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

The Korean Society of Mechanical Engineers (대한기계학회)
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Chaotic Thermal Convection of a Intermediate Prandtl-Number Fluid in a Horizontal Annulus: Pr=0.2

수평 환형 공간에서의 중간 Prandtl 수 유체의 혼돈 열대류: Pr=0.2

  • 유주식 (안동대학교, 기계공학교육과) ;
  • 김용진 (한국기계연구원, 열유체환경연구부)
  • Published : 2001.03.01
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Abstract

Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

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References

  1. Lee, Y. and Korpela, S. A., 1983, 'Multicellular Natural Convection in a Vertical Slot,' J. Fluid Mech., Vol. 126, pp. 91-121 https://doi.org/10.1017/S0022112083000063
  2. Busse, F. H., 'Transition to Turbulence in Rayleigh- Benard Convection,' In Topics in Applied Physics, Vol. 45, Edited by H. L. Swinney and J. P. Gollub. Springer-Verlag, 1981, pp. 97-137
  3. Gebhart, B., Jaluria, Y., Mahajan, R. L. and Sammakia, B., 1988, 'Buoyancy-Induced Flows and Transport,' Springer-Verlag, pp. 761-771
  4. Kuehn, T. H. and Goldstein, R. J., 1976, 'An Experimental and Theoretical Study of Natural Convection in the Annulus Between Horizontal Concentric Cylinders,' J. Fluid Mech. Vol. 74, pp. 695-719 https://doi.org/10.1017/S0022112076002012
  5. Yoo, J.-S., 1998, 'Natural Convection in a Narrow Horizontal Cylindrical Annulus,' Int. J. Heat and Mass Transfer, Vol. 41, pp. 3055-3073 https://doi.org/10.1016/S0017-9310(98)00051-9
  6. Yoo, J.-S.,1999, 'Transition and Multiplicity of Flows in Natural Convection in a Narrow Horizontal Cylindrical Annulus : Pr=0.4,' Int. J Heat and Mass Transfer, Vol. 42, pp. 709-722 https://doi.org/10.1016/S0017-9310(98)00197-5
  7. Yoo, J.-S., 1999, 'Prandtl Number Effect on Bifurcation and Dual Solutions in Natural Convection in a Horizontal Annulus,' Int. J Heat and Mass Transfer, Vol. 42, pp. 3275-3286 https://doi.org/10.1016/S0017-9310(98)00384-6
  8. Yoo, J.-S., 1999, 'Prandtl Number Effect on Transition of Free-Convective Flows in a Wide-Gap Horizontal Annulus,' Int. Comm.. Heat Mass Transfer, Vol. 26, pp. 811-817 https://doi.org/10.1016/S0735-1933(99)00069-X
  9. Schuster, H. G., 1984, 'Deterministic Chaos,' Physik-Verlag, pp. 1-136
  10. Gollub, J. P., Benson, S. V., 1980. 'Many Routes to Turbulent Convection,' J Fluid Mech. Vol. 100, pp. 449-470 https://doi.org/10.1017/S0022112080001243
  11. McLaughlin, J. B., Orszag, S. A., 1982, 'Transition from Periodic to Chaotic Thermal Convection,' J Fluid Mech. Vol. 122, pp. 123-142 https://doi.org/10.1017/S0022112082002122
  12. Yoo, J.-S., Kim, M.-U., 1991. 'Two-Dimensional Convection in a Horizontal Fluid Layer with Spatially Periodic Boundary Temperatures,' Fluid Dynamics Research, Vol. 7, pp. 181-200 https://doi.org/10.1016/0169-5983(91)90057-P
  13. Guzman, A. M., Amon, C. H., 1994, 'Transition to Chaos in Converging -Diverging Channel Flows: Ruelle -Takens -Newhouse Scenario,' Phys. Fluids A, Vol. 6, pp. 1994-2002 https://doi.org/10.1063/1.868206
  14. Vittori, G., Blondeaux, P., 1993. 'Quasiperiodicity and phase locking route to chaos in the 2-D oscillatory flow around a circular cylinder,' Phys. Fluids A 5, pp. 1866-1868 https://doi.org/10.1063/1.858886
  15. Mukutmoni, D. and Yang, K. T., 1993, 'Rayleigh-Benard Convection in a Small Aspect Ratio Enclosure: Part II- Bifurcation to Chaos,' J. Heat Transfer, Vol. 115, pp. 367-376
  16. 유주식, 김용진, 2000, '수평 환형 공간에서의 혼돈 열대류로의 분기,' 대한기계학회논문집 B권, 제 24권 제 9호, pp. 1-9
  17. Feigenbaum, M., 1980, 'The Transition to Aperiodic Behavior in Turbulent Systems,' Commun. Math. Phys. Vol. 77, pp. 65-80 https://doi.org/10.1007/BF01205039
  18. Ruelle, D. and Takens, F., 1971, 'On the Nature of Turbulence,' Commun. Math. Phys. Vol. 20, pp. 167-185 https://doi.org/10.1007/BF01646553
  19. Manneville, P. and Pomeau, Y., 1980, 'Different Ways to Turbulence in Dissipative Dynamical Systems,' Physica D., Vol. 1, pp. 219-235 https://doi.org/10.1016/0167-2789(80)90013-5
  20. Roache, P. J., 1972, 'Computational Fluid Dynamics,' Hermosa, pp. 53-64
  21. Buzbee, B. L., Golub, G. H. and Nielson, C. W., 1970, 'On Direct Methods for Solving Poisson's Equations,' SIAM J. Numerical Analysis, Vol. 7, pp. 627-656 https://doi.org/10.1137/0707049
  22. Bendat, J. S. and Piersol, A. G., 1986, Random data : Analysis and Measurement Procedures, John Wiley and Sons, New York, pp. 325-424