Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T03:05:34.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Independent caudal fin actuation enables high energy extraction and control in two-dimensional fish-like group swimming

Published online by Cambridge University Press:  04 July 2018

Amy Gao Open the ORCID record for Amy Gao [Opens in a new window]  and
Michael S. Triantafyllou Open the ORCID record for Michael S. Triantafyllou [Opens in a new window]
Amy Gao*
Affiliation:
Center for Ocean Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Michael S. Triantafyllou
Affiliation:
Center for Ocean Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study through numerical simulation the optimal hydrodynamic interactions and basic vorticity control mechanisms for two fish-like bodies swimming in tandem. We show that for a fish swimming in the wake of an upstream fish, using independent pitch control of its caudal fin, in addition to optimized body motion, results in reduction of the energy needed for self-propulsion by more than 50 %, providing a quasi-propulsive efficiency of 90 %, up from 60 % without independent caudal fin control. Such high efficiency is found over a narrow parametric range and is possible only when the caudal fin is allowed to pitch independently from the motion of the main body. We identify the vorticity control mechanisms employed by the body and tail to achieve this remarkable performance through thrust augmentation and destructive interference with the upstream fish-generated vortices. A high sensitivity of the propulsive performance to small variations in caudal fin parameters is found, underlying the importance of accurate flow sensing and feedback control. We further demonstrate that using lateral line-like flow measurements to drive an unscented Kalman filter, the near-field vortices can be localized within 1 % of the body length, and be used with a phase-lock controller to drive the body and tail undulation of a self-propelled fish, moving within the wake of an upstream fish, to stably reach the optimal gait and fully achieve maximum energy extraction.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 304 - 335
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aleyev, Yu G. 1977 Nekton. Dr. W. Junk.Google Scholar
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.Google Scholar
Bale, R., Hao, M., Bhalla, A. P. S. & Patankar, N. A. 2014 Energy efficiency and allometry of movement of swimming and flying animals. Proc. Natl Acad. Sci. USA 111 (21), 7517–7521.Google Scholar
Barrett, D. S., Triantafyllou, M. S., Yue, D. K. P., Grosenbaugh, M. A. & Wolfgang, M. J. 1999 Drag reduction in fish-like locomotion. J. Fluid Mech. 392, 183–212.Google Scholar
Beal, D. N., Hover, F. S., Triantafyllou, M. S., Liao, J. C. & Lauder, G. V. 2006 Passive propulsion in vortex wakes. J. Fluid Mech. 549, 385–402.Google Scholar
Bleckmann, H., Mogdans, J. & Coombs, S. L. 2014 Flow Sensing in Air and Water. Springer.Google Scholar
Borazjani, I. & Daghooghi, M. 2013 The fish tail motion forms an attached leading edge vortex. Proc. R. Soc. B 280, 20122071.Google Scholar
Dewar, H. & Graham, J. 1994 Studies of tropical tuna swimming performance in a large water tunnel-kinematics. J. Expl Biol. 192 (1), 45–59.Google Scholar
Engelmann, J., Hanke, W. & Bleckmann, H. 2002 Lateral line reception in still-and running water. J. Compar. Physiol. A 188 (7), 513–526.Google Scholar
Fernandez, V. I.2011 Performance analysis for lateral-line-inspired sensor arrays. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Fierstine, H. L. & Walters, V. 1968 Studies in locomotion and anatomy of scombroid fishes. Biol. Sci. 6, 4.Google Scholar
Fish, F. E. 1993 Power output and propulsive efficiency of swimming bottlenose dolphins (Tursiops truncatus). J. Expl Biol. 185 (1), 179–193.Google Scholar
Fish, F. E. 2010 Swimming strategies for energy economy. In Fish Swimming: An Etho-Ecological Perspective, pp. 90–122. Science Publishers Enfield (NH).Google Scholar
Fletcher, T., Altringham, J., Peakall, J., Wignall, P. & Dorrell, R. 2014 Hydrodynamics of fossil fishes. Proc. R. Soc. B 281, 20140703.Google Scholar
Gazzola, M., Chatelain, P., Van Rees, W. M. & Koumoutsakos, P. 2011 Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 7093–7114.Google Scholar
Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A. & Koumoutsakos, P. 2016 Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789, 726–749.Google Scholar
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, 1–21.Google Scholar
Hassan, E. S. 1989 Hydrodynamic imaging of the surroundings by the lateral line of the blind cave fish anoptichthys jordani. In The Mechanosensory Lateral Line, pp. 217–227. Springer.Google Scholar
Hertel, H. 1966 Structure, Form, Movement. Reinhold.Google Scholar
Hover, F. S., Haugsdal, Ø. & Triantafyllou, M. S. 2004 Effect of angle of attack profiles in flapping foil propulsion. J. Fluids Struct. 19 (1), 37–47.Google Scholar
Humphreys, W. F. & Feinberg, M. N. 1995 Food of the blind cave fishes of northwestern australia. Records of the Western Australian Museum 17, 29–33.Google Scholar
Izraelevitz, J. S. & Triantafyllou, M. S. 2014 Adding in-line motion and model-based optimization offers exceptional force control authority in flapping foils. J. Fluid Mech. 742, 5–34.Google Scholar
Izraelevitz, J. S., Zhu, Q. & Triantafyllou, M. S. 2017 State-space adaptation of unsteady lifting line theory: twisting/flapping wings of finite span. AIAA J. 55, 1279–1294.Google Scholar
Julier, S. J. & Uhlmann, J. K. 2004 Unscented filtering and nonlinear estimation. Proc. IEEE 92 (3), 401–422.Google Scholar
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics, vol. 13. Cambridge University Press.Google Scholar
Kelly, S. D. & Xiong, H. 2010 Self-propulsion of a free hydrofoil with localized discrete vortex shedding: analytical modeling and simulation. Theor. Comput. Fluid Dyn. 24 (1–4), 45–50.Google Scholar
Kim, S., Huang, W.-X. & Sung, H. J. 2010 Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J. Fluid Mech. 661, 511–521.Google Scholar
Koochesfahani, M. M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27 (9), 1200–1205.Google Scholar
Lang, T. G. & Daybell, D. A.1963 Porpoise performance tests in a sea-water tank. Naval Ordnance Test Station China Lake, CA.Google Scholar
Lauder, G. V., Anderson, E. J., Tangorra, J. & Madden, P. G. A. 2007 Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J. Expl Biol. 210 (16), 2767–2780.Google Scholar
Lentink, D., Muijres, F. T., Donker-Duyvis, F. J. & van Leeuwen, J. L. 2008 Vortex-wake interactions of a flapping foil that models animal swimming and flight. J. Expl Biol. 211 (2), 267–273.Google Scholar
Liao, J. C. 2007 A review of fish swimming mechanics and behaviour in altered flows. Phil. Trans. R. Soc. B 362 (1487), 1973–1993.Google Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003a Fish exploiting vortices decrease muscle activity. Science 302 (5650), 1566–1569.Google Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003b The Kármán gait: novel body kinematics of rainbow trout swimming in a vortex street. J. Expl Biol. 206 (6), 1059–1073.Google Scholar
Licht, S. C., Wibawa, M. S., Hover, F. S. & Triantafyllou, M. S. 2010 In-line motion causes high thrust and efficiency in flapping foils that use power downstroke. J. Expl Biol. 213 (1), 63–71.Google Scholar
Lighthill, M. S. 1975 Mathematical Biofluiddynamics. (CBMS-NSF Regional Conference Series in Applied Mathematics) , Society for Industrial and Applied Mathematics.Google Scholar
Maertens, A. P.2011 Touch at a distance: underwater object identification using pressure sensors. Masters thesis, Massachusetts Institute of Technology.Google Scholar
Maertens, A. P.2015 Fish swimming optimization and exploiting multi-body hydrodynamic interactions for underwater navigation. PhD thesis, Massachusetts Institute of Technology, Dept. of Mechanical Engineering.Google Scholar
Maertens, A. P., Gao, A. & Triantafyllou, M. S. 2017 Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers. J. Fluid Mech. 813, 301–345.Google Scholar
Maertens, A. P., Triantafyllou, M. S. & Yue, D. K. P.2015 Efficiency of fish propulsion. Bioinspiration and Biomimetics 10 (5), 046013.Google Scholar
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, 106–129.Google Scholar
Melli, J. & Rowley, C. W. 2010 Models and control of fish-like locomotion. Expl Mech. 50 (9), 1355–1360.Google Scholar
Novati, G., Verma, S., Alexeev, D., Rossinelli, D., van Rees, W. M. & Koumoutsakos, P. 2017 Synchronisation through learning for two self-propelled swimmers. Bioinspir. Biomim. 12 (3), 036001.Google Scholar
Partridge, B. L. & Pitcher, T. J. 1980 The sensory basis of fish schools: relative roles of lateral line and vision. J. Compar. Physiol. 135 (4), 315–325.Google Scholar
Pitcher, T. J., Partridge, B. L. & Wardle, C. S. 1976 A blind fish can school. Science 194 (4268), 963–965.Google Scholar
Polet, D. T., Christensen, T., Rival, D. E. & Weymouth, G. 2014 On the effect of rapid area change in perching-like maneuvers. In 32nd AIAA Applied Aerodynamics Conference.Google Scholar
Polet, D. T., Rival, D. E. & Weymouth, G. D. 2015 Unsteady dynamics of rapid perching manoeuvres. J. Fluid Mech. 767, 323–341.Google Scholar
Read, D. A., Hover, F. S. & Triantafyllou, M. S. 2003 Forces on oscillating foils for propulsion and maneuvering. J. Fluids Struct. 17 (1), 163–183.Google Scholar
Ren, Z. & Mohseni, K. 2012 A model of the lateral line of fish for vortex sensing. Bioinspir. Biomim. 7 (3), 036016.Google Scholar
Sachinis, M.2000 The design and testing of a biologically inspired underwater robotic mechanism. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423.Google Scholar
Schouveiler, L., Hover, F. S. & Triantafyllou, M. S. 2005 Performance of flapping foil propulsion. J. Fluids Struct. 20 (7), 949–959.Google Scholar
Schulmeister, J. C., Dahl, J. M., Weymouth, G. D. & Triantafyllou, M. S. 2017 Flow control with rotating cylinders. J. Fluid Mech. 825, 743–763.Google Scholar
Sharma, S., Coombs, S., Patton, P. & de Perera, T. B. 2009 The function of wall-following behaviors in the mexican blind cavefish and a sighted relative, the mexican tetra (astyanax). J. Compar. Physiol. A 195 (3), 225–240.Google Scholar
Steele, S. C., Weymouth, G. D. & Triantafyllou, M. S. 2017 Added mass energy recovery of octopus-inspired shape change. J. Fluid Mech. 810, 155–174.Google Scholar
Streitlien, K., Triantafyllou, G. S. & Triantafyllou, M. S. 1996 Efficient foil propulsion through vortex control. AIAA J. 34 (11), 2315–2319.Google Scholar
Suzuki, T. & Colonius, T. 2003 Inverse-imaging method for detection of a vortex in a channel. AIAA J. 41 (9), 1743–1826.Google Scholar
Triantafyllou, M. S., Techet, A. H., Zhu, Q., Beal, D. N., Hover, F. S. & Yue, D. K. P. 2002 Vorticity control in fish-like propulsion and maneuvering. Integr. Compar. Biol. 42 (5), 1026–1031.Google Scholar
Triantafyllou, M. S., Techet, A. H. & Hover, F. S. 2004 Review of experimental work in biomimetic foils. IEEE J. Ocean. Engng 29 (3), 585–594.Google Scholar
Triantafyllou, M. S. & Triantafyllou, G. S. 1995 An efficient swimming machine. Sci. Am. 272, 64–70.Google Scholar
Triantafyllou, M. S., Weymouth, G. D. & Miao, J. 2016 Biomimetic survival hydrodynamics and flow sensing. Annu. Rev. Fluid Mech. 48, 1–24.Google Scholar
Uddin, E., Huang, W.-X. & Sung, H. J. 2013 Interaction modes of multiple flexible flags in a uniform flow. J. Fluid Mech. 729, 563–583.Google Scholar
Videler, J. J. 1993 Fish Swimming. Springer.Google Scholar
Weymouth, G. D., Dommermuth, D. G., Hendrickson, K. & Yue, D. K.-P.2006 Advancements in Cartesian-grid methods for computational ship hydrodynamics. In 26th Symposium on Naval Hydrodynamics, Rome, Italy, 17–22 September 2006.Google Scholar
Weymouth, G. D. & Triantafyllou, M. S. 2013 Ultra-fast escape of a deformable jet-propelled body. J. Fluid Mech. 721, 367–385.Google Scholar
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), 6233–6247.Google Scholar
Wibawa, M. S., Steele, S. C., Dahl, J. M., Rival, D. E., Weymouth, G. D. & Triantafyllou, M. S. 2012 Global vorticity shedding for a vanishing wing. J. Fluid Mech. 695, 112–134.Google Scholar
Ye, T., Mittal, R., Udaykumar, H. S. & Shyy, W. 1999 An accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156 (2), 209–240.Google Scholar
Zhu, Q. & Peng, Z. 2009 Mode coupling and flow energy harvesting by a flapping foil. Phys. Fluids 21 (3), 033601.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.Google Scholar