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Simple equations to evaluate the mean fluid temperature of double-U-tube borehole heat exchangers

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  • Zanchini, Enzo
  • Jahanbin, Aminhossein

Abstract

The design of ground-coupled heat pump systems requires the knowledge of the mean temperature Tfm of the working fluid in borehole heat exchangers. This quantity is usually approximated by the arithmetic mean of inlet and outlet temperature. The approximation yields an overestimation of the thermal resistance of the heat exchanger in thermal response tests, as well as errors in the estimation of the outlet fluid temperature in the dynamic simulation of ground-coupled heat pumps. Recently (Applied Energy 206, 2017, 1406–1415), Zanchini and Jahanbin determined, by finite element simulations, correlations that allow an immediate evaluation of Tfm in any working condition, with reference to double U-tube boreholes with length 100 m and shank spacing 85 mm. In this paper, the analysis presented there is extended to double U-tube boreholes with any length, between 50 and 200 m, and any shank spacing, between 65 and 105 mm. The results hold for every thermal conductivity of the sealing grout between 0.9 and 1.6 W/(m K), every volume flow rate between 12 and 24 L per minute, every diameter of the BHE and every working condition (heating, cooling, thermal response test), both in quasi-stationary and in transient regime.

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  • Zanchini, Enzo & Jahanbin, Aminhossein, 2018. "Simple equations to evaluate the mean fluid temperature of double-U-tube borehole heat exchangers," Applied Energy, Elsevier, vol. 231(C), pages 320-330.
    • Handle: RePEc:eee:appene:v:231:y:2018:i:c:p:320-330
    DOI: 10.1016/j.apenergy.2018.09.094
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    References listed on IDEAS

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    1. Zanchini, E. & Lazzari, S., 2013. "Temperature distribution in a field of long Borehole Heat Exchangers (BHEs) subjected to a monthly averaged heat flux," Energy, Elsevier, vol. 59(C), pages 570-580.
    2. Ruiz-Calvo, F. & De Rosa, M. & Acuña, J. & Corberán, J.M. & Montagud, C., 2015. "Experimental validation of a short-term Borehole-to-Ground (B2G) dynamic model," Applied Energy, Elsevier, vol. 140(C), pages 210-223.
    3. Zanchini, Enzo & Jahanbin, Aminhossein, 2017. "Correlations to determine the mean fluid temperature of double U-tube borehole heat exchangers with a typical geometry," Applied Energy, Elsevier, vol. 206(C), pages 1406-1415.
    4. Beier, Richard A., 2011. "Vertical temperature profile in ground heat exchanger during in-situ test," Renewable Energy, Elsevier, vol. 36(5), pages 1578-1587.
    5. Zhang, Linfeng & Zhang, Quan & Huang, Gongsheng & Du, Yaxing, 2014. "A p(t)-linear average method to estimate the thermal parameters of the borehole heat exchangers for in situ thermal response test," Applied Energy, Elsevier, vol. 131(C), pages 211-221.
    6. Zanchini, E. & Lazzari, S., 2014. "New g-functions for the hourly simulation of double U-tube borehole heat exchanger fields," Energy, Elsevier, vol. 70(C), pages 444-455.
    7. Beier, Richard A. & Spitler, Jeffrey D., 2016. "Weighted average of inlet and outlet temperatures in borehole heat exchangers," Applied Energy, Elsevier, vol. 174(C), pages 118-129.
    8. Marcotte, D. & Pasquier, P., 2008. "On the estimation of thermal resistance in borehole thermal conductivity test," Renewable Energy, Elsevier, vol. 33(11), pages 2407-2415.
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    Cited by:

    1. Zhang, Changxing & Wang, Xinjie & Sun, Pengkun & Kong, Xiangqiang & Sun, Shicai, 2020. "Effect of depth and fluid flow rate on estimate for borehole thermal resistance of single U-pipe borehole heat exchanger," Renewable Energy, Elsevier, vol. 147(P1), pages 2399-2408.
    2. Ding Ding & Wenjing He & Chunlu Liu, 2021. "Mathematical Modeling and Optimization of Vanadium-Titanium Black Ceramic Solar Collectors," Energies, MDPI, vol. 14(3), pages 1-20, January.
    3. Zhang, Changxing & Xu, Hang & Fan, Jianhua & Sun, Pengkun & Sun, Shicai & Kong, Xiangqiang, 2020. "The coupled two-step parameter estimation procedure for borehole thermal resistance in thermal response test," Renewable Energy, Elsevier, vol. 154(C), pages 672-683.
    4. Christopher Vella & Simon Paul Borg & Daniel Micallef, 2020. "The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 13(3), pages 1-16, January.
    5. Aminhossein Jahanbin & Claudia Naldi & Enzo Zanchini, 2020. "Relation Between Mean Fluid Temperature and Outlet Temperature for Single U-Tube Boreholes," Energies, MDPI, vol. 13(4), pages 1-23, February.
    6. Aminhossein Jahanbin & Giovanni Semprini & Andrea Natale Impiombato & Cesare Biserni & Eugenia Rossi di Schio, 2020. "Effects of the Circuit Arrangement on the Thermal Performance of Double U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 13(12), pages 1-19, June.

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