Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (1): 99-116.doi: https://doi.org/10.1007/s10483-012-1536-9

• Articles • 上一篇    下一篇

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

 A. MALATIP1, N. WANSOPHARK2, P. DECHAUMPHAI2   

  1. 1. Computer-Aided Research Unit, National Metal and Materials Technology Center,Pathumthani 12120, Thailand;
    2. Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University,Patumwan, Bangkok 10330, Thailand
  • 收稿日期:2010-12-16 修回日期:2011-08-17 出版日期:2011-12-29 发布日期:2012-01-01

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

 A. MALATIP1, N. WANSOPHARK2, P. DECHAUMPHAI2   

  1. 1. Computer-Aided Research Unit, National Metal and Materials Technology Center,Pathumthani 12120, Thailand;
    2. Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University,Patumwan, Bangkok 10330, Thailand
  • Received:2010-12-16 Revised:2011-08-17 Online:2011-12-29 Published:2012-01-01

摘要: An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Abstract: An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin (SUPG) method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid are performed by the Galerkin method. The second-order semiimplicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are linearized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

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