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Stabilization of the Finite element Analysis of the Fluid-Structure Interaction in Micro Systems in Small Time Steps

Afrasiab, Hamed | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 41996 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Movahhedy, Mohammad Reza; Assempour, Ahmad
  7. Abstract:
  8. Fluid-structure interaction plays an important role in the performance of various Microsystems. In many micro-devices such as micropumps, microvalves and micromixers, the fluid flow is driven by a vibrating solid membrane. Since the fluid also plays a role in resistance to the solid vibration and deformation, the solid vibration and the fluid flow are always coupled and a full fluid-structure interaction (FSI) analysis is required in order to investigate the performance characteristics of these devices. Since the frequency of the solid vibration is normally high in micro-devices, the time step size required for the finite element analysis of the fluid-structure interaction in these devices is usually very small which makes the analysis of the fluid part vulnerable to the so-called small time step instability.
    Due to the shortcomings of purely Lagrangian and Eulerian descriptions in modeling of fluid-structure interaction problems, the arbitrary Lagrangian-Eulerian (ALE) approach is recommended for simulation of general FSI problems. The ALE approach is based on the arbitrary movement of the reference frame, which is continuously rezoned to allow a precise description of the moving FSI interface.
    In this study, the arbitrary Lagrangian-Eulerian approach is used for simulation of the fluid-structure interaction in Microsystems. In order to verify the employed formulations and methodologies, two benchmark problems are simulated and their results are compared with those presented in the literature. Two different approaches are presented to overcome the small time step instability in the finite element analysis of the fluid-structure interaction problem in Microsystems. In the first approach, a residual-based variational multiscale method (VMS) is used in combination with appropriate stabilization parameters for formulating the fluid problem in the ALE description. In the second approach, the dimensionless form of the full set of equations governing the fluid-structure interaction problem is employed to scale up the problem time step to a proper level that precludes the potential small time step instability. Some two and three-dimensional finite element simulations of the fluid-structure interaction problem in Microsystems are performed to examine the capability of these approaches and the results are compared with available experimental data. Finally, the finite element code derived from presented algorithms and formulations is used for simulation of various two and three-dimensional examples of the fluid-structure interaction problem in Microsystems
  9. Keywords:
  10. Finite Element Method ; Fluid-Solid Interaction ; Arbitrary Lagrangian-Eulerian Method ; Microsystems ; Small Time Instability

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