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Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

Published online by Cambridge University Press:  06 March 2009

KUNIHIKO TAIRA  and
TIM COLONIUS
KUNIHIKO TAIRA*
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
*
†Present address for correspondence: Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA. Email: ktaira@princeton.edu.
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Abstract

Three-dimensional flows over impulsively translated low-aspect-ratio flat plates are investigated for Reynolds numbers of 300 and 500, with a focus on the unsteady vortex dynamics at post-stall angles of attack. Numerical simulations, validated by an oil tow-tank experiment, are performed to study the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate. Immediately following the impulsive start, the separated flows create wake vortices that share the same topology for all aspect ratios. At large time, the tip vortices significantly influence the vortex dynamics and the corresponding forces on the wings. Depending on the aspect ratio, angle of attack and Reynolds number, the flow at large time reaches a stable steady state, a periodic cycle or aperiodic shedding. For cases of high angles of attack, an asymmetric wake develops in the spanwise direction at large time. The present results are compared to higher Reynolds number flows. Some non-rectangular planforms are also considered to examine the difference in the wakes and forces. After the impulsive start, the time at which maximum lift occurs is fairly constant for a wide range of flow conditions during the initial transient. Due to the influence of the tip vortices, the three-dimensional dynamics of the wake vortices are found to be quite different from the two-dimensional von Kármán vortex street in terms of stability and shedding frequency.

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Papers
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Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 187 - 207
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Ahuja, S., Rowley, C. W., Kevrekidis, I. G., Colonius, T. & Tadmor, G. 2007 Low-dimensional models for control of leading-edge vortices: equilibria and linearized models. AIAA Paper 2007-709.Google Scholar
Anderson, J. D. 1999 Aircraft Performance and Design. McGraw-Hill.Google Scholar
Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412, 729–733.Google Scholar
Birch, J. M., Dickson, W. B. & Dickinson, M. H. 2004 Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers. J. Exp. Biol. 207, 1063–1072.CrossRefGoogle Scholar
Blondeaux, P., Fornarelli, F., Guglielmini, L., Triantafyllou, M. S. & Verzicco, R. 2005 Numerical experiments on flapping foils mimicking fisk-like locomotion. Phys. Fluids 17, 113601.CrossRefGoogle Scholar
Bos, F. M., Lentink, D., Van Oudheusden, B. W. & Bijl, H. 2008 Influence of wing kinematics on aerodynamic performance in hovering insect flight. J. Fluid Mech. 594, 341–368.CrossRefGoogle Scholar
Braza, M., Faghani, D. & Persillon, H. 2001 Successive stages and role of natural vortex dislocations in three-dimensional wake transition. J. Fluid Mech. 439, 1–41.CrossRefGoogle Scholar
Buchholz, J. H. J. & Smits, A. J. 2006 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 433–443.CrossRefGoogle Scholar
Carr, L. W. 1988 Progress in analysis and prediction of dynamic stall. J. Aircraft 25 (1), 6–17.CrossRefGoogle Scholar
Cosyn, P. & Vierendeels, J. 2006 Numerical investigation of low-aspect-ratio wings at low Reynolds numbers. J. Aircraft 43 (3), 713–722.CrossRefGoogle Scholar
Dickinson, M. H. & Götz, K. G. 1993 Unsteady aerodynamic performance of model wings at low Reynolds numbers. J. Exp. Biol. 174, 45–64.CrossRefGoogle Scholar
Dickson, W. B. & Dickinson, M. H. 2004 The effect of advance ratio on the aerodynamics of revolving wings. J. Exp. Biol. 207, 4269–4281.CrossRefGoogle ScholarPubMed
Dong, H., Mittal, R. & Najjar, F. M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 1999 Locomotor forces on a swimming fish: three dimensional vortex wake dynamics quantified using digital particle image velocimetry. J. Exp. Biol. 202, 2393–2412.CrossRefGoogle ScholarPubMed
von Ellenrieder, K. D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138.CrossRefGoogle 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.CrossRefGoogle Scholar
Freymuth, P., Finaish, F. & Bank, W. 1987 Further visualization of combined wing tip and starting vortex systems. AIAA J. 25 (9), 1153–1159.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Gursul, I., Gordnier, R. & Visbal, M. 2005 Unsteady aerodynamics of nonslender delta wings. Prog. Aero. Sci. 41, 515–557.CrossRefGoogle Scholar
Hamdani, H. & Sun, M. 2000 Aerodynamic forces and flow structures of an airfoil in some unsteady motions at small Reynolds number. Acta Mech. 145, 173–187.Google Scholar
Helmbold, H. B. 1942 Der unverwundene ellipsenflugel als tragende flanche. Jahrbuch 1942 der Deutch Luftfahrtforsch pp. I111–I113.Google Scholar
Hornung, H. 1989 Vorticity generation and transport. 10th Australasian fluid mechanics conference, Paper KS-3.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Technical Report CTR-S88. Center for Turbulent Research.Google Scholar
Jeon, D. & Gharib, M. 2004 On the relationship between the wake vortex formation process and cylinder wake vortex patterns. J. Fluid Mech. 519, 161–181.CrossRefGoogle Scholar
Liu, H. & Kawachi, K. 1998 A numerical study of insect flight. J. Comput. Phys. 146, 124–156.Google Scholar
Milano, M. & Gharib, M. 2005 Uncovering the physics of flapping flat plates with artificial evolution. J. Fluid Mech. 534, 403–409.Google Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.CrossRefGoogle Scholar
Mittal, S. & Tezduyar, T. E. 1995 Parallel finite element simulation of 3D incompressible fluid-structure interactions. Intl J. Numer. Meth. Fluids 21, 933–953.CrossRefGoogle Scholar
Parker, K., vonEllenrieder, K. D. Ellenrieder, K. D. & Soria, J. 2007 Morphology of the forced oscillatory flow past a finite-span wing at low Reynolds number. J. Fluid Mech. 571, 327–357.CrossRefGoogle Scholar
Pelletier, A. & Mueller, T. J. 2000 Low Reynolds number aerodynamics of low-aspect-ratio, thin/flat/cambered-plate wings. J. Aircraft 37 (5), 825–832.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numer. 11, 479–517.CrossRefGoogle Scholar
Pines, D. J. & Bohorquez, F. 2006 Challenges facing future micro-air-vehicle development. J. Aircraft 34 (2), 290–305.CrossRefGoogle Scholar
Poelma, C., Dickson, W. B. & Dickinson, M. H. 2006 Time-resolved reconstruction of the full velocity field aournd a dynamically-scaled flapping wing. Exp. Fluids 41, 213–225.Google Scholar
Pullin, D. I. & Wang, Z. J. 2004 Unsteady forces on an accelerating plate and application to hovering insect flight. J. Fluid Mech. 509, 1–21.Google Scholar
Ringuette, M. J., 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, 453–468.CrossRefGoogle Scholar
Sun, M. 2005 High-lift generation and power requirements of insect flight. Fluid Dyn. Res. 37, 21–39.CrossRefGoogle Scholar
Taira, K. 2008 The immersed boundary projection method and its application to simulation and control of flows around low-aspect-ratio wings. PhD thesis, California Institute of Technology.Google Scholar
Taira, K. & Colonius, T. 2007 The immersed boundary method: a projection approach. J. Comput. Phys. 225, 2118–2137.CrossRefGoogle Scholar
Taira, K., Dickson, W. B., Colonius, T., Dickinson, M. H. & Rowley, C. W. 2007 Unsteadiness in flow over a flat plate at angle-of-attack at low Reynolds numbers. AIAA Paper 2007-710.Google Scholar
Torres, G. E. & Mueller, T. J. 2004 Low-aspect-ratio wing aerodynamics at low Reynolds numbers. AIAA J. 42 (5), 865–873.CrossRefGoogle Scholar
Usherwood, J. R. & Ellington, C. P. 2002 The aerodynamics of revolving wings, I model hawkmoth wings. J. Exp. Biol. 205, 1547–1564.Google Scholar
Wang, Z. J. 2000 a Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 85 (10), 2216–2219.CrossRefGoogle Scholar
Wang, Z. J. 2000 b Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323–341.CrossRefGoogle Scholar
Wang, Z. J. 2004 The role of drag in insect hovering. J. Exp. Biol. 207, 4147–4155.Google Scholar
Winkelmann, A. E. & Barlow, J. B. 1980 Flowfield model for a rectangular planform wing beyond stall. AIAA J. 18 (8), 1006–1007.CrossRefGoogle Scholar
Yon, S. A. & Katz, J. 1998 Study of the unsteady flow features on a stalled wing. AIAA J. 36 (3), 305–312.Google Scholar
Zhu, Q., Wolfgang, M. J., Yue, D. K. P. & Triantafyllou, M. S. 2002 Three-dimensional flow structures and vorticity control in fish-like swimming. J. Fluid Mech. 468, 1–28.CrossRefGoogle Scholar