#
Numerical Simulation of Swirl Flow Characteristics of CO_{2} Hydrate Slurry by Short Twisted Band

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## Abstract

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_{2}hydrate slurry in low concentration has been simulated by the RSM and DPM models. The results show that the heat transfer efficiency is also related to Re and particle concentration. The velocity distribution has the form of symmetrical double peaks, and the peaks finally merge at the center of the pipeline. Vortexes firstly appear on both sides of the edge of the twisted band, and then move to the middle part of the twisted band. Finally, the vortex center almost coincides with the velocity center. The rotation direction of hydrate particles is the same as the twisted direction of the twisted band, twist rate (Y) is smaller, Re is larger, and the symmetric vortex lines merge farther away. The initial swirl number is mainly related to Y, but not Re. The swirl flow attenuates exponentially, and its attenuation rate is mainly related to Re, but not Y. Compared with ordinary pipelines, the swirl flow can obviously improve the transportation distance of hydrate slurry.

## 1. Introduction

_{2}hydrates in the spiral flow pipeline in a short twisted band. The deposition and heat transfer characteristics of CO

_{2}hydrate particles in the spiral flow pipeline have been studied. The velocity distribution, turbulence intensity, temperature distribution, vortex line distribution, attenuation law of swirl number, and deposition law of hydrate particles have been investigated using the computational fluid dynamics (CFD) technology.

## 2. Numerical Simulation Method

#### 2.1. Physical Model

#### 2.1.1. Geometric Model

_{1}is 400 mm. L

_{2}is 2100 mm. The cartesian coordinate system is adopted for calculations. The origin of coordinates is located at the center of the inlet surface of the pipeline. The Y-axis is the flow direction and flows from the left end of the pipeline to the right end.

#### 2.1.2. Boundary Conditions

_{2}hydrate particles is 1116 kg/m

^{3}, the particle size is 0.001 mm, and particle volume concentration is 1%~8%. The medium is water with a density of 1000 kg/m

^{3}. The inlet boundary is the velocity inlet to flow horizontally along the pipeline. Export border is the outflow. The temperature of the hydrate is higher than the pipeline wall because of the heat release during the formation process. The inlet hydrate temperature is 280 K, and the wall and liquid temperature is 277 K. The pressure reference point is at the outlet center of the pipeline with a reference pressure of 0 Pa. The turbulence intensity is that the liquid phase flow velocity is substituted into the turbulence calculation formula, and the twisted band is fixed at the entrance of the pipeline, so the solid wall non-slip boundary is adopted. The effect of gravity on deposition is considered. It is assumed that hydrate particles are uniformly distributed at the pipeline entrance. The data parameters are shown in Table 1.

#### 2.2. Meshing

#### 2.3. Mathematical Model

#### 2.3.1. Governing Equations

_{p}, $T$, and λ are liquid density, specific heat at constant pressure, temperature, thermal conductivity, respectively, and $u$, v, and $w$ are speed.

#### 2.3.2. Discrete Phase Model

#### 2.4. Calculation Method

^{−4}s. The turbulence model is the RSM model, and the DPM model is a two-phase flow model. The simulation is carried out at low pressure and flow velocity, so an implicit solver based on pressure is used. The finite volume method is used to discretize the equation. The SIMPLEC algorithm is used for pressure–velocity coupling. The convergence condition is that residual value <10

^{−6}. In addition, in order to improve the accuracy, the pressure equation, momentum equation, turbulent kinetic energy equation, and turbulent diffusivity equation are presented with the second-order upwind scheme.

#### 2.5. Grid Independence Test

#### 2.6. Experimental Verification

## 3. Results and Discussion

#### 3.1. Velocity Distribution

#### 3.2. Turbulence Intensity

#### 3.3. Temperature Distribution

^{2}·k)); and $\lambda $ is thermal conductivity (w/(m·k)).

#### 3.4. Vortex Line Distribution

#### 3.5. Attenuation Law of Wall Shear Stress

#### 3.6. Attenuation Law of Swirl Number

#### 3.7. Deposition Law of Hydrate Particles

## 4. Conclusions

- The swirl flow velocity presents a symmetrical bimodal structure. The two velocity centers gradually move closer to the center of the pipeline and finally merge together with the attenuation of the swirl flow. The axial velocity is an “M” shape in the twisted segment, the peak value is 1/2r away from the pipeline wall, and the axial velocity is a parabolic shape in the rear pipeline segment. The absolute value of radial velocity is relatively small, which is the result of the redistribution of velocity by twisted band and it rapidly drops to 0 m/s in the posterior segment. The tangential velocity is the “M” shape in the twisted band section and the back pipe section. The peak value appears 1/6~1/7r away from the pipe wall.
- Swirl flow can improve the heat transfer efficiency between the pipeline wall and the fluid, which is mainly related to Reynolds number, twist rate, and particle concentration. In the twisted band section, the Nu increases firstly, and it is removed after the twisted band. The Nu decreases and the slowing rate decreases continuously. The increase in Re has a more obvious induction effect on the motion of solid particles, thus Nu increases. With the increase in the volume fraction of particles, the increase rate of Nu number on the wall slows down. The twist rate is smaller, the Nu is larger, and the heat efficiency is higher.
- The turbulence intensity distribution in the twisted band section shows a “W” shape at the center of the rigid main vortex. The vortex in the free vortex area near the twisted band has a small scale and large unstable velocity pulsation, so the turbulence intensity is large. In the merging process of two symmetric vortexes outside the twisted band, the pulsation velocity at the central vortexes is increased, and the turbulence intensity distribution curve shows a “U” shape.
- The swirl direction of hydrate particles is the same as that of the twisted band. The vortex line swirl center begins to appear at both ends of the proximal twisted band, then it moves to the center of the proximal twisted band, and it finally moves to the edge of the pipeline to achieve stability. After leaving the twisted band, the vortex attenuates rapidly. The twist rate Y is smaller, the Re is larger, and the vortex attenuates more slowly. The attenuation rate of vorticity is mainly affected by Re, while the twist rate mainly affects the initial vorticity size. The shear stress is the main reason for the decrease in swirl strength, and the shear stress decreases exponentially in the pipe section with strong swirl flow. The twist rate mainly affects the initial swirl number, but it has little influence on the attenuation rate of swirl flow. The twist rate is smaller, the initial swirl number is larger. The attenuation of swirl flow is mainly related to Re, and the Re is larger, and it is slower. The swirl flow decreases exponentially, and the relation expression between swirl flow attenuation exponent and Re is obtained.
- The hydrate particles are distributed near the pipe wall under the action of centrifugal force generated by the swirl flow. The hydrate particles do not enter the forced vortex region. Due to the effect of shear force, the carrying distance of particles is increased. However, the swirl flow rapidly attenuates with the increase in carrying distance, the swirl radius of the particles decreases, and deposition occurs at the end of the pipe. The twist rate is larger, the swirl flow intensity is smaller, the attenuation is faster, and the particles are more likely to accumulate. In addition, the Re is larger, the cross-section particle distribution is more uniform, and the particle concentration is smaller.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Velocity distribution at each position on the center line of different sections. Re = 6000, Y = 6.2.

Particle Concentration (%) | Particle Size (mm) | Twist rate Y | Initial Velocity (m/s) |
---|---|---|---|

1~8 | 0.001 | 6.2/7.4/8.8 | 0.5~12 |

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**MDPI and ACS Style**

Rao, Y.; Liu, Z.; Wang, S.; Li, L.; Sun, Q.
Numerical Simulation of Swirl Flow Characteristics of CO_{2} Hydrate Slurry by Short Twisted Band. *Entropy* **2021**, *23*, 913.
https://doi.org/10.3390/e23070913

**AMA Style**

Rao Y, Liu Z, Wang S, Li L, Sun Q.
Numerical Simulation of Swirl Flow Characteristics of CO_{2} Hydrate Slurry by Short Twisted Band. *Entropy*. 2021; 23(7):913.
https://doi.org/10.3390/e23070913

**Chicago/Turabian Style**

Rao, Yongchao, Zehui Liu, Shuli Wang, Lijun Li, and Qi Sun.
2021. "Numerical Simulation of Swirl Flow Characteristics of CO_{2} Hydrate Slurry by Short Twisted Band" *Entropy* 23, no. 7: 913.
https://doi.org/10.3390/e23070913