- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Mode competition in a plunging foil with an active flap: A multiscale modal analysis approach

Tso-Kang Wang and Kourosh Shoele*

  • Department of Mechanical Engineering, Joint College of Engineering Florida State University–Florida A&M University, Tallahassee, Florida 32310, USA

  • *kshoele@eng.famu.fsu.edu
PDF

Phys. Rev. Fluids 7, 044701 – Published 12 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.044701

Abstract

Flow-induced fluttering has a significant role in aircraft stability, renewable energy extraction, animal locomotion, and many other applications. While being a ubiquitous phenomenon, the control of the flutter response has been primarily limited to simplified systems and, often, with the help of linear inviscid flow theories. In this paper, we numerically investigate how the plunging response of a foil can be regulated using an active flap to improve structural safety or enhance the energy extraction efficiency of the foil with a tightly coupled fluid-structure interaction algorithm. A broad range of foil and flap settings was tested, and their flow dynamics have been investigated. A multiscale modal analysis technique suitable for fluid-structure interaction systems is employed to systematically isolate the active flap-induced and flow-induced modes. It is observed that the competition between these two modes dictates the plunging response of the foil. The active flap can modulate the leading edge vortex shedding with larger flapping amplitude and regulate the foil heaving motion. The ratio of the competing modal energy is proposed to evaluate the control efficacy of the morphing surface, and the onset of the lock-in is associated with the ratio approaching unity. It is shown that the morphing flap is a good candidate for active flow control.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (63)

  1. R. L. Bisplinghoff, H. Ashley, and R. L. Halfman, Aeroelasticity (Courier Corporation, North Chelmsford, MA, 2013).
  2. A. Collar, The expanding domain of aeroelasticity, J. Roy. Aeronaut. Soc. 50, 613 (1946).
  3. M. H. Hansen, Aeroelastic instability problems for wind turbines, Wind Energy 10, 551 (2007).
  4. A. Ducoin and Y. L. Young, Hydroelastic response and stability of a hydrofoil in viscous flow, J. Fluids Struct. 38, 40 (2013).
  5. D. Poirel, V. Metivier, and G. Dumas, Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers, J. Fluids Struct. 27, 1262 (2011).
  6. Y. Zhu, Y. Su, and K. Breuer, Nonlinear flow-induced instability of an elastically mounted pitching wing, J. Fluid Mech. 899, A35 (2020).
  7. M. W. Kehoe, A historical overview of flight flutter testing, in AGARD Structures and Materials Panel Meeting, No. NASA-TM-4720 (NASA, Washington, DC, 1995).
  8. V. Mukhopadhyay, Historical perspective on analysis and control of aeroelastic responses, J. Guid. Control. Dyn. 26, 673 (2003).
  9. R. D. Blevins, Flow-Induced Vibration (Van Nostrand Reinhold, New York, 1977).
  10. M. O. L. Hansen, J. N. Sørensen, S. Voutsinas, N. Sørensen, and H. A. Madsen, State of the art in wind turbine aerodynamics and aeroelasticity, Prog. Aerospace Sci. 42, 285 (2006).
  11. O. H. Amman, T. von Kármán, and G. B. Woodruff, The Failure of the Tacoma Narrows Bridge (Federal Works Agency, Washington, DC, 1941).
  12. H. L. Fierstine and V. Walters, Studies in locomotion and anatomy of scombroid fishes, Mem. South. Calif. Acad. Sci. 6, 1 (1968).
  13. M. Sfakiotakis, D. M. Lane, and J. B. C. Davies, Review of fish swimming modes for aquatic locomotion, IEEE J. Oceanic Eng. 24, 237 (1999).
  14. Q. Zhu and K. Shoele, Propulsion performance of a skeleton-strengthened fin, J. Exp. Biol. 211, 2087 (2008).
  15. P. Freymuth, Thrust generation by an airfoil in hover modes, Exp. Fluids 9, 17 (1990).
  16. H. Liu and K. Kawachi, A numerical study of insect flight, J. Comput. Phys. 146, 124 (1998).
  17. D. A. Read, F. Hover, and M. Triantafyllou, Forces on oscillating foils for propulsion and maneuvering, J. Fluids Struct. 17, 163 (2003).
  18. K. Sum Wu, J. Nowak, and K. S. Breuer, Scaling of the performance of insect-inspired passive-pitching flapping wings, J. R. Soc. Interface 16, 20190609 (2019).
  19. X. Wu, X. Zhang, X. Tian, X. Li, and W. Lu, A review on fluid dynamics of flapping foils, Ocean Eng. 195, 106712 (2020).
  20. Q. Zhu and Z. Peng, Mode coupling and flow energy harvesting by a flapping foil, Phys. Fluids 21, 033601 (2009).
  21. A. Abdelkefi, Aeroelastic energy harvesting: A review, Int. J. Eng. Sci. 100, 112 (2016).
  22. A. B. Rostami and M. Armandei, Renewable energy harvesting by vortex-induced motions: Review and benchmarking of technologies, Renew. Sustain Energy Rev. 70, 193 (2017).
  23. Q. Xiao and Q. Zhu, A review on flow energy harvesters based on flapping foils, J. Fluids Struct. 46, 174 (2014).
  24. D. Li, Y. Wu, A. Da Ronch, and J. Xiang, Energy harvesting by means of flow-induced vibrations on aerospace vehicles, Prog. Aerospace Sci. 86, 28 (2016).
  25. Y. Lee, A. Vakakis, L. Bergman, D. M. McFarland, and G. Kerschen, Suppression aeroelastic instability using broadband passive targeted energy transfers, Part 1: Theory, AIAA J. 45, 693 (2007).
  26. S. Fatimah and F. Verhulst, Suppressing flow-induced vibrations by parametric excitation, Nonlin. Dyn. 31, 275 (2003).
  27. V. Giurgiutiu, Review of smart-materials actuation solutions for aeroelastic and vibration control, J. Intell. Mater. Syst. Struct. 11, 525 (2000).
  28. S. Barbarino, O. Bilgen, R. M. Ajaj, M. I. Friswell, and D. J. Inman, A review of morphing aircraft, J. Intell. Mater. Syst. Struct. 22, 823 (2011).
  29. K. W. Moored, III and H. Bart-Smith, The analysis of tensegrity structures for the design of a morphing wing, ASME. J. Appl. Mech. 74, 668 (2007).
  30. J. J. Block and T. W. Strganac, Applied active control for a nonlinear aeroelastic structure, J. Guid. Control. Dyn. 21, 838 (1998).
  31. T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter, NACA Technical Report TR-496 (1949).
  32. Z. Wang, A. Behal, and P. Marzocca, Model-free control design for multiinput multi-output aeroelastic system subject to external disturbance, J. Guid. Control. Dyn. 34, 446 (2011).
  33. G. Platanitis and T. W. Strganac, Control of a nonlinear wing section using leading-and trailing-edge surfaces, J. Guid. Control. Dyn. 27, 52 (2004).
  34. A. Medina, M. S. Hemati, and M. Rockwood, Separated flow response to rapid flap deflection, AIAA J. 58, 1446 (2020).
  35. H. Ohta, A. Fujimori, P. Nikiforuk, and M. Gupta, Active flutter suppression for two-dimensional airfoils, J. Guid. Control. Dyn. 12, 188 (1989).
  36. D. Tang, E. Dowell, and L. Virgin, Limit cycle behavior of an airfoil with a control surface, J. Fluids Struct. 12, 839 (1998).
  37. K. Zhang and A. Behal, Continuous robust control for aeroelastic vibration control of a 2-D airfoil under unsteady flow, J. Vibration Control 22, 2841 (2016).
  38. A. Goza and T. Colonius, Modal decomposition of fluid–structure interaction with application to flag flapping, J. Fluids Struct. 81, 728 (2018).
  39. E. Liberge and A. Hamdouni, Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder, J. Fluids Struct. 26, 292 (2010).
  40. K. Menon and R. Mittal, Dynamic mode decomposition based analysis of flow over a sinusoidally pitching airfoil, J. Fluids Struct. 94, 102886 (2020).
  41. T.-K. Wang and K. Shoele, Geometrically weighted modal decomposition techniques, J. Fluid Mech. 911, A41 (2021).
  42. M. Mendez, M. Balabane, and J.-M. Buchlin, Multi-scale proper orthogonal decomposition of complex fluid flows, J. Fluid Mech. 870, 988 (2019).
  43. C. Van Dam, The aerodynamic design of multi-element high-lift systems for transport airplanes, Prog. Aerospace Sci. 38, 101 (2002).
  44. H. L. Morgan Jr., Experimental test results of energy efficient transport (EET) high-lift airfoil in Langley low-turbulence pressure tunnel, NASA Technical Memorandum, NASA/TM-2002-211780 (NASA, Washington, DC, 2002).
  45. E. Nissim, Flutter suppression using active controls based on the concept of aerodynamic energy, NASA Technical Note, NASA-TN-D-6199 (NASA, Washington, DC, 1971).
  46. K. Reddy, J. Chen, A. Behal, and P. Marzocca, Multi-input/multi-output adaptive output feedback control design for aeroelastic vibration suppression, J. Guid. Control. Dyn. 30, 1040 (2007).
  47. L. Guglielmini and P. Blondeaux, Propulsive efficiency of oscillating foils, Eur. J. Mech. B 23, 255 (2004).
  48. E. J. Chae, D. T. Akcabay, and Y. L. Young, Dynamic response and stability of a flapping foil in a dense and viscous fluid, Phys. Fluids 25, 104106 (2013).
  49. C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics (Oxford University Press, Oxford, 2011).
  50. J. D. Eldredge, Mathematical Modeling of Unsteady Inviscid Flows (Springer, Berlin, Heidelberg, 2019).
  51. G. Birkhoff, R. S. Varga, and D. Young, Alternating direction implicit methods, in Advances in Computers, edited by F. L. Alt and M. Rubinoff (Elsevier, Amsterdam, 1962), Vol. 3, pp. 189–273.
  52. T.-K. Wang, T. Solano, and K. Shoele, Bridge the gap: correlate face mask leakage and facial features with 3D morphable face models, J. Expo. Sci. Environ. Epidemiol. (2021).
  53. K. Menon and R. Mittal, Flow physics and dynamics of flow-induced pitch oscillations of an airfoil, J. Fluid Mech. 877, 582 (2019).
  54. M. La Mantia and P. Dabnichki, Added mass effect on flapping foil, Engi. Anal. Boundary Elements 36, 579 (2012).
  55. P.-F. Lei, J.-Z. Zhang, W. Kang, S. Ren, and L. Wang, Unsteady flow separation and high performance of airfoil with local flexible structure at low Reynolds number, Commun. Comput. Phys. 16, 699 (2014).
  56. G. Jones, M. Santer, and G. Papadakis, Control of low Reynolds number flow around an airfoil using periodic surface morphing: A numerical study, J. Fluids Struct. 76, 95 (2018).
  57. W. Kang, M. Xu, W. Yao, and J. Zhang, Lock-in mechanism of flow over a low-Reynolds-number airfoil with morphing surface, Aerospace Sci. Technol. 97, 105647 (2020).
  58. L. Sirovich, Turbulence and the dynamics of coherent structures. I. coherent structures, Q. Appl. Math. 45, 561 (1987).
  59. C. Gotsman, X. Gu, and A. Sheffer, Fundamentals of spherical parameterization for 3D meshes, in ACM SIGGRAPH 2003 Papers (SIGGRAPH '03) (ACM Press, New York, NY, 2003), pp. 358–363.
  60. M. S. Floater and K. Hormann, Surface parameterization: A tutorial and survey, in Advances in Multiresolution for Geometric Modelling, edited by N. A. Dodgson, M. S. Floater, and M. A. Sabin (Springer, Berlin, Heidelberg, 2005), pp. 157–186.
  61. H. Li and R. Hartley, Conformal spherical representation of 3D genus-zero meshes, Pattern Recognit. 40, 2742 (2007).
  62. W. Zeng and X. D. Gu, Registration for 3D surfaces with large deformations using quasi-conformal curvature flow, in CVPR 2011 (IEEE, New York, 2011), pp. 2457–2464.
  63. Y. T. Lee, K. C. Lam, and L. M. Lui, Landmark-matching transformation with large deformation via n-dimensional quasi-conformal maps, J. Sci. Comput. 67, 926 (2016).

Outline

Information

Phys. Rev. Fluids 7, 044701– Published 12 April, 2022
  • Received 24 September 2021
  • Accepted 23 March 2022
Article part of CHORUS
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation