An improved correlation to predict the heat transfer in pulsating heat pipes over increased range of fluid-filling ratios and operating inclinations

Abstract

Previous correlations that have been used to predict the heat transfer performance of pulsating heat pipes (PHPs) offer limited thermal predictions within a narrow range of fluid-filling ratios and PHP inclinations. In this paper, a novel semi-empirical correlation with improved scope is proposed, with an increased range of fluid-filling ratios and PHP inclinations. The proposed correlation employs the dimensionless numbers governing the thermo-hydrodynamic operation of PHPs, and achieved ±30 % accuracy when predicting selected experimental data, showing reasonably good agreement. Unlike previous correlations, the new correlation can be used for different working fluids, geometrical aspect ratios, and heat loads. A comprehensive assessment of the relative significance of the correlation parameters on the total heat transfer performance is discussed. The new correlation with its flexible application range is expected to assist in faster and more enhanced thermal predictions as interest in PHPs grows.

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Abbreviations

a* :

Exponent, (-1258φ4+2662.1 φ3+655.28φ2-1.22)

ASD Ku :

Average standard deviation, \(\left(\begin{array}{c}\frac{1}{N}\end{array}\right)\sum_{i=1}^n|(Ku_{exp}-Ku_{pred})/Ku_{exp}|\)

b* :

Coefficient, (-142.5φ4+301.5φ3-227.6φ2+ 72.21φ-6.87)

Bo :

Bond number, (di [(gl - ρv)/ σ)05] = Eo0.5)

C p :

Specific heat, J/kg-K

d :

Diameter, m

d crit :

Critical diameter, (2[σ/gl - ρv)]0.5)

Ëo :

Eötvös number, (Bo2)

f :

Friction factor

g :

Gravitational acceleration, m/s2

h fg :

Heat of vaporization, J/kg

Ja :

Jakob number, (cplΔTe-c, sat / hfg)

Ja* :

Adjusted Ja, ((φ cplΔTe-c, sat /(1 - φ) hfg)

K :

Conductivity, W/mK

Ka :

Karman number (f Rel2) = (ρl ΔPl di2/ μl2Leff)

Ku :

Kutateladze number, Eq. (2)

L :

Length, m

Leff :

Effective length, (0.5Le + 0.5Lc)+La, m

Mo :

Morton number, (g Δρ μ4/ ρ12 σ3)

N :

Number of turns, number of datasets

ΔP :

Pressure difference, Pa

Pr :

Prandtl number, (cplμl / kl)

q :

Heat transfer, W

:

Heat flux, W/m2

Re :

Reynolds number (ρvdj /μ)

SD :

Standard deviation

T :

Temperature, K

Wa :

Wallis number, (1 +(ρv/ρj)0.25)

μ :

Viscosity, Pas

φ :

Filling ratio, %

β :

Inclination angle, degrees

ρ:

Density, (Kg/m3)

σ :

Surface tension (N/m)

a :

Adiabatic, ambient air

c :

Condenser, coolant, closed

crit :

Critical

eff :

Effective

e :

Evaporator

exp :

Experiment

fg :

Liquid-vapour

i :

Inner

l :

Liquid

o :

Outer, open

pred :

Prediction

sat :

Saturation

t :

Total, thickness

v :

Vapor

CEPHP :

Closed-end PHP

CLPHP :

Closed-looped PHP

HP :

Heat pipes

OHP :

Oscillating heat pipes

PHP :

Pulsating heat pipes

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Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B0 7046034). We wish to convey our utmost thanks to Rolls Royce plc. for their support in this study through the University Technology Centre (UTC) programme.

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Correspondence to June Kee Min.

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Recommended by Editor Yong Tae Kang

Foster Kwame Kholi received his M.S. in Oil and Gas Engineering from the University of Aberdeen, Scotland, and Chemical Engineering from Imperial College London, London. He is currently a Ph.D. student at the School of Mechanical Engineering, Pusan National University, in Busan, South Korea. His research interest includes energy systems related to aerother-mal management.

June Kee Min received his Ph.D. degree from Korea Advanced Institute of Science and Technology, Korea, in 1999. Currently, he is a Professor at the School of Mechanical Engineering at Pusan National University in Busan, Korea. His research interest focuses on the development of advanced CFD models for various complicated flow and heat transfer problems.

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Kholi, F.K., Mucci, A., Kallath, H. et al. An improved correlation to predict the heat transfer in pulsating heat pipes over increased range of fluid-filling ratios and operating inclinations. J Mech Sci Technol 34, 2637–2646 (2020). https://doi.org/10.1007/s12206-020-0537-1

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Keywords

  • Critical number of turns
  • Fluid-filling ratio
  • Heat transfer correlation
  • Inclination angles
  • Kutateladze number
  • Pulsating heat pipes