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Finite-Element Analysis of Nonlinear Fluid–Membrane Interactions Using a Modified Characteristic-Based Split (CBS) Scheme

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Book cover Complex Motions and Chaos in Nonlinear Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 15))

Abstract

A finite-element scheme based on a modified characteristic-based split (CBS) method is proposed for fluid–membrane interactions (FMIs) at low Reynolds numbers, and in particular the effects of structural density on the dynamic response of a flexible membrane wing are investigated. In this method, a flow field with moving boundaries is solved by a modified semi-implicit CBS scheme and dual time stepping (DTS) method, membrane vibration is computed by the Galerkin finite-element method (FEM) and generalized-α algorithm, mesh movement is realized using the segment spring analogy method, and fluid and structure solvers are coupled using the loosely coupled partitioned method. Moreover, the Aitken method is introduced to decrease the computing time of the flow solver. For verification, two FMI problems, including a lid-driven cavity with a flexible bottom and a membrane wing in laminar flow, are simulated. In both cases, the developed fluid–structure interaction (FSI) scheme shows very good stability and the computed results agree very well with those reported in other papers. Additionally, it is also found that the convergence speed of the DTS method could be increased by about four times by the Aitken method. In particular, for membrane wings, it is found that the structural density, which is usually ignored in existing FMI studies, has a very significant influence on their dynamic features, such as vibration modes and dominant frequencies. With little modification, the proposed finite-element solution procedure could be applied to various FSI problems involving continuous structures.

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References

  1. de Matteis G, de Socio L (1986) Nonlinear aerodynamics of a two-dimensional membrane airfoil with separation. J Aircr 23(11):831–836

    Article  Google Scholar 

  2. Rast MP (1994) Simultaneous solution of the Navier-Stokes and elastic membrane equations by a finite element method. Int J Numer Methods Fluids 19:1115–1135

    Article  MATH  Google Scholar 

  3. Smith R, Shyy W (1995) Computation of unsteady laminar flow over a flexible two-dimensional membrane wing. Phys Fluids 7:2175

    Article  MATH  Google Scholar 

  4. Smith R, Shyy W (1996) Computation of aerodynamic coefficients for a flexible membrane airfoil in turbulent flow: a comparison with classical theory. Phys Fluids 8:3346

    Article  MATH  Google Scholar 

  5. Ling SJ, Neitzel GP, Aidun CK (1997) Finite element computations for unsteady fluid and elastic membrane interaction problems. Int J Numer Methods Fluids 24:1091–1110

    Article  MATH  Google Scholar 

  6. Lorillu O, Weber R, Hureau J (2002) Numerical and experimental analysis of two-dimensional separated flows over a flexible sail. J Fluid Mech 466:319–341

    Article  MathSciNet  MATH  Google Scholar 

  7. Matthews LA, Greaves DM, Williams CJK (2008) Numerical simulation of viscous flow interaction with an elastic membrane. Int J Numer Methods Fluids 57:1577–1602

    Article  MathSciNet  MATH  Google Scholar 

  8. Stanford B, Ifju P, Albertani R, Shyy W (2008) Fixed membrane wings for micro air vehicles: experimental characterization, numerical modelling, and tailoring. Prog Aerosp Sci 44:258–294

    Article  Google Scholar 

  9. Gursul I, Gordnier R, Visbal M (2005) Unsteady aerodynamics of nonslender delta wings. Prog Aerosp Sci 41:515–557

    Article  Google Scholar 

  10. Talor G, Wang Z, Vardaki E, Gursul I (2007) Lift enhancement over flexible nonslender delta wings. AIAA J 45:2979–2993

    Article  Google Scholar 

  11. Rojratsirikul P, Wang Z, Gursul I (2009) Unsteady fluid–structure interactions of membrane airfoils at low Reynolds numbers. Exp Fluids 46(5):859–72

    Article  Google Scholar 

  12. Rojratsirikul P, Wang Z, Gursul I (2010) Effect of pre-strain and excess length on unsteady fluid-structure interactions of membrane airfoils. J Fluid Struct 26(3):359–376

    Article  Google Scholar 

  13. Rojratsirikul P, Genc M, Wang Z et al (2011) Flow-induced vibrations of low aspect ratio rectangular membrane wings. J Fluid Struct 27:1296–1309

    Article  Google Scholar 

  14. Gordnier RE (2009) High-fidelity computational simulation of a membrane wing airfoil. J Fluid Struct 25:897–917

    Article  Google Scholar 

  15. Visbal MR, Gordnier RE, Galbraith MC (2009) High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers. Exp Fluids 46:903–922

    Article  Google Scholar 

  16. Jaworski JW, Gordnier RE (2012) High-order simulations of low Reynolds number membrane airfoils under prescribed motion. J Fluid Struct 31:49–66

    Article  Google Scholar 

  17. Gordnier RE, Attar PJ (2009) Implicit LES simulations of a low Reynolds numbers flexible membrane wing airfoil. In: 47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, Florida, USA, 5–8 January 2009

    Google Scholar 

  18. Visbal MR, Yilmaz TO, Rockwell D (2013) Three-dimensional vortex formation on a heaving low-aspect-ratio wing: computations and experiments. J Fluid Struct 38:58–76

    Article  Google Scholar 

  19. Gordnier RE, Attar PJ (2014) Impact of flexibility on the aerodynamics of an aspect ratio two membrane wing. J Fluid Struct 45:138–152

    Article  Google Scholar 

  20. Zienkiewicz OC, Codina R (1995) A general algorithm for compressible and incompressible flow, part І: the split, characteristic-based scheme. Int J Numer Meth Fluids 20(8-9):869–885

    Article  MathSciNet  MATH  Google Scholar 

  21. Zienkiewicz OC, Morgan K, SatyaSai BVK et al (1995) A general algorithm for compressible and incompressible flow, part ІІ: tests on the explicit form. Int J Numer Methods Fluids 20(8-9):887–913

    Article  MathSciNet  Google Scholar 

  22. Zienkiewicz OC, Taylor RL, Nithiarasu P (2005) The finite element method for fluid dynamics, 6th edn. Butterworth-Heinemann, Elsevier

    MATH  Google Scholar 

  23. Nithiarasu P, Liu CB (2005) Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme. Int J Numer Methods Fluids 63:380–397

    Article  MATH  Google Scholar 

  24. Duan QL, Li XK (2007) An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method. Comput Meth Appl Mech Eng 196:4911–4933

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang XH, Ouyang J, Zhang L (2011) The characteristic-based sple (CBS) meshfree method for free surface flow problems in ALE formulation. Int J Numer Methods Fluids 65:798–811

    Article  MathSciNet  MATH  Google Scholar 

  26. Nobari MRH, Naderan H (2006) A numerical study of flow past a cylinder with cross flow and inline oscillation. Comput Fluids 35:393–415

    Article  MATH  Google Scholar 

  27. Nobari MRH, Ghazanfarian J (2009) A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation. Comput Fluids 38:2026–2036

    Article  MATH  Google Scholar 

  28. Nobari MRH, Ghazanfarian J (2010) Convective heat transfer from a rotating cylinder with inline oscillation. Int J Therm Sci 49:2026–2036

    Article  MATH  Google Scholar 

  29. Bao Y, Zhou D, Tu JH (2011) Flow interference between a stationary cylinder and an elastically mounted cylinder arranged proximity. J Fluid Struct 27:1425–1446

    Article  Google Scholar 

  30. Bao Y, Huang C, Zhou D et al (2012) Two-degree-of-freedom flow-induced vibrations on isolated and tandem cylinders with varying natural frequency ratios. J Fluid Struct 35:50–75

    Article  Google Scholar 

  31. He T, Zhou D, Bao Y (2012) Combined interface boundary condition method for fluid-rigid body interaction. Comput Meth Appl Mech Eng 223–224:81–102

    Article  MathSciNet  MATH  Google Scholar 

  32. Donea J, Huerta A, Ponthot J-Ph, Rodríguez-Ferran A (2004) Arbitrary Lagrangian–Eulerian methods. In: The encyclopedia of computational mechanics, vol 1. Wiley, Chapter 14, pp. 413–437

    Google Scholar 

  33. Sun X, Zhang JZ, Ren XL (2012) Characteristic-based split (CBS) finite element method for incompressible viscous flow with moving boundaries. Eng Appl Comp Fluid Mech 6(3): 461–474

    Google Scholar 

  34. Sun X, Zhang JZ, Mei GH (2012) An improved characteristic-based split (CBS) scheme for compressible and incompressible moving boundary flows. Int J Aerosp Lightweight Struct 2(2):281–297

    Article  Google Scholar 

  35. Jameson J (1991) Time dependent calculations using multigrid with application to unsteady flows past airfoils and wings. AIAA paper 91-1596

    Google Scholar 

  36. Küttler U, Wall WA (2008) Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput Mech 43(1):61–72

    Article  MATH  Google Scholar 

  37. Chung J, Hulbert G (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J Appl Mech 60(2):371–375

    Article  MathSciNet  MATH  Google Scholar 

  38. Blom FJ (2000) Considerations on the spring analogy. Int J Numer Methods Fluids 32(6): 647–668

    Article  MATH  Google Scholar 

  39. Bathe KJ, Zhang H (2009) A mesh adaptivity procedure for CFD and fluid-structure interactions. Comput Struct 87(11):604–617

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by Science Foundation of China University of Petroleum, Beijing (01JB0303), the National Fundamental Research Program of China (973 Program, 2012CB026002), and the National High Technology Research Program of China (863 Program, SS2012AA052303). The authors would like to thank these foundations for their support.

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Authors and Affiliations

  1. National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China

    Xu Sun

  2. School of Energy and Power Engineering, Xi’an Jiaotong University, Shaanxi Province, China

    Jiazhong Zhang

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  1. Xu Sun
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  2. Jiazhong Zhang
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Correspondence to Xu Sun .

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Editors and Affiliations

  1. San Luis Potosi University, San Luis Potosi, Mexico

    Valentin Afraimovich

  2. Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    José António Tenreiro Machado

  3. School of Energy&PowerEngineering, Xi’an Jiaotong University, Shaanxi Province, Shaanxi, China

    Jiazhong Zhang

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Sun, X., Zhang, J. (2016). Finite-Element Analysis of Nonlinear Fluid–Membrane Interactions Using a Modified Characteristic-Based Split (CBS) Scheme. In: Afraimovich, V., Machado, J., Zhang, J. (eds) Complex Motions and Chaos in Nonlinear Systems. Nonlinear Systems and Complexity, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-28764-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-28764-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28762-1

  • Online ISBN: 978-3-319-28764-5

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