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

  • 제24권9호
  • /
  • Pages.1210-1218
  • /
  • 2000
  • /
  • 1226-4881(pISSN)
  • /
  • 2288-5324(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지
DOI QR코드

DOI QR Code

수평 환형 공간에서의 혼돈 열대류로의 분기

Bifurcation to Chaotic Thermal Convection in a Horizontal Annulus

  • 유주식 (안동대학교, 기계공학교육과) ;
  • 김용진 (한국기계연구원, 열유체환경연구부)
  • 발행 : 2000.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Thermal convection in a horizontal annulus is considered, and the bifurcation phenomena of flows from time-periodic to chaotic convection are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady flow bifurcates to a time-periodic flow with a fundamental frequency, and afterwards a period-tripling bifurcation occurs with further increase of the Rayleigh number. Chaotic convection is established after a period-doubling bifurcation. A periodic convection with period 4 appears after the first chaotic convection. At still higher Rayleigh numbers, chaotic flows reappear.

키워드

참고문헌

  1. Powe, R.E., Carley, C.T. and Bishop, E.H., 1969, 'Free Convective Flow Patterns in Cylindrical Annuli,' J. Heat Transfer, Vol. 91, pp. 310-314
  2. Rao, Y.F., Miki, Y., Fukuda, K., Takata, Y. and Hasegawa, S., 1985, 'Flow Patterns of Natural Convection in Horizontal Cylindrical Annuli,' Int. J Heat and Mass Transfer, Vol. 28, pp. 705-714 https://doi.org/10.1016/0017-9310(85)90193-0
  3. Mack, L.R. and Bishop, E.H., 1968, 'Natural Convection Between Horizontal Concentric Cylinders for Low Rayleigh Numbers,' Quarterly J. Mech. and Appl. Math., Vol. 21, pp. 223-241 https://doi.org/10.1093/qjmam/21.2.223
  4. Custer, J.R. and Shaughnessy, E.J., 1977, 'Thermoconvective Motion of Low Prandtl Number Fluids Within a Horizontal Cylindrical Annulus,' J. Heat Transfer, Vol. 99, pp. 596-602
  5. Fant, D.B., Prusa, J. and Rothmayer, A.P., 1990, 'Unsteady Multicellular Natural Convection in a Narrow Horizontal Cylindrical Annulus,' J. Heat Transfer, Vol. 112, pp. 379-387
  6. Yoo, J.-S., Choi, J.Y. and Kim, M.-U., 1994, 'Multicellular Natural Convection of a Low Prandtl Number Fluid Between Horizontal Concentric Cylinders,' Numerical Heat Transfer, Part A, Vol. 25, pp. 103-115 https://doi.org/10.1080/10407789408955939
  7. 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
  8. 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
  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. 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
  15. Roache, P.J., 1972, 'Computational Fluid Dynamics', Hermosa, pp. 53-64
  16. 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
  17. Bendat, J.S. and Piersol, A.G., 1986, 'Random data : Analysis and Measurement Procedures,' John Wiley and Sons, New York, pp. 325-424
  18. Guzman, A.M., Amon, C.H., 1996, 'Dynamical Flow Characterization of Transitional and Chaotic Regimes in Converging-Diverging Channels,' J. Fluid Mech. Vol. 321, pp. 25-57 https://doi.org/10.1017/S002211209600763X
  19. Goswami, B., 1997, 'The Role of Period Tripling in the Development of a Self Similar Bifurcation Structure,' Int. J Bifurcation and Chaos, Vol. 7, pp. 2691-2706 https://doi.org/10.1142/S0218127497001813
  20. Kimura, K., Schubert, G., Straus, J.M, 1986, 'Route to Chaos in Porous-Medium Thermal Convection,' J. Fluid Mech. Vol. 166, pp. 305-324 https://doi.org/10.1017/S0022112086000162
  21. 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