Skip to main content Accessibility help
×
Home

Performance augmentation mechanism of in-line tandem flapping foils

  • L. E. Muscutt (a1), G. D. Weymouth (a2) and B. Ganapathisubramani (a1)

Abstract

The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing ( $S$ ) and phasing ( $\unicode[STIX]{x1D711}$ ) to be investigated over a range of non-dimensional frequencies (or Strouhal number, $St$ ). Results indicate that the hind foil can produce from no thrust to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flow fields indicates that high thrust occurs when the hind foil weaves between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the $S-\unicode[STIX]{x1D711}$ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered $(0.2\leqslant St\leqslant 0.5)$ . A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.

Copyright

Corresponding author

Email address for correspondence: luke@muscutt.org

References

Hide All
Akhtar, I., Mittal, R., Lauder, G. V. & Drucker, E. 2007 Hydrodynamics of a biologically inspired tandem flapping foil configuration. Theor. Comput. Fluid Dyn. 21, 155170.
Alexander, D. E. 1984 Unusual phase relationships between the forewings and hindwings in flying dragonflies. J. Expl Biol. 109, 379383.
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 4172.
Boschitsch, B. M., Dewey, P. A. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26, 131139.
Broering, T. M. & Lian, Y. 2010 Numerical investigation of energy extraction in a tendem flapping wing configuration. In 48th AIAA Aerospace Sciences Meeting.
Broering, T. M. & Lian, Y. 2012 The effect of phase angle and wing spacing on tandem flapping wings. Acta Mechanica Sin. 28, 15571571.
Broering, T. M., Lian, Y. & Henshaw, W. 2012 Numerical study of two flapping airfoils in tandem configuration. AIAA J. 50, 22952307.
Ellington, C. P. 1984a The aerodynamics of hovering insect flight i. The quasi-steady analysis. Phil. Trans. R. Soc. Lond. B 305 (1122), 115.
Ellington, C. P. 1984b The aerodynamics of hovering insect flight iv. Aerodynamic mechanisms. Phil. Trans. R. Soc. Lond. B 305 (1122), 79113.
Gong, W. Q., Jia, B. B. & Xi, G. 2015 Experimental study on mean thrust of two plunging wings in tandem. AIAA J. 53 (6), 16931705.
Gong, W. Q., Jia, B. B. & Xi, G. 2016 Experimental study on instantaneous thrust and lift of two plunging wings in tandem. Exp. Fluids 57, 8.
Gopalkrishnan, R., Triantafyllou, M. S., Triantafyllou, G. S. & Barrett, D. 1994 Active vorticity control in a shear flow using a flapping foil. J. Fluid Mech. 274, 121.
Jensen, M. 1956 Biology and Physics of locust flight iii. The aerodynamics of locust flight. Phil. Trans. R. Soc. Lond. B 239 (667), 511552.
Kinsey, T. & Dumas, G. 2012 Optimal tandem configuration for oscillating-foils hydrokinetic turbine. Trans. ASME J. Fluids Engng 134 (3), 031103.
Kumar, A. G. & Hu, H. 2011 An experimental investigation on the wake flow characteristics of tandem flapping wings. In 6th AIAA Theoretical Fluid Mechanics Conference.
Lian, Y., Broering, T. M., Hord, K. & Prater, R. 2014 The characterisation of tandem and corrugated wings. Prog. Aerosp. Sci. 65, 4169.
Maertens, A. P. & Triantafyllou, M. S. 2014 The boundary layer instability of a gliding fish helps rather than prevents object identification. J. Fluid Mech. 757, 179207.
Maertens, A. P. & Weymouth, G. D. 2015 Accurate cartesian-grid simulations of near-body flows at intermediate Reynolds numbers. Comput. Meth. Appl. Mech. Engng 283, 106129.
Nakata, T., Liu, H. & Bomphrey, R. J. 2015 A cfd-informed quasi-steady model of flapping-wing aerodynamics. J. Fluid Mech. 783, 323343.
Nudds, R. L., Taylor, G. K. & Thomas, A. L. R. 2004 Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds. Proc. R. Soc. Lond. 271, 20712076.
Platzer, M. F. & Jones, K. D. 2006 Flapping-wing aerodynamics: progress and challenges. AIAA J. 46 (9), 21362149.
Polet, D. T., Rival, D. E. & Weymouth, G. D. 2015 Unsteady dynamics of rapid perching manoeuvres. J. Fluid Mech. 767, 323341.
Read, D. A., Hover, F. S. & Triantafyllou, M. S. 2003 Forces on oscillating foils for propulsion and maneuvering. J. Fluids Struct. 17, 163183.
Rival, D., Hass, G. & Tropea, C. 2011 Recovery of energy from leading and trailing edge vortices in tandem airfoil configurations. J. Aircraft 48, 203211.
Sane, S. P. & Dickinson, M. H. 2002 The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. J. Expl Biol. 205, 10871096.
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 (6959), 707711.
Thomas, A. L. R., Taylor, G. K., Srygley, R. B., Nudds, R. L. & Bomphrey, R. J. 2004 Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating mechanism, controlled primarily via angle of attack. J. Expl Biol. 207, 42994323.
Triantafyllou, M. S., Tariantafyllou, G. S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3, 28362837.
Weis-Fogh, T. 1972 Energetics of hovering flight in hummingbirds and drosophila. J. Expl Biol. 56, 79104.
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Expl Biol. 59, 169230.
Weymouth, G. D. 2014 Chaotic rotation of a towed elliptical cylinder. J. Fluid Mech. 743, 385398.
Weymouth, G. D.2015 Towards real-time interactive computational fluid dynamics. arXiv:1510.06886 [physics.comp-ph].
Weymouth, G. D. & Yue, D. K. P. 2011 Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems. J. Comput. Phys. 230 (16), 62336247.
Weymouth, G. D. & Triantafyllou, M. S. 2012 Global vorticity shedding for a shrinking cylinder. J. Fluid Mech. 702, 470487.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Type Description Title
VIDEO
Movies

Muscutt et al. supplementary movie 1
Contour plot of instantaneous vorticity magnitude for single foil over one flapping cycle

 Video (643 KB)
643 KB
VIDEO
Movies

Muscutt et al. supplementary movie 2
Contour plot of instantaneous vorticity magnitude for tandem foil high-thrust case over one flapping cycle

 Video (1.1 MB)
1.1 MB
VIDEO
Movies

Muscutt et al. supplementary movie 3
Contour plot of instantaneous vorticity magnitude for tandem foil low-thrust case over one flapping cycle

 Video (970 KB)
970 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed