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Estimating lift from wake velocity data in flapping flight

Published online by Cambridge University Press:  15 April 2019

Shizhao Wang Open the ORCID record for Shizhao Wang [Opens in a new window] ,
Guowei He Open the ORCID record for Guowei He [Opens in a new window]  and
Tianshu Liu Open the ORCID record for Tianshu Liu [Opens in a new window]
Shizhao Wang
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Guowei He
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Tianshu Liu*
Affiliation:
LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China Mechanical and Aerospace Engineering, Western Michigan University, Kalamazoo, MI 49008, USA
*
†Email address for correspondence: [email protected]
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Abstract

The application of the Kutta–Joukowski (KJ) theorem to estimating the lift of a flying animal based on wake velocity fields often leads to significant underprediction of the lift, which is known as the wake momentum paradox. This work attempts to answer the puzzling question on whether the KJ theorem is legitimate in its use for complex viscous unsteady wakes generated by flapping wings. The limitations in applying the KJ theorem to flapping wings are quantitatively examined through numerical simulations of viscous incompressible flows over three flapping wing models. The three flapping wing models studied in this work are a flapping wing with a fixed wingspan, a flapping wing with a dynamically changing wingspan and a dihedral flapping wing. The KJ theorem fails to give a satisfactory prediction of the time-averaged lift unless an effective span length is correctly computed. We propose a wake-sectional Kutta–Joukowski (WS-KJ) model to predict the time-averaged lift, where the effective span length is computed based on the time-averaged distance between the streamwise vorticity centroids in the right and left half sides of the Trefftz plane. The WS-KJ model incorporates the spatial evolutionary effects of the complex vortex structures in the wake and significantly improves the prediction of the time-averaged lift. The physical foundation for such improvement is explored. In addition, the time-dependent amplitude and phase changes of the unsteady lift are discussed as the fluid acceleration effect.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 501 - 537
Copyright
© 2019 Cambridge University Press 

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References

del Alamo, J. C. & Jimenez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26.10.1017/S0022112009991029Google Scholar
Blondeaux, P., Fornarelli, F., Guglielmini, L., Triantafyllou, M. S. & Verzicco, R. 2005 Numerical experiments on flapping foils mimicking fish-like locomotion. Phys. Fluids 17, 113601.10.1063/1.2131923Google Scholar
Buchholz, J. H. & Smits, A. J. 2005 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 564, 433–443.10.1017/S0022112005006865Google Scholar
Chang, C.-C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. Lond. Ser. A 437 (1901), 517–525.10.1098/rspa.1992.0077Google Scholar
Chopra, M. G. 1976 Large-amplitude lunate-tail theory of fish locomotion. J. Fluid Mech. 74 (MAR9), 161–182.10.1017/S0022112076001742Google Scholar
Dabiri, J. O. 2005 On the estimation of swimming and flying forces from wake measurements. J. Exp. Biol. 208, 3519–3532.10.1242/jeb.01813Google Scholar
Dong, H., Mittal, R. & Najjar, F. M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.10.1017/S002211200600190XGoogle Scholar
Gennaretti, M., Salvatore, F. & Morino, L. 1996 Forces and moments in incompressible quasi-potential flows. J. Fluids Struct. 10 (3), 281–303.10.1006/jfls.1996.0017Google Scholar
Guan, Z. & Yu, Y. 2014 Aerodynamic mechanism of forces generated by twisting model-wing in bat flapping flight. Appl. Math. Mech. Engl. Ed. 35 (12), 1607–1618.10.1007/s10483-014-1882-6Google Scholar
Guan, Z. & Yu, Y. 2015 Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat. Appl. Math. Mech. Engl. Ed. 36 (5), 669–680.10.1007/s10483-015-1931-7Google Scholar
Gutierrez, E., Quinn, D. B., Chin, D. D. & Lentink, D. 2016 Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics. Bioinspir. Biomim. 12, 016004.10.1088/1748-3190/12/1/016004Google Scholar
He, G., Jin, G. & Yang, Y. 2017 Space–time correlations and dynamic coupling in turbulent flows. Annu. Rev. Fluid. Mech. 49 (1), 51–70.10.1146/annurev-fluid-010816-060309Google Scholar
Hedenstrom, A., Muijres, F. T., Busse, R., Johansson, L. C., Winter, Y. & Spedding, G. R. 2009 High-speed stereo DPIV measurement of wakes of two bat species flying freely in a wind tunnel. Exp. Fluids 46 (5), 923–932.10.1007/s00348-009-0634-5Google Scholar
Henningsson, P. & Hedenstrom, A. 2011 Aerodynamics of gliding flight in common swifts. J. Exp. Biol. 214, 382–393.10.1242/jeb.050609Google Scholar
Hu, H., Clemons, L. & Igarashi, H. 2011 An experimental study of the unsteady vortex structures in the wake of a root-fixed flapping wing. Exp. Fluids 51 (2), 347–359.10.1007/s00348-011-1052-zGoogle Scholar
Hubel, T. Y., Hristov, N. I., Swartz, S. M. & Breuer, K. S. 2009 Time-resolved wake structure and kinematics of bat flight. Exp. Fluids 46, 933–943.10.1007/s00348-009-0624-7Google Scholar
Hubel, T. Y., Riskin, D. K., Swartz, S. M. & Breuer, K. S. 2010 Wake structure and wing kinematics: the flight of the lesser dog-faced fruit bat, Cynopterus brachyotis . J. Exp. Biol. 213 (20), 3427–3440.10.1242/jeb.043257Google Scholar
Kim, D., Hussain, F. & Gharib, M. 2013 Vortex dynamics of clapping plates. J. Fluid Mech. 714, 5–23.10.1017/jfm.2012.445Google Scholar
Korotkin, A. 2009 Added Masses of Ship Structures. Springer.10.1007/978-1-4020-9432-3Google Scholar
Lee, J., Park, Y. J., Jeong, U., Cho, K. J. & Kim, H. Y. 2013 Wake and thrust of an angularly reciprocating plate. J. Fluid Mech. 720, 545–557.10.1017/jfm.2013.50Google Scholar
Li, G. J. & Lu, X. Y. 2012 Force and power of flapping plates in a fluid. J. Fluid Mech. 712, 598–613.10.1017/jfm.2012.443Google Scholar
Liu, T., Wang, S., Zhang, X. & He, G. 2015 Unsteady thin-airfoil theory revisited: application of a simple lift formula. AIAA J. 53, 1492–1502.10.2514/1.J053439Google Scholar
Muijres, F. T., Bowlin, M. S., Johansson, L. C. & Hedenstrom, A. 2012 Vortex wake, downwash distribution, aerodynamic performance and wingbeat kinematics in slow-flying pied flycatchers. J. R. Soc. Interface 9, 292–303.10.1098/rsif.2011.0238Google Scholar
Muijres, F. T., Johansson, L. C., Barfield, R., Wolf, M., Spedding, G. R. & Hedenstrom, A. 2008 Leading-edge vortex improves lift in slow-flying bats. Science 319, 1250–1253.10.1126/science.1153019Google Scholar
Muijres, F. T., Spedding, G. R., Winter, Y. & Hedenstrom, A. 2011 Actuator disk model and span efficiency of flapping flight in bats based on time-resolved PIV measurements. Exp. Fluids 51 (2), 511–525.10.1007/s00348-011-1067-5Google Scholar
Noca, F., Shiels, D. & Jeon, D. 1997 Measuring instantaneous fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct. 11 (3), 345–350.10.1006/jfls.1997.0081Google Scholar
Park, H., Park, Y.-J., Lee, B., Cho, K.-J. & Choi, H. 2016 Vortical structures around a flexible oscillating panel for maximum thrust in a quiescent fluid. J. Fluids Struct. 67, 241–260.10.1016/j.jfluidstructs.2016.10.004Google Scholar
Pennycuick, C. J. 1968 Power requirements for horizontal flight in the pigeon Columba livia . J. Exp. Biol. 49, 527–555.Google Scholar
Rayner, J. M. V. 1979a Vortex theory of animal flight. Part 1. Vortex wake of a hovering animal. J. Fluid Mech. 91, 697–730.10.1017/S0022112079000410Google Scholar
Rayner, J. M. V. 1979b Vortex theory of animal flight. Part 2. Forward flight of birds. J. Fluid Mech. 91, 731–763.10.1017/S0022112079000422Google Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49 (4), 371–380.10.1002/sapm1970494371Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Sane, S. P. 2003 The aerodynamics of insect flight. J. Exp. Biol. 206 (23), 4191–4208.10.1242/jeb.00663Google Scholar
Sane, S. P. & Dickinson, M. H. 2002 The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. J. Exp. Biol. 205 (8), 1087–1096.Google Scholar
Shyy, W., Trizila, P., Kang, C.-K. & Aono, H. 2009 Can tip vortices enhance lift of a flapping wing? AIAA J. 47 (2), 289–293.10.2514/1.41732Google Scholar
Spedding, G. R. & Hedenstrom, A. 2009 PIV-based investigations of animal flight. Exp. Fluids 46 (5), 749–763.10.1007/s00348-008-0597-yGoogle Scholar
Spedding, G. R., Rosen, M. & Hedenstrom, A. 2003 A family of vortex wakes generated by a thrush nightingale in free flight in a wind tunnel over its entire natural range of flight speeds. J. Exp. Biol. 206, 2313–2344.10.1242/jeb.00423Google Scholar
Sun, M. 2014 Insect flight dynamics: stability and control. Rev. Mod. Phys. 86 (2), 615–646.10.1103/RevModPhys.86.615Google Scholar
Suzuki, K., Minami, K. & Inamuro, T. 2015 Lift and thrust generation by a butterfly-like flapping wing–body model: immersed boundary–lattice Boltzmann simulations. J. Fluid Mech. 767, 659–695.10.1017/jfm.2015.57Google Scholar
Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. 2003 Flying and swimming animals cruise at a strouhal number tuned for high power efficiency. Nature 425, 707–711.10.1038/nature02000Google Scholar
Theodorsen, T.1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Tech. Rep. 496.Google Scholar
Tian, X. D., Iriarte-Diaz, J., Middleton, K., Galvao, R., Israeli, E., Roemer, A., Sullivan, A., Song, A., Swartz, S. & Breuer, K. 2006 Direct measurements of the kinematics and dynamics of bat flight. Bioinspir. Biomim. 1, S10–S18.10.1088/1748-3182/1/4/S02Google Scholar
Waldman, R. M. & Breuer, K. S. 2012 Accurate measurement of streamwise vortices using dual-plane PIV. Exp. Fluids 53 (5), 1487–1500.10.1007/s00348-012-1368-3Google Scholar
Wang, S., He, G. & Zhang, X. 2013a Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation. Comput. Fluids 88, 210–224.10.1016/j.compfluid.2013.09.001Google Scholar
Wang, S., He, G. & Zhang, X. 2015a Lift enhancement on spanwise oscillating flat-plates in low-Reynolds-number flows. Phys. Fluids 27, 061901.10.1063/1.4922236Google Scholar
Wang, S. & Zhang, X. 2011 An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows. J. Comput. Phys. 230, 3479–3499.10.1016/j.jcp.2011.01.045Google Scholar
Wang, S., Zhang, X., He, G. & Liu, T. 2013b A lift formula applied to low-Reynolds-number unsteady flows. Phys. Fluids 25, 093605–22.10.1063/1.4821520Google Scholar
Wang, S., Zhang, X., He, G. & Liu, T. 2014 Lift enhancement by dynamically changing wingspan in forward flapping flight. Phys. Fluids 26, 061903.10.1063/1.4884130Google Scholar
Wang, S., Zhang, X., He, G. & Liu, T. 2015b Evaluation of lift formulas applied to low-Reynolds-number unsteady flows. AIAA J. 53, 161–175.10.2514/1.J053042Google Scholar
Wu, J., Liu, L. & Liu, T. 2018 Fundamental theories of aerodynamic force in viscous and compressible complex flows. Prog. Aerosp. Sci. 99, 27–63.10.1016/j.paerosci.2018.04.002Google Scholar
Wu, J. C. 1981 Theory for aerodynamic force and moment in viscous flows. AIAA J. 19 (4), 432–441.10.2514/3.50966Google Scholar
Wu, J. Z., Ma, H. Y. & Zhou, M. D. 2006 Vorticity and Vortex Dynamics. Springer.10.1007/978-3-540-29028-5Google Scholar
Yu, Y., Amandolese, X., Fan, C. & Liu, Y. 2018 Experimental study and modelling of unsteady aerodynamic forces and moment on flat plate in high amplitude pitch ramp motion. J. Fluid Mech. 846, 82–120.10.1017/jfm.2018.271Google Scholar
Yu, Y. L., Tong, B. G. & Ma, H. Y. 2003 An analytic approach to theoretical modeling of highly unsteady viscous flow excited by wing flapping in small insects. Acta Mechanica Sin. 19 (6), 508–516.Google Scholar
Zhang, J. 2017 Footprints of a flapping wing. J. Fluid Mech. 818, 1–4.10.1017/jfm.2017.173Google Scholar