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straw materials
J. agric. Engng Res. (1990) 46, 275-290
Aerodynamic Properties of Grain/Straw Materials B. Y. GORIAL, J. R. O'CALLAGHAN The drag coefficients of a wide range of grains and straws have been measured experimentally by finding the suspension velocities of the particles in an air stream. The representation of shape is discussed and volume shape factors are proposed for non-spherical particles. The effect of nodes on the orientation of straws in a vertical air stream is examined. Drag coefficients have been correlated for different seeds and straws as a function of Reynolds number by grouping the particles within the limits of a sphere and a cylinder. A formula for calculating terminal velocity is proposed.
1. Introduction The processes of pneumatic conveying of grain, fluidization, and the separation of grain/chaff-straw mixtures and grain/grain mixtures all depend on the behaviour of particles in an air stream. While there is a large amount of literature on aspects of the subject, in particular the m e a s u r e m e n t of drag coefficients for cereal grains, there has been little effort towards correlating the results for a wide range of both seeds and straw in such a way that they could be used as a basis for the design of separating, cleaning and grading equipment. The lack of such correlations is attributed to the difficulties involved in accounting for the wide range of shapes found in seeds and straw. Cooper 1 stated that the amount of material r e m o v e d by aerodynamic means in a conventional combine is much less than that r e m o v e d in laboratory studies. H e pointed out that there is a greater difference between the terminal velocities of wheat kernels and wheat straw than is the case with oats or barley. This characteristic makes wheat easier to separate than other grains. Tiwari 2 investigated the possibilities of pneumatic separation of good beans from mixtures of threshed, dry, edible beans containing d a m a g e d beans, stones, leaves, stems and roots. He pointed out that the actual suspension velocities for individual beans were found to be less than the calculated values. H e attributed this to the effects of spinning and the rotation of the beans in the air stream. Using the geometric mean diameter, the drag coefficients for four varieties of beans were found to vary between 0-45 and 0-65. H e concluded that 80% of d a m a g e d beans could be separated without significant loss of whole beans. Bilanski and Lal 3 determined the terminal velocities of wheat grains and straws of various lengths. They found the terminal velocities of wheat grains to be in the range 8-8-9.2 m/s. The results showed that straws less than 6 cm long with a node at one end, had the highest terminal velocity (4.9 m/s). Shellard and MacMillan 4 measured the terminal velocities of a range of threshed wheat materials. They concluded that partly threshed heads are the most variable c o m p o n e n t s , and the terminal velocity values for these and the white caps, containing single grains, overlap the lighter materials without grains. Bilanski et al. s and Bilanski and Lal 3 concluded that rotation of particles in an air stream caused a higher drag and lower terminal velocity. G a r r e t t and B r o o k e r e also observed the tumbling of grains falling in still air. Department of Agricultural and Environmental Science, University of Newcastle upon Tyne, UK Received 31 July 1989; accepted in revised form 9 December 1989 275
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Notation
A Cd d dg de Fd Fg g
area of particle projected to the airstream, mm 2 drag coefficient of particle diameter of particle, mm geometric diameter, mm diameter of equivalent sphere, mm drag force, N gravitational force, N gravitational acceleration, m/s 2
M Re Va Vt
mass of particle, Kg Reynolds number air velocity, m/s terminal velocity of particle, m/s
Z volume shape factor Pa specific density of air, Kg/m 3 pp specific density of particle, Kg/m a /z kinematic viscosity of air, Kg/m. s C1, C2 constants Vg volume of grain, mm 3 VT total volume of cylinder and pipe, mm 3 Vcy~ volume of cylinder, mm 3 Vpir~ volume of air in the pipe, mm 3 V~2 volume of liquid displaced, mm 3
Farran and MacMillan 7 found that higher air velocities were required to separate chaff from grain than to suspend chaff on its own. Uhl and Lamp 8 concluded that if straws were reduced to shorter lengths (less than 5 cm) during threshing, it was quite probable that a complete separation of grain from the threshed material would be achieved. Smith and Stroshine 9 found that complete pneumatic separation of corn cobs from stalks was impractical because of the overlapping of the terminal velocities of some stalks with those of the cobs.
1.1. Particle orientation and frontal area In applying aerodynamic principles to agricultural products, a method for expressing the projected area of the particle must be chosen. Mohsenin 10 reported that in most cases particles have been assumed to be spherical; the diameter of the particle being taken as the diameter of a sphere of the same volume as the particle. In cases where the volume of the object is difficult to evaluate, the geometric mean diameter (dg) is a good approximation of the diameter of the equivalent sphere (de), provided that the shape factor (Z) is close to unity. Very little work has been done on irregular shapes, which are complicated by their random orientation, and the variety of methods used to express their size and dimensions in the calculation of frontal area and drag coefficient. Keck and Goss 1~ used the geometric mean diameter of three mutually perpendicular measured seed dimensions. They observed that using the diameters of the equivalent spheres gave lower terminal velocities than the measured values. This indicates that the geometric mean diameter may vary considerably for irregular objects such as seeds. For different seeds, they suggested the determination of a shape factor, defined as the ratio of geometric mean diameter to the diameter of an equivalent sphere. The shape factor for clover seed (1.04) was closer to that of a sphere (1.0) than the shape factor of alfalfa seed (1.16). The greater sphericity of clover seed was also demonstrated by its drag coefficient. 1.2. Drag coefficient and Reynolds number The Reynolds number, Re, associated with the terminal velocity, Vt, of a particle can be based on the square root of the projected area, to make it consistent with the drag
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coefficient, Cd, which is based on the projected area, A. The drag coefficient includes both skin friction and pressure drag. The unstable behaviour of threshed material such as wheat straw and alfalfa stems, was investigated by Bilanski and Lala and Menzies and Bilanski. TM They concluded that a node at one end of a straw has a significant effect on its drag coefficient, by causing the straw to orient itself towards the vertical. Many coefficients have been defined in the literature to characterize the aerodynamic properties of materials. Shellard and MacMillan4 used the value of CdA, while Bilanski and Lala used a resistance coefficient, K, where K = Mg/V2t. The K values of Bilanski and Lala are directly proportional to CdA. They concluded that the resistance coefficient, K, which did not involve an assumption about the effective area, that was necessary when calculating drag coefficient Co, appeared to be a better criterion for the separation of various particles than the drag coefficient. They discovered that the drag coefficients of middle node straws were of the order of that of a circular cylinder and within the same range of Reynolds number. Drag coefficients for various grains, reported by Bilanski et al.,S were lower than drag coefficients reported for similar grains by Uhl and Lamp. a Mohsenin TM suggested that the primary reason for this could be the differences in the assumptions made about the frontal area.
2. Theory The aerodynamic properties of a particle can be determined by measuring the equilibrium conditions, when the particle is suspended in a stream of air. The vertical force balance on a suspended particle is given by F = . tz C d p A V za = Mg
(1)
A general expression for the terminal velocity of a particle is obtained by setting the gravitational force, Mg, equal to the resistance drag force, Fd, and by assuming that the air velocity, Va, is equal to the terminal velocity of the particle, Vt If
Mg=Fd then
when
Va=Vt
1 Mg = ~CdpaA Vt2
(2)
and
VZt= 2Mg CdPaA
(3)
For a sphere of diameter d,
A = aid2~4 and
M = ~ppd3/6 Lapple la reported that the drag coefficient of spherical particles, Cd, is 0.44 in the range R = 1000-200 000. Substituting for A, M and Cd in Eqn (3), the terminal velocity is given by,
V2t = 3gdpp/Pa
(4)
Reynolds numbers of particles (based on the square root of the projected area) were calculated from
Re = paVad/# in the range Re = 1000-200 000
(5)
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The net force on a particle moving in a fluid is the difference between the gravitational force, Mg, and the resultant drag force, Fd. Therefore, Net Force = ½Cdp,AV~ - Mg
(6)
2.1. Volume shape-factor of non-spherical particles Different methods have been used for expressing the size and dimensions of irregular shaped particles in the calculation of Reynolds numbers and frontal areas. Schiller 14 showed that, for Reynolds numbers of less than 50, the assumption of sphericity for irregular particles is not extreme if the diameter is taken as the diameter of an equivalent sphere. For Reynolds numbers greater than 50, however, the drag coefficient curves level off and the assumption of sphericity will result in considerable errors. Heywood 15 concluded that Eqn (3), for predicting the terminal velocity of spheres, could be applied to granular materials other than spheres by applying a correction factor (z/6Z) to the drag coefficient of spheres. Substituting the value of spherical drag coefficient (0-44) in Eqn (3) yields V ~ - 4gdpp( 6Z / ~r)
(7)
3 x p. x0-44 Heywood found that the value of Z for a range of granular particles was 0-4 while for spheres it was equal to ~/6.
2.1.1. Predictions of volume shape-factor Sphericity is a criterion for describing the shape of particles. Curray ~6 expressed the degree of sphericity by assuming that the volume of the particle is equal to the volume of a tri-axial ellipsoid, and the diameter of the circumscribed sphere is the longest intercept of the ellipsoid. Thus, Sphericity = volume of solid/volume of circumscribed sphere = geometric mean diameter/major diameter
(8) (9)
Mohsenin ~° reported that in some cases, the shape of the solid can be approximated by one of the following geometric shapes and its volume can be calculated using the appropriate equations: (a) Prolate spheroid (e.g. lemon) Volume = ycab2/6 = ~d3/6
(10)
(b) Oblate spheroid (e.g. grapefruit) Volume = ~a2b/6 = ~d3/6
(11)
Volume = ~h(r~ + rlrz + r2)/3
(12)
(c) Right circular cone (e.g. carrot) where a and b are the major and minor diameters of the ellipse, respectively; rl and rz are the radii of the base and top, respectively; h is the height; and dg is the geometric mean diameter.
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Mohsenin 1° suggested that by estimating the volume in this manner, the actual volume can be determined experimentally, and a correction factor, K, can be established for the "typical" shape of each product. In this analysis, the correction factor was assumed to be a function of grain sphericity. If K = C~ sphericity, the actual volume of prolate and oblate spheroids is Volume = :rd3K/6 = [ :r d3C1"~ (sphericity) \6
g
(13)
]
However, considering the diameter of the equivalent sphere, de, the volume of prolate or oblate spheroids can be assumed to be: Volume = C2d~
(14)
where C2 = constant. Solving Eqns (13) and (14) yields
Cdg/6 (sphericity) = or
j.g
C2d 3
----(ag]
Z = C2/CI = ~ \de/ 3 (sphericity)
(15) (16)
3. Materials and m e t h o d s
3.1. Suspension velocity tests A duct, 1.225 m long with a rectangular cross-section of 0.16 m x 0-12 m and two walls which diverged at 2°, was used to suspend particles in an air stream. Air was supplied by a centrifugal fan driven by a 0-75 kW d.c. motor connected through a rectifier. The fan delivered air through a flow straightener section, which consisted of two layers of fine wire mesh above and below a honeycomb grid. Mean air velocity in the test section was determined as a function of the mid-stream velocity, obtained from calibration tests using a pitot tube and micromanometer in a 56 point traverse. Air velocity close to the duct wall was 5 - 1 0 % less than the average and was neglected. The micromanometer and pitot used were capable of reading to 0.2 m/s. The average deviation of air velocity from the mean value was found to be 3%. The duct was calibrated so that the air velocity at any given height could be determined from the velocity of the mid-air stream. Suspension tests were carried out by placing particles in the duct, while the fan discharge was increased until the particles, seen through the transparent wall, floated in the central area of the air stream. Floating tests for straws were repeated in a second rig of cross-section 0.22 m x 0-4 m. Ten samples from each group were tested and each particle was tested twice. The average values of terminal velocities were recorded. Suspension velocities of the straw pieces were difficult to determine because of the unstable behaviour of straws in the air stream. Average particle mass and its suspension velocity were obtained by taking the arithmetic mean of each group of 20 readings. Dimensions of particles were carefully measured along three perpendicular axes using a micrometer. The moisture content of particles was 7% wet basis. Each particle was weighed by an electronic balance capable of reading to 0-0001 g. 3.2. Grain and straw samples Wheat, barley and oilseed rape straw were cut into lengths (10-110 mm) to form three groups for each crop according to the node position; end-node straw, middle-node straw and straw without node.
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Various types of grain were used to cover wide ranges of drag coefficient, size, density, shape and sphericity. Different sizes were collected for each type of grain. Less dense grains of the same crop were discarded. The diameter of the equivalent sphere was obtained from the density and mass of the grain. The weight and suspension velocity of grain and straw were measured for ten samples from each size. The suspension velocity and mass for any particular size of each crop were estimated by taking the arithmetic mean of the ten samples. 3.2.1. Drag coefficient of straw Since the effective frontal area of a straw suspended in an air stream is required when calculating the drag force, orientation of the straw pieces must be taken into consideration. The projected area of the inclined straw was difficult to determine because of the unstable behaviour of straw in an air stream. Drag coefficients were measured for flow both normal and parallel to the axis of the straw since the projected area of the straw could be determined easily for both these cases. Drag coefficients for inclined straws could then be estimated by interpolating between these two values. 3.2.2. Floating of straw horizontally It was possible to float the node-free and middle-node straws horizontally in the lower part of the duct, where the air flow was more uniform; these straws were cut to have a shape similar to ideal symmetrical cylinders. During the tests straws were observed to float in the air stream without appreciable inclination or vertical movement. However, this was not possible for end-node straws because of their non-symmetrical shapes. This lack of symmetry was due to the presence of a node at one end. Another group of wheat stt;aws, each with two nodes, was prepared and cut to resemble symmetrical cylinders. These were suspended horizontally within the air stream. Since the drag coefficients of spheres and circular cylinders are well established, circular cylinders and spheres of different sizes were used to check the method and the apparatus. The results of 13 trials for measuring drag coefficients of spheres and cylinders gave satisfactory agreement with values of 0.44 and 1.0, respectively. 3.2.3. Floating of straws vertically Trial experiments were carried out to measure the drag coefficient of straws when floated vertically within the air stream (axial flow). Plastic cylinders were used to simulate individual straw particles, because they have diameters and terminal velocities similar to those of straw. These cylinders were cut into different lengths (5-50 mm), and one of the ends was filled with plasticine in order to simulate the end-node straws. The quantity of plasticine used was varied for the same particle until it floated vertically without appreciable vibration along its long axis. The height at which the particle was floated and the mid-air stream velocity were both recorded and later checked against calibration curves. Further trials were then conducted with the aim of extending the previous trials to the end-node straws of wheat, barley and oilseed rape straw. Samples of end-node straws which floated at oblique angles were trimmed carefully by a fine file from the end of an existing node and then floated in the air stream. The length of the test sample was gradually decreased after each run until the straw was suspended vertically without any appreciable indication of vibration in its vertical movement. Then the velocity of the mid-air stream at suspension was recorded.
3.3. Volume and density of grain The irregular shape of most intact agricultural products and the small size of materials, such as grains, present certain problems in volume and density measurements. The diameter of an equivalent sphere is an important factor for calculating the drag
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coefficients of grains. Hence it was considered useful to measure the density of grain in order to see what variation lay between geometric mean diameter and the diameter of an equivalent sphere. Three different methods were used for the measurement of volume and density. 3.3.1. Water displacement m e t h o d
Because of the irregular shape of the product, the volume is determined by water displacement. However, since water has a tendency to soak into the kernel, the volume of water transferred into the kernel was taken into consideration in calculating the actual volume of the treated sample. Five samples of wheat, barley and oilseed rape were collected randomly during the harvest of 1988 and stored at a moisture content of approximately 7% (wet basis). Absolute grain densities were calculated from the sample weight and the change in the volume measured from the relationship: Actual volume = volume of water displaced + volume of water transferred into the kernels
(17)
Ten tests for the same type of grain were carried out and the mean value was recorded. 3.3.2. D r y p y c n o m e t e r m e t h o d This method is used to determine the density or porosity of an unconsolidated mass of material such as grain. The advantage of this method is that there is no tendency for air to soak into the kernel surface. This method is based on the principles of the perfect gas law. The apparatus consists of a cylinder of known volume connected to a U-shaped tube manometer. The procedure of measuring grain density entailed determining the exact capacity of the pycnometer. A known mass of grain was placed in the pycnometer, covered and sealed to prevent any leakage of air. When both sides of the manometer (containing a liquid of low specific gravity, 0-786) were in balance with the atmospheric pressure, P1, the free arm of the manometer was lifted causing a new equilibrium pressure, P2. Under these isothermal conditions, according to the perfect gas law: (18)
P1VI = m R T = P2V2
where, V1 = g T -
Vg ~-- Vcg I -
Vg + Vpipe
v2=vT-vg-va2 Vg(P2 - P,) = VT(Pz -- PO - PzV~ or
Vg = l i t - Pz Vaz
(19)
The grain samples were tested five times and the average grain density was recorded. 3.3.3. Size m e a s u r e m e n t
Grains of a similar type were classified into different and significant ranges according to their size by sieving. Thirty grains for each sub-sample size were randomly chosen and measured carefully along three perpendicular axes using a micrometer. The mean weights and geometric mean diameters of grains were determined in order to calculate the grain density for each specific size from the same crop. 4. Results and discussion 4.1. Grains
While the main focus of this study was wheat, barley and oilseed rape, the behaviour of the following grains in an air stream was also measured in order to give a fuller picture about the characteristics of seeds: rice, soybean, bean, maize, rye groat, whole lentil,
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MATERIALS
sorgham, mung, adzuki bean, buckwheat, pinto, marrowfat, black eye, white kidney, chickpeas, sesame and millet. Aerodynamic and physical properties of these grains are summarized in Table 1. The ideal, stable condition in the floating experiments was not obtained because grains assumed different positions within the air stream, since they rotated and tumbled due to their irregular shape and the turbulence of flow. Most of the grains were tested twice and the average readings were recorded when the particle was suspended in the central region of the duct, free from the interference due to the duct wall. Since the drag coefficient for spheres is well established, different sizes (12 to 20 mm) of plastic and wooden spheres were used as a check on the experimental method. Results of six trials for drag coefficient gave satisfactory agreement with the value of 0-44. While spheres had a tendency to cling to the duct walls due to the boundary layer at the wall of the duct, grains did not have this tendency; due to their irregular shape, they tumbled and rotated as mentioned by other experimenters. As the grain approached the duct wall, it would collide with the wall and then rebound towards the centre of the duct. 4.2. Volume and density The densities of wheat, barley, rice, rapeseed, soybean, maize and sorgham were measured by the three different methods described in Section 3.3. The results are presented in Table 2. Satisfactory agreement was obtained between the results of the water displacement and dry pycnometer methods for similar grains. However, a significant difference was found between them and the results obtained by the size measurement method. The actual density was taken as the average value of the results of the water displacement and dry pycnometer methods. This actual density was used in calculating the diameter of an equivalent sphere by using de = [ ( M / p p ) ( 6 / g ) ] 1/3 (20) Table 1 Parameter mean values for various grains
Grain
Wheat Barley Soybean Maize Beans Rapeseed Sesame Millet Sorgham Buckwheat Mung Adzuki Marrowfat Rye Rice
Green lentil Whole lentil Pinto Chickpeas Black eye
Geom.
Equiv.
Drag
Mass, mg
Terminal velocity, m/s
dia.,
dia.,
mm
mm
coeff. Ca
Re
Spherity
Z m measured
Zp predicted
30.2 37-6 197 321.2 444.0 4.46 2.36 6.00 30.9 27.6 75.5 115-6 397-2 33-4 16.5 78.7 33.4 360.3 391-4 136.4
7.8 7.5 14-0 11-6 13.3 6.7 4.4 7.6 9.7 8.9 12.0 12.6 15-2 7-8 7-2 8.3 9.9 14.0 12.7 12-7
3-36 4-08 6.22 7.50 8.35 2-05 1.66 2-04 3-61 3.60 4-60 5-40 8-10 3.70 2.75 5-00 3.50 8-10 8-50 5.90
3.29 3.70 6.14 7.62 -1.94 1.62 -3.5 -----2.75 ------
0.85 0.98 0.50 0.81 0-80 0.57 0.76 0.56 0.59 0-61 0-55 0-57 0-60 0.87 0.84 1.00 0-62 0.63 0.81 0-79
1692 1802 5646 5721 6970 0828 0450 0971 2156 1983 3466 4200 7714 1804 1269 2068 2178 7120 6823 3993
0-61 0.49 0-93 0.70 0.55 0.93 0-64 0.95 0.80 0.84 0.90 0.79 0.83 0-46 0-45 0.71 0.85 0-65 0.82 0.73
0.27 0.23 0.46 0.29 0.29 0-40 0.30 0-41 0.39 0.38 0.42 0.40 0-38 0.26 0-27 0.23 0-37 0-37 0.28 0.29
0.3 0-19 0.47 0-38 0.30 0-41 0.31 0-47 0.38 0.41 0-44 0.39 0.40 0.23 0-24 0.35 0.42 0.32 0-36 0.34
Shape factor
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Table 2 Grain densities (kg/m 3) based on three different methods Grain
Size measurement
Water displacement
Dry pycnometer
1260 1320 1020 1340 1370 1000 1250
1260 1440 1340 1370 1450 1140 1380
1240 1370 1370 1420 1400 1180 1410
Maize Wheat Barley Soybean Rice Rapeseed Sorgham
Results for the densities of wheat, maize and soybean grain obtained by Uhl and Lamp a were lower than the densities obtained in this study for similar grain, measured by a similar water displacement method. The reason for this could be that the quantity of water soaked into the kernels was not taken into consideration with the method used by Uhl and Lamp. On the other hand, a satisfactory agreement was found between the current results and the results obtained by Bilanski et al.,S except for maize grain. The method used was size measurement. No significant difference was found between the diameters of equivalent spheres and the geometric diameters for most of the grains except for barley as shown in Fig. 1. This difference for barley is probably due to the elongated shape of barley grain. Therefore, the equivalent diameter for other grains used was taken as the geometric mean of the three dimensions, and was used to calculate the Reynolds number, projected area and drag coefficient. 4.3. Drag coefficients The drag coefficient of any particle depends on its density, suspension velocity and projected area. Since agricultural grains cover a wide range of sizes, suspension velocities, o
!
E
8i
Soyb
E F:
6
'5 5 U "E 4 ~
3 2
1 y
ize Barley_~/~ ~ "2~ Rice
Rapeseed
Equivalent diameter, mm Fig. 1. Relationship between geometric diameter and the diameter of an equivalent sphere for different grains
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A E R O D Y N A M I C P R O P E R T I E S OF G R A I N / S T R A W M A T E R I A L S
densities and shapes, an array of drag coefficient values in the range of spheres and cylinders (0.44-1-0) was expected. The drag coefficients measured for all grains in this study may be summarized within four different groups, which lie between the drag coefficients of spheres and circular cylinders. Drag coefficients are plotted against Reynolds numbers in Fig. 2, which also shows the curves for ideal particles: Group 1 represents soybean, adzuki bean, mung, sorgham, millet and oilseed rape. The average drag coefficient is 0.47. Group 2 represents lentil, sesame, pinto, marrowfat and buckwheat. The average drag coefficient was found to be 0.6. Group 3 represents wheat, chickpeas, beans, rye, maize and rice. The average drag coefficient is 0.8. Group 4 represents barley and green lentil with an average drag coefficient of 1-0. Although the range of Reynolds numbers was relatively large (1000-10000), no obvious variation of the drag coefficient with the Reynolds number was found within each group and no apparent difference was noted between the drag coefficients for different sizes of the same group. Higher scatter was observed in the drag coefficients of group 3 than in that of other groups. The primary reason for this is that group 3 represents grains of elongated shapes, which behave more unstably in an air stream than others which are closer to spheres. Drag coefficients of maize grains were found to vary from 0-8-1.0 and they are included in both groups 3 and 4. This wide range of drag coefficients was probably due to the difference in the shape of grains of the different varieties used. It was observed that grains with flatter shapes have higher drag because they assume a horizontal position and have larger projected areas than other shapes. Drag coefficients of grains obtained by Shellard and MacMillan, 4 Hawk, Brooker and Cassidy, w Bilanski et al. s and Uhl and Lamp a were compared with the present experimental results. Satisfactory agreement was obtained between the results of 2-0 1.8 1.6 1-4 1-2 1.0 ,P 0.8
~[]
c:
u
0'6
o u
0"4
~I~B r
0.2
1()00
2 ( ) 0 0 3(~00 Reynolds number
' 5()00'7()0() 9000
Fig. 2. Drag coefficients of grain as a function of Reynolds number:~(, group 1;]'T, group 2; ~, group 3; ~7, group 4; ~ , cylinders; ~, spheres.
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J. R. O ' C A L L A G H A N
Shellard, Bilanski and Uhi for wheat, soybean and maize grain. However, a difference was found in the results of Bilanski for wheat and barley. The reason for this could be differences in the assumption regarding frontal area. In general, it can be concluded that the drag coefficients of different grains depend mainly on shape. 4.4. V o l u m e s h a p e f a c t o r Since the drag coefficients of grains are dependent on shape, the correction factor ( ~ / 6 Z ) applied to the drag coefficient of a sphere as suggested by H e y w o o d ~s was applied to the results for understanding the volume shape factor (Z) of grains. The correction factor was substituted by the drag coefficient term of Eqn (3), and Eqn (7) was obtained, which was then simplified with little loss in accuracy by assuming a constant air density of 1-15 g/m 3 giving. Vt = 7V~ppdp
(21)
in the range of Reynolds number (500-200 000). Values of the volume shape-factor (Z) were calculated for the different grains from Eqn (21) and are presented in Table 1. In order to check the accuracy of the calculated shape factors of grains, the predicted values of the terminal velocities of different grains [from Eqn (21)] were compared with other published results 4"s'a in Table 3. Correlation of volume shape factors (Z), calculated from Eqn (16), with the sphericity of grains is shown in Fig. 3. Satisfactory agreement was found with the shape-factor results of Keck and Goss. 1~ G o o d agreement was also found between measured values of Z based on Eqn (7) and the values from Eqn (16). Finally, as shown in Fig. 4, satisfactory agreement was found between measured velocities of grains in suspension and values calculated according to Eqn (21). 4.5. S u s p e n s i o n
velocity-diameter
correlation
The suspension velocity of any particle in a vertical air stream is a function of particle size, density and shape-factor [Eqn (21)]. Experimental results show that the volumeTable 3 Comparison of results for measured terminal velocity and density by different researchers Current Grain type
Barley Soybean Maize Rye Sphere Wheat Whitecaps
Vt, m/s
Uhl s pp kg/m 3
Vt , m/s
5.9-9.4 976-1156 -[6-8-9-0] 1 0 . 8 - 1 4 . 9 1066-1537 9.0-18.0 [11-5-14.51 [11-2-13-0] 10.4-12.8 1178-1396 7-8-12-6 [9.6-13.9] [10.8-11-6] 6-8-8-3 1040-1063 6 - 0 - 8 - 1 [7.2-8.4] [6.1-6-7] 19-9-14.5 640-782 -[20.3-15.4] 6.50-10.0 430-1562 5.7-9-0 [6.6-10.11 [6-0-7.4] 5.0 299 . . [5-11
Bilanski 3 Vt, m/s k;f;'n 3
p , kgfm 3
6.9 1005 [7.6] 1250-1218 13.3 1336 [14-4] 1196-1260 10.5 1482 [12.6] 1218-1280 . . .
Shellard 4 Vt , m/s kgTmP" 3
--
--
16-5 [16.81 8.9 [8-91
1049-1302 .
Numbers in brackets represent predicted values from Eqn (21)
.
--
--
--
--
--
--
1227
--
--
1321
8.0 [8-3] 5-3 I5"61
1335
.
473
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AERODYNAMIC
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OF
GRAIN/STRAW
MATERIALS
1.0 =
0-9 0-8
P ~
N
B .~ u
0.7
0.6
0-5
~ 0.4 e~
~ 0.3 ~0
0-2
•
o.1
I1..
(3
6.1
0"2
£)'3 6"4
6'5
0:6
0"7
0:8
0"9
110
Sphericity
Fig. 3. Variation of volume shape-factor, Z with grain sphericity. [], current results; ~7, Keck and Goss ; " ~>, sphere
shape factor (Z) and grain density (pp) for different types of grain lie between 0-27-0.49 and 1.15-1.4, respectively. This indicates that Z covers a wider range than po for different grains. When suspension velocity was plotted against grain size, a very low correlation coefficient was obtained. However, by plotting the square of suspension velocity against diameter for each group of similar shape-factors, the correlation was improved as shown in Fig. 5. 4.6. Straws Straw is one of the major contaminants in the mixture of threshed crop material to be separated from grain. Straws are neither symmetrical in shape nor uniform in density and this lack of symmetry causes aerodynamic instability. 2O E
.
18
~ ~6 ._u 1 4 Q.) ~¢-1 1 2
~
lO
g g
4 2 2
4 6 8 10 12 14 16 Suspension velocity (measured), m/s
18
20
Fig. 4. Comparison of calculated and measured values of suspension velocity of grains
287
B. Y. G O R 1 A L ; J. R. O ' C A L L A G H A N 6OO 55O 5OO
ul
F
450 400 35O
>
3OO 250 2OO 150 100 5O 0
0
1
2
3
4
Equivalent
5
6
7
8
9
10
diammter, mrn
Fig. 5. Variation of suspension velocity with grain size. F~, Zm(0.37-0.48) V~ = - 1 8 - 5 + 34.5dc; ~7 , Zm(0.27-0.30) V,2_- 20"3de; ~), Zm(0.23-0.29) V~ = - 14.9 + 19.2d~
As reported by Bilanski and Lal, 3 and Shellard and MacMillan 4 lack of motion at the terminal velocity was not achieved in their experiments, especially with end-node straw. In the present work, straws were found to have a wider range of suspension velocities than grains. Both straws and grains tended to rise to a cross-section with an air velocity slightly lower than the suspension velocity and then fall to a lower cross-section with a higher one. Some straws tended to m o v e at an oblique angle across the air stream, while others floated slantingly, and this gave them a higher terminal velocity than when floating horizontally. Straws greater than 6 c m long, and all straws with the node at one end assumed a m o r e vertical orientation in the air stream than others. 4.6.1. Drag coefficient o f straw Since the projected area of any particle suspended in an air stream is necessary for the calculation of its drag coefficient, the orientation of the straw must be taken into consideration. H o w e v e r , inclination is difficult to determine because of the unstable behaviour of the straws in the air stream. It was necessary to float some of the straws normal to the air flow so that when the straw is suspended horizontally, the projected area is a product of its length and diameter. T h e drag coefficient of straws floating horizontally in an air stream are shown in Fig. 6 as a function of Reynolds n u m b e r , where the characteristic dimensions is ~ / L . d. T h e average drag coefficient of 1-0 corresponds to the value for horizontal cylinders. When straws with a node at one end were floated vertically in an air stream, the terminal velocity at which the straws were held in suspension increased as either the length a n d / o r the mass of the straw increased as shown in Table 4. H o w e v e r , when t h e drag coefficient was correlated as a function of Reynolds number, using the diameter of the straw as the characteristic dimension, the drag coefficient was similar to that of a cylinder with its axis parallel to the air stream, 1.0.
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2.0 1.8 1-6 14 1.2
[]
1.0
0.8
0-6 u
0
u
0.4
tC3
0"2
1 0I 0 0
2 0 ,0 0
3 0 0I 0
4 0 I0 0
I
6 000
18000
Reynolds number
~
. 6. Drag coefficient as a function o f Reynolds number for different grains and ideal particles. , straw, vertical orientation;-ff, cylinder, vertical orientation; V , cylinder, horizontal orientation; 5~, straw, horizontal orientation Table 4 Results for end-node wheat and barley straw floated vertically
Length, mm
Diameter, mm
Mass, mg
Suspension velocity, m/s
Drag coefficient
Reynolds number
11.5 36.5 22.2 28.5 27-5 21.0 30.0 22.2 11.5 16-9 24-5 14.5 16.8 31.2 13.0 8.5 16.5 27.3 36.5 23.5 22.7 10.3 10.5
3-5 4-7 4-0 3.5 3.7 4.0 3.4 4.0 3.6 3.5 4-8 4.0 3.2 4.7 4.0 3.7 4.5 3.6 4.8 4.4 4.4 4-1 4-6
34.2 77.7 41.5 49.3 29.3 33.6 54.1 41.8 34.3 29.4 82.9 28.3 21-8 77-6 31-9 18.2 39.3 55.9 78-5 57.6 54.8 38-3 47-5
8.0 8.8 7.5 9-5 7.0 6.7 10-4 7-5 7-5 7-5 8.8 6-6 6.8 9.2 6-6 5-6 6.5 9.5 8.6 8.0 7.5 6.9 7.2
0-92 0-97 1-00 1.1.97 0.95 1.01 0.91 0.99 1-02 0.93 1.01 0-88 0.93 0.88 0.99 0-92 0-99 1-03 1.00 1.03 1.06 1.04 0.92
1814 2654 1917 2124 1655 1712 2292 1917 1725 1677 2699 1687 1412 2792 1687 1324 1869 2185 2610 2223 2132 181.17 2139
B. Y. GORIAL; J. R. O'CALLAGHAN
289
Table 5 Summary results of threshed wheat material from floating tests
Type of particle
Condition
Wheat grain Wheat grain Wheat (whitecap) Wheat head Wheat head Wheat head
---Unthreshed Part-threshed Threshed
Size
Geometric diameter, mm
Suspension velocity, m/s
Mass, mg
Drag coefficient
Small Large -Large Pieces Pieces
2.3 4.5 4.4-5.3 ----
6-5 9.9 4-5-5-0 6.8 4.5-5.4 2.6
8.0 66.7 17.2-30.0 1840 120-180 100
0.84 0-73 0.77 ----
4.7. O t h e r materials tested
Straws are considered the most difficult part of a threshed mixture to separate since the terminal velocity of some straws approaches that of the grains. It is assumed that if the straw is separated from the grain, the chaff will also be separated, because it has a much lower terminal velocity than the straw. T h e terminal velocity of chaff was not measured. Threshed, part-threshed heads and whitecaps of wheat were obtained from the sieves of a whole crop harvester, while unthreshed heads and long straws were cut directly from the crop and their characteristics are presented in Table 5. Whitecaps, a single grain covered by the husk, are larger in size and, as a result, have a lower suspension velocity and higher drag coefficient than the grain. Part-threshed heads have terminal velocities lower than unthreshed heads. 5. C o n c l u s i o n s
1. The range of grains found in the normal sample at harvest corresponds to a range of terminal velocities rather than a single characteristic velocity. 2. Pieces of straw with a node at one end, which tend to align themselves vertically in an air stream, have a higher terminal velocity than nodeless, or middle-node straw, which tends to take up a horizontal position in a vertical air stream. 3. The drag coefficients of grains, which may be correlated as a function of Reynolds number, lie within the limits of a sphere (0.44) and of a cylinder (1-0) depending on the shape of the grain. The drag coefficients of oilseed rape, soybean and millet approach that of a sphere while those of beans and maize tend towards that of a cylinder. 4. The drag coefficient of straw is approximately 1-0, similar to that of a cylinder. 5. The shape factor of grain is closely related to its sphericity. 6. The terminal velocity of a grain can be estimated from the values of its diameter, density and shape factor. References
1 Cooper, G. R. Combine shaker shoe performance. Transactions of the American Society of Agricultural Engineers 1966, Paper no. 66-607 2 Tiwari, S. N. Aerodynamic behaviour of dry edible beans and associated materials in pneumatic separation. M.S. Thesis in Agricultural Engineering, University of Maine, Orono, Maine, 1962 3 Bilanski, W. K.; Lal, R. Behaviour of threshed materials in a vertical wind tunnel. Transactions of the American Society of Agricultural Engineers 1965, 8(3): 411
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AERODYNAMIC PROPERTIES OF GRAIN/STRAW MATERIALS
4 Shellard, J. E.; MacMillan, R. H. Aerodynamic properties of threshed wheat materials. Journal of Agricultural Engineering Research 1978, 23(3): 273-281 Bilanski, W. K.; Collins, S. H.; Chu, P. Aerodynamic properties of seed grains. Agricultural Engineering 1962, 43(3): 216-219 • Garrett, R. E.; Brooker, D. B. Aerodynamic drag of grains. Transactions of the American Society of Agricultural Engineers 1965, 8(1): 49-52 7 Fan'an, i. G.; MacMillan, R. H. Grain-chaff separation in a vertical air stream. Journal of Agricultural Engineering Research 1979, 24(2): 115-129 a Uhl, J. B.; Lamp, B. J. Pneumatic separation of grain and straw mixtures. Transactions of the American Society of Agricultural Engineers 1966, 9(2): 244-246 9 Smith, R. D.; Stroshine, R. L. Aerodynamic separation of cobs from corn harvest residues. Transactions of the American Society of Agricultural Engineers 1985, 28(3): 893-897 lo Mohsenin, N. N. The properties of plant and animal materials. New York: Gordon and Breach, 1970 11 Keek, H.; Goss, J. R. Determining aerodynamic drag coefficients and terminal velocities of seeds in free fall. Transactions of the American Society of Agricultural Engineers 1965, 8(4): 553-554 12 Meazies, D.; Biinski, W. K. Aerodynamic properties of alfalfa particles. Transactions of the American Society of Agricultural Engineers 1967, 11(6): 829-831 13 Lapple, C. E. Fluid and particle mechanics. University of Delaware, Newark, 1956 14 Schiller, L. Fallversuche mit kugeln und scheiben. (Drop tests with spheres and discs.) Handbook Experimental Physics 1932, 4(2): 338 is Heywood, H. Calculation of particle terminal velocity. Journal of Imperial College Chemical Engineering Society 1948, 4:17 16 Curray, J. K. Analysis of Sphericity and Roundness of quartz grains. M.S. Thesis in Mineralogy, The Pennsylvania State University, University Park, Pennsylvania, 1951 1~ Hawk, A. L.; Brooker, D. B.; Cassifly, J. J. Aerodynamic characteristics of selected farm grains. Transactions of the American Society of Agricultural Engineers 1966, 9(1): 48-51
Aerodynamic Properties of Grain/Straw Materials B. Y. GORIAL, J. R. O'CALLAGHAN The drag coefficients of a wide range of grains and straws have been measured experimentally by finding the suspension velocities of the particles in an air stream. The representation of shape is discussed and volume shape factors are proposed for non-spherical particles. The effect of nodes on the orientation of straws in a vertical air stream is examined. Drag coefficients have been correlated for different seeds and straws as a function of Reynolds number by grouping the particles within the limits of a sphere and a cylinder. A formula for calculating terminal velocity is proposed.
1. Introduction The processes of pneumatic conveying of grain, fluidization, and the separation of grain/chaff-straw mixtures and grain/grain mixtures all depend on the behaviour of particles in an air stream. While there is a large amount of literature on aspects of the subject, in particular the m e a s u r e m e n t of drag coefficients for cereal grains, there has been little effort towards correlating the results for a wide range of both seeds and straw in such a way that they could be used as a basis for the design of separating, cleaning and grading equipment. The lack of such correlations is attributed to the difficulties involved in accounting for the wide range of shapes found in seeds and straw. Cooper 1 stated that the amount of material r e m o v e d by aerodynamic means in a conventional combine is much less than that r e m o v e d in laboratory studies. H e pointed out that there is a greater difference between the terminal velocities of wheat kernels and wheat straw than is the case with oats or barley. This characteristic makes wheat easier to separate than other grains. Tiwari 2 investigated the possibilities of pneumatic separation of good beans from mixtures of threshed, dry, edible beans containing d a m a g e d beans, stones, leaves, stems and roots. He pointed out that the actual suspension velocities for individual beans were found to be less than the calculated values. H e attributed this to the effects of spinning and the rotation of the beans in the air stream. Using the geometric mean diameter, the drag coefficients for four varieties of beans were found to vary between 0-45 and 0-65. H e concluded that 80% of d a m a g e d beans could be separated without significant loss of whole beans. Bilanski and Lal 3 determined the terminal velocities of wheat grains and straws of various lengths. They found the terminal velocities of wheat grains to be in the range 8-8-9.2 m/s. The results showed that straws less than 6 cm long with a node at one end, had the highest terminal velocity (4.9 m/s). Shellard and MacMillan 4 measured the terminal velocities of a range of threshed wheat materials. They concluded that partly threshed heads are the most variable c o m p o n e n t s , and the terminal velocity values for these and the white caps, containing single grains, overlap the lighter materials without grains. Bilanski et al. s and Bilanski and Lal 3 concluded that rotation of particles in an air stream caused a higher drag and lower terminal velocity. G a r r e t t and B r o o k e r e also observed the tumbling of grains falling in still air. Department of Agricultural and Environmental Science, University of Newcastle upon Tyne, UK Received 31 July 1989; accepted in revised form 9 December 1989 275
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AERODYNAMIC PROPERTIES OF GRAIN/STRAW MATERIALS
Notation
A Cd d dg de Fd Fg g
area of particle projected to the airstream, mm 2 drag coefficient of particle diameter of particle, mm geometric diameter, mm diameter of equivalent sphere, mm drag force, N gravitational force, N gravitational acceleration, m/s 2
M Re Va Vt
mass of particle, Kg Reynolds number air velocity, m/s terminal velocity of particle, m/s
Z volume shape factor Pa specific density of air, Kg/m 3 pp specific density of particle, Kg/m a /z kinematic viscosity of air, Kg/m. s C1, C2 constants Vg volume of grain, mm 3 VT total volume of cylinder and pipe, mm 3 Vcy~ volume of cylinder, mm 3 Vpir~ volume of air in the pipe, mm 3 V~2 volume of liquid displaced, mm 3
Farran and MacMillan 7 found that higher air velocities were required to separate chaff from grain than to suspend chaff on its own. Uhl and Lamp 8 concluded that if straws were reduced to shorter lengths (less than 5 cm) during threshing, it was quite probable that a complete separation of grain from the threshed material would be achieved. Smith and Stroshine 9 found that complete pneumatic separation of corn cobs from stalks was impractical because of the overlapping of the terminal velocities of some stalks with those of the cobs.
1.1. Particle orientation and frontal area In applying aerodynamic principles to agricultural products, a method for expressing the projected area of the particle must be chosen. Mohsenin 10 reported that in most cases particles have been assumed to be spherical; the diameter of the particle being taken as the diameter of a sphere of the same volume as the particle. In cases where the volume of the object is difficult to evaluate, the geometric mean diameter (dg) is a good approximation of the diameter of the equivalent sphere (de), provided that the shape factor (Z) is close to unity. Very little work has been done on irregular shapes, which are complicated by their random orientation, and the variety of methods used to express their size and dimensions in the calculation of frontal area and drag coefficient. Keck and Goss 1~ used the geometric mean diameter of three mutually perpendicular measured seed dimensions. They observed that using the diameters of the equivalent spheres gave lower terminal velocities than the measured values. This indicates that the geometric mean diameter may vary considerably for irregular objects such as seeds. For different seeds, they suggested the determination of a shape factor, defined as the ratio of geometric mean diameter to the diameter of an equivalent sphere. The shape factor for clover seed (1.04) was closer to that of a sphere (1.0) than the shape factor of alfalfa seed (1.16). The greater sphericity of clover seed was also demonstrated by its drag coefficient. 1.2. Drag coefficient and Reynolds number The Reynolds number, Re, associated with the terminal velocity, Vt, of a particle can be based on the square root of the projected area, to make it consistent with the drag
B. Y. G O R I A L ;
277
J. R. O ' C A L L A G H A N
coefficient, Cd, which is based on the projected area, A. The drag coefficient includes both skin friction and pressure drag. The unstable behaviour of threshed material such as wheat straw and alfalfa stems, was investigated by Bilanski and Lala and Menzies and Bilanski. TM They concluded that a node at one end of a straw has a significant effect on its drag coefficient, by causing the straw to orient itself towards the vertical. Many coefficients have been defined in the literature to characterize the aerodynamic properties of materials. Shellard and MacMillan4 used the value of CdA, while Bilanski and Lala used a resistance coefficient, K, where K = Mg/V2t. The K values of Bilanski and Lala are directly proportional to CdA. They concluded that the resistance coefficient, K, which did not involve an assumption about the effective area, that was necessary when calculating drag coefficient Co, appeared to be a better criterion for the separation of various particles than the drag coefficient. They discovered that the drag coefficients of middle node straws were of the order of that of a circular cylinder and within the same range of Reynolds number. Drag coefficients for various grains, reported by Bilanski et al.,S were lower than drag coefficients reported for similar grains by Uhl and Lamp. a Mohsenin TM suggested that the primary reason for this could be the differences in the assumptions made about the frontal area.
2. Theory The aerodynamic properties of a particle can be determined by measuring the equilibrium conditions, when the particle is suspended in a stream of air. The vertical force balance on a suspended particle is given by F = . tz C d p A V za = Mg
(1)
A general expression for the terminal velocity of a particle is obtained by setting the gravitational force, Mg, equal to the resistance drag force, Fd, and by assuming that the air velocity, Va, is equal to the terminal velocity of the particle, Vt If
Mg=Fd then
when
Va=Vt
1 Mg = ~CdpaA Vt2
(2)
and
VZt= 2Mg CdPaA
(3)
For a sphere of diameter d,
A = aid2~4 and
M = ~ppd3/6 Lapple la reported that the drag coefficient of spherical particles, Cd, is 0.44 in the range R = 1000-200 000. Substituting for A, M and Cd in Eqn (3), the terminal velocity is given by,
V2t = 3gdpp/Pa
(4)
Reynolds numbers of particles (based on the square root of the projected area) were calculated from
Re = paVad/# in the range Re = 1000-200 000
(5)
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MATERIALS
The net force on a particle moving in a fluid is the difference between the gravitational force, Mg, and the resultant drag force, Fd. Therefore, Net Force = ½Cdp,AV~ - Mg
(6)
2.1. Volume shape-factor of non-spherical particles Different methods have been used for expressing the size and dimensions of irregular shaped particles in the calculation of Reynolds numbers and frontal areas. Schiller 14 showed that, for Reynolds numbers of less than 50, the assumption of sphericity for irregular particles is not extreme if the diameter is taken as the diameter of an equivalent sphere. For Reynolds numbers greater than 50, however, the drag coefficient curves level off and the assumption of sphericity will result in considerable errors. Heywood 15 concluded that Eqn (3), for predicting the terminal velocity of spheres, could be applied to granular materials other than spheres by applying a correction factor (z/6Z) to the drag coefficient of spheres. Substituting the value of spherical drag coefficient (0-44) in Eqn (3) yields V ~ - 4gdpp( 6Z / ~r)
(7)
3 x p. x0-44 Heywood found that the value of Z for a range of granular particles was 0-4 while for spheres it was equal to ~/6.
2.1.1. Predictions of volume shape-factor Sphericity is a criterion for describing the shape of particles. Curray ~6 expressed the degree of sphericity by assuming that the volume of the particle is equal to the volume of a tri-axial ellipsoid, and the diameter of the circumscribed sphere is the longest intercept of the ellipsoid. Thus, Sphericity = volume of solid/volume of circumscribed sphere = geometric mean diameter/major diameter
(8) (9)
Mohsenin ~° reported that in some cases, the shape of the solid can be approximated by one of the following geometric shapes and its volume can be calculated using the appropriate equations: (a) Prolate spheroid (e.g. lemon) Volume = ycab2/6 = ~d3/6
(10)
(b) Oblate spheroid (e.g. grapefruit) Volume = ~a2b/6 = ~d3/6
(11)
Volume = ~h(r~ + rlrz + r2)/3
(12)
(c) Right circular cone (e.g. carrot) where a and b are the major and minor diameters of the ellipse, respectively; rl and rz are the radii of the base and top, respectively; h is the height; and dg is the geometric mean diameter.
279
B. Y. G O R I A L ; J. R. O ' C A L L A G H A N
Mohsenin 1° suggested that by estimating the volume in this manner, the actual volume can be determined experimentally, and a correction factor, K, can be established for the "typical" shape of each product. In this analysis, the correction factor was assumed to be a function of grain sphericity. If K = C~ sphericity, the actual volume of prolate and oblate spheroids is Volume = :rd3K/6 = [ :r d3C1"~ (sphericity) \6
g
(13)
]
However, considering the diameter of the equivalent sphere, de, the volume of prolate or oblate spheroids can be assumed to be: Volume = C2d~
(14)
where C2 = constant. Solving Eqns (13) and (14) yields
Cdg/6 (sphericity) = or
j.g
C2d 3
----(ag]
Z = C2/CI = ~ \de/ 3 (sphericity)
(15) (16)
3. Materials and m e t h o d s
3.1. Suspension velocity tests A duct, 1.225 m long with a rectangular cross-section of 0.16 m x 0-12 m and two walls which diverged at 2°, was used to suspend particles in an air stream. Air was supplied by a centrifugal fan driven by a 0-75 kW d.c. motor connected through a rectifier. The fan delivered air through a flow straightener section, which consisted of two layers of fine wire mesh above and below a honeycomb grid. Mean air velocity in the test section was determined as a function of the mid-stream velocity, obtained from calibration tests using a pitot tube and micromanometer in a 56 point traverse. Air velocity close to the duct wall was 5 - 1 0 % less than the average and was neglected. The micromanometer and pitot used were capable of reading to 0.2 m/s. The average deviation of air velocity from the mean value was found to be 3%. The duct was calibrated so that the air velocity at any given height could be determined from the velocity of the mid-air stream. Suspension tests were carried out by placing particles in the duct, while the fan discharge was increased until the particles, seen through the transparent wall, floated in the central area of the air stream. Floating tests for straws were repeated in a second rig of cross-section 0.22 m x 0-4 m. Ten samples from each group were tested and each particle was tested twice. The average values of terminal velocities were recorded. Suspension velocities of the straw pieces were difficult to determine because of the unstable behaviour of straws in the air stream. Average particle mass and its suspension velocity were obtained by taking the arithmetic mean of each group of 20 readings. Dimensions of particles were carefully measured along three perpendicular axes using a micrometer. The moisture content of particles was 7% wet basis. Each particle was weighed by an electronic balance capable of reading to 0-0001 g. 3.2. Grain and straw samples Wheat, barley and oilseed rape straw were cut into lengths (10-110 mm) to form three groups for each crop according to the node position; end-node straw, middle-node straw and straw without node.
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MATERIALS
Various types of grain were used to cover wide ranges of drag coefficient, size, density, shape and sphericity. Different sizes were collected for each type of grain. Less dense grains of the same crop were discarded. The diameter of the equivalent sphere was obtained from the density and mass of the grain. The weight and suspension velocity of grain and straw were measured for ten samples from each size. The suspension velocity and mass for any particular size of each crop were estimated by taking the arithmetic mean of the ten samples. 3.2.1. Drag coefficient of straw Since the effective frontal area of a straw suspended in an air stream is required when calculating the drag force, orientation of the straw pieces must be taken into consideration. The projected area of the inclined straw was difficult to determine because of the unstable behaviour of straw in an air stream. Drag coefficients were measured for flow both normal and parallel to the axis of the straw since the projected area of the straw could be determined easily for both these cases. Drag coefficients for inclined straws could then be estimated by interpolating between these two values. 3.2.2. Floating of straw horizontally It was possible to float the node-free and middle-node straws horizontally in the lower part of the duct, where the air flow was more uniform; these straws were cut to have a shape similar to ideal symmetrical cylinders. During the tests straws were observed to float in the air stream without appreciable inclination or vertical movement. However, this was not possible for end-node straws because of their non-symmetrical shapes. This lack of symmetry was due to the presence of a node at one end. Another group of wheat stt;aws, each with two nodes, was prepared and cut to resemble symmetrical cylinders. These were suspended horizontally within the air stream. Since the drag coefficients of spheres and circular cylinders are well established, circular cylinders and spheres of different sizes were used to check the method and the apparatus. The results of 13 trials for measuring drag coefficients of spheres and cylinders gave satisfactory agreement with values of 0.44 and 1.0, respectively. 3.2.3. Floating of straws vertically Trial experiments were carried out to measure the drag coefficient of straws when floated vertically within the air stream (axial flow). Plastic cylinders were used to simulate individual straw particles, because they have diameters and terminal velocities similar to those of straw. These cylinders were cut into different lengths (5-50 mm), and one of the ends was filled with plasticine in order to simulate the end-node straws. The quantity of plasticine used was varied for the same particle until it floated vertically without appreciable vibration along its long axis. The height at which the particle was floated and the mid-air stream velocity were both recorded and later checked against calibration curves. Further trials were then conducted with the aim of extending the previous trials to the end-node straws of wheat, barley and oilseed rape straw. Samples of end-node straws which floated at oblique angles were trimmed carefully by a fine file from the end of an existing node and then floated in the air stream. The length of the test sample was gradually decreased after each run until the straw was suspended vertically without any appreciable indication of vibration in its vertical movement. Then the velocity of the mid-air stream at suspension was recorded.
3.3. Volume and density of grain The irregular shape of most intact agricultural products and the small size of materials, such as grains, present certain problems in volume and density measurements. The diameter of an equivalent sphere is an important factor for calculating the drag
B. Y. G O R I A L ;
J. R. O ' C A L L A G H A N
281
coefficients of grains. Hence it was considered useful to measure the density of grain in order to see what variation lay between geometric mean diameter and the diameter of an equivalent sphere. Three different methods were used for the measurement of volume and density. 3.3.1. Water displacement m e t h o d
Because of the irregular shape of the product, the volume is determined by water displacement. However, since water has a tendency to soak into the kernel, the volume of water transferred into the kernel was taken into consideration in calculating the actual volume of the treated sample. Five samples of wheat, barley and oilseed rape were collected randomly during the harvest of 1988 and stored at a moisture content of approximately 7% (wet basis). Absolute grain densities were calculated from the sample weight and the change in the volume measured from the relationship: Actual volume = volume of water displaced + volume of water transferred into the kernels
(17)
Ten tests for the same type of grain were carried out and the mean value was recorded. 3.3.2. D r y p y c n o m e t e r m e t h o d This method is used to determine the density or porosity of an unconsolidated mass of material such as grain. The advantage of this method is that there is no tendency for air to soak into the kernel surface. This method is based on the principles of the perfect gas law. The apparatus consists of a cylinder of known volume connected to a U-shaped tube manometer. The procedure of measuring grain density entailed determining the exact capacity of the pycnometer. A known mass of grain was placed in the pycnometer, covered and sealed to prevent any leakage of air. When both sides of the manometer (containing a liquid of low specific gravity, 0-786) were in balance with the atmospheric pressure, P1, the free arm of the manometer was lifted causing a new equilibrium pressure, P2. Under these isothermal conditions, according to the perfect gas law: (18)
P1VI = m R T = P2V2
where, V1 = g T -
Vg ~-- Vcg I -
Vg + Vpipe
v2=vT-vg-va2 Vg(P2 - P,) = VT(Pz -- PO - PzV~ or
Vg = l i t - Pz Vaz
(19)
The grain samples were tested five times and the average grain density was recorded. 3.3.3. Size m e a s u r e m e n t
Grains of a similar type were classified into different and significant ranges according to their size by sieving. Thirty grains for each sub-sample size were randomly chosen and measured carefully along three perpendicular axes using a micrometer. The mean weights and geometric mean diameters of grains were determined in order to calculate the grain density for each specific size from the same crop. 4. Results and discussion 4.1. Grains
While the main focus of this study was wheat, barley and oilseed rape, the behaviour of the following grains in an air stream was also measured in order to give a fuller picture about the characteristics of seeds: rice, soybean, bean, maize, rye groat, whole lentil,
282
AERODYNAMIC
PROPERTIES
OF
GRAIN/STRAW
MATERIALS
sorgham, mung, adzuki bean, buckwheat, pinto, marrowfat, black eye, white kidney, chickpeas, sesame and millet. Aerodynamic and physical properties of these grains are summarized in Table 1. The ideal, stable condition in the floating experiments was not obtained because grains assumed different positions within the air stream, since they rotated and tumbled due to their irregular shape and the turbulence of flow. Most of the grains were tested twice and the average readings were recorded when the particle was suspended in the central region of the duct, free from the interference due to the duct wall. Since the drag coefficient for spheres is well established, different sizes (12 to 20 mm) of plastic and wooden spheres were used as a check on the experimental method. Results of six trials for drag coefficient gave satisfactory agreement with the value of 0-44. While spheres had a tendency to cling to the duct walls due to the boundary layer at the wall of the duct, grains did not have this tendency; due to their irregular shape, they tumbled and rotated as mentioned by other experimenters. As the grain approached the duct wall, it would collide with the wall and then rebound towards the centre of the duct. 4.2. Volume and density The densities of wheat, barley, rice, rapeseed, soybean, maize and sorgham were measured by the three different methods described in Section 3.3. The results are presented in Table 2. Satisfactory agreement was obtained between the results of the water displacement and dry pycnometer methods for similar grains. However, a significant difference was found between them and the results obtained by the size measurement method. The actual density was taken as the average value of the results of the water displacement and dry pycnometer methods. This actual density was used in calculating the diameter of an equivalent sphere by using de = [ ( M / p p ) ( 6 / g ) ] 1/3 (20) Table 1 Parameter mean values for various grains
Grain
Wheat Barley Soybean Maize Beans Rapeseed Sesame Millet Sorgham Buckwheat Mung Adzuki Marrowfat Rye Rice
Green lentil Whole lentil Pinto Chickpeas Black eye
Geom.
Equiv.
Drag
Mass, mg
Terminal velocity, m/s
dia.,
dia.,
mm
mm
coeff. Ca
Re
Spherity
Z m measured
Zp predicted
30.2 37-6 197 321.2 444.0 4.46 2.36 6.00 30.9 27.6 75.5 115-6 397-2 33-4 16.5 78.7 33.4 360.3 391-4 136.4
7.8 7.5 14-0 11-6 13.3 6.7 4.4 7.6 9.7 8.9 12.0 12.6 15-2 7-8 7-2 8.3 9.9 14.0 12.7 12-7
3-36 4-08 6.22 7.50 8.35 2-05 1.66 2-04 3-61 3.60 4-60 5-40 8-10 3.70 2.75 5-00 3.50 8-10 8-50 5.90
3.29 3.70 6.14 7.62 -1.94 1.62 -3.5 -----2.75 ------
0.85 0.98 0.50 0.81 0-80 0.57 0.76 0.56 0.59 0-61 0-55 0-57 0-60 0.87 0.84 1.00 0-62 0.63 0.81 0-79
1692 1802 5646 5721 6970 0828 0450 0971 2156 1983 3466 4200 7714 1804 1269 2068 2178 7120 6823 3993
0-61 0.49 0-93 0.70 0.55 0.93 0-64 0.95 0.80 0.84 0.90 0.79 0.83 0-46 0-45 0.71 0.85 0-65 0.82 0.73
0.27 0.23 0.46 0.29 0.29 0-40 0.30 0-41 0.39 0.38 0.42 0.40 0-38 0.26 0-27 0.23 0-37 0-37 0.28 0.29
0.3 0-19 0.47 0-38 0.30 0-41 0.31 0-47 0.38 0.41 0-44 0.39 0.40 0.23 0-24 0.35 0.42 0.32 0-36 0.34
Shape factor
283
B. Y. G O R I A L ; J. R. O ' C A L L A G H A N
Table 2 Grain densities (kg/m 3) based on three different methods Grain
Size measurement
Water displacement
Dry pycnometer
1260 1320 1020 1340 1370 1000 1250
1260 1440 1340 1370 1450 1140 1380
1240 1370 1370 1420 1400 1180 1410
Maize Wheat Barley Soybean Rice Rapeseed Sorgham
Results for the densities of wheat, maize and soybean grain obtained by Uhl and Lamp a were lower than the densities obtained in this study for similar grain, measured by a similar water displacement method. The reason for this could be that the quantity of water soaked into the kernels was not taken into consideration with the method used by Uhl and Lamp. On the other hand, a satisfactory agreement was found between the current results and the results obtained by Bilanski et al.,S except for maize grain. The method used was size measurement. No significant difference was found between the diameters of equivalent spheres and the geometric diameters for most of the grains except for barley as shown in Fig. 1. This difference for barley is probably due to the elongated shape of barley grain. Therefore, the equivalent diameter for other grains used was taken as the geometric mean of the three dimensions, and was used to calculate the Reynolds number, projected area and drag coefficient. 4.3. Drag coefficients The drag coefficient of any particle depends on its density, suspension velocity and projected area. Since agricultural grains cover a wide range of sizes, suspension velocities, o
!
E
8i
Soyb
E F:
6
'5 5 U "E 4 ~
3 2
1 y
ize Barley_~/~ ~ "2~ Rice
Rapeseed
Equivalent diameter, mm Fig. 1. Relationship between geometric diameter and the diameter of an equivalent sphere for different grains
284
A E R O D Y N A M I C P R O P E R T I E S OF G R A I N / S T R A W M A T E R I A L S
densities and shapes, an array of drag coefficient values in the range of spheres and cylinders (0.44-1-0) was expected. The drag coefficients measured for all grains in this study may be summarized within four different groups, which lie between the drag coefficients of spheres and circular cylinders. Drag coefficients are plotted against Reynolds numbers in Fig. 2, which also shows the curves for ideal particles: Group 1 represents soybean, adzuki bean, mung, sorgham, millet and oilseed rape. The average drag coefficient is 0.47. Group 2 represents lentil, sesame, pinto, marrowfat and buckwheat. The average drag coefficient was found to be 0.6. Group 3 represents wheat, chickpeas, beans, rye, maize and rice. The average drag coefficient is 0.8. Group 4 represents barley and green lentil with an average drag coefficient of 1-0. Although the range of Reynolds numbers was relatively large (1000-10000), no obvious variation of the drag coefficient with the Reynolds number was found within each group and no apparent difference was noted between the drag coefficients for different sizes of the same group. Higher scatter was observed in the drag coefficients of group 3 than in that of other groups. The primary reason for this is that group 3 represents grains of elongated shapes, which behave more unstably in an air stream than others which are closer to spheres. Drag coefficients of maize grains were found to vary from 0-8-1.0 and they are included in both groups 3 and 4. This wide range of drag coefficients was probably due to the difference in the shape of grains of the different varieties used. It was observed that grains with flatter shapes have higher drag because they assume a horizontal position and have larger projected areas than other shapes. Drag coefficients of grains obtained by Shellard and MacMillan, 4 Hawk, Brooker and Cassidy, w Bilanski et al. s and Uhl and Lamp a were compared with the present experimental results. Satisfactory agreement was obtained between the results of 2-0 1.8 1.6 1-4 1-2 1.0 ,P 0.8
~[]
c:
u
0'6
o u
0"4
~I~B r
0.2
1()00
2 ( ) 0 0 3(~00 Reynolds number
' 5()00'7()0() 9000
Fig. 2. Drag coefficients of grain as a function of Reynolds number:~(, group 1;]'T, group 2; ~, group 3; ~7, group 4; ~ , cylinders; ~, spheres.
B. Y. G O R I A L ;
285
J. R. O ' C A L L A G H A N
Shellard, Bilanski and Uhi for wheat, soybean and maize grain. However, a difference was found in the results of Bilanski for wheat and barley. The reason for this could be differences in the assumption regarding frontal area. In general, it can be concluded that the drag coefficients of different grains depend mainly on shape. 4.4. V o l u m e s h a p e f a c t o r Since the drag coefficients of grains are dependent on shape, the correction factor ( ~ / 6 Z ) applied to the drag coefficient of a sphere as suggested by H e y w o o d ~s was applied to the results for understanding the volume shape factor (Z) of grains. The correction factor was substituted by the drag coefficient term of Eqn (3), and Eqn (7) was obtained, which was then simplified with little loss in accuracy by assuming a constant air density of 1-15 g/m 3 giving. Vt = 7V~ppdp
(21)
in the range of Reynolds number (500-200 000). Values of the volume shape-factor (Z) were calculated for the different grains from Eqn (21) and are presented in Table 1. In order to check the accuracy of the calculated shape factors of grains, the predicted values of the terminal velocities of different grains [from Eqn (21)] were compared with other published results 4"s'a in Table 3. Correlation of volume shape factors (Z), calculated from Eqn (16), with the sphericity of grains is shown in Fig. 3. Satisfactory agreement was found with the shape-factor results of Keck and Goss. 1~ G o o d agreement was also found between measured values of Z based on Eqn (7) and the values from Eqn (16). Finally, as shown in Fig. 4, satisfactory agreement was found between measured velocities of grains in suspension and values calculated according to Eqn (21). 4.5. S u s p e n s i o n
velocity-diameter
correlation
The suspension velocity of any particle in a vertical air stream is a function of particle size, density and shape-factor [Eqn (21)]. Experimental results show that the volumeTable 3 Comparison of results for measured terminal velocity and density by different researchers Current Grain type
Barley Soybean Maize Rye Sphere Wheat Whitecaps
Vt, m/s
Uhl s pp kg/m 3
Vt , m/s
5.9-9.4 976-1156 -[6-8-9-0] 1 0 . 8 - 1 4 . 9 1066-1537 9.0-18.0 [11-5-14.51 [11-2-13-0] 10.4-12.8 1178-1396 7-8-12-6 [9.6-13.9] [10.8-11-6] 6-8-8-3 1040-1063 6 - 0 - 8 - 1 [7.2-8.4] [6.1-6-7] 19-9-14.5 640-782 -[20.3-15.4] 6.50-10.0 430-1562 5.7-9-0 [6.6-10.11 [6-0-7.4] 5.0 299 . . [5-11
Bilanski 3 Vt, m/s k;f;'n 3
p , kgfm 3
6.9 1005 [7.6] 1250-1218 13.3 1336 [14-4] 1196-1260 10.5 1482 [12.6] 1218-1280 . . .
Shellard 4 Vt , m/s kgTmP" 3
--
--
16-5 [16.81 8.9 [8-91
1049-1302 .
Numbers in brackets represent predicted values from Eqn (21)
.
--
--
--
--
--
--
1227
--
--
1321
8.0 [8-3] 5-3 I5"61
1335
.
473
286
AERODYNAMIC
PROPERTIES
OF
GRAIN/STRAW
MATERIALS
1.0 =
0-9 0-8
P ~
N
B .~ u
0.7
0.6
0-5
~ 0.4 e~
~ 0.3 ~0
0-2
•
o.1
I1..
(3
6.1
0"2
£)'3 6"4
6'5
0:6
0"7
0:8
0"9
110
Sphericity
Fig. 3. Variation of volume shape-factor, Z with grain sphericity. [], current results; ~7, Keck and Goss ; " ~>, sphere
shape factor (Z) and grain density (pp) for different types of grain lie between 0-27-0.49 and 1.15-1.4, respectively. This indicates that Z covers a wider range than po for different grains. When suspension velocity was plotted against grain size, a very low correlation coefficient was obtained. However, by plotting the square of suspension velocity against diameter for each group of similar shape-factors, the correlation was improved as shown in Fig. 5. 4.6. Straws Straw is one of the major contaminants in the mixture of threshed crop material to be separated from grain. Straws are neither symmetrical in shape nor uniform in density and this lack of symmetry causes aerodynamic instability. 2O E
.
18
~ ~6 ._u 1 4 Q.) ~¢-1 1 2
~
lO
g g
4 2 2
4 6 8 10 12 14 16 Suspension velocity (measured), m/s
18
20
Fig. 4. Comparison of calculated and measured values of suspension velocity of grains
287
B. Y. G O R 1 A L ; J. R. O ' C A L L A G H A N 6OO 55O 5OO
ul
F
450 400 35O
>
3OO 250 2OO 150 100 5O 0
0
1
2
3
4
Equivalent
5
6
7
8
9
10
diammter, mrn
Fig. 5. Variation of suspension velocity with grain size. F~, Zm(0.37-0.48) V~ = - 1 8 - 5 + 34.5dc; ~7 , Zm(0.27-0.30) V,2_- 20"3de; ~), Zm(0.23-0.29) V~ = - 14.9 + 19.2d~
As reported by Bilanski and Lal, 3 and Shellard and MacMillan 4 lack of motion at the terminal velocity was not achieved in their experiments, especially with end-node straw. In the present work, straws were found to have a wider range of suspension velocities than grains. Both straws and grains tended to rise to a cross-section with an air velocity slightly lower than the suspension velocity and then fall to a lower cross-section with a higher one. Some straws tended to m o v e at an oblique angle across the air stream, while others floated slantingly, and this gave them a higher terminal velocity than when floating horizontally. Straws greater than 6 c m long, and all straws with the node at one end assumed a m o r e vertical orientation in the air stream than others. 4.6.1. Drag coefficient o f straw Since the projected area of any particle suspended in an air stream is necessary for the calculation of its drag coefficient, the orientation of the straw must be taken into consideration. H o w e v e r , inclination is difficult to determine because of the unstable behaviour of the straws in the air stream. It was necessary to float some of the straws normal to the air flow so that when the straw is suspended horizontally, the projected area is a product of its length and diameter. T h e drag coefficient of straws floating horizontally in an air stream are shown in Fig. 6 as a function of Reynolds n u m b e r , where the characteristic dimensions is ~ / L . d. T h e average drag coefficient of 1-0 corresponds to the value for horizontal cylinders. When straws with a node at one end were floated vertically in an air stream, the terminal velocity at which the straws were held in suspension increased as either the length a n d / o r the mass of the straw increased as shown in Table 4. H o w e v e r , when t h e drag coefficient was correlated as a function of Reynolds number, using the diameter of the straw as the characteristic dimension, the drag coefficient was similar to that of a cylinder with its axis parallel to the air stream, 1.0.
288
AERODYNAMIC
P R O P E R T I E S OF G R A I N / S T R A W
MATERIALS
2.0 1.8 1-6 14 1.2
[]
1.0
0.8
0-6 u
0
u
0.4
tC3
0"2
1 0I 0 0
2 0 ,0 0
3 0 0I 0
4 0 I0 0
I
6 000
18000
Reynolds number
~
. 6. Drag coefficient as a function o f Reynolds number for different grains and ideal particles. , straw, vertical orientation;-ff, cylinder, vertical orientation; V , cylinder, horizontal orientation; 5~, straw, horizontal orientation Table 4 Results for end-node wheat and barley straw floated vertically
Length, mm
Diameter, mm
Mass, mg
Suspension velocity, m/s
Drag coefficient
Reynolds number
11.5 36.5 22.2 28.5 27-5 21.0 30.0 22.2 11.5 16-9 24-5 14.5 16.8 31.2 13.0 8.5 16.5 27.3 36.5 23.5 22.7 10.3 10.5
3-5 4-7 4-0 3.5 3.7 4.0 3.4 4.0 3.6 3.5 4-8 4.0 3.2 4.7 4.0 3.7 4.5 3.6 4.8 4.4 4.4 4-1 4-6
34.2 77.7 41.5 49.3 29.3 33.6 54.1 41.8 34.3 29.4 82.9 28.3 21-8 77-6 31-9 18.2 39.3 55.9 78-5 57.6 54.8 38-3 47-5
8.0 8.8 7.5 9-5 7.0 6.7 10-4 7-5 7-5 7-5 8.8 6-6 6.8 9.2 6-6 5-6 6.5 9.5 8.6 8.0 7.5 6.9 7.2
0-92 0-97 1-00 1.1.97 0.95 1.01 0.91 0.99 1-02 0.93 1.01 0-88 0.93 0.88 0.99 0-92 0-99 1-03 1.00 1.03 1.06 1.04 0.92
1814 2654 1917 2124 1655 1712 2292 1917 1725 1677 2699 1687 1412 2792 1687 1324 1869 2185 2610 2223 2132 181.17 2139
B. Y. GORIAL; J. R. O'CALLAGHAN
289
Table 5 Summary results of threshed wheat material from floating tests
Type of particle
Condition
Wheat grain Wheat grain Wheat (whitecap) Wheat head Wheat head Wheat head
---Unthreshed Part-threshed Threshed
Size
Geometric diameter, mm
Suspension velocity, m/s
Mass, mg
Drag coefficient
Small Large -Large Pieces Pieces
2.3 4.5 4.4-5.3 ----
6-5 9.9 4-5-5-0 6.8 4.5-5.4 2.6
8.0 66.7 17.2-30.0 1840 120-180 100
0.84 0-73 0.77 ----
4.7. O t h e r materials tested
Straws are considered the most difficult part of a threshed mixture to separate since the terminal velocity of some straws approaches that of the grains. It is assumed that if the straw is separated from the grain, the chaff will also be separated, because it has a much lower terminal velocity than the straw. T h e terminal velocity of chaff was not measured. Threshed, part-threshed heads and whitecaps of wheat were obtained from the sieves of a whole crop harvester, while unthreshed heads and long straws were cut directly from the crop and their characteristics are presented in Table 5. Whitecaps, a single grain covered by the husk, are larger in size and, as a result, have a lower suspension velocity and higher drag coefficient than the grain. Part-threshed heads have terminal velocities lower than unthreshed heads. 5. C o n c l u s i o n s
1. The range of grains found in the normal sample at harvest corresponds to a range of terminal velocities rather than a single characteristic velocity. 2. Pieces of straw with a node at one end, which tend to align themselves vertically in an air stream, have a higher terminal velocity than nodeless, or middle-node straw, which tends to take up a horizontal position in a vertical air stream. 3. The drag coefficients of grains, which may be correlated as a function of Reynolds number, lie within the limits of a sphere (0.44) and of a cylinder (1-0) depending on the shape of the grain. The drag coefficients of oilseed rape, soybean and millet approach that of a sphere while those of beans and maize tend towards that of a cylinder. 4. The drag coefficient of straw is approximately 1-0, similar to that of a cylinder. 5. The shape factor of grain is closely related to its sphericity. 6. The terminal velocity of a grain can be estimated from the values of its diameter, density and shape factor. References
1 Cooper, G. R. Combine shaker shoe performance. Transactions of the American Society of Agricultural Engineers 1966, Paper no. 66-607 2 Tiwari, S. N. Aerodynamic behaviour of dry edible beans and associated materials in pneumatic separation. M.S. Thesis in Agricultural Engineering, University of Maine, Orono, Maine, 1962 3 Bilanski, W. K.; Lal, R. Behaviour of threshed materials in a vertical wind tunnel. Transactions of the American Society of Agricultural Engineers 1965, 8(3): 411
290
AERODYNAMIC PROPERTIES OF GRAIN/STRAW MATERIALS
4 Shellard, J. E.; MacMillan, R. H. Aerodynamic properties of threshed wheat materials. Journal of Agricultural Engineering Research 1978, 23(3): 273-281 Bilanski, W. K.; Collins, S. H.; Chu, P. Aerodynamic properties of seed grains. Agricultural Engineering 1962, 43(3): 216-219 • Garrett, R. E.; Brooker, D. B. Aerodynamic drag of grains. Transactions of the American Society of Agricultural Engineers 1965, 8(1): 49-52 7 Fan'an, i. G.; MacMillan, R. H. Grain-chaff separation in a vertical air stream. Journal of Agricultural Engineering Research 1979, 24(2): 115-129 a Uhl, J. B.; Lamp, B. J. Pneumatic separation of grain and straw mixtures. Transactions of the American Society of Agricultural Engineers 1966, 9(2): 244-246 9 Smith, R. D.; Stroshine, R. L. Aerodynamic separation of cobs from corn harvest residues. Transactions of the American Society of Agricultural Engineers 1985, 28(3): 893-897 lo Mohsenin, N. N. The properties of plant and animal materials. New York: Gordon and Breach, 1970 11 Keek, H.; Goss, J. R. Determining aerodynamic drag coefficients and terminal velocities of seeds in free fall. Transactions of the American Society of Agricultural Engineers 1965, 8(4): 553-554 12 Meazies, D.; Biinski, W. K. Aerodynamic properties of alfalfa particles. Transactions of the American Society of Agricultural Engineers 1967, 11(6): 829-831 13 Lapple, C. E. Fluid and particle mechanics. University of Delaware, Newark, 1956 14 Schiller, L. Fallversuche mit kugeln und scheiben. (Drop tests with spheres and discs.) Handbook Experimental Physics 1932, 4(2): 338 is Heywood, H. Calculation of particle terminal velocity. Journal of Imperial College Chemical Engineering Society 1948, 4:17 16 Curray, J. K. Analysis of Sphericity and Roundness of quartz grains. M.S. Thesis in Mineralogy, The Pennsylvania State University, University Park, Pennsylvania, 1951 1~ Hawk, A. L.; Brooker, D. B.; Cassifly, J. J. Aerodynamic characteristics of selected farm grains. Transactions of the American Society of Agricultural Engineers 1966, 9(1): 48-51