Numerical simulation analysis of high-temperature bent sodium heat pipes

Xiongwei Cheng; Hualei Jiang; Taosheng Li; Siwei Zhang; Chengjun Duan; Huaping Mei

doi:10.1515/kern-2023-0121

Article

Numerical simulation analysis of high-temperature bent sodium heat pipes

Xiongwei Cheng , Hualei Jiang , Taosheng Li , Siwei Zhang , Chengjun Duan and Huaping Mei

Published/Copyright: March 27, 2024

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Kerntechnik Volume 89 Issue 3

Abstract

High-temperature bent heat pipes are safety-level heat transfer components used in heat pipe cooled reactor, and their applications are becoming increasingly widespread. In this study, a comprehensive three-dimensional numerical model was established to evaluate the effects of different bending angles and radii on the performance of high-temperature heat pipes. The model solved for the temperature, pressure, and velocity fields in the wall, wick, and evaporator, considers the compressibility effect of the vapor. The study investigated parameters such as vapor pressure, vapor velocity, radial secondary flow field, wall temperature, wick temperature, and equivalent thermal resistance of powder sintered core sodium heat pipes with bending angles of 45°, 90°, 135°, 180°, and a bending radius under 90°. The results showed that when sodium vapor enters the bent pipe, the vapor flow deviates towards the outer side, resulting in higher vapor pressure at the outer side than the vapor pressure at the inner side, and the generation of radial secondary vortex. This leads to higher temperature in the evaporator and adiabatic sections of the bent heat pipe, while lower temperature in the condenser. Fractal patterns are observed in the outer and inner wall temperature curve in the adiabatic section, with lower temperatures on the inner side and higher temperatures on the outer side. The bent heat pipe exhibits higher equivalent thermal resistance than that of a straight heat pipe, and the equivalent thermal resistance increases with increasing bending angle, and the equivalent thermal resistance decreases with increasing bending radius.

Keywords: bent heat pipe; heat transfer; numerical simulation; bending angle; bending radius

Corresponding author: Siwei Zhang, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China, E-mail: siwei.zhang@inest.cas.cn

Funding source: Anhui Provincial Key Research and Development Project

Award Identifier / Grant number: No. 2022107020018

Research ethics: Not applicable.
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission. Xiongwei Cheng: Writing – original draft, Validation, Investigation, Formal analysis. Hualei Jiang: Writing – review & editing, Investigation. Taosheng Li: Supervision, Conceptualization. Siwei Zhang: Writing – review & editing, Resources, Conceptualization. Chengjun Duan: Writing – review & editing, Investigation. Huaping Mei: Funding acquisition.
Competing interests: The authors state no conflict of interest.
Research funding: This work is supported by Anhui Provincial Key Research and Development Project (No. 2022107020018).
Data availability: The raw data can be obtained on request from the corresponding author.

Nomenclature

C _p: specific heat (J/kg K)
h _fg: latent heat of vaporization (kJ/kg)
k: thermal conductivity (W/m K)
K: permeability (m²)
L: length (m)
P: pressure (Pa)
Q: heat transfer (W)
R _g: gas constant (J/[mol K])
T: temperature (k)
V: velocity vector
μ: dynamic viscosity (kg/m s)
ρ: density, (kg/m³)
n: unit normal vector
u: Velocity(m/s)
ε: wick porosity
Q _evap: heat transfer of evaporator (W)
h _f: convective heat transfer coefficient(W/m² k)
σ: Stefan-Boltzmann constant (W/[m² K⁴])
ω: spectral emissivity
r _p: radius of outer wall (m)
l _e: length of evaporator (m)
M: Molar mass (g/mol)

Subscripts

eff: effective
w: wick
v: vapor
l: liquid
ref: reference

References

Camarda, C. (1977). Analysis and radiant heating tests of a heat-pipe-cooled leading edge, NASA TN-8486, NASA, Available from: https://ui.adsabs.harvard.edu/abs/1977argt.rept.C.Search in Google Scholar

Chen, J.-S. and Chou, J.-H. (2015). The length and bending angle effects on the cooling performance of flat plate heat pipes. Int. J. Heat Mass Transfer 90: 848–856, https://doi.org/10.1016/j.ijheatmasstransfer.2015.06.032.Search in Google Scholar

Costello, F., Montague, A., and Merrigan (1986).Detailed transient model of a liquid-metal heat pipe, United States, Available from: https://www.osti.gov/servlets/purl/5847432.Search in Google Scholar

Elnaggar, M.H.A. (2014). Numerical investigation of characteristics of wick structure and working fluid of U-shape heat pipe for CPU cooling. Microelectronics Reliability 54: 297–302, https://doi.org/10.1016/j.microrel.2013.08.019.Search in Google Scholar

Fadhl, B., Wrobel, L.C., and Jouhara, H. (2015). CFD modelling of a two-phase closed thermosyphon charged with R134a and R404a. Appl. Therm. Eng. 78: 482–490, https://doi.org/10.1016/j.applthermaleng.2014.12.062.Search in Google Scholar

Faghri, A. and Chen, M.-M. (1989). A numerical analysis of the effects of conjugate heat transfer, vapor compressibility, and viscous dissipation in heat pipes. Numer. Heat Transf. A 16: 389–405, https://doi.org/10.1080/10407788908944723.Search in Google Scholar

Humphrey, J.a. C., Whitelaw, J.H., and Yee, G. (1981). Turbulent flow in a square duct with strong curvature. J. Fluid Mech. 103: 443–463, https://doi.org/10.1017/S0022112081001419.Search in Google Scholar

Ivanovski, M., Sorokin, V.P., and Yagodkin, I. (1982). Physical principles of heat pipes. Oxford University Press, Oxford.Search in Google Scholar

Jang, J. (1988). An analysis of startup from the frozen state and transient performance of heat pipes. Ph.D. thesis. Atlanta, Georgia Institute of Technology (Accessed 1 May 1988).Search in Google Scholar

Jang, J.H., Faghri, A., Chang, W.S., and Mahefkey, E.T. (1990). Mathematical modeling and analysis of heat pipe start-up from the frozen state. J. Heat Transfer 112: 586–594, https://doi.org/10.1115/1.2910427.Search in Google Scholar

Jiang, L., Tang, Y., and Pan, M. (2011). Effects of bending on heat transfer performance of axial micro-grooved heat pipe. J. Cent. South Univ. 18: 580–586, https://doi.org/10.1007/s11771-011-0734-2.Search in Google Scholar

Jin, Z., Wang, C., Liu, X., Dai, Z., Tian, W., Su, G., and Qiu, S. (2022). Operation and safety analysis of space lithium-cooled fast nuclear reactor. Ann. Nucl. Energy 166: 108729, https://doi.org/10.1016/j.anucene.2021.108729.Search in Google Scholar

Johns, A., Thurlow, E., Barez, F., and Shabany, Y. (2018). Performance evaluation of bent heat pipes. 2018 17th IEEE intersociety conference on thermal and thermomechanical phenomena in electronic systems (ITherm), May 29–June 1, 2018.10.1109/ITHERM.2018.8419621Search in Google Scholar

Mahdavi, M., Faghri, A., and Shabgard, H. (2021). Thermal performance of U-shaped and L-shaped heat pipes. Numer. Heat Transf. A 80: 411–435, https://doi.org/10.1080/10407782.2021.1947627.Search in Google Scholar

Merrigan, M.A., Keddy, E.S., Sena, J.T., and Elder, M.G. (1984). Heat pipe technology development for high temperature space radiator applications. LA-UR-84-1673, Los Alamos National Lab. Available from: https://www.osti.gov/biblio/6820159.Search in Google Scholar

Naemsai, T., Kammuang-lue, N., Terdtoon, P., and Sakulchangsatjatai, P. (2019). Numerical model of heat transfer characteristics for sintered-grooved wick heat pipes under non-uniform heat loads. Appl. Therm. Eng. 148: 886–896, https://doi.org/10.1016/j.applthermaleng.2018.10.058.Search in Google Scholar

Odhekar, D.D. and Harris, D.K. (2006). Experimental investigation of bendable heat pipes using sintered copper felt wick. Thermal and thermomechanical proceedings 10th intersociety conference on phenomena in electronics systems, May 8, 2006.ITHERM 2006. p. 57710.1109/ITHERM.2006.1645396Search in Google Scholar

Reay, D., Kew, P., and McGlen, R. (2014). Heat pipes: theory, design and applications. Butterworth-Heinemann, Oxford.Search in Google Scholar

Rohsenow, W.M., Hartnett, J.P. and Ganic, E.N. (1985). Handbook of heat transfer applications, 2nd ed. McGraw-Hill Book Co., New York, NY, United States. Available from: https://www.osti.gov/biblio/5893663.Search in Google Scholar

Sakulchangsatjatai, P., Thuchayapong, N., Terdtoon, P., and Sangsirakoup, N. (2011). Effect of tube bending on heat transfer characteristics of miniature heat pipe with sintered porous media. Defect Diffus. Forum 312–315: 1015–1020, https://doi.org/10.4028/www.scientific.net/DDF.312-315.1015.Search in Google Scholar

Taylor, A.M.K.P., Whitelaw, J.H., and Yianneskis, M. (1982). Curved ducts with strong secondary motion: velocity measurements of developing laminar and turbulent flow. J. Fluids Eng. 104: 350–359, https://doi.org/10.1115/1.3241850.Search in Google Scholar

Tian, Z., Wang, C., Huang, J., Guo, K., Zhang, D., Liu, X., Su, G., Tian, W., and Qiu, S. (2021). Code development and analysis on the operation of liquid metal high temperature heat pipes under full condition. Ann. Nucl. Energy 160: 108396, https://doi.org/10.1016/j.anucene.2021.108396.Search in Google Scholar

Tournier, J. and El‐Genk, M.S. (1995) HPTAM for modeling heat and mass transfers in a heat pipe wick, during startup from a frozen state. AIP Conf. Proc. 324: 123–134, https://doi.org/10.1063/1.47213.Search in Google Scholar

Tournier, J.-M. and El-Genk, M.S. (1995a) HPTAM, a two-dimensional heat pipe transient analysis model, including the startup from a frozen state, NAS 1.26:199553, NASA, Available from: https://ntrs.nasa.gov/citations/19960001697.Search in Google Scholar

Tournier, J.-M. and El-Genk, M.S. (1995b) User’s manual for HPTAM: a two-dimensional heat pipe transient analysis model, including the startup from a frozen state, NASA-CR-199552, NASA, Available from: https://ntrs.nasa.gov/citations/19960001689.Search in Google Scholar

Wang, C., Sun, H., Tang, S., Tian, W., Qiu, S., and Su, G. (2020). Thermal-hydraulic analysis of a new conceptual heat pipe cooled small nuclear reactor system. Nucl. Eng. Technol. 52: 19–26, https://doi.org/10.1016/j.net.2019.06.021.Search in Google Scholar

Wang, J. (2009). Experimental investigation of the transient thermal performance of a bent heat pipe with grooved surface. Appl. Energy 86: 2030–2037, https://doi.org/10.1016/j.apenergy.2009.01.003.Search in Google Scholar

Yan, B.H., Wang, C., and Li, L.G. (2020). The technology of micro heat pipe cooled reactor: a review. Ann. Nucl. Energy 135: 106948, https://doi.org/10.1016/j.anucene.2019.106948.Search in Google Scholar

Zhang, Z., Chai, X., Wang, C., Sun, H., Zhang, D., Tian, W., Qiu, S., and Su, G. (2021). Numerical investigation on startup characteristics of high temperature heat pipe for nuclear reactor. Nucl. Eng. Des. 378: 111180, https://doi.org/10.1016/j.nucengdes.2021.111180.Search in Google Scholar

Received: 2023-11-01

Accepted: 2024-03-07

Published Online: 2024-03-27

Published in Print: 2024-06-25

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/kern-2023-0121

Keywords for this article

bent heat pipe; heat transfer; numerical simulation; bending angle; bending radius