On the mixing of granular materials in a screw feeder

POWDER

TECtiNOlOGY Powder Technology

ELSEVIER

On the mixing of granular

80 (1994) 119-126

materials

in a screw feeder

Wei-Ren Tsai, Chun-I Lin* Department

of Chemical

Engineering

National

Taiwan Znsfihde of Technology,

Taipei 106, Taiwan

Received 2.0 August 1993; in revised form 18 April 1994

Abstract Experimental studies on the mixing of granular materials in a screw feeder were conducted in this study. It was observed that the granular flow in a screw feeder is similar to plug flow. The degree of mixing of the screw feeder was found to be increased by either (1) increasing the shaft diameter, (2) decreasing the pitch, (3) increasing the flight diameter, (4) increasing the flight thickness, (5) increasing the angle between the upper feeder and the lower feeder, (6) increasing the length of the lower feeder, or (7) decreasing the rotational speeds of the upper screw and the lower screw. The degree of mixing was also increased by employing a screw with paddle and decreased by employing a tapering shaft screw, a cut-flight screw or a steppedflight diameter screw. The degree of mixing was also found to be reduced if the ratio of rotational speeds of upper screw to lower screw was either too low or too high. The degree of mixing was found to increase whenever the feed order of a large granular material following a small one was inversed. The degree of mixing of the screw feeder fed with two different materials was higher than that with the same material. Keywordx

Degree of mixing; Granular materials; Screw feeder

1. Introduction Screw feeders are usually employed in transporting a granular or powder material from one place to another. The flowrate [l-5] through the screw feeder and the torque [2, 4-61 needed to rotate the screw have been the objects of research efforts in recent years. The screw feeder is used in industry today as a reactor for the production of iron [7, S]. The degree of mixing in the reactor is one of the important factors determining reactor performance. Previous literature on the degree of mixing in a screw feeder is unfortunately limited [4, 9-121. The degree of mixing of granular materials in a screw feeder is examined in the present study using different screws and under different operating conditions.

2. Experimental 2.1. The screw feeder The experimental set-up for the present study of granular material in a screw feeder is shown sche*Corresponding author.

0032-5910/94/$07.00 0 1994 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94102839-G

matically in Fig. 1. The upper and lower columns were constructed of cast iron with 0.062 m inside diameter. The upper screw was manufactured of acetal and the lower one of carbon steel. The upper screw and lower screw were rotated by separate motors using the attached gear boxes. Fourteen screws with different dimensions or different shapes, as listed in Table 1, were used in the experiments. The shapes and dimensions of some special screws are depicted in Fig. 2. The upper screw and the lower screw for each experimental run were identical except that the upper screw length was 0.45 m and the lower screw 1.00 m. Additional lengths of lower screw of 0.6 m and 0.8 m were also employed whenever the effect of the length of screw was studied. The angle between the two screws was normally 30”. However, angles of 45” and 60” were also used if the influence of the angle between two screws was examined. Tachometers were employed for determining the rotational speeds of the screws. The granular material was fed through a funnel attached to the upper screw and left the feeder from the right end of the lower screw. 2.2. Granular materials Steel balls of four sizes, 16-18 mesh, 18-20 mesh, 20-25 mesh and 30-35 mesh, as well as alumina balls

120

K-R.

Fig. 1. Schematic diagram of experimental 7, motor; 8, bearing; 9, tachometer. Table 1 Conditions” Run

and equivalent

number

Screw

number

Shaft

diameter

number

Tsai, C.-I. Lin I Powder Technology 80 (1994) 119-126

set-up.

of tanks

1, steel tube; 2, upper

for experimental

screw; 3, lower screw; 4, acrylic hopper;

5, coupling;

6, torque

meter;

runs

1

2

3

4

5

6

7

8

9

10

11

12

13

14

1

2

3

4

5

6

7

8

9

10

11

12

13.

14

0.030

0.025

0.040

0.030

0.030

0.030

0.030

0.030

0.030

Tapering

0.030

0.030

0.030

0.030

0.044

0.044

0.044

0.056

0.068

0.044

0.044

0.044

0.044

0.044

0.044

0.044

0.044

0.022

0.056

0.056

0.056

0.056

0.056

0.052

0.054

0.056

0.056

0.056

0.056

0.056

Stepped

0.056

0.006

0.006

0.006

0.006

0.006

0.006

0.006

0.009

0.012

0.006

0.006

0.006

0.006

0.006

34

46

31

37

49

48

40

32

29

56

52

31

44

21

02 (m) Pitch L Cm) Flight

diameter

03 Cm) Flight

thickness

T Cm) Equivalent of tanks n

number

“Angle between upper screw and lower screw=30”, length steel balls, second material = 16-18 mesh steel balls.

of lower feeder-

1.0 m, ratio of rotational

speeds=

l:l,

first material=3635

mesh

of 30-35 mesh were employed in the experiment. Physical properties of the granular materials are listed in Table 2.

used, were separated by a magnet and the composition of the granular mixture determined.

2.3. Experimental procedure

3. Results

At the beginning of each experiment the motors were started and the gear boxes were adjusted such that the ratio of rotational speeds was 1:l. The small steel balls (30-35 mesh) were fed first. Once the flowrate became stable and the small balls maintained the same level in the hopper, the small steel balls were replaced by the large steel bails (16-18 mesh) and the time measurement begun. From 1800 to 7200 s, a sample was taken from the exit every 300 s. Screen analysis was employed for analyzing the particle size composition of the sample. The steel balls and alumina balls, if

Data directly obtained from the experiments are shown in Fig. 3. Mean residence time f,,,, which is based on the data shown in Fig. 3, can be obtained from the integration of the plot of time, t, against wt.% of the larger particle, F, according to Eq. (1) [14]: 1

t,=

s

tdF

0

Dimensionless i.e.:

time t* can be calculated using Eq. (2),

W-R.

Tsai, C.-I. Lin I Powder

nnn

~100.0 z .P : 80.0

v Tapering

Cut

shaft

flight

(cut

screw,

conveyor

screw

screw,

depth,O.O065m;

121

Technology 80 (1994) 119-126

Shaft q-•o:O.OZm o--o:O.O3m - b--a :O.O4m

/a,0 p

//

_

,/-

-

//’

10

screw

; 60.0 r x b 40.0 P _o z 20.0 ‘.

11

Jl

0)

2

width,O.Olm)

0.0

0

0

1200

’

I

.z

2400

I

J 3600

4800

6000

7200

Time(s)

Fig. 3. Content of larger particle as a function of time (data obtained directly from experiments).

Cut

flight

conveyor

screw

with

(cut depth,O.O065m; paddle height,O.O13m;

paddles,

screw

12

width,O.Olm; width,O.Olm)

GA 00.0 z .$ .E. 00.0

z

60.0

x

Stepped

diameter (0.056m

conveyor vs.

screw,

acrew

13

0.046m)

II 0.5

/

I

a

II

Shaft diameter a a :O.O25m o--o:O.O3m A---b :O.O4m

PFR

-I

1 .o

1.5 t’=t

Double

flight

conveyor

screw,

/

2.0

tm

Fig. 4. F curves of screw feeders with different shaft diameters.

screw 14

Fig. 2. Shapes and dimensions of screw 10 to screw 14. TABLE

2. Physical properties of steel balls and A1203 powder

Material

Compressibility (%)

Angle of response

Bulk density (g/cm’)

(“)

Aerated density

Packed density

Working density

30-35 mesh steel balls

21

3.97

4.11

3.98

3.26

16-18 mesh steel balls

19

4.03

4.16

4.04

3.03

30-35 mesh A120, powder

34

1.65

1.87

1.68

11.76

A tanks-in-series model is a one-parameter model widely applied to represent non-ideal flow in a vessel. The only parameter is the number, n, of tanks in the series. The degree of mixing in a reactor is related to values of n. A higher degree of mixing would occur for a lower value of n. The vessel contents are completely mixed whenever the value of n is equal to one. When the value of it equals infinity, the vessel functions similarly to a plug flow reactor, with no mixing occurring between the former element and the latter element. The value of IZfor a specific vessel can be calculated according to Eq. (4) [15]: 2 n=t, (4) a2

t*=

f m

A plot of F against t* can consequently be plotted as Fig. 4. The variance a2 of the residence time distribution of the granule in a screw feeder can be obtained using Eq. (3) [15]: 1 c?=

(t-t,)2dF s 0

(3)

The F curves for different experimental conditions are similar to those in Fig. 4. The equivalent number of tanks in series, it, for each case is listed in Tables 1 and 3. The equivalent number of tanks for all runs is observed in these tables to be quite high and F curves are similar to those for a plug flow reactor (PFR). The degree of mixing in a screw feeder is found to be low. The influences of the variables on the degree of mixing are also found to be mild.

W-R.

Tsai, C.-I. Lin I Powder

Technology 80 (1994) 119-I26

4. Discussion 4.1. Variation in screw dimension The effect of shaft diameter on the mixing of granular material in a screw feeder is known from the curves of Fig. 4 and the 12values of Table 1. It is observed that as the shaft diameter increases, the value of n decreases, i.e. the degree of mixing is higher. The trend is consistent with that reported by Pinto and Tadmor [ll] and Sheridan [12], although their materials were in the molten state or liquid polymer. Simplified flow theory [ll, 15, 161 can be employed to explain mixing in a screw feeder. The space between the flight shown in Fig. 5 can be visualized as a rectangular channel. Both walls of the channel are the flights, the bottom base and the upper cover are the shaft and the inner surface of the column of the feeder, respectively. In practice, the screw is rotated, not translated, and the column is static during operation. However, the system can be visualized as the upper cover moves with a velocity of 2, relative to both vertical walls and the bottom base of the channel, which are considered as static. The upper cover moves in a direction having an angle of (p from the channel axis. The velocity v can be decomposed into two components, V, and v,. V, has the same direction as that of the channel (flight) and v, is perpendicular to that of the channel (flight). In the following, the velocity profile of granular materials in the x and z directions will be discussed. As stated before, the column wall is considered as moving relative to the shaft. The velocity profile in the z direction may be linear, as shown in Fig. 6(a). The granule next to the column wall has the same velocity as that of the wall, V, = v,; meanwhile, the granule close to the shaft remains stationary, V, = 0. In the x direction,

Fig. 5. Geometrical configuration of a screw and its expanded channel.

W.-R. Tsai, C.-I. Lin I Powder

Column wall

Shaft

VX

surface

Column wall

Shaft

surface

Fig. 6. Velocity profiles of granular material in a screw feeder. (a) Down-channel component, (b) cross-channel component.

the velocity of the granule next to the column wall is the same as that of the column, v,=v,; in addition, that material close to the shaft surface is static, v,=O. However, the velocity profile in the x direction is totally different from that in the z direction, as shown in Fig. 6(b). The granular velocity profile next to the column wall still remains linear. Close to the shaft surface, a compensating flow in the opposite direction must occur, since no transportation of granular material through the gap between the flight and the column wall is assumed. This compensating flow may be one of the reasons for mixing in the screw feeder. The effect of the shaft diameter on mixing in the screw feeder can be seen in Fig. 7. The distance between column wall and shaft surface increases when the shaft diameter is decreased. The compensating flow ‘of the granular material in the direction opposite to the x axis is therefore small, such that the degree of mixing is less severe. Comparisons of the values of n of run numbers 1, 2 and 3 also lead to the above results. The degree of mixing drops when the pitch of the screw is increased, as observed from a comparison of the values of IZ in cases 1, 4 and 5. The degree of mixing is reduced as the angle between flight and shaft is increased, as previously pointed out by Pinto and Tadmor [ll] as well as Sheridan [12]. The increase in the angle would increase the pitch. Their results consequently agree with those of the present study. As the pitch is increased, the flowrate of granular material is increased and the residence time in the feeder is

Technology 80 (1994) 119-126

123

reduced, therefore the probability of mixing is reduced. Another reason can be stated as follows. The degree af mixing for a long-pitch screw and that for a short one are the same. Hence, the degree of mixing per unit length of screw is smaller for a long-pitch screw. An increase in the diameter of the flight would increase the degree of mixing, as indicated from a comparison of the values of n in cases 1, 6 and 7. The effect of shear stress on mixing should be discussed prior to accounting for the above results. The interfacial area between adjacent layers, A and B, of granular material increases whenever the shear stress is increased, as shown in Fig. 8. The probability of interchange of granular material between layers A and B is thus higher. Increasing the diameter of the flight may possibly increase the surface area of a flight, such that the shear stress on the granular material is increased. The degree of mixing is consequently increased. Increasing the thickness of flight may increase the degree of mixing, as indicated from the results in cases 1, 8 and 9. The space between the flight is reduced as the thickness of the flight is increased; consequently, the velocity of the granule is slowed. Therefore, the residence time of granular material in the screw feeder is reduced and the degree of the mixing is lower. When screw No. 10, the shaft diameter of which was gradually reduced, was employed, the value of n obtained was 56 compared to 34 for a standard shaft (Table 1). A screw feeder with a tapered shaft consequently has a lower degree of mixing than that with a standard shaft. The space between flights is enlarged whenever the shaft diameter is reduced. The void space in the zone of reduced shaft diameter is therefore not fully packed with granular material, such that the compensating flow mentioned above is mild. Hence, the degree of mixing is reduced. 4.2. Variation of the shape of the flight Three varieties of flight besides the standard one were employed in this series of experiments, i.e. (1) cut-flight conveyor screw (screw 11); (2) cut-flight conveyor screw with paddles (screw 12); and (3) steppedflight diameter conveyor screw (screw 13). The configurations of these flights are depicted in Fig. 2. The degree of mixing of a screw feeder with cutflight conveyor screw is observed from Table 2 to be lower than that with a standard screw. This result is in disagreement with those of Colijn [9] and Kulwiec [lo]. The probable reason is that their experiments were carried out in a trough, while ours were in a column and their rotational speeds were high (>40 rpm), while ours were low (1 x-pm).The granular material is closely packed together whenever the experiment is carried out in a column. The cuts of the flights are incapable of destroying the stream of granules. Hence,

124

K-R.

Tsai, C.-I. Lin / Powder

Technology 80 (1994) 119-126

Column wall

Column wall

Column wall

(4

(b)

(c)

t c-

X

Shaft surface

Shaft surface

X

Shaft surface

X

Fig. 7. Velocity profiles of granular material in the x direction. Shaft diameter: (a) 0.04, (b) 0.03, (c) 0.025 m.

4.3. Variation of the angle between upper feeder and lower feeder

Adjacent

powder

layer

Shear --

___--

-.

A

L-B Shear

/

A

/

Fig. 8. Increasing the surface area between adjacent layers (A, B) by shear stress.

the cuts cannot enhance the degree of mixing. On the other hand, the flight with the cut has a lower surface area to exert shear stress on the granular material. Hence, the degree of mixing is lower. When the cut-flight conveyor screw with paddles (screw 12) was employed, the value of IZ was reduced from 52 (screw 11) to 31. The paddles attached to the shaft definitely enhanced the degree of mixing. The value of n was increased from 34 (standard screw) to 44 whenever the stepped flight diameter conveyor screw was used. In other words, the degree of mixing was reduced. The reason for this would be similar to the case of employing a screw with a reduced flight diameter.

The equivalent number of CSTR,n was decreased from 34 to 29 or 28 when the angle between upper feeder and lower feeder was increased from 30” to 45” or 60” respectively, as shown in Table 3. This means that increasing the angle between the feeders increases the mixing in the feeder. The following phenomena occur when the angle between feeders increases: (1) the interface area between feeders decreases such that the number of flights decreases and the transport capability of the feeder decreases [5,18,19]; (2) the transport rate of the upper feeder is higher than that of the lower feeder due to gravity; and (3) the transportation resistance of the granules in the interface region between feeders is high. The above factors may possibly increase the residence time of a granule in the feeder. Consequently, the degree of mixing is increased.

4.4. Variation of the length of the feeder

Three different lengths of the lower feeder, 0.6, 0.8 and 1.0 m, were employed in this series of experiments. The results are indicated by run numbers 17, 18 and 1 in Table 3, respectively. It is seen that as the length of the lower feeder is increased, the value of n is reduced, which means the degree of mixing is increased. This result agrees with those of Pinto and Tadmor [ll] as well as Sheridan [13]. The reason for this is simple: a longer feeder increases the residence time of the granule, which enhances the degree of mixing.

W.-R

Tsai. C.-I. Lin I Powder

Technology 80 (1994) 119-126

125

4.7. Variation in size of granules

4.5. Variation of the ratio of the rotational speeds of the screws

Five ratios of rotational speeds of the screws were employed in this series of experiments. The calculated values of n are plotted against the ratio of rotational speed in Fig. 9. As the ratio is increased from 0.9:1, the value of IZ is decreased. This value reaches a minimum when the ratio is 0.987:1. The value of n increases again when the ratio is further increased. This means that the degree of mixing in the feeder is low when the ratio is either too high or too low; additionally the degree of mixing reaches a maximum when the ratio is 0.987:1. When the ratio of the rotational speeds is low, the material in the feeder is loose and the shear stress exerted by the flight is small, such that the degree of mixing is low. When the ratio of speed is high, e.g. l.l:l, the granular flowrate in the upper feeder is higher than that in the lower feeder. The compression exerted on the granules in the lower feeder causes the granular material in the feeder to simulate a rigid body. The interchange of material between the layers in the feeder is difficult, hence the degree of mixing in this case is also low.

In three experimental runs in this series of experiments, steel balls of 30-35 mesh were fed first. The second feed material was steel balls of one of the following sizes: 1618 mesh, 18-20 mesh or 20-25 mesh. The difference among the n values of these three runs is not significant, probably since the variation in the second feed granule is not large (Table 3). 4.8. Variation in feed order Two variations in feed order, i.e. 16-18 mesh steel balls fed after 30-35 mesh balls (run number 1) and 30-35 mesh balls fed after 1618 mesh balls (run number 23) have been employed in this series of experiments. The feed order of small balls after large balls leads to a higher degree of mixing, as indicated from the experimental results listed in Table 3. Whenever the small particles are fed after large particles, the small particles penetrate more easily among the large ones, due to gravity and pressure differences between the upper feeder and lower feeder. Consequently, the degree of mixing is higher.

4.9. Variation in granular material 4.6. Variation in rotational speed The rotational speeds of the upper screw and that of the lower screw are the same in this series of experiments. Rotational speeds of 1, 2 and 3 rpm were employed. The experimental results are indicated by run numbers 1, 21 and 22 in Table 3, respectively. It is found that increasing the rotational speeds increases the value of n, i.e. reduces the degree of mixing. This result agrees with that of Sheridan [13]. The reason is quite simple: a shorter residence time occurs for faster rotational speeds and the possibility of mixing between granules is therefore low.

55.0 / 50.0

45.0

-

c

\.,.’ 30.0

-

1 0.7

I 0.8

1.0 RPM(upper)/RPM(lower)

0.9

1.1

1.2

1.3

Fig. 9. Plot of n against ratio of rotational speeds of upper screw and lower screw.

The degree of mixing was found to be higher (the value of n is found to be lower in Table 3), whenever the second feed granule was changed from steel balls of 30-35 mesh to alumina balls of the same size. The degree of rearrangement of two materials with different hardnesses and shapes is suggested by German [20] to be higher than that with the same hardness and shape. The degree of mixing is therefore higher whenever alumina balls (rather than steel balls) are used as the second feed material.

5. Conclusions The following conclusions can be drawn from these experiments: (1) the degree of mixing in a screw feeder within a column is low, and the granular flow in it is similar to plug flow; (2) increasing the screw diameter, flight diameter, flight thickness or decreasing the pitch may increase the degree of mixing of the screw feeder; (3) the degree of mixing is reduced when the shaft diameter is reduced; (4) the degree of mixing is reduced when a cut-flight conveyor screw or stepped-flight diameter conveyor screw is employed; (5) the degree of mixing is markedly increased when a cut-flight conveyor screw with paddles is used;

126

W-R. Tsai, C.-I. Lin / Powder TechnoZogy80 (1994) 119-I26

(6) increasing the angle between the upper feeder and the lower feeder may possibly increase the degree of mixing; (7) the degree of mixing is reduced if the ratio of rotational speeds of the screws is too high or too low. In the present system the maximum degree of mixing was found at the ratio of 0.987:1; (8) the degree of mixing of the screw feeder is increased as the rotational speeds of both screws are decreased; (9) the degree of mixing was found to be increased whenever the order of feed of granular materials was changed from large particle size following small particle size to small particle size following large particle size; (10) the degree of mixing for two different materials is better than that of two identical materials.

References [l] W.H. Dame11 and E.A Mol, SPE I., April (1956) 20. [2] J.R. Metcalf, Proc. Inst. Mech. Eng., I80 (1965) 131. [3] G.J. Burkhardt, Trans. Am. Sot. Agric. Eng. (1967) 685.

141 G.E. Rehkugler, Trans. Am. Sot. Agric. Eng., 10 (1967) 615. PI R. Rautenbach and W. Schumacher, Bulk Solids Handling, 7 (1987) 675. [61 H. Colijn, Mechanical Conveyors for Bulk Solids, Elsevier, Amsterdam, 1985. [71 C. Bryk and W.-K. Lu, Can. Metall. Q., 2.5 (1986) 241. PI W.-K. Lu, C. Bryk and H.Y. Gou, Proc. 5th Znt. Iron Steel Congr., Washington DC, 1986, Book 3, Iron and Steel Society of the AIME, Warrendale, PA, 1986, pp. 1065-1075. PI H. Colijn, Mechanical Conveyors for Bulk Solids, Elsevier, New York, 1985, pp. 110-168. WI R.A. Kulwiec, Handbook of MateriaIs Handling, Wiley, New York, 1985, pp. 1023-1058. WI G. Pinto and Z. Tadmor, PoIym. Eng. Sci., 10 (1970) 279. L.A. Sheridan, Chem. Eng. Progr., 71 (1975) 83. ;:i; W.R. Tsai, M.Sc. Thesis, National Taiwan Institute of Technology, 1993. P41 H.S. Fogler, Elements of Chemical Reaction Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1986, pp. 629-679. 1151 R.M. Griffith, Znd. Eng. Chem. Fundam., 1 (1962) 180. P61 E.B. Nauman and B.A. B&ham, Miring in Continuous Flow Systems, Wiley, New York, 1983, pp. 53-93. L. Bates, Chem. Eng., I4 (1969) 1072. t:;; K. McNaghton et al., Solids Handling, McGraw-Hill, New York, 1981, pp. 102-119. P91 R.M. German, Particle Packing Characteristics, Metal Powder Industries Federation, New York, 1989, pp. 121-133; 219-252.