DOI QR코드

DOI QR Code

Simulating flow-induced fiber motion with finite element based explicit coupling method

  • Diwei Zhang (Department of Mechanical Engineering, Roy G. Perry College of Engineering, Prairie View A&M University) ;
  • Xiaobo Peng (Department of Mechanical Engineering, Roy G. Perry College of Engineering, Prairie View A&M University) ;
  • Dongdong Zhang (Department of Mechanical Engineering, Roy G. Perry College of Engineering, Prairie View A&M University)
  • 투고 : 2019.06.06
  • 심사 : 2024.09.11
  • 발행 : 2024.07.25

초록

This paper presents a finite element based explicit coupling method. The derived method is proposed to solve a certain type of fluid-structure interaction problem, which is the motion of a single or flexible fiber with the motion induced by the low-Reynolds-number fluid. The particle motion is treated as a non-linear geometric dynamic problem. The Total-lagrangian finite element method is applied to describe and discretize the particle domain. The Bathe method is used to integrate the time domain. The Stokes equation is used as the governing equation of the fluid domain. The inertia term of the Stokes equation is ignored, and Reynolds number flow is assumed as zero. Since the time term is also canceled, we solve it as a quasi-static problem. Mixed finite element is to solve the fluid equation. An explicit strategy is implemented to couple the particle and the zero-Reynolds number flow. Simulations with the proposed method are presented, including the motion of single and double rigid particle immersed in the double Couette flow and the Poiseuille flow. Simulation of single flexible fiber immersed in a Poiseuille flow is also presented. Effect of particle's density, aspect ratio, and geometry are discussed.

키워드

과제정보

The research described in this paper was financially supported by the National Science Foundation Grant Number 1505530.

참고문헌

  1. Bathe, K.J. (2007), "Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme", Comput. Struct., 85(7-8), 437-445. https://doi.org/10.1016/j.compstruc.2006.09.004
  2. Bretherton, F.P. (1962), "The motion of rigid particles in a shear flow at low Reynolds number", J. Fl. Mech., 14(2), 284-304. https://doi.org/10.1017/S002211206200124X
  3. Burnett, D.S. (1987), Finite Element Analysis: From Concepts to Application, Addison-Wesley Publishing Company, Whippany, New Jersey., U.S.A.
  4. Callister, W.D.J. and Rethwisch, D.G. (2009), Materials Science and Engineering an Introduction, Eight edition, John Wiley & Sons, Inc, U.S.A.
  5. Courtney, T.H. (2005), Mechanical Behavior of Materials, Waveland Press, Inc, Long Grove, Illinois, U.S.A.
  6. De Corato, M., Greco, F. and Maffettone, P.L. (2015), "Locomotion of a microorganism in weakly viscoelastic liquids", Phys. Rev. E, 92(5), 3008. https://doi.org/10.1103/PhysRevE.92.053008
  7. Donea, J., Huerta, A., Ponthot, J.P. and Rodriguez-Ferran, A. (1999), "Arbitrary Lagrangian-Eulerian Methods", Encyclopedia Comput. Mech., 1-25.
  8. Folgar, F. and Tucker, C.L. (1984), "Orientation behavior of fibers in concentrated suspensions", J. Reinforced Plast. Compos., 3(2), 98-119. https://doi.org/10.1177/0731684484003002
  9. Forgacs, O.L. and Mason, S.G. (1959), "Particle motions in sheared suspensions: X. Orbits of flexible threadlike particles", J. Colloid Sci., 14(5), 473-491. https://doi.org/10.1016/0095-8522(59)90013-3
  10. Ho, B.P. and Leal, L.G. (1974), "Inertial migration of rigid spheres in two-dimensional unidirectional flows", J. Fl. Mech., 65(2), 365-400. https://doi.org/10.1017/S0022112074001431
  11. Hu, H.H., Joseph, D.D. and Crochet, M.J. (1992), "Direct simulation of fluid particle motions", Theor. Comput. Fl. Dyn., 3(5), 285-306. https://doi.org/10.1007/BF00717645
  12. Jeffery, G.B. (1922), "The motion of ellipsoidal particles immersed in a viscous fluid", Proceedings of the Royal Society of London, Series A, 102(715), 161-179. https://doi.org/10.1098/rspa.1922.0078
  13. Kuraray (2018), Fibers and Textiles/Man-Made Leather/Nonwoven Fabrics/Hook-and-Loop Fasteners/Vinyl Acetate Derivatives/KURALON, Kuraray Co., Ltd, Tokyo, Japan. www.kuraray.com/products/vinylon
  14. Malvern, L.E. (1977), Introduction to the Mechanics of a Continuous Medium, Prentice Hall, Inc, New Jersey, U.S.A.
  15. Oersson, P.O. and Strang, G. (2012), Distmesh - A Simple Mesh Generator in MATLAB, Department of Mathematics, UC Berkeley, California, U.S.A. http://persson.berkeley.edu/distmesh/.
  16. Papathanasiou, T.D. and Guell, D.C. (1997), Flow-Induced Alignment in Composite Materials, Elsevier, Cambridge, U.K.
  17. Park, K.C., Felippa, C.A. and Farhat, C. (2001), "Partitioned analysis of coupled systems", Comput. Meth. Transient Anal., 190(24-25), 3247-3270.
  18. Peskin, C.S. (2002), "The immersed boundary method", Acta Numerica, 11, 479-517. https://doi.org/10.1017/S0962492902000077 
  19. Qi, D. (2007), "A new method for direct simulations of flexible filament suspensions in non-zero raynolds number flow", Int. J. Numer. Method Fl., 54(1), 103-118. https://doi.org/10.1002/fld.1398
  20. Reddy, J.N. (2004), An Introduction To Nonlinear Finite Element Analysis, Oxford University Press, Oxford University Press, Oxford, U.K.
  21. Reddy, J.N. and Gartling, D.K. (1985), The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, New York, U.S.A.
  22. Ross, R.F. and Klingenberg, D.J. (1997), "Dynamic simulation of flexible fibers composed of linked rigid bodies", J. Chem. Phys., 106(7), 2949-2960. https://doi.org/10.1063/1.473067
  23. Segre, G. and Silberberg, A. (1961), "Radial particle displacements in poiseuille flow of suspensions", Nature, 189(4760), 209-210. https://doi.org/10.1038/189209a0
  24. Slowicka, A.M., Wajnryb, E. and Ekiel-Jezewska, M.L. (2015), "Dynamics of flexible fibers in shear flow", J. Chem. Phys., 143(12), 124904. https://doi.org/10.1063/1.4931598
  25. Stover, C.A. and Cohen, C. (1990), "The motion of rodlike particles in the pressure-driven flow between two flat plates", Rheologica Acta, 29(3), 192-203. https://doi.org/10.1007/BF01331355
  26. Sugihara-Seki, M. (1996), "The motion of an ellipsoid in tube flow at low Reynolds numbers", J. Fl. Mech., 324, 287-308. https://doi.org/10.1017/S0022112096007926
  27. Tan, J., Keller, W., Sohrabi, S., Yang, J. and Liu, Y. (2016), "Characterization of nanoparticle dispersion in red blood cell suspension by the lattice boltzmann-immersed boundary method", Nanomaterials, 6(2), 30. https://doi.org/10.3390/nano6020030
  28. Tezduyar, T., Sathe, S. and Senga, M. (2006), "Finite element modeling of fluid-structure interactions with space-time and advanced mesh update techniques", Fl. Struct. Interact. Lecture Notes Comput. Sci. Eng., 53, 50-81.
  29. Wang, G., Yu, W. and Zhou, C. (2006), "Optimization of the rod chain model to simulate the motions of a long flexible fiber in simple shear flows", Eur. J. Mech. B Fluids, 25(3), 337-347. https://doi.org/10.1016/j.euromechflu.2005.09.004
  30. Wiens, J.K. and Stockie, J.M. (2015), "Simulating flexible fiber suspensions using a scalable immersed boundary algorithm", Comput. Meth. Appl. Mech. Eng., 290, 1-18. https://doi.org/10.1016/j.cma.2015.02.026
  31. Yamamoto, S. and Matsuoka, T. (1993), "A method for dynamic simulation of rigid and flexible fibers in a flow field", J. Chem. Phys., 98(1), 644-650. https://doi.org/10.1063/1.464607
  32. Zhang, D. (2013), Flow-Induced Micro- and Nano-Fiber Suspensions in Short-Fiber Reinforced Composite Materials Processing, University of Missouri, U.S.A.
  33. Zhang, D. and Smith, D.E. (2016), "Dynamic simulation of discrete fiber motion in fiber-reinforced composite materials processing", J. Compos. Mater., 50(10), 1301-1319. https://doi.org/10.1177/0021998315590266