulted in unstable operation. By independent control of the mobilizing and accelerating flows, conditions for stable mobilization of the tobacco were investigated.
2.4.1. No accelerating flow When the mobilizing flow is started, the bed moves away from the inclined walls of the distributor. The material is compressed and a cavity appears in the lower region adjacent to the lower orifices. As the flow is increased, the upper bed surface becomes domed and the bed lifts. Suddenly, the surface of the bed breaks and motion is apparent from the central vertical axis towards the walls. At this point, the entire bed becomes mobile, with a rolling circulating pattern. Gas and solids together move upwards in the central core near the bed axis, while solids move outwards in the freeboard and then
750 O
: Start up conditions
[]
: M i n i m u m mobilisntion conditions
~,
: F a s t mebilisntion conditions
O
. . . .
0
I
50
. . . .
I
. . . .
100
I
150
,
,
,
,
I
,
,
,
,
200
250
,
,
,
300
Accelerating flowrate (l/min I
Fig. 3. Phase diagram for mobilizationof tobacco particles (bed load= 100 g).
downwards along the inclined walls. With increasing gas flow, the motion becomes more violent, until eventually the rolling mobilization is disrupted and the charge is transported out of the column. Once mobilization is established, it is possible to reduce the gas flow below the level required to induce the initial motion, without losing circulation. The solid motion suggests that the fibres are largely disentangled.
2.4.2. Both mobilizing and accelerating flows Stable mobilization is possible over a range of flows when mobilizing and accelerating flows are used in combination. The behaviour of the bed is the same as that observed without accelerating flow. The mobilizing flow needed to initiate motion is dependent upon the accelerating flowrate. The relationship between mobilizing and accelerating flowrates at minimum incipient mobilization is also dependent upon the orifice size of the accelerating nozzle. As the orifice size is reduced (from 10 to 7 mm in diameter), the dependence upon the magnitude of the accelerating flow becomes more important. Fig. 3 shows the range of stable mobilization for a bed mass of 100 g and an accelerating flow nozzle of 7 mm in diameter. Start up represents the conditions where the rolling motion of the bed starts, as distinct from minimum mobilization conditions which correspond to the minimum flow conditions to maintain motion. The fast mobilization regime corresponds to excessive entrainment of the bed material. Tobacco particle size analyses before and after 10 rain of mobilization at M-- 1050 l/rain, A = 501/min, with dn= 7 mm and initial bed inventory = 100 g, showed that breakage of particles was minimal. Some dust particles and small sections of lamina were collected in the cyclone, but this material amounted to less than 2% of the initial bed inventory.
2.5. Scale up of the mobile bed The effect of scale up on the mobilizing operation was also examined qualitatively at this stage of the development. The
R. Legros et al. / Powder Technology 85 (1995) 105-114
108
larger scale distributor was geometrically equivalent to the 15 cm distributor, with a 30 cm square top section and a 5 cm square bottom section. Details of the profile and spacing of the mobilization orifices are given in Fig. 2(b). The number of rows of mobilizing orifices was increased to 4, containing, from the lower to the upper row respectively, 2, 3, 3 and 5 orifices of 4 mm diameter. The orifices were not profiled in this distributor in order to investigate the effect on the mobilization behaviour. No scale-up criterion was used and this configuration, which was found by trial and error, gave the best results. The lower section still contained a single accelerating nozzle. A 1 m high column was fitted on top of the distributor. Both distributor and column were of plexiglass to permit visual observations. The behaviour of cut lamina tobacco in the larger distributor was similar to that observed in the smaller distributor. However, the accelerating flow had a noticeably smaller effect upon the mobilizing flowrate necessary to initiate mobilization. In general, operation remained stable at the larger scale. However the maximum bed load that could be mobilized, approximately 500 g, was below that corresponding to the volume of a full distributor. This therefore suggests the existence of a limit in the possible scale-up of a mobile bed distributor.
3. The onset of mobilization
The mechanisms involved during the onset of mobilization of a bed of cut lamina tobacco can be better described with the help of a plot of the bed pressure drop as a function of mobilizing gas flowrate. Such curves were obtained for several bed loads in the 30 cm distributor, and Fig. 4 shows a typical behaviour. The following sequence of events is observed as the mobilizing flowrate is increased. No accelerating flow was used during these experiments; its effect will be seen later.
B
2
"D
tion
Q m
Mobillsing flowrate Fig. 4. Typical pressure drop vs. mobiliNng llowrate curves.
(i) For small mobilizing flowrates, the tobacco behaves as a packed bed, with the pressure drop steadily increasing as the airflow is increased. (ii) The lower region of the bed starts to move away from the walls and a cavity appears. The compressed layers above the cavity act as a higher resistance medium and the pressure drop continues to rise along A-B. (iii) At point B, the bed is supported by the action of the gas flow and the bed starts to expand, causing the pressure drop to fall after this point. This leads to the existence of a peak in the bed pressure drop curve. (iv) After point B, the relationship between pressure drop and mobilizing flow is dependent upon the fibre length of the tobacco or in other words, upon the self-cohesion of the bed. It was observed that for short fibre tobacco, the mobilizing jets push the particles out of their way and start behaving like free jets, thereby diminishing the interaction between the gas and solids. With long fibre tobacco, the particles are entangled and the jets only penetrate to short distances before losing their identity. (v) At a certain mobilizing flowrate, corresponding to point C in Fig. 4, the pressure drop suddenly falls over a very short time interval and the bed becomes mobile. This sharp switch in bed behaviour occurs suddenly and corresponds to a discontinuity in the relationship between bed pressure drop and mobilizing flow. The value of the mobilizing flowrate at point C, called the incipient mobilization flowrate, is very dependent upon the bed history and is not exactly reproducible. (vi) Once the bed is mobilized, the pressure drop remains substantially constant for further increase of mobilizing flow. The excess flow results in more violent bed action and higher bed expansion, without significant effect on the pressure drop. (vii) When the mobilizing flow is decreased, the bed remains mobilized until point C' which corresponds to a lower value of mobilizing flow than point C. This value is called the minimum mobilizing flowrate. The bed pressure drop curve beyond this point depends on the manner in which the mobilization stops. The bed material may collapse in an orderly fashion into a packed bed with no channel. In this case, the bed pressure drop increases sharply as mobilization is lost and then decreases smoothly with reducing mobilizing flow (path C'B'A). More frequently, the bed may collapse in such way that a preferential channel still exists. The pressure drop then remains at a low value, since most of the airflow passes through the channel and decreases slowly with decreasing mobilizing flow (path C'B"A). If mobilization is restarted after the formation of such a channel, the pressure drop does not return to the original path ABC but remains approximately constant up to the point of incipient mobilization. Fig. 5 shows the actual pressure drop as a function of the mobilizing flowrate in the 30 cm square model without accelerating flow.
R. Legros et al. / Powder Technology 85 (1995) 105-114 200
~ i15o I_
/:-.
Q.
.
.o o
Io In
o.",, ~,"o'..
i~
.
'\
IA
."zlsg :z~g .. 3oo g
v
..315,
O
"~. \ . * .
Io
existence of E when the bed is in a mobilized state. The existence of entrainment from high velocity jets in a fluidized bed was also noted by Kvasha [ 8 ] in what he describes as the injected bed. He noted that this entrained gas flow was restricted to the periphery of the bed, within a ring of thickness 25-30 mm, and reported that the entrained gas flow can be up to 13 times the injected flow. Some tracer experiments were also carried out with a bed below the point of incipient mobilization. In this case, the tracer gas was found mainly in the top sampling stream, thereby showing an upwards flow of gas. Therefore entrainment of gas from the freeboard, leading to downward flow near the walls of the distributor, is only present once the bed is mobilized.
400 g
:450g
100
500
1000
1500
2000
2500
3000
109
3500
Mobili$1ng flowrate (llmin) Fig. 5. B e d pressure d r o p m e a s u r e m e n t d u r i n g onset o f mobilization.
4. G a s f l o w p a t t e r n i n m o b i l i z e d
beds
Visual observations through the plexiglass walls of the distributor suggested that the particles were being entrained downwards by a flow of gas, since the particle velocity was much higher than expected if driven by gravity alone. The existence of this entrained gas flow was verified in several ways. The rolling action observed during mobilization was inferred to result from an entrained gas flow, hereafter referred as E, pulling the particles downwards along the distributor walls. Therefore if E is responsible for the stability of mobilization, inhibition of E would result in destabilization of the rolling mobilized flow. Square masks, which consisted of a 15 cm × 15 cm plate (the internal dimensions of the plexiglass column) with a central square hole of different sizes, were constructed. The masks, with different open areas, were lowered down inside the 15 cm square side perspex column towards a mobilized bed. At a certain height, the system became unstable, with the bed suddenly lifting up to the top of the column. The height at which mobilization is disrupted was a function of the open area of the mask. The hypothesis advanced at this stage was that, with E interrupted by the mask, the tobacco particles were no longer entrained downwards at the walls, so that the entire bed moved upwards. A tracer experiment was performed to confirm the existence of E. Five small holes, 3 mm in diameter, were made on one side of the distributor. Helium tracer was injected through the central hole, at a very low flowrate, so that any gas flowing along the walls would immediately entrain the tracer. Gas was sampled from the other four holes, which were located at a distance of 2.5 cm up, down, right and left from the central hole, at a constant volumetric flowrate with a vacuum pump. The relative concentrations of helium in the four streams were determined and it was observed that the gas stream sampled from the bottom point contained more helium than the gas stream from the top point. Therefore the gas near the wall is flowing downwards, which proves the
5. M o d e l l i n g
of incipient mobilization
From the observations of the incipient mobilization conditions, it is possible to identify two predominant events in the bed pressure drop-mobilizing flowrate curve: the peak pressure drop and the incipient mobilization point. For design purposes, these values are of most interest. It was also seen that the onset of mobilization depends upon the bed history and the properties of the tobacco (cohesion of the bed). These variables were difficult to control, particularly for the tobacco properties which changed from one batch to another. It was therefore decided to consider only the case of long fibre tobacco and the first cycle of mobilization, since this combination gave the largest peak pressure drop and the maximum mobilizing flowrate at the point of incipient mobilization. These values can then be considered as the maximum peak pressure drop and the maximum incipient mobilization flowrate.
5.1. Peak pressure drop conditions Before point B in Fig. 4, the plug of tobacco was seen to behave as a packed bed with the bed pressure drop steadily rising with increasing mobilizing flowrate. Assuming that the mobilizing gas jets lose their momentum in a very short distahoe, allowing the airflow to become uniformly distributed over the bed cross-section, the pressure gradient through the bed at any height can be expressed by Ergun's equation:
-dP=Au + BU2
(I)
dr
where U is the superficialgas velocityat height y, and A and B are empirical coefficients.Conditions in the bed below point B can be represented as in Fig. 6. The flowrate in each region is considered to be the sum of the totalgas flow entering below itslower boundary:
Q,=(--~-~t + Q,_ , \ntoud]
(2)
R. Legroset al./ PowderTechnology85(1995)105-114
110
Yi
y
~;~,~,~q,~ ,\ u(y)
BQ2n a)2] } Fei=f((AQi)-l-[(b_l_2yta
,~t,t~i,/~ /
dy
dy
(10)
Yi - l
one obtains:
zone 3,,~
8Q,~ F p i = A Q i ( Y i - - Y i - 1 ) -~" -
ZONOt~
[
1
1 ]
X b+2yi-ltana
where n~ represents the number of mobilizing jets entering the t~hregion. The airflow is assumed to be uniformly distributed so that the velocity at height y is given by:
-
Q, ( b + 2 y tan a) 2
(3)
The pressure drop through each region i can then be obtained by integrating Eq. ( 1) from Yi- 1 to y:
Y~
-AP'= I [AUi(y) +BU~(y) ] dy
(4)
Solving Eq. (4) with Ui given by Eq. (3), one obtains:
]
+ BQ~i F" 1 1 ] 6tan al(b+2yi_~ tan a) 3 (b+2y~tan a ) i (5) The total bed pressure drop is then obtained by adding the contributions fiat'~ APto~ = ~APi
(6)
The total force on the plug of tobacco due to the pressure drop can be calculated from Eq. (1). The force per unit volume of bed is given by the pressure gradient: dF dV
dP dy
(7)
Therefore, using Eq. (1) with: dV= ( b + 2 y tan a) 2 dy
(11)
Fptot= EFpi
(12)
The upward force due to the gas jets can be calculated, assuming that each jet transfers all its momentum. The force transmitted to the plug of tobacco is therefore equal to the momentum flux carried by the jet at the vena contracta section, where the gas is no longer accelerated. Therefore, each mobilizing jet exerts an upward force on the tobacco plug equal to:
FM1= [pu~¢Sv¢] sin a
(13)
where
Yi--I
_Api=AQI I 1 i 2tan a b+2y~-l tan a b+2y~tan
b+2yitanot
The total pressure force, Fvtot is obtained by adding the contributions Fpi:
Fig. 6. Plugof tobaccoat the pointof peakpressuredrop.
U,(y)
-
2tan a
(M/n) svo
Uvc= ~
(14)
The cross-sectional area at the vena contracta, Sv¢, can be calculated from the orifice discharge coefficient, which is obtained empirically from the pressure drop-flowrate curve measured in the empty distributor, since:
ave
Ccm~ ~m
"ffd2m
where Sm= 4
(15)
Substituting Eqs. (14) and ( 15 ) into Eq. (13), and for n jets: 4pM2 sin a
FMI ---- Ccmn2Trd2m
(16)
The momentum flux carded by the gas leaving through the top section of the bed, assuming uniform gas distribution, is:
FM2=pU~S~
M where Uc = ~ A Sc = ~
(17)
Therefore: (8) FM2= pM~
(18)
one obtains for the total force:
H
Fp=J[AU(y) +BU2(y) ] ( b + 2 y tan a) 2 dy
(9)
0 The velocity U is different for different sections of the bed. Therefore, substituting Eq. (3) into Eq. (9):
From a momentum balance on the plug of tobacco as represented in Fig. 6, one obtains for the upward force Fy: Fy= [FM,--FM2]
+Fp
(19)
Substituting Eqs. (16) and (18) into Eq. (19), one obtains:
R. Legros et al. ~Powder Technology 85 (1995) 105-114
4pM 2 sin a
Fy(g)
.
pM 2 . . . . .
[ CcmnTFd2m ] [~] .
.
.
.
.
.
.
~.rpt~)
200
.
.
.
I
.
.
.
.
I
.
.
.
.
i
.
.
.
.
I
.
.
.
.
(20)
At the point of peak pressure drop, the weight of the bed is entirely supported. Thus: Fy(M) = mg
.
111
~,
0
: experiments
Q. 150 f,
--
:
. ~
(21) 100
From Eqs. (20) and (21), it is possible to calculate the mobilizing flowrate necessary to support a bed of cut lamina tobacco, provided the resistance of the bed as expressed by the coefficients A and B are known. These coefficients were obtained from packed bed experiments. It was found that A and B can be calculated from:
[
0
(1 - ~)2
A = 25440 ~
(22)
(l-e) B = 12740 - 7 - -
(23)
for the range of e > 80%. The voidage e was determined from the measured bulk density PB with the tobacco moisture content W as: Pb = Pp( I - e)
Q.
(24)
~
.
.
.
.
I
'
'
I
~
I
i
I
I
I
[
I
I
I
I
I
I
I
I
I
500
200 300 400 Tobacco load (g) Fig. 7. Comparisonbetweenmodel predictionsand experimentalpeak pressure drop measurementsfor differentbed loads. 100
increase in the momentum transfer from the mobilizing jets. From a momentum balance around the plug of tobacco, a similar result to Eq. (20) is obtained, with the upward force equal to the weight of the bed:
with 4pM2 sin a pp= 665(1 +IV)
(25)
Therefore, to estimate the point of 'peak pressure drop' of a bed of cut lamina tobacco of bulk density ~, and moisture content W, the procedure is as follows: (i) Calculate the bed voidage from Eqs. (24) and (25). (ii) Calculate the coefficientsA and B from Eqs. (22) and (23). (iii) Plot the ratio Fy(M)/mg as a function of M, with Fy(M) calculated from Eq. (20). (iv) Determine the value of M for which value
Fy(M) /mg = 1. (v) Calculate the Aptot~ for the value of M found in Eq. (4), from Eq. (5). The coefficients A and B, calculated from Eqs. (22) and (23) respectively, for the conditions Pb = 95 kg/m 3 and W= 16%, were A = 5 7 0 and B=2330. The ratio (Fy(M)/mg) was calculated from F,q. (20) for different bed loads. The points of 'peak pressure drop' were then compared to the measured values in Fig. 7. The close agreement between expected and actual values suggests that the procedure is valid to predict the value of the 'peak pressure drop'.
6. I n c i p i e n t m o b i l i z a t i o n c o n d i t i o n s
For long fibre tobacco, it was observed that the entire bed is supported by the gas flow at the point of 'peak pressure drop'. The bed is then lifted away from the walls of the distributor. From point B (see Fig. 4) to point C, the fall in the bed pressure drop is therefore compensated by the
momentum] [momentum]
-I-
-rag
Fp
•0
[pressure]
f]uxin J-L f,uxout/+Lfor
in/-[w°ight] (26)
Therefore the force due to the pressure drop, from the point of 'peak pressure drop' to the point of incipient mobilization, can be calculated from: J - 4 sin a Fp = D'lg -- ~ I / z L " C - ~ m
11 ~¢'J
( 27 )
It was noted above that, in the mobilized state, the gas flow pattern shows a region of downward flow near the walls of the distributor. This downward flow is due to the entrainment of gas by the mobilizing jets, which behave essentially as free jets when the bed is mobilized. Before mobilization, this downward flow of gas is not present. Therefore, corresponding to the sudden transition in gas flow pattern at the point of incipient mobilization, a certain discontinuity must exist. Examining Eq. (27), it is clear that at a certain value of mobilizing flowrate, the momentum transfer from the jets becomes sufficient to support the weight of the bed. At this point the pressure gradient through the bed becomes zero. Any further increase of the mobilizing flow would result in an unstable situation, since the momentum dissipation from the jets has become greater than the weight of the bed. The jets then start entraining gas from the freeboard and are able to do so since the pressure drop has become zero. Once the mobilizing jets have started entraining gas downwards, the
112
R. Legros et al. /Powder Technology 85 (1995) 105-114
3.~00
.
.
.
.
.
i
. . . .
i
. . . .
i
. . . .
i
ues. The close agreement suggests that Eq. (29) is valid and can be used to predict Mi.m..
. . . .
0 3000
15 cm
[dmbu'°rl I
0
tO
7. Influence of accelerating flow on mobilization
. . . .
2000
t~
._~ 1500 O
E ._ ._~
i
/
I I
- -
0
:
experiments
1000 30 cm distributor
¢J
_c
: model
s00
200
100
300
400
500
Tobacco load (g)
Fig. 8. Comparisonbetween predicted and measured maximum incipient mobilizingflowratesfor differentbed loadswithoutacceleratingflow.
plug of tobacco is subject to a new distribution of forces and the bed is mobilized. Therefore from Eq. (27), the point of incipient mobilization can be predicted as the point where Fp = 0. ThUS:
,Ma[ 4 sin a 1 p /'C-~m--~d2 d2]=mg
(28)
or
Mim--
o~ 4 s i m g
1
(29)
Eq. (29) can be used to predict the maximum of the range of conditions corresponding to incipient mobilization, since it was derived assuming the entire bed to be supported by the gas jets. From visual observations through the perspex distributor walls, it was noted that this complete support of the bed was only possible in the case of long fibre tobacco or small bed load, in which case the bed displays great cohesion so that, before mobilization, the tobacco behaves as a single plug. In most cases, especially in the larger scale model (30 cm square), the plug of tobacco was not completely lifted away from the walls due to either the weaker self-cohesion of the bed observed for shorter fibre tobacco, or the larger bed load. The mobilization started at lower mobilizing flowrates in these cases. This can be explained by the fact that a part of the bed weight is still supported by the distributor walls, thereby requiring lower mobilizing flowrate to fulfill the requirement expressed by Eq. (29), since the effective weight to be supported is lower. Nevertheless, Eq. (29) was compared to the maximum incipient mobilization flowrates that were obtained in the small and large beds for different masses. Fig. 8 compares the experimental and calculated val-
It was seen above that a bed of cut lamina tobacco cannot be mobilized solely by the action of the accelerating flow. However, the circulation of the bed was much improved when the accelerating flow was present. It was also noted that the mobilizing flow necessary to initiate mobilization is dependent upon the accelerating gas flowrate. A first attempt to model the influence of the accelerating flow at the point of incipient mobilization was presented by Legros et al. [9]. The model was based on a force balance leading to calculation of an internal normal stress distribution along the central plane of the bed. The criterion for incipient mobilization was that the bed becomes mobilized once the tension in its upper layer exceeds a certain value. This limiting value was then used to obtain a relationship between mobilizing flow, M, and accelerating flow, A, at the point of incipient mobilization. The model predicted quite well the influence of the accelerating flow in the small 15 cm distributor using a 7 mm diameter accelerating nozzle. For larger accelerating nozzles, the influence of A upon M at incipient mobilization becomes weaker; the model does not predict this behaviour. For the 30 cm model, the predictions were even less reliable: the model predicted a stronger influence of the accelerating flow on the mobilizing flow needed at incipient mobilization, while in fact the opposite behaviour was observed. Therefore, because of several inconsistencies between the predictions and the actual observations, the force distribution model was rejected. Its derivation was nevertheless useful since it provided the first indication of a possible downward flow of gas along the distributor walls which was demonstrated subsequently. A simpler approach was then used to predict the influence of the accelerating flow. Considering Eq. (29), which was used to predict the point of incipient mobilization, and adding the contribution of the accelerating flow to the momentum flux in and out, one obtains:
4pM 2 sin a 4pA2 p(M+A) 2 +- -I-Fp-mg=O Ccmnlrd2m Ccalrd~ d~
(30)
where C~a is the discharge coefficient of the accelerating nozzle. A similar approach was recently used to take into account the contribution of atomizing air in a spouted bed coating process. Choi and Meisen [ 10] added the momentum of the atomizing air to the spouting air and found that the minimum spouting velocity of a shallow spouted bed could be predicted from this simple model. At the point of incipient mobilization, the bed pressure drop is assumed to be zero. Eq. (30) then gives a relationship between M and A which, after algebraic manipulation, can be written:
R. Legros et al. / Powder Technology 85 (1995) 105-114 3500
. . . .
i . . . .
.g~-
t . . . .
Model (equation
--
Experimental data
(31))
3ooo
O
: da=10mrn, 400g
O
: da = 7ram, 400g
A
: da=10mm , 200g : da = 7ram, 200g
2500 20001
V
v '~
1500
: da=10mm, 100g : da= 7mm, 100g
1000
: da=10mm, 50g
._Q. 5oo~ : da= 7mm, 50g o|1 0
i
, 50
, , , , 100
, , , 150
Accelerating flowrate (I/mini
2O0
Fig. 9. Comparisonbetweenmodelpredictionsand experimentalincipient mobilizingflowratesfor differentbed loads as a functionof accelerating flowrateand nozzlediameter(top: 30 cm distributor;bottom:15 cmdistributor).
,M21- 4 sin a p
reaches a value greater than rm = 0.6. However, the agreement observed between the model and the actual results confirmed that the mobilization of a fibrous materials is a 'momentum controlled' process and this is a significant result for further development of the mobilization concept.
8. Conclusions
•
e, l¢
113
1 P 2A [-C-~m--~-~2m ~ ] - ' M [ ~ ' ¢ ] + [ "4pA2
mg]=0
(31)
LCo,,~'~
Eq. (31 ) predicts the correct trends observed from the experimental data, i.e. a larger influence of A in the smaller scale model than in the large one, for identical accelerating nozzle diameter, and a greater influence of A in terms of flowrate as da is reduced. These characteristics of Eq. (31) are shown in Fig. 9. Fig. 9 also compares the predictions from Eq. (31) and actual measurements obtained in both 15 and 30 cm distributors. In general, the model predicts adequately the observed behaviour except for large accelerating flowrate and small accelerating nozzle diameter. In these cases, much lower mobilizing flowrates are predicted at incipient mobilization than are actually required. The observations showed that the value of M does not continuously decrease with increasing A, as predicted by Eq. (31 ), but in fact reaches a constant value. At this point, the mobilizing flowrate at incipient mobilization is no longer dependent upon the accelerating flowrate. This is due to the smaller contribution of the accelerating jet in the momentum balance. At high accelerating jet inlet momentum, the tobacco is pushed out of the jet path and the jet interaction with the solid is reduced. Therefore, the simplistic assumption of instantaneous transfer of momentum from the gas jet to the solids is no longer valid for the accelerating jet at this point. The model seems to deviate largely from the actual measurements when the ratio rm = (accelerating jet momentum/total jet momentum) or:
I
4/:lA2
A simple momentum balance has led to the derivation of a model capable of predicting adequately the two engineering parameters important for the design of a mobilized bed process unit: the peak pressure drop and the maximum incipient mobilizing flowrate. The model also describes the influence of the accelerating flow and gives good predictions of the effects of the accelerating nozzle diameter upon the relationship between M and A at incipient mobilization. However, the model is inconsistent for large accelerating flow, because the assumption of uniform flow above the tobacco plug is too simplistic. This assumption is reasonable when only mobilizing flow is present or at low accelerating flow, since the jets in those cases lose their identity before reaching the surface of the plug. Further development of the model should therefore take into account the fact that the momentum flux carried by the outgoing gas is larger than calculated by assuming uniformly distributed flow above the bed. Determination of the gas flow pattern showed the existence of a downward flow near the distributor walls due to entrainment into the jets. Because of this recirculation of gas, the gas phase can be regarded as perfectly mixed. The particular 'rolling action' of a mobilized bed permitted the same assumption to be made concerning the solid phase. The heat and mass transfer characteristics of the mobilized bed are presented elsewhere [ 11,12]. 9. List of symbols A
B
c~a Ccm d~ d¢ dm d~ F
F~
]
C c a q'/'d~a J
rm-- r4pMZ sin_o(.] = M 2 sin
L C¢~'a~m J
L
A2Ccm?ld2ra
aCca~
(32)
m
M n
coefficient in Ergun's Eq. (1) (kg/m 3 s) or accelerating volumetric flowrate (m3/s) coefficient in Ergun's Eq. ( 1) (kg/m 4) accelerating orifice discharge coefficient (-) mobilizing orifice discharge coefficient (-) accelerating orifice diameter (m) column diameter (m) mobilizing orifice diameter (m) tobacco particle diameter based on sphere of equivalent volume (m) force (N) momentum flux carried by the mobilizing gas flow (N) force due to pressure gradient (N) upwards force from momentum balance (N) length of tobacco particle (m) mass of tobacco (kg) mobilizing flowrate (m3/s) number of mobilizing orifices (-)
114
P Qi
R. Legros et al. /Powder Technology 85 (1995) 105-114
pressure (Pa) volumetric flowrate in each zone of the distributor (m3/s)
rm Sc Sm Sp Svc X y U Uc uv¢ V Vp W
ratio of accelerating jet to mobilizing jet momentums (-) column cross-sectional area (m 2) orifice cross-sectional area (m 2) surface area of a tobacco particle (m 2) vena contracta cross-sectional area (m 2) katharometer' s reading (1/min) upwards vertical distance from the base of the distributor (m) superficial gas velocity (m/s) superficial velocity based on column crosssectional area (m/s) gas velocity based on vena contracta crosssectional area (m/s) bed volume (m 3) tobacco particle volume (m 3) moisture content (kg H20 / kg dry tobacco)
Greek letters bed voidage (-) p gas density (kg/m 3)
Pp
r~
xp
particle density (kg/m 3) ratio of column diameter to orifice diameter (-) particle sphericity (-)
References [ 1] V. Vanecek, M. Markvart and R. Drbohlav, Fluidized Bed Drying, Leonard Hill, London, 1966. [2] H.A. Becker and H.R. Sallans, Chem. Eng. Sci., 13 (1960) 97. [3] D.F. Farkas, M.E. Lazar and T.A. Butterworth, Food Technol., 23 (1969) 1457. [4] R.L. Roberts, R.A. Carlson and D.F. Farkas, J. Food Sci., 44 (1979) 248. [5] G.M. Piggott, Food Proc., 24 (1963) 79. [6] G.F. Sachsel, FoodProc., 24 (1963) 77. [7] A. Chatterjee, Ind. Eng. Chem. Proc. Des. Dev., 9 (1970) 340. [8] V.B. Kvasha, in J.F. Davidson, R. Clift and D. Harrison (eds.), Fluidization, Academic Press, London, UK, 1985, p. 675. [9] R. Legros, C.A. Millington and R. Clift, in K. Ostergaard and A. Serensen (eds.), Fluidization V, Engineering Foundation, New York, 1986, p. 225. [10] M. Choi and A. Meisen, CJChE, 70 (1992) 916. [ l 1 ] R. Legros, Ph.D. Dissertation, University of Surrey, UK (1987). [ 12] R. Legros, C.A. Millington and R. Clift, Drying Technol., 12 (1994) 517.