Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Vorticity transfer in a leading-edge vortex due to controlled spanwise bending

Kun Jia1, Tyler Scofield2, Mingjun Wei1, and Samik Bhattacharya2,*

  • 1Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, Kansas 66506, USA
  • 2Mechanical and Aerospace Engineering Department, University of Central Florida, Orlando, Florida 32816, USA

  • *Corresponding author: samik.bhattacharya@ucf.edu

Phys. Rev. Fluids 6, 024703 – Published 25 February, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.024703

Abstract

Many natural flyers and swimmers routinely flex their lifting or propulsive surfaces to control the leading-edge vortex (LEV) that forms on the suction side during maneuvering at a high angle of attack. In this paper, we studied the effect of a similar bending on the vortex dynamics of a flat-plate airfoil of aspect ratio 3 (chord 5cm) and held at an angle of attack of 30. This flat plate is accelerated from rest to a Reynolds number of 2400, while being dynamically bent along the span in a controlled manner with a bending ratio of 0.65 and a maximum bending angle of 30. We investigated the effect of such spanwise bending on the resultant vorticity transfer via both experiments and numerical simulation. It shows that a dynamic spanwise bending induces a change in the effective shear layer velocity along the span's bent part and creates spanwise vorticity convection. As a result, the growth of circulation in the LEV gets delayed along the bent part, and the final circulation is smaller than the no-bending case.

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. K. N. Lucas, N. Johnson, W. T. Beaulieu, E. Cathcart, G. Tirrell, S. P. Colin, B. J. Gemmell, J. O. Dabiri, and J. H. Costello, Bending rules for animal propulsion, Nat. Commun. 5, 3293 (2014).
  2. M. H. Dickinson and K. G. Gotz, Unsteady aerodynamic performance of model wings at low Reynolds numbers, J. Expt. Biol. 174, 45 (1993).
  3. J. D. Eldredge and A. R. Jones, Leading-edge vortices: Mechanics and modeling, Annu. Rev. Fluid Mech. 51, 75 (2019).
  4. J. O. Dabiri, Optimal vortex formation as a unifying principle in biological propulsion, Annu. Rev. Fluid Mech. 41, 17 (2009).
  5. D. Lentink and M. H. Dickinson, Rotational accelerations stabilize leading edge vortices on revolving fly wings, J. Expt. Biol. 212, 2705 (2009).
  6. C. P. Ellington, C. Van Den Berg, A. P. Willmott, and A. L. Thomas, Leading-edge vortices in insect flight, Nature (London) 384, 626 (1996).
  7. J. G. Wong and D. E. Rival, Determining the relative stability of leading-edge vortices on nominally two-dimensional flapping profiles, J. Fluid Mech. 766, 611 (2015).
  8. D. E. Rival, J. Kriegseis, P. Schaub, A. Widmann, and C. Tropea, Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry, Expt. Fluids 55, 1660 (2014).
  9. D. Kim and M. Gharib, Flexibility effects on vortex formation of translating plates, J. Fluid Mech. 677, 255 (2011).
  10. C.-K. Kang, H. Aono, C. E. Cesnik, and W. Shyy, Effects of flexibility on the aerodynamic performance of flapping wings, J. Fluid Mech. 689, 32 (2011).
  11. A. C. DeVoria and M. J. Ringuette, The force and impulse of a flapping plate performing advancing and returning strokes in a quiescent fluid, Expt. Fluids 54, 1515 (2013).
  12. J.-T. Kim, Y. Jin, and L. P. Chamorro, Dynamics of flexible plates and flow under impulsive oscillation, J. Fluids Struct. 87, 319 (2019).
  13. P. M. Mancini, A. R. Jones, K. O. Granlund, and M. V. Ol, Unsteady aerodynamic response of a rapidly started flexible wing, Intl. J. Micro Air Veh. 7, 147 (2015).
  14. R. Wootton, R. Herbert, P. Young, and K. Evans, Approaches to the structural modeling of insect wings, Philos. Trans. R. Soc. London B 358, 1577 (2003).
  15. S. Heathcote, Z. Wang, and I. Gursul, Effect of spanwise flexibility on flapping wing propulsion, J. Fluids Struct. 24, 183 (2008).
  16. P. Liu and N. Bose, Propulsive performance from oscillating propulsors with spanwise flexibility, Proc. Royal Soc. Lond. Ser. A: Math., Phys. Eng. Sci. 453, 1763 (1997).
  17. J. G. Wong and D. E. Rival, Rapid manoeuvring with spanwise-flexible wings, J. Fluids Struct. 75, 1 (2017).
  18. W. Thielicke and E. Stamhuis, pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab, J. Open Res. Software 2, e30 (2014).
  19. C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25, 220 (1977).
  20. T. Yang, M. Wei, and H. Zhao, Numerical study of flexible flapping wing propulsion, AIAA J. 48, 2909 (2010).
  21. M. Xu and M. Wei, Using adjoint-based approach to study flapping wings, in 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (AIAA, 2013), p. 839.
  22. M. Wei and M. Xu, A continuous adjoint-based approach for the optimization of wing flapping, in 32nd AIAA Applied Aerodynamics Conference (AIAA, 2014), p. 2048.
  23. M. Xu, M. Wei, C. Li, and H. Dong, Adjoint-based optimization of flapping plates hinged with a trailing-edge flap, Theor. Appl. Mech. Lett. 5, 1 (2015).
  24. T. Yang, M. Wei, K. Jia, and J. Chen, A monolithic algorithm for the flow simulation of flexible flapping wings, Intl. J. Micro Air Veh. 11, 1756829319846127 (2019).
  25. M. Cerrolaza, S. Shefelbine, and D. Garzón-Alvarado, Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes (Academic Press, Barcelona, Spain, 2017), p. 454.
  26. M. Xu, M. Wei, T. Yang, and T. Burton, Nonlinear structural response in flexible flapping wings with different density ratio, in 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (AIAA, 2011), p. 376.
  27. M. Xu and M. Wei, Using adjoint-based optimization to study kinematics and deformation of flapping wings, J. Fluid Mech. 799, 56 (2016).
  28. M. Xu, M. Wei, C. Li, and H. Dong, Adjoint-based optimization for thrust performance of three-dimensional pitching-rolling plate, AIAA J. 57, 3716 (2019).
  29. J. G. Wong, J. Kriegseis, and D. E. Rival, An investigation into vortex growth and stabilization for two-dimensional plunging and flapping plates with varying sweep, J. Fluids Struct. 43, 231 (2013).
  30. C. P. Ford and H. Babinsky, Lift and the leading-edge vortex, J. Fluid Mech. 720, 280 (2013).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation