Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-16T02:04:21.007Z Has data issue: false hasContentIssue false

Hydrodynamics of flexible fins propelled in tandem, diagonal, triangular and diamond configurations

Published online by Cambridge University Press:  08 February 2018

Sung Goon Park
Affiliation:
Department of Mechanical Engineering, KAIST 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
Hyung Jin Sung*
Affiliation:
Department of Mechanical Engineering, KAIST 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
*
Email address for correspondence: [email protected]

Abstract

A fish may gain hydrodynamic benefits from being a member of a school. Inspired by fish schools, a two-dimensional simulation was performed for flexible fins propelled in tandem, diagonal, triangular and diamond configurations. The flow-mediated interactions between the flexible fins were analysed by using an immersed boundary method. A transverse heaving motion was prescribed on the leading edge of each fin, and other posterior parts passively adapted to the surrounding fluid as a result of the fluid–flexible-body interaction. The flexible fins were allowed to actively adjust their relative positions in the horizontal direction. The four basic stable configurations are spontaneously formed and self-sustained purely by the vortex–vortex and vortex–body interactions. The hydrodynamic benefits depend greatly on the local positions of the members. For the same heaving motion prescribed on the leading edge, the input power of the following fin in the stable tandem and diagonal configurations is lower by 14 % and 6 %, respectively, than that of the leading fin. The following fin in the diagonal formation can keep pace with the leading fin even for reduced heaving amplitudes because of the help of the leader via their shared fluid environment, where its required input power is reduced by 21 %. The heaving amplitudes of the trailing fins are reduced to optimize the propulsive efficiency, and the average efficiencies in the triangular and diamond configurations increase by up to 14 % and 19 %, respectively, over that of the isolated swimmer. The propulsive efficiencies are enhanced by 22 % for the fins in the second row and by 36 % for the fin in the third row by decreasing the heaving amplitude in the diamond formation.

Type
JFM Papers
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

Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489496.CrossRefGoogle 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, 385402.Google Scholar
Boschitsch, B. M., Dewey, P. D. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26, 051901.Google Scholar
Daghooghi, M. & Borazjani, I. 2015 The hydrodynamic advantages of synchronized swimming in a rectangular pattern. Bioinspir. Biomim. 10, 056018.Google Scholar
Deng, J. & Shao, X.-M. 2006 Hydrodynamics in a diamond-shaped fish school. Project supported by the National Lab of Hydrodynamics of China. J. Hydrodyn. B 18 (3), 438442.CrossRefGoogle Scholar
Deng, J., Shao, X.-M. & Yu, Z.-X. 2007 Hydrodynamic studies on two travelling wavy foils in tandem arrangement. Phys. Fluids 19, 113104.Google Scholar
Dewey, P. A., Quinn, D. B. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in a side-by-side configuration. Phys. Fluids 26, 041903.Google Scholar
Dong, G.-J. & Lu, X.-Y. 2007 Characteristics of flow over traveling wavy foils in a side-by-side arrangement. Phys. Fluids 19, 057107.Google Scholar
Eldredge, J. D. & Pisani, D. 2008 Passive locomotion of a simple articulated fish-like system in the wake of an obstacle. J. Fluid Mech. 607, 279288.Google Scholar
Fish, F. E. 2010 Swimming strategies for energy economy. In Fish Locomotion: An Eco-ethological Perspective (ed. Domenici, P. & Kapoor, B. G.), pp. 90122. Science Publishers.Google Scholar
Fish, F. E. & Hui, C. A. 1991 Dolphin swimming – a review. Mammal Rev. 21, 181195.Google Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. 2014a Scaling macroscopic aquatic locomotion. Nat. Phys. 10, 758761.Google Scholar
Gazzola, M., Chatelain, P., Ress, W. M. V. & Koumoustsakos, P. 2011 Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 70937114.Google Scholar
Gazzola, M., Hejazialhosseini, B. & Koumoutsakos, P. 2014b Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM J. Sci. Comput. 36 (3), B622B639.Google Scholar
Gazzola, M., Tchieu, A. A., Alexeev, D., Brauer, A. D. & Koumoutsakos, P. 2016 Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789, 726749.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, 121.Google Scholar
Hemelrijk, C. K., Reid, D. A. P., Hildenbrandt, H. & Paddling, J. T. 2015 The increased efficiency of fish swimming in a school. Fish Fisheries 16, 511521.Google Scholar
Herskin, J. & Steffensen, J. F. 1998 Energy savings in sea bass swimming in a school: measurements of tail beat frequency and oxygen consumption at different swimming speeds. J. Fish Biol. 53, 366376.Google Scholar
Huang, W.-X., Shin, S. J. & Sung, H. J. 2007 Simulation of flexible flags in a uniform flow by the immersed boundary method. J. Comput. Phys. 226, 22062228.CrossRefGoogle Scholar
Huang, W.-X. & Sung, H. J. 2010 Three-dimensional simulation of a flapping flag in a uniform flow. J. Fluid Mech. 653, 301336.Google Scholar
Kern, S. & Koumoutsakos, P. 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209, 48414857.Google Scholar
Killen, S. S., Marras, S., Steffensen, J. F. & Mckenzie, D. J. 2012 Aerobic capacity influences the spatial position of individuals within fish schools. Proc. R. Soc. Lond. B 279, 357364.Google Scholar
Kim, K., Baek, S. J. & Sung, H. J. 2002 An implicit velocity decoupling procedure for incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38, 125138.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, 511521.Google Scholar
Lauder, G. V. & Tytell, E. D. 2005 Hydrodynamics of undulatory propulsion. Fish Physiol. 23, 425468.CrossRefGoogle Scholar
Liao, J. C. 2004 Neuromuscular control of trout swimming in a vortex street: implications for energy economy during the Karman gait. J. Expl Biol. 207, 34953506.Google Scholar
Liao, J. C. 2007 A review of fish swimming mechanics and behaviour in altered flows. Phil. Trans. R. Soc. Lond. B 362, 19731993.Google Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003a The Kármán gait: novel body kinematics of rainbow trout swimming in a vortex street. J. Expl Biol. 206, 10591073.Google Scholar
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003b Fish exploiting vortices decrease muscle activity. Science 302, 15661569.Google Scholar
Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9, 305317.CrossRefGoogle Scholar
Lin, X., He, G., He, X., Wang, Q. & Chen, L. 2017 Numerical study of the hydrodynamic performance of two wiggling hydrofoils in diagonal arrangement. Z. Angew. Math. Phys. 5, 3138.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, 301345.Google Scholar
Marras, S., Killen, S. S., Lindstrom, J., McKenzie, D. J., Steffensen, J. F. & Domenici, P. 2015 Fish swimming in schools save energy regardless of their spatial position. Behav. Ecol. Sociobiol. 69, 219226.Google Scholar
Novati, G., Verma, S., Alexeev, D., Rossinelli, D., Rees, W. M. V. & Koumoutsakos, P. 2017 Synchronisation through learning for two self-propelled swimmers. Bioinspir. Biomim. 12, 036001.Google Scholar
Park, S. G., Chang, C. B., Huang, W. H. & Sung, H. J. 2014 Simulation of swimming oblate jellyfish with a paddling-based locomotion. J. Fluid Mech. 748, 731755.Google Scholar
Park, S. G., Kim, B. & Sung, H. J. 2016 Self-propelled flexible fin in the wake of a circular cylinder. Phys. Fluids 28, 111902.Google Scholar
Park, S. G., Kim, B. & Sung, H. J. 2017 Hydrodynamics of a self-propelled flexible fin near the ground. Phys. Fluids 29, 051902.Google Scholar
Park, S. G. & Sung, H. J. 2016 Vortex interaction between two tandem flexible propulsors with a paddling-based locomotion. J. Fluid Mech. 793, 612632.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479517.Google Scholar
Ramananarivo, S., Godoy-Diana, R. & Thira, B. 2011 Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proc. Natl Acad. Sci. USA 108, 59645969.Google Scholar
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101, 194502.Google Scholar
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.Google Scholar
Shin, S. J., Huang, W.-X. & Sung, H. J. 2008 Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method. Intl J. Numer. Meth. Fluids 58, 263286.Google Scholar
Son, Y. & Lee, J. H. 2017 Flapping dynamics of coupled flexible flags in a uniform viscous flow. J. Fluids Struct. 68, 339355.CrossRefGoogle Scholar
Streitlien, K. & Triantafyllou, G. S. 1996 Efficient foil propulsion through vortex control. AIAA J. 34, 23152319.Google Scholar
Svendsen, J. C., Skov, J., Bildsoe, M. & Steffensen, J. F. 2003 Intra-school positional preference and reduced tail beat frequency in trailing positions in schooling roach under experimental conditions. J. Fish Biol. 62, 834846.Google Scholar
Tchieu, A. A., Kanso, E. & Newton, P. K. 2012 The finite-dipole dynamical system. Proc. R. Soc. Lond. A 468 (2146), 30063026.Google Scholar
Thiria, B. & Godoy-Diana, R. 2010 How wing compliance drives the efficiency of self-propelled flapping flyers. Phys. Rev. E 82, 015303.Google ScholarPubMed
Tian, F. B., Wang, W., Wu, J. & Sui, Y. 2016 Swimming performance and vorticity structures of a mother–calf pair of fish. Comput. Fluids 124, 111.Google Scholar
Tsang, A. C. H. & Kanso, E. 2013 Dipole interactions in doubly periodic domains. J. Nonlinear Sci. 23, 971991.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, 563583.Google Scholar
Uddin, E., Huang, W.-X. & Sung, H. J. 2015 Actively flapping tandem flexible flags in a viscous flow. J. Fluid Mech. 780, 120142.CrossRefGoogle Scholar
Uhlmann, U. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448476.Google Scholar
Ulrike, K. M. 2003 Fish ’n flag. Science 302, 15111512.Google Scholar
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241, 290291.Google Scholar
Yu, Z. 2005 A DLM/FD method for fluid/flexible–body interactions. J. Comput. Phys. 207, 127.CrossRefGoogle Scholar
Zhang, J., Liu, N.-S. & Lu, X.-Y. 2010 Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 4368.Google Scholar
Zhu, L. 2009 Interaction of two tandem deformable bodies in a viscous incompressible flow. J. Fluid Mech. 635, 455475.Google Scholar
Zhu, X., He, G. & Zhang, X. 2014a Flow-mediated interactions between two self-propelled flapping flags in tandem configuration. Phys. Rev. Lett. 113, 238105.Google Scholar
Zhu, X., He, G. & Zhang, X. 2014b Numerical study on hydrodynamic effect of flexibility in a self-propelled plunging foil. Comput. Fluids 97, 120.CrossRefGoogle Scholar
Zhu, L. & Peskin, C. S. 2003 Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15, 19541960.Google Scholar

Park and Sung supplementary movie 1

Two flexible fins propelled in the tandem configuration for different streamwise gap distances.

Download Park and Sung supplementary movie 1(Video)
Video 1.5 MB

Park and Sung supplementary movie 2

Two flexible fins propelled in the diagonal and side-by-side configurations for different spanwise gap distances.

Download Park and Sung supplementary movie 2(Video)
Video 1.6 MB

Park and Sung supplementary movie 3

Three flexible fins propelled in the triangular configuration.

Download Park and Sung supplementary movie 3(Video)
Video 1.1 MB

Park and Sung supplementary movie 4

Three flexible fins propelled in the triangular and side-by-side configurations for different spanwise gap distances.

Download Park and Sung supplementary movie 4(Video)
Video 3.2 MB

Park and Sung supplementary movie 5

Four flexible fins propelled in the diamond configuration.

Download Park and Sung supplementary movie 5(Video)
Video 1.4 MB