Motion Characteristics of Shaped Grains in Gas-solid Two-phase
Flow
Yongyu Zhang
1
, Chao Wu
2
, Anbiao Wang
3
and Zhongying Wang
4
1 School of Mechanical & electric Engineering, Henan University of Technology, Zhengzhou, China
2 College of Mechanical and Electrical Engineering ， Zhengzhou University of Light Industry,
Zhengzhou, China
Keywords: Cereal grains, shaped particles, gas solid, two-phase flow, motion characteristics.
Abstract: In order to simplify the calculation and analysis process, the the difference of shape and size of cereal grain
shaped particles was converted to projected diameter. Using the theory of multiphase flow, resistance
coefficient, fluid drag force and relaxation time of entrance flow on single grain particle and grain particles
of dilute phase and dense phase flow conveying were researched. The results showed that the different kind
of grain particle can be characterized as volume shape factor and projected diameter. The fluid drag force of
single grain particles or particles in different regions with different Reynolds number have different
variation. The same type of particles is also affected by projection diameter, suspension speed and other
parameters. The inlet relaxation time of the dense phase transport particle group is higher than that of dilute
phase transport, and the single particle fluidization relaxation time is one order of magnitude. Different
kinds of raw material grains flow of the relaxation time is different, so the energy consumption to achieve
the suspended feed status is also different.
1 INTRODUCTION
Pipeline pneumatic conveying is characterized by
high speed and large quantity of conveying by
conveying the scattered material through the
pipeline using the flowing air. With the development
of industry and the progress of science and
technology, the pneumatic conveying technology is
widely used in many fields, such as port loading and
unloading, mining, coal, chemical, building
materials, pharmaceutical, casting and textile[1-3].
The application and research of the pipeline
pneumatic conveying in the grain industry is mainly
embodied in two aspects, one is the pipeline
pneumatic conveying part on the single machine
equipment, such as the pipe conveying system,
which is widely used in the grain absorbing
equipment of the station, the port and the warehouse,
and the transportation distance varies from several
tens to hundreds of meters[4]. On the other hand, it
is the pneumatic conveying in the factory, including
the component of the pneumatic conveying of the
distribution of the bulk material, or the pipe
connection between the different equipment in the
plant. The transmission distance is usually about
hundreds of meters, and the longest distance is up to
1000 meters[5].
The flow field of grain pipeline conveying is a
gas solid multiphase flow field with air medium as a
continuous phase, raw grain particles with different
shapes and sizes and the impurities mixed in them as
discrete phases. The multiphase flow can be divided
into thin phase suspension transport and dense phase
suspension transport according to the transport
concentration of central grain particles, but the thin
phase suspension transportation has high transport
wind speed, large power consumption, easy wear of
the pipe wall and high crushing rate of conveying
material[6].
In order to increase the flow rate and flow of the
fluid in order to increase the transport capacity, it
will not only produce large energy loss, but also
consume a large amount of fluid medium, which
makes the transportation benefit low and the
economy is poor. The concentrated phase suspension
transport can effectively utilize the energy of the
airflow, for example, Tong Deng[7] and so on, a
fluid model which considers the particle size

distribution effect in the dense phase pneumatic
conveying of particle flow is proposed, and the size
distribution of the material particle size of the
plugging pipe is calculated.
In relation to the calculation of the drag force of
the fluid, the modified drag force model for dense
gas solid two phase flow is proposed by Wang
Xueyao[8] and so on, and a three-dimensional flow
model based on the multi scale is established in
combination with the theory of particle dynamics. In
the study of particle flow characteristics in
multiphase flow field, PIV two phase simultaneous
measurement method was used, SuJing, Jiang
Guifeng, Liu Zhaohui[9] and so on to study the
particle motion characteristics in high Reynolds
number of gas solid two nozzles against impinging
jet.
In this paper, in view of the motion
characteristics of the grain original grain in the
pipeline pneumatic conveying flow field, the multi
phase flow theory is applied to the non spherical
grain grain projecting. The results of the study of the
dilute phase flow field and the relaxation time of the
fluid drag force and the entrance fluidization in the
concentrated phase flow field are calculated. It
provides theoretical support for the design of
pneumatic conveying system for grain raw grain and
optimization of the structural parameters of
conveying equipment.
2 SIZE CHARACTERISTICS OF
HETEROMORPHIC GRAINS IN
CEREAL
In the process of pipeline pneumatic conveying,
different kinds of grain produce different
hydrodynamic characteristics in the gas solid
multiphase suspension because of the difference in
the shape and size of the particles, which leads to the
different stress conditions in the multiphase flow
field.
In order to study the motion characteristics of
the grain original grain in the gas solid two phase
flow field, and to determine the fluid force of the
continuous phase air flow to the non spherical
discrete grain grain particles, the characteristic
parameters of different heteromorphic particles
should be determined.
Based on the analysis method proposed by
Heywood[10] to indicate the size of non spherical
irregular shape particles with the projection diameter,
the projection diameter dp and other characteristic
parameters of several typical grain raw grains are
calculated.
In the typical cereal grains, soybean particles can
be considered as spherical particles, while wheat,
rice and corn grains are typical non spherical and
heteromorphic particles. In order to simplify
calculation and convenient analysis, the particle size
distribution function is calculated according to the
average size of particle size. The system is
simplified as a gas solid two phase flow system with
monodisperse particle size, and the characteristic
parameters of several representative grain grain
heteromorphic particles are shown in table 1.
Table 1: Characteristic parameter values of several representative cereal grains based on Heywood analysis method.
type Ratio of
Width to
thickness
（m）
Ratio
of length to
width
（n）
Volume
shape coefficient
（Z）
Particle
volume/mm
3
(V
p
)
Projection
diameter/mm
（d
p
）
soybean - - 0.5236 87.07 5.5
wheat
(common)
3.2/2.9 6.2/3.2 0.3226 28.78 4.47
Rice 3.4/2.3 7.4/3.4 0.2293 20.88 4.50
Corn 8.5/5 10/8.5 0.2712 291.67 10.25

It is known from table 1 that the irregular shape
of grain original grain is characterized by the
parameter of volume shape coefficient Z, according
to its shape and size. The Z value of the soybean
particle near the spherical shape can be directly
taken as π/6, the volume shape number and the
diameter of the projection of the other three raw
grains can be based on the width to thickness ratio
and the ratio of length to width. By comparing the
volume shape coefficient, it is found that except for
soybean granules, the grain shape of rice grains is
close to the lowest sphere, and the wheat grain is
nearly spherical. Although the volume of wheat
grain is larger than that of paddy grain, the volume
shape coefficient is different, which makes the two
kinds of particles basically close to the projected
diameter. Because of the large volume of corn
granules, the projection diameter is also large.
3 DRAG COEFFICIENT AND
FLUID DRAG FORCE
In the flow field of pipeline pneumatic conveying of
grain, the grain particles are moving along the
direction of flow under the action of flow force.
Only considering the movement of a single grain in
the fluid, the drag force of the fluid can be calculated
by formula (1).
22
8
1
pfpDD
udCF  
(1)
In the formula, C
d
is the drag coefficient, which
varies with the Reynolds number R
e
, and the
parameter d
p
is the projection diameter of the grain
grain, which is used to replace the spherical particle
diameter in the stationary viscous fluid, and the ρ
f
f
is the fluid density (the air density is about
1.29Kg/m³), and the u
p
is the velocity of the grain
particles in the stationary fluid.
At low Reynolds number (Re 1), ≦ Cd increases
linearly with decreasing Re, and the corresponding
formula for calculating fluid drag is obtained by
using Stokes's formula (2).
22
3
pfp
e
D
ud
R
F  
(2)
When the Reynolds number is 1≦Re 700, the ≦
parameter Cd decreases with the increase of Re, and
the effect of friction resistance becomes smaller. The
inertia force will gradually increase with the increase
of Reynolds number. According to the formula of
Rowe, the formula of the calculation of the drag
force can be obtained, such as formula (3).
22
687.0
)15.01(
3
pfpe
e
D
udR
R
F  
(3)
When the Reynolds number is 700≦Re 2×10≦ 5,
the friction resistance effect can be ignored at this
time and the inertia force is dominant, and the
resistance coefficient Cd is approximately constant,
and the corresponding calculation formula of the
fluid drag force can be obtained (4).
22
055.0
pfpD
udF  
(4)
When the Reynolds number exceeds the critical
Reynolds number of 2×105, the drag coefficient will
suddenly decrease, because the viscous fluid layer
on the particle surface will change to a turbulent
state.
According to the formula (2), (3) and (4), the
relation curve of the fluid drag-force Fd of several
typical single grain particle with the change of
Reynolds number Re is obtained, as shown in Figure
1.
Among them, up is assumed to be the suspension
velocity of grain grains, and the suspension velocity
of soybean, common wheat, rice and corn grains are
10m/s, 8.4m/s, 7.5m/s and 13.5m/s respectively[11].
Figure 1: relationship between the drag force and the
Reynolds number of a single grain particle.
For the gas solid two phase flow of cereal grain
particles, when the porosity ε is large enough
(ε>0.92), the interaction between the particles can be
ignored. The calculation of the resistance coefficient
Cd can further calculate the force of the single grain
grain in the continuous phase fluid. According to the
variation of Reynolds number Re, the variation of

fluid drag force produced by air flow on the grain in
the dilute phase system can be obtained.
From Fig. 1, it can be see that the variation of Fd
of different single grain in different regions is
basically the same as that of Reynolds number Re.
Because the soybean particles are close to the
spherical particles, the average diameter of the
particles is calculated for the diameter of the ball
according to the particle size distribution, and the
other three kinds of cereal grains are converted to
the projection diameter dp.
Although the projection diameter of wheat grains
is slightly smaller than the projection diameter of
rice grains, the suspension velocity is higher than
that of rice grains, making the difference in the drag
force of the fluid under the same Reynolds number.
The projective diameter of the corn grains is larger
and the suspension speed is higher, so the fluid drag
force of the particles under the same Reynolds
number is also larger, which means that more energy
is consumed during the pipeline transportation.
With the increase of grain transport
concentration, the concentration of discrete phase in
the gas-solid two-phase flow system increases. At
this time, the system is gradually transformed from
dilute phase system to concentrated phase system.
The above calculation is no longer applicable, but it
should be considered according to the movement
law of grain group. According to the expression of
the air clearance degree ε of the gas solid suspension
system determined by Wen, the void function φ(ε) is
considered in the calculation of the resistance
coefficient. The drag force of the grain group fluid
suitable for the dense phase conveying system can
be given by the by the following formulas.
85.422
3

 
pfp
e
D
ud
R
F
（R
e
1≦ ） (5)
7.422
687.0
)15.01(
3

 
pfpe
e
D
udR
R
F
(1< R
e
700≦ ）
(6)
78.422
055.0

 
pfpD
udF
(700< Re 2×10≦
5
)
(7)
The formula (5), (6) and (7) can be used to
determine the relationship between the fluid drag
force F
d
of the bulk grain and the change of the
Reynolds number R
e
in the different flow areas, as
shown in Figure 2.
（a）Soybean granules（dp=5.5mm，up=10m/s）
（b）Wheat grain（dp=4.47mm，up=8.4m/s）
（c）Rice grain（dp=4.5mm，up=7.5m/s）

（d）Corn grain（dp=10.25mm，up=13.5m/s）
Figure 2: relationship between the drag force and the
Reynolds number of grains in the grain stock group.
As shown in Fig. 2, when the porosity parameter
ε is close to 0.9, the fluid drag force of different
types of grain grains is close to that of a single
particle. However, with the reduction of the porosity
parameter ε (the volume fraction of the particle
phase increases) and the same Reynolds number R
e
,
the numerical value of the drag force increases
significantly if the different types of particles are to
reach the corresponding suspension velocity.
In addition, the larger the projective diameter of
a single particle and the higher the suspension
velocity, the greater the fluid drag force of the
particle group. The projection diameter and the
suspension speed of the corn grains are higher than
other grains of raw grain, so the drag force of the
particle group is much larger than that of the other
grains.
4 RELAXATION TIME OF
ENTRANCE FLUIDIZATION
Before the normal grain delivery is realized, the
grain supply must be fluidization through the feeder
at the entrance of the pipe, and the material particles
and the air flow are fully mixed, so that the particle
phase is accelerated by the continuous phase flow
and transported under the action of the flow force.
If the conveying air velocity is u, when the raw
grain particles enter at zero speed, the particles will
be accelerated at the condition that the gravity effect
is ignored. The particle velocity u
p
increases from 0
to the levitation speed and is evaluated with the time
required for the movement of the air. Under the
initial conditions t=0 and up=0, the law of individual
particle velocity varying with time t is shown in
formula 8.
)1(
2
18
t
d
p
pp
euu




(8)
According to the above formula, the relationship
curves of single grain velocity up and time t are
obtained, as shown in Figure 2.
In the formula, ρp is the grain density of raw
grain, the average density of soybean is 1200Kg/m3,
and the density of medium wheat is 760Kg/m3. The
average density of paddy in China is1195Kg/m3, the
density of corn kernel is about 1150Kg/m3, and that
of μ is aerodynamic viscosity coefficient, which is
1.83×10-5Paꞏs.
Figure 3: Relationship between grain velocity and grain
time in cereal grain.
Figure 3 is the relation curve of speed changing
with time when the grain is accelerated. It is shown
from the diagram that the time of the grain grain
with different shapes and sizes to reach their
respective floating speed after entering the air flow
is different. The relaxation time is related to the
projection diameter and the suspension speed of
grain particles, and the relaxation time of the
particles with larger projection diameter is
significantly reduced. This is because the higher the
velocity of the suspended velocity is, the higher the
flow velocity is, and the relaxation time of the
particles with similar projection diameter is also
basically the same. In addition, the relaxation time
of grain particles with higher suspension speed will
also decrease, which means that the particle
acceleration time of the grain in the initial stage of
air flow will be reduced.

For the dense phase conveying system with the
void fraction ε increasing , the interaction and
influence between particles should be considered.
The voidage function of the grain group is
determined in advance. When the relaxation time τ is
replaced by the formula (8), the relation expression
of the particle swarm velocity up with time t can be
obtained as shown in the formula (9).
)1(
)75.1(
2
tu
d
d
p
f
pp
pp
euu






(9)
(a) soybean particle swarm
(b) grain group of Wheat
(c) rice grain group
(d) corn grain group
Figure 4: relaxation time of the fluidization of grain
group.
Figure 4 compares the velocity changes of grain
groups of different kinds of raw grain. It can be seen
from the diagram that the acceleration process of the
grain group in the concentrated phase system is
more than one order of magnitude compared with
the dilute phase system. This shows that the starting
and accelerating process of the grain group with a
certain volume rate at a lower initial speed or near
the velocity of zero speed will take longer to reach
the complete suspension state. Because the
interaction time between the air flow and the grain
grain is longer, the loss of the energy is greater.
It can be seen from the diagram that the
relaxation time of the grain group of different kinds
of grain is mainly related to the suspension speed.
The higher the suspension speed, the shorter the time
for the grain group to accelerate to the required
speed, the higher the flow velocity and pressure will
be needed. If the inlet air velocity is increased,
although the relaxation time can be reduced, the
pressure loss of the pipeline will also increase, and
the energy loss will be increased. The relaxation
time of the particle group in the dense phase system
is related to the shape and size of the different
shaped particles and the air gap of the particle group,
as well as the inlet air velocity.
5 CONCLUSIONS
The motion characteristics of the special-shaped
grain particles in the gas-solid two-phase flow are
studied in the process of grain pipeline pneumatic
conveying. The heterogeneous grains of non
spherical raw grain are converted into volume shape
coefficient and projection diameter use the
multiphase flow theory to adapt to the calculation

and the analysis of gas solid multiphase flow of
grains with different shapes and feet.
Through the calculation and analysis of the
resistance coefficient, the fluid drag force and the
entrance fluidization relaxation time of the particle
and particle swarm in the gas solid two phase flow
system, the particle movement law in the raw grain
pneumatic conveying flow field is found, which
provides theoretical support about grain pneumatic
conveying system design and the application of the
pneumatic conveying engineering.
ACKNOWLEDGEMENTS
It is funded by the high level scientific research fund
of Henan University of Technology.
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