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Trajectory and Distribution of Particles Conveyed in
Horizontal Pipe
Journal: Journal of the Chinese Institute of Engineers
Manuscript ID: TCIE-2013-0287
Manuscript Type: Mechanical Engineering – Full Paper
Manuscript Subject Index: ME1 Aerodynamics < Mechanical Engineering Subject Index
Keywords in Manuscript: Gas-solid two-phase flow, Large size particles, Pneumatic conveying, Pressure loss
URL: http://mc.manuscriptcentral.com/tcie Email: [email protected]
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Trajectory and Distribution of Particles Conveyed in Horizontal Pipe
Abstract::::In order to study the particles mechanical properties in pneumatic conveying, the pneumatic
conveying experiments and simulations of large size particles have been done. The trajectory and distribution
of particles in pipe were researched; the influence of different gas velocity, particle size, pipe diameter,
solid-gas ratio on the pressure loss was analyzed. The results indicate that the large size particles (>5 mm)
mainly subsiding at the bottom of the horizontal pipe are symmetrical about the longitudinal section of the
horizontal pipe. The gas flow is unstable when the gas velocity is close to the particle suspension velocity.
The pressure loss reduces with the increase of the particle size while the gas velocity is more than 30m/s. In
simulations, the pressure loss increases with the gas velocity and solid-gas ratio and decreases with the pipe
diameter; in experiments, the pressure loss decreases firstly then increases with the gas velocity, which means
that there is an optimum gas velocity when the pressure loss is minimum.
Key words:::: Gas-solid two-phase flow; Large size particles; Pneumatic conveying; Pressure loss
Subject Index No. : ME1 & ME10
Introductions
For a long time, research on the fluid flow containing particles has become an important scientific
engineering. The gas-solid two-phase flow is a common phenomenon, and pneumatic conveying focusing on
gas-solid two-phase flow plays an important role in bulk material conveying system. Pneumatic conveying is
widely used in energy, chemical industry, metallurgy, food processing and other fields. Piping system is
usually taken in pneumatic conveying process, and the gas-solid two-phase flow has complex motion
distribution. Due to the interface effects and relative speed between the gas and solid, the randomness of the
phase interface, two-phase flow system is more complex than single-phase flow system. In recent years,
scholars did lots of studies on gas-solid two-phase flow. HUBER [1] summarized the Euler/Lagrange method
of pipeline gas-solid two-phase flow and simulated two-phase flow of horizontal pipe, bend pipe and vertical
pipe under different pipe diameters and flowing conditions. The research found that the particles would be
more decentralized with the roughness and diameter; meanwhile roughness would increase system pressure
loss and cause secondary flow. Sommerfeld [2, 3] studied the collision distribution characteristics of gas-solid
flow in horizontal pipe, indicating that wall roughness and collisions between particles have a significant
influence on particle behavior and properties of the particle phase. AKILLI [4, 5], YANG [6] and KUAN [7]
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used experiment and numerical simulation methods to study the distribution of gas-solid flow in 90° elbow.
The results showed that gas velocity and mass flow ratio of gas-solid flow will affect the distribution of
particle mass concentration, but they scarcely affect the characteristic of velocity distribution and particle
mass concentration distribution in the fully developed stage. And particle subside speed is greatly affected by
mass flow ratio of gas and solid, and diameter ratio of pipe and bend. HIDAYAT [8, 9] studied the distribution
characteristics of gas-solid flow in U-bend and the results showed that the dispersion and the slip velocity of
particles became relatively larger after through the curve of the U-bend. ZHANG [10] studied the distribution
of gas-solid flow inside the pipes and the wear causing by particle collision on the wall, and then the results
showed that the scouring erosion zone of gas-solid two-phase flow centered on about the front 1/5 part of
the pipe and its maximum erosion occurred behind the pipe entrance, the erosion quantity and shear stress
increased with increasing of the flue gas flow rate, in a certain range of particles diameter,the erosion
quantity decreased whereas the shear stress nearly kept constant with the increasing of the particle diameter,
the erosion quantity increased whereas the shear stress nearly kept constant with increasing of the particle
content. CONG [11] did experiments on pneumatic conveying of pulverized coal in a horizontal pipe, and the
results showed that changing multiple flow patterns with one or two dominant flow for each of the seven sets
of experimental conveying conditions and that a finite change in the dominant flow pattern would occur with
an increasing superficial gas velocity. YAN [12] studied the Multi-scale particle dynamics of low air velocity
in a horizontal self-excited gas-solid two-phase pipe flow, and the results showed that the particle fluctuation
velocities of a horizontal self-excited gas-solid two-phase pipe flow with soft fins near MPD (minimum
pressure drop) air velocity were measured by high-speed PIV in the acceleration and fully-developed regimes.
The research above focuses almost on the distribution characteristics, the pressure loss and the wear of the
particles whose size is less than 5mm in the pipe, but the studies on transmission characteristics for the
particles whose size is larger than 5mm are not thorough enough. In order to expand the application range of
pneumatic conveying, such as for roadway and subsidence area filling, then the study on transmission
characteristics for large size particles is necessarily needed.
Based on the analysis above, this paper put forward a numerical simulation which studies on the
mechanical characteristics of large size particles in pneumatic conveying of horizontal pipe. The experiments
on the influence factors (particle properties, operating conditions and gas velocity) of pressure loss provide
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the foundation for further experimental and theoretical studies.
1 Numerical approach
The particle movement is determined by the interaction between particles and gas flow. The
particle-trajectory model was built for obtaining the trajectories of particles.
1.1 Governing equations of gas phase
In the particle-trajectory mode, the gas phase is regarded as the continuous medium while the solid
phase is discrete. The equations of continuity, momentum and energy were acquired based on the laws of
conservation of mass, conservation of energy and Newton's second law.
Equations of continuity:
( )j
j
v St x
ρρ
∂ ∂+ =
∂ ∂ (1)
where ρ is the density of gas phase, xj is the j direction of coordinate, vj is the velocity component of gas phase
on the j direction, S is the volume fraction of solid phase in gas-solid mixture.
Equation of momentum:
( ) ( ) [ ( )] ( ) /j i
i j i i i p pi i r
j i j i j
v vpv v v g v S v v
t x x x x xρ ρ ρ µ ρ τ
∂ ∂∂ ∂ ∂ ∂+ = − + ∆ + + + + −
∂ ∂ ∂ ∂ ∂ ∂∑
(2)
where µ is the gas dynamic viscosity, ρp is the density of solid phase, vpki is the velocity component of solid
phase on the j direction, τrk is particle relaxation time.
Equation of energy:
( ) ( ) ( )p j p p
j j j
Tc T v c T k c TS
t x x xρ ρ
∂ ∂ ∂ ∂+ = +
∂ ∂ ∂ ∂ (3)
where cp is the specific heat capacity of solid phase, T is the temperature of gas phase, k is the thermal
conductivity of solid phase, cpTS— is the source term of changing gas phase.
The above equations are the governing equations of gas phase which requires the k-ε turbulence model
to be solved[2]
. In the k-ε turbulence model, the turbulence kinetic energy and its rate of dissipation are
obtained from the following equations:
tk b M k( ) ( )i
i j k j
kku G G Y S
x x x
µρ µ ρε
σ
∂ ∂ ∂= + + + − − +
∂ ∂ ∂ (4)
and
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2
t1 k 3 b 2( ) [( ) ] ( )i
i j j
u C G C G C Sx x x k k
ε ε ε εε
µ ε ε ερε µ ρ
σ∂ ∂ ∂
= + + + − +∂ ∂ ∂
(5)
The parameters in the Eq.(3) and Eq.(4) are obtained from the Yakhot and Orszag[13]
.
1.2 Motion equations of gas phase
1.2.1 Particle motion equations
The particle motion equation obtained from the Newton's second law is shown as follows:
d
d
p
p g d S
vm f f f
t= + + (6)
where vp is the particle velocity, mp is the particle mass, fg is the gravitational force of particle, fd is the drag
force of particle which is given by
3( )
4
p
d D p p
p p
mf c v v v v
d
ρ
ρ= − − (7)
and fs is the Saffman lift force of particle which is
1 2
1/4
2( )
( )
ij
S p
p p lk kl
Kv df v v
d d d
ρ
ρ= − (8)
The Eq.(8) generated from the velocity gradient is obtained by Li and Ahmadi[14]
which was based on the
analytical result of Saffman[15].
1.2.2Particle trajectory equations
The force equations of particle acquired in the uniform flow field are shown as follows:
x-direction
2
2
p
p dx
d xm f
dt= (9)
y-direction
2
2
p
p dy g Sy
d ym f f f
dt= + + (10)
z-direction
2
2
p
p dz Sz
d zm f f
dt= + (11)
There is an assumption that the initial position of particles is xp0, yp0 and zp0 at the beginning. The
trajectory equations of particle on the three directions are obtained by twice integration.
x-direction 0
1ln( 1)p p x rxx x v t av t
a= + − + (12)
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y-direction
2
0 2
1 ( 1)( ) ln
2 1
ct
p p y ct
b c f f ey y v t
a c a e fa
−= + + − +
− (13)
z-direction
/
0 /
1ln
bt a
p p z bt a
n nez z v t
a ne
−= + − (14)
where a is the computing coefficient of drag force, b is the computing coefficient of Saffman lift force,
vri is the difference value between the gas and solid, f and n are the coefficients generated from the solution of
elliptic integral.
The parameters a, b, vri, f and n are given by
4
3
p p
D
da
c
ρ
ρ= (15)
1 2
1/4
2
( )
ij
p p p lk kl
Kv db
m d d d
ρ
ρ= (16)
0ri i piv v v= − (17)
2
2
2 4
2 4
ri
ri
av b b agf
av b b ag
− − ±=
− + ± (18)
ri
ri
av bn
av
−= (19)
Particles will collide with the wall in the pipe transportation and the collision recovery factor is obtained
by Forder’s recovery factor equations[16]
. The equations established by the collision test of sand and alloy
steel which include the normal recovery factor en and the tangential recovery factor er are is expressed by
impact angle θ:
2 3 40.988 0.78 0.19 0.024 0.027ne θ θ θ θ= − + − + (20)
2 3 4 51 0.78 0.84 0.21 +0.028 0.022re θ θ θ θ θ= − + − − (21)
2 Numerical model
The diameters of the pipes used in the numerical simulation were 70 mm, 100 mm and 150 mm and the
length of horizontal pipes were 4 m and 6 m. The cross-section mesh and partial mesh of the numerical
simulation model were shown in Fig.1.
The boundary conditions and parameters of injection were shown in Tab.1. The seamless steel pipes
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were used in the experiments and the wall roughness was 0.05 mm. The density of particle was 2800 kg/m3.
The particles were injected into the pipe inlet uniformly. The transmission medium was air, which was
considered as incompressible gas. The gas density was 1.225 kg/m3 and the dynamic viscosity was 1.8×10-5
kg/(m·s).
The particle trajectory model and the two-way coupling method were used in the numerical simulation,
because the volumetric rate of the particles was less than 10% in the gas flow [17]. The simulation considered
the interaction between gas and particle phase, and the interactions among particles were ignored. The
standard k-ε method was used in the turbulence model.
3 Results and Analysis
3.1 Distribution Characteristics of Gas-solid Flow
3.1.1 Particle Trajectory
In all the simulations, particles were injected into the pipe inlet uniformly with the initial velocity was
zero. In order to show the particles trajectories in horizontal pipe clearly, the pipe was scaled in the
x-direction and the scale factor was 0.2. The trajectories were displayed interval for 10, which was shown in
Fig.2. Along the y-direction due to the gravity, particles trajectories were in the downstream of pipeline and
concentrate at the bottom of pipe. Particles trajectories were influenced by the injected position greatly. The
particles which jumped greatly and moved to the upper of the pipe were mostly injected in the top of pipe.
The particles swung laterally were probably injected in the both sides of pipe.
Comparing Fig.2-(a) with Fig.2-(b), the particles jumped height and the free path in Fig.2-(a) were
bigger than that in Fig.2-(b), which showed that the small particles were easily accelerated and suspended.
Comparing Fig.2-(a) with Fig.2-(c), the particles trajectories were smooth and the particle-wall collisions
were few, the jump heights of particles were invariable with the increase of the gas velocity in Fig.2-(c). It
was because that the gas velocity was three times the particle suspension velocity and the impact of particles
on gas flow was tiny. Comparing Fig.2-(a) with Fig.2-(d), the jump of particles was obvious and the particles
could still jump to the upper pipe even after the distance of 6m.
3.1.2 Particles Distribution
The motions of particles were determined by drag force, gravity, particle-wall collision, turbulent
diffusion and other factors. The particles distribution on cross-sections in horizontal pipe was shown in Fig.3.
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The cross-sections were extracted every 0.5 m along the x-direction from 0.5 to 4 m.
The particles distribution on the cross-section of horizontal pipe was shown in Fig.3. From Fig.3-(a) to
Fig.3-(d), the particles were mainly distributed at the bottom of pipe and there was little particle on the upper
part of the pipe. The particle distribution along y-direction on pipe outlet was shown in Fig.4. Comparing
Fig.3-(a) with Fig.3-(b), the particle distribution was more symmetrical with the pipe diameter. The particles
distribution had a significant asymmetry when x=2 m, x=2.5 m and x=3 m in Fig.3-(a). It means that particles
in the pipe cross-section had a velocity component, making the particles collided with the wall, which may be
the reason that the smaller of the pipe diameter, the higher of pressure loss. Comparing Fig.3-(c) with
Fig.3-(b), the particles distributions were similar and the particles occupy the larger cross-sectional area of the
pipe in Fig.3-(c). Comparing Fig.3-(d) with Fig.3-(b), the particles concentration and the region of the red
area reduce causing by the smaller particle size. The regions with larger particle concentration near the
longitudinal plane of symmetry appear in x=1 m cross section in Fig.3-(b) and Fig.3-(c). That also appeared
in x=2 m and x=2.5 m cross section in Fig.3-(d), which was due to particle-wall collision and the gravity of
particles. The particles distribution along z-direction on pipe outlet of Fig.3-(b) is shown in Fig.5. The
distribution of particles along the z-direction at the pipe cross-section was symmetric.
3.2 Pressure Loss in Horizontal Pipe
The energy of particles movement came from the gas flow, which increased the pressure loss of gas flow.
The energy consumption of pneumatic conveying was mainly influenced by particles movement, but the
particles movement was also influenced by the operating conditions of system, the physical properties of
material and the characteristics of pipeline. This paper studied three influencing factors (particle size, pipe
diameter and solid-gas ratio) of pressure loss. According to the continuity equations and Bernoulli's equations,
the average velocity of gas flow in equal diameter pipeline was regarded as constant. That means the pressure
loss mainly came from the static pressure loss. The changes of total pressure were used to measure the
pressure loss in horizontal pipe.
3.2.1 Effect of Particle Size on Pressure Loss
The particle sizes were 5 mm, 10 mm, 15 mm, 20 mm and 25 mm, which was used in the numerical
simulation. The simulation parameters were shown in Tab.2. The pressure loss was obtained by the numerical
simulations with the different gas velocity and particle size in horizontal pipe. The conveying capacity was
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1.5 kg/s.
Fig.6 showed the relationship between pressure loss and particle size. When the gas velocity was not
more than 20 m/s, the relationship between pressure loss and particle size was indeterminate. The relation
curve presented convex shape while gas velocity was 10 m/s and it presented concave shape while gas
velocity was 20 m/s. That was because that the gas velocity was too small and it was close to the particles
suspension velocity, which made the pneumatic conveying in the unstable region. The particles suspension
velocity was shown in Tab.3. When the gas velocity was not less than 30 m/s, the total pressure loss
decreased with particle size, but the tendency was smaller and smaller. The pressure loss was no longer
changing while the particle sizes were 15 mm and 20 mm and the gas velocity was 30 m/s. It demonstrated
that the increase of particle size reduced pressure loss in the same conveying capacity and gas velocity. The
increase of particle size was limited by air velocity and pipe diameter. The particles would be stranded in
pipeline when the particle size increased to a certain value. But improving the gas velocity would increase the
pressure loss significantly. The relationship between the pressure loss and the gas velocity was shown in Fig.7.
It was clear that the pressure loss increased with the gas velocity.
3.2.2 Effect of Solid-Gas Ratio on Pressure Loss
According to Fig.2, the greater the pipe diameter was, the more uniform the movement of particles was.
The uniform movement of particles avoided the concentrated wear of pipeline. It was known from the
analysis of pressure loss and particle size that increasing the particle size could reduce the pressure loss. It
could further improve the system efficiency by increasing the conveying capacity and the particle size at the
same time. The solid-gas ratio was used to measure the conveying capacity. The process of pneumatic
conveying was simulated with three kinds of pipeline diameter and solid-gas ratio, and the simulation
parameters were shown in Tab.4.
The relationship between the pressure loss and the pipe diameter was shown in Fig.8. The pressure loss
reduced with the pipe diameter. The increase of pipe diameter meant the increase of conveying capacity. The
relationship between the pressure loss and the solid-gas ratio was shown in Fig.9. The pressure loss increased
with the solid-gas ratio. Increasing the solid-gas ratio could increase conveying capacity without any increase
of gas consumption, which could give full play to the ability of the equipment.
4 Pneumatic Conveying Experiments of Particles
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4.1 Experimental System and Method of Pneumatic Conveying
The experimental system of pneumatic conveying was shown in Fig.10. The experimental system
included gas source, injector, rotary feeder, conveying pipeline and test system. The feeding of particles was
controlled by the frequency converter. The conveying pipelines were contained by series of seamless steel
pipes, the length of conveying pipelines was 14 m and the diameter was 70 mm. The rapid joint flange was
used to connect the pipeline. The test system included pressure transducers, signal amplifier, data acquisition
instrument and computer.
The dynamic pressure in pipeline was measured by pitot tube. The gas velocity was controlled by valve
in the pneumatic conveying. The gas velocity was non-uniform in pipeline. The four measuring points were
taken in the cross-section according to the measuring method of circular pipe flow. The measuring points
were shown in Fig.11. The dynamic pressure of each measuring point was measured and the gas velocity was
obtained by formula (1), and then the average velocity of gas in the pipeline could be obtained.
2 ( ) 2 (1 )i g i g
i
gh pv
γ γ ρ ρ
γ ρ
− ∆ −= =
(1)
Where the hi was the height differential of operating fluid in U-tube of measuring point i, γ and γg was
the specific gravity of gas and operating fluid respectively, △pi was the pressure differential of operating fluid
in U-tube of measuring point i.
The large size particles were used in the experiments. The bulk density was 1024 kg/m3 when particle
size was 10mm. According to the revolving speed of rotary feeder, the relationship between the supply
frequency and the feeding mass was shown in Tab.5.
Two pressure transducers were decorated along the conveying pipeline to measure the signals of static
pressure. The pressure loss was obtained by disposing the two signals of static pressure. The gas velocity was
set by pitot tube and valve, the feeding mass was controlled by the frequency converter in the experiments.
The pressure loss of each feeding mass was measured at each gas velocity.
4.2 Experimental Results and Analysis
The movement of particles in horizontal pipe was divided into uniform motion and accelerated motion.
For long distance pneumatic conveying, the pressure loss of accelerated motion section accounted for only a
small proportion in the whole conveying process. The pressure loss mainly was in uniform motion section
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and the pressure of uniform motion section was measured in the experiments. The distance between first
pressure transducer (PT01) and the outlet of injector was 7m, the distance between second pressure
transducer (PT02) and first pressure transducer (PT01) was 4m. The pressure loss between PT01 and PT02
was obtained by comparing with the two pressure signals of pressure transducers. The two pressure signals of
pressure transducers were shown in Fig.12. The particle size was 10mm, the gas velocity was 44.9m/s and the
feeding mass was 2.45kg/s. The pressure signal of PT01 was shown in Fig.12-(a) and PT02 was shown in
Fig.12-(b). It could be seen from Fig.12-(a), the pressure increased gradually from 0 to 5s, and then it was
stable relatively from 5s to 30s, which indicated that the gas flow was fully developed and the steady flow
had been formed. The pressure increased rapidly and kept the high value from 30s to 45s, which due to
materials joined in pipeline hinders the gas flow and the pressure increased at the back of the particles. It was
called as the particle conveying stage. The pressure fluctuated largely at the beginning and end of this stage.
From 45s, the amount of particles reduced and the pressure began to decline until similar with initial pressure.
In Fig.12-(b), there was the same pressure distribution with Fig.12-(a) and the correlation coefficient was 0.95,
while the pressure value was smaller comparing with PT01.
Under the conditions of different revolving speed of rotary feeder, the relationship between the pressure
loss and the gas velocity in horizontal pipe was shown in Fig.13. The curves included numerical and
experimental results and their fitting value.
It could be seen from Fig.13, the pressure loss decreased firstly and then increased with the increase of
the gas velocity under the certain feeding of particles. It indicated that there was a gas velocity made the
pressure loss was the minimum, which was called as the optimum gas velocity. The optimum gas velocity
was 31.6m/s and 33m/s when the feeding of particles was 0.98kg/s and 1.5kg/s. The optimum gas velocity
was used as the symbol of particle conveying mode. The particle conveying changed from dilute-phase
pneumatic conveying to dense-phase pneumatic conveying with the reducing of gas velocity. When the gas
velocity was greater or close to the optimum gas velocity, the experimental results are consistent with the
numerical results that the pressure loss increases with the gas velocity. It demonstrated that the numerical
method was reliable when the gas velocity was greater than the optimum gas velocity in dilute-phase
pneumatic conveying.
5 Conclusions
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(1) The particle trajectory equations on the three directions obtained by twice integration from the
Newton's second law were utilized to calculate the positions of particles in the uniform flow field. The large
size particles subsided in the pneumatic conveying are mainly symmetrical about the longitudinal
cross-section at the bottom of the pipeline. At the same gas velocity, particle size and solid-gas ratio, the
particle distribution is more symmetrical when the diameter of pipeline is greater.
(2) In the same diameter of pipeline, conveying capacity and gas velocity, the moderate increase of
particle size will reduce the pressure loss. In the numerical simulation, the relationship between the pressure
loss and the gas velocity are clear, namely, the pressure loss increases significantly with the gas velocity. The
pressure loss decreases with the diameter of pipeline, while the pressure loss increases with the solid-gas ratio
at the same diameter of pipeline, particle size and gas velocity.
(3) According to the experimental results, the pressure loss decreases firstly and then increases with the
increase of the gas velocity under the certain feeding of particles, which indicates there is an optimum gas
velocity when the pressure loss is the minimum.
References
[1] Huber, N., and M. Sommerfeld. 1998. “Modeling and Numerical Calculation of Dilute-phase Pneumatic
Conveying in Pipe Systems.” Powder Technology 99(1): 90-101. doi: 10.1016/S0032-5910(98)00065-5.
[2] Sommerfeld, M. 2003. “Analysis of collision effects for Turbulent Gas-particle Flow in a Horizontal
Channel (Part I): Particle Transport.” International Journal of Multiphase Flow 29(4):675-699. doi:
10.1016/S0301-9322(03)00031-4.
[3] Sommerfeld, M., and J. Kussin. 2003. “Analysis of Collision Effects for Turbulent Gas-Particle Flow in a
Horizontal Channel (Part II): Integral Properties and Validation.” International Journal of Multiphase
Flow 29(4):701-718. doi: 10.1016/S0301-9322(03)00033-8.
[4] Akilli, H., E. K. Levy, and B. Sahin. 2001. “Gas-solid Flow Behavior in a Horizontal Pipe after a 90°
Vertical-to-horizontal Elbow.” Powder Technology 116(1):43-52. doi: 10.1016/S0032-5910(00)00360-0.
[5] Akilli, H., E. K. Levy, and B. Sahin. 2005. “Investigation of Gas-Solid Flow Structure after a 90°
Vertical-to-horizontal Elbow for Low Conveying Gas Velocities.” Advanced Powder Technology
16(3):261-274. doi: 10.1163/1568552053750233.
[6] Yang, W., and B. Kuan. 2006. “Experimental Investigation of Dilute Turbulent Particulate Flow Inside a
Page 11 of 30
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Curved 90° Bends.” Chemical Engineering Science 61(11):3593-3601. doi: 10.1016/j.ces.2006.01.013.
[7] Kuan, B., W. Yang, and M. P. Schwarz. 2007. “Dilute Gas-solid Two-phase Flows in a Curved 90° Duct
Bend: CFD Simulation with Experimental Validation.” Chemical Engineering Science 62(7):2068-2088.
doi: 10.1016/j.ces.2006.12.054.
[8] Hidayat, M., and A. Rasmuson. 2007. “Heat and mass transfer in U-Bend of a pneumatic conveying
dryer.” Chemical Engineering .Research and Design 85(3): 307-319. doi: 10.1205/cherd06162.
[9] Hidayat, M., and A. Rasmuson. 2007. “A Computational Investigation of Non-isothermal Gas-solid Flow
in a U-bend.” Powder Technology 175(2):104-114. doi: 10.1016/j.powtec.2007.01.024.
[10] Zhang, Y., W. Zhou, Z. Q. Sun, and J. M. Zhou. 2011. “Numerical Simulation of Scouring Erosion
Characteristics for Gas-solid Two-phase Flow in Pipes.” Metal Materials and Metallurgy Engineering
39(1):11-15.doi:10.3969/j.issn.1005-6084.2011.01.003.
[11] Cong, X. L., X. L. Guo, X. Gong, H. F. Lu, and W. B. Dong. 2011. “Experimental Research of Flow
Patterns and Pressure Signals in Horizontal Dense Phase Pneumatic Conveying of Pulverized Coal.”
Powder Technology, 208(3):600-609. doi: 10.1016/j.powtec.2010.12.027.
[12] Yan, Z., and R. Akira. 2013. “Multi-scale Particle Dynamics of Low Air Velocity in a Horizontal
Self-excited Gas-solid Two-phase Pipe Flow.” International Journal of Multiphase Flow 53
(2013):114-123. doi: 10.1016/j.ijmultiphaseflow.2013.02. 005.
[13] Yakhot, V., and S. A. Orszag. 1986. “Renormalization Group Analysis of Turbulence. I. Basic Theory.”
Journal of Scientific Computing 1(1):3-51. doi: 10.1007/BF01061452.
[14] Li, A., and R. S. Tankin. 1992. “Dispersion and Deposition of Spherical Particles from Point Sources in a
Turbulent Channel Flow.” Aerosol Science and Technology 16(4):209-206. doi:
10.1080/02786829208959550.
[15] Saffman, P. G. 1965. “The Lift on a Small Sphere in a Slow Shear Flow.” Fluid Mech 22(2):385-400. doi:
10.1017/S0022112065000824.
[16] Dritselis, C., and N. Vlachos. 2011. “Large Eddy Simulation of Gas-particle Turbulent Channel Flow
with Momentum Exchange between the Phases.” International Journal of Multiphase Flow
37(7):706-721. doi: 10.1016/j.ijmultiphaseflow.2011.01.012.
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Tab.1 Boundary Conditions and Particle Parameters
Boundary Boundary
Type Parameter Setting
Particle
Parameters Value
Inlet of Horizontal
Pipe Velocity Inlet 10-60 m/s Density (ρp)
2800
kg/m3
Outlet of Horizontal
Pipe
Pressure
Outlet 1 atm Diameter (dp) 5-25 mm
Wall Non-Slipping Roughness=0.05
mm Velocity (vp) 0 m/s
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Tab.2 Simulation Parameters
Parameters Value
Mass Flow Rate
Pipe Diameter
Roughness
Particle Density
0.5 kg/s
70 mm
0.05 mm
2800 kg/m3
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Tab.3 Particle Suspension Velocity
Particle Size (mm) Suspension Velocity (m/s)
5
10
15
20
25
13.17
20
23
26.55
29.68
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Tab.4 Simulation Parameters
Parameters Value
Solid-Gas Ratio
Pipe Diameter
Particle Size
Gas Velocity
Roughness
10/15/20
70/100/150 mm
15 mm
60 m/s
0.05 mm
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Tab.5 Relationship between Supply Frequency and Feeding Mass
Supply Frequency (Hz) Feeding Mass (kg/s)
50
40
30
20
2.45
1.96
1.47
0.98
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Figure 1 Calculation Model
29x13mm (300 x 300 DPI)
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Figure 2 Particle Trajectory in Horizontal Pipe
29x25mm (300 x 300 DPI)
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Figure 3 Particle Distribution on Cross-section of Horizontal Pipe 29x25mm (600 x 600 DPI)
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Figure 4 Particle Distribution along Y-Axis on Pipe Outlet of Figure 3-(c) 29x19mm (300 x 300 DPI)
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Figure 5 Particle Distribution along Z-Axis on Pipe Outlet of Figure 3-(b) 29x19mm (300 x 300 DPI)
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Figure 6 Relationship between Pressure Loss and Particle Size
29x20mm (300 x 300 DPI)
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Figure 7 Relationship between Pressure Loss and Gas Velocity
29x22mm (300 x 300 DPI)
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Figure 8 Relationship between Pressure Loss and Pipe Diameter
29x23mm (300 x 300 DPI)
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Figure 9 Relationship between Pressure Loss and Solid-gas Ratio
29x25mm (300 x 300 DPI)
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Figure 10 Pneumatic Conveying Experimental System
29x11mm (300 x 300 DPI)
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Figure 11 Measuring Locations
29x27mm (300 x 300 DPI)
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Figure 12 Pressure Signal
59x25mm (300 x 300 DPI)
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Figure 13 Relationship between Pressure Loss and Gas Velocity in Horizontal Pipe
29x23mm (300 x 300 DPI)
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