Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106
Abstract
:1. Introduction
2. Numerical Models
2.1. Numerical Method
2.2. Boundary Conditions and Grid System
3. Convergence Study and Calculation Validation
4. Results and Discussion
4.1. Flow Patterns
- Single bluff body flow
- Deflected gap flow
- Anti-phase flow
- In-phase flow
- Co-shedding flow
4.2. Fluid Force Coefficients
4.3. Vortex Shedding Frequencies
4.4. Separation Angles
5. Conclusions
- (i)
- Five flow regimes are identified depending on the spacing ratios, i.e, single bluff body flow (), deflected gap flow ( = 1.2–1.4), anti-phase flow ( = 1.5–2), in-phase flow ( = 2–3.5), and co-shedding flow ().
- (ii)
- When in deflected gap flow, the downstream cylinder with a wide wake experiences lower drag and higher lift (absolute value and RMS), compared to the cylinder with narrow wake. However, their vortex shedding frequencies are identical. In addition, the sum of lift forces of the three cylinders at the deflected gap flow is not zero, either a positive or negative lift may exist.
- (iii)
- When , the separation points on the free-flow-side of the downstream cylinders are always lower than that of the single cylinder, indicating that the violent flow at the gap also causes the flow separation on the outer side of the cylinder to advance. When , the separation point of the cylinder in upper stream is close to that of single cylinder, indicating that the minimum for negligible interaction among the cylinders is .
Author Contributions
Funding
Conflicts of Interest
References
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Case | Cell Count (Million) | |||||
---|---|---|---|---|---|---|
Coarse Mesh | ||||||
Medium Mesh | ||||||
Fine Mesh |
Researchers | Description | |||||
---|---|---|---|---|---|---|
Present study | k– IDDES | |||||
Roshko [40] | Experiments | 0.30 | − | − | 0.37 | |
Experiments | 0.42 | − | − | 0.62 | ||
Experiments | 0.69 | − | − | 0.85 | ||
Schmidt [41] | (2.6–3.3) × 10 | Experiments | 0.25–0.44 | − | − | 0.51–0.61 |
Jones et al. [42] | Experiments | 0.21 | − | − | 0.53 | |
Experiments | 0.53 | − | − | 0.59 | ||
Experiments | 0.56 | − | − | 0.61 | ||
Schewe [24] | Experiments | 0.45 | − | − | − | |
Shih et al. [43] | (3–3.1) × 10 | Experiments | 0.35–0.38 | − | − | 0.45–0.46 |
Travin et al. [44] | DES | |||||
Catalanoet al. [45] | LES | − | ||||
Ong et al. [46] | k– URANS | − |
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Zhang, M.; Yin, B.; Guo, D.; Ji, Z.; Yang, G. Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106. Appl. Sci. 2022, 12, 11835. https://doi.org/10.3390/app122211835
Zhang M, Yin B, Guo D, Ji Z, Yang G. Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106. Applied Sciences. 2022; 12(22):11835. https://doi.org/10.3390/app122211835
Chicago/Turabian StyleZhang, Mohan, Bo Yin, Dilong Guo, Zhanling Ji, and Guowei Yang. 2022. "Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106" Applied Sciences 12, no. 22: 11835. https://doi.org/10.3390/app122211835
APA StyleZhang, M., Yin, B., Guo, D., Ji, Z., & Yang, G. (2022). Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106. Applied Sciences, 12(22), 11835. https://doi.org/10.3390/app122211835