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RESEARCH PAPERS: Porous Media and Fluidized Beds

Deterministic Chaotic Behavior of Heat Transfer in Gas Fluidized Beds

[+] Author and Article Information
D. V. Pence, D. E. Beasley, J. B. Riester

Thermal-Fluid Sciences Research Laboratory, Department of Mechanical Engineering, Clemson University, Clemson, SC 29634

J. Heat Transfer 117(2), 465-472 (May 01, 1995) (8 pages) doi:10.1115/1.2822545 History: Received February 01, 1994; Revised August 01, 1994; Online December 05, 2007

Abstract

Instantaneous heat transfer signals acquired in the bubble flow regime in a gas fluidized bed were examined for evidence of deterministic chaotic behavior. Signals were acquired using a heat flux sensor mounted on the surface of a horizontal, heated cylinder. Both standard statistical measures and nonlinear analysis techniques were employed to provide qualitative as well as quantitative information regarding dynamic behavior of heat transfer in such a facility. Power spectra provided preliminary evidence that heat transfer in fluidized beds may be chaotic in nature. Positive finite estimates of the Kolmogorov entropy provide further evidence of behavior consistent with chaos. Mutual information has a dual purpose in this work. It was used to evaluate a time delay in which to embed the time series heat transfer signal, and as a qualitative measure of the degree of chaos inherent in the signals. The quantitative information derived from mutual information allows the system dynamics to be represented as phase trajectories in a pseudo-phase space created by embedding a measured discrete signal in the space defined by time-delay coordinate axes. Embedding dimensions determined via the correlation integral suggest that four degrees of freedom quantify the system dynamics for the fluidizing conditions investigated in this work. Embedding dimensions were found to be independent of the fluidization velocity. This is a consequence of maintaining operating conditions within the bubble flow regime. The Kolmogorov entropy was shown to delineate fundamental changes in hydrodynamics conditions at the surface of the cylinder. Phase plots provide a means of analyzing the dynamics of heat transfer occurring at the surface of the cylinder. Two distinct characteristic emulsion phase contacts were identified using phase space trajectories. Phase space trajectories that result from particles remaining motionless at the heat transfer surface are distinctly different from those that result from particles actively mixing at the surface of the cylinder.

Copyright © 1995 by The American Society of Mechanical Engineers
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