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A numerical study of flow interaction between a cylinder and an oscillating airfoil by using an immersed boundary method

基于浸入式边界方法的圆柱-振荡翼型流动干涉数值模拟研究

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Abstract

The dynamic performance of an oscillating airfoil subjected to the wake of a circular cylinder is studied in this paper. Two-dimensional numerical simulations are conducted at Re = 1100 by using an immersed boundary method together with the adaptive mesh refinement technique. The effects of two parameters, the gap between the cylinder and the airfoil and the oscillation frequency, are of particular interest to the present study. Therefore, dynamic responses are presented as functions of the two parameters, including the fluid forces, the associated frequency characteristics, and the energy exchange between the airfoil and the fluid. The results show that the cylinder wake can significantly reduce the drag as well as the energy extraction of the lift on the airfoil. Different synchronization behaviors between the airfoil’s oscillation and the wake pattern have been observed for some specific cases, i.e., the 1:1, 1:2 and 1:3 patterns. Remarkably, the 1:2 pattern is associated with an asymmetric vortex shedding pattern, which can further result in non-zero time-averaged lift and moment on the airfoil even though both the upstream vortices from the cylinder and the oscillation of the airfoil are periodic. Due to the strong nonlinear interaction between the cylinder wake and the airfoil’s oscillation, new frequency branches associated with nonlinear frequency superposition are formed in the responses of the airfoil and their characteristics have been demonstrated. The present study also finds that the oscillation amplitudes are important in determining the synchronization behavior.

摘要

本文研究了圆柱尾迹中振荡翼型的动力学特性, 通过浸入式边界方法结合自适应网格技术对雷诺数为1100 的二维模型开展了数值模拟计算, 重点关注圆柱翼型间距和振荡频率这两个关键参数的影响. 文中给出了翼型动力学响应随上述两个参数的变化规律, 包括流动作用力、 频率特征以及翼型与流动之间的能量交换过程, 结果表明圆柱尾迹能够显著改变翼型阻力的大小, 并且对通过翼型升力所产生的能量交换过程具有重要影响. 在某些特定流动工况下, 翼型振荡会与尾迹之间呈现出1:1, 1:2和1:3 不同的同步模式. 值得注意的是, 1:2 同步对应着一种非对称的涡脱落形态, 在此工况下, 即使翼型的振荡和上游圆柱尾迹都存在明显的周期性, 翼型上依然存在非零的时均升力及力矩. 此外由于圆柱尾迹与翼型振荡之间的强烈非线性干涉, 在翼型响应中出现了新的频率条带, 该条带满足非线性频率叠加关系. 本文还发现振荡幅值对于同步现象具有重要影响.

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References

  1. W. McKinney, and J. DeLaurier, Wingmill: An oscillating-wing windmill, J. Energy 5, 109 (1981).

    Article  Google Scholar 

  2. Z. J. Wang, Vortex shedding and frequency selection in flapping flight, J. Fluid Mech. 410, 323 (2000).

    Article  Google Scholar 

  3. T. Kinsey, and G. Dumas, Parametric study of an oscillating airfoil in a power-extraction regime, AIAA J. 46, 1318 (2008).

    Article  Google Scholar 

  4. D. Lentink, F. T. Muijres, F. J. Donker-Duyvis, and J. L. van Leeuwen, Vortex-wake interactions of a flapping foil that models animal swimming and flight, J. Exp. Biol. 211, 267 (2008).

    Article  Google Scholar 

  5. A. W. Mackowski, and C. H. K. Williamson, Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching, J. Fluid Mech. 765, 524 (2015).

    Article  Google Scholar 

  6. Y. Su, M. Miller, S. Mandre, and K. Breuer, Confinement effects on energy harvesting by a heaving and pitching hydrofoil, J. Fluids Struct. 84, 233 (2019).

    Article  Google Scholar 

  7. M. Boudreau, and G. Dumas, Vortex dynamics in the wake of three generic types of freestream turbines, J. Fluids Eng. 140, 021106 (2018).

    Article  Google Scholar 

  8. W. Shyy, H. Aono, S. K. Chimakurthi, P. Trizila, C. K. Kang, C. E. S. Cesnik, and H. Liu, Recent progress in flapping wing aerodynamics and aeroelasticity, Prog. Aerosp. Sci. 46, 284 (2010).

    Article  Google Scholar 

  9. J. Young, J. C. S. Lai, and M. F. Platzer, A review of progress and challenges in flapping foil power generation, Prog. Aerospace Sci. 67, 2 (2014).

    Article  Google Scholar 

  10. X. Wu, X. Zhang, X. Tian, X. Li, and W. Lu, A review on fluid dynamics of flapping foils, Ocean Eng. 195, 106712 (2020).

    Article  Google Scholar 

  11. D. Weihs, Hydromechanics of fish schooling, Nature 241, 290 (1973).

    Article  Google Scholar 

  12. J. C. Liao, D. N. Beal, G. V. Lauder, and M. S. Triantafyllou, fish exploiting vortices decrease muscle activity, Science 302, 1566 (2003).

    Article  Google Scholar 

  13. D. N. Beal, F. S. Hover, M. S. Triantafyllou, J. C. Liao, and G. V. Lauder, Passive propulsion in vortex wakes, J. Fluid Mech. 549, 385 (2006).

    Article  Google Scholar 

  14. Q. Liao, G. J. Dong, and X. Y. Lu, Vortex formation and force characteristics of a foil in the wake of a circular cylinder, J. Fluids Struct. 19, 491 (2004).

    Article  Google Scholar 

  15. X. Shao, D. Pan, J. Deng, and Z. Yu, Hydrodynamic performance of a fishlike undulating foil in the wake of a cylinder, Phys. Fluids 22, 111903 (2010).

    Article  Google Scholar 

  16. X. Shao, and D. Pan, Hydrodynamics of a flapping foil in the wake of a D-section cylinder, J. Hydrodyn. 23, 422 (2011).

    Article  Google Scholar 

  17. H. Yuan, and W. Hu, A numerical study of tadpole swimming in the wake of a D-section cylinder, J. Hydrodyn. 29, 1044 (2017).

    Article  Google Scholar 

  18. J. Li, P. Wang, X. An, D. Lyu, R. He, and B. Zhang, Investigation on hydrodynamic performance of flapping foil interacting with oncoming von Karman wake of a D-section cylinder, J. Mar. Sci. Eng. 9, 658 (2021).

    Article  Google Scholar 

  19. J. Li, X. Wang, X. An, B. Zhang, D. Lyu, and P. Wang, Performance improvement of flapping foils in von Karman wake, Ocean Eng. 243, 110207 (2022).

    Article  Google Scholar 

  20. S. Kim, W. X. Huang, and H. J. Sung, Constructive and destructive interaction modes between two tandem flexible flags in viscous flow, J. Fluid Mech. 661, 511 (2010).

    Article  Google Scholar 

  21. Y. Bao, and J. J. Tao, Dynamic reactions of a free-pitching foil to the reverse Karman vortices, Phys. Fluids 26, 031704 (2014).

    Article  Google Scholar 

  22. E. Uddin, W. X. Huang, and H. J. Sung, Actively flapping tandem flexible flags in a viscous flow, J. Fluid Mech. 780, 120 (2015).

    Article  MathSciNet  Google Scholar 

  23. B. L. R. Ribeiro, Y. Su, Q. Guillaumin, K. S. Breuer, and J. A. Franck, Wake-foil interactions and energy harvesting efficiency in tandem oscillating foils, Phys. Rev. Fluids 6, 074703 (2021), arXiv: 2103.05892.

    Article  Google Scholar 

  24. P. Han, Y. Pan, G. Liu, and H. Dong, Propulsive performance and vortex wakes of multiple tandem foils pitching in-line, J. Fluids Struct. 108, 103422 (2022).

    Article  Google Scholar 

  25. R. Gopalkrishnan, M. S. Triantafyllou, G. S. Triantafyllou, and D. Barrett, Active vorticity control in a shear flow using a flapping foil, J. Fluid Mech. 274, 1 (1994).

    Article  Google Scholar 

  26. Y. Bao, and J. Tao, Active control of a cylinder wake flow by using a streamwise oscillating foil, Phys. Fluids 25, 053601 (2013).

    Article  Google Scholar 

  27. L. Du, X. Sun, and V. Yang, Generation of vortex lift through reduction of rotor/stator gap in turbomachinery, J. Propulsion Power 32, 472 (2016).

    Article  Google Scholar 

  28. L. Du, X. Sun, and V. Yang, Vortex-lift mechanism in axial turbomachinery with periodically pitched stators, J. Propulsion Power 32, 486 (2016).

    Article  Google Scholar 

  29. C. Chen, Z. Wang, L. Du, D. Sun, and X. Sun, Simulating unsteady flows in a compressor using immersed boundary method with turbulent wall model, Aerosp. Sci. Tech. 115, 106834 (2021).

    Article  Google Scholar 

  30. C. Chen, Y. Wang, Z. Wang, L. Du, and X. Sun, Application of immersed boundary method in turbomachines, Chin. J. Aeronaut. 36, 268 (2023).

    Article  Google Scholar 

  31. L. Du, X. Jing, and X. Sun, Modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder, J. Fluids Struct. 49, 554 (2014).

    Article  Google Scholar 

  32. L. Du, and X. Sun, Suppression of vortex-induced vibration using the rotary oscillation of a cylinder, Phys. Fluids 27, 023603 (2015).

    Article  Google Scholar 

  33. Z. Wang, L. Du, and X. Sun, Adaptive mesh refinement for simulating fluid-structure interaction using a sharp interface immersed boundary method, Numer. Methods Fluids 92, 1890 (2020).

    Article  MathSciNet  Google Scholar 

  34. Z. Wang, L. Du, F. Gao, and X. Sun, Adaptive forcing distance in an immersed boundary method for internal flow simulation at high Reynolds numbers, Comput. Math. Appl. 140, 44 (2023).

    Article  MathSciNet  Google Scholar 

  35. M. A. Ashraf, J. Young, J. C. S. Lai, and M. F. Platzer, Numerical analysis of an oscillating-wing wind and hydropower generator, AIAA J. 49, 1374 (2011).

    Article  Google Scholar 

  36. B. L. R. Ribeiro, S. L. Frank, and J. A. Franck, Vortex dynamics and Reynolds number effects of an oscillating hydrofoil in energy harvesting mode, J. Fluids Struct. 94, 102888 (2020).

    Article  Google Scholar 

  37. C. M. Hoke, J. Young, and J. C. S. Lai, Enhancing the power-extraction efficiency of a flapping foil by active morphing, AIAA J. 61, 4056 (2023).

    Article  Google Scholar 

  38. P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43, 357 (1981).

    Article  MathSciNet  Google Scholar 

  39. X. Li, and C. Gu, An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour, J. Comput. Phys. 227, 5144 (2008).

    Article  MathSciNet  Google Scholar 

  40. B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method, J. Comput. Phys. 32, 101 (1979).

    Article  Google Scholar 

  41. A. Gilmanov, F. Sotiropoulos, and E. Balaras, A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids, J. Comput. Phys. 191, 660 (2003).

    Article  Google Scholar 

  42. A. Gilmanov, and F. Sotiropoulos, A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies, J. Comput. Phys. 207, 457 (2005).

    Article  Google Scholar 

  43. K. W. Thompson, Time dependent boundary conditions for hyperbolic systems, J. Comput. Phys. 68, 1 (1987).

    Article  MathSciNet  Google Scholar 

  44. R. Mittal, and G. Iaccarino, Immersed boundary methods, Annu. Rev. Fluid Mech. 37, 239 (2005).

    Article  MathSciNet  Google Scholar 

  45. J. Zhao, J. S. Leontini, D. Lo Jacono, and J. Sheridan, Fluid-structure interaction of a square cylinder at different angles of attack, J. Fluid Mech. 747, 688 (2014).

    Article  Google Scholar 

  46. J. Zhao, K. Hourigan, and M. C. Thompson, Flow-induced vibration of D-section cylinders: An afterbody is not essential for vortex-induced vibration, J. Fluid Mech. 851, 317 (2018).

    Article  Google Scholar 

  47. Z. Wang, L. Du, J. Zhao, M. C. Thompson, and X. Sun, Flow-induced vibrations of a pitching and plunging airfoil, J. Fluid Mech. 885, A36 (2020).

    Article  MathSciNet  Google Scholar 

  48. Z. Wang, L. Du, J. Zhao, M. C. Thompson, and X. Sun, Pivot location and mass ratio effects on flow-induced vibration of a fully passive flapping foil, J. Fluids Struct. 100, 103170 (2021).

    Article  Google Scholar 

  49. L. He, Method of simulating unsteady turbomachinery flows with multiple perturbations, AIAA J. 30, 2730 (1992).

    Article  Google Scholar 

  50. F. Mazda, Telecommunications Engineer’s Reference Book (Elsevier, Amsterdam, 1993).

    Google Scholar 

  51. F. Kameier, and W. Neise, Rotating blade flow instability as a source of noise in axial turbomachines, J. Sound Vib. 203, 833 (1997).

    Article  Google Scholar 

  52. P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5 (2010).

    Article  MathSciNet  Google Scholar 

  53. P. J. Schmid, Application of the dynamic mode decomposition to experimental data, Exp. Fluids 50, 1123 (2011).

    Article  Google Scholar 

  54. J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. Nathan Kutz, On dynamic mode decomposition: Theory and applications, J. Comput. Dyn. 1, 391 (2014).

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52022009), the Science Center for Gas Turbine Project of China (Grant No. P2022-A-II-003-001), Key Laboratory Foundation, China (Grant No. 2021-JCJQ-LB-062-0102), and the Fundamental Research Funds for the Central Universities of China.

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Authors and Affiliations

  1. Aeroengine Research Institute, Beihang University, Beijing, 100191, China

    Zhuo Wang  (王卓) & Lin Du  (杜林)

  2. School of Energy and Power Engineering, Beihang University, Beijing, 100191, China

    Xiaofeng Sun  (孙晓峰)

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  1. Zhuo Wang  (王卓)
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  2. Lin Du  (杜林)
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  3. Xiaofeng Sun  (孙晓峰)
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Contributions

Author contributions Zhuo Wang Data curation, Formal analysis, Software, Writing–original draft. Lin Du Investigation, Methodology, Resources, Validation, Visualization, Writing–review & editing. Xiaofeng Sun Conceptualization, Funding acquisition, Supervision, Writing–review & editing.

Corresponding author

Correspondence to Lin Du  (杜林).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Wang, Z., Du, L. & Sun, X. A numerical study of flow interaction between a cylinder and an oscillating airfoil by using an immersed boundary method. Acta Mech. Sin. 40, 323554 (2024). https://doi.org/10.1007/s10409-023-23554-x

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