Fluidisation in a Pulsed Gas Flow

H. W. WONG” AND M. H. I. BAIRD

Department of Chemical Engineering, McMaster University, Hamilton (Canada)

(Received: 23 April, 1970; In final form 15 July, 1970)

ABSTRACT

The effect offlow pulsations on a 4 in dia air-fiuidised

bed of glass beads has been investigated in the fre-

quency range 1 to 10 Hz. It was found that the beds

have a natural frequency which can be calculated

approximately from a model which assumes piston- like behaviour. The shape of the air bubbles rising

through the bed fluctuates synchronously with the

applied pulsations. Tracer studies using helium gas have shown that pulsation can increase the gas reten-

tion time by as much as 51%.

For many years, a problem in the design of gas- lluidised equipment has been the by-passing of the gas phase in the form of ‘bubbles’.’ This has led to extensive investigations of the nature of the bubbles’ and to the development of sophisticated models for fluidised reactors3 While the main effort has been directed towards an understanding of the bubbling phenomenon, various equipment modifications aimed at reducing the effect of the bubbles have also been proposed. 4, 5 These include special distributor de- signs, tapered beds, multi-stage beds, insertion of baffles and packings, and mechanical agitation. In the latter category, vibration and pulsation have been popular techniques.

Various means have been employed, such as vibrating baffle plates6s7 or vibrating the gas dis- tributor 8 or the bed support’*l’. High intensity sound, directed at the bed support, has been found effective.” At frequencies below about 20 Hz, the usual technique has been to pulse the gas flow. 12* 1 3, I4 The main effect of vibration-pulsation is to improve ‘fluidisation quality’. Channelling and bypassing are reduced and difficult systems can be more readily fluidised than in steady conditions. Heat

* Now at Rice University, Houston, Texas (USA).

transfer between the bed and a solid heating surface is greatly improved,7p9*10 as is the conversion in a

spouted-bed reactor. l2 A disadvantage of vibration

is that in some cases 8*1 3 the time-average pressure drop was seen to increase compared with steady conditions.

Understandably, there is considerable industrial interest in the above effects, as shown by many patents, some of which are cited here. ’ 5 - ’ 7 Kobayashi et al. I4 cite further examples of pulsed bed applica- tions.

The theoretical understanding of pulsed and vibrating fluidised beds is still far from complete. Molerus18 has recently proposed a mechanism for stabilisation of particulate fluidisation by vibration, based on one-dimensional particle motions in an incompressible fluid. His conclusion’ ’ confirmed that frequencies of approximately 50Hz are effective in reducing by-passing. However, his model does not account for the fact that much lower frequencies, in the order of 5 Hz, have also been found effective in gas-fluidised beds; 12- I4 nor does it allow for the compressibility of the fluidising gas. Compressibility is known to have a profound effect on the behaviour of gas bubbles in vibrating liquid columns, 1 9,20 and it might also be important in vibro-fluidised beds.

The present investigation concerns the behaviour of pulsed cylindrical gas-fluidised beds in the fre- quency range 1 to 10 Hz. The objective has been to collect new data on bed and bubble behaviour, and to test some simple theoretical models for predicting the ‘natural frequency’ of a fluidised bed. It is felt that this is an important parameter since it determines the response of the fluidised bed to an imposed vibration or pulsation. For the most pronounced effect, the applied frequency should equal the natural frequency. Three experimental techniques have been used; visual and photographic observation, pressure drop measurement, and tracer studies.

104

The Chemical Engineering Journal (2) (1971)-Q Elsevier Publishing Company Ltd. England-Printed in Great Britain

FLUIDISATION IN A PULSED GAS FLOW 105

OSCILLOSCOPE

FLUIDIZED BED

PRESSURE TRANSDUCER

I SOLENOID WATER VALVE MANOMETER

SURGE

TANK

FLOW CONTROL

v ROTAMETERS

FILTERED

AIR

U Fig. 1. Experimental apparatus for studying dynamics of bed.

EXPERIMENTAL EQUIPMENT

The investigation was carried out with a four-inch diameter bed formed in a glass tube. The flow diagram for the pressure measuring and photographic tests is given in Fig. 1, while the arrangement for tracer studies is shown in Fig. 2.

Referring first to Fig. 1, the fluidising air supply is passed through calibrated rotameters with an overall capacity range of 0.5 to 50 scfm. The air enters a 7 ft3 steel drum at about 5 psig pressure, thereby isolating the rotameters from the effects of flow pulsation. The air flow is finely controlled by a needle valve situated just upstream of the timed solenoid valve which provides the flow pulsations. The timing device is capable of actuating the solenoid for periods of 0.03 set to 10.0 set (Eagle Signal Co., Series CA 100). Thus, it was possible to provide square wave flow pulsations at frequencies up to about 11 Hz, above which the response of the solenoid valve led to unreliable operation. As well as frequency, the ‘intermittency’ of the square wave, i.e. the fraction of the period in which flow is allowed to occur, could be independently adjusted.

The air flow from the solenoid valve enters the air space below the bed support, which is also connected to a diaphragm pressure transducer (Pace Engi- neering Co) whose signal can be either observed in an oscilloscope or recorded on a high-speed recorder

(Honeywell ‘Visicorder’). Alternatively, the ‘time- averaged’ pressure beneath the bed could be measured

on a water manometer equipped with a damping

THERMAL

CONDUCTIVITY CELL

VACUUM

TRACER SOLENOID

SUPPORT- HELIUM GAS

DISTRIBUTOR TIM;;;FRATED

PULSING -

AIR

Fig. 2. Experimental apparatus for tracer studies.

106 H. W. WONG AND M. H. I. BAIRD

valve. The bed support in most of this work is a

loo-mesh stainless steel wire screen. In a few cases, Nylon filter cloth was used. The particles used are

glass beads supplied by the 3M Company in the following nominal sizes: 100, 200, 390 and 470 microns. Examination showed that 5 to 20% of the beads were perceptibly non-spherical. The density was quoted as 2.5 g/cm3. The measured minimum fluidisation velocity was compared with the value calculated from Leva’s’ ’ correlation, assuming uniform, spherical particles. The extent of agreement is reasonable, with the exception of the 390 p particle

bed (Table 1).

TABLE 1

OBSERVED AND CALCULATED VALUES OF uMF IN STEADY FLOW

Particle size Minimum fluidking velocity, ft/s (PI (Observed) (Calculatedzl)

100 0.038

200 0.117 0.11 390 0.268 0.35

470 0.404 0448

(62.5%) 390 (37.5 %) 470

Mixture 0.402 0.40

Figure 2 shows the arrangement used in the tracer experiments. The tracer is pure helium, introduced at a flow of about 2 % of the air flow in a step function. The solenoid valve which permits the flow is activated by a time switch which sends a corresponding signal to the high-speed recorder. The helium flow is distributed into the air stream just beneath the bed support as shown. The distributor is a 3 in dia ring of l/S in OD copper tubing provided with 20 equally spaced l/64 in holes opening horizontally. Ten of the holes are directed towards the centre, and 10 are directed radially outwards. The space immediately above the fluidised bed is provided with an impeller, and a bundle of vertical l/4 in plastic tubes is placed about 4 in above the bed. In this way, a perfectly mixed cell is effectively connected in series with the fluidised bed. A continuous gas sample is drawn from this cell through a l/8 in dia stainless steel tube at approxima- tely 40 ml/set giving a sampling time lag of about 0.6 sec. Experiments with different lengths of sample tube suggest that most of the lag was due to the detector cell rather than the length of sample tube. The detector was a thermal conductivity cell (Gow- Mac Instrument Co, model 460). Preliminary testsz2 with step injection directly into the stirred gas space indicated that the assumption of ‘perfect mixing’ in the space was reasonable.

VISUAL OBSERVATIONS

At very low frequencies of flow pulsation, the bed was alternately fully fluidised and quiescent. This phenomenon, also noted by Massimilla et al. 1 3 is not of primary interest in this work. At higher frequencies, above approximately 1 Hz, the bed did not have time to adjust completely to the changes in flow rate, and this state is described as pulsed fluidisa- tion. Massimilla et &.I3 further subdivided the pulsed fluidisation regime into three sub-regimes:

(a) Transition at 1.2 to 2.7 Hz; (b) piston-like fluidisation at 2.7 to 4.8 Hz; and (c) plain fluidisation at frequencies above 4.8 Hz.

In the present work, piston-like behaviour as described by Massimilla13 occurred only in a com- paratively narrow range of operating conditions

under which the pressure could build up very rapidly, i.e. low intermittency, low frequency, and a low volume of the gas space beneath the bed support. At the highest frequencies used in this work (c. 10 Hz), the fluidising gas was better distributed than in steady flow, although piston-like motion of the bed could not be seen. At intermediate frequencies (c. 5 Hz) and high gas rates, some vertical oscillation of the bed was noticeable, but because of bubbling the bed as a whole did not appear to oscillate uniformly. The shapes of the rising bubbles fluctuated, as discussed below. Another interesting phenomenon, noted in occasional cases, was the tilting oscillation of the upper surface of the bed. The frequency of the tilting was not necessarily that of flow pulsation, for example 3 Hz and 6.7 Hz respectively.

PRESSURE FLUCTUATIONS

The pressure fluctuations occurring in steady flow are illustrated in Fig. 3 for a typical case. It will be seen that the mass of beads used, and hence the mean pressure drop, had little effect on the magnitude of

SYSTEM = 37.5 % .4x)p + 62.5 oh, 390~ ” = 1.5 “,‘

BED MASS - 6 lb. - 20 6

I

6lb.

3 lb.

I I I I 3.0 2.0 1.0 00

TIME, lSEC.1

Fig. 3. Instantaneous pressure drop in steady flow,

FLUIDISATION IN A PULSED GAS FLOW

SYSTEM = 8lb, 39OP

107

U

%tlf = 1.8

f = 7.1 Hz f =3.45 Ht f =I,61 Hz I =0.5

4.5 4.0 3.5 3.0 2.5 2.0 1.5 02

I.0 0.5 0

TIME , (SEC) !

Fig. 4. Instantaneous pressure drop in pulsed flow.

the fluctuations. The lowest curve, for a 3 lb mass of beads, shows a definite periodicity at a frequency of about 3.7 Hz. This will be discussed in the section on models for bed behaviour.

Figure 4 shows the pressure record for a typical case of pulsed flow at three different frequencies. Referring to the curve at 1.61 Hz, a sharp positive peak occurs shortly after the start of the gas flow (A). A decaying oscillation of the pressure occurs, until the cessation of gas feed (at B) causes a sharp drop in the pressure. There is then a pressure recovery, due to the falling of the bed which compresses the gas in the space below the support. Without further gas feed the pressure drop would eventually decay to zero, but the renewed gas flow causes the cycle to repeat. A similar effect may be seen at 3.45 Hz, with A and B again denoting the beginning and end of the gas supply period.

The curves at 1.61 Hz and 3.45 Hz are quite similar to those of Kobayashi et a1.14 for the pulsed opera- tion of an annular bed (4 in and 1.25 in dia) of 580 p particles. In their I4 work, however, the secondary oscillations appeared to damp out more rapidly, perhaps because of the extra friction at the central cylinder and the fact that larger particles were used than in the present work.

Returning to Fig. 4, it will be seen that at 7.1 Hz the applied frequency is of the same order as the ‘natural frequency’ exhibited by the bed at the lower frequencies. There are no secondary peaks and troughs, and the pressure amplitude is high. In some tests2 2 the minimum pressure was sub-atmospheric. The nature of the ‘natural frequency’ will be dis- cussed later. The instantaneous pressure fluctuations reported by Massimilla’ 3 do not show any secondary activity, irrespective of frequency. It is thought that

this difference is due to wall friction in their bed, which was a two-dimensional one of thickness 1.5 cm.

Another difference between this work and the earlier investigation’ 3 is the effect of pulsation on the time-averaged pressure drop. Massimilla et al. ’ 3 found that pulsation increased the pressure drop, whereas in Fig. 5 it can be seen that, at high gas velocities, the effect was to decrease the pressure drop. It will be noticed that the curve at the highest frequency (7.14 Hz) approaches that for continuous fluidisation. This is to be expected because of the damping effect discussed above. At the lowest frequency (1.6 Hz) the bed’s behaviour approaches ‘intermittent fluidisation’ in which the time-averaged pressure (for u > 0.5,,) would be one half of the fluidisation pressure, for an intermittency of 0.5. The effect of intermittency is also shown in Fig. 5 for a

constant frequency of 3 Hz. As may be expected, the higher I value gives a curve closer to the continuous fluidisation curve while for lower values of I the

ii 6 I I I 0 05 10 15

i / “,f

Fig. 5. Time-average pressure drop in pulsed and steady flow.

108 H. W. WONG AND M. H. I. BAIRD

mean pressure drop is reduced. This effect of inter- mittency was also noted by Kobayashi et al. ’ 4 who pointed out that for a very long off-period (I + 0)

one would obviously expect a very low time-averaged pressure drop.

It was found that the use of a high-resistance bed support (Nylon filter cloth) damped out the flow pulsations at lower frequencies, and therefore the effects of flow pulsation were small. The stainless steel screen was therefore used in the major parts of the investigation.

BUBBLE SHAPES

As mentioned previously, pulsation resulted in smaller and more uniformly distributed gas bubbles than obtained in continuous flow. The bubble shape was seen to fluctuate with time as illustrated in Fig. 6.

This figure shows part of an oscillation cycle at l/l00 set intervals. Initially (top right) the bubble shape is close to that normally observed. As we move down the right hand column of Fig. 6, the bed as a whole

accelerates downwards and a tongue of wake particles is thrown into the void of the bubble. Eventually (top left) this eruption of wake particles appears to cut the bubble in two. After this point, the upward motion of the bed resumes, and the wake particles fall back (this is not shown very clearly in Fig. 6.). In the case of smaller bubbles, the bubble could not be seen to reform after this wake eruption.

There is an interesting resemblance between the wake eruption effect seen here, and a photograph’ of a water bubble injected into a water-fluidised bed of lead shot. This suggests that the effect of the lead shot system may have been partly due to inertia of the wake particles following the injection of water into the system.

Fig. 6. High-speed cinephotograph of a rising bubble in a pulsed bed, 100 framesisec. Bed mass = 8 lb; U/U, = 1.8; particle size =390~ (62.5%) + 470~ (37.5%); Frequency =

6.7 Hz; Intermittency = 0.3.

SIMPLE PISTON MODEL

The major simplifying assumptions in this model are that the bed oscillates in response to the flow pulsations as a coherent whole, and that the bed support does not contribute to the force acting on the bed. Further, we assume a sinusoidal pulsation of the pressure drop. The piston model may be used to derive the natural frequency of the bed, taking into account the mass of the particles and the compres- sibility of the air in the space beneath the bed support. The analysis is similar to that for an air-

pulsed liquid column, 2 3 and its application to a fluidised bed was first suggested by Davidson. 24 For

undamped free oscillation, it can be shown that

Thus the period of oscillation would be given by:

mV + 7=2x - ( ) yPA2

(la)

Davidson24 suggested that this was a possible explanation for the spontaneous oscillations reported recently by Avery and Tracy.25

A refinement of this analysis is given hereunder and includes the effect of the permeability of the bed, an effect which is of course absent in the case of liquid columns. 23 A balance of forces on the bed, neglecting the effect of the bed support, gives:

A(P - P,,) = m(Z + g) (2)

FLUIDISATION IN A PULSED GAS FLOW 109

The ‘equation of state’ of the gas

Hence,

Pvy = const

- yPz; PC-

V

beneath the bed is:

(3)

(4)

If N is the total number of moles of gas in the gas space, then

Hence

N = (V + AZ) (5)

V

Ai (V + Az)N i,=-- N N2

(6)

The accumulation, I?, is the difference between the molar inflow, QI and the molar outflow, which for laminar flow in a packed bed is proportional to (P - P,):

ti = Q, - k(P - P,,) (7)

The piston model in this form does not allow for fluidisation, in which case the pressure drop would be constant and the gas outflow would be indepen- dent of (P - P,).

Substitution of eqns. (6) and (7) into eqn. (4) gives :

i = yP(v[Q, - k(P - P,,)] - Ai)/(V + AZ) (8)

For relatively small perturbations, we assume that

P P N - and v N ti

V+Az V Hence

P = $ ([e(Ql - k(P - PO))] - Ai) (9)

Differentiating eqn. (9) with respect to time, and substituting for Z from eqn. (2) gives a second- order differential equation in the pressure drop AP(= P - P,) across the bed.

(10) This equation is analogous to that of a linearly damped mass-spring system with an external forcing function in Q,. In the absence of a forcing function, it can be shown that for sub-critical damping the natural frequency is

W” = (I$)+ [(1 - ‘y$)]’ (11)

Thus the natural frequency will be somewhat less than that given by eqn. (1).

As already pointed out, the pressure drop across a fluidised bed is independent of gas flow rate, so k

would effectively increase with gas velocity, i.e., it would be a function of time. The analytical solution

of eqn. (10) for this case would be difficult if not impossible. As an approximation, however, we will assume that k is independent of gas velocity, as it is up to the minimum fluidisation velocity. Thus it can readily be shown that

‘MF A2 kc---

fimg (12)

Substitution of eqn. (12) in eqn. (11) gives:

I _ yhMF2A2 +

4mg2 V 1 (13)

The period is thus:

l- yhMF2A2 +

4mg2 V 1 (14)

The natural period calculated above will always be greater than that from eqn. (la) and particularly so

in highly ‘damped’ systems such as coarse particle beds with a high uMF. For very heavily damped systems, the square bracketed terms in eqns. (13) and (14) becomes imaginary and no secondary oscillations can occur. Friction between the particles and the wall is thought to contribute significantly to damping in previous work.i3*14

Observed natural frequency and period It can be seen from Fig. 4 that in pulsed operation

at low frequencies the pressure drop undergoes secondary oscillations during both the active and inactive parts of the cycle. These oscillations are particularly distinct at low intermittencies.

The half-period of the secondary oscillations was measured as the time between the first minimum AP following shut-off of gas, and the recovery maximum. For example, in Fig. 4 at 1.61 Hz the natural half- period is 0.1 seconds. The periods observed in this way can be compared with the calculated values from eqn. (14), and the simpler eqn. (la).

Referring to Fig. 7, it will be seen that the effect of varying bed mass conforms quite well with eqns. (la) and (14) at low gas flow rates, but at higher rates the period is about 20% greater than predicted. The effective permeability of a fluidised bed, in steady flow conditions, increases with gas flow rate. Thus from eqn. (14) one would expect a lower natural frequency and longer period at high gas rates. Figure 8 shows similar results for coarser particles, for which the difference between eqns. (la) and (14) is more significant. The periods are greater than those shown in Fig. 7, probably due to the greater per- meability of the coarser particle bed, as predicted by eqn. (14).

110 H. W. WONG AND M. H. I. BAIRD

Fig. 7. Effect of bed mass on period of oscillation.

Fig. 8. Effect of bed mass on period for larger particles than in Fig. 7.

According to theory, the natural period is a func-

tion of the gas volume, V, beneath the bed support. In order to investigate this dependence, the volume was enlarged by including an extra pipe section. The results, given in Fig. 9, show that increasing V does

3.0

Fig. 9. Effect of bed mass on period for larger gas space than in Fig. 8.

increase the period but not to the extent predicted by eqn. (14). Even at high gas flow rates, the period is shorter than predicted. No firm explanation for this

is available, although it is thought that the effect of

the bed support may be a factor. The applied frequency and the intermittency were

found22 to have no significant effect upon the natural

period. It may be concluded from Figs. 7 to 9, and the

foregoing discussion, that the pressure fluctuations in

response to a flow disturbance are approximately consistent with the simple piston model. The major shortcomings of the piston model are that it does not take account of the effect of the bed support, and it assumes that the fluidised bed moves as a single

entity. An alternative model has been proposed by Hiby’ 6

to account for the spontaneous vertical oscillation sometimes observed in shallow beds (see Fig. 3). A balance of forces on a single particle leads to a differential equation with a cyclic solution. The natu- ral frequency of the particles (and hence the bed) is

given by

In the present case of a 4 in bed with a voidage of approximately 0.4 and bulk density 1.5 g/ml, the natural period relates to the bed mass in lb as follows

according to the Hiby model:

r z 0.14 m+ (16)

It will be seen from Figs. 7 to 9 that this equation substantially over-predicts the ‘natural period’ as measured in pulsed flow conditions. Moreover it does not predict that there is any effect of the gas space

volume, contrary to eqn. (14). On the other hand, the Hiby model does seem to

be more accurate than the piston model in regard to spontaneous oscillations. In the case of the 3 lb bed with steady fluidisation (Fig. 3) the observed period was 0.27 set, compared with 0.24 set according to the Hiby modelz6 and only 0.069 set according to the piston model.

An intriguing possibility, not investigated in this work, is to operate a fluidised bed under such condi- tions that the ‘Hiby natural frequency’ is the same as the ‘piston natural frequency’. It is possible that in such conditions the bed would oscillate strongly in the absence of any external pulsing arrangement.

In concluding this section, it may be mentioned that Mitkevich lo reported ‘resonant’ frequencies of 23.3 to 50 Hz in beds of depth 20 to 10 cm (respective limits). These frequencies are much greater than those predicted by either of the models already mentioned, and it is thought that this is due to the somewhat special system used, namely calcining sodium bicarbonate, in which each particle emits carbon dioxide and steam.

FLUIDISATION IN A PULSED GAS FLOW 111

Tracer studies TABLE 2

As mentioned at the beginning of this paper, previous workers have found that fluidisation quality is improved by vibration or pulsation. Visually, it has been observed in this work that the bubbles are smaller and better distributed in pulsed than in steady flow. Some preliminary gas tracer studies were also carried out in order to gain a quantitative measure of the effect of flow pulsation.

GAS RETENTION TIMES IN CONTINUOUS AND PULSED FLUIDISATION

Particle _a_ f Z Retention time TG Ratio

system UMF (HZ) continuouspulsed ZG pulsed

(set) 56 cant

Coarse : 3 lb. 470~ 0.8 6.25 ,375 1.32 1.24 0.94 + 5 lb, 1.5 6.25 .375 0.974 1.025 1.05 390.u 1.5 4.6 .5 0.947 1.05 1.08

The technique used has already been described and is similar to that of Gilliland et al.27 except that in their work the tracer flow was suddenly shut off and in this work the tracer flow was suddenly initiated. The resulting F curve is shown, for a typical case, in Fig. 10.

Medium : 9 lb, 200~ 3.0 6.25 .31 1.65 1.855 1.12

3.0 6.67 .30 1.65 2.11 1.28 3.0 5.26 .475 1.65 1.776 1.07

The curve shown has been corrected for the effect of the well-mixed volume, V,, above the bed as follows :

Fine : 10 lb, 100~ 5.3 6.68 .33 4.10 6.16 1.51

5.3 4.35 ,43 4.10 4.57 1.12 7.4 6.67 .33 3.92 4.0 1.04

time’ of the gas expressed as:

z SC 0 - t,)U - ‘3 dt

G= J; (1 - C> dt (18)

c = Cobs + ($2) (17) It should be stressed that a single parameter such

as this is not adequate to describe fluidised bed behaviour,3 but in the present work it does provide a useful index for the effect of pulsation on the F-

curve. Referring to Table 2, it will be seen that in the

case of coarse particles the value of rG for pulsed flow is within &- 8 % of the value for continuous flow. The experimental error in measuring rG at these low values is estimated to be of the same order, so it

Also shown on Fig. 10 are the ideal curves for plug flow and perfect mixing (with due allowance for the sampling lag).

It is notable that the shape of the F-curve is not changed significantly by pulsation; the main effect of pulsation is to shift it to the right. A similar effect was seen in most of the other cases investigated.22 These are summarised in Table 2, with the ‘retention

I I I I I I I I I I.1 -

1.0 -

0.9 -

0.8 -

0.7 -

c 0.6 -

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -

o A MEASURED RESPONSE AA.

. A CORRECTED RESPONSE bf=

GAS RATE = 1.47 SCFM

0

t,=0.6 TIME ,(SEC)

Fig. 10. Step tracer response in continuous and pulsed flow.

112 H. W. WONG AND M. H. I. BAIRD

would appear that pulsation had no significant effect on the value of ro for coarse particles. In the medium and fine particle systems, however, the effect of flow pulsation on rG is significant. The amount of data does not permit a detailed analysis, but three possible reasons can be put forward for the increase of zc by

pulsation. Firstly, it was observed that distribution was improved, leading to smaller bubbles which would therefore rise more slowly through the bed. A second possible effect was the retardation of the rising bubbles by bed oscillation. It has been observed that gas hold-up in gas-liquid bubble columns can be increased as much as 75% by vertical oscilla- tions. ’ 9 The third factor is the fluctuation in shape of the rising bubbles as illustrated in Fig. 6. The periodic eruption of wake particles into the bubble might be expected to enhance gas mixing between the particulate and bubble phases, thereby reducing the by-pass effect of the bubbles.

These suggestions are consistent with the absence

of any significant effect for coarse particles, in which case u/uMF was small enough to allow most of the gas to pass through the particulate phase rather than the bubble phase. Consequently, ro in this case was essentially independent of bubble behaviour. An effect might have been found at higher values of u/uMF but the equipment imposed an upper limit on the gas flow rate.

CONCLUSIONS

The major conclusion of this work is that the piston model gives a fair approximation to the behaviour of a pulsed fluidised bed, even when bubbles are present. The model allows approximate prediction of the natural frequency of the bed, so that the pulsing frequency can be set to match the natural frequency in a given case. The behaviour of bubbles at the wall has also been observed; the bubble shape in the pulsed bed undergoes fluctuations which are thought to be due to inertial effects. The tracer experiments have shown that, in a bubbling bed, pulsation increases the retention time of the gas by as much as

51%. Further work in this area should include a compari-

son between tracer studies and gas-solid reaction conversion in a pulsed fluidised bed, with the eventual aim of obtaining a design method for such reactors.

ACKNOWLEDGEMENTS

We are grateful for financial assistance from the National Research Council of Canada (Grant No. A4600) and the Ontario Department of University

Affairs.

A

c

g

H

I

k

m

N

P

PO

AP

Q, t

t s

u

uMF

u

V

V,

Z

NOMENCLATURE

cross-sectional area of bed

dimensionless tracer concentration

gravitional acceleration

height of bed

intermittency, fraction of time during which

gas is supplied

permeability of bed (eqn. (7))

mass of bed

moles of gas in gas space beneath bed

pressure beneath bed

pressure above bed

pressure drop (= P - PO)

gas inflow

time

sampling lag

superficial gas velocity

minimum fluidisation velocity

molar volume of gas

volume of gas space beneath bed

volume of well-mixed space above bed

bed displacement from equilibrium (piston

model)

Greek letters

Y exponent in equation of state (= 1.4 for air)

z natural period of bed

TG retention time of gas (eqn. (18))

w frequency

0” natural frequency of piston-like bed

Superscripts

. .

1.

2.

3.

4.

5.

time-averaged value

first differential with respect to time

second differential with respect to time

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ZABRODSKY, S. S. Hydrodynamics and Heat Transfer in Fluidised Beds, MIT Press, Cambridge, Mass. 1966.

FLUIDISATION IN A PULSED GAS FLOW 113

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R_&JM&

Les auteurs ont recherchP I’inJluence depulsations de lhir sur un litfluidise’ de billes de verre, duns un domaine

Der Ein$uJ der pulsierenden Striimung auf ein

de fre’quences allant de 1 ci 10 Hertz. IIs observent que luftdurchstriimtes FlieJbett volt Glaskugeln mit einem Durchmesser von 4 inch (IO cm) wurde in dem Fre-

les 1itsJuidisPs possedent une fre’quence propre qui est calculable approximativement Li partir d’un modgle

quenzbereich von l-10 Hz untersucht. Man fund, daj3 die FlieJbetten natiirliche Frequenzen haben, welche

supposant un comportement du type piston. La forme des bulles ascendantesfluctue d’une manikre synchrome

sich durch ein Model1 mit Pfropfen-Striimung niihe-

avec les pulsations du d&bit de gaz. Des e’tudes de rungsweise berechnen lassen. Die Form der Luftblasen, die durch das Bett steigen, schwankt synchron mit dem

traceur, utilisant l’he’lium comme gaz-traceur, ont angewendeten Pulsieren. Spurgasuntersuchungen mit montre’ que la pulsation peut augmenter jusqu’d 51 x, Helium wiesen darauf hin, dap das Pulsieren die le temps de re’tention du gaz. Aufenthaltszeit des Gases bis zu 51% erhiihen kann.

ZUSAMMENFASSUNG