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Transitional Flow Dynamics Past a Passively Flapping Airfoil in Gusty Flow

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Advances in Critical Flow Dynamics Involving Moving/Deformable Structures with Design Applications

Abstract

This paper investigates the transitional flow dynamics behind a passively flapping airfoil supported by nonlinear springs in the presence of gusty inflow. The fluid-structure interaction (FSI) framework is composed of an incompressible Navier-Stokes solver weakly coupled with a two degree-of-freedom (dof) nonlinear structural model. The fluid-elastic system shows a rich bifurcation behavior in terms of successive Hopf bifurcations in uniform flow condition as the mean wind speed is increased. Presence of gusty fluctuations in the inflow makes the dynamics more complex through transitional states that we refer to as ‘intermittency’ between different dynamical states. A regular intermittent state between quasi-periodic dynamics and low amplitude aperiodic response has been observed when the FSI system is subjected to a time harmonic gust in terms of sinusoidal fluctuation. A parametric study has been carried out for various amplitudes and frequencies of the sinusoidal fluctuation to demarcate the transitional regimes. Thereafter, the system is subjected to random gusts modeled as Ornstein-Uhlenbeck process and ‘on-off’ and ‘burst’ type intermittent dynamics have been observed for long time-scale and short time-scale input fluctuations respectively. The intermittent states have been characterized through time series analyses tools and the corresponding flow-field dynamics has been investigated in detail.

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References

  1. Jones, K., Platzer, M.: Bio-inspired design of flapping-wing micro air vehicles-an engineer’s perspective. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, p. 37 (2006)

    Google Scholar 

  2. Wang, Z.J.: Vortex shedding and frequency selection in flapping flight. J. Fluid Mech., 410, 323–341 (2000)

    Google Scholar 

  3. Young, J., Lai, J.C.: Oscillation frequency and amplitude effects on the wake of a plunging airfoil. AIAA J. 42(10), 2042–2052 (2004)

    Google Scholar 

  4. Chirarattananon, P., Chen, Y., Helbling, E.F., Ma, K.Y., Cheng, R., Wood, R.J.: Dynamics and flight control of a flapping-wing robotic insect in the presence of wind gusts. Interface Focus, 7(1). 20160080 (2017)

    Google Scholar 

  5. Watkins, S., Milbank, J., Loxton, B.J., Melbourne, W.H.: Atmospheric winds and their implications for microair vehicles. AIAA J. 44(11), 2591–2600 (2006)

    Google Scholar 

  6. Lian, Yongsheng, Shyy, Wei: Laminar-turbulent transition of a low reynolds number rigid or flexible airfoil. AIAA J. 45(7), 1501–1513 (2007)

    Article  Google Scholar 

  7. Lian, Y.: Numerical investigation of boundary effects on flapping wing study. In: 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, p. 539 (2009)

    Google Scholar 

  8. Russell Prater and Yongsheng Lian. Aerodynamic response of stationary and flapping wings in oscillatory low reynolds number flows. In: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p. 418 (2012)

    Google Scholar 

  9. Jones, M., Yamaleev, N.: The effect of a gust on the flapping wing performance. In: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p. 1080 (2012)

    Google Scholar 

  10. Fisher, Alex, Ravi, Sridhar, Watkins, Simon, Watmuff, Jon, Wang, Chun, Liu, Hao, Petersen, Phred: The gust-mitigating potential of flapping wings. Bioinspiration Biomimet. 11(4), 046010 (2016)

    Article  Google Scholar 

  11. Shyy, W.E.I., Jenkins, D., Smith, R.: Study of adaptive shape airfoils at low reynolds number in oscillatory flows. AIAA J. 35(9), 1545–1548 (1997)

    Article  Google Scholar 

  12. Williams, D., Buntain, S., Quach, V., Kerstens, W.: Flow field structures behind a 3d wing in an oscillating freestream. In: 39th AIAA Fluid Dynamics Conference, p. 3690 (2009)

    Google Scholar 

  13. Zhu, Jianyang, Jiang, Lin, Zhao, Hui, Tao, Bo, Lei, Bin: Numerical study of a variable camber plunge airfoil under wind gust condition. J. Mech. Sci. Technol. 29(11), 4681–4690 (2015)

    Article  Google Scholar 

  14. Golubev, V., Hollenshade, T., Nguyen, L., Visbal, M.: High-accuracy low-re simulations of airfoil-gust and airfoil-vortex interactions. In: 40th Fluid Dynamics Conference and Exhibit, p. 4868 (2010)

    Google Scholar 

  15. Raveh, D.E.: Gust-response analysis of free elastic aircraft in the transonic flight regime. J. Aircraft 48(4), 1204–1211 (2011)

    Google Scholar 

  16. Bartels, R.: Developing an accurate cfd based gust model for the truss braced wing aircraft. In: 31st AIAA Applied Aerodynamics Conference, p. 3044 (2013)

    Google Scholar 

  17. Bose, C., Sarkar, S., Gupta, S.: Stochastic bifurcation analysis of an elastically mounted flapping airfoil. In: MATEC Web of Conferences, vol. 148, p. 08001. EDP Sciences (2018)

    Google Scholar 

  18. Lee, B.H.K., Jiang, L.Y.: Flutter of an airfoil with cubic restoring force. J. Fluids Struct. 13, 75–101 (1999)

    Article  Google Scholar 

  19. Ferziger, J.H., Peric, M.: Computational Methods for Fluid Dynamics, 3rd edn. Springer, Berlin (2002)

    Book  Google Scholar 

  20. OpenFOAM. The Open Source CFD Toolbox User Guide. (2013)

    Google Scholar 

  21. Bose, Chandan, Badrinath, Sandeep, Gupta, Sayan, Sarkar, Sunetra: Dynamical stability analysis of a fluid structure interaction system using a high fidelity navier-stokes solver. Procedia Eng. 144, 883–890 (2016)

    Article  Google Scholar 

  22. Trimarchi, D.: Analysis of downwind sail structures using non-linear shell finite elements: wrinkle development and fluid interaction effects. Ph.D. thesis, University of Southampton, 2012

    Google Scholar 

  23. Graham, R., Schenzle, A.: Stabilization by multiplicative noise. Phys. Rev. A 26(3), 1676 (1982)

    Article  MathSciNet  Google Scholar 

  24. Gillespie, D.T.: Exact numerical simulation of the ornstein-uhlenbeck process and its integral. Phys. Rev. E 54(2), 2084 (1996)

    Google Scholar 

  25. Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43(3), 525–546 (2001)

    Google Scholar 

  26. Bose, Chandan, Gupta, Sayan, Sarkar, Sunetra: Dynamical behavior of unsteady flowfield of an elastically mounted flapping airfoil. AIAA J. 56(5), 2062–2069 (2018)

    Article  Google Scholar 

  27. Venkatramani, J., Krishna Kumar, S., Sarkar, S., Gupta, S.: Physical mechanism of intermittency route to aeroelastic flutter. J. Fluids Struct. 75, 9–26 (2017)

    Google Scholar 

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Bose, C., Gupta, S., Sarkar, S. (2021). Transitional Flow Dynamics Past a Passively Flapping Airfoil in Gusty Flow. In: Braza, M., Hourigan, K., Triantafyllou, M. (eds) Advances in Critical Flow Dynamics Involving Moving/Deformable Structures with Design Applications. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-030-55594-8_14

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  • DOI: https://doi.org/10.1007/978-3-030-55594-8_14

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  • Online ISBN: 978-3-030-55594-8

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