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CN 34-1054/N

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Numerical investigation on flapping of a flexible filament in a viscoelastic fluid flow

  • 1.

    Department of Modern Mechanics, School Engineering Science, University of Science and Technology of China, Hefei 230027, China

  • 2.

    School of Computer and Information Science, Hefei University of Technology, Hefei 230009, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.05.007
  • Received Date: 14 February 2017
  • Accepted Date: 30 May 2017
  • Rev Recd Date: 30 May 2017
  • Publish Date: 31 May 2018
    Abstract

  • Abstract

    The flapping of a flexible filament in a uniform incoming flow of viscoelastic fluid of polymeric solution was numerically investigated. This paper aims at examining the effects of fluid elasticity on the filament flapping behavior by a comparison with its counterpart in the Newtonian flow. Specifically, the FENE-MCR model was used as the constitutive equation for the viscoelastic fluid. The simulations of fluid flow were based on the lattice Boltzmann method to solve the Navier-Stokes (N-S) equations, the finite difference method to solve the constitutive equation of the polymer stress, the finite element method to solve the motion equation of the filament, and a penalty immersed boundary method to deal with the fluid-structure interaction. From the numerical results obtained, it was found that for a relatively weak fluid elasticity of We<20, the critical mass ratio of the filament to the fluid increases dramatically for the transition from a steady state to a periodically flapping state. However, for a stronger elasticity of We>20, increasing We number leads to a tendency of the critical mass ratio to be an approximate value of ～0.43. Moreover, it was demonstrated that increasing We number is also commensurate with the decrease of the time-averaged drag coefficient, the flapping amplitude, and the flapping frequency of the flexible filament. The above-mentioned facts indicate that enhancing the fluid elasticity has the increasing suppressing effects on the filament flapping behaviors.

    Abstract

    The flapping of a flexible filament in a uniform incoming flow of viscoelastic fluid of polymeric solution was numerically investigated. This paper aims at examining the effects of fluid elasticity on the filament flapping behavior by a comparison with its counterpart in the Newtonian flow. Specifically, the FENE-MCR model was used as the constitutive equation for the viscoelastic fluid. The simulations of fluid flow were based on the lattice Boltzmann method to solve the Navier-Stokes (N-S) equations, the finite difference method to solve the constitutive equation of the polymer stress, the finite element method to solve the motion equation of the filament, and a penalty immersed boundary method to deal with the fluid-structure interaction. From the numerical results obtained, it was found that for a relatively weak fluid elasticity of We<20, the critical mass ratio of the filament to the fluid increases dramatically for the transition from a steady state to a periodically flapping state. However, for a stronger elasticity of We>20, increasing We number leads to a tendency of the critical mass ratio to be an approximate value of ～0.43. Moreover, it was demonstrated that increasing We number is also commensurate with the decrease of the time-averaged drag coefficient, the flapping amplitude, and the flapping frequency of the flexible filament. The above-mentioned facts indicate that enhancing the fluid elasticity has the increasing suppressing effects on the filament flapping behaviors.
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    • References(21)
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    HANSSEN A G, GIRARD Y, OLOVSSON L, et al. A numerical model for bird strike of aluminium foam-based sandwich panels[J]. International Journal of Impact Engineering, 2006, 32(7): 1127-1144.
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    MIN T, YOO J Y, CHOI H, et al. Drag reduction by polymer additives in a turbulent channel flow[J]. Journal of Fluid Mechanics, 2003, 486: 213-238.
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    HUA R N, ZHU L, LU X Y. Locomotion of a flapping flexible plate[J]. Physics of Fluids, 2013, 25(12): 121901.
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    ZHU L. Numerical investigation of the dynamics of a flexible filament in the wake of cylinder[J]. Advances in Applied Mathematics and Mechanics, 2014, 6(4): 478-493.
    [14]
    HE X, LUO L S. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation[J]. Physical Review E, 1997, 56(6): 6811-6817.
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    MALASPINAS O, FIETIER N, DEVILLE M. Lattice Boltzmann method for the simulation of viscoelastic fluid flows[J]. Journal of Non-Newtonian Fluid Mechanics, 2010, 165(23): 1637-1653.
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    SU J, OUYANG J, WANG X, et al. Lattice Boltzmann method coupled with the Oldroyd-B constitutive model for a viscoelastic fluid[J]. Physical Review E, 2013, 88(5): 053304.
    [17]
    GUO Z, ZHENG C, SHI B. Discrete lattice effects on the forcing term in the lattice Boltzmann method[J]. Physical Review E, 2002, 65(4): 046308.
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    FERREIRA V G, TOM M F, MANGIAVACCHI N, et al. High-order upwinding and the hydraulic jump[J]. International Journal for Numerical Methods in Fluids, 2002, 39(7): 549-583.
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    LEONARD B P. A stable and accurate convective modelling procedure based on quadratic upstream interpolation[J]. Computer Methods in Applied Mechanics and Engineering, 1979, 19(1): 59-98.
    [20]
    DOYLE J F. Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability[M]. New York: Springer Science & Business Media, 2013.
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    HUANG W X, SHIN S J, SUNG H J. Simulation of flexible filaments in a uniform flow by the immersed boundary method[J]. Journal of Computational Physics, 2007, 226(2): 2206-2228.)
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    [1]
    HANSSEN A G, GIRARD Y, OLOVSSON L, et al. A numerical model for bird strike of aluminium foam-based sandwich panels[J]. International Journal of Impact Engineering, 2006, 32(7): 1127-1144.
    [2]
    HELFMAN G, COLLETTE B B, FACEY D E, et al. The Diversity of Fishes: Biology, Evolution, and Ecology[M]. Chichester,UK: Wiley-Blackwell, 2009.
    [3]
    GROTBERG J B, JENSEN O E. Biofluid mechanics in flexible tubes[J]. Annual Review of Fluid Mechanics, 2004, 36(1): 121-147.
    [4]
    WEINBERG E J, SHAHMIRZADI D, MOFRAD M R K. On the multiscale modeling of heart valve biomechanics in health and disease[J]. Biomechanics and Modeling in Mechanobiology, 2010, 9(4): 373-387.
    [5]
    LIU B, POWERS T R, BREUER K S. Force-free swimming of a model helical flagellum in viscoelastic fluids[J]. Proceedings of the National Academy of Sciences, 2011, 108(49): 19516-19520.
    [6]
    ZHU L, PESKIN C S. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method[J]. Journal of Computational Physics, 2002, 179(2): 452-468.
    [7]
    SHELLEY M J, ZHANG J. Flapping and bending bodies interacting with fluid flows[J]. Annual Review of Fluid Mechanics, 2011, 43: 449-465.
    [8]
    CONNELL B S H, YUE D K P. Flapping dynamics of a flag in a uniform stream[J]. Journal of Fluid Mechanics, 2007, 581:33-67.
    [9]
    ZHU L, PESKIN C S. Interaction of two flapping filaments in a flowing soap film[J]. Physics of Fluids, 2003, 15(7): 1954-1960.
    [10]
    SCHOWALTER W R. Mechanics of Non-Newtonian fluid[M]. Oxford: Pergamon, 1978.
    [11]
    MIN T, YOO J Y, CHOI H, et al. Drag reduction by polymer additives in a turbulent channel flow[J]. Journal of Fluid Mechanics, 2003, 486: 213-238.
    [12]
    HUA R N, ZHU L, LU X Y. Locomotion of a flapping flexible plate[J]. Physics of Fluids, 2013, 25(12): 121901.
    [13]
    ZHU L. Numerical investigation of the dynamics of a flexible filament in the wake of cylinder[J]. Advances in Applied Mathematics and Mechanics, 2014, 6(4): 478-493.
    [14]
    HE X, LUO L S. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation[J]. Physical Review E, 1997, 56(6): 6811-6817.
    [15]
    MALASPINAS O, FIETIER N, DEVILLE M. Lattice Boltzmann method for the simulation of viscoelastic fluid flows[J]. Journal of Non-Newtonian Fluid Mechanics, 2010, 165(23): 1637-1653.
    [16]
    SU J, OUYANG J, WANG X, et al. Lattice Boltzmann method coupled with the Oldroyd-B constitutive model for a viscoelastic fluid[J]. Physical Review E, 2013, 88(5): 053304.
    [17]
    GUO Z, ZHENG C, SHI B. Discrete lattice effects on the forcing term in the lattice Boltzmann method[J]. Physical Review E, 2002, 65(4): 046308.
    [18]
    FERREIRA V G, TOM M F, MANGIAVACCHI N, et al. High-order upwinding and the hydraulic jump[J]. International Journal for Numerical Methods in Fluids, 2002, 39(7): 549-583.
    [19]
    LEONARD B P. A stable and accurate convective modelling procedure based on quadratic upstream interpolation[J]. Computer Methods in Applied Mechanics and Engineering, 1979, 19(1): 59-98.
    [20]
    DOYLE J F. Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability[M]. New York: Springer Science & Business Media, 2013.
    [21]
    HUANG W X, SHIN S J, SUNG H J. Simulation of flexible filaments in a uniform flow by the immersed boundary method[J]. Journal of Computational Physics, 2007, 226(2): 2206-2228.)
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