0
Research Papers: Two-Phase Flow and Heat Transfer

# Rationalized Concise Descriptions of Fluid Motions in an Oscillating/Pulsating Heat Pipe

[+] Author and Article Information
Masao Furukawa

Department of Electrical Systems Engineering,
Kogakuin University,
1-24-2, Nishi-Shinjuku, Shinjuku-ku,
Tokyo 163-8677, Japan
e-mail: au40740@ns.kogakuin.ac.jp

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 16, 2013; final manuscript received April 7, 2014; published online May 28, 2014. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 136(9), 092901 (May 28, 2014) (11 pages) Paper No: HT-13-1488; doi: 10.1115/1.4027553 History: Received September 16, 2013; Revised April 07, 2014

## Abstract

Various ways developed so far in modeling oscillating/pulsating heat pipes (OHPs/PHPs) are briefly reviewed to find which way would be serviceable for design purposes and also be helpful to mathematically plainly describe oscillatory/circulatory motions of the charged working fluid. A selected way basically follows Ma's approach but a theoretically new attempt is made to derive the oscillation angular frequency ratio from two differently represented expressions of the oscillation velocity. A two-phase flow and evaporative/condensing heat transfer analysis is then carried out to get the wave equation of pressure oscillation. Finally obtained are closed-form algebraic expressions, providing us with convenient means of predicting the oscillation frequency- and-amplitude and the wave velocity. To demonstrate the applicability of those expressions, numerical comparisons are extensively done between our predictions and many other ones.

<>

## References

Akachi, H., 1990, “Structure of a Heat Pipe,” U.S. Patent No. 4921041.
Akachi, H., 1993, “Structure of Micro-Heat Pipe,” U.S. Patent No. 5219020.
Groll, M., and Khandekar, S., 2002, “Pulsating Heat Pipes: A Challenge and Still Unsolved Problem in Heat Pipe Science,” Arch. Thermodyn., 23(4), pp. 17–28.
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.
Khandekar, S., Groll, M., Charoensawan, P., Rittidech, S., and Terdtoon, P., 2004, “Closed and Open Loop Pulsating Heat Pipes,” K-4, Proceedings of 13th International Heat Pipe Conference, China Academy of Space Technology, Shanghai, China, Vol. 1, pp. 38–51.
Zhang, Y., and Faghri, A., 2008, “Advances and Unsolved Issues in Pulsating Heat Pipes,” Heat Transfer Eng., 29(1), pp. 20–44.
Khandekar, S., Panigrahi, P. K., Lefevre, F., and Bonjour, J., 2010, “Local Hydrodynamics of Flow in a Pulsating Heat Pipe: A Review,” Front. Heat Pipes, 1, p. 023003.
Faghri, A., 2012, “Review and Advances in Heat Pipe Science and Technology,” ASME J. Heat Transfer, 134(12), p. 123001.
Taft, B. S., Williams, A. D., and Drolen, B. L., 2012, “Review of Pulsating Heat Pipe Working Fluid Selection,” AIAA J. Thermophys. Heat Transfer, 26(4), pp. 651–656.
Zuo, Z. J., North, M. T., and Ray, L., 1999, “Combined Pulsating and Capillary Heat Pipe Mechanism for High Heat Flux Electronics,” Proceedings of ASME Heat Transfer Division, L. C.Witte, ed., ASME, New York, HTD-Vol. 364-4, pp. 237–243.
Zuo, Z. J., North, M. T., and Wert, K. L., 2001, “High Heat Flux Heat Pipe Mechanism for Cooling of Electronics,” IEEE Trans. Comp. Packag. Technol., 24(2), pp. 220–225.
Wong, T. N., Tong, B. Y., Lim, S. M., and Ooi, K. T., 1999, “Theoretical Modeling of Pulsating Heat Pipe,” 11th International Heat Pipe Conference, Japan Association for Heat Pipes, Tokyo, Japan, pp. 378–382.
Liang, S. B., and Ma, H. B., 2004, “Oscillating Motions of Slug Flow in Capillary Tubes,” Int. Commun. Heat Mass Transfer, 31(3), pp. 365–375.
Dobson, R. T., and Harms, T. M., 1999, “Lumped Parameter Analysis of Closed and Open Oscillatory Heat Pipes,” 11th International Heat Pipe Conference, Japan Association for Heat Pipes, Tokyo, Japan, pp. 361–366.
Dobson, R. T., 2004, “Theoretical and Experimental Modeling of an Open Oscillatory Heat Pipe Including Gravity,” Int. J. Therm. Sci., 43(2), pp.113–119.
Ma, H. B., Hanlon, M. A., and Chen, C. L., 2001, “An Investigation of Oscillation Motions in a Pulsating Heat Pipe,” NHTC2001-20149, ASME 35th National Heat Transfer Conference, New York, pp. 1–7.
Ma, H. B., Maschmann, M. R., and Liang, S. B., 2002, “Heat Transport Capability in a Pulsating Heat Pipe,” 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, St Louis, Missouri, June 24–26, pp. 1–7.
Ma, H. B., Hanlon, M. A., and Chen, C. L., 2006, “An Investigation of Oscillating Motions in a Miniature Pulsating Heat Pipe,” Microfluidics Nanofluidics, 2(2), pp. 171–179.
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.
Cheng, P., and Ma, H. B., 2011, “A Mathematical Model of an Oscillating Heat Pipe,” Heat Transfer Eng., 32(11–12), pp. 1037–1046.
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.
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.
Zhang, Y., Faghri, A., and Shafii, M. B., 2002, “Analysis of Liquid-Vapor Pulsating Flow in a U-Shaped Miniature Tube,” Int. J. Heat Mass Transfer, 45(12), pp. 2501–2508.
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.
Zhang, Y., and Faghri, A., 2003, “Oscillatory Flow in Pulsating Heat Pipes With Arbitrary Numbers of Turns,” AIAA J. Thermophys. Heat Transfer, 17(3), pp. 340–347.
Mameli, M., Marengo, M., and Zinna, S., 2012, “Numerical Model of a Multi-Turn Closed Loop Pulsating Heat Pipe: Effects of the Local Pressure Losses Due to Meanderings,” Int. J. Heat Mass Transfer, 55(4), pp. 1036–1047.
Miyazaki, Y., and Akachi, H., 1998, “Self Excited Oscillation of Slug Flow in a Micro Channel,” Third International Conference on Multiphase Flow, Ecole Centrale de Lyon, Lyon, pp. 1–5.
Davies, J. T., 1972, Turbulence Phenomena, Academic, New York, pp. 49–62.
Moholkar, V. S., and Prandit, A. B., 1997, “Bubble Behavior in Hydrodynamic Cavitation: Effect of Turbulence,” AIChE J., 43(6), pp. 1641–1648.
Kosky, P. G., and Staub, F. W., 1971, “Local Condensing Heat Transfer Coefficients in the Annular Flow Regime,” AIChE J., 17(5), pp. 1037–1043.
Davis, E. J., and David, M. M., 1961, “Heat Transfer to High-Quality Steam-Water Mixtures Flowing in a Horizontal Rectangular Duct,” Can. J. Chem. Eng., 39(3), pp. 99–105.
Chen, J. C., 1966, “Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow,” Ind. Eng. Chem. Process Des. Dev., 5(3), pp. 322–329.
Akers, W. W., Deans, H. A., and Crosser, O. K., 1959, “Condensing Heat Transfer Within Horizontal Tubes,” Heat Transfer—Chicago, Chemical Engineering Progress Symp. Ser. No. 29, AIChE, New York, Vol. 55, pp. 171–176.
Cai, Q., Chen, C. L., and Asfia, J., 2006, “Operating Characteristic Investigations in Pulsating Heat Pipes,” ASME J. Heat Transfer, 128(12), pp. 1329–1334.
Xu, J. L., Li, Y. X., and Wong, T. N., 2005, “High Speed Flow Visualization of a Closed Loop Pulsating Heat Pipe,” Int. J. Heat Mass Transfer, 48(16), pp. 3338–3351.
Borgmeyer, B., and Ma, H. B., 2007, “Experimental Investigation of Oscillating Motions in a Flat Plate Pulsating Heat Pipe,” AIAA J. Thermophys. Heat Transfer, 21(2), pp. 405–409.
Kim, J. S., Bui, N. H., Jung, H. S., and Lee, W. H., 2003, “The Study on Pressure Oscillation and Heat Transfer Characteristics of Oscillating Capillary Tube Heat Pipe,” KSME Int. J., 17 (10), pp. 1533–1542.
Zhang, X. M., Xu, J. L., and Zhou, Z. Q., 2004, “Experimental Study of a Pulsating Heat Pipe Using FC-72, Ethanol, and Water as Working Fluids,” Exp. Heat Transfer, 17(1), pp. 47–67.
Xu, J. L., and Zhang, X. M., 2005, “Start-Up and Steady Thermal Oscillation of a Pulsating Heat Pipe,” Heat Mass Transfer, 41(8), pp. 685–694.
Das, S. P., Nikolayev, V. S., Lefevre, F., Pottier, B., Khandekar, S., and Bonjour, J., 2010, “Thermally Induced Two-Phase Oscillatory Flow Inside a Capillary Tube,” Int. J. Heat Mass Transfer, 53(19–20), pp. 3905–3913.
Miyazaki, Y., and Arikawa, M., 1999, “Oscillatory Flow in the Oscillating Heat Pipe,” Proceedings of 11th International Heat Pipe Conference, Japan Association for Heat Pipes, Tokyo, Japan, pp. 367–372.
Kim, J. S., Lee, E. S., Bae, N. S., Im, Y. B., and Bui, N. H., 2004, “Numerical Analysis of Pulsating Heat Pipe Based on the Separated Flow Model,” Proceedings of 13th International Heat Pipe Conference, China Academy of Space Technology, Shanghai, China, Vol. 2, pp. 200–205.
Lips, S., and Bonjour, J., 2007, “Oscillating Two-Phase Flow in a Capillary Tube: Experiments and Modeling,” Proceedings of 14th Heat Pipe Conference, M. B. H.Mantelli and S.Colle, eds., Federal University of Santa Catarina, Florianopolis, Brazil, pp. 292–297.
Xu, J., Zhang, Y., and Ma, H., 2009, “Effect of Internal Wick Structure on Liquid-Vapor Oscillatory Flow and Heat Transfer in an Oscillating Heat Pipe,” ASME J. Heat Transfer, 131(12), p. 121012.
Yuan, D., Qu, W., and Ma, T., 2010, “Flow and Heat Transfer of Liquid Plug and Neighboring Vapor Slugs in a Pulsating Heat Pipe,” Int. J. Heat Mass Transfer, 53(7–8), pp. 1260–1268.
Xian, H., Yang, Y., Liu, D., Liu, X., and Du, X., 2010, “Theoretical Analysis on the Thermal Characteristics of Oscillating Heat Pipe,” Proceedings of 14th International Heat Transfer Conference, ASME, New York, Vol. 5, pp. 321–326.
Shao, W., and Zhang, Y., 2011, “Effects of Film Evaporation and Condensation on Oscillatory Flow and Heat Transfer in an Oscillating Heat Pipe,” ASME J. Heat Transfer, 133(4), p. 042901.
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.
Furukawa, M., 2011, “Heat Transport by Inverse-Piezoelectric Driven Dream Pipe,” ASME J. Heat Transfer, 133(10), p. 101701.
Brennen, C. E., 1995, Cavitation and Bubble Dynamics, Oxford Engineering Science Series, Vol. 44, Oxford University Press, New York, pp. 162–203.
Zivi, S. M., 1964, “Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production,” ASME J. Heat Transfer, 86(2), pp. 247–252.
Stephan, K., 1992, Heat Transfer in Condensation and Boiling, C. V. Green, Translated, Springer-Verlag, New York, pp. 217–228.

## Figures

Fig. 1

Closed-loop oscillating/pulsating heat pipe

Fig. 4

Fig. 5

Angular frequency ratio versus heat load

Fig. 6

Fig. 7

Fig. 8

Fig. 9

(a) Wave to sonic velocity ratio versus heat load. (b) Reference wave velocity to sonic velocity ratio versus heat load.

Fig. 2

Temperature differences in evaporator or condenser versus heat load

Fig. 3

Maximum temperature difference versus heat load

## 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 Proceedings Articles
Related eBook Content
Topic Collections