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Explicit Multipole Formula for the Local Thermal Resistance in an Energy Pile—The Line-Source Approximation

Author

Listed:
  • Johan Claesson

    (Building Physics, Lund University, 221 00 Lund, Sweden)

  • Saqib Javed

    (Building Services, Lund University, 221 00 Lund, Sweden)

Abstract

This paper presents a closed-form quite handy formula for the local thermal resistance R b between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy’s mean value theorem of analytical functions is used. The formula for thermal resistance R b0 for the zero-order approximation ( J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation ( J = 0) are shown to be quite small by comparisons with eight-order approximation ( J = 8) with its accuracy of more than eight digits. The relative error for the local thermal resistance R b0 for the zero-order approximation ( J = 0) lies below 5% for a wide range of input parameter values. These ranges are judged to cover most practical cases of application. The smallest local thermal resistance R bmin is, with some exceptions, obtained when the pipes lie directly in contact with the pile periphery. A neat formula for this minimum is presented.

Suggested Citation

  • Johan Claesson & Saqib Javed, 2020. "Explicit Multipole Formula for the Local Thermal Resistance in an Energy Pile—The Line-Source Approximation," Energies, MDPI, vol. 13(20), pages 1-24, October.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:20:p:5445-:d:431040
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    References listed on IDEAS

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    1. Ana Vieira & Maria Alberdi-Pagola & Paul Christodoulides & Saqib Javed & Fleur Loveridge & Frederic Nguyen & Francesco Cecinato & João Maranha & Georgios Florides & Iulia Prodan & Gust Van Lysebetten , 2017. "Characterisation of Ground Thermal and Thermo-Mechanical Behaviour for Shallow Geothermal Energy Applications," Energies, MDPI, vol. 10(12), pages 1-51, December.
    2. Johan Claesson & Saqib Javed, 2018. "Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 11(1), pages 1-17, January.
    3. Javed, Saqib & Spitler, Jeffrey, 2017. "Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers," Applied Energy, Elsevier, vol. 187(C), pages 790-806.
    4. Park, Hyunku & Lee, Seung-Rae & Yoon, Seok & Choi, Jung-Chan, 2013. "Evaluation of thermal response and performance of PHC energy pile: Field experiments and numerical simulation," Applied Energy, Elsevier, vol. 103(C), pages 12-24.
    5. Loveridge, Fleur & Powrie, William, 2013. "Temperature response functions (G-functions) for single pile heat exchangers," Energy, Elsevier, vol. 57(C), pages 554-564.
    6. Matteo Rivoire & Alessandro Casasso & Bruno Piga & Rajandrea Sethi, 2018. "Assessment of Energetic, Economic and Environmental Performance of Ground-Coupled Heat Pumps," Energies, MDPI, vol. 11(8), pages 1-23, July.
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    Cited by:

    1. Park, Sangwoo & Lee, Seokjae & Park, Sangyeong & Choi, Hangseok, 2022. "Empirical formulas for borehole thermal resistance of parallel U-type cast-in-place energy pile," Renewable Energy, Elsevier, vol. 197(C), pages 211-227.
    2. Charles Maragna & Fleur Loveridge, 2021. "A New Approach for Characterizing Pile Heat Exchangers Using Thermal Response Tests," Energies, MDPI, vol. 14(12), pages 1-18, June.

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