IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v13y2020i20p5445-d431040.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/13/20/5445/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/13/20/5445/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Maragna, Charles & Loveridge, Fleur, 2019. "A resistive-capacitive model of pile heat exchangers with an application to thermal response tests interpretation," Renewable Energy, Elsevier, vol. 138(C), pages 891-910.
    3. Faizal, Mohammed & Bouazza, Abdelmalek & McCartney, John S., 2022. "Thermal resistance analysis of an energy pile and adjacent soil using radial temperature gradients," Renewable Energy, Elsevier, vol. 190(C), pages 1066-1077.
    4. Paul Christodoulides & Ana Vieira & Stanislav Lenart & João Maranha & Gregor Vidmar & Rumen Popov & Aleksandar Georgiev & Lazaros Aresti & Georgios Florides, 2020. "Reviewing the Modeling Aspects and Practices of Shallow Geothermal Energy Systems," Energies, MDPI, vol. 13(16), pages 1-45, August.
    5. 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.
    6. Cunha, R.P. & Bourne-Webb, P.J., 2022. "A critical review on the current knowledge of geothermal energy piles to sustainably climatize buildings," Renewable and Sustainable Energy Reviews, Elsevier, vol. 158(C).
    7. Zhao, Qiang & Chen, Baoming & Tian, Maocheng & Liu, Fang, 2018. "Investigation on the thermal behavior of energy piles and borehole heat exchangers: A case study," Energy, Elsevier, vol. 162(C), pages 787-797.
    8. Matt S. Mitchell & Jeffrey D. Spitler, 2020. "An Enhanced Vertical Ground Heat Exchanger Model for Whole-Building Energy Simulation," Energies, MDPI, vol. 13(16), pages 1-27, August.
    9. Bi, Yuehong & Lyu, Tianli & Wang, Hongyan & Sun, Ruirui & Yu, Meize, 2019. "Parameter analysis of single U-tube GHE and dynamic simulation of underground temperature field round one year for GSHP," Energy, Elsevier, vol. 174(C), pages 138-147.
    10. Cardoso de Freitas Murari, Milena & de Hollanda Cavalcanti Tsuha, Cristina & Loveridge, Fleur, 2022. "Investigation on the thermal response of steel pipe energy piles with different backfill materials," Renewable Energy, Elsevier, vol. 199(C), pages 44-61.
    11. 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.
    12. Sani, Abubakar Kawuwa & Singh, Rao Martand & Amis, Tony & Cavarretta, Ignazio, 2019. "A review on the performance of geothermal energy pile foundation, its design process and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 106(C), pages 54-78.
    13. Joanna Piotrowska-Woroniak, 2021. "Assessment of Ground Regeneration around Borehole Heat Exchangers between Heating Seasons in Cold Climates: A Case Study in Bialystok (NE, Poland)," Energies, MDPI, vol. 14(16), pages 1-32, August.
    14. Joanna Piotrowska-Woroniak, 2021. "Determination of the Selected Wells Operational Power with Borehole Heat Exchangers Operating in Real Conditions, Based on Experimental Tests," Energies, MDPI, vol. 14(9), pages 1-21, April.
    15. Linden Jensen-Page & Fleur Loveridge & Guillermo A. Narsilio, 2019. "Thermal Response Testing of Large Diameter Energy Piles," Energies, MDPI, vol. 12(14), pages 1-25, July.
    16. Alberdi-Pagola, Maria & Poulsen, Søren Erbs & Loveridge, Fleur & Madsen, Søren & Jensen, Rasmus Lund, 2018. "Comparing heat flow models for interpretation of precast quadratic pile heat exchanger thermal response tests," Energy, Elsevier, vol. 145(C), pages 721-733.
    17. 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.
    18. 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.
    19. Tomasz Sliwa & Kinga Jarosz & Marc A. Rosen & Anna Sojczyńska & Aneta Sapińska-Śliwa & Andrzej Gonet & Karolina Fąfera & Tomasz Kowalski & Martyna Ciepielowska, 2020. "Influence of Rotation Speed and Air Pressure on the Down the Hole Drilling Velocity for Borehole Heat Exchanger Installation," Energies, MDPI, vol. 13(11), pages 1-18, May.
    20. Choi, Wonjun & Kikumoto, Hideki & Choudhary, Ruchi & Ooka, Ryozo, 2018. "Bayesian inference for thermal response test parameter estimation and uncertainty assessment," Applied Energy, Elsevier, vol. 209(C), pages 306-321.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:13:y:2020:i:20:p:5445-:d:431040. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.