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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]

Journal of the Chinese Institute of Engineers

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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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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.

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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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