Research Papers: Fundamental Issues and Canonical Flows

Hysteresis Curve in Reproduction of Reynolds’ Color-Band Experiments

[+] Author and Article Information
Hidesada Kanda1

Department of Computer Science and Engineering, University of Aizu, Aizu-Wakamatsu, Fukushima 965-8580, Japankanda@u-aizu.ac.jp

Takayuki Yanagiya

Department of Computer Science and Engineering, University of Aizu, Aizu-Wakamatsu, Fukushima 965-8580, Japan


Corresponding author.

J. Fluids Eng 130(5), 051202 (Apr 29, 2008) (10 pages) doi:10.1115/1.2903741 History: Received September 25, 2007; Revised February 04, 2008; Published April 29, 2008

This article describes the reproduction and extended analysis of Reynolds’ color-band experiment. Reynolds found two critical Reynolds numbers (Rc) in pipe flows: Rc1 of 12,830 from laminar to turbulent flow and Rc2 of 2030 from turbulent to laminar flow. Since no clear relationship has been established between them, we studied how the entrance shape affects Rc. Thus, for the first time, a hysteresis graph can be drawn by connecting the two curves of Rc1 and Rc2 such that the two Rc values lie on separate branches of the hysteresis plot.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Flow state versus contraction ratio Cb and Re

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Figure 2

Schematic diagram of the experimental apparatus

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Figure 3

Sizes of ten pipe entrance shapes (unit: cm, D=2.6, L2=150)

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Figure 4

Frequency of flow states against Re in the vicinity of Rc for St and Be4 (Procedures 1 and 2); (a) Straight pipe (St), (b) bellmouth (Be4)

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Figure 5

Hysteresis curve drawn by connecting two lines of Rc1 and Rc2 against contraction ratio Cb



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