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A qualitative theoretical approach to the problem of winnowing
348
A Qualitative Theoretical Approach to the Problem of Winnowing M. M. KASHAYAP*; A. C. PANDYA* Particle trajectories, obtained with a digital computer, clearly show the effects of various parameters on air velocity requirements for winnowing operations. They can also ascertain the sizes of particles that can be separated effectively by pneumatic means and indicate that the distance resolved between two particles decreases as the height of free fall above the air stream is increased. The particles are better resolved by providing a free space below the air stream or by incorporating an upward directed air blast.
1.
Introduction
Study of the dynamics of a grain in a fluid is essential for understanding the process of pneumatic separation. The movement of a single grain and its behaviour in a fluid can lead to the solution of the more complicated problem of interaction between air stream and a mixture of grain and chaff. Comparison of the trajectories of individual particles shows how effectively these can be separated from each other under a given set of conditions of velocity and depth (diameter) of the air blast, or under what circumstances particles cannot be separated by winnowing. It can also help in the generalization of experimental results, for example on the optimum air velocity range for winnowing of paddy grains obtained earlier,’ which holds good only for a 1.3 ft dia fan with horizontal air stream, by determining the effects of fan diameter and upward inclination of the air stream on air velocity requirements. The effects of free fall of grains and chaff before and after the action of an air stream can also be determined. Equations of motion The study was based upon two dimensional motion of a particle in a gravitational field.‘ms The equations of motion are 2.
Al/h = AuZ, -= (32.2 ??Department of Agricultural Technology, Kharagpur, India
Pf cd2AMu “*) Engineering,
At.
Indian Institute of
The relative velocity U is further given by c/2 ZZ (//&a + u,,2 :~ (& --- uoh)’ + (U&9 4 &a)“. The particle trajectories were obtained from the equations & = uh At = (uh + uo,,) At S, ~=-ul. At = (ULx ~~uo?,) At. KEY TO SYMBOLS ~ particle mass, lb A = mean projected area of particle, ftr CC1 = drag coefficient .!J -= relative velocity of particle, ftjs I40 = air velocity, ft/s 2 actual particle velocity, ftjs : = distance travelled by particle, ft = fluid density (0.075 lb/ft%) F/ .z time interval, s I De = equivalent diameter of particle, ft 6?‘ 2 gravitational constant, lb ft/lbf s” II = angle with the horizontal at which stream is directed upwards, deg D x diameter of fan, ft P 2 acceleration of particle, ft/s” h,a; 77 horizontal and vertical components F drag force, lb ft/s2 A4
3.
air
Solution of the equations
3. I . Procedure The equations are solved by a method of incremental approximation.2*4 The process was simplified for a digital computer by making the time interval much smaller (0.001 s), so that in one step the final values of velocity increments at From the end of the time interval were obtained. the velocity components at the end of the time interval the distances moved by the particle in the respective directions were calculated. The
7.1. hl.
K\SHAYAP:
A
I;‘.
349
PANDYA
work wax done on an IBM 1620 Fortran Computer.
Digital
3.2. Particle parameters and drag coeficient The particles were assumed to be spherical. Six particles. one comparable in mass and mean projected area to paddy grain (Particle 1) and the remaining to particles of chaff, were selected for it. Their mean projected area, equivalent diameter.6 mass, and mass over prqjected area ratio are given in Table I. TABLE I
Characteristics
of
particles incorporated calculations
in theoretical
-
.4.
If/ ’fi”
’
De, IO 2 fi
_~___
I .656
I.452 2.358 4.426 2.81 1 I.433 I.045
4.366 15,392 6.204 I.612 0.857
MIA, lb/fi 2
M,
10 "lb
---__
7.055 8.600 16.097 6.174 1.544 0.441
0.4260 0.1970 0.1046 0.0995 0.0958 0.0515
The drag coefficients were obtained from the following general relations for spheres’:IO 1 (’ Re c 2, Cd = 24/Re . . Rc -i 500. Cd == 0.4 + 40/Re 2 500 <’ Re c 105, Cd =; 0.50 The last value for C,t is an average of 0.45-0.56 obtained experimentally for seed grains.’ 3.3.
Zones
of‘motion and the subdivisions
qf the
stud)
The motion of the particle was subdivided into three zones:(I) Free fall of the particle before coming into the air stream. (2) Motion in the air stream. (3) Motion in free space after coming out of the air stream. Six series of experiments were carried out :In Series A, the eflect of different heights of Zone I was studied, assuming values of up to 5 ft. The height of Zone 2 was taken as 1.3 ft and the air velocity in the horizontal direction as 1000 ft/min, this being within the optimum air velocity range for paddy grains, obtained earlier experimentally.’ Zone 3 was neglected. For Series B, Zone 1 was neglected while the height of Zone 3 was taken as 5 ft. The height
and air velocity of Zone 2 were the same as in A. In Series C the height (diameter 1.3 ft) and air velocity were the same as in A, except that the air stream was directed upwards at angles of 5-75” to the horizontal. The motion of the particle was considered (i) in the air stream alone ; (ii) up to a vertical fall of I.3 ft and (iii) I .3!cos 0 ft, where 0 is the upward inclination of the air stream to the horizontal. All six particles were incorporated in the above series. In Series D, Zones I and 3 were neglected. Velocity of air was assumed to be horizontal and was varied from 5 to 25 ft/s. The height of Zone 2 was taken as 10 ft. In Series E and F, Zones I and 3 were neglected. Height and air velocity of Zone 2 were the same as in A. Particle 1 and similar particles were incorporated. In one case its mass was kept constant while the mean projected area, and hence equivalent diameter, was gradually increased: in the other case the mean prqjected area was kept constant, while the mass was gradually decreased. These fixed the sizes of which could only be effectively particles, separated by pneumatic means. 4. Results and discussions qffiee fall above air stream (Series A) 4.1. &kt Fig, I shows the distances traversed by the six particles with different free falls above air stream. These plots on logarithmic co-ordinates are straight lines in sections, which are slightly diverging, but slope downwards towards lower scales, thereby showing that distances resolved between the various particles decrease as free fall above the air stream is increased. The particles were divided into two groups, one consisting of all six particles, distances being resolved between Particle 1 and the others. The second group consisted of Particles 3, 4 and 5, which formed a distinct cluster. Distances were resolved between two particles of all the particle pair combinations (Table II). As the free fall above the air stream was varied from I to 60 in, there was a decrease of l9-82’,;,, in the distances resolved between the particles in the first group and IO-84% in the second group, as compared to the corresponding values without free fall. In other words, to resolve two particles through a certain fixed distance will require
350
A QUALITATIVE
THEORETICAL
APPROACH
higher air velocity with free fall than without free fall. Obviously, once the height of free fall is such that the particles attain terminal velocity, there is no further decrease in distances resolved with the increase in height of dropping. These findings confirm the experimental conclusions stated earlier.’
0.01
I I lllllll I I IiIIlll 0.02 0.04 0.1 0.2 0.4 0.81 Height
of free
fall,
4.2.
TO
THE
PROBLEM
E#ect
of,fieefdl
stream
(Series
OF
WINivOWIN(;
gfier coming out c?f’the ait B)
On coming out of the air stream the particles attain certain velocity and hence have a certain amount of kinetic energy, which can be made use of by allowing a free motion to the particles below the air stream (Fig. 2). Table III shows
1 I/III. 2 4 6810 0
ft Vertical
Fig. 1. Effct of height of free fall above air stream on horizontal distance traversed by Particles l-6 from the origin, on just coming out of the air stream
Trajectories
Fig. 2.
distance
below air stream,
ft
of Particles 1-6 after passing through an air stream
TABLE II
Horizontal
distances
Height of free fall above air stream, in
(in) resolved between particles (of a pair of particles) and the decrease in distances resolved (ii parenthesis), % of the corresponding values without free fall Particle
pair
-
-
-
-
1-6
--__ 5.16
13.70
14.46
15.06
26.54
0.76
I.36
4-5 _--0.60
1
4.04 (30)
10.14 (26)
10.76 (26)
11.27 (25)
21.41 (19)
0.62 (18)
1.13 (17)
0.51 (15)
6
2.29 (60)
6.43 (53)
6.89 (52)
7.66 (49)
15.32 (42)
0.46 (39)
1.23 (10)
0.47 (22)
12
1.71 (70)
5.18 (62)
5.61 (61)
5.54 (63)
13.21 (50)
0.43 (43)
0.82 (40)
0.39 (35)
36
1.21 (79)
3.55 (74)
3.47 (76)
3.84 (75)
10.35 (61)
0.12 (84)
0.29 (79)
0.17 (72)
1.02
3.18 (77)
3.43 (76)
3.63 (76)
IO.16 (62)
0.25 (67)
0.45 (67)
0.20 (67)
0
60
l-2
(82)
I-3
J-4
-
__
-
1-5
34 __-
-
-_
-
3-5
-
M.
\I.
KASIIAYAI’:
A.
(‘.
35 I
PANDYA
The suspension
that thete was an increase of 13-1730/;, and 40241 ‘I() in the distances resolved for the two particle groups. as the free fall was varied from 3 to 60 in. 4.3.
E/fivt (Scrics
of’ lrp~arrl
inclination
of’ air
velocity
for a particle
1s given
by Mg,. ; pf C,, A w2 As it is the vertical component of the velocity which supports the particle. uo is replaced by r/o sin 0. 4 ff C,, A ~0~ sin:! 0 :. Mg,. The angle 0 at which a particle would get suspended was calculated for all the particles from the above equation assuming uo as 1000 ft/min and C,, as 0.5 (Re .. 500). It was observed that Particles I and 2 would not get suspended in the assumed velocity, whereas Particles 3 6 would get suspended at angles of 53.5, 5 I .6. 50.3 and 34.3 respectively. Once a particle gets suspended, its direction of motion in the vertical plane changes. Fi,q. 3 show5 that for all these particles, up to a
streanl
C)
For two given particles, given diameter of the fan and air velocity, the resolution of the particles is a function ‘of’time t for which the particles remain suspended in the air stream. An upward directed air stream can be resolved into an upward and a forward component. The former will support the particle, whereas the forward component will {carry it forward. Thus the time of suspension of a particle can be appreciably increased. as compared with a horizontal air stream (Fi,?. 3). 80 r
2
I
31
23
x +
x
75
x
70
II
I I
ii
ii
65
i
60
I
3
T i i I i i x
I
II I
iv
xx
x
III
I I/ xx x
ii ii
IO
xx
5
0 0.2
Horizontal Fix. 3
Eflect (I
of upward inclinaiion
I on ,just coming
4
3
0.3
of the air stream
out of the air stream
(2)
distance on horizontal at a vertical
traversed,
distance
56
ft
traversed
by a particle
di.stanca of 1.3 ft and (3)
atgO
from fi
the origin
352
A QUALITATIVE
THEORETICAL
APRROACH
certain angle, there is a gradual increase in the distances traversed with the increase in upward inclination of the air stream; beyond this point there is a decrease. The angle has a different value for different particle pairs (Table IV), it being 50-60” for pairs formed with Particle 1. Thus, by directing the air stream upwards at an angle of 50-60”, the particles may be better resolved or the same operation may be done at a comparatively lower air velocity. Incidentally, by comparing Tables 111 and IV, it was observed that in these two cases the resolution of the particles was almost of the same order. Therefore, the same effect can be achieved without free fall, and hence in a more compact space, by directing the air stream upwards. Eflect of’fbn
4.4.
diameter (Series
i-HI. PROBLEM
Efikct of’particle EFFECT JECTED
WINNOWIKb
size (S2rie.v E and F)
OF PARTICLE AREA
OF
MASS. KEEPING
PRO-
CONSTANT
The lighter a particle the more time it takes to pass through an air stream and hence the further it is carried away. Fig. 5, Curve I, shows distances resolved between Particle 1 and identical particles having lesser mass. Mass ratios of the lighter particles to that of Particle I were plotted versus distances resolved (with respect to Particle 1). The plot shows that for a particle to be resolved through 3-6 in, it should have a mass of 62-48 I’;) that of Particle 1, at the same projected area
100 80
D)
The correlation between fan diameter and air velocity required is shown in Fig. 4. It was obtained by, first, calculating the distance travelled by Particle 1 in an air stream 1.3 ft across having a velocity of 1000 ft/min without free fall above or below it. The depths of the air stream required to move a given particle through the same distance with different air velocities were then obtained by plotting its trajectories at air velocities of 300-l 500 ft/min up to a depth of 10 ft. The correlations may be expressed as 0.6 ft < D < 2.5 ft MO= 19.50 D--o.5’ 2.5 ft < D < 6.0 ft uo = 2344
4.5. 4.5. I.
TO
60
o
40
‘;, L
i/ J O(
Distance resolved, in Fig. 5.
D- o.72
E#ect of mass and projected area on horizontal distance resolved between fwo particles
40
c
I
4.5.2.
EFFECT
OF
PROJECTED
AREA,
KEEPING
MASS CONSTANT
4
1”” O-6
0.6
I.0
I 2 Diameter.
Fig. 4.
I
I 4
I
lllil 6
6
IO
ft
Correlation between fan diameter and optimum air velocity .for winnowing qf paddy grains
The greater the projected area of a particle, the further it is carried away in unit time in a given air stream as the drag force acting on the particle is directly proportional to its projected area. Fig. 5, Curve 2, shows distances resolved between Particle 1 and identical particles having a larger projected area. The projected area ratios of a particle and that of Particle 1 were plotted versus distances resolved (with respect to Particle 1). The plot shows that for a particle to be resolved through 3-6 in it should have a projected area 1.63-2.16 times that of Particle I at the same mass.
Horizontal distances (in) resolved between particles (of a pair of particles) and the increase parenthesis), 4/, of the corresponding values without free fall
Psrriclr
in distances
resolved
(in
ouir
____ l-5
.f 4
1 h
__-..-_ .ij
.~ /
-I 5
13.70
14.46
15.06
26.54
0.76
I .36
0.60
15.77 (15)
17.09 (18)
18.05
(20)
31.13 (17)
I.32 (74)
2 2x (68)
O-Y6 (60)
17.21 (26)
18.77 (30)
19.73 (31)
34.0 I (28)
I .56 (105)
2 52 (X5)
O.Y6 (60)
21.01 (53)
22.2 I (54)
23.05 (53)
38.55 (45)
I .20 (58)
2.04 (50)
i/
O-84 (40)
28.72 (110)
30.37 (110)
31.30
46.88
( 108)
(77)
I.65 (117)
2.58 (YO)
; 1
0.93 (55)
31.72 (132)
34.36 (138)
35.56 (136)
51.63 (Y5)
2.64 (247)
3.x4 (182)
~
I.20 I 100)
!_
--
-
TABLE IV
Horizontal distances (in) resolved between particles (of a pair of particles) at the end of a vertical fall of 1.3 ft from the origin, and the increase in distances resolved (in parenthesis), “d of the corresponding values without inclination Particle
puir
I-3
I-4
l-5
I6
3 3
18.69 (36)
20.03 (39)
20.62 (37)
39.03 (47)
I .33 (75)
I.Y3 (42)
I .0x (X0)
23.97 (75)
25.87 (79)
26.97 (7%
49.65 (87)
I .90
( 1.50)
3.00 (1’1)
(X3)
29.58 (76)
31.87 (120)
33.33 (121)
56.Y7 (I 15)
2.29 (201)
3.75 (176)
I .46 (143)
34.88 (155)
36.14 (154)
38.38 (155)
61.58 (132)
I.87 (146)
3.50 (157)
I ,64 (173)
38.36 (180)
40.8 I (182)
42.22 (180)
62.86 (137)
2.45 (222)
3.86 (184)
t 135)
14.97 (160)
40.40 (195)
42.63 (195)
43.96 (192)
60.Y6 (130)
2.22 (192)
3.56 (162)
(112)
15.28 (165)
39.81 (191)
41.57 (187)
42.68 (183)
55.56 (109)
1.76 (132)
2.87 (III)
-
I.10
I.11
I.33
I II (X5)
354
A
QUALITATIVI:
TH~ORt’II(‘Al.
APPROACH
4.5.3. EFFECT OF M/A RATIO The preceding two correlations define the minimum requirements of particles that can be separated by pneumatic means. By definition, drag force F ==4 pf Cd A Us = M P,, :. P,, -- gf Cc/ A U’/2M To separate two particles they should be differently accelerated under a given set of conditions. In the above equation, pf is constant,& can be taken as 0.5, as all the particles come in the turbulent zone for a 1000 ft/min air stream. and the value of U is the same for all particles at the instance when these just start moving in the same air stream. Hence, Pa, = $ (A/M) or $ (M/A) thereby indicating that the M/A ratio is an important property of a particle in pneumatic separation. 0.; r 0.6 c I
r
THE
I’ROBl.~~~
OI-
WJN\OWI\(,
given set of conditions. These trajectories can also help in the generalization of certain experimental results. With the increase in height of free fall above air stream, the distance resolved between two particles decreases. This shows that to resolve two particles through a certain distance requires higher air velocity with free fall than without free fall above the air stream. By increasing the depth of free fall below the air stream or by directing the air stream upwards up to a certain angle (depending upon the particles and air stream involved) either the particles can be better resolved or the same operation can he carried out at a lower air velocity. To separate two particles, either one should be lighter than the other (the projected area remaining the same) or the projected area of one should be greater than that of the other (the mass remaining the same). In other words there should be certain minimum difference in the values of M/A ratios of the two particles. 6.
L
0.1
p
0.06
I
0.06 t
-
0.04
\
2
)
0.02
1 .1’!’
0.01 0.4
Fig. 6.
O-6
I
i 2
1 1 ‘1~111 4
6
6
IO
I
I I
20
40
I
3i.il.i 60
100
in Distance resolved , Eflect sf M/A ratio on horizon& distance resolved between
Acknowledgements The authors wish to express their gratitude to the authorities concerned with the digital computer installed in the Institute. Special thanks go to K. Venkatratanam and A. Maity, who programmed and processed the problem for the solution on the computer. Thanks are also due to the Council of Scientific and industrial Research, Government of India. for providing the research facilities.
two particles
Thus to separate two particles they should have different values of M/A ratios. Fig. ci shows a correlation based upon Curves 1 and 2 of Fig. 5, as obtained by plotting M/A ratio of a particle versus distances resolved with respect to Particle 1. It shows that for a particle to be resolved through 3-6 in it should have a M/A ratio of 0.27-0.19.
KEFEKENCLS
Kashayap, M. M.; Pandya, A. C. Air velocity* reylrirc~ment for winnowing operations. J. agric. Engng Res.. 1966, 11 (I) ’ Lapple, C. E.; Shepherd, C. B. Calculation of purticlr trajectories. Ind. Engng Chem., 1940, 32 (5) 605 ’ Co&on, J. M.; Richardson, J. F. Chemical engineering Vol. II: Unit operations. English Language Bk Sot.: ’
Pergamon Press, Lond., 1962, chap. 14 ’ Dallavaile, J. M. Micromeritics, the technologv qffim particles. Pitman Publishing Corp., N.Y.. 1948. chap. 2 5 Zenz, F. A.; Othmer. D. F. Fluidizatiorr urrd .flNidparticle systems. Reinhold Publishing Corp., N.Y.: Chapman & Hall Ltd, Lond., 1960, chap. 6
’ Henderson, S. M.; Perry, R. L. Agricultural 5.
Conclusions Comparison of particle trajectories obtained with a digital computer shows how effectively two particles can be resolved from each other under a
engineering.
proces.,
John Wiley & Sons Inc., N.Y.. 1955. p.
155 ’ Bilanski, W. K.; Collins, S. H.; Chu, P. Aerodynamic properties
qf seed grains,
their behaviour
in free .fall.
Agric. Engng. St Joseph, Mich.. 1962, 43 (4) 216
A Qualitative Theoretical Approach to the Problem of Winnowing M. M. KASHAYAP*; A. C. PANDYA* Particle trajectories, obtained with a digital computer, clearly show the effects of various parameters on air velocity requirements for winnowing operations. They can also ascertain the sizes of particles that can be separated effectively by pneumatic means and indicate that the distance resolved between two particles decreases as the height of free fall above the air stream is increased. The particles are better resolved by providing a free space below the air stream or by incorporating an upward directed air blast.
1.
Introduction
Study of the dynamics of a grain in a fluid is essential for understanding the process of pneumatic separation. The movement of a single grain and its behaviour in a fluid can lead to the solution of the more complicated problem of interaction between air stream and a mixture of grain and chaff. Comparison of the trajectories of individual particles shows how effectively these can be separated from each other under a given set of conditions of velocity and depth (diameter) of the air blast, or under what circumstances particles cannot be separated by winnowing. It can also help in the generalization of experimental results, for example on the optimum air velocity range for winnowing of paddy grains obtained earlier,’ which holds good only for a 1.3 ft dia fan with horizontal air stream, by determining the effects of fan diameter and upward inclination of the air stream on air velocity requirements. The effects of free fall of grains and chaff before and after the action of an air stream can also be determined. Equations of motion The study was based upon two dimensional motion of a particle in a gravitational field.‘ms The equations of motion are 2.
Al/h = AuZ, -= (32.2 ??Department of Agricultural Technology, Kharagpur, India
Pf cd2AMu “*) Engineering,
At.
Indian Institute of
The relative velocity U is further given by c/2 ZZ (//&a + u,,2 :~ (& --- uoh)’ + (U&9 4 &a)“. The particle trajectories were obtained from the equations & = uh At = (uh + uo,,) At S, ~=-ul. At = (ULx ~~uo?,) At. KEY TO SYMBOLS ~ particle mass, lb A = mean projected area of particle, ftr CC1 = drag coefficient .!J -= relative velocity of particle, ftjs I40 = air velocity, ft/s 2 actual particle velocity, ftjs : = distance travelled by particle, ft = fluid density (0.075 lb/ft%) F/ .z time interval, s I De = equivalent diameter of particle, ft 6?‘ 2 gravitational constant, lb ft/lbf s” II = angle with the horizontal at which stream is directed upwards, deg D x diameter of fan, ft P 2 acceleration of particle, ft/s” h,a; 77 horizontal and vertical components F drag force, lb ft/s2 A4
3.
air
Solution of the equations
3. I . Procedure The equations are solved by a method of incremental approximation.2*4 The process was simplified for a digital computer by making the time interval much smaller (0.001 s), so that in one step the final values of velocity increments at From the end of the time interval were obtained. the velocity components at the end of the time interval the distances moved by the particle in the respective directions were calculated. The
7.1. hl.
K\SHAYAP:
A
I;‘.
349
PANDYA
work wax done on an IBM 1620 Fortran Computer.
Digital
3.2. Particle parameters and drag coeficient The particles were assumed to be spherical. Six particles. one comparable in mass and mean projected area to paddy grain (Particle 1) and the remaining to particles of chaff, were selected for it. Their mean projected area, equivalent diameter.6 mass, and mass over prqjected area ratio are given in Table I. TABLE I
Characteristics
of
particles incorporated calculations
in theoretical
-
.4.
If/ ’fi”
’
De, IO 2 fi
_~___
I .656
I.452 2.358 4.426 2.81 1 I.433 I.045
4.366 15,392 6.204 I.612 0.857
MIA, lb/fi 2
M,
10 "lb
---__
7.055 8.600 16.097 6.174 1.544 0.441
0.4260 0.1970 0.1046 0.0995 0.0958 0.0515
The drag coefficients were obtained from the following general relations for spheres’:IO 1 (’ Re c 2, Cd = 24/Re . . Rc -i 500. Cd == 0.4 + 40/Re 2 500 <’ Re c 105, Cd =; 0.50 The last value for C,t is an average of 0.45-0.56 obtained experimentally for seed grains.’ 3.3.
Zones
of‘motion and the subdivisions
qf the
stud)
The motion of the particle was subdivided into three zones:(I) Free fall of the particle before coming into the air stream. (2) Motion in the air stream. (3) Motion in free space after coming out of the air stream. Six series of experiments were carried out :In Series A, the eflect of different heights of Zone I was studied, assuming values of up to 5 ft. The height of Zone 2 was taken as 1.3 ft and the air velocity in the horizontal direction as 1000 ft/min, this being within the optimum air velocity range for paddy grains, obtained earlier experimentally.’ Zone 3 was neglected. For Series B, Zone 1 was neglected while the height of Zone 3 was taken as 5 ft. The height
and air velocity of Zone 2 were the same as in A. In Series C the height (diameter 1.3 ft) and air velocity were the same as in A, except that the air stream was directed upwards at angles of 5-75” to the horizontal. The motion of the particle was considered (i) in the air stream alone ; (ii) up to a vertical fall of I.3 ft and (iii) I .3!cos 0 ft, where 0 is the upward inclination of the air stream to the horizontal. All six particles were incorporated in the above series. In Series D, Zones I and 3 were neglected. Velocity of air was assumed to be horizontal and was varied from 5 to 25 ft/s. The height of Zone 2 was taken as 10 ft. In Series E and F, Zones I and 3 were neglected. Height and air velocity of Zone 2 were the same as in A. Particle 1 and similar particles were incorporated. In one case its mass was kept constant while the mean projected area, and hence equivalent diameter, was gradually increased: in the other case the mean prqjected area was kept constant, while the mass was gradually decreased. These fixed the sizes of which could only be effectively particles, separated by pneumatic means. 4. Results and discussions qffiee fall above air stream (Series A) 4.1. &kt Fig, I shows the distances traversed by the six particles with different free falls above air stream. These plots on logarithmic co-ordinates are straight lines in sections, which are slightly diverging, but slope downwards towards lower scales, thereby showing that distances resolved between the various particles decrease as free fall above the air stream is increased. The particles were divided into two groups, one consisting of all six particles, distances being resolved between Particle 1 and the others. The second group consisted of Particles 3, 4 and 5, which formed a distinct cluster. Distances were resolved between two particles of all the particle pair combinations (Table II). As the free fall above the air stream was varied from I to 60 in, there was a decrease of l9-82’,;,, in the distances resolved between the particles in the first group and IO-84% in the second group, as compared to the corresponding values without free fall. In other words, to resolve two particles through a certain fixed distance will require
350
A QUALITATIVE
THEORETICAL
APPROACH
higher air velocity with free fall than without free fall. Obviously, once the height of free fall is such that the particles attain terminal velocity, there is no further decrease in distances resolved with the increase in height of dropping. These findings confirm the experimental conclusions stated earlier.’
0.01
I I lllllll I I IiIIlll 0.02 0.04 0.1 0.2 0.4 0.81 Height
of free
fall,
4.2.
TO
THE
PROBLEM
E#ect
of,fieefdl
stream
(Series
OF
WINivOWIN(;
gfier coming out c?f’the ait B)
On coming out of the air stream the particles attain certain velocity and hence have a certain amount of kinetic energy, which can be made use of by allowing a free motion to the particles below the air stream (Fig. 2). Table III shows
1 I/III. 2 4 6810 0
ft Vertical
Fig. 1. Effct of height of free fall above air stream on horizontal distance traversed by Particles l-6 from the origin, on just coming out of the air stream
Trajectories
Fig. 2.
distance
below air stream,
ft
of Particles 1-6 after passing through an air stream
TABLE II
Horizontal
distances
Height of free fall above air stream, in
(in) resolved between particles (of a pair of particles) and the decrease in distances resolved (ii parenthesis), % of the corresponding values without free fall Particle
pair
-
-
-
-
1-6
--__ 5.16
13.70
14.46
15.06
26.54
0.76
I.36
4-5 _--0.60
1
4.04 (30)
10.14 (26)
10.76 (26)
11.27 (25)
21.41 (19)
0.62 (18)
1.13 (17)
0.51 (15)
6
2.29 (60)
6.43 (53)
6.89 (52)
7.66 (49)
15.32 (42)
0.46 (39)
1.23 (10)
0.47 (22)
12
1.71 (70)
5.18 (62)
5.61 (61)
5.54 (63)
13.21 (50)
0.43 (43)
0.82 (40)
0.39 (35)
36
1.21 (79)
3.55 (74)
3.47 (76)
3.84 (75)
10.35 (61)
0.12 (84)
0.29 (79)
0.17 (72)
1.02
3.18 (77)
3.43 (76)
3.63 (76)
IO.16 (62)
0.25 (67)
0.45 (67)
0.20 (67)
0
60
l-2
(82)
I-3
J-4
-
__
-
1-5
34 __-
-
-_
-
3-5
-
M.
\I.
KASIIAYAI’:
A.
(‘.
35 I
PANDYA
The suspension
that thete was an increase of 13-1730/;, and 40241 ‘I() in the distances resolved for the two particle groups. as the free fall was varied from 3 to 60 in. 4.3.
E/fivt (Scrics
of’ lrp~arrl
inclination
of’ air
velocity
for a particle
1s given
by Mg,. ; pf C,, A w2 As it is the vertical component of the velocity which supports the particle. uo is replaced by r/o sin 0. 4 ff C,, A ~0~ sin:! 0 :. Mg,. The angle 0 at which a particle would get suspended was calculated for all the particles from the above equation assuming uo as 1000 ft/min and C,, as 0.5 (Re .. 500). It was observed that Particles I and 2 would not get suspended in the assumed velocity, whereas Particles 3 6 would get suspended at angles of 53.5, 5 I .6. 50.3 and 34.3 respectively. Once a particle gets suspended, its direction of motion in the vertical plane changes. Fi,q. 3 show5 that for all these particles, up to a
streanl
C)
For two given particles, given diameter of the fan and air velocity, the resolution of the particles is a function ‘of’time t for which the particles remain suspended in the air stream. An upward directed air stream can be resolved into an upward and a forward component. The former will support the particle, whereas the forward component will {carry it forward. Thus the time of suspension of a particle can be appreciably increased. as compared with a horizontal air stream (Fi,?. 3). 80 r
2
I
31
23
x +
x
75
x
70
II
I I
ii
ii
65
i
60
I
3
T i i I i i x
I
II I
iv
xx
x
III
I I/ xx x
ii ii
IO
xx
5
0 0.2
Horizontal Fix. 3
Eflect (I
of upward inclinaiion
I on ,just coming
4
3
0.3
of the air stream
out of the air stream
(2)
distance on horizontal at a vertical
traversed,
distance
56
ft
traversed
by a particle
di.stanca of 1.3 ft and (3)
atgO
from fi
the origin
352
A QUALITATIVE
THEORETICAL
APRROACH
certain angle, there is a gradual increase in the distances traversed with the increase in upward inclination of the air stream; beyond this point there is a decrease. The angle has a different value for different particle pairs (Table IV), it being 50-60” for pairs formed with Particle 1. Thus, by directing the air stream upwards at an angle of 50-60”, the particles may be better resolved or the same operation may be done at a comparatively lower air velocity. Incidentally, by comparing Tables 111 and IV, it was observed that in these two cases the resolution of the particles was almost of the same order. Therefore, the same effect can be achieved without free fall, and hence in a more compact space, by directing the air stream upwards. Eflect of’fbn
4.4.
diameter (Series
i-HI. PROBLEM
Efikct of’particle EFFECT JECTED
WINNOWIKb
size (S2rie.v E and F)
OF PARTICLE AREA
OF
MASS. KEEPING
PRO-
CONSTANT
The lighter a particle the more time it takes to pass through an air stream and hence the further it is carried away. Fig. 5, Curve I, shows distances resolved between Particle 1 and identical particles having lesser mass. Mass ratios of the lighter particles to that of Particle I were plotted versus distances resolved (with respect to Particle 1). The plot shows that for a particle to be resolved through 3-6 in, it should have a mass of 62-48 I’;) that of Particle 1, at the same projected area
100 80
D)
The correlation between fan diameter and air velocity required is shown in Fig. 4. It was obtained by, first, calculating the distance travelled by Particle 1 in an air stream 1.3 ft across having a velocity of 1000 ft/min without free fall above or below it. The depths of the air stream required to move a given particle through the same distance with different air velocities were then obtained by plotting its trajectories at air velocities of 300-l 500 ft/min up to a depth of 10 ft. The correlations may be expressed as 0.6 ft < D < 2.5 ft MO= 19.50 D--o.5’ 2.5 ft < D < 6.0 ft uo = 2344
4.5. 4.5. I.
TO
60
o
40
‘;, L
i/ J O(
Distance resolved, in Fig. 5.
D- o.72
E#ect of mass and projected area on horizontal distance resolved between fwo particles
40
c
I
4.5.2.
EFFECT
OF
PROJECTED
AREA,
KEEPING
MASS CONSTANT
4
1”” O-6
0.6
I.0
I 2 Diameter.
Fig. 4.
I
I 4
I
lllil 6
6
IO
ft
Correlation between fan diameter and optimum air velocity .for winnowing qf paddy grains
The greater the projected area of a particle, the further it is carried away in unit time in a given air stream as the drag force acting on the particle is directly proportional to its projected area. Fig. 5, Curve 2, shows distances resolved between Particle 1 and identical particles having a larger projected area. The projected area ratios of a particle and that of Particle 1 were plotted versus distances resolved (with respect to Particle 1). The plot shows that for a particle to be resolved through 3-6 in it should have a projected area 1.63-2.16 times that of Particle I at the same mass.
Horizontal distances (in) resolved between particles (of a pair of particles) and the increase parenthesis), 4/, of the corresponding values without free fall
Psrriclr
in distances
resolved
(in
ouir
____ l-5
.f 4
1 h
__-..-_ .ij
.~ /
-I 5
13.70
14.46
15.06
26.54
0.76
I .36
0.60
15.77 (15)
17.09 (18)
18.05
(20)
31.13 (17)
I.32 (74)
2 2x (68)
O-Y6 (60)
17.21 (26)
18.77 (30)
19.73 (31)
34.0 I (28)
I .56 (105)
2 52 (X5)
O.Y6 (60)
21.01 (53)
22.2 I (54)
23.05 (53)
38.55 (45)
I .20 (58)
2.04 (50)
i/
O-84 (40)
28.72 (110)
30.37 (110)
31.30
46.88
( 108)
(77)
I.65 (117)
2.58 (YO)
; 1
0.93 (55)
31.72 (132)
34.36 (138)
35.56 (136)
51.63 (Y5)
2.64 (247)
3.x4 (182)
~
I.20 I 100)
!_
--
-
TABLE IV
Horizontal distances (in) resolved between particles (of a pair of particles) at the end of a vertical fall of 1.3 ft from the origin, and the increase in distances resolved (in parenthesis), “d of the corresponding values without inclination Particle
puir
I-3
I-4
l-5
I6
3 3
18.69 (36)
20.03 (39)
20.62 (37)
39.03 (47)
I .33 (75)
I.Y3 (42)
I .0x (X0)
23.97 (75)
25.87 (79)
26.97 (7%
49.65 (87)
I .90
( 1.50)
3.00 (1’1)
(X3)
29.58 (76)
31.87 (120)
33.33 (121)
56.Y7 (I 15)
2.29 (201)
3.75 (176)
I .46 (143)
34.88 (155)
36.14 (154)
38.38 (155)
61.58 (132)
I.87 (146)
3.50 (157)
I ,64 (173)
38.36 (180)
40.8 I (182)
42.22 (180)
62.86 (137)
2.45 (222)
3.86 (184)
t 135)
14.97 (160)
40.40 (195)
42.63 (195)
43.96 (192)
60.Y6 (130)
2.22 (192)
3.56 (162)
(112)
15.28 (165)
39.81 (191)
41.57 (187)
42.68 (183)
55.56 (109)
1.76 (132)
2.87 (III)
-
I.10
I.11
I.33
I II (X5)
354
A
QUALITATIVI:
TH~ORt’II(‘Al.
APPROACH
4.5.3. EFFECT OF M/A RATIO The preceding two correlations define the minimum requirements of particles that can be separated by pneumatic means. By definition, drag force F ==4 pf Cd A Us = M P,, :. P,, -- gf Cc/ A U’/2M To separate two particles they should be differently accelerated under a given set of conditions. In the above equation, pf is constant,& can be taken as 0.5, as all the particles come in the turbulent zone for a 1000 ft/min air stream. and the value of U is the same for all particles at the instance when these just start moving in the same air stream. Hence, Pa, = $ (A/M) or $ (M/A) thereby indicating that the M/A ratio is an important property of a particle in pneumatic separation. 0.; r 0.6 c I
r
THE
I’ROBl.~~~
OI-
WJN\OWI\(,
given set of conditions. These trajectories can also help in the generalization of certain experimental results. With the increase in height of free fall above air stream, the distance resolved between two particles decreases. This shows that to resolve two particles through a certain distance requires higher air velocity with free fall than without free fall above the air stream. By increasing the depth of free fall below the air stream or by directing the air stream upwards up to a certain angle (depending upon the particles and air stream involved) either the particles can be better resolved or the same operation can he carried out at a lower air velocity. To separate two particles, either one should be lighter than the other (the projected area remaining the same) or the projected area of one should be greater than that of the other (the mass remaining the same). In other words there should be certain minimum difference in the values of M/A ratios of the two particles. 6.
L
0.1
p
0.06
I
0.06 t
-
0.04
\
2
)
0.02
1 .1’!’
0.01 0.4
Fig. 6.
O-6
I
i 2
1 1 ‘1~111 4
6
6
IO
I
I I
20
40
I
3i.il.i 60
100
in Distance resolved , Eflect sf M/A ratio on horizon& distance resolved between
Acknowledgements The authors wish to express their gratitude to the authorities concerned with the digital computer installed in the Institute. Special thanks go to K. Venkatratanam and A. Maity, who programmed and processed the problem for the solution on the computer. Thanks are also due to the Council of Scientific and industrial Research, Government of India. for providing the research facilities.
two particles
Thus to separate two particles they should have different values of M/A ratios. Fig. ci shows a correlation based upon Curves 1 and 2 of Fig. 5, as obtained by plotting M/A ratio of a particle versus distances resolved with respect to Particle 1. It shows that for a particle to be resolved through 3-6 in it should have a M/A ratio of 0.27-0.19.
KEFEKENCLS
Kashayap, M. M.; Pandya, A. C. Air velocity* reylrirc~ment for winnowing operations. J. agric. Engng Res.. 1966, 11 (I) ’ Lapple, C. E.; Shepherd, C. B. Calculation of purticlr trajectories. Ind. Engng Chem., 1940, 32 (5) 605 ’ Co&on, J. M.; Richardson, J. F. Chemical engineering Vol. II: Unit operations. English Language Bk Sot.: ’
Pergamon Press, Lond., 1962, chap. 14 ’ Dallavaile, J. M. Micromeritics, the technologv qffim particles. Pitman Publishing Corp., N.Y.. 1948. chap. 2 5 Zenz, F. A.; Othmer. D. F. Fluidizatiorr urrd .flNidparticle systems. Reinhold Publishing Corp., N.Y.: Chapman & Hall Ltd, Lond., 1960, chap. 6
’ Henderson, S. M.; Perry, R. L. Agricultural 5.
Conclusions Comparison of particle trajectories obtained with a digital computer shows how effectively two particles can be resolved from each other under a
engineering.
proces.,
John Wiley & Sons Inc., N.Y.. 1955. p.
155 ’ Bilanski, W. K.; Collins, S. H.; Chu, P. Aerodynamic properties
qf seed grains,
their behaviour
in free .fall.
Agric. Engng. St Joseph, Mich.. 1962, 43 (4) 216