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Unsteady pitching flat plates

Published online by Cambridge University Press:  26 September 2013

Kenneth O. Granlund*
Affiliation:
Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, USA
Michael V. Ol
Affiliation:
Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, USA
Luis P. Bernal
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
Email address for correspondence: kenneth.granlund@wpafb.af.mil

Abstract

Direct force measurements and qualitative flow visualization were used to compare flow field evolution versus lift and drag for a nominally two-dimensional rigid flat plate executing smoothed linear pitch ramp manoeuvres in a water tunnel. Non-dimensional pitch rate was varied from 0.01 to 0.5, incidence angle from 0 to 90°, and pitch pivot point from the leading to the trailing edge. For low pitch rates, the main unsteady effect is delay of stall beyond the steady incidence angle. Shifting the time base to account for different pivot points leads to collapse of both lift/drag history and flow field history. For higher rates, a leading edge vortex forms; its history also depends on pitch pivot point, but linear shift in time base is not successful in collapsing lift/drag history. Instead, a phenomenological algebraic relation, valid at the higher pitch rates, accounts for lift and drag for different rates and pivot points, through at least 45° incidence angle.

Type
Rapids
Creative Commons
This is a work of the U.S. Government and is not subject to copyright protection in the United States.
Copyright
©2013 Cambridge University Press.

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References

Baik, Y., Bernal, L., Granlund, K. & Ol, M. 2012 Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J. Fluid Mech. 709, 3768.Google Scholar
Barlow, J. B., Rae, W. H. B., Rae, W. H. & Pope, A. 1999 Low-Speed Wind-Tunnel Testing, 3rd edn. Wiley.Google Scholar
Carruthers, A., Thomas, A. & Taylor, G. 2007 Automatic aeroelastic devices in the wings of a steppe eagle aquila nipalensis . J. Expl Biol. 210, 41364149.CrossRefGoogle ScholarPubMed
Chakravarthy, A., Grant, D. T. & Lind, R. 2012 Time-varying dynamics of a micro air vehicle with variable-sweep morphing. J. Guid. Control Dyn. 35 (3), 890903.CrossRefGoogle Scholar
Dabiri, J. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 1733.Google Scholar
Eldredge, J. D., Toomey, J. & Medina, A. 2010 On the roles of chord-wise flexibility in a flapping wing with hovering kinematics. J. Fluid Mech. 659, 94115.CrossRefGoogle Scholar
Garmann, D. & Visbal, M. 2011 Numerical investigation of transitional flow over a rapidly pitching plate. Phys. Fluids 23 (9).CrossRefGoogle Scholar
Gendrich, C., Koochesfahani, M. & Visbal, M. 1995 Effects of initial acceleration of the flow field development around rapidly pitching aerofoils. J. Fluids Engng 117, 4549.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.Google Scholar
Glauert, H. 1947 The Elements of Aerofoil and Airscrew Theory, 2nd edn. Cambridge University Press.Google Scholar
Graham, G. M. & Yeow, K. F. 1990 Two-dimensional post stall maneuver of a NACA 0015 aerofoil at high pitching rates. AIAA Paper 1990-2810.Google Scholar
Harper, P. W. & Flanigan, R. E. 1950 The effect of rate of change of angle of attack on the maximum lift of a small model. NACA TN-2061.Google Scholar
Jones, A. R. & Babinsky, H. 2011 Reynolds number effects on leading edge vortex development on a waving wing. Exp. Fluids 51 (1), 197210.CrossRefGoogle Scholar
Koochesfahani, M. 1989 Vortical patterns in the wake of an oscillating aerofoil. AIAA J. 27 (9), 12001205.Google Scholar
Koochesfahani, M. & Smiljanovski, V. 1993 Initial acceleration effects on flow evolution around aerofoils pitching to high angles of attack. AIAA J. 31 (8), 15291531.Google Scholar
Kurosaka, M., Christensen, W., Tirres, L. & Wohlman, A. 1988 Crossflow transport induced by vortices. AIAA J. 26, 14031405.Google Scholar
Leishman, J. G. 2006 Principles of Helicopter Aerodynamics, 2nd edn. Cambridge University Press.Google Scholar
McCroskey, W. J., Carr, L. W. & McAlister, K. W. 1976 Dynamic stall experiments on oscillating aerofoils. AIAA J. 14 (1), 5763.Google Scholar
McGowan, G. Z., Granlund, K. O., Ol, M. V., Gopalarathnam, A. & Edwards, J. 2011 Investigations of lift-based pitch-plunge equivalence for aerofoils at low Reynolds numbers. AIAA J. 49 (7), 15111524.Google Scholar
Ol, M. V., Altman, A., Eldredge, J., Garmann, D. & Lian, Y. 2010 Summary of progress on pitching plates: canonical problems in low-Re unsteady aerodynamics. AIAA Paper 2010-1085.Google Scholar
Ol, M. V., Bernal, L. P., Kang, C.-K. & Shyy, W. 2009 Shallow and deep dynamic stall for flapping low Reynolds number aerofoils. Exp. Fluids 46 (5), 883901.CrossRefGoogle Scholar
Reich, G., Eastep, F., Altman, A. & Albertani, R. 2011 Transient poststall aerodynamic modelling for extreme maneuvers in micro air vehicles. J. Aircraft 48 (2), 403411.CrossRefGoogle Scholar
Ringuette, M., Milano, M. & Gharib, M. 2007 Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J. Fluid Mech. 581, 453468.Google Scholar
Strickland, J. H. & Graham, G. M. 1987 Force coefficients for a NACA 0015 aerofoil undergoing constant pitch rate motions. AIAA J. 54 (4), 622624.Google Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA R-496.Google Scholar
Visbal, M. & Shang, J. K. 1989 Investigation of the flow structure around a rapidly pitching aerofoil. AIAA J. 27, 10441051.Google Scholar
Yu, H.-T. & Bernal, L. P. 2013 Effect of pivot point on aerodynamic force and vortical structure of pitching flat plate wings. AIAA Paper 2013-0792.CrossRefGoogle Scholar

Granlund et al. supplementary movie

Flowfield of pitching plate, pivoting around the leading edge at reduced frequency of K=0.2

Download Granlund et al. supplementary movie(Video)
Video 9.1 MB

Granlund et al. supplementary movie

Flowfield of pitching plate, pivoting around the trailing edge at reduced frequency of K=0.2

Download Granlund et al. supplementary movie(Video)
Video 3.9 MB

Granlund et al. supplementary movie

Flowfield of pitching plate, pivoting around the leading edge at reduced frequency of K=0.03

Download Granlund et al. supplementary movie(Video)
Video 7.8 MB

Granlund et al. supplementary movie

Flowfield of pitching plate, pivoting around the trailing edge at reduced frequency of K=0.03

Download Granlund et al. supplementary movie(Video)
Video 6.4 MB