IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v11y2018i1p214-d127184.html
   My bibliography  Save this article

Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers

Author

Listed:
  • Johan Claesson

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

  • Saqib Javed

    (Building Services Engineering, Chalmers Technical University, Gothenburg 412 96, Sweden)

Abstract

Borehole thermal resistance is both an important design parameter and a key performance characteristic of a ground heat exchanger. Another quantity that is particularly important for ground heat exchangers is the internal thermal resistance between the heat exchanger pipes. Both these resistances can be calculated to a high degree of accuracy by means of the well-known multipole method. However, the multipole method has a fairly intricate mathematical algorithm and is thus not trivial to implement. Consequently, there is considerable interest in developing explicit formulas for calculating borehole resistances. This paper presents derivation and solutions of newly derived second-order and higher-order multipole formulas for calculating borehole thermal resistance and total internal thermal resistance of single U-tube ground heat exchangers. A new and simple form of the first-order multipole formula is also presented. The accuracy of the presented formulas is established by comparing them to the original multipole method. The superiority of the new higher-order multipole formulas over the existing formulas is also demonstrated.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:1:p:214-:d:127184
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/11/1/214/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/11/1/214/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Spitler, Jeffrey D. & Gehlin, Signhild E.A., 2015. "Thermal response testing for ground source heat pump systems—An historical review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 50(C), pages 1125-1137.
    2. 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.
    3. Ma, WeiWu & Li, Min & Li, Ping & Lai, Alvin C.K., 2015. "New quasi-3D model for heat transfer in U-shaped GHEs (ground heat exchangers): Effective overall thermal resistance," Energy, Elsevier, vol. 90(P1), pages 578-587.
    4. Spitler, Jeffrey D. & Javed, Saqib & Ramstad, Randi Kalskin, 2016. "Natural convection in groundwater-filled boreholes used as ground heat exchangers," Applied Energy, Elsevier, vol. 164(C), pages 352-365.
    5. 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.
    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. 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.
    2. David Huber & Viktoria Illyés & Veronika Turewicz & Gregor Götzl & Andreas Hammer & Karl Ponweiser, 2021. "Novel District Heating Systems: Methods and Simulation Results," Energies, MDPI, vol. 14(15), pages 1-23, July.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

    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. Wilke, Sascha & Menberg, Kathrin & Steger, Hagen & Blum, Philipp, 2020. "Advanced thermal response tests: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 119(C).
    3. Oleg Todorov & Kari Alanne & Markku Virtanen & Risto Kosonen, 2021. "Different Approaches for Evaluation and Modeling of the Effective Thermal Resistance of Groundwater-Filled Boreholes," Energies, MDPI, vol. 14(21), pages 1-25, October.
    4. 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.
    5. Yoshitaka Sakata & Takao Katsura & Ahmed A. Serageldin & Katsunori Nagano & Motoaki Ooe, 2021. "Evaluating Variability of Ground Thermal Conductivity within a Steep Site by History Matching Underground Distributed Temperatures from Thermal Response Tests," Energies, MDPI, vol. 14(7), pages 1-17, March.
    6. Tang, Fujiao & Nowamooz, Hossein, 2019. "Sensitive analysis on the effective soil thermal conductivity of the Thermal Response Test considering various testing times, field conditions and U-pipe lengths," Renewable Energy, Elsevier, vol. 143(C), pages 1732-1743.
    7. Li, Min & Zhang, Liwen & Liu, Gang, 2019. "Estimation of thermal properties of soil and backfilling material from thermal response tests (TRTs) for exploiting shallow geothermal energy: Sensitivity, identifiability, and uncertainty," Renewable Energy, Elsevier, vol. 132(C), pages 1263-1270.
    8. Arghand, Taha & Javed, Saqib & Trüschel, Anders & Dalenbäck, Jan-Olof, 2021. "Cooling of office buildings in cold climates using direct ground-coupled active chilled beams," Renewable Energy, Elsevier, vol. 164(C), pages 122-132.
    9. Javadi, Hossein & Mousavi Ajarostaghi, Seyed Soheil & Rosen, Marc A. & Pourfallah, Mohsen, 2019. "Performance of ground heat exchangers: A comprehensive review of recent advances," Energy, Elsevier, vol. 178(C), pages 207-233.
    10. 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.
    11. Pasquier, Philippe & Marcotte, Denis, 2020. "Robust identification of volumetric heat capacity and analysis of thermal response tests by Bayesian inference with correlated residuals," Applied Energy, Elsevier, vol. 261(C).
    12. 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.
    13. Ravi Shanker, Ganesh & Homan, K.O., 2022. "Convective transport from geothermal borehole heat exchangers embedded in a fluid-saturated porous medium," Renewable Energy, Elsevier, vol. 196(C), pages 328-342.
    14. 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.
    15. 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.
    16. 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.
    17. Zhang, Bo & Gu, Kai & Shi, Bin & Liu, Chun & Bayer, Peter & Wei, Guangqing & Gong, Xülong & Yang, Lei, 2020. "Actively heated fiber optics based thermal response test: A field demonstration," Renewable and Sustainable Energy Reviews, Elsevier, vol. 134(C).
    18. 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.
    19. Magraner, Teresa & Montero, Álvaro & Cazorla-Marín, Antonio & Montagud-Montalvá, Carla & Martos, Julio, 2021. "Thermal response test analysis for U-pipe vertical borehole heat exchangers under groundwater flow conditions," Renewable Energy, Elsevier, vol. 165(P1), pages 391-404.
    20. 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.

    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:11:y:2018:i:1:p:214-:d:127184. 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.