Dynamics of a Partially Confined, Vertical Upward-Fluid-Conveying, Slender Cantilever Pipe with Reverse External Flow
Abstract
:1. Introduction
2. Problem Formulation
2.1. Derivation of the Motion Equation of Theoretical Model
2.2. Boundary Conditions
2.3. Dimensionless Motion Equation and Boundary Conditions
3. Solution of Equations by a Galerkin Method
4. Theoretical Analysis for Slender, Leaching-Tubing-Like Systems
4.1. Effect of the Radial Confinement αch
4.2. Effect of the Confinement Length rann
4.3. Effect of the Cantilevered Pipe Length L
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Dimensional parameters | Di (m) | Do (m) | Dch (m) | L (m) | Ls (m) | EI (N·m2) | Mp (kg/m) | |
0.159 | 0.1778 | 0.298 | 1283 | 1085 | 3.47 × 106 | 38.7 | ||
Dimensionless parameters | α | αch | ε | βi | βo | h | γ | rann |
0.897 | 1.676 | 7216 | 0.239 | 0.297 | 1.479 | 2.019 × 105 | 0.85 |
Behavior a | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
D1 | F2 | F3 | F1 | F2 | ||||||
αch | 1.10 | 1.20 | 1.27 | 1.32 | 1.35 | … | 4.46 | … | 20 | … |
Behavior a | ||||||||||
F1 | F2 | |||||||||
rann | 0 | 0.15 | 0.30 | 0.45 | 0.60 | 0.72 | 0.75 | 0.80 | 0.85 | 0.90 |
Behavior b | ||||||||||
F2 | F1 | F2 | ||||||||
rann | 0 | 0.15 | 0.19 | 0.45 | 0.60 | 0.69 | 0.75 | 0.80 | 0.85 | 0.90 |
Behavior a, b, c | ||||||||||
F1 | ||||||||||
L (m) | 5 | 150 | 300 | 450 | 500 | |||||
Behavior d | F2 | |||||||||
L (m) | 5 | 150 | 300 | 450 | 500 |
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Ge, X.; Li, Y.; Chen, X.; Shi, X.; Ma, H.; Yin, H.; Zhang, N.; Yang, C. Dynamics of a Partially Confined, Vertical Upward-Fluid-Conveying, Slender Cantilever Pipe with Reverse External Flow. Appl. Sci. 2019, 9, 1425. https://doi.org/10.3390/app9071425
Ge X, Li Y, Chen X, Shi X, Ma H, Yin H, Zhang N, Yang C. Dynamics of a Partially Confined, Vertical Upward-Fluid-Conveying, Slender Cantilever Pipe with Reverse External Flow. Applied Sciences. 2019; 9(7):1425. https://doi.org/10.3390/app9071425
Chicago/Turabian StyleGe, Xinbo, Yinping Li, Xiangsheng Chen, Xilin Shi, Hongling Ma, Hongwu Yin, Nan Zhang, and Chunhe Yang. 2019. "Dynamics of a Partially Confined, Vertical Upward-Fluid-Conveying, Slender Cantilever Pipe with Reverse External Flow" Applied Sciences 9, no. 7: 1425. https://doi.org/10.3390/app9071425
APA StyleGe, X., Li, Y., Chen, X., Shi, X., Ma, H., Yin, H., Zhang, N., & Yang, C. (2019). Dynamics of a Partially Confined, Vertical Upward-Fluid-Conveying, Slender Cantilever Pipe with Reverse External Flow. Applied Sciences, 9(7), 1425. https://doi.org/10.3390/app9071425