0
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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Shafii, M. B. , Faghri, A. , and Zhang, Y. , 2001, “ Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes,” ASME J. Heat Transfer, 123(6), pp. 1159–1172. [CrossRef]
Shafii, M. B. , Faghri, A. , and Zhang, Y. , 2002, “ Analysis of Heat Transfer in Unlooped and Looped Pulsating Heat Pipes,” Int. J. Numer. Methods Heat Fluid Flow, 12(5), pp. 585–609. [CrossRef]
Zhang, Y. , and Faghri, A. , 2002, “ Heat Transfer in a Pulsating Heat Pipe With Open End,” Int. J. Heat Mass Transfer, 45(4), pp. 755–764. [CrossRef]
Zhang, Y. , and Faghri, A. , 2003, “ Oscillatory Flow in Pulsating Heat Pipes With Arbitrary Numbers of Turns,” J. Thermophys. Heat Transfer, 17(3), pp. 340–347. [CrossRef]
Zhang, Y. , and Faghri, A. , 2008, “ Advances and Unsolved Issues in Pulsating Heat Pipes,” Heat Transfer Eng., 29(1), pp. 20–44. [CrossRef]
Shao, W. , and Zhang, Y. , 2011, “ Thermally-Induced Oscillatory Flow and Heat Transfer in an Oscillating Heat Pipe,” J. Enhanced Heat Transfer, 18(3), pp. 177–190. [CrossRef]
Kim, S. , Zhang, Y. , and Choi, J. , 2013, “ Entropy Generation Analysis for a Pulsating Heat Pipe,” Heat Transfer Res., 44(1), pp. 1–30. [CrossRef]
Kim, S. , Zhang, Y. , and Choi, J. , 2013, “ Effects of Fluctuations of Heating and Cooling Section Temperatures on Performance of a Pulsating Heat Pipe,” Appl. Therm. Eng., 58(1), pp. 42–51. [CrossRef]
Ma, H. B. , Borgmeyer, B. , Cheng, P. , and Zhang, Y. , 2008, “ Heat Transport Capability in an Oscillating Heat Pipe,” ASME J. Heat Transfer, 130(8), p. 081501. [CrossRef]
Thompson, S. M. , Ma, H. B. , Winholtz, R. A. , and Wilson, C. , 2009, “ Experimental Investigation of Miniature Three-Dimensional Flat-Plate Oscillating Heat Pipe,” ASME J. Heat Transfer, 131(4), p. 043210. [CrossRef]
Thompson, S. M. , Cheng, P. , and Ma, H. B. , 2011, “ An Experimental Investigation of a Three-Dimensional Flat-Plate Oscillating Heat Pipe With Staggered Microchannels,” Int. J. Heat Mass Transfer, 54(17), pp. 3951–3959. [CrossRef]
Ma, H. B. , 2015, Oscillating Heat Pipes, Springer, New York.
Shafii, M. B. , Arabnejad, S. , Saboohi, Y. , and Jamshidi, H. , 2010, “ Experimental Investigation of Pulsating Heat Pipes and a Proposed Correlation,” Heat Transfer Eng., 31(10), pp. 854–861. [CrossRef]
Qu, J. , Wu, H. , and Cheng, P. , 2009, “ Experimental Study on Thermal Performance of a Silicon-Based Micro Pulsating Heat Pipe,” ASME Paper No. MNHMT2009-18525.
Qu, J. , Wu, H. , and Wang, Q. , 2012, “ Experimental Investigation of Silicon-Based Micro-Pulsating Heat Pipe for Cooling electronics,” Nanoscale Microscale Thermophys. Eng., 16(1), pp. 37–49. [CrossRef]
Turkyilmazoglu, M. , 2015, “ Anomalous Heat Transfer Enhancement by Slip Due to Nanofluids in Circular Concentric Pipes,” Int. J. Heat Mass Transfer, 85, pp. 609–614. [CrossRef]
Turkyilmazoglu, M. , 2015, “ Analytical Solutions of Single and Multi-Phase Models for the Condensation of Nanofluid Film Flow and Heat Transfer,” Eur. J. Mech. B/Fluids, 53, pp. 272–277. [CrossRef]
Turkyilmazoglu, M. , 2015, “ A Note on the Correspondence Between Certain Nanofluid Flows and Standard Fluid Flows,” ASME J. Heat Transfer, 137(2), p. 024501. [CrossRef]
Xian, H. , Xu, W. , Zhang, Y. , Du, X. , and Yang, Y. , 2015, “ Experimental Investigations of Dynamic Fluid Flow in Oscillating Heat Pipe Under Pulse Heating,” Appl. Therm. Eng., 88, pp. 376–383. [CrossRef]
Jiaqiang, E. , Zhao, X. , Deng, Y. , and Zhu, H. , 2016, “ Pressure Distribution and Flow Characteristics of Closed Oscillating Heat Pipe During the Starting Process at Different Vacuum Degrees,” Appl. Therm. Eng., 93, pp. 166–173. [CrossRef]
Khandekar, S. , Schneider, M. , and Groll, M. , 2002, “ Mathematical Modeling of Pulsating Heat Pipes: State of the Art and Future Challenges,” Heat and Mass Transfer, S. K. Saha , S. P. Venkateshen , B. V. S. S. S. Prasad , and S. S. Sadhal , eds., Tata McGraw-Hill Publishing Company, New Delhi, India, pp. 856–862. [PubMed] [PubMed]
Dobson, R. T. , 2004, “ Theoretical and Experimental Modelling of an Open Oscillatory Heat Pipe Including Gravity,” Int. J. Therm. Sci., 43(2), pp. 113–119. [CrossRef]
Xiao-Ping, L. , and Cui, F. Z. , 2008, “ Modelling of Phase Change Heat Transfer System for Micro-channel and Chaos Simulation,” Chin. Phys. Lett., 25(6), pp. 2111–2114. [CrossRef]
Song, Y. , and Xu, J. , 2009, “ Chaotic Behavior of Pulsating Heat Pipes,” Int. J. Heat Mass Transfer, 52(13), pp. 2932–2941. [CrossRef]
Qu, J. , Wu, H. , Cheng, P. , and Wang, X. , 2009, “ Non-Linear Analyses of Temperature Oscillations in a Closed-Loop Pulsating Heat Pipe,” Int. J. Heat Mass Transfer, 52(15), pp. 3481–3489. [CrossRef]
Pouryoussefi, S. M. , and Zhang, Y. , 2016, “ Numerical Investigation of Chaotic Flow in a 2D Closed-Loop Pulsating Heat Pipe,” Appl. Therm. Eng., 98, pp. 617–627. [CrossRef]
Kantz, H. , and Schreiber, T. , 2004, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge.
Bradley, E. , 1999, “ Time-Series Analysis,” Intelligent Data Analysis: An Introduction, Springer, Berlin.
Strogatz, S. H. , 2014, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press, Boulder, CO.

Figures

Grahic Jump Location
Fig. 1

Schematic cross-sectional view of the 3D PHP

Grahic Jump Location
Fig. 2

Meshing configuration

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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)

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 9

Vapor and liquid plugs in the PHP

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
Fig. 11

Liquid film thickness versus heating power

Grahic Jump Location
Fig. 12

Vapor bubbles combination

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 17

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

Grahic Jump Location
Fig. 18

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

Grahic Jump Location
Fig. 19

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 21

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

Grahic Jump Location
Fig. 22

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In