Abstract
The influence of trailing edge shape and Strouhal number on the performance and wakes of bio-inspired pitching panels is investigated. Measurements of thrust and efficiency show that positive mean thrust and efficiency only develop for panels of reduced aspect ratio that have straight or pointed trailing edges, and high aspect ratio panels with forked trailing edges fail to produce positive mean thrust. Wake behaviors reveal that forked panels can produce strong trailing edge vortices while minimizing the three-dimensional effects of tip vortices, yet still do not generate positive mean thrust. Regardless of planform, the time-averaged wake contains one or more jets of surplus streamwise momentum when Strouhal number is large enough. As Strouhal number and trailing edge convexity increase, streamwise momentum in the time-averaged wake grows, and different jet structures may arise. Multiple jets of large inclination angles can be present during high performance, and single or dual jets of negligible or small inclination angles may be present during degraded performance. Just as recent work has demonstrated that direct connections between time-varying vortex patterns and mean performance are difficult to establish, caution must be used when connecting time-averaged jet structures to performance characteristics.
Similar content being viewed by others
Availability of data and materials
The authors are not making data, code, or materials publicly available, but they may be provided on a case-by-case basis upon reasonable request.
References
Andersen A, Bohr T, Schnipper T, Walther JH (2017) Wake structure and thrust generation of a flapping foil in two-dimensional flow. J Fluid Mech 812:R4
Ayancik F, Zhong Q, Quinn DB, Brandes A, Bart-Smith H, Moored KW (2019) Scaling laws for the propulsive performance of three-dimensional pitching propulsors. J Fluid Mech 871:1117–1138
Ayancik F, Fish FE, Moored KW (2020) Three-dimensional scaling laws of cetacean propulsion characterize the hydrodynamic interplay of flukes’ shape and kinematics. J R Soc Interface 17(163):20190655
Bandyopadhyay PR, Beal DN, Menozzi A (2008) Biorobotic insights into how animals swim. J Exp Biol 211:206–214
Bohl DG, Koochesfahani MM (2009) Mtv measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J Fluid Mech 620:63–88
Boschitsch BM, Dewey PA, Smits AJ (2014) Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys Fluids 26(5):051901
Buchholz JHJ, Smits AJ (2008) The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J Fluid Mech 603:331–365
Buchholz JH, Green MA, Smits AJ (2011) Scaling the circulation shed by a pitching panel. J Fluid Mech 688:591–601
Carr ZR, DeVoria AC, Ringuette MJ (2015) Aspect-ratio effects on rotating wings: circulation and forces. J Fluid Mech 767:497–525
Corfield S, Hillenbrand C (2003) Technology and applications of underwater autonomous vehicles. In: Chapter Defence applications for unmanned underwater vehicles. Taylor and Francis, London, pp 161–178
Dabiri JO (2009) Optimal vortex formation as a unifying priciple in biological propulsion. Annu Rev Fluid Mech 41:17–33
Danson EFS (2003) Technology and applications of autonomous underwater vehicles. In: Chapter AUV tasks in the offshore industry. Taylor and Francis, London, pp 127–138
Das A, Shukla RK, Govardhan RN (2016) Existence of a sharp transition in the peak propulsive efficiency of a low-re pitching foil. J Fluid Mech 800:307–326
David MJ, Govardhan R, Arakeri J (2017) Thrust generation from pitching foils with flexible trailing edge flaps. J Fluid Mech 828:70–103
DeVoria AC (2013) On the flow generated by rotating flat plates of low aspect ratio. PhD thesis, State University of New York at Buffalo
DeVoria AC, Ringuette MJ (2012) Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins. Exp Fluids 52:441–462
Dong H, Mittal R, Najjar F (2006) Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J Fluid Mech 566:309–343
Dong H, Bozkurttas M, Mittal R, Madden P, Lauder G (2010) Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J Fluid Mech 645:345–373
Feilich KL, Lauder GV (2015) Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion. Bioinspir Biomim 10(3):036002
Floryan D, Buren TV, Rowley C, Smits A (2017) Scaling the propulsive performance of heaving and pitching airfoils. J Fluid Mech 822(386):386–397
Floryan D, Van Buren T, Smits AJ (2020) Swimmers’ wake structures are not reliable indicators of swimming performance. Bioinspir Biomim 15(2):024001
Garrick IE (1936) Propulsion of a flapping and oscillating airfoil. NACA report. 567
Gazzola M, Argentina M, Mahadevan L (2014) Scaling macroscopic aquatic locomotion. Nat Phys 10(10):758–761
Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140
Godoy-Diana R, Aider JL, Wesfreid JE (2008) Transitions in the wake of a flapping foil. Phys Rev E 77(1):016308
Gong C, Han J, Yuan Z, Fang Z, Chen G (2019) Numerical investigation of the effects of different parameters on the thrust performance of three dimensional flapping wings. Aerosp Sci Technol 84:431–445
Hemmati A, Van Buren T, Smits AJ (2019) Effects of trailing edge shape on vortex formation by pitching panels of small aspect ratio. Phys Rev Fluids 4(3):033101
Kim D, Gharib M (2011) Characteristics of vortex formation and thrust performance in drag-based paddling propulsion. J Exp Biol 214(13):2283–2291
King JT, Green M (2022) Experimental investigation into the time-varying propulsive performance and unsteady wakes of bio-inspired pitching panels. In: AIAA AVIATION 2022 forum
Koochesfahani M (1989) Vortical patterns in the wake of an oscillating foil. AIAA J 27(9):1200–1205
Lee J, Park YJ, Cho KJ, Kim D, Kim HY (2017) Hydrodynamic advantages of a low aspect-ratio flapping foil. J Fluids Struct 71:70–77
Li G, Luodin Z, Xy Lu (2012) Numerical studies on locomotion performance of fish-like tail fins. J Hydrodyn Ser. B 24(4):488–495
Lighthill MJ (1971) Large-amplitude elongated-body theory of fish locomotion. Proc R Soc Lond. Ser B. Biol Sci 179(1055):125–138
Lighthill MJ (1969) Hydromechanics of aquatic animal propulsion. Annu Rev Fluid Mech 1:413–446
Mackowski A, Williamson C (2015) Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J Fluid Mech 765:524–543
Magnuson JJ (1978) Fish physiology volume VII locomotion. In: Chapter locomotion by Scombrid Fishes: hydromechanics, morphology, and behavior. Academic Press, pp 239–313
Milano M, Gharib M (2005) Uncovering the physics of flapping flat plates with artificial evolution. J Fluid Mech 534:403–409
Moored KW, Dewey PA, Smits A, Haj-Hariri H (2012) Hydrodynamic wake resonance as an underlying principle of efficient unsteady propulsion. J Fluid Mech 708:329–348
Moored KW, Quinn DB (2019) Inviscid scaling laws of a self-propelled pitching airfoil. AIAA Journal 57(9):3686–3700
Mueller TJ, DeLaurier JD (2003) Aerodynamics of small vehicles. Annu Rev Fluid Mech 35:89–111
Nursall JR (1958) The caudal fin as a hyrdofoil. Evolution 12(1):116–120
Prasad AK, Jensen K (1995) Scheimpflug stereocamera for particle image velocimetry in liquid flows. Appl Opt 34(30):7092–7099
Raffel M, Willert CE, Wereley, ST, Kompenhans J (2007) Particle image velocimetry: a practical guide. Springer
Rival D, Prangemeier T, Tropea C (2009) The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight. Exp Fluids 46:823–833
Roper D, Sharma S, Sutton R, Culverhouse P (2010) A review of developments towards biologically inspired propulsion systems for autonomous underwater vehicles. Proc IMechE 225:77–96
Saffman P (1992) Vortex dynamics. Cambridge monographs on mechanics and applied mathematics. Cambridge University Press
Senturk U, Smits AJ (2018) Numerical simulations of the flow around a square pitching panel. J Fluids Struct 76:454–468
Siddall R, Kovac M (2014) Launching the aquamav: bioinspired design for aerial-aquatic robotic platforms. Bioinspir Biomim 9:031001
Smits AJ (2019) Undulatory and oscillatory swimming. J Fluid Mech 874:P1
Taylor GK, Nudds RL, Thomas ALR (2003) October. Flying and swimming animals cruise at a strouhal number tuned for high power efficiency. Nature 425:707–711
Triantafyllou G, Triantafyllou M, Grosenbaugh M (1993) Optimal thrust development in oscillating foils with application to fish propulsion. J Fluids Struct 7:205–224
Tytell ED (2006) Median fin function in bluegill sunfish Lepomis macrochirus: streamwise vortex structure during steady swimming. J Exp Biol 209(8):1516–1534
Van Buren T, Floryan D, Brunner D, Senturk U, Smits AJ (2017) Impact of trailing edge shape on the wake and propulsive performance of pitching panels. Phys Rev Fluids 2(1):014702
Van Buren T, Floryan D, Wei N, Smits AJ (2018) Flow speed has little impact on propulsive characteristics of oscillating foils. Phys Rev Fluids 3:013103
Wu TYT (1971) Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J Fluid Mech 46(2):337–355
Zhang C, Huang H, Lu XY (2020) Effect of trailing-edge shape on the self-propulsive performance of heaving flexible plates. J Fluid Mech 887(A7)
Acknowledgements
This work was supported by ONR Award No. N00014-17-1-2759. The information, data, or work presented herein was funded in part by an award from NYS Department of Economic Development (DED) through the Syracuse Center of Excellence. Any opinions, findings, conclusions, or recommendations expressed are those of the author(s) and do not necessarily reflect the views of the DED.
Funding
This work was supported by ONR Award No. N00014-17-1-2759 and in part by an award from NYS Department of Economic Development through the Syracuse Center of Excellence.
Author information
Authors and Affiliations
Contributions
Both authors contributed to the study. Justin King designed and performed the experiments, conducted the data analysis, and prepared the first draft of the manuscript; Melissa Green provided resources and feedback throughout. Both authors contributed to manuscript revisions and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflicts of interest or competing interests to declare that are relevant to the content of this article.
Ethical approval
The work presented here by the authors did not require ethics approval or consent to participate.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
King, J.T., Green, M.A. The influence of trailing edge shape on the wake circulation and time-averaged wake of bio-inspired pitching panels. Exp Fluids 64, 116 (2023). https://doi.org/10.1007/s00348-023-03655-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-023-03655-2