**3. Experimental results**

#### **3.1 Gas velocity along the pipe**

The gas velocity along the pipe is an important parameter, and it can be expressed by the following equation.

$$
\mu\_{\mathcal{g}} = \frac{M\_{\mathcal{g}}}{A\varepsilon\rho\_{\mathcal{g}}} = \frac{M\_{\mathcal{g}}}{A\varepsilon} \frac{RT}{p} \tag{1}
$$

Numerical Simulation of Dense Phase Pneumatic Conveying in Long-Distance Pipe 377

Fig. 3. Variable curve of static pressures with the feed pressure 0.32Mpa.

increasing of gas velocity.

0

Fig. 4. Experimental values of solid velocity along pipeline.

4

Solid velocity(m/s

8

12

Fig. 4 shows the trend of solid velocity along the pipeline under different feeder pressure. solid velocity increased gradually with the increase of feed pressure. And under the same feed pressure, solid velocity increases gradually along pipeline, which is caused by the

> 0 30 60 90 120 150 180 210 Distance along pipe(m)

0.28MPa 0.32MPa 0.36MPa 0.40MPa

Where, Mg is the gas mass flow ratio. A is the cross section of pipeline. *T* stands for Kelvin temperature. P is static pressure in the pipe. is porosity, and it can be achieved by the following equation.

$$
\varepsilon = \frac{\rho\_s}{k\rho\_\mathcal{g} + \rho\_s} \tag{2}
$$

In this equation, *<sup>s</sup>* is solid density. *<sup>g</sup>* is gas density. k is solids loading ratio, the ratio of solids mass versus gas mass in total.

Fig. 2 shows the trend of gas velocity along the pipeline under different feeder pressure. Gas velocity increases gradually with the increase of feed pressure. While under the same feed pressure, gas velocity increases gradually along pipeline, which is caused by gas volume expansion.

Fig. 2. Experimental values of gas velocity along pipeline.

#### **3.2 Solid velocity along the pipe**

In this paper, the solid velocity along the pipe can be given by the following equations.

$$
\mu\_{ij} = \frac{L\_{ij}}{t\_{ij}} \tag{3}
$$

Where Lij means the distance between the transmitter of NO. i and NO. j. and tij stands for the time interval of the pressure signal appearance between NO. i and NO. j transmitters. The relationship between pressure drop and transport distance along pipeline in different feed pressure was obtained based on the measured data from the four differential pressure transmitters in the experiment process, as shown in Fig. 3.

Where, Mg is the gas mass flow ratio. A is the cross section of pipeline. *T* stands for Kelvin

*s <sup>g</sup> <sup>s</sup> k* 

0 30 60 90 120 150 180 210 Distance along pipe(m)

In this paper, the solid velocity along the pipe can be given by the following equations.

*ij*

*u*

*ij*

*<sup>t</sup>* (3)

*ij L*

Where Lij means the distance between the transmitter of NO. i and NO. j. and tij stands for the time interval of the pressure signal appearance between NO. i and NO. j transmitters. The relationship between pressure drop and transport distance along pipeline in different feed pressure was obtained based on the measured data from the four differential pressure

Fig. 2 shows the trend of gas velocity along the pipeline under different feeder pressure. Gas velocity increases gradually with the increase of feed pressure. While under the same feed pressure, gas velocity increases gradually along pipeline, which is caused by gas volume

> 0.28MPa 0.32MPa 0.36MPa 0.40MPa

is porosity, and it can be achieved by the

(2)

*<sup>g</sup>* is gas density. k is solids loading ratio, the ratio of

temperature. P is static pressure in the pipe.

0

Fig. 2. Experimental values of gas velocity along pipeline.

transmitters in the experiment process, as shown in Fig. 3.

5

10

Gas velocity(m/s)

**3.2 Solid velocity along the pipe** 

15

20

25

*<sup>s</sup>* is solid density.

solids mass versus gas mass in total.

following equation.

In this equation,

expansion.

Fig. 3. Variable curve of static pressures with the feed pressure 0.32Mpa.

Fig. 4 shows the trend of solid velocity along the pipeline under different feeder pressure. solid velocity increased gradually with the increase of feed pressure. And under the same feed pressure, solid velocity increases gradually along pipeline, which is caused by the increasing of gas velocity.

Fig. 4. Experimental values of solid velocity along pipeline.

Numerical Simulation of Dense Phase Pneumatic Conveying in Long-Distance Pipe 379

<sup>0</sup> *s s sj s s*

*g g gi g g gi gj ij cd*

*s s si s s si sj <sup>s</sup> sij cd*

 *g s* ; *<sup>g</sup>* , 

density respectively ; *ugi* , *ugj* , *usi* , *usj* are instantaneous velocity component of gas, solid in *i* , *j* direction. *<sup>g</sup> p* 、 *<sup>s</sup> p* are pressure of gas, solid; *<sup>i</sup> g* is component of gravitation in *i* direction; *cd Fi* is interaction between gas and solid, which includes the inter-phase resistance, false mass force, and pressure gradient force. In horizontal pipe, drag force is the dominant

> *cd F uu <sup>i</sup>*

2.65 0.75 *g s D s g g p*

*d*

0.44

24 Re

*p*

CD is single particle drag force coefficient, the calculation equations are given as following.

*D*

*C*

 

*C*

 

*C*

*D*

Here, <sup>24</sup> 0.68 1 0.15Re Re *D p p*

 

*C*

  *u u*

*<sup>u</sup> u u <sup>p</sup> <sup>g</sup> <sup>F</sup> tx x x*

*u uu <sup>p</sup> <sup>g</sup> <sup>F</sup> tx xx*

 

*t x*

 

 

 

*<sup>s</sup>* are gas, solid volume rate, 1

is drag force coefficient between the two phase.

Re 1000 1000 Re 1

*p*

Re 1

*p*

Re*p* is defined as particle Reynolds number,

*p*

As *αg*≥0.8, according to experiment results, the expression of

Gas momentum equation:

Solid momentum equation:

Where,

Where

 *<sup>g</sup>* , 

factor. So here

  *j*

*u*

*jij*

*ji j*

 

 

(6)

(5)

*gi pi* (8)

can be given as below.

(10)

(9)

0.68

*C* (11)

<sup>24</sup> (1 0.15Re ) Re

*D p p*

*<sup>s</sup>* are gas density and solid

*g gg i i*

*s ssi i*

(7)
