Assessment of Measured Mixing Time in a Water Model of Eccentric Gas-Stirred Ladle with a Low Gas Flow Rate: Tendency of Salt Solution Tracer Dispersions
Abstract
:1. Introduction
2. Materials and Methods
2.1. Physical Model Experiment
2.1.1. Water Model Size
2.1.2. Experimental Program
2.2. Numerical Simulation
2.2.1. Model Assumptions
2.2.2. Euler–Euler Model
2.2.3. Turbulence Model
2.2.4. Tracer Transport Model
2.2.5. Boundary Conditions
- In this simulation, the walls (for example, the bottom and side walls) of the ladle were set to a wall, i.e., non-slip boundary condition.
- The ladle’s surface was treated with a phase permeability condition that lets gas bubbles escape while stopping the liquid phase from penetrating.
- The inlet of the porous plug was set to a velocity inlet, and the velocity was calculated according to the gas flow rate.
- For the tracer inlet, during the tracer injection time interval, the tracer inlet was set to a velocity inlet and the mass fraction of the tracer was set to 1. After the injection of the tracer was completed, the tracer inlet was set to the phase permeable wall condition, which is identical to the free surface. Additionally, a mass fraction of 0 was assigned to the tracer inlet.
- For the tracer concentration on all the walls and surface, the zero flux condition was utilized.
- The turbulent kinetic energy and turbulent dissipation rate of the gas phase at the gas inlet were calculated using the method proposed by Ilegbusi et al. [124].
2.3. Solution Process
3. Results
3.1. Numerical Simulation Result
3.1.1. Mesh Independence
3.1.2. Numerical Simulation Results of Tracer Transport Process
- (1)
- When the tracer is added from the center directly above the ladle, the tracer first transports on the free surface of the ladle toward the left and right sides. At around 8 s, the tracer on the left begins to transport downward. (Note that the left means the direction away from the gas inlet, the right means the direction that is opposite, and this applies in all the later sections).
- (2)
- At 15 to 20 s, the tracer on the left side of the gas column has moved to the left wall of the ladle, and the front of the tracer is located at half the height of the liquid level. At the same time, on the right side of the gas column, the tracer has just dispersed to the vicinity of the right wall.
- (3)
- At 35 to 45 s, the tracer on the left side continues to move toward the bottom of the ladle along the left wall. At 45 s, the diffusion front of tracer is located at the bottom of the left side, and the tracer continues to transport along the bottom toward the right side of the ladle. At this time, the tracer on the right side still stays in the upper right area of the ladle.
- (4)
- At 55~65 s, the tracer on the left side of the gas column moves toward the right wall along the bottom of the ladle. When the tracer passes the gas column, a portion of the tracer is brought to the free surface of the ladle by the gas column, and the other portion of the tracer continues to move toward the right wall along the bottom of the ladle.
- (5)
- At 75~110 s, the tracer flows from the bottom of the left side of the ladle, reaching the right wall, and it gradually transports upwards to the upper right side of the ladle due to the influence of the main circulation. At this time, the concentration of the tracer in the ladle is relatively low. The tracer near the upper right wall of the ladle is transported downward to the ladle. The tracers in the whole ladle gradually reaches the mixing.
3.2. Tracer Transport Path and Analysis
3.2.1. First Transport Path of the Tracer
3.2.2. Second Transport Path of the Tracer
3.2.3. Third Transport Path of the Tracer
3.2.4. Fourth Transport Path of the Tracer
3.2.5. Fifth Transport Path of the Tracer
3.3. Analysis of Mixing Time of Five Transport Paths
3.3.1. Analysis of Mixing Time at Each Monitoring Point in Five Transport Paths
3.3.2. Analysis of Average Mixing Time of Each Transport Path
4. Discussion
5. Conclusions
- The results of a large number of repeated experiments on the water model show that there are five transport paths for the tracer in the ladle. The tracer of the first path was mainly transported by the left-side main circulation flow, and the tracer began to transport to the right side after it was transported to the bottom of the ladle. The tracer of the second and third paths were also mainly transported by the left-side circulation flow, but bifurcations occurred when the tracer in the middle area was transported downward. In the third path, the portion and intensity of the tracer transferring to the right side from the central region was higher than in the second path. The fourth path is that the tracer was transported downward from the left, middle, and right sides with a similar intensity at the same time, and the portions on the left and right sides were close. The fifth path is that the tracer was mainly transported on the right side, and the tracer formed a clockwise circulation flow on the right side due to the influence of the gas column.
- Numerical simulation results show that after the tracer was added, it primarily followed the left-side anticlockwise main circulating flow for transport. Most of the tracer was transported downward along the left side wall, and after reaching the bottom, it started to transport to the right. When passing through the gas column, a portion of the tracer reached the bottom of the right side and gradually transported upward along the right side wall, and the other portion of the tracer was carried to the free surface by the gas column. The numerical simulation results are similar only to the first transport path in the water model results and are significantly different from the other four transport paths.
- The mixing time in the third and fifth transport paths shows the maximum and minimum values among all paths, respectively. The error between the mixing time and the averaged mixing time at each monitoring point in the five transport paths of the tracer is between −34.7% and 40.9%. In particular, the errors of mixing time at each monitoring point in the third and fifth transport paths are relatively large. In addition, the mixing time at monitoring points 2 and 3 in the third transport path is twice that of mixing time at the same monitoring points in the fifth transport path. Furthermore, the error of the averaged mixing time of each path and the path-based average value is between 5.5% and 32.6%, and the errors of the second and fourth transport paths are relatively small, while the errors of the third and fifth transport paths are considerably large.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | Industrial Prototype | Water Model |
---|---|---|
The inner diameter of the ladle top (mm) | 3908 | 977 |
The inner diameter of the ladle bottom (mm) | 3716 | 929 |
Height of the ladle (mm) | 4144 | 1036 |
Height of the liquid level (mm) | 3000 | 1000 |
Total number of nozzles | 1 | 1 |
Gas flow rate at the bottom injection (L/min) | 400 | 2.3 |
Radial position of the nozzle (r/R) | 0.2 | 0.2 |
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Tao, X.; Qi, H.; Guo, Z.; Wang, J.; Wang, X.; Yang, J.; Zhao, Q.; Lin, W.; Yang, K.; Chen, C. Assessment of Measured Mixing Time in a Water Model of Eccentric Gas-Stirred Ladle with a Low Gas Flow Rate: Tendency of Salt Solution Tracer Dispersions. Symmetry 2024, 16, 1241. https://doi.org/10.3390/sym16091241
Tao X, Qi H, Guo Z, Wang J, Wang X, Yang J, Zhao Q, Lin W, Yang K, Chen C. Assessment of Measured Mixing Time in a Water Model of Eccentric Gas-Stirred Ladle with a Low Gas Flow Rate: Tendency of Salt Solution Tracer Dispersions. Symmetry. 2024; 16(9):1241. https://doi.org/10.3390/sym16091241
Chicago/Turabian StyleTao, Xin, Hongyu Qi, Zhijie Guo, Jia Wang, Xiaoge Wang, Jundi Yang, Qi Zhao, Wanming Lin, Kun Yang, and Chao Chen. 2024. "Assessment of Measured Mixing Time in a Water Model of Eccentric Gas-Stirred Ladle with a Low Gas Flow Rate: Tendency of Salt Solution Tracer Dispersions" Symmetry 16, no. 9: 1241. https://doi.org/10.3390/sym16091241
APA StyleTao, X., Qi, H., Guo, Z., Wang, J., Wang, X., Yang, J., Zhao, Q., Lin, W., Yang, K., & Chen, C. (2024). Assessment of Measured Mixing Time in a Water Model of Eccentric Gas-Stirred Ladle with a Low Gas Flow Rate: Tendency of Salt Solution Tracer Dispersions. Symmetry, 16(9), 1241. https://doi.org/10.3390/sym16091241