Abstract
The problem of flapping filaments in an uniform incoming flow is tackled using a Lattice Boltzmann—Immersed Boundary method. The fluid momentum equations are solved on a Cartesian uniform lattice while the beating filaments are tracked through a series of markers, whose dynamics are functions of the forces exerted by the fluid, the filament flexural rigidity and the tension. The instantaneous wall conditions on the filament are imposed via a system of singular body forces, consistently discretised on the lattice of the Boltzmann equation. We first consider the case of a single beating filament, and then the case of multiple beating filaments in a side-by-side configuration, focussing on the modal behaviour of the whole dynamical systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Païdoussis, M.P.: Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 2. Elsevier Academic Press, Cambridge (2004)
Shelley, M.J., Zhang, J.: Flapping and bending bodies interacting with fluid flows. Ann. Rev. Fluid Mech. 43(1), 449–465 (2011)
Zhang, J., Childress, S., Libchaber, A., Shelley, M.: Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835–839 (2000)
Zhu, L., Peskin, C.S.: Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15, 1954–1960 (2000)
Pinelli, A., Naqavi, I.Z., Piomelli, U., Favier, J.: Immersed-boundary methods for general finite-difference and finite-volume navier-stokes solvers. J. Comput. Phys. 229(24), 9073–9091 (2010)
Domenichini, F.: On the consistency of the direct forcing method in the fractional step solution of the navier-stokes equations. J. Comput. Phys. 227(12), 6372–6384 (2008)
Schouweiler, L., Eloy, C.: Coupled flutter of parallel plates. Phys. Fluids 21, 081703 (2009)
Michelin, S., Llewellyn Smith, S.G.: Linear stability analysis of coupled parallel flexible plates in an axial flow. J. Fluids Struct. 25(7), 1136–1157 (2009)
Favier, J., Dauptain, A., Basso, D., Bottaro, A.: Passive separation control using a self-adaptive hairy coating. J. Fluid Mech. 627, 451 (2009)
Favier, J., Revell, A., Pinelli, A.: A lattice boltzmann—immersed boundary method to simulate the fluid interaction with moving and slender flexible objects. HAL, hal(00822044) (2013)
Succi, S.: The Lattice Boltzmann Equation. Oxford University Press, New York (2001)
Bhatnagar, P., Gross, E., Krook, M.: A model for collision processes in gases. i: small amplitude processes in charged and neutral one-component system. Phys. Rev. 94, 511–525 (1954)
Qian, Y., D’Humieres, D., Lallemand, P.: Lattice bgk models for navier-stokes equation. Europhys. Lett. 17(6), 479–484 (1992)
Guo, Z., Zheng, C., Shi, B.: Discrete lattice effects on the forcing term in the lattice boltzmann method. Phys. Rev. E 65, 046308 (2002)
Zhu, L., Peskin, C.S.: Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. Phys. Fluids 179, 452–468 (2002)
Huang, W.-X., Shin, S.J., Sung, H.J.: Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226(2), 2206–2228 (2007)
Bagheri, Shervin, Mazzino, Andrea, Bottaro, Alessandro: Spontaneous symmetry breaking of a hinged flapping filament generates lift. Phys. Rev. Lett. 109, 154502 (2012)
Bailey, H.: Motion of a hanging chain after the free end is given an initial velocity. Am. J. Phys. 68, 764–767 (2000)
Tian, F.-B., Luo, H., Zhu, L., Lu, X.-Y.: Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 23(11), 111903 (2011)
Acknowledgments
The authors acknowledge the financial help of the PELskin European project (FP7 AAT.2012.6.3-1). This work was partially supported by the Spanish Ministry of Economics through the grant DPI2010-20746-C03-02.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Favier, J., Revell, A., Pinelli, A. (2016). Fluid Structure Interaction of Multiple Flapping Filaments Using Lattice Boltzmann and Immersed Boundary Methods. In: Braza, M., Bottaro, A., Thompson, M. (eds) Advances in Fluid-Structure Interaction. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-27386-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-27386-0_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27384-6
Online ISBN: 978-3-319-27386-0
eBook Packages: EngineeringEngineering (R0)