Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Setup
2.2. Numerical Model
2.3. Numerical Solutions
2.3.1. Two-Order Reconstruction of the Flow Variable
2.3.2. Spatial Discretization
2.3.3. Time Discretization
2.3.4. Initial and Boundary Conditions
2.3.5. Convergence and Stability Criteria
3. Results and Discussion
3.1. Observed Flow Patterns Varying during Water Slow Filling
3.2. The Water–Air Interface
3.3. Numerical Validation
3.3.1. The Pressure Evolution in Pipe during Water Slow Filling
3.3.2. The Air Velocity Evolution of Air Valves
4. Summary and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Air Valve | Distance to the Inlet (m) | Relative Elevation (mm) | Pipe Length (m) | Slope (‰) |
---|---|---|---|---|
0 | 156 | 60.578 | −3.527 | |
60.578 | 370 | |||
7.014 | +49.985 | |||
67.592 | 24 | |||
4.200 | 0 | |||
71.792 | 24 | |||
1.990 | −50.197 | |||
1# | 73.782 | 113 | ||
60.640 | +1.000 | |||
2# | 134.422 | 53 | ||
22.210 | ||||
3# | 156.632 | 31 | ||
29.880 | ||||
186.512 | 0 | |||
20.684 | −4.877 | |||
4# | 207.196 | 92 | ||
93.146 | −0.202 | |||
300.342 | 116 |
Initial Condition | = 10−10 m2, = 0, = 0, = 1.29 kg/m3, = 0, = 0.0452 m2, = 0.0583 kg/m, = 0 |
Left boundary condition | = 0.00402 m3/s, = 0, = 0 |
Right boundary condition | = 0, = 0, = 0 |
Air Valve No. | Cell Location of Air Valves (i) | ||
---|---|---|---|
1# | 73 | 24 | 4.5216 |
2# | 134 | 24 | 4.5216 |
3# | 156 | 24 | 4.5216 |
4# | 207 | 24 | 4.5216 |
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Liu, J.; Xu, D.; Zhang, S.; Bai, M. Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition. Water 2019, 11, 2511. https://doi.org/10.3390/w11122511
Liu J, Xu D, Zhang S, Bai M. Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition. Water. 2019; 11(12):2511. https://doi.org/10.3390/w11122511
Chicago/Turabian StyleLiu, Jintao, Di Xu, Shaohui Zhang, and Meijian Bai. 2019. "Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition" Water 11, no. 12: 2511. https://doi.org/10.3390/w11122511
APA StyleLiu, J., Xu, D., Zhang, S., & Bai, M. (2019). Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition. Water, 11(12), 2511. https://doi.org/10.3390/w11122511