STUDY ON A SELF-PROPELLED FISH SWIMMING IN VISCOUS FLUID BY A FINITE ELEMENT METHOD

A self-propelled fish swimming in viscous fluid is investigated by solving the incompressible Navier–Stokes equations numerically with the space-time finite element method to understand the mechanisms of aquatic animal locomotion. Two types of propulsion strategies, undulatory body and traveling wave surface (TWS), are considered. Based on the simulations, we find that by performing lateral undulation, the fish is able to move forward with a reverse von Karman vortex street in its wake. In addition, there is no vortex street in the wake of the fish using TWS. In this case, the thrust of the fish is generated by the jets outside the boundary layer and the high pressure on the leeward side of the traveling wave. The results obtained in this paper will be of help in understanding of the propulsive performance of aquatic animal locomotion.

[1]  Liu,et al.  A computational fluid dynamics study of tadpole swimming , 1996, The Journal of experimental biology.

[2]  K. Kawachi,et al.  The three-dimensional hydrodynamics of tadpole locomotion. , 1997, The Journal of experimental biology.

[3]  Fang Li,et al.  Coupling modes between two flapping filaments , 2007, Journal of Fluid Mechanics.

[4]  Xie-zhen Yin,et al.  Secondary vortex street in the wake of two tandem circular cylinders at low Reynolds number. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Hu Dai,et al.  On numerical modeling of animal swimming and flight , 2013 .

[6]  Marek Behr,et al.  Parallel finite-element computation of 3D flows , 1993, Computer.

[7]  Jialei Song,et al.  Force production and asymmetric deformation of a flexible flapping wing in forward flight , 2013 .

[8]  T. Y. Wu.  On theoretical modeling of aquatic and aerial animal locomotion , 2002 .

[9]  Tayfun E. Tezduyar,et al.  Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces , 1994 .

[10]  F. Tian.  Role of mass on the stability of flag/flags in uniform flow , 2013 .

[11]  Luoding Zhu,et al.  Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis , 2013, Comput. Biol. Medicine.

[12]  C. Peskin,et al.  Interaction of two flapping filaments in a flowing soap film , 2003 .

[13]  S. Mittal,et al.  A finite element study of incompressible flows past oscillating cylinders and aerofoils , 1992 .

[14]  S. Y. Kim,et al.  Constructive and destructive interaction modes between two tandem flexible flags in viscous flow , 2010, Journal of Fluid Mechanics.

[15]  Xi-Yun Lu,et al.  Characteristics of flow over traveling wavy foils in a side-by-side arrangement , 2007 .

[16]  Haoxiang Luo,et al.  Propulsive performance of a body with a traveling-wave surface. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Luoding Zhu,et al.  Interaction between a flexible filament and a downstream rigid body. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Xie-Zhen Yin,et al.  Passive oscillations of two tandem flexible filaments in a flowing soap film. , 2008, Physical review letters.

[19]  Luoding Zhu.  Interaction of two tandem deformable bodies in a viscous incompressible flow , 2009, Journal of Fluid Mechanics.

[20]  Luoding Zhu,et al.  Coupling modes of three filaments in side-by-side arrangement , 2011 .

[21]  Hao Liu,et al.  Recent progress in flapping wing aerodynamics and aeroelasticity , 2010 .

[22]  Hu Dai,et al.  Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems , 2014, J. Comput. Phys..

[23]  G. Lauder,et al.  Passive and Active Flow Control by Swimming Fishes and Mammals , 2006 .

[24]  Xi-Yun Lu,et al.  Numerical analysis on the propulsive performance and vortex shedding of fish‐like travelling wavy plate , 2005 .

[25]  Silas Alben,et al.  Wake-mediated synchronization and drafting in coupled flags , 2009, Journal of Fluid Mechanics.

[26]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[27]  F. Tian,et al.  AN EFFICIENT RED BLOOD CELL MODEL IN THE FRAME OF IB-LBM AND ITS APPLICATION , 2013 .

[28]  Jian Deng,et al.  Hydrodynamic studies on two traveling wavy foils in tandem arrangement , 2007 .

[29]  Xiang Zhang,et al.  Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion , 2003, Journal of Fluid Mechanics.

[30]  T. Y. Wu.  Fish Swimming and Bird/Insect Flight , 2011 .

[31]  Jun Zhang,et al.  Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind , 2000, Nature.

[32]  Luoding Zhu,et al.  An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments , 2011, J. Comput. Phys..

[33]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[34]  Yu Yongliang,et al.  Two-Dimensional Self-Propelled Fish Motion in Medium: An Integrated Method for Deforming Body Dynamics and Unsteady Fluid Dynamics , 2008 .