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RESEARCH PAPERS: Forced Convection

Transition of Chaotic Flow in a Radially Heated Taylor-Couette System

[+] Author and Article Information
R. Kedia, M. L. Hunt, T. Colonius

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125

J. Heat Transfer 121(3), 574-582 (Aug 01, 1999) (9 pages) doi:10.1115/1.2826018 History: Received July 07, 1998; Revised March 26, 1999; Online December 05, 2007

Abstract

Numerical simulations have been performed to study the stability of heated, incompressible Taylor-Couette flow for a radius ratio of 0.7 and a Prandtl number of 0.7. As Gr is increased, the Taylor cell that has the same direction of circulation as the natural convection current increases in size and the counterrotating cell becomes smaller. The flow remains axisymmetric and the average heat transfer decreases with the increase in Gr. When the cylinder is impulsively heated, the counterrotating cell vanishes and n = 1 spiral is formed for Gr = 1000. This transition marks an increase in the heat transfer due to an increase in the radial velocity component of the fluid. By slowly varying the Grashof number, the simulations demonstrate the existence of a hysteresis loop. Two different stable states with same heat transfer are found to exist at the same Grashof number. A time-delay analysis of the radial velocity and the local heat transfer coefficient time is performed to determine the dimension at two Grashof numbers. For a fixed Reynolds number of 100, the two-dimensional projection of the reconstructed attractor shows a limit cycle for Gr = −1700. The limit cycle behavior disappears at Gr = −2100, and the reconstructed attractor becomes irregular. The attractor dimension increases to about 3.2 from a value of 1 for the limit cycle case; similar values were determined for both the local heat transfer and the local radial velocity, indicating that the dynamics of the temperature variations can be inferred from that of the velocity variations.

Copyright © 1999 by The American Society of Mechanical Engineers
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