Chaotic Thermal Convection of a Intermediate Prandtl-Number Fluid in a Horizontal Annulus: Pr=0.2

- Journal title : Transactions of the Korean Society of Mechanical Engineers B
- Volume 25, Issue 3, 2001, pp.433-441
- Publisher : The Korean Society of Mechanical Engineers
- DOI : 10.22634/KSME-B.2001.25.3.433

Title & Authors

Chaotic Thermal Convection of a Intermediate Prandtl-Number Fluid in a Horizontal Annulus: Pr=0.2

Yu, Ju-Sik; Kim, Yong-Jin;

Yu, Ju-Sik; Kim, Yong-Jin;

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.

Keywords

Oscillatory Convection;Bifurcation;Chaos;Periodic Flow;Quasi-Periodic Flow;

Language

Korean

References

1.

Lee, Y. and Korpela, S. A., 1983, 'Multicellular Natural Convection in a Vertical Slot,' J. Fluid Mech., Vol. 126, pp. 91-121

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

5.

Yoo, J.-S., 1998, 'Natural Convection in a Narrow Horizontal Cylindrical Annulus,' Int. J. Heat and Mass Transfer, Vol. 41, pp. 3055-3073

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

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

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

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

11.

McLaughlin, J. B., Orszag, S. A., 1982, 'Transition from Periodic to Chaotic Thermal Convection,' J Fluid Mech. Vol. 122, pp. 123-142

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

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

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

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

18.

Ruelle, D. and Takens, F., 1971, 'On the Nature of Turbulence,' Commun. Math. Phys. Vol. 20, pp. 167-185

19.

Manneville, P. and Pomeau, Y., 1980, 'Different Ways to Turbulence in Dissipative Dynamical Systems,' Physica D., Vol. 1, pp. 219-235

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

22.

Bendat, J. S. and Piersol, A. G., 1986, Random data : Analysis and Measurement Procedures, John Wiley and Sons, New York, pp. 325-424