**4.4.1 Pressure distribution along the pipe**

Fig.6 gives the static pressure distribution along the pipe. From this figure, it can be seen that the static pressure and differential pressure gradient decreases along the pipe. That is to say, the differential pressure reduces with the decreasing of static pressure. It is because, with the gas solid flow moving in pipeline, more static pressure transit to dynamic power to impel and accelerate particles. This conclusion agrees with experimental results well.

Fig. 6. Distribution diagram of static pressure.


Fig. 7. Distribution diagram of dynamic pressure.

388 Computational Simulations and Applications

Because of the existence of inter phase coupled and nonlinear, the governing equations of gas solid two phase flow became more complex. So sometimes, low relaxation interation

0.5 0.4 0.4 0.3 0.3 0.2

On the basis of simulation analysis above, high concentration gas solid flow in horizontal pipe sufficient development was simulated. Flow information such as pressure, solid

Fig.6 gives the static pressure distribution along the pipe. From this figure, it can be seen that the static pressure and differential pressure gradient decreases along the pipe. That is to say, the differential pressure reduces with the decreasing of static pressure. It is because, with the gas solid flow moving in pipeline, more static pressure transit to dynamic power to

impel and accelerate particles. This conclusion agrees with experimental results well.

Gas velocity, ug

Solid velocity us Granule volume ratio,α<sup>s</sup>

may be adopted to ensure the stable constriction during the simulation process.

Turbulent dissipation rate, ε

The relaxation factors of this study can be given as the following table.

Turbulent kinetic energy k

**4.3.4 Relaxation factor** 

Table 3. Relaxation factor.

**4.4 Simulation result and analysis** 

**4.4.1 Pressure distribution along the pipe** 

Fig. 6. Distribution diagram of static pressure.

concentration, gas and granule velocity can be achieved.

Pressure, p

Fig.7 shows dynamic pressure distribution along the pipe. From the diagram, we can know that the dynamic pressure decreased gradually in the upper of the pipe, while at the bottom of pipe the dynamic pressure increased on the contrary. The reason for the phenomenon is the increasing of particle concentration at the bottom of pipe.

### **4.4.2 Solid concentration distribution along the pipe**

Solid concentration can reflect the solid motion style directly in process of pneumatic conveying. But in the experiment research, it's hard to measure this parameter accurately. In this study, we use numerical simulation method to gain the solid concentration in pipeline, as shown in Fig.8.

Fig. 8. Graph of concentration distribution.

Numerical Simulation of Dense Phase Pneumatic Conveying in Long-Distance Pipe 391

In all, the gas velocity distribution is more unstable, and the value is much higher near pipe center, while lower near the pipe boundary, which is chiefly because no slip of gas phase. Fig.9 and 10 show gas and particle velocity vector along pipe respectively. As can be seen from the diagrams, gas and particle velocity increased gradually along pipe, as expected, near the pipeline wall velocity is less, and the velocity upper part is larger than the velocity of the bottom. The particle velocity at the inlet is 4.3 m/s, and which at the outlet is 4.6 m/s. The gas velocity of inlet is set as 9.9 m/s, while the velocity at the outlet is 10.3 m/s. then all

Fig.11 gives the contrast of experiment data and simulation result for gas velocity in the selected pipe section under a set conveying pressure. From the figure, the trend of the two

> 127.7 127.9 128.1 128.3 128.5 128.7 Distance along pipe(m)

127.7 127.9 128.1 128.3 128.5 128.7 Distance along pipe(m)

Fig. 11. Relationship of gas velocity between simulated and experimental value.

Fig. 12. Relationship of solid velocity between simulated and experimental value.

Experiment data Simuation data

Experiment data Simuation data

this is approximately consistent

**4.5.1 Comparison of gas velocity** 

results is similar. And its relative error is less.

9.8

4.25 4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.65

Solid velocity(m/s)

10

10.2

Gas velocity(m/s)

10.4

**4.5 Comparison of experimental data and simulation result** 

Fig.9 shows that the particle is accelerated by gas phase along the axial direction, so the concentration becomes lower. But at the same time, the turbulent kinetic energy of two phase flow increases at the tube center, which lead to more pressure difference.

The particles near pipe center diffuse to upper or bottom of pipeline under high pressure gradient. Meanwhile, with the action of gravity force, the solid particles continue moving to the bottom of pipe, which result in the concentration increasing of pipe bottom.

As in all, particle concentration decreased in the upper of the pipe, while at the bottom of the pipe the particle concentration was growing. This illuminated that particles were not homogeneous suspension in conveying process, but the settlement of particles, so particle concentration at the bottom of the pipe was greater than that of the upper part.

#### **4.4.3 Velocity distribution along the pipe**

In the pneumatic conveying of horizontal pipe, the original pure gas flow style doesn't exist any more. The largest gas velocity value position will deviate from the pipe centre and rise to upper parts of the pipe. By contraries, the gas velocity reduces under the pipe centre.

Fig. 9. Vector graph of gas velocity.

Fig. 10. Vector graph of particle velocity.

Fig.9 shows that the particle is accelerated by gas phase along the axial direction, so the concentration becomes lower. But at the same time, the turbulent kinetic energy of two

The particles near pipe center diffuse to upper or bottom of pipeline under high pressure gradient. Meanwhile, with the action of gravity force, the solid particles continue moving to

As in all, particle concentration decreased in the upper of the pipe, while at the bottom of the pipe the particle concentration was growing. This illuminated that particles were not homogeneous suspension in conveying process, but the settlement of particles, so particle

In the pneumatic conveying of horizontal pipe, the original pure gas flow style doesn't exist any more. The largest gas velocity value position will deviate from the pipe centre and rise to upper parts of the pipe. By contraries, the gas velocity reduces under the pipe centre.

phase flow increases at the tube center, which lead to more pressure difference.

the bottom of pipe, which result in the concentration increasing of pipe bottom.

concentration at the bottom of the pipe was greater than that of the upper part.

**4.4.3 Velocity distribution along the pipe** 

Fig. 9. Vector graph of gas velocity.

Fig. 10. Vector graph of particle velocity.

In all, the gas velocity distribution is more unstable, and the value is much higher near pipe center, while lower near the pipe boundary, which is chiefly because no slip of gas phase. Fig.9 and 10 show gas and particle velocity vector along pipe respectively. As can be seen from the diagrams, gas and particle velocity increased gradually along pipe, as expected, near the pipeline wall velocity is less, and the velocity upper part is larger than the velocity of the bottom. The particle velocity at the inlet is 4.3 m/s, and which at the outlet is 4.6 m/s. The gas velocity of inlet is set as 9.9 m/s, while the velocity at the outlet is 10.3 m/s. then all this is approximately consistent

#### **4.5 Comparison of experimental data and simulation result 4.5.1 Comparison of gas velocity**

Fig.11 gives the contrast of experiment data and simulation result for gas velocity in the selected pipe section under a set conveying pressure. From the figure, the trend of the two results is similar. And its relative error is less.

Fig. 11. Relationship of gas velocity between simulated and experimental value.

Fig. 12. Relationship of solid velocity between simulated and experimental value.

Numerical Simulation of Dense Phase Pneumatic Conveying in Long-Distance Pipe 393

Fig.13 gives the contrast case of experiment data and simulation result for pressure drop. From the figure, we can gain that the experiment data point lie in the simulation average

In this work, we also set another several set of boundary conditions to simulate corresponding experiment cases in the selected pipe section. Figure 14 shows the comparison of the experimental data and simulation results. From this figure, we can know, the relative error between the experiment and simulation range from -8.48% to 4.70%, which

In this paper, dense phase pneumatic conveying is carried out. The trend of flow characteristic along the pipe is given in different cases. And based the experimental results, the k-ε-kp-εp two-fluid model was established with the consideration of gas-solid turbulent flow and taking into account the issue of gas-solid two-way coupling. Numerical simulation of fly ash flow for dense-phase pneumatic conveying was carried out by using Fluent software. The numerical simulation and experimental results were compared. The simulated

1. Along pipe axial direction, pressure and pressure gradient decreased, dynamic pressure increased gently. Meanwhile the dynamic pressure in the upper part of pipe decreased, while at the bottom of pipe dynamic pressure enlarged gradually. It can be seen that gas and particle velocity increase along the pipeline, the velocity in the upper pipe part was larger than that of the bottom of pipe. Particle concentration is different along pipe

2. The results of numerical simulation were compared with experimental results. The simulation results were validated by the experimental data, which indicate that the model and the corresponding algorithm have higher accuracy and better prediction. So it can reveal the basic characteristics of dense phase pneumatic conveying in horizontal pipe.

The authors gratefully acknowledgements the financial support from the National Natural Science Foundation of China (No. 50946032) and Shandong Provincial .Education

Examples of fluid engineering and application of computer simulation. (Han zhan-zhong,

Modeling of the Gas–Solid Turbulent Flow in a Riser Reactor. (ZHENG Yu, WAN Xiao-tao,

Numerical study on the I nfluence of various physical parameters over the gas-solid two-

Numerical simulation of the gas-particle turbulent flow in riser reactor based on k-ε-kp-εp-Θ

two-fluid model. ( Zheng Y, Wan X T, Qian Z, et al., 2001).

phase flow in the 2D riser of a circulating fluidized bed.( Luben Cabezas-Gomez,

radial direction. The solid consistency is larger at the bottom of pipe.

value dot.

**5. Conclusions** 

illustrate good agreement and accuracy.

conclusions are given as below.

**6. Acknowledgment** 

2005).

**7. References** 

Department of China (No. J10LD05)

WEI Fei, etl., 2001).

Fernando Eduardo Milioli. 2003).

#### **4.5.2 Comparison of solid velocity**

Actually, the experimental solid velocity in selected pipe section concentrates a point velocity which stands for the average velocity in this segment.

Fig 12 gives the contrast of experiment data and simulation result for solid velocity in the selected pipe section under a stationary pressure. From the figure, we can conclude that the simulation data is approximately equal to the average value of experiment value. So, numerical simulation can be used to predict the gas solid flow parameter precisely.

#### **4.5.3 Comparison of pressure drop**

Similar to the solid velocity distribution, the experimental value of pressure drop is to be regarded as the average value along the pipe.

Fig. 13. Relationship of pressure drop between simulated and experimental value.

Fig. 14. Relationship between experiment data and simulation result.

Fig.13 gives the contrast case of experiment data and simulation result for pressure drop. From the figure, we can gain that the experiment data point lie in the simulation average value dot.

In this work, we also set another several set of boundary conditions to simulate corresponding experiment cases in the selected pipe section. Figure 14 shows the comparison of the experimental data and simulation results. From this figure, we can know, the relative error between the experiment and simulation range from -8.48% to 4.70%, which illustrate good agreement and accuracy.
