Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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The Basic Study on the Technique of Fluid Flow Analysis Using the Immersed Boundary Method

가상 경계 방법을 이용한 유동 해석 기법에 관한 기초 연구

  • 양승호 (부산대학교 공과대학 기계공학부) ;
  • 하만영 (부산대학교 공과대학 기계공학부) ;
  • 박일룡 (한국해양연구원 해양시스템안전연구)
  • Published : 2004.06.01
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Abstract

In most industrial applications, the geometrical complexity is combined with the moving boundaries. These problems considerably increase the computational difficulties since they require, respectively, regeneration and deformation of the grid. As a result, engineering flow simulation is restricted. In order to solve this kind of problems the immersed boundary method was developed. In this study, the immersed boundary method is applied to the numerical simulation of stationary, rotating and oscillating cylinders in the 2-dimensional square cavity. No-slip velocity boundary conditions are given by imposing feedback forcing term to the momentum equation. Besides, this technique is used with a second-order accurate interpolation scheme in order to improve the accuracy of flow near the immersed boundaries. The governing equations for the mass and momentum using the immersed boundary method are discretized on the non-staggered grid by using the finite volume method. The results agree well with previous numerical and experimental results. This study presents the possibility of the immersed boundary method to apply to the complex flow experienced in the industrial applications. The usefulness of this method will be confirmed when we solve the complex geometries and moving bodies.

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References

  1. Park, I.R. and Chun, H.H., 2001, 'A Study of Accuracy Improvement of an Analysis of Flow Around Arbitrary Bodies by Using an Eulerian-Lagrangian Method,' J. of Computational Fluids Engineering, Vol. 6, No.3, pp. 19-26
  2. Ye, T., Mittal, R., Udaykumar, H. S. and Shyy, W., 1999, 'An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries,' J. of Computational Physics, Vol. 156, pp. 209-240 https://doi.org/10.1006/jcph.1999.6356
  3. Calhoun, D. and LeVeque, R. J., 2000, 'A Cartesian Grid Finite-Volume Method for the Advection-Diffusion Equation in Irregular Geometries,' J. of Computational Physics, Vol. 157, pp. 143-180 https://doi.org/10.1006/jcph.1999.6369
  4. Udaykuma, H. S., Kan, H. C., Shyy W. and Tran-Son-Tay R., 1997, 'Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids,' J. of Computational Physics, Vol. 137, pp. 366-405 https://doi.org/10.1006/jcph.1997.5805
  5. Goldstein, D., Handler, R. and Sirovich, L., 1993, 'Modeling a No-Slip Boundary with an External Force Field,' J. of Computational Physics, Vol. 105, pp. 354-366 https://doi.org/10.1006/jcph.1993.1081
  6. Saiki, E. M. and Biringen, S., 1996, 'Numerical Simulation of a Cylinder in Uniform Flow; Application of a Virtual Boundary Method,' J. of Computational Physics,' Vol. 123, pp. 450-465 https://doi.org/10.1006/jcph.1996.0036
  7. Fadlun, E. A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., 2000, 'Combined Immersed Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations, ' J. of Computational Physics, Vol. 161, pp. 35-60 https://doi.org/10.1006/jcph.2000.6484
  8. Stokie, J. M. and Wetton, B. R., 1999, 'Analysis of Stiffness in the Immersed Boundary Method and Implications for Time-Stepping Schemes, ' J. of Computational Physics, Vol. 154, pp. 41-64 https://doi.org/10.1006/jcph.1999.6297
  9. Cortez, R., 1996, 'An Impulse-Based Approximation of Fluid Motion due to Boundary Forces,' J. of Computational Physics, Vol. 123, pp. 341-353 https://doi.org/10.1006/jcph.1996.0028
  10. Peskin, C.S., 1982, 'The Fluid Dynamics of Heart Valves: Experimental, Theoretical, and Computational Methods,' Annu. Rev. Fluid Mech., Vol. 14, pp. 235-259 https://doi.org/10.1146/annurev.fl.14.010182.001315
  11. Lai, M. C. and Peskin, C. S., 2000, 'An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity,' J. of Computational Physics, Vol. 160, pp.705-719 https://doi.org/10.1006/jcph.2000.6483
  12. Ghia, U., Ghia, K.N. and Shin, C.T., 1982, 'High-Re Solution for Incompressible Flow Using the Navier-Stokes Equation and Multigrid Method,' J. of Computational Physics, Vol. 48, pp.387-410 https://doi.org/10.1016/0021-9991(82)90058-4
  13. Yang, S. Y., 2003, 'The Study of the Characteristics of the Stationary, Rotating and Oscillating Cylinders Using the Immersed Boundary Method,' M.S. Thesis, Pusan National University
  14. Gresho, P. M., Chan, S. T., Lee, R. L. and Upson, C. D., 1984, 'A Modified Finite Element Method for Solving the Time-Dependent, Incompressible Navier-Stokes Equations. Part 2: Applications,' Int. J. Numer Methods in Fluids, 4(7), 619-640 https://doi.org/10.1002/fld.1650040703
  15. Coutanceau, M. and Bouard, R., 1977, 'Experimental Determination of the Viscous Flow in the Wake of a Circular Cylinder in Uniform Translation. Part 1: Steady Flow, Part 2: Unsteady Flow,' J. Fluid Mech., Vol. 79, No. 2, pp. 231-272 https://doi.org/10.1017/S0022112077000135