The influence of surcharge level on the flowrate of bulk solids from mass flow bins

141

Powder Technology, 74 (1993) 141-151

The influence of surcharge level on the flowrate of bulk solids from mass flow bins Z. H. Gu, P. C. Arnold and A. G. McLean Department of Mechanical Engineering, University of Wollongong, Wollongong, NSW 2522 (Australia)

(Received October 15, 1991; in revised form October 10, 1992)

Abstract In this paper, theoretical and experimental results are presented which indicate that the influence of material surcharge level can be significant for relatively low permeability materials. Three regions of particle permeability are proposed to generalize the effect of surcharge level. For very fine powders an unsteady condition of particle flow (periodic flow) was observed and it was noted that the lowest flowrate occurring in the unsteady flow can be regarded as the maximum attainable steady flowrate when a feeder is used to diminish the flowrate fluctuation. It it found that the extent of this flowrate oscillation is material level dependent.

Introduction

Based on the experimental results for coarse materials, the effect of surcharge level on the flowrate of bulk solids from mass flow bins has long been considered to be slight [l]. However, as the bulk solid becomes finer, the insiginificant level effect is not always true. For example, considering an extremely troublesome phenomenon of fine material - flooding - the particles can suddenly discharge from a bin at a very high flowrate in comparison with the normal steady state flowrate. Lloyd and Webb [2] reported that the flooding phenomenon occurs when particles become very fine or when there is the addition of very fine particles, say less than 40 pm. Rathbone et al. [3] maintained that this rapid flowrate may approach that of an inviscid liquid, i.e., the flowrate is proportional to G, namely, the flowrate in this casevaries with the surcharge level. It is believed that as particle size varies from coarse towards tine, the effect of surcharge level cannot suddenly jump from insignificant in the case of coarse material to significant in the flooding case. There may be some transition phenomenon in-between. Willis [4], Arnold et al. [S, 61 and Gu et al. [7] observed that the flowrate decreases as the surcharge level increases for fine material. Gu et al. [7, 81 developed two theoretical models for predicting the particle flowrate and the air pressure distribution in the bin generated by flowing bulk solids, which explained that the level-effect phenomenon is related to the air pressure gradients generated by the particle flow. This paper extends this

0032-591Ol93/$6.00

former work by providing more evidence to establish an appropriate description of the influence of surcharge level on the flowrate.

Experimental

Using a double-hopper apparatus, as detailed in refs. 5 and 7, a number of experiments were conducted to examine the effect of surcharge level on the flowrate of bulk solids from mass flow bins. The geometry of the test bin is listed in Table 1. The bulk solids used and the actual surcharge levels applied in the two test bins are listed in Tables 2 and 3. In Tables 2 and 3, level 1 to level 4 indicate the different material heights in the vertical section of the test bins (measured from the transition section of the bins). Sand mixtures MDl, MD2, MD3 and MD4 were specially made to examine the effect of particle size distribution on the flowrate, having different particle size distributions but the same median particle size (200 pm) PI. TABLE 1. Test bin details Outlet 1

Parameters Hopper half angle CY(degree) Diameter of outlet D, (m) Diameter of cylinder D (m) Range of surcharge H (m)

Outlet 2 15

0.044 5

0.02

0.145 0.0 to 0.66

0 1993 - Elsevier Sequoia. All rights reserved

142

TABLE

2. The actual surcharge

level of solids in the test bin with 0.020 m outlet

Bulk solids

Co [7, 91 x 1o-9 (m’ N-’ s-‘)

Level 1 (m)

Level 2 (m)

Level 3 (m)

Level 4 (m)

PVC Sugar Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand

1567 21357 6518 4354 2328 1536 1156 298 246 2228 1054 576 1336

0.010 0.010 0.010

0.220 0.220 0.220 0.250 0.250 0.250 0.220 0.220 0.230 0.230 0.230 0.230 0.230

0.480 0.480 0.480 0.530 0.530 0.530 0.480 0.480 0.500 0.500 0.500 0.500 0.500

0.590 0.610 0.610

powder Ml M2 M3 M4 M5 M6 M7 MD1 MD2 MD3 MD4

TABLE

3. The actual surcharge

Bulk solids

PVC Sugar Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand

powder Ml M2 M3 M4 M5 M6 M7 MD1 MD2 MD3 MD4

(no test) 0.010 0.010 0.010 0.010 0.010 0.010 0.010

(no test) 0.610 0.600 0.600 0.600 0.600 0.600 0.600

level of solids in the test bin with 0.0445 m outlet

Co [7, 91 x 1o-9 (m4 N-’ s-r)

Level 1

1567 21357 6518 4354 2328 1536 1156 298 246 2228 1054 576 1336

0.010 0.010 0.010

(m)

(no test) 0.010 0.010 0.010 0.010 0.010 0.010 0.010

The steady state flowrates obtained, corresponding to the surcharge levels in Tables 2 and 3, are shown in Figs. l-3. Figures l-3 show the variation of mass flowrates with H/D ratio for different bulk sulids. From an examination of Figs. 1 to 3 the relationship between measured mass flowrate Qp and H/D ratio can be considered as a linear function over the range of H/D ratios examined in the experiments, except for Sand MD3 from 0.0445 m outlet which is discussed later (Gu et al. [7] predicted that the effect of surcharge level becomes weaker as the surcharge level increases). For the fine materials tested, increasing the material level caused the flowrate to decrease. This decreased flowrate is due to the presence of adverse interstitial air pressure gradients which increase in magnitude as the H/D ratio increases [8]. The significance of these pressure gradients for fine materials was identified by Nedderman et al. [l], Arnold et al. [5, 6, lo] and Gu

Level 2 (m)

Level 3 (m)

Level 4 (m)

0.310 0.220 0.235 0.235 0.190 0.215 0.220 0.220 0.270 0.270 0.270 0.270 0.270

(no test) 0.480 0.535 0.535 0.510 0.525 0.480 (no test) 0.480 0.530 0.530 0.530 0.530

0.570 0.600 0.610 (no test) 0.610 0.600 0.630 0.660 0.660 0.660 0.660

et al. [7]. Hence for fine materials subject to unhindered gravity discharge from a bin, the lowest material level is associated with the highest discharge rate. From the experiments reported, it can be seen that the extent to which the mass flowrate depends on the H/D ratio varies with the outlet size of the bin and the particle size of the bulk solids. For the coarse solids the effect of level is insignificant, while for the finer solids, the effect of level becomes significant, especially when the solids are discharged from the hopper with the larger outlet. Specifically, for Sand M5 discharged from the 0.0445 m outlet, the flowrate reduced 22.5% as the H/D varied from 0.07 to 4.2. In addition, the flowrate of PVC powder from the 0.0445 m outlet reduced 52.5% as the HID changed from 0.07 to 3.93. In comparison, when Sand M5 and PVC powder were discharged from the 0.020 m hopper outlet, the flowrate decreased 13.5% and 20.9% respectively, as the HID varied from 0.07 to 3.93.

A _

s

3

3

0.16

0.10 0.08

w

0.04’

’

’

’

H/D

(a) 0.9)

.

I

.

I

’

’

2

1

0

’

.

3

’

i 0.06 4

m

4

.

I

0

5

Ratio

l SandM2 A SandM3 X Sand M4 + Sand M5 1

(4 -

I

-

2

3

4

5

4

5

HID Ratio

1

c

0.9

:! 3

0.8

E”

0.7

3 1 2

0.6 0.5 0.4

0 @I

1

’ 2 H/D

3

4

0.3

5

Ratio

0

@I

1 &D

Rati:

Fig. 1. Measured flowrate (Q,) vs. H/D ratio for PVC pqwder and sugar: (a) 0.020 m outlet; (b) 0.0445 m outlet.

Fig. 2. Measured flowrate (Q& vs. H/D ratio for.Sand Sand M5: (a) 0.020 m outlet; (b) 0.0445 m outlet.

MJ to

The extent to which the mass flowrate depends on the H/D ratio is also influenced by the particle size distribution. Sand MD1 to Sand MD4 had the same median particle size but different size distributions, however, from Fig. 3 it is seen that the effect of level on the flowrate is different for each of these solids. This confirms that the use of median particle size alone is not sufficient to describe the size of solids mixtures; permeability is a more suitable parameter to describe the flow behaviour of the bulk solids [7]. From Fig. 3(b) it is noted that the flowrate variation of Sand MD3 crosses that of Sand MD2 at high surcharge level (H/D= 4). As a result when H/D <4 the flowrate of Sand MD3 is less than that of Sand MD2 while when H/D > 4 the flowrate of Sand MD3 is greater than that

of, Sand MD2. The postulated explanation for .this seemly high flowrate is that when Sand MD3 is discharged from the hopper with 0.0445 m outlet at high surcharge level, the negative air pressure gradient generated at the hopper outlet is high enough to introduce the fluidisation effect at the hopper outlet, resulting in the higher flowrate. More details of this effect will be presented below. As described by Gu et al. [8], both theoretical and experimental results on air pressures indicated that the negative air pressure increases with increasing surcharge level; Willis [4] found that the negative pressures depend on the hopper outlet size; Crewdson et al. [ll] provided evidence of the variation in the negative air pressures for different sand mixtures; Head [12] and Spink and

144

_

0.18

4

0.16

A4 v

0.14

F

0.12

0

0.10

E

0.08

1FJ E

OLm 0.04

fine sand (which roughly corresponds to the Sand M5) Beverloo et al. [14] reported that the dependence of flowrate on material level is insignificant. The present results for the Sand M5 show a significant dependence on material level for both outlet sizes. It is felt that there are two principal reasons for the difference. l Beverloo used outlet sizes of ranging from 2.5 to 10 mm compared with 20 mm to 44.5 mm in the present work. l Beverloo’s bin had a flat bottom which caused funnel flow and prevented the establishment of significant negative pressures in the converging flow channel. Such a situation can be compared with a hopper having semipermeable walls. For this situation the flowrate would be friction controlled not air pressure gradient controlled.

0.02 IlM “.W

0

1

2

3

H/D

(a) 1.2r

*

,

.

,

4

5

/

,

Comparison predictions

Fbtio .

,

*

,

.

-1 at SandMD4 1 0.0

I 0

@I

1

.

I

.

2 HID

I 3

.

I 4

. 5

Ratio

Fig. 3. Measured flowrate (QJ vs. HID ratio for Sand MD1 to Sand MD4: (a) from 0.020 m outlet; (b) from 0.0445 m outlet.

Nedderman [13] examined the flow of fine sand mixtures from a conical hopper and plane flow hopper fitted with variable orifice diameters respectively. In agreement with these previous findings, the present experimental observations indicate that the negative pressure gradient retarding the flow of a fine bulk solid will increase with increasing hopper outlet size or with increasing surcharge level. A comparison of present experimental results with others found in the literature is tabulated in Table 4 [5]. This comparison has been restricted to situations where the bins had either conical hoppers or flat bottoms. From Table 4, it is obvious that the effect of material level in the bin on the flowrate is insignificant for coarse solids. It is interesting to note that for their

of experimental

results with theoretical

A further comparison of experimental flowrates was made with theoretical predictions [7], resulting in the general variations plotted in the QP- C, diagram, as shown in Fig. 4. In Fig. 4 both experimental and theoretical results demonstrate that the flowrate of fine material flowing from a mass flow bin decreases as the surcharge level increases. This effect of material level depends on the outlet size of the bin and particle size distribution. For material with higher permeability, the effect is negligible. From Fig. 4, it is appropriate to delineate the conditions when material level has a significant effect on flowrate using a similar concept to the critical permeability discussed in ref. 15. The value of C, where material level is insignificant is rC,i (y> 1, as H/D 2 0); y depends on the bin geometry, the surcharge level and particle flow properties. For sand mixtures measured in experiments, y is about 2 as H/D ~4.5. This is confirmed by referring to Tables 2 and 3 where it is seen that the Sand Ml, the only sand whose flowrate was not affected by material surcharge level in the experiments, had a permeability constant of about 6500 X 10m9 (M4 N-’ s-l), whereas the C,-riin this case is about 3500x 10V9 (M4 N-’ s-l).

Problems which may be caused by increasing surcharge level

the

The generation of the air pressure gradient requires bulk solid flow. In particular the air pressure gradient at the hopper outlet can be regarded as proportional to the particle flowrate. However, it is also noted that the air pressure gradient increases with a decrease in

30-370

65-211

10&300

Hoppered bins

Flat bottom bins

Flat bottom bins

Rose et al. (1959)

Brown et al. (1959)

Hoppered 10-610

- 1000-2440

Hoppered bin

Smith (1978)

This work

H/D-3, 5 (1000-2300)

Flat bottom bins

McCabe (1974)

(1W

Beverboo et al.

25-100

(-)

H

Flat bottom bins

Bins used in experiments

145

582

330, 460

50-100 50-150 150

175

25-170

57, 100, 165

D (mm)

of the results with other previous works [5]

Fowler et al. (1959)

Researchers

TABLE 4. Comparison

20 44.5

75

25, 33, 42, 48

2.5-10 2.5-10 2.5-5

4

9, 12

13, 19, 25, 51

Do (mm)

0.129 0.138 0.307

Sugar, sand, alumina, PVC powder

0.054-0.145

0.05-0.1 0.017-0.1 0.017-0.03

0.023

0.053-0.470

0.0784889

D,,lD

Shirley phosphate (140 W)

1.3 mm sand 2.5 mm sand 5.8 mm sand

93-210 pm sand 210-300 pm sand 300-590 Km sand

560 pm sand

1.32 mm steel balls

918 w sand 1.924 mm rape 4.128 mm wheat 1.095 mm sugar 3.156 mm rice

dm or dp materials tested

co > 2Cd co < 2C&

0.0019

0.027-0.232

0.015-0.06 0.026-0.104 0.09-0.18

0.1396

0.1124-0.147

0.018-0.322

40 (or d,YDo

insignificant significant

significant

insignificant

independent

independent

HID, > 2.5 independent

insignificant

Effect of HID results

146

1.4

1 Predicted ) Measured 1.2

0.4

0.2

I

1000

2ooo

3oorJ

4ooo

5ooo

6@4IO

00

Permeability Constant C 0 *1O-9 (M4 N-l Set-l) Fig. 4. Comparison

of experimental

results with theoretical

results for Sand mixtures flowing from 0.0445 m outlet.

bulk solid permeability. For bulk solids with very low permeability, the very high pressure gradients generated near the outlet of a bin reduce the flowrate dramatically and may cause difficulties in controlling the particle flow, if, for example, fluidisation occurs. For sufficiently fine material (with low cohesion), the air pressure gradient generated at the hopper outlet by the flowing bulk solid may be sufficient to fluidize the particles at the hopper outlet. The fluidised particles contain more voidage and provide some relief to the high negative pressure gradient. The reduction of the air pressure gradient results in an increase in particle flowrate, and may even result in flooding. Provided the flooding is not too severe, the negative pressure gradient gradually builds up again until fluidisation occurs again; no steady state flow results. The resulting periodic flow behaviour is described schematically in Fig. 5. Evidence of periodic flow was observed by Miles et al. [16], as shown in Fig. 6. Since a higher material level results in a greater air pressure gradient being relieved by the fluidising effect, this periodic phenomenon is aggravated by increasing the surcharge level. In the present investigation it was observed that the flow of Sand MD3 from the 0.0445 m outlet at higher surcharge level was slightly affected by this flooding phenomenon. For Sand M6 and Sand M7 with lower permeability, this effect occurred even for flow from the 0.020 m outlet; Fig. 7 shows the effect of material level on the flowrate of

i

Buildup of the Hiph,t’rere;treGradient

Releaseof the HighPressureGndient at Outlet 9

f

.

:

..$-&G+fQ--t+... 4

Pluidisation :.....................................,..,..,..................................~. Fig. 5. The periodic

flow behaviour

for fine material.

Sand M6 and Sand M7 flowing from the 0.020 m outlet. In this figure, the pseudo-steady flowrate represents a mean flowrate. From Fig. 7, it can be seen that for Sand M6 flowing from the 0.020 m outlet the variation of flowrate with the material level HID ratio is similar to that for Sand MD3 flowing from the 0.0445 m outlet, Fig. 3; flowrate decreases at lower surcharge levels then tends to increase at higher surcharge levels due to the fluidisation effect. The only difference between these two cases is that when H/D is greater than about 2.7 (point a, Fig. 7) the flowrate of Sand M6 is greater than that at the lowest surcharge level, while the flowrate of Sand MD3 at the lowest surcharge level is the highest flowrate for the range of surcharge levels tested. The difference

147

10

40

60

80 TIME (1)

Km

120

140

I60

Fig. 6. Weight variations for discharge of 55 Frn calcite (adopted from Miles et al. [16]). _

0.07

I

I

I

I

Inviscid Flowrate Curve Fitted for Sand M7

confirmed that the flow of Sand M7 was steady at the lowest level (at level 1, H/D=O.O7) with the flowrate of Qlow (approx 0.2 kg s-l) but unsteady at higher surcharge levels with the flowrate varying between Qlow and Qhigh,where Qlow is about 0.2 kg S-’ and Qhigh is about 0.6-0.7 kg s- ‘. This suggests that Q,_,, is the flowrate unaffected by fluidisation and QhiBh is the fluidised flowrate. In order to diminish the fluctuations during flow and obtain a steady flowrate, a small variable speed belt feeder was designed to control the attainable steady flow. A tachometer was used to measure the belt velocity. The distance between the belt and outlet of the test bin was maintained at 10 mm. The observations were carried out to focus on the effect of feeder belt velocity on the flow behaviour of Sand M7 from the 0.0445 m hopper outlet. The subsequent flowrate variations obtained for different belt velocities are plotted in Figs. 9(a) to (f). These results show that reducing the belt speed reduces the extent of unstable flow. In particular when the belt velocity was lower than a critical value, steady flow occurred. For the flow conditions observed, this critical value corresponded to a flowrate of 0.2 kg S -’ which was the value of QioWin Fig. 8. This suggests that Qlow is the maximum attainable steady flowrate for this particular bin configuration and material.

0.03

0.02

0

I

I

1

2

I

HiD

I

I

3

4

I 5

Classification of the effect of the surcharge level on the flowrate

Ratio

7. Pseudo-steady flowrate affected (from the 0.020 m hopper outlet).

by the surcharge

level

in these trends can be explained as the fluidising effect at higher material levels being more significant for the Sand M6 case. However, from Fig. 7, the variation of flowrate for Sand M7 gives evidence of a typical flooding phenomenon, the flowrate increases as the H/D ratio increases. Rathbone et al. [3] suggested that the flowrate of fine powder during flooding can be estimated by an inviscid flowrate model where the flowrate is proportional to the square root of the height of material in the bin (measured from the hopper outlet). To validate this prediction the inviscid flowrate, fitted from the experimental data for Sand M7, is also plotted in Fig. 7 where it can be seen that the variation of flowrate with surcharge level for Sand M7 is close to the inviscid flowrate curve. Hence the flowrate of the material predicted assuming inviscid fluid behaviour is expected to be the average flowrate from the hopper. For periodic flow, the particle flowrate varies between two values, Qlowand Qhigh. Figure 8 shows the flowrate variations of Sand M7 discharging from the 0.0445 m outlet at different surcharge levels. From Fig. 8, it is

The effects of surcharge level on the flowrate is summarised in Fig. 10. This summary is facilitated by grouping the bulk solids into three regions A, B and C. The flowrate of a bulk solid with permeability constant in Region C is independent of the surcharge level, while the flowrate of bulk solids with permeability constants in Regions A and B will be affected by the material surcharge level. In particular the flow of a bulk solid in Region B is steady and the flowrate decreases with an increase in surcharge level; the flow of a bulk solids in Region A is unsteady and the flooding phenomenon may occur, i.e., the flowrate increases as the surcharge level increases. The b-b line is a criterion to determine whether the effect of surcharge level is significant or not. This criterion was assumed to be rC,,i (y > 1) above. The a-a line is a criterion to distinguish whether the flow is steady or unsteady depending on the surcharge level. These two critical lines depend on bin geometry and particle properties. According to the observations discussed in this work, the classification of the flow for all sand mixtures is listed in Table 5. However, to describe the flow in Region A or determine the criterion a-a line quantitatively, further work is required.

148 I.$-, _ z ;

1.4

, . ,

‘, . , . , . , , , , , , , . . . I .

-

I.)I.2

-

At Level 1

0 I.It l.E.o z .a2 .l-

3 i2 4.

.G z5

.S-

d

.4.3

.2

8.

S.lB.lS.29.2S.SS.1S.4B.4S.SB.SS.CO.SS.?B.?S.SB.BS.SS. TIME

8.

5.

IO.

IS.

20.

(Saeondrl

2s.

SB.

35.

4B.

4s.

51.

IS.

SB.

1.1.1.1.l.1.1.1.1.1.1. I. IB. IS. 2B.

TIME 1Ssconds)

TIME

IS.

11.

IS.

(Socondtl

0.

4S.

IS.

IS.

0.

Fig. 8. The flowrate variation plots for Sand M7 discharging from the bin with 0.0445 m outlet.

Conclusions

Region B: bulk material: particle flow:

For fine materials, the effect of surcharge level on the particle flowrate is due to the presence of the negative interstitial air pressure gradient. The extent to which the flowrate depends on the material surcharge level varies with the outlet size of the bin and the property permeability which includes the effect of particle size and particle size distribution. l This investigation suggests that particular attention should be paid to the influence of material level on the flowrate when a fine material is being discharged. In this study, three regions of particle permeability, as indicated in Fig. 10, have been proposed to generalize the effect of surcharge level.

l

Region A: bulk material: particle flow: effect of surcharge level:

effect of surcharge level:

Region C: bulk solids: particle flow:

effect of surcharge level: very fme or with very low permeability unsteady with flooding from bin likely significant; the flowrate increases with increasing material surcharge level.

fine or with low permeability steady, flowrate increases with increasing permeability of the bulk solids. significant; the flowrate decreases as the material surcharge level increases; the lower the permeability, the more significant the effect of surcharge level on flowrate becomes. coarse or with high permeability steady; the flowrate depends on the bin geometry and bulk density of the particulate material and is independent of the permeability of the bulk solid. insignificant.

The boundaries between these regions depend on the bin geometry, material surcharge level and bulk solid properties. The selected criterion for assessing the significance of the effect of surcharge level (the boundary between Region B and Region C) is $cri (y > 1 as H/

149

8

0.8

B 0

0.6

No Feeder

= 0.638mlsec

$ 3 Ii 1 9) E:

Q low

0.4

m-w- J __-_____I

0.2

0.01 0

20

40

60

80

100

“I”““““‘]

0

120

Time (second)

20

40

60

80

100

120

Time (second)

(b)

l.O( = 0.247 mlsec

= 0.367mlsec

. 0.0 p 0

20

40

60

80

100

l.01 .,

.,

2%

2

rzJ

g E

Q low

0.4-

’ 20

n

’ 40

*

’ 60

60

80

100

120

.

,

.

,

.

,

.

,

.

,

.

,

= 0.200m/see

6% 0 0.6-

0

40

Time (second)

1.01

.,

ii o'8.

0.01 *

20

Cd)

.,.,.I

‘belt

2

0

120

Time (second)

w

.

’ 80

-

’ 100

’

0.6

-

Vbe*t=0.193(m/sec)

-

V,,~,=O.l08(m/@

0.4

J 120

0

40

80

120

160

Time (second)

200

240

Time (second) @I 0 Fig. 9. Flowrate variations with different belt feeder velocities for Sand M7 from 0.0445 m, hopper outlet. (a) Without feeder; (b) With belt feeder velocity of 0.638 m s-‘; (c) With belt feeder velocity of 0.367 m s-‘; (d) With belt feeder velocity of 0.247 m s-‘; (e) With belt feeder velocity of 0.200 m s-‘; (f) With belt feeder velocities of 0.193 and 0.108 m s-‘.

150

bl Increase in Surcharge Level

Region C Steady Flow Independent of Surcharge Level

-7

f

Region A Unsteady Flow or Flooding Dependent on Surcharge Level

1

Permeability Constant C 0

-

Fig. 10. The general description of flowrate affected by surcharge level.

TABLE 5. The classification of the flow for all sand mixtures used in experiments in terms of the effect of material surcharge level Sand mixture

Permeability constant C, x 1o-9 (M4 N-r s-‘)

Sand M7 Sand M6

246 298

Sand MD3

576

Sand Sand Sand Sand Sand Sand Sand Sand

MD2 M5 MD4 M4 MD1 M3 M2 Ml

1054 1156 1336 1536 2228 2328 4354 6518

In flowing from 0.020 m outlet case

In Aowing from 0.0445 m outlet case

Region A Region A Region A close to a-a line Region A close to a-a line

,

Region B Region B

Region C Region C

D,O). From the experimental results this criterion is considered to be about 2Cmi for typical values of Hl D equal to approximately 4.5 where the C-i is estimated by the method provided by Arnold and Gu [15]. However, since only two bin outlets (Do = 0.02 m and 0.0445 m) were used in experiments, further work is required to ge,nerate an empirical equation to evaluate y or flui*

l The unsteady flow associated with a high surcharge level has two distinct flowrate values, Q,OWand Qhifi, where the QhiBhis the fluidised flowrate and the Qlow is the flowrate unaffected by fluidisation. The value of Qlowis also the maximum steady flowrate attainable when a feeder is installed below the hopper outlet to eliminate the tluidisation effect.

List of symbols bulk solid permeability constant (at lowest compaction), x10-’ (m4 N-’ s-l) CCTi critical permeability constant where insignificant effect of negative air pressure gradient on flow rate occurs (at surcharge level H/D =O) D diameter of vertical section of the bin, m H material surcharge level, as defined as the height of bulk solids in the vertical section of the bin, m H max tota!..material height in the bin, as measured from the hopper outlet, m QP flowrate of a bulk solid, kg s-l Vbelt belt feeder velocity, m s-’ Greek letters bulk density of particles at lowest compaction, kg mm3

PO

151

Y

coefficient depending on the surcharge level, bin geometry and particle flow properties

References R. M. Nedderman, U. Ttiaiin, S. B. Savage and G. T. Houlsby, Chem. Eng. SC& 37 (1982) 1597. P. J. Lloyd and P. J. Webb, Powder Technol., 51 (1987) 125. T. Rathbone, R. M. Nedderman and J. F. Davison, Chem. Eng. SC& 42 (1987) 725. G. J. Willis, Interstitial gas pressures during flow of simple bulk solids from a plane flow bin, 77resi.r (BE.), University of Wollongong, 1978. P. C. Arnold and Z. H. Gu, Rot. Z7aird Int. Con$ on Bulk Materials, Storage, Handling and Transportation, Newcastle, 1989, p. 196. P. C. Arnold, Z. H. Gu and A. G. McLean, Proc. Part II at 2nd World Congress Particle Technology, Kyoto, Japan, Sept., 1990, p. 2.

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