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Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition

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  • Zhou, Yang
  • Zheng, Zhi-xiang
  • Zhao, Guang-si

Abstract

Ground heat exchanges (GHEs) are widely applied in the ground source heat pump (GSHP) system for exploration of shallow geothermal energy. Heat transfer around a single GHE in the presence of both horizontal and vertical groundwater flow under a convective boundary condition is investigated. To describe the heat transfer process, three typical GHE models including the solid cylindrical heat source (SCS) model, the ring coil heat source (RCS) model and the finite line source (FLS) model are improved by incorporating the effect of horizontal and vertical groundwater flow and considering convection between the air and the ground surface. After introducing a new variable, analytical solutions for the three improved models are established using the Green's function method. Comparison between the analytical solution and a numerical solution of COMSOL is made, and the agreement between the two solutions confirms the derivation and programming process of the analytical solution. Effects of horizontal and vertical groundwater flow on the temperature increment caused by a SCS are investigated using the analytical solution. For situations with high velocities of horizontal groundwater flow, the curve relating the temperature increment and the depth has a depth-independent segment, and the temperature increment for locations near the mid-depth of heat source remains unchanged with the velocity of vertical groundwater flow changing; the variation of average temperature increment of pipe wall with the variation of vertical groundwater velocity is negligible. For situations with low velocities of horizontal groundwater flow (Pex = 10), strong vertical groundwater flow (Pez = 100) makes the aforementioned depth-independent segment disappear, and the temperature increment at a downstream location increases from 0.58 °C to 7.79 °C with the depth increasing from 0 to lc. With Pez increasing from 10 to 100, the average temperature increment of pipe wall decreases from 10.14 °C to 6.92 °C, which reduces the thermal resistance of ground and improves the economic performance of the GSHP system.

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  • Zhou, Yang & Zheng, Zhi-xiang & Zhao, Guang-si, 2022. "Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition," Energy, Elsevier, vol. 245(C).
    • Handle: RePEc:eee:energy:v:245:y:2022:i:c:s0360544222000627
    DOI: 10.1016/j.energy.2022.123159
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    References listed on IDEAS

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    1. Zhou, Guoqing & Zhou, Yang & Zhang, Donghai, 2016. "Analytical solutions for two pile foundation heat exchanger models in a double-layered ground," Energy, Elsevier, vol. 112(C), pages 655-668.
    2. Mustafa Omer, Abdeen, 2008. "Ground-source heat pumps systems and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 12(2), pages 344-371, February.
    3. Pasquier, Philippe & Marcotte, Denis, 2012. "Short-term simulation of ground heat exchanger with an improved TRCM," Renewable Energy, Elsevier, vol. 46(C), pages 92-99.
    4. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2016. "A finite line source model with Cauchy-type top boundary conditions for simulating near surface effects on borehole heat exchangers," Energy, Elsevier, vol. 98(C), pages 50-63.
    5. Yang, H. & Cui, P. & Fang, Z., 2010. "Vertical-borehole ground-coupled heat pumps: A review of models and systems," Applied Energy, Elsevier, vol. 87(1), pages 16-27, January.
    6. Zhang, Wenke & Yang, Hongxing & Lu, Lin & Fang, Zhaohong, 2013. "The analysis on solid cylindrical heat source model of foundation pile ground heat exchangers with groundwater flow," Energy, Elsevier, vol. 55(C), pages 417-425.
    7. Li, Min & Lai, Alvin C.K., 2012. "Heat-source solutions to heat conduction in anisotropic media with application to pile and borehole ground heat exchangers," Applied Energy, Elsevier, vol. 96(C), pages 451-458.
    8. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2015. "Ground energy balance for borehole heat exchangers: Vertical fluxes, groundwater and storage," Renewable Energy, Elsevier, vol. 83(C), pages 1341-1351.
    9. Pan, Aiqiang & McCartney, John S. & Lu, Lin & You, Tian, 2020. "A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground," Energy, Elsevier, vol. 200(C).
    10. Beier, Richard A. & Acuña, José & Mogensen, Palne & Palm, Björn, 2013. "Borehole resistance and vertical temperature profiles in coaxial borehole heat exchangers," Applied Energy, Elsevier, vol. 102(C), pages 665-675.
    11. Cui, Ping & Li, Xin & Man, Yi & Fang, Zhaohong, 2011. "Heat transfer analysis of pile geothermal heat exchangers with spiral coils," Applied Energy, Elsevier, vol. 88(11), pages 4113-4119.
    12. Eslami-nejad, Parham & Bernier, Michel, 2012. "Freezing of geothermal borehole surroundings: A numerical and experimental assessment with applications," Applied Energy, Elsevier, vol. 98(C), pages 333-345.
    13. Li, Min & Lai, Alvin C.K., 2015. "Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales," Applied Energy, Elsevier, vol. 151(C), pages 178-191.
    14. Li, Min & Lai, Alvin C.K., 2012. "New temperature response functions (G functions) for pile and borehole ground heat exchangers based on composite-medium line-source theory," Energy, Elsevier, vol. 38(1), pages 255-263.
    15. Go, Gyu-Hyun & Lee, Seung-Rae & Yoon, Seok & Kang, Han-byul, 2014. "Design of spiral coil PHC energy pile considering effective borehole thermal resistance and groundwater advection effects," Applied Energy, Elsevier, vol. 125(C), pages 165-178.
    16. Zhou, Yang & Wu, Zi-han & Wang, Kang, 2021. "An analytical model for heat transfer outside a single borehole heat exchanger considering convection at ground surface and advection of vertical water flow," Renewable Energy, Elsevier, vol. 172(C), pages 1046-1062.
    17. Beier, Richard A., 2011. "Vertical temperature profile in ground heat exchanger during in-situ test," Renewable Energy, Elsevier, vol. 36(5), pages 1578-1587.
    18. 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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