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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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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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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