Hostname: page-component-6b989bf9dc-jks4b Total loading time: 0 Render date: 2024-04-14T09:17:38.581Z Has data issue: false hasContentIssue false
  • English
  • Français

Surging and plunging oscillations of an airfoil at low Reynolds number

Published online by Cambridge University Press:  15 December 2014

Jeesoon Choi ,
Tim Colonius  and
David R. Williams
Jeesoon Choi*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
David R. Williams
Affiliation:
Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA
*
†Email address for correspondence: jschoi@caltech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the forces and unsteady flow structures associated with harmonic oscillations of an airfoil in the streamwise (surging) and transverse (plunging) directions in two-dimensional simulations at low Reynolds number. For the surging case, we show that there are specific frequencies where the wake instability synchronizes with the unsteady motion of the airfoil, leading to significant changes in the mean forces. Resonant behaviour of the time-averaged forces is observed near the vortex shedding frequency and its subharmonic; the behaviour is reminiscent of the dynamics of the generic nonlinear oscillator known as the Arnol’d tongue or the resonance horn. Below the wake instability frequency, there are two regimes where the fluctuating forces are amplified and attenuated, respectively. A detailed study of the flow structures associated with leading-edge vortex (LEV) growth and detachment are used to relate this behaviour with the LEV acting either in phase with the quasi-steady component of the forces for the amplification case, or out of phase for the attenuation case. Comparisons with wind tunnel measurements show that phenomenologically similar dynamics occur at higher Reynolds number. Finally, we show that qualitatively similar phenomena occur during both surging and plunging.

JFM classification

Aerodynamics: Aerodynamics Wakes/Jets: Separated flows Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 237 - 253
Check for updates
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andro, J. Y. & Jacquin, L. 2009 Frequency effects on the aerodynamic mechanisms of a heaving airfoil in a forward flight configuration. Aerosp. Sci. Technol. 13 (1), 71–80.Google Scholar
Baik, Y. S., Bernal, L. P., Granlund, K. & Ol, M. 2012 Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J. Fluid Mech. 709, 37–68.CrossRefGoogle Scholar
Boyland, P. L. 1986 Bifurcations of circle maps: Arnol’d tongues, bistability and rotation intervals. Commun. Math. Phys. 106 (3), 353–381.Google Scholar
Calderon, D. E., Wang, Z. & Gursul, I. 2013 Lift-enhancing vortex flows generated by plunging rectangular wings with small amplitude. AIAA J. 51 (12), 2953–2964.Google Scholar
Choi, J., Colonius, T. & Williams, D.2013 Dynamics and energy extraction of a surging and plunging airfoil at low Reynolds number. AIAA Paper 2013-0672.Google Scholar
Cleaver, D. J., Wang, Z. & Gursul, I. 2012 Bifurcating flows of plunging aerofoils at high strouhal numbers. J. Fluid Mech. 708, 349–376.Google Scholar
Cleaver, D. J., Wang, Z. & Gursul, I. 2013 Investigation of high-lift mechanisms for a flat-plate airfoil undergoing small-amplitude plunging oscillations. AIAA J. 51 (4), 968–980.Google Scholar
Cleaver, D. J., Wang, Z., Gursul, I. & Visbal, M. R. 2011 Lift enhancement by means of small-amplitude airfoil oscillations at low Reynolds numbers. AIAA J. 49 (9), 2018–2033.Google Scholar
Colonius, T. & Taira, K. 2008 A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. Comput. Meth. Appl. Mech. Engng 197 (25–28), 2131–2146.Google Scholar
Denny, M. 2009 Dynamic soaring: aerodynamics for albatrosses. Eur. J. Phys. 30, 75–84.Google Scholar
Dickinson, M. H. & Gotz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Expl Biol. 174, 45–64.Google Scholar
Ellington, C. P., Van Den Berg, C., Willmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.Google Scholar
Fage, A. & Johansen, F. C. 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. R. Soc. Lond. A 116 (773), 170–197.Google Scholar
Graftieaux, L., Michard, M. & Grosjean, N. 2001 Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12 (9), 1422–1429.Google Scholar
Granlund, K., Monnier, B., Ol, M. & Williams, D. 2014 Airfoil longitudinal gust response in separated vs. attached flows. Phys. Fluids 26 (2), 027103.Google Scholar
Greenberg, J. M.1947 Airfoil in sinusoidal motion in a pulsating stream. NACA Tech Rep. 1326.Google Scholar
Gursul, I. & Ho, C. M. 1992 High aerodynamic loads on an airfoil submerged in an unsteady stream. AIAA J. 30 (4), 1117–1119.Google Scholar
Gursul, I., Lin, H. & Ho, C. M. 1994 Effects of time scales on lift of airfoils in an unsteady stream. AIAA J. 32 (4), 797–801.CrossRefGoogle Scholar
Huang, R. F. & Lin, C. L. 1995 Vortex shedding and shear-layer instability of wing at low-Reynolds numbers. AIAA J. 33 (8), 1398–1403.Google Scholar
Jones, K. D., Dohring, C. M. & Platzer, M. F.1996 Wake structures behind plunging airfoils: a comparison of numerical and experimental results. AIAA Paper 1996-78.CrossRefGoogle Scholar
von Karman, T. & Sears, W. R. 1938 Airfoil theory for non-uniform motion. J. Aeronaut. Sci. 5 (10), 379–390.CrossRefGoogle Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441–469.CrossRefGoogle Scholar
Langelaan, J. W. 2009 Gust energy extraction for mini and micro uninhabited aerial vehicles. J. Guid. Control Dyn. 32 (2), 463–472.Google Scholar
Lewin, G. C. & Haj-Hariri, H. 2003 Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 492, 339–362.Google Scholar
Lissaman, P.2005 Wind energy extraction by birds and flight vehicles. AIAA Paper 2005-241.CrossRefGoogle Scholar
Lissaman, P. B. S. & Patel, C. K.2007 Neutral energy cycles for a vehicle in sinusoidal and turbulent vertical gusts. AIAA Paper 2007-863.Google Scholar
Munday, P. M. & Taira, K. 2013 On the lock-on of vortex shedding to oscillatory actuation around a circular cylinder. Phys. Fluids 25, 013601.Google Scholar
Pesavento, U. & Wang, Z. J. 2009 Flapping wing flight can save aerodynamic power compared to steady flight. Phys. Rev. Lett. 103 (11), 118102.Google Scholar
Rival, D. E., Kriegseis, J., Schaub, P., Widmann, A. & Tropea, C.2013 A criterion for vortex separation on unsteady aerodynamic profiles. AIAA Paper 2013-836.Google Scholar
Sreenivasan, K. R., Strykowski, P. J. & Olinger, D. J. 1987 Hopf bifurcation, Landau equation, and vortex shedding behind circular cylinders. In Forum on Unsteady Flow Separation, ASME FED, vol. 52, pp. 1–13.Google Scholar
Taira, K. & Colonius, T. 2007 The immersed boundary method: a projection approach. J. Comput. Phys. 225 (2), 2118–2137.Google Scholar
Tchieu, A. A. & Leonard, A. 2011 A discrete-vortex model for the arbitrary motion of a thin airfoil with fluidic control. J. Fluids Struct. 27 (5–6), 680–693.CrossRefGoogle Scholar
Theodorsen, T.1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Tech Rep. (496).Google Scholar
Wang, Z. J. 2005 Dissecting insect flight. Annu. Rev. Fluid Mech. 37, 183–210.Google Scholar
Weimerskirch, H., Chastel, O., Barbraud, C. & Tostain, O. 2003 Flight performance: frigatebirds ride high on thermals. Nature 421, 333–334.Google Scholar
Young, J. & Lai, J. C. S. 2007 Vortex lock-in phenomenon in the wake of a plunging airfoil. AIAA J. 45 (2), 485–490.Google Scholar