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Research Papers: Heat and Mass Transfer

Nonlinear Analysis of Chaotic Flow in a Three-Dimensional Closed-Loop Pulsating Heat Pipe

[+] Author and Article Information
S. M. Pouryoussefi

Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MO 65211

Yuwen Zhang

Fellow ASME
Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: zhangyu@missouri.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 9, 2016; final manuscript received June 22, 2016; published online August 2, 2016. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 138(12), 122003 (Aug 02, 2016) (13 pages) Paper No: HT-16-1184; doi: 10.1115/1.4034065 History: Received April 09, 2016; Revised June 22, 2016

Numerical simulation has been conducted for the chaotic flow in a 3D closed-loop pulsating heat pipe (PHP). Heat flux and constant temperature boundary conditions were applied for evaporator and condenser sections, respectively. Water and ethanol were used as working fluids. Volume of fluid (VOF) method has been employed for two-phase flow simulation. Spectral analysis of temperature time series was carried out using power spectrum density (PSD) method. Existence of dominant peak in PSD diagram indicated periodic or quasi-periodic behavior in temperature oscillations at particular frequencies. Correlation dimension values for ethanol as working fluid were found to be higher than that for water under the same operating conditions. Similar range of Lyapunov exponent values for the PHP with water and ethanol as working fluids indicated strong dependency of Lyapunov exponent on the structure and dimensions of the PHP. An O-ring structure pattern was obtained for reconstructed 3D attractor at periodic or quasi-periodic behavior of temperature oscillations. Minimum thermal resistance of 0.85 °C/W and 0.88 °C/W were obtained for PHP with water and ethanol, respectively. Simulation results showed good agreement with the experimental results from other work under the same operating conditions.

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References

Figures

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Fig. 1

Schematic cross-sectional view of the 3D PHP

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Fig. 2

Meshing configuration

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Fig. 3

Comparison of thermal resistance versus heating power between simulation results of this study and experimental results of Ref. [13]

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Fig. 4

Volume fractions of liquid and vapor at t = 0.1 s under heating power of 70 W and condenser temperature of 20 °C for ethanol, FR of 40% (a) and water, FR of 65% (b)

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Fig. 5

Volume fractions of liquid and vapor under heating power of 70 W and condenser temperature of 20 °C for ethanol as working fluid with FR of 40% at t = 0.8 s

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Fig. 6

Volume fractions of liquid and vapor under heating power of 70 W and condenser temperature of 20 °C for ethanol as working fluid with FR of 40% at t = 20 s

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Fig. 7

Volume fractions of liquid and vapor under heating power of 70 W and condenser temperature of 20 °C for water as working fluid with FR of 65% at t = 0.8 s

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Fig. 8

Volume fractions of liquid and vapor under heating power of 70 W and condenser temperature of 20 °C for water as working fluid with FR of 65% at t = 20 s

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Fig. 9

Vapor and liquid plugs in the PHP

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Fig. 10

Liquid film around the vapor plugs at evaporator (a), adiabatic section (b), and condenser (c)

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Fig. 11

Liquid film thickness versus heating power

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Fig. 12

Vapor bubbles combination

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Fig. 13

Time series of temperature (a) and PSD diagram (b) for point #16 under heating power of 90 W, condenser temperature of 20 °C, filling ratio of 45%, and water as working fluid

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Fig. 14

Time series of temperature (a) and PSD diagram (b) for point #11 under heating power of 90 W, condenser temperature of 20 °C, filling ratio of 55%, and ethanol as working fluid

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Fig. 15

Time series of temperature (a) and PSD diagram (b) for point #20 under heating power of 90 W, condenser temperature of 20 °C, filling ratio of 70%, and water as working fluid

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Fig. 16

Time series of temperature (a) and PSD diagram (b) for point #25 under heating power of 90 W, condenser temperature of 20 °C, filling ratio of 65%, and ethanol as working fluid

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Fig. 17

Correlation dimension values (Dc) with water (a) and ethanol (b) as working fluids

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Fig. 18

ACF versus time with water (a) and ethanol (b) as working fluids

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Fig. 19

Lyapunov exponents versus evaporator heating power at different filling ratios with water (a) and ethanol (b) as working fluids

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Fig. 20

Reconstructed 3D attractor patterns under (a) heating power of 75 W, condenser temperature of 20 °C, filling ratio of 55%, and ethanol as working fluid and (b) heating power of 40 W, condenser temperature of 20 °C, filling ratio of 60%, and water as working fluid, and (c) heating power of 80 W, condenser temperature of 20 °C, filling ratio of 65%, and ethanol as working fluid

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Fig. 21

Thermal resistance versus heating power at different filling ratios and water as working fluid

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Fig. 22

Thermal resistance versus heating power at different filling ratios and ethanol as working fluid

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