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EFFECT OF MOISTURE ON FLOW OF GRANULAR MATERIAL
by
HONG TAN, B.S.
A THESIS
IN
AGRICULTURAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
AGRICULTURAL ENGINEERING
Approved
Accepted
December, 1992
~D5 ;-.3 I ~,2..
tJo.II'
Cop.'- ACKNOWLEDGEMENTS
,Clj
F+bY- -17~0 JA-r_ 8).).1c/9..J
I sincerely acknowledge the helpful academic assistance
from my graduate committee. My special appreciation goes to
Dr. Clifford B. Fedler, for his two years' of patience, kind
advice, guidance, and support and to Dr. James M. Gregory,
for his enthusiasm and invaluable guidance in my research
and thesis work. Also, I gratefully thank Dr. Hossein
Mansouri for his kind help with my graduate project.
Finally, I thank my parents, my sister, and her husband for
their consistent encouragement and support.
ii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
LIST OF TABLES
LIST OF FIGURES
CHAPTER
I. INTRODUCTION 1.1. Statement of the problem 1.2. Objectives
II. THE REVIEW OF LITERATURE 2.1. Granular flow through orifices 2.2. The effects of moisture content 2.3. The Gregory and Fedler model
ii
iv
v
1 1 3
4 4
12 16
III. METHODS AND MATERIALS 18
IV.
3.1. The materials used 18 3.2. Experimental procedure and measurement 19 3.3. Data collection 23
RESULTS 4.1. 4.2. 4.3. 4.4
4.5.
AND DISCUSSION The effects of moisture on granules Mass and volumetric flow rate The flow resistance coefficient k Model development for flow resistance coefficient,k Model verification
24 24 41 42
48 52
V. CONCLUSIONS 62
REFERENCES 64
APPENDIX 69
iii
LIST OF TABLES
3.1. Oven temperature and heating period for moisture content determinations 21
4.1. Changes of bulk density with moisture content 25
4.2. The second-degree polynomial relationship between bulk density and moisture content (percent, dry basis) 26
4.3. The linear relationship between bulk density and moisture content (percent, dry basis) 27
4.4. The linear relationship between Bulk density and moisture content (percent, wet basis) 27
4.5. The linear relationship between minimum particle dimension and moisture content (percent, dry basis) 33
4.6. The linear relationship between average particle length and moisture content (percent, dry basis) 33
4.7. Repose angle (degree) of grains at various moisture content levels 37
4.8. The effect of moisture content on flow resistance coefficient, k, and particle size 46
A.1. Mass flow rate (gfs) of wheat at various moisture content levels 70
A.2. Mass flow rate (gfs) of soybean at various moisture content levels 71
A.3. Mass flow rate (gfs) of sorghum at various moisture content levels 72
A.4. Mass flow rate (gfs) of corn at various moisture content levels 73
A.5. Mass flow rate (gfs) of blackeyed peas at various moisture content levels 74
A.6. Volumetric flow rate (cm3fs) of wheat at various moisture content levels 75
iv
A.7. Volumetric flow rate (cm3/s) of soybean at various moisture content levels
A.a. Volumetric flow rate (cm3/s) of sorghum at various moisture content levels
A.9. Volumetric flow rate (cm3/s) of corn at various moisture content levels
A.lo. Volumetric flow rate (cm3js) of blackeyed peas
76
77
78
at various moisture content levels 79
v
LIST OF FIGURES
1.1. Schematic of device (a) cylindrical bin, (b) conical hopper, and (c) simple bin-hopper system
4.1. Comparison of bulk density-moisture relationship for corn
4.2. Comparison of bulk density-moisture relationship for wheat
4.3. The relationship between least particle dimension and moisture content
4.4. The relationship between average particle length and moisture content
4.5. Repose angle of sorghum at various moisture content levels
4.6. Repose angle of wheat at various moisture content levesls
4.7. Repose angle of corn at various moisture content levels
4.8. The linear relationship between least dimension length of particle and resistance coefficient
4.9. The flow resistance coefficient against (a) minimum particle length; (b) average particle length (data from Table 4.8)
4.10. The linear relationship between average particle length and resistance coefficient
4.11. Plot of predicted versus measured flow resistance coefficient (Data from Table 4.8)
4.12. Plot of predicted versus measured flow resistance coefficient (Data includes Gregory and Fedler's data, 1987)
4.13. Plot of predicted versus measured mass flow rate of sorghum at various moisture content levels
vi
6
29
30
34
35
38
39
40
45
47
50
53
54
56
4.14. Plot of predicted versus measured mass flow rate of wheat at various moisture content levels
4.15. Plot of predicted versus measured mass flow rate of corn at various moisture content levels
4.16. Plot of predicted versus measured mass flow rate of blackeyed peas at various moisture content levels
4.17. Plot of predicted versus measured mass flow rate of soybean at various moisture content levels
vii
57
58
59
60
CHAPTER I
INTRODUCTION
1.1. Statement of the problem
Granular material, like fluids and gases, is one of the
most common items used in industry. Knowledge of the laws
governing flow of solids through orifices would be of value
in design. Almost all the granular materials are stored in
a bin, hopper, silo, or bunker. In many cases, these
materials are removed through an opening in the bottom of
the container under the influence of gravity.
Bins and hoppers constitute major items of equipment in
storage and handling of granular materials. An improperly
designed bin or hopper may cause flow obstruction of
granular material due to bridging of the granules above the
orifice. It may cause a restricted flow condition under
which only the solids directly above the opening are
removed.
The control and metering of flowing granular material
through the orifice in a storage vessel has been practiced
for many years. Researchers and engineers have developed
many models and tried to precisely describe the flow
process. Although considerable effort has been devoted to
predicting gravity caused flow of granular solids from
storage bins and hoppers, there is still a need for a
1
reliable, general formula for predicting the flow rate of
granular solids with different physical characteristics.
The most significant physical properties of granular
solids that influence the flow rate through an orifice
include bulk density, particle size, shape, and friction or
flow resistance coefficient. Also known, but not understood
physically, is the effect of moisture content of granular
materials on the flow rate. Since many physical properties
of granular material vary with their moisture, analyzing the
impact of moisture content on the flow process and
developing a mathematical model to predict the flow rate is
quite complex.
Previous work relating the effect of moisture content
on bulk density, true density, angle of repose, internal
friction, porosity, sphericity, and particle volume of grain
materials have been done by Zink (1935), Miles (1937),
Browne (1962), Thompson and Isaacs (1967), Chung and
Converse (1971), Loewer et al (1977), Gustafson and Hall
(1972), Brusewitz (1975) and Thompson and Ross (1983). The
direct measurement of the influence of moisture content on
the flow through an orifice was carried out by Ewalt and
Buelow (1963), and Chang (1984, 1988). They developed their
models with regression analysis, but their models are
restricted by coefficients that must be recalibrated for
each new material and moisture content.
2
1.2. Objectives
The general objective of this study is to develop an
understanding of how moisture content affects granular flow
through horizontal orifices. This objective will be
completed by reviewing and analyzing data that describe the
relation between moisture content of granular materials and
other properties, and by using the Gregory and Fedler (1987)
model to predict the flow rate of several types of granular
materials at different moisture contents.
The specific objectives are to:
1. evaluate the effect of moisture content on the
material properties of five different grain and
2. evaluate the Gregory and Fedler (1987) model and to
modify their model to account for moisture content of the
grain.
3
CHAPTER II
REVIEW OF THE LITERATURE
2.1. Granular flow through orifices
Fluids follow the laws of fluid mechanics or rheology
well, but the flow of a granular material that occurs under
the force of gravity is more difficult to predict than that
of a fluid. Though the subject of granular flow has been
studied for more than 100 years, there is still no model
that can be used to accurately predict the flow for all
granular materials and all different orifice geometries.
Mohsenin (1986) states the following reasons that the
laws of hydrodynamics could not be applied to the flow of
granular materials through orifices:
1. Pressure is not distributed equally in all directions due to the development of arches and to frictional forces between the granules.
2. The rate of flow is not proportional to the head, except at heads smaller than the container diameter.
3. No provision is made in hydrodynamics for size and shape of particles, which greatly influence the flow rate. (p. 737)
By testing the distribution of pressure in a storage
bin, it is found that weight of a column of granular
material is borne largely by the walls and only a small
extent on the base. The pressure on the bottom no longer
increases as the bin model is filled to a certain height
(Ketchum, 1919). This independence of the pressure near the
bottom on head can be used to explain why the gravity flow
4
rate of granules through orifice is not dependent upon the
head. Although Newton (1945) found that the mass flow rate
was related to the head raised to the 0.04 power, most
researchers agree that the flow was not a function of head.
It is widely accepted that the flow rate is a function
of the geometry of the container and the orifices as well as
certain properties of granular materials, such as density,
particle shape, size, and roughness, porosity, angle of
repose, and moisture content. The geometry parameters which
have been studied include the size, shape, and location of
the orifice through which flow occurs, the roughness of the
wall of the container, and the ratio of hydraulic orifice
diameter to the average particle diameter. The hydraulic
radius, which is defined as the ratio of cross sectional
area of the opening to the perimeter of the opening, is
widely used for non-circular orifices.
The flow of granular materials through orifices under
the force of gravity is best described in terms of the
typical cylindrical bins or conical hoppers (Figure 1.1a,
and b). Also, a combined system of bin and hopper is used
quite often, as shown in Figure 1.1c.
The earliest investigation of granular flow began with
Hagen (1852). He measured the flow of sand through a
circular aperture in an hourglass, and correlated data by
using dimensional analysis.
5
H
~D ~D (a) (b)
(c)
Figure 1.1. Schematic of device {a) cylindrical bin, (b) conical hopper, and {c) simple bin-hopper system
6
Deming and Mehring (1929} studied the flow of a variety
of materials through an inverted truncated cone orifice. It
was found that flow rate varied with a power of the orifice
size, and was influenced by the size and apparent density of
the particles, the angle of repose of the materials, and the
cone angle. The following equation was developed:
where
Qd = the flow rate in grams per minute
tr = the filling angle of repose, degrees
8 = the conical angle between two walls, degrees
Dd = the orifice diameter, mm
Pb = the bulk density, gjcm3•
( 2. 1}
For the nonspherical particles, dd was calculated from the
average major diameter d 1 and average minor diameter d 2 •
Franklin and Johanson (1955} developed an empirical
equation for the flow rate of granular materials through
circular horizontal orifices:
P D2.93
p f 0
t = (6.29tan~i+23.16) (dt+1.890) -44.9
where
7
(2.2)
Or = flow rate, lb/min
Dr = orifice diameter, in.
dr = particle size, in.
P, = particle density, lb/ft3
ti = internal kinetic angle, degree.
Equation (2.2) was derived for circular orifices only for
particles ranging from 0.03 to 0.20 inches and orifice
diameters 0.236 to 2.28 inches. An overall mean deviation
of 7% was claimed. An apparatus consisted of a rotating
drum was used to measure the internal kinetic angle in order
to give a better correlation of the flow rate data than
either static or surface kinetic angle.
Fowler and Glastonbury {1959) investigated the factors
that affect the flow of granular solids through orifices of
different diameters and shapes under gravity conditions at
various heads. The effects of head and container diameter
are found to be insignificant in the statistical analysis.
For the granular materials tested (such as sand, sugar, rape
seed, wheat and rice), the following equation was found with
dimensional analysis from a total of 347 runs:
where
( 2. 3)
Q~ = mass flow rate, lb/s
Db = hydraulic diameter =4 x A/perimeter of orifice, ft
Pb = bulk density, lb/ft3
8
d. = spherical diameter of particles, ft
A = or if ice area, ft2 •
Beverloo et al. (1961) suggested that flow rate should
be proportional to pbg0·so2·s based on dimensional analysis.
They plotted Qus against orifice diameter, D and found that
the effective orifices diameter was reduced to D-nd, (d is
the particle size) and correlated their results using the
follow expression
where
Qb = mass flow rate, gjmin
Pb = bulk density, gjcm3
g = gravitational constant, cmjs2
Db = diameter of circular orifice, em
db = average screen size of particle, em
nb = an empirical coefficient.
(2.4)
This equation has been widely accepted (Nedderman 1982).
For all the seeds tested, the k value was about 1.4.
Harmens (1963) theoretically analyzed discharge of
granular solids through a horizontal orifice by using the
concept of "free-fall arch" which is the surface dome above
the orifice forming the lower boundary of the packed bed.
Below this arch the particles are not in contact with one
another and accelerate freely under gravity. Assuming the
height on the free-fall arch is of the order of the orifice
9
diameter and the particles leave the arch with a negligible
velocity, Harmens concluded that the velocity at the orifice
is of the order (2gD) 1n; therefore, the flow rate is
proportional to g 1nosn. The resulting flow equation is
with
where
0. 38 (dh/Dh} 1. 5
0. 045+ (dh/Dh} 1. 5
Qh = mass flow rate, gfs
Pp = particle density, sfcm3
A = orifice surface area, cm2
Dh = orifice diameter or hydraulic diameter, em
f = tangent of static angle of repose
dh = mean particle diameter, em.
Some researchers, such as Beverloo et al. (1961),
( 2. 5)
Moysey (1985), Fowler and Glastonbury (1959), and Fedler and
Gregory (1989) indicate that flow rate could be a function
of one or several material property parameters such as
density, angle of repose, size, and shape. The influence of
moisture content on the other material property parameters
also cause the change in flow rate. Chang et al. (1984)
found that incresasing the moisture content of corn from 12
to 23% decreased the mass flow rate through square and
circular orifices appreciably.
10
Most orifice flow models can be expressed simply as:
where Q is mass (or volumetric) flow rate, D is the orifice
diameter or hydraulic diameter, C1 is a constant or a
function of some physical properties of the flowing material
and geometry variables of the container, and the value of c2
varies, but is normally above 2.5 and equal to or less than
3.0. Deming and Mehring (1929) determined the value of c 2
as 2.5; Franklin and Johanson (1955) as 2.93; Newton et al.
(1945) as 2.96; Ketchum (1919) as 3; Fowler and Glastonbury
(1959) between 2.5 and 2.84; Beverloo (1961) as 2.5; and
Gregory and Fedler (1987) as theoretically bounded by 2.5
for laminar flow and 3.0 for turbulent flow.
Ewalt and Buelow (1963) found that the coefficients C1
and C2 in Equation 2.6 for shelled corn were 0.1196 and 3.10
at 8.4 percent moisture percent (d.b.); Chang et al. {1984)
and Chang and Converse (1988) tested the flow rate of corn,
wheat and sorghum through horizontal orifices, and they
indicated that coefficients C1 and C2 changed with different
moisture contents. For circular orifices, their C2 values
were from 2.47 to 2.76. Because these coefficients
developed from regression analyses were specific to a given
moisture content and could not explain how moisture content
affected the flow process, it seems that more work needs to
be completed in this area.
11
2.2. The effects of moisture content
Grain moisture content (percent dry basis) is defined
as the ratio of the weight of water that can be removed
without changing the grain chemical structure to the final
dry weight of the grain. Information on the moisture
content of grain is important because it affects the grade
and market value by means of test weight. Relationships
between moisture and other grain properties are also of
value in working with the design of grain storage, drying,
aeration, and handling systems.
For design of grain storage structures, Janssen's
theory of stress analysis is generally used. The wall
pressure is determined by grain bulk density, coefficient of
wall materials, and ratio of horizontal to vertical
pressure.
Stewart (1968) found that the angle of internal
friction varied with moisture content for grain sorghum,
and the relation was in the form of a straight line within
the moisture content range of 12 to 29%. Thompson and Ross
(1983) evaluated the effects of moisture content and
internal pressure of grain on bulk density using red winter
wheat and found the bulk density increased with increases in
both overburden pressure and moisture content. The
coefficient of friction for wheat on steel was found to vary
with moisture content, overburden pressure and sliding·
velocity. Loewer et al. (1977) studied the influence of
12
various levels of moisture content, vertical pressure and
particle size on the bulk density and Janssen's ~-value
(ratio of unit lateral pressure to unit vertical pressure at
any point in the grain mass). Two equations were given to
determine the influence of various levels of vertical
pressure and moisture content on the bulk density and
Janssen's ~-value. Ross et al. {1979) investigated the
effects of grain moisture content and vertical pressure on
the grain bin loads. Their study showed that consideration
of the variation in physical properties of stored material
with pressure and moisture content can be used to explain
experimentally observed pressures in bins that are higher
than those predicted by the Janssen equation.
The effect of moisture content on granular flow was
tested by Ewalt and Buelow (1963), and Chang (1984, 1988).
They derived an experimental equation using regression
analysis and included only orifice diameter (or orifice
length and width) and two coefficients similar to Equation
2.6. These coefficients varied with moisture content, but
no physical explanation was given. The disadvantage of
their model is that the model is limited by the calibration
for the particular material used, and it cannot be used to
predict the flow of other materials. It is expected that a
general explanation could be found through analyzing the
effects of moisture content on certain properties of the
13
granular materials, such as density, particle size,
roughness and shape.
One fact that most people accept is that the volume
of grain will increase with an increase in moisture.
Actually, the bulk density of most hygroscopic material will
decrease first then increase with the increased moisture
content (Brusewitz, 1975; Loewer et al. 1977; and Nelson
1980). Miles (1937) measured the test weight of corn at
moisture contents (MC) between 10 and 40% (wet basis), and
found that the test weight at 30-31% MC was minimum and that
there was a higher test weight as moisture contents
increased further. The bulk density data collected by
Brusewitz (1975) fit a second degree polynomial very well.
Some grains, such as oats, rye, corn, wheat, and barley were
found to display a decrease in bulk density with increasing
moisture content up to 30% (w.b.), and then the density
increases. A similar result was also observed by Chung and
Converse (1971) who measured the test weight of corn between
9 and 27% and wheat between 9 and 19% moisture content
(w.b.). Thwse results show that the moisture content at
which the minimum test weight occurred is different for each
type of material. Chung and Converse also found small
differences in the test weight during the absorption and
desorption process. The hysteresis differences in test
weight are greater for corn than those for wheat. Chung and
Converse also observed the differences in bulk density for
14
different corn classes separated according the kernel shape
and size, but the moisture dependent relationship for the
different classes was similar.
The true density (particle or solid density) of grain
was observed to decrease with an increasing moisture
content. The liquid displacement technique was initially
used to determine the void space between grain particles
(Zink, 1935). Thompson and Isaacs (1967) and Chung and
Converse (1971) used an air-comparison pycnometer in the
study concerning the true volume of total particles.
Brusewitz (1975), Chung and Converse (1971), Nelson (1980)
and Gustafson and Hall (1972) used a negative sloping linear
relationship to show the overall trend between true density
and moisture content. The regression equation is
where
DP = Dpo (1-bMC,)
DP = the particle density
D~ = the particle density at dry condition
MCw =moisture content, (w.b.)
b = a coefficient.
(2.7)
The friction coefficient of granular material can be
easily determined by measuring its angle of repose. When
non-cohesive granules are discharged through a vertical or a
horizontal opening, the angle formed by the free surface of
the grain is called the "angle of repose." The coefficient
15
of friction for each grain material equals the tangent of
its angle of repose. The extent of the angle of repose
depends on the grain size composition, the sphericity of the
individual grain particles, moisture content, and
orientation of the particles.
Fowler and Wyatt (1960) tested the effect of moisture
content on the angle of repose of granular solids. They
found that the angle of repose depends on diameter, shape
factor, specific gravity, and moisture content of granular
solids, and the increase in moisture content causes an
increase in angle of repose.
2.3. The Gregory and Fedler model
Gregory and Fedler (1987) derived a mathematical model
to describe the flow of granular material through circular,
horizontal orifices based on analyzing the balance of the
downward force causing flow by gravity and the upward force
resisting flow, or friction as
where
Q = 1t g p D3 16k b
Q =volume flow rate, cm 3 js
D = orifice diameter,cm
Pb = bulk density of material, gjcm2
g = gravitational acceleration, cmjs2
k =flow resistance coefficient, gjs-cm2.
16
(2.8)
Several types of granular materials were tested with orifice
diameters ranging from 1.9 to 7.7 em for verification. This
model fit measured data with R2 value in excess of 0.9.
Further development by Fedler and Gregory (1989) indicated
that the resistance coefficient, k, was a function of
minimum particle thickness and surface roughness, and the
primary variable was the minimum particle thickness.
Knowing the relationship between the flow resistance
coefficient and minimum particle thickness, the Gregory and
Fedler (1987) model can be used conveniently to predict flow
rate without costly laboratory investigation.
Fedler (1988) reviewed four orifices flow models by
using the same data set. The constant contained in the
Fowler and Glastonbury (1959) model has to be modified for
different materials to fit the data reasonably; the
coefficient in Beverloo's (1961) model has to be determined
for various materials; the coefficients obtained in the
Ewalt and Buelow (1963) model are limited to specific
material and they will vary for all materials. Among these
four models, the Gregory and Fedler (1987) model most
reliably predicts flow of granular materials through
horizontal orifices less than 12 em in diameter and is
verified by using various grains and food products.
Therefore, the Gregory and Fedler (1987) model will be used
in this analysis to evaluate the effect of moisture content
on granular flow through horizontal orifices.
17
CHAPTER III
MATERIALS AND METHODS
3.1. The materials used
To complete the objectives of this research, it was
necessary to measure several parameters that will be
affected by moisture content and also affect the flow rate,
such as bulk density, particle size, and friction
coefficient.
Each type of hygroscopic materials will respond
differently to varying levels of moisture content; thus,
several kinds of grain, including sorghum, wheat, corn,
blackeyed pea, and soybean, were used in this research
because of their sensitivity to the moisture content and
popularity in the grain industry. Also, using several types
of grain materials with different physical property
parameters would help to determine which parameter had more
influence on the flow rate and which one had less. For
example, bird seed has a much higher flow rate than
blackeyed peas although their bulk densities are almost
same; therefore, the difference in their flow rate is caused
by the variation of other material properties, such as the
particle size, shape, or angle of repose.
Among these five types of grain materials, sorghum has
small and relatively spherical particles; wheat has small
and irregular particles with a rough surface; the particles
18
of corn are large, flat and smooth; blackeyed peas are
large, smooth and almost symmetrical; and soybean are almost
spherical, smooth and larger than wheat and sorghum but
smaller corn and blackeyed peas.
Three property parameters of granular materials, bulk
density, particle size and angle of repose, were tested
along with moisture content in each experiment. Bulk
density is used in almost all empirical equations derived by
researchers. The angle of repose is chosen to estimate the
friction coefficient of granules because of the ease of its
measurement. Fedler and Gregory (1989) found that an
increase in minimum particle size increases the flow
resistance coefficient thus reducing flow.
At each level of moisture content, the flow rate through
an orifice is measured along with other properties of the
granules. The properties examined include bulk density,
angle of repose, particles size in the three dimensions, and
moisture content. The methods of testing and measuring are
described in the following sections.
3.2. Experimental procedure and measurement
3.2.1 Pretreatment of grain materials. Before each
test, the foreign material and smaller damaged grain
particles were removed by sieving and large foreign material
were removed by hand.
19
3.2.2. Flow rate measurement. A cylinder with a 25 em
diameter and 60 em height was used to store test grain for
experiments. A series of removable circular orifices, which
ranged in size from 3.2 to 10.3 em in diameter, were
installed in the bottom of the cylinder (Figure 1.1a).
For each measurement of flow rate, the cylinder was
filled with grain and then emptied by opening the orifice
sliding gate. The flow rate was measured in pounds per
measured time by weighing the materials that flowed through
each orifice and timing the period the flow continued and
converted to mass flow rate in grams per second. For each
different orifice size, three replications were performed to
test for sample variation.
3.2.3. Moisture content. A wide range of moisture
content (0 to about 45 percent dry basis, d.b.) was used in
this research to model the effects of moisture content on
the granular flow process.
All grains were moistened to the different levels of
moisture content from about 10% (d.b.). The maximum
moisture content reached was about 45% (d.b.), since a
higher moisture content would lead to surface moisture and
sticking of particles to each other. First, each material
was soaked in water until the core of the particle was wet
(usually up to 2 or 3 hours), next, the material was aerated
with ambient air for about 15 minutes to one hour to remove
surface moisture.
20
Drying whole grain in a forced-convection air-oven
according to ASAE Standard S352.1 (ASAE Standards 1986) is
the most widely used method to determine moisture content
and yields highly reproducible results under selected
conditions of time and temperature. The disadvantage of this
method is the long drying time requirement. The oven
temperature and heating period depend on the material being
tested, as shown in Table 3.1. To avoid the bias of
moisture content during the flow testing, nine samples were
used in each test, three from the beginning of each test,
three from the middle, and three from the end. The average
moisture content from the nine samples was treated as the
actual moisture content.
Table 3.1. Oven temperature and heating period for moisture content determinations*
Seeds Oven temperature, Heating ± 1 oc hour
Blackeyed peas+ 103 72 Corn 130 72 Sorghum 130 18 Soybean 103 72 Wheat 130 19
* quoted from ASAE S352.1 (ASAE STANDARDS 1986). + used data for beans
21
time min
0 0 0 0 0
3.2.4. Bulk density measurement. Bulk density was
measured for each level of moisture content tested. The
bulk density determination was made by pouring the material
into a one dry-quart container and scraping off the excess
with a straight edge. The container was then weighed. The
volume of container was converted to cubic centimeters so
that bulk density could be reported in units of gjcm3 • The
standard unit conversion of 67.2 in3 per quart was used to
make the conversion. Three samples were chosen randomly
from of grain mass at the beginning of each test and another
three at the end for measuring bulk density. These two
sampling times were used to avoid the variations in test
weight due to air drying during each experiment.
3.2.5. Particle size measurement. Because grain
particles vary considerably in size, using a small sample
size could lead to a large error in the estimate of the
particle size. Fifty particles were measured accurately at
each level of moisture content by using digital calipers.
Each particle was measured in three dimensions to determine
the major, minor, and intermediate diameters (Mohsenin,
1986).
3.2.6. Angle of repose measurement. Because of the
ease of measurement and the connection with other
parameters, the angle of repose was assumed as a potential
independent variable. After letting the granular material
flow slowly down into the circular container to form a
22
static pile, the filling angle of repose, which had the
maximum angular deviation from horizontal to the surface of
the pile, was measured. An alternative method was to
measure the height of the pile and the container radius,
then calculate the tangent of the two lengths.
The emptying angle of repose was measured when granules
were discharged from the cylindrical vessel through a
circular orifice at the center of a smooth horizontal base.
3.3. Collection of experimental data
For each material, the following relations were
analyzed:
1. The effect of moisture content on bulk density.
2. The effect of moisture content on particles size.
3. The effect of moisture content on the friction
coefficient.
4. The changes of mass flow rate at different levels of
moisture content.
5. The change in the flow resistance coefficient (k) in the
Gregory and Fedler (1987) model under different moisture
contents.
23
CHAPTER IV
RESULTS AND DISCUSSION
The properties of grain material examined and their
flow rate through orifices are both significantly influenced
by moisture content (dry basis). The effects of moisture
content on bulk density, particle size, and repose angle of
granules are discussed and compared with other previous
work. The Gregory and Fedler (1987) orifice flow model and
Fedler and Gregory (1989} flow resistance model are used to
explain and predict the impact of moisture content on
gravity flow of bulk solids through horizontal orifices.
4.1. The effects of moisture content on granules
4.1.1 Bulk density Bulk density decreased
significantly as the moisture content increased from 10 to
46% (dry basis) for all types of materials used in this
experiment (Table 4.1). The same results were reported by
Chung and Converse (1971}, Brusewitz (1975), and Lorenzen
(1958). A reasonable explanation for this phenomenon is
that each grain particle swells while it absorbs moisture,
increasing the size faster than the mass increases. This
explanation matches the results found by Gustafson and Glenn
(1972) where a linear relationship between true density and
moisture content (dry basis) for shell corn was found. The
confidence levels of the relationship was 99 and 90% for the
24
high {drying from 54 to about 7% d.b.) and low (drying from
35 to about 7% d.b.) initial moisture content, respectively.
Brusewitz {1975) suggested a straight line relationship
between true density and moisture content on a wet basis for
barley, corn, grain sorghum, oats, rye, soybeans, and wheat
within a wide moisture content range of 15 to 45% on wet
basis {about 17 to 81% on dry basis). The same results were
also obtained by Chung and Converse {1971) for corn and
wheat, and Shepherd and Bhardwaj (1985) for pigeon pea.
Table 4.1. Changes of bulk density with moisture content
Moisture bulk Moisture bulk content, density, content, density,
' d.b. gfcm3 ' d.b. g/cm3
Sorghum 13.16 0.771 Soybean 10.77 0.748 18.76 0.752 14.32 0.731 21.53 0.740 17.02 0.720 28.40 0.736 27.69 0.692 39.80 0.728 35.68 0.673
Wheat 10.25 0.816 Blackeyed 12.83 0.784 17.59 0.765 peas 14.07 0.779 25.01 0.707 21.76 0.749 29.98 0.679 27.86 0.728 36.33 0.659 44.26 0.703
46.02 0.692 Corn 10.04 0.750
18.23 0.726 24.06 0.683 28.56 0.649 33.00 0.632
25
The relationship between bulk density and moisture
content in this research was found to be best described by
an equation of a second degree polynomial for a moisture
content range of 10 to 45% (dry basis). The equations given
in Table 4.2 for the materials tested in this research were
developed by regression analysis. A regression analysis was
also used to determine how well the data fit a linear
function for both the dry and wet basis (Tables 4.3 and
4.4). The linear fit was almost as highly correlated with
the data as the second degree polynomial, which indicates
that a linear function is a reasonable approximation (except
for sorghum).
Because both kinds of moisture content (dry basis and
wet basis) are often used, the comparison was made by using
moisture content on wet basis in the linear fit (Table 4.4).
Within the moisture content range tested, the linear
relationship exits between bulk density and moisture content
on dry basis as well as on wet basis.
Table 4.2. The second-degree polynomial relationship between Bulk density and moisture content (percent, dry basis)
Materials Second degree polynomial R2
Sorghum Pb = 0.832 - 5.83E-3 MC + 8.10E-5 MC2 0.94 Wheat Pb = 0.921 - l.llE-3 MC + 1.05E-5 MC2 0.99 Corn Pb = 0.782 - 2.07E-3 MC - 7.97E-5 MC2 0.97 Blackeyed peas Pb = 0.850 - 5.87E-3 MC + 5.48E-5 MC2 0.99 soybean Pb = 0.798 - 5.38E-3 MC + 5.30E-5 MC2 0.99
26
Table 4.3. The linear relationship between Bulk density and moisture content (percent, dry basis)
Materials Linear function R2
Sorghum Pb = 0.781 - 1.46E-3 MC 0.81
Wheat Pb = 0.874 - 6.24E-3 MC 0.98 Corn Pb = 0.813 - 5.48E-3 MC 0.97
B1ackeyed peas Pb = 0.811 - 2.60E-3 MC 0.97
Soybean Pb = 0.774 - 2.91E-3 MC 0.98
Table 4.4. The linear relationship between Bulk density and moisture content (percent, wet basis)
Materials Linear
Sorghum Pb = 0.791
Wheat Pb = 0.902
Corn Pb = 0.832
Blackeyed peas Pb = 0.830
Soybean Pb = 0.787
Pb Bulk density, gjcm3
MC Moisture content (percent)
27
function
- 2.39E-3
- 9.41E-3
- 7.93E-3
- 4.34E-3
- 4.39E-3
MC
MC
MC
MC
MC
0.85
0.99
0.96
0.98
0.99
Brusewitz {1975} found that barley, corn, oats, rye,
and wheat have a minimum bulk density at a moisture near 30%
wet basis (about 45% d.b.). This phenomenon was not
detected in these experiments, because the maximum moisture
content was only about 45% (d.b.). Also, the relationships
between bulk density and moisture content in Tables 4.2, 4.3
and 4.4 were not held beyond the moisture range of 10 to 45%
(d.b.} in these experiments. Through an additional test,
the bulk densities of wheat and corn decreased 9 and 6%, as
the materials were dried from 13 and 10% moisture content
d.b. to 0%, respectively.
Nelson (1980} measured the bulk and particle density of
seven lots of hard red wheat and 21 lots of shelled, yellow
dent corn over moisture content ranges of 3 to 32% and 11 to
54% (d.b.}, respectively. The grain density-moisture
relationships shown by Nelson (1980} were well described by
third-order and fourth-order polynomial equations. The
highest value of bulk density for wheat was found at about
9% moisture content (d.b.}; and the lowest bulk density of
corn with a 48% moisture content (d.b.). The comparisons of
bulk density-moisture relationships for corn and wheat are
shown in Figures 4.1. and 4.2.
For the corn material used, the bulk density data agree
with Brusewitz's data very well within the moisture
contentrange of 18 to 33% (d.b.). As the moisture content
fell below 18% (d.b.}, Nelson's equation gives a better
28
N
1..0
t.O
r---
----
----
----
----
----
----
----
----
-
- r o. 9
E
0 ' O'l -o
. a
~
~
.-4
(I
) 5i o.
7 "'0
X
r-4
~ 0
. 6
0
o.s~----~----~----~-----~----~---
0 1
0
20
3
0
40
50
M
ois
ture
co
ntG
nt
(%
db
) 60
Fig
ure
4
.1.
Co
mp
ari
son
o
f b
ulk
d
en
sit
y-m
ois
ture
re
lati
on
sh
ip
for
co
rn.
Th
e d
ots
: th
is
stu
dy
; U
pp
er li
ne:
Nels
on
, 1
98
0;
low
er
lin
e:
Bru
sew
itz,
19
75
.
w
0
LO
r---
----
----
----
----
----
----
----
---
- (T') 0. 9
(
E
0 " I
0 m
-·
a. a
~
+) ......
(J) @
0. 7
-o
I
~0
~
...-
4 ~ 0
. 6
0.5~----~----~----~------L------L----_J
0 1
0
20
3
0
40
5
0
60
M
ois
ture
co
nte
nt
(4
db
)
Fig
ure
4
.2.
Co
mp
ari
son
o
f b
ulk
d
en
sit
y-m
ois
ture
re
lati
on
sh
ip
for
wh
eat.
T
he
do
ts:
this
stu
dy
; U
pp
er
lin
e:
Nels
on
, 1
98
0;
low
er
lin
e:
Bru
sew
itz,
19
75
.
description of bulk density-moisture content relationship.
For the wheat material, the bulk density data are higher
than both Nelson's and Brusewitz's data within the whole
range of moisture content tested, and has the similar shape
as described by Nelson (Figure 4.2). The maximum of wheat
bulk density obtained by Nelson occurs between 9 and 10%
moisture content (d.b.).
Because of the wide, natural variation in physical
properties of the same kind of grain, it is difficult to
conclude which model is the best to describes the bulk
density-moisture content relationship. Also, different
moisture content ranges examined causes different kinds of
density-moisture models. The overall tendency of the
density-moisture relation of wheat or corn could be
described by a third degree polynomial, which has the lowest
bulk density at about 455 moisture content (d.b.) and the
highest at about 10%.
Since the simple linear relationship in Table 4.3 is
obtained from analyses of experimental data, it will be used
for flow model development.
4.1.2. Particle size. Particle swelling was observed
during the experimental process as moisture increased. The
particle size is measured in three dimensions for each grain
material at each moisture content level. Because of the
large variance between particles, a statistical method was
used to test the hypothesis that the average particle size
31
(the arithmetic mean of three particle dimensions, largest,
intermediate, and least) increased as moisture content
increased. Through an analysis of variance, it was found,
at a=0.05, the particle minor dimension and arithmetic
average particle length are significantly increased within
the moisture range examined~ It was also found that the
increases in the three dimensions were unequal, which
implies a change in sphericity of the particle occurred.
Among five types of grain tested, soybean was found to
have the biggest change in particle size. An 8.4% increase
in average particle length is reached with an increase in
moisture content from 10.8 to 35.7% d.b. For other grains,
the increases in average particle length are, in ascending
order, corn (3.3%), sorghum (4.4%), wheat (5.9), and
blackeyed peas (6.1%) within the range of moisture content
examined. Assuming that the volume of particle is
approximately equal to the volume of a triaxial ellipsoid,
then the maximum increase in particle volume are, in order,
corn (11.4%), wheat (15.0%), blackeyed peas (19.8), sorghum
(19.9), and soybean (26.4%). The different increase in
particle size or particle volume for different materials can
be explained by their abilities to absorb moisture, which
depends on their chemical composition and structure.
The relationship between particle size (both average and
least dimension) and moisture content of grain can be
32
described by a simple linear equation (Table 4.5 and 4.6).
Such relationships are shown in Figures 4.3. and 4.4.
Table 4.5. The linear relationship between minimum particle dimension and moisture content (percent, dry basis)
Materials Linear function R2
Sorghum L = m 0.249 + 8.2E-4 MC 0.87 Wheat L .. = 0.249 + 7.1E-4 MC 0.99 Corn L = m 0.424 + 7.9E-4 MC 0.78 Blackeyed peas L .. = 0.534 + l.lE-3 MC 0.93 Soybean L = m 0.545 + 9.7E-4 MC 0.79
Table 4.6. The linear relationship between average particle length and moisture content (percent, dry basis)
Materials Linear function R2
Sorghum L. = 0.343 + 5.7E-4 MC 0.94
Wheat L. = 0.364 + 7.9E-4 MC 0.92
Corn L. = 0.762 + l.lE-3 MC 0.88
Blackeyed peas L. = 0.717 + 1.3E-3 MC 0.98
Soybean L. = 0.608 + 2.0E-3 MC 0.96
33
. w
~
I
0.8~----------------------------------
0. 7
....
] 0
.6 [
a
+
tJ. a
+ +
a
+ .f
J:
0.5
""" !o.J
D
D
D
II
D
0. 3
t-D
M
D
M
M
D
M
D
M
D
0.2
0 10
20
30
40
50
M
oist
ure
Co
nte
nt
(%
d. b
.)
Fro
m
bo
tto
m t
o t
op
, o
sorg
hu
m,
* w
hea
t,
o co
rn,
+
bla
ckey
ed p
eas,
an
d
a so
yb
ean
Fig
ure
4
.3.
The
re
lati
on
ship
b
etw
een
le
ast
part
icle
d
imen
sio
n a
nd
mo
istu
re co
nte
nt.
w
U1
0.9
r---
----
----
----
----
----
----
----
----
0. 8
t-D
D
D
D
D
+
+
+
+
++
] 0
. 7 t
tl
tl
tl
tl
tl
.r;O
.Sf-
"'"'
C) c ~ 0
.5 ~
0.
4 t-
M
M
M
M
M
0 D
D
D
0
0.3
0 1
0
20
30
4
0
50
Moi
stur
e C
onte
nt
(%
d. b
.)
Fro
m b
ott
om
to
to
p,
o so
rgh
um
, *
wh
eat,
a
soy
bean
, *
bla
ck
ey
ed
p
eas,
an
d
o co
rn,
Fig
ure
4
.4.
Th
e re
lati
on
sh
ip
betw
een
av
era
ge p
arti
cle
le
ng
th
and
m
ois
ture
co
nte
nt.
4.1.3. Angle of repose Two types of repose angles
(filling and emptying) were measured for sorghum, wheat, and
corn. In all cases, the emptying repose angle is
consistently larger than the filling repose angle. similar
results were also reported by Stahl (1950) and Brown and
Richards (1970). The maximum difference of 11 degrees
between filling and emptying angle of repose was found for
corn at 33% moisture content (d.b.).
The reason why the filling and emptying angle of
repose are different from each other can be explained as
follows: for the filling angle of repose, particles separate
when moving downward and there is no interference between
them. For the emptying angle of repose, particles converge
and the interference amplifies between them when moving
downward, thus the movement of particles is retarded by
their predecessors.
The result of added moisture is an increase in the
angle of repose. One explanation of the variation of repose
angle with moisture content is that the surface tension of
solids increases due to the increased moisture and makes it
easier to hold solids together, therefore, causing an
increase in the angle of repose.
The data for angle of repose is given in Table 4.7.
Both filling and emptying angle of repose increased as the
moisture content increased, but the difference between them
is inconsistent with the increasing moisture content. The
36
increase of repose angles with an increasing moisture
content are shown in Figures 4.5, 4.6, and 4.7. Although
the same trend was found for all these kinds of grain, it
seems that there is no single model to describe all the
data.
Table 4.7. Repose angle (degree) of grains at various moisture content levels
Materials Moisture content (% dry basis) in parenthesis
Sorghum (13.2) (18.8) (21.5) (28.4) (39.8) filling 32.5 33.0 32.5 34.5 35.5 emptying 38.5 41 43 44 44.5
Wheat (10.3) (17.6) (25.0) (30.0) (36.3) filling 28.2 30 33.2 37.3 40 emptying 35 40 43 45 47.5
Corn (10.0) (18.2) (24.1) (28.6) (33. 0) filling 31 32 34 36 38
emptying 32 35 43.5 48 51
Blackeyed peas (12.8) (14.1) (21.8) (27.9) (44.3)
filling 20.5 22.6 27.6 29.8 31.6
Soybean (10.8) (14.3) (17.0) (27.7) (35.7)
filling 24.4 25 26.5 29 32
37
50
-------------------------------------
0 0
0
0
" 40
,..
0 (I
)
• (J
I •
QJ
L •
• O
l •
.g 3
0 1
-~
w
OJ
I (J
.....
en
cam
ptyi
ng
0 ~ 20
~ ...
Fil
lin
g
10
0 1
0
20
3
0
40
50
M
ois
ture
co
nta
nt
% d
b
Fig
ure
4
.5.
Rep
ose
an
gle
o
f so
rgh
um
at
vari
ou
s m
ois
ture
co
nte
nt
lev
els
.
w
I 1.
0
SO I
0
0
0
4o
l 0
• "
• m
I OJ
0
cu •
'- m
~ 3o
r •
• OJ
.....
m
0 em
pty
ing
~ 20~
Fil
lin
g
*
to~------------~---------------------
0 1
0
20
3
0
40
so
Motstu~a
co
ntg
nt
% d
b
Fig
ure
4
.6.
Rep
ose
an
gle
o
f w
heat
at
vari
ou
s
mo
istu
re
co
nte
nt
lev
els
.
~
0
55
1
0
0
"45 ~
CD
0
(J
OJ
• L r 35
r •
0 •
le~
0 •
• ~
tn
emp
tyin
g 0
~ 25~
* fi
11
ing
15------~------~------~----~------~
0 1
0
20
3
0
40
M
ois
ture
co
ntg
nt
% d
b
Fig
ure
4
.7.
Rep
ose
an
gle
o
f co
rn at
vari
ou
s
mo
istu
re
co
nte
nt
lev
els
.
50
4.2. Mass and volumetric flow rate
For all the grain material used, mass flow decreased as
moisture content increased. With the 7.3 em diameter
orifice, mass flow rate of wheat dropped 24.8% when moisture
content increased from 10.25% to 36.33% (Appendix Table
A.1), at the same time, bulk density of wheat dropped 19.2%
(Table 4.1). The primary cause for the change in flow rate
could be explained by the change in bulk density; the
remainder of the change is associated with changes in flow
resistance. Therefore, the focus of this section is on
moisture effect on flow resistance.
The volumetric flow rate was obtained from the mass
flow rate by dividing by the respective bulk density (Tables
A.S, A.6, A.7, A.8, A.9, and A.10). Based on the comparison
between Tables A.S and A.6, wheat, with a small particle
size has a higher volumetric flow rate than soybean with a
larger particle size for all sizes of orifice openings at
about an 11% moisture content (d.b.). Further investigation
reveals that from small to large, the order of the
volumetric flow rate through the same orifice for the five
types of material examined is corn, blackeyed peas, soybean,
wheat, and sorghum. Contrarily, the average particle length
from large to small, is in the same order. This phenomenon,
in some degree, coincides with the conclusion by Fedler and
Gregory (1989) that the flow resistance coefficient, k, is a
linear function of minimum particle dimension.
41
The gravity flow through small orifices is affected
more by resistance than that through large orifices. This
phenomenon could be explained as follows: the flow through
the outside annulus of a small orifice was more affected by
resistance than that through the core of the orifice and
therefore had a low velocity. With the increasing orifice
diameter, the percentage of the area of outside annulus
decreased as compared to the core flow, and the effect on
resistance decreased.
An obstruction in flow through a 3.2 em diameter
orifice was observed at the maximum moisture content of
soybean {35.7%, d.b.) and blackeyed peas {45%, d.b.), which
suggests that the critical design aperture increases for an
increase in moisture content to prevent irregular flow or
total flow obstruction. The increase of critical aperture
dimension at a high moisture content is caused by the
increase in surface friction of particles, the increase in
particle size {less than 10%), and possibly by particles
becoming more elastic than dry particles.
4.3. The flow resistance coefficient, k
Most models used to predict the flow of granular
material through orifices include several physical
characteristics of the material. Particle size is one of
the most popular physical property parameter used in
existing flow models. Deming and Mehring {1929) used the
42
average diameter of an assumed spherical particle in their
model. In the case of nonspherical particles, they derived
Equation (2.1) to calculate the average diameter of
particles. Franklin and Johanson (1955) also used the
average particle diameter in their formula; the diameter was
determined by the average of direct measurement for large
particles and by arithmetic average screen mesh size for
small particles. Fowler and Glastonbury (1959) considered
the coefficient of friction to be a function of particle
size, shape, roughness, and void fraction of the bed of
packed material. After dimensional analysis and fitting
experimental data, they included two material characteristic
variables in their Equation (2.3): bulk density and
spherical diameter of particles. Instead of spherical
diameter of particles, Beverloo et al. (1961) only used the
average screen size of particles and bulk density in their
flow Equation (2.4). The use of particle size to describe
the flow rate of granular materials through orifices was
also reported by other researchers (Rose and Tanaka 1959,
Harmens 1963).
Gregory and Fedler (1987) treated the granular material
as a fluid in their derivation, but they restricted the
shear or resistance coefficient to a thin boundary layer at
the perimeter of the orifice. Therefore, they assumed the k
coefficient to be a function of the boundary layer thickness
that could have a minimum value equal to the minimum length
43
dimension, {Lm) of the granule. The relationship between
the measured k and the minimum particle dimension, Lm, which
was obtained by Fedler and Gregory {1989), was reproduced as
shown in Figure 4.8.
The k coefficients, as determined with the Gregory and
Fedler {1987) model for the 5 grain materials examined at
the various moisture contents, are listed in Table 4.8. The
values of k decreased as the moisture content increased for
corn, soybean and blackeyed peas. For wheat and sorghum, k
values first decreased then increased slightly when moisture
content exceeded 30% {d.b.).
Figure 4.9a shows the plot of k coefficient versus
minimum particle dimension, {Lm), under dry condition
{moisture content ranging from 10 to 13% d.b.) for the five
types of grain tested. The corn data point did not follow
the linear relationship very well. Although the flat shaped
corn used in the experiment has a smaller minimum particle,
Lm. than soybean and blackeyed peas, it has a larger
particle volume and average particle length than both of the
others. Therefore, from this data it appears that average
particle length or particle volume is better for predicting
the k coefficient than the minimum particle dimension
{Figure 4.9b).
44
~
U1
50~----------------------------------~
40
,....
CD
'30
N
' E u ' 3'2
0
~
10
0
R2=
=0.
777
a~----~------~------~----~------~
0 o.
2
0.
4 o.
6
o. 8
1.
0
Lm
(em
>
Fig
ure
4
.8.
Th
e li
near
rela
tio
nsh
ip
betw
een
le
ast
dim
en
sio
n
len
gth
o
f p
arti
cle
an
d re
sis
tan
ce co
eff
icie
nt.
(D
ata
fr
om
G
reg
ory
an
d
Fed
ler,
1
98
7)
Table 4.8. The effect of moisture content on flow resistance coefficient, k, and particle size
Granular Moisture Coefficient Particle size * materials content k Lm t L. :1:
' d.b. gfcm2-s em em
Sorghum 13.16 27.07 0.259 0.349 18.76 25.96 0.262 0.353 21.53 25.79 0.269 0.354 28.40 25.99 0.277 0.361 39.80 26.27 0.279 0.364
Wheat 10.25 27.12 0.257 0.373 17.59 24.79 0.262 0.378 25.01 23.38 0.267 0.380 29.98 23.63 0.272 0.387 36.33 24.23 0.273 0.395
Corn 10.04 36.67 0.429 0.769 18.23 35.78 0.445 0.787 24.06 32.65 0.439 0.787 28.56 31.01 0.447 0.793 33.00 30.27 0.450 0.794
Blackeyed peas 12.83 32.45 0.543 0.733 14.07 32.44 0.543 0.733 21.76 31.30 0.565 0.749 27.86 29.71 0.566 0.756 44.26 28.36 0.581 0.771 46.02 28.45 0.581 0.778
Soybean 10.77 30.53 0.549 0.624 14.32 30.28 0.559 0.637 17.02 29.67 0.569 0.648 27.69 29.46 0.572 0.662 35.68 28.98 0.577 0.677
* These values were calculated by measuring 50 seeds each time.
t The least length dimension of the particles. + The arithmetic mean length dimension of the particles.
46
50~----------------------------------~
40 1-
-" c{, 30 ~ c E u
' Sl2o ~
10
0
0 0
* Corn
0----~~-·~------~·~------~·~------~------~ 0 0.2 0.4 0.6 o. 8 1. 0
Lm <em>
(a)
50r-----------------------------------------
40
-CD
~ 30 c E u
' Slzo
10
•
R"'2=0.83 * Corn
0~----~~------~--------~------~------~ 0 D. 2 0. 4 0.6 0. 8 1. 0
LQ (em)
(b)
Figure 4.9. The flow resistance coefficient against (a) m1n1mum particle length; (b) average particle length. (data from Table 4.8)
47
4.4. Model development for flow resistance coefficient, k
Gregory and Fedler (1987) developed a boundary layer
(the layer between the flowing core and the non-flowing
material) concept that friction occurs as the core material
slides past the stationary material external to the core and
the shear or resistance of this boundary layer is near the
perimeter of the orifice. In their next paper, Fedler and
Gregory (1989) found the resistance term to be related to
the boundary thickness, and the minimum thickness of the
boundary layer is equal to the minimum length dimension of
the granule.
Brown and Richards (1960) also found that there was a
decrease in the number of particles flowing per unit time in
the layer adjacent to the orifice edge. Laohakaul {1978)
reported that flow was retarded in a region of a few
particles in thickness adjacent to a solid boundary (quoted
from Nedderman and Tuzun, 1982, p. 1599). This decrease in
flow rate near the orifice edge can be easily explained by
Gregory and Fedler's {1987) boundary layer concept.
Based on the consideration that the boundary layer
thickness is related to the particle size, the k coefficient
can be expressed as a function of average particle size. For
granular materials with an irregular shape, the average
particle length has a much better relationship to particle
volume or surface area than the minimum length dimension
48
(Figure 4.10). Also, the average particle size is used more
widely than Lm in industry.
A linear relationship between average particle length
and flow resistance coefficient, k, which is calculated by
using Gregory and Fedler's (1987) model, is shown in Figure
4.10. Compared with Figure 4.8., the average particle
length predicts k values as well as the minimum length
dimension of particles.
Considering the particle roughness and shape, Fedler
and Gregory (1989) divided the data of Lm into two classes
of materials: Type I (materials with smooth, symmetrical
shapes) and Type II (other materials with either rough or
irregular shapes) . They developed a much stronger linear
relationship between k and Lm for both types of materials,
with an R2 value of 0.99 and 0.98, respectively. such a
division of materials does not occur when using average
particle length.
Although the repose angle varies significantly with the
moisture content, the strong correlation between flow
resistance coefficient (k) and particle size reveals that
the effect of repose angle on flow rate or k is small. Rose
and Tanaka (1959) found that the rate of discharge from a
bin is practically independent of the coefficient of
friction of material (tangent of the emptying angle of
repose). Nedderman (1982) concluded that the effects of
49
U1
0
50~--------------------------------~
40
" (I) ~ 3
0
c E
0 ' I !!' 2
0
~
10
0
k•1
2.9
+2
4.5
La
R
·2•0
. 83
7
o~----_.------~----~~----~----~
0 0
.2
0.
4 o.
6
o. 8
1.
0
La
Ccm
)
Fig
ure
4
.10
. T
he
lin
ear
rela
tio
nsh
ip
betw
een
av
era
ge p
arti
cle
le
ng
th
an
d re
sis
tan
ce co
eff
icie
nt.
(d
ata
fr
om
G
reg
ory
an
d fe
dle
r,
19
87
)
friction and the particle shape of a material on its flow
rate seem to be small. Jenike (1964) argues that repose
angle is not a proper measure of flowing properties of bulk
solids, but it is a result of the interplay of physical and
chemical properties of the materials. Also, no clear
evidence of the effect of repose angle on orifice flow is
found through this experiment.
Since the k coefficient can be determined by average
particle length, which in turn is influenced by the moisture
content, models containing average particle size (L.) and
moisture content (MC) were tested to give a good prediction
of k by using a computer program called MERV (Gregory and
Fedler, 1986). Based on the linear relationship between
flow resistance coefficient, k, and average particle length
(Figure 4.10), and the decrease in the k value with an
increasing moisture content (d.b.), the flow resistance
coefficient, k, is assumed to be a multiple linear function
of average particle length (L.) and moisture content (MC).
( 4. 1)
where a 1 , a 2 , and a 3 are coefficients. The model fit the
data with an R2 of 0.73. Since the particle length of
granules are highly correlated to the moisture content
(discussed in 4.1.2), the interaction term of average
particle length and moisture content (L.MC) was expected to
51
be related to flow resistance and was used to replace the
second term of Equation 4.1.
The resulting model is
(4.2)
where
k = flow resistance, gjcm2-s
L. = average particle length, em
MC =percent moisture content, (d.b.).
Using MERV, coefficients a 1 , a 2 , and a 3 in Equation (4.2)
were determined to be 16.6, 22.7, and -0.102, respectively.
The function was obtained for both Gregory and Fedler's data
and data from this experiment, and gave an R2 of 0.75. The
data of predicted k values versus measured k values are
shown in Figure 4.11 for data from this experiment and 4.12
for both wet and dry materials including data from Fedler
and Gregory (1989).
This modified Equation (4.2), which is based on the
Fedler and Gregory {1989} model, can be used easily to
predict the flow resistance coefficient, k, by simply using
moisture contents (% d.b.} and the average particle length
of granular material.
4.5. Model verification
By analyzing the effects of moisture content on bulk
density and flow resistance coefficient, k, and combining
52
40 _.... Ul I
C\.1 30 <
E u
" Ol -X 20 "'0 Q)
-'-' u 10 RA2=0.867 ·r-t -a Q) (._ a_
0 0 10 20 30 .40
Measured k (g/cm~2-s)
Figure 4.11. Plot of predicted versus measured flow resistance coefficient. (Data from Table 4.8)
53
40r----------------------------
-(/) I
30 C\J c E u
' CJ) -..Y 20
'0 Q)
....... u ·r-i
10 '0 RA2=0.753 QJ (_
n..
0 ~------~------~------~----~ 0 10 20 30 40
Measured k (g/cm-'\2-s)
Figure 4.12. Plot of predicted versus measured flow resistance coefficient. (Data includes Gregory and Fedler's data, 1987)
54
Equation 2.8 and 4.2, the modified Gregory and Fedler model
(1987) for predicting the mass flow rate (Qm) of granular
materials with various moisture contents through circular
orifices is given as:
(4.3}
This modified equation was developed for orifice diameters
less than 11 em and for moisture contents of grain materials
ranging from 10 to 45% (d.b.). Two easily measurable
properties, bulk density and average particle length, were
used to predict mass flow rate at various moisture contents.
By using the linear density-moisture relationship
{Table 4.3) and coefficients obtained in Equation 4.2, the
mass flow rates were easily calculated by Equation 4.3. For
the five types of materials tested, the plots of predicted
versus measured mass flow rate at various moisture content
are shown in Figures 4.13 through 4.17. Different clusters
in these figures represent different orifice sizes and the
points in each cluster represent different moisture
contents.
The modified Equation (4.3) predicted measured mass
flow rate with R2 values higher than 0.92; the highest R2 of
0.99 was obtained in Figure 4.17 for soybean.
For the small orifice (less than 9.0 em diameter), the
modified flow model predicts mass flow rate well; for the
55
" (/)
' m "" (U .., 0 L
6000~--------------------------~
4500
~ 3000 r-4
4-
"'C OJ
t 1500 ...... "'C
Q1 L
n..
R~2=0.957
0 ~------~------~~------~------~ 0 1500 3000 4500 6000
Measured Flow rote Cg/s)
Figure 4.13. Plot of predicted versus measured mass flow rate of sorghum at various moisture content levels.
56
6000 0
"' m
' 0 en ~
4500 0
(J
+> 0 L
~ 3000 0 r-t
4-
"U cu ...,
1500 u ..... "'0
OJ L
a..
0 0 1500 3000 4500 6000
Measured flow rate (g/s)
Figure 4.14. Plot of predicted versus measured mass flow rate of wheat at various moisture content levels.
57
" U)
' Ol ""'
OJ .,_, 0 L
~ 0 ~
tJ-
-o OJ .,_, 0 .....
-o OJ L
Q_
6000
4500
3000
1500
0 0 1500
0
0
3000
R"'2=0.982
6000 Measured flow rate
4500 <g/s)
~------------~~----~~~--~~~~~ -~~~
Figure 4.15. Plot of predicted versus measured mass flow rate of corn at various moisture content levels.
58
6000
""' (/)
' 01 ..._, 4500
QJ +> 0 L
~ 3000 0 ,...... 4-
1J cv +l
1500 u RA2=0.995 .,..... 1J Cll L a...
0 0 1500 3000 A500 6000
Measured Flow rate (g/s)
Figure 4.16. Plot of predicted versus measured mass flow rate of blackeyed peas at various moisture content levels.
59
6000
"' en
" m """"
4500 01
-1-l 0 L
~ 3000 0
........ (f..
"0 QJ ~ 0 1500 R"2=0.999
r-t
:J 0
r-t
0 u
0 0 1500 3000 4500 6000
Measured flow rate Cg/s)
Figure 4.17. Plot of predicted versus measured mass flow rate of soybean at various moisture content levels.
60
largest orifice (10.4 em diameter), the model overestimates
the mass flow rate for all five types of materials. The
overestimation of flow rate can be explained by the concept
of laminar versus turbulent flow condition (Gregory and
Fedler 1987), which means that the flow through the small
orifice is regular and laminar, and becomes irregular and
turbulent when the orifice is large. From the laminar to
turbulent flow, transition flow occurs and the power on
orifice diameter in Equation 4.3 will decrease from 3.0 to
2.5.
The modified flow model is developed based on the
Gregory and Fedler (1987) model for laminar flow condition.
Therefore, the overestimation of flow rate at the 10.4 em
diameter orifice could imply the existence of transition
flow and the relating discussion is beyond the objective of
this study.
61
CHAPTER V
CONCLUSIONS
Five kinds of grain materials were used to test the
effect of moisture content on flow rate of grain through
horizontal orifices by gravity. Within a wide range of
moisture content (10 to 45% d.b.), flow rate of grain and
some of material property parameters, such as bulk density,
particle, and coefficient of friction were significantly
affected by the change in moisture content. The decrease in
bulk density with an increasing moisture content can be well
described by a second-degree polynomial equation. A linear
relationship is found between average particle length and
moisture content of grain. Also, the internal friction
coefficient of grain is affected by moisture content by
means of increasing of both emptying and filling angle of
repose.
With the orifice diameter ranging from 3.18 to 10.4 em,
the mass flow rate decreases as moisture content increases,
and the main decrease is caused by the decrease in bulk
density of the materials. The remainder of the effect can
be explained by the variation in the flow resistance
coefficient.
The flow resistance coefficient (k) for dry granular
materials is highly correlated with the average particle
length and can be easily estimated by a simple linear
62
equation. At various moisture contents, the flow resistance
is a multiple linear function of average particle length of
the granule and the interaction between average particle
length and moisture content. This new function predicts
approximately 75% of the variation in the k value.
The Gregory and Fedler {1987) model at laminar condition
is modified to predict the granular flow of five grain
materials with various levels of moisture content. For the
five types of materials tested, the modified flow model is
verified with R2 values in excess of 0.92.
To complete the study of the effect of material
moisture content on flow, it is suggested that other
materials be studied to test the validity of the modified
flow resistance function and flow model at various moisture
contents. Since the modified Gregory and Fedler {1987)
laminar flow model overestimates the granular flow rate for
large orifices, it is recommended that further investigation
be done to determine what relationship exists between
orifice size and particle size or other granule properties
under turbulent flow conditions.
63
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64
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Fedler, C.B. 1988. Mathematical models describing the flow of granular materials. Mathematical and Computer Modeling. Vol II. pp. 510-513. England:Pergamon Press.
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66
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67
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68
APPENDIX
EXPERIMENTAL DATA OF MASS AND
VOLUMETRIC FLOW RATES
69
TABLE A.1. Mass flow rate (g/s) of wheat at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 10.25% 17.59% 25.05% 29.98% 36.33%
3.18 171.5* 157.4 145.2 130.2 117.0
5.00 673.1 596.9 526.2 480.8 450.9
6.15 1171.3 1107.2 978.0 889.5 816.9
7.31 1771.3 1734.1 1590.8 1452.0 1331.8
8.95 2908.0 2837.7 2723.0 2523.4 2358.7
10.37 4417.2 4208.5 4093.7 3745.4 3581.6
* Mean of three replications.
70
TABLE A.2. Mass flow rate (gjs) of soybean at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 10.77% 14.32% 17.02% 27.69% 35.68%
3.18 108.7* 104.3 104.3 95.3 stop
5.00 462.7 440.0 444.5 412.8 390.1
6.15 870.9 816.5 807.4 762.1 721.2
7.31 1447.0 1383.5 1374.4 1242.9 1179.4
8.95 2571.9 2481.2 2458.5 2281.6 2186.4
10.37 3869.2 3724.1 3692.3 3447.4 3324.9
* Mean of three replications
71
TABLE A.3. Mass flow rate (g/s) of sorghum at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 13.16% 18.76% 21.53% 28.40% 39.80%
3.18 175.5* 172.4 169.7 159.2 147.4
5.00 651.8 635.5 600.1 569.3 548.7
6.15 1175.7 1142.6 1081.4 1052.8 1006.5
7.31 1887.0 1824.8 1766.3 1726.4 1638.0
8.95 3152.5 3133.5 3092.6 2989.7 2855.4
10.37 4492.9 4470.7 4354.6 4300.6 4213.4
* Mean of three replications.
72
TABLE A.4. Mass flow rate (g/s) of corn at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 10.25% 18.23% 24.06% 28.56% 33.00%
3.18 ___ +
5.00 394.2* 371.0 357.4 336.6 325.2
6.15 742.1 717.1 681.7 650.0 627.8
7.31 1196.6 1159.0 1102.3 1043.3 995.7
8.95 2146.4 2079.8 1996.8 1901.5 1851.1
10.37 3247.8 3106.7 3025.1 2877.2 2802.8
* Mean of three replications + flow discontinues or stops
73
TABLE A.5. Mass flow rate (gjs) of blackeyed peas at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 12.83% 14.07% 21.76% 27.86% 44.26% 46.02%
3.18 96.6* 99.8 95.3 95.3 stop stop
5.00 445.9 462.7 449.1 444.5 421.9 394.6
6.15 880.0 884.5 861.8 848.2 839.2 753.0
7.31 1460.6 1447.0 1388.0 1388.0 1338.1 1270.1
8.95 2649.0 2608.2 2549.2 2544.7 2444.9 2376.9
10.37 4023.4 3969.0 3778.5 3751.3 3687.8 3569.8
* Mean of three replications.
74
TABLE A.6. Volumetric flow rate (cm3js) of wheat at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 10.25% 17.59% 25.05% 29.98% 36.33%
3.18 210.2* 205.8 205.4 191.8 177.5
5.00 824.9 780.3 744.3 708.1 684.2
6.15 1435.4 1447.3 1383.3 1310.0 1239.6
7.31 2170.7 2266.8 2250.1 2138.4 2020.9
8.95 3563.7 3709.4 3851.5 3716.3 3579.2
10.37 5413.2 5501.3 5790.2 5516.1 5434.9
* Volumetric flow rate = mass flow rate I bulk density.
75
TABLE A.7. Volumetric flow rate (cm3js) of soybean at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 10.77% 14.32% 17.02% 27.69% 35.68%
3.18 145.6* 142.7 146.0 137.7 stop
5.00 618.6 601.9 622.2 596.5 579.6
6.15 1164.3 1117.0 1130.2 1101.3 1071.6
7.31 1934.5 1892.6 1923.9 1796.1 1752.5
8.95 3438.4 3394.3 3441.3 3297.1 3248.7
10.37 5172.7 5094.5 5168.4 4981.8 4940.4
* Volumetric flow rate = mass flow rate I bulk density.
76
TABLE A.a. Volumetric flow rate (cm3fs) of sorghum at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 13.16% 18.76% 21.53% 28.40% 39.80%
3.18 227.7* 229.2 229.3 216.3 202.5
5.00 845.4 845.1 811.0 773.5 753.9
6.15 1524.9 1519.4 1461.9 1430.4 1382.7
7.31 2447.4 2426.6 238609 2345.7 2249.9
8.95 4088.9 4166.8 4179.2 4062.1 3922.3
10.37 5827.4 5945.1 5884.5 5843.2 5788.4
* Volumetric flow rate = mass flow rate I bulk density.
77
TABLE A.9. Volumetric flow rate (cm3js) of corn at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 10.04% 18.23% 24.06% 28.56% 33.00%
3.18 ___ +
5.00 525.6* 511.1 523.3 518.6 514.6
6.15 989.5 987.8 998.2 1001.6 993.3
7.31 1595.5 1596.3 1613.8 1607.5 1575.4
8.95 2861.9 2864.7 2923.5 2929.9 2929.0
10.37 4330.4 4279.2 4429.1 4433.3 4434.8
* Volumetric flow rate = mass flow rate I bulk density. + Flow discontinues or stops.
78
TABLE A.10. Volumetric flow rate (cm3fs) of blackeyed peas at various moisture content levels
Orifice Diameter Moisture content, % d.b.
em 12.83% 14.07% 21.76% 27.86% 44.26% 46.02%
3.18 123.2* 128.1 127.2 130.8 stop stop
5.00 568.7 594.0 599.5 610.6 600.1 570.3
6.15 1122.4 1135.5 1150.7 1165.2 1193.7 1088.1
7.31 1863.0 1857.5 1853.2 1906.6 1903.4 1835.4
8.95 3378.9 3348.1 3403.5 3495.5 3477.8 3434.8
10.37 5131.9 5095.0 5044.7 5152.8 5233.0 5158.7
* Volumetric flow rate = mass flow rate I bulk density.
79
