FINITE HOLLOW CYLINDRICAL SURFACE SOURCE MODEL AND ANALYTICAL SOLUTION FOR VERTICAL BOREHOLE GROUND BURIED TUBE HEAT EXCHANGER

Shi Zhigang; Zhang Luyao; Li Zhigang; Liu Wanqing; Liu Demin; Cai Chao

doi:10.19912/j.0254-0096.tynxb.2023-2036

PDF(1260 KB)

Acta Energiae Solaris Sinica ›› 2025, Vol. 46 ›› Issue (4) : 66-73. DOI: 10.19912/j.0254-0096.tynxb.2023-2036

FINITE HOLLOW CYLINDRICAL SURFACE SOURCE MODEL AND ANALYTICAL SOLUTION FOR VERTICAL BOREHOLE GROUND BURIED TUBE HEAT EXCHANGER

Shi Zhigang¹, Zhang Luyao¹, Li Zhigang¹, Liu Wanqing¹, Liu Demin², Cai Chao²

Author information +

History +

Abstract

A novel model is introduced to describe the finite length hollow cylindrical surface source（FHCS）, and an analytical solution for this innovative model is obtained using Green’s function method. A comparative analysis was conducted between the proposed model, finite line source model（FLS）, and finite cylindrical surface source model（FCS）. The research results show that in the vertical direction, the three models exhibit consistent variation trends with relatively small differences. When the operating time is short, the temperature rise of FHCS is greater than that of FCS, while FLS experiences minimal temperature rise. However, as the operating time increases, the temperature differences among the three models decrease. Based on this model, the temperature distributions in the borehole and surrounding soil were examined, followed by a thorough comparative analysis across different times, radial distances, borehole radius and axial orientations. The study demonstrates that the finite hollow cylindrical surface source model can reveal the heat transfer characteristics of boreholes.

Key words

geothermal energy / ground source heat pumps / heat exchangers / temperature distribution / analytical models / Green's function

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

Shi Zhigang, Zhang Luyao, Li Zhigang, Liu Wanqing, Liu Demin, Cai Chao. FINITE HOLLOW CYLINDRICAL SURFACE SOURCE MODEL AND ANALYTICAL SOLUTION FOR VERTICAL BOREHOLE GROUND BURIED TUBE HEAT EXCHANGER[J]. Acta Energiae Solaris Sinica. 2025, 46(4): 66-73 https://doi.org/10.19912/j.0254-0096.tynxb.2023-2036

References

[1] 张哲菲, 刘洪涛, 刘攀峰, 等. 中深层地热地埋管实际运行影响因素研究[J]. 太阳能学报, 2022, 43(12): 503-509.
ZHANG Z F, LIU H T, LIU P F, et al.Study on actual operation and influencing factors of middle-deep geothermal buried pipe[J]. Acta energiae solaris sinica, 2022, 43(12): 503-509.
[2] 朱强, 杨轩, 马凌, 等. 中深层地热单井循环系统传热强化方法研究[J]. 太阳能学报, 2023, 44(1): 410-417.
ZHU Q, YANG X, MA L, et al.Research on heat transfer enhancement method of medium-deep single geothermal well circulation system[J]. Acta energiae solaris sinica, 2023, 44(1): 410-417.
[3] 张晨, 关鹏, 段新胜, 等. 地埋管间断工作进出孔平均温度预测方法研究[J]. 太阳能学报, 2022, 43(5): 30-35.
ZHANG C, GUAN P, DUAN X S, et al.Research on prediction of average inlet and outlet temperature of ground heat exchangers in intermittent operation condition[J]. Acta energiae solaris sinica, 2022, 43(5): 30-35.
[4] BI Y H, WANG X H, LIU Y, et al.Comprehensive exergy analysis of a ground-source heat pump system for both building heating and cooling modes[J]. Applied energy, 2009, 86(12): 2560-2565.
[5] ZHAI Y J, ZHANG T Z, TAN X F, et al.Environmental impact assessment of ground source heat pump system for heating and cooling: a case study in China[J]. The international journal of life cycle assessment, 2022, 27(3): 395-408.
[6] ZHANG T Z, ZHAI Y J, FENG S T, et al.Does it pay to develop a ground source heat pump system? Evidence from China[J]. Journal of environmental management, 2022, 305: 114378.
[7] JIAO K T, SUN C Z, YANG R T, et al.Long-term heat transfer analysis of deep coaxial borehole heat exchangers via an improved analytical model[J]. Applied thermal engineering, 2021, 197: 117370.
[8] FANG L, DIAO N R, SHAO Z K, et al.A computationally efficient numerical model for heat transfer simulation of deep borehole heat exchangers[J]. Energy and buildings, 2018, 167: 79-88.
[9] LAW Y L E, DWORKIN S B. Characterization of the effects of borehole configuration and interference with long term ground temperature modelling of ground source heat pumps[J]. Applied energy, 2016, 179: 1032-1047.
[10] DENG J W, WEI Q P, HE S, et al.Simulation analysis on the heat performance of deep borehole heat exchangers in medium-depth geothermal heat pump systems[J]. Energies, 2020, 13(3): 754.
[11] TANG F J, HOSSEIN N.Long-term performance of a shallow borehole heat Exchanger installed in a geothermal field of Alsace region[J]. Renewable energy, 2018, 128: 210-222.
[12] 蔡皖龙, 刘俊, 王沣浩, 等. 深层地埋管换热器换热性能模拟及稳定性研究[J]. 太阳能学报, 2020, 41(2): 158-164.
CAI W L, LIU J, WANG F H, et al.Research on heat transfer performance and stability of deep borehole heat exchanger[J]. Acta energiae solaris sinica, 2020, 41(2): 158-164.
[13] CUI Y L, ZHU J, TWAHA S, et al.A comprehensive review on 2D and 3D models of vertical ground heat exchangers[J]. Renewable and sustainable energy reviews, 2018, 94: 84-114.
[14] ESKILSON P.Thermal analysis of heat extraction boreholes[M]. Lund: Lund University, 1987.
[15] ZENG H Y, DIAO N R, FANG Z H.A finite line-source model for boreholes in geothermal heat exchangers[J]. Heat transfer—Asian research, 2002, 31(7): 558-567.
[16] 李鹏. 渗流对岩土体传热性能影响及热泵系统换热效率优化研究[D]. 武汉: 中国地质大学, 2023.
LI P.Study on the effect of seepage on heat transfer performance of rock and soil mass and optimization of heat transfer efficiency of heat pump system[D]. Wuhan: China University of Geosciences, 2023
[17] INGERSOLL L R, ZOBEL O J, INGERSOLL A C.Heat conduction[M]. University of Wisconsin Press, 1954.
[18] CARSLAW H S, JAEGER J C.Conduction of heat in solids[J]. 2nd edition. London: Oxford University Press, 1959.
[19] KAVANAUGH S.Simulation and experimental verification of vertical ground-coupled heat pump systems[D]. Stillwater: Oklahoma State University, 1985.
[20] MAN Y, YANG H X, DIAO N R, et al.A new model and analytical solutions for borehole and pile ground heat exchangers[J]. International journal of heat and mass transfer, 2010, 53(13/14): 2593-2601.
[21] CONTI P.Dimensionless maps for the validity of analytical ground heat transfer models for GSHP applications[J]. Energies, 2016, 9(11): 890.
[22] 张琳邡, 张东海, 周扬, 等. 分层岩土中地埋管换热器传热解析模型与分析[J]. 太阳能学报, 2022, 43(10): 378-385.
ZHANG L F, ZHANG D H, ZHOU Y, et al.Analytical mode and analysis of heat transfer of ground heat exchangers in layered stratum[J]. Acta energiae solaris sinica, 2022, 43(10): 378-385.
[23] HAHN D W, ÖZIŞIK M N. Heat Conduction[M]. 3nd ed. John Wiley & Sons, 2012.
[24] GRADSHTEYN I S, RYZHIK I M.Table of integrals, series, and products[M]. New York: Academic Press, 2014.
[25] 张长兴, 胡松涛, 李绪泉. 格林函数法在竖直U型地埋管传热计算中的应用[J]. 太阳能学报, 2010, 31(2): 158-162.
ZHANG C X, HU S T, LI X Q.Application of green function method in calculation on heat conduction of vertical U-tubes heat exchanger[J]. Acta energiae solaris sinica, 2010, 31(2): 158-162.
[26] 战国会, 俞亚南. 地源热泵有限长圆柱面和圆柱体热源模型[J]. 浙江大学学报(工学版), 2011, 45(6): 1104-1107.
ZHAN G H, YU Y N.Finite long cylindrical surface and cylinder source model of ground source heat pump[J]. Journal of Zhejiang University (engineering science), 2011, 45(6): 1104-1107.
[27] LI M, LAI A.Heat-source solutions to heat conduction in anisotropic media with application to pile and borehole ground heat exchangers[J]. Applied energy, 2012, 96: 451-458.