为准确预测地埋管换热器在分层岩土中的传热特征,采用分离变量法和格林函数法,基于单个圆环热源基本传热单元问题的解答,建立考虑岩土结构分层和横观各项同性特征的地埋管传热解析模型。该模型适用于工程中常见的垂直钻孔和桩基埋管换热器分层传热问题,具有较好的普适性。以2层岩土为例,利用模型解答对分层岩土中地埋管的传热特征以及分层参数对其影响规律进行研究。结果表明：均匀介质假设计算误差随作用时间的增加而逐渐增大,在靠近热源处误差更加明显,预测地埋管长时间温度响应时,应采用分层传热模型;在临界区域范围内,可用均质假设模型预测地埋管的传热特性,均质等效热物性参数取为对应岩土分层的热物性参数值;分层岩土导热系数对地埋管传热性能影响较大,岩土平衡温度随分层导热系数比的增大而明显降低;地埋管长度和直径的比值对地埋管传热性能有所影响,岩土平衡温度随长径比的增大而升高,且其影响程度随分层导热系数比的减小而增强。
Abstract
In order to better describe the thermal behavior of ground heat exchangers（GHE） in a layer stratum, a general analytical model is developed and the corresponding analytical solution is obtained using Green's function method; The Green's function, which is the temperature response of single instantaneous ring source, is obtained using the separation of variables technique. The proposed model considers layer stratum and anisotropic properties, and it is applicable for both borehole heat exchanger and pile foundation heat exchanger which are two types of GHEs mostly used in engineering application. Computational examples of the model in a double-layered stratum are presented. The results show that it is necessary to adopt the layered model when long-term temperature response of a GHE is considered, since the error of neglecting the inhomogeneous feature increases with increasing time. There is a critical zone, and the temperature response in this zone can be described by a homogenous model using thermal properties of the corresponding layer. The thermal conductivity of each layer has great effect on the temperature response of a GHE. The steady temperature of soil decreases markedly as the ratio of thermal conductivity between soil layers increases. The ratio of GHE length to diameter also affect the thermal behavior of a GHE, and the steady temperature increases with increasing ratio of GHE length to diameter. The effect of GHE length to diameter on the steady temperature is more pronounced when the thermal conductivity ratio is smaller.
关键词
地热能 /
地源热泵 /
岩土传热 /
地埋管换热器 /
岩土分层 /
解析模型
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参考文献
[1] 赵军, 段征强, 宋著坤, 等. 基于圆柱热源模型的现场测量地下岩土热物性方法[J]. 太阳能学报, 2006, 27(9): 934-936.
ZHAO J, DUAN Z Q, SONG Z K, et al.A method for in situ determining underground thermal properties based on the cylindrical heat source model[J]. Acta energiae solaris sinica, 2006, 27(9): 934-936.
[2] SPITLER J D, GEHLIN S E A. Thermal response testing for ground source heat pump systems——an historical review[J]. Renewable and sustainable energy reviews. 2015, 50: 1125-1137.
[3] 张东海. 分层和渗流条件下竖直地埋管换热器传热特性研究[D]. 徐州: 中国矿业大学, 2020.
ZHANG D H,Investigation on heat transfer behavior of vertical ground heat exchangers in a layered subsurface in the presence of groundwater advection[D]. Xuzhou: China University of Mining and Technology, 2020.
[4] SUTTON M G, COUVILLION R J, NUTTER D W, et al.An algorithm for approximating the performance of vertical bore heat exchangers installed in a stratified geological regime[J]. ASHARE transactions, 2002, 108: 177-184.
[5] LI M, LAI A C K. 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.
[6] 王泽生, 颜爱斌, 郭进京. 地下层状结构土体中埋管换热器的传热分析[J]. 太阳能学报, 2009, 30(2): 188-192.
WANG Z S, YAN A B, GUO J J, et al.Heat transfer analysis of underground heat exchangers in multi-soil beds[J]. Acta energiae solaris sinica, 2009, 30(2): 188-192.
[7] ABDELAZIZ S L, OZUDOGRU T Y, OLGUN C G, et al.Multilayer finite line source model for vertical heat exchangers[J]. Geothermics, 2014, 51: 406-416.
[8] 王子阳, 邵卫云, 张仪萍. 考虑土壤分层的地源热泵圆柱面热源模型[J]. 浙江大学学报(工学版), 2013, 47(8): 1338-1345.
WANG Z Y, SHAO W Y, ZHANG Y P.Cylindrical surface model of ground source heat pump considering soil stratification[J]. Journal of Zhejiang University (engineering science), 2013, 47(8): 1338-1345.
[9] 张琳琳, 赵蕾, 杨柳. 分层土壤中竖直埋管换热器传热特性[J]. 化工学报, 2015, 66(12): 4836-4842.
ZHANG L L, ZHAO L, YANG L.Heat transfer characteristics of vertical borehole heat exchanger in stratified soils[J]. CIESC journal, 2015, 66(12): 4836-4842.
[10] 金光, 李政, 张凯, 等. 分层岩土中地埋管管群区域热效率分析[J]. 太阳能学报, 2021, 42(6): 487-492.
JIN G, LI Z, ZHANG K, et al.Analysis of regional thermal efficiency of buried pipe groups in layered rock-soils[J]. Acta energiae solaris sinica, 2021, 42(6): 487-492.
[11] INGERSOLL L R, PLASS H J.Theory of the ground pipe heat source for the heat pump[J]. Heating, piping and air conditioning, 1948, 20(7): 119-122.
[12] 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.
[13] CARSLAW H S, JAEGER J C.Conduction of heat in solids[G]. Oxford UK: Oxford University Press, 1959.
[14] 杨卫波, 施明恒. 二区域U型埋管传热模型及其实验验证[J]. 工程热物理学报, 2008, 29(5): 857-860.
YANG W B, SHI M H.Two-region heat transfer model of U-tube ground heat exchanger and its experiment validation[J]. Journal of engineering thermophysics, 2008, 29(5): 857-860.
[15] 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): 2593-2601.
[16] CUI P, LI X, MAN Y, et al.Heat transfer analysis of pile geothermal heat exchangers with spiral coils[J]. Applied energy, 2011, 88(11): 4113-4119.
[17] ZHANG D H, GAO P H, ZHOU Y, et al.An experimental and numerical investigation on temperature profile of underground soil in the process of heat storage[J]. Renewable energy, 2020, 148: 1-21.
基金
江苏省高等学校自然科学研究面上项目（20KJD560008）; 国家自然科学基金项目（51876218）; 江苏省重点研发计划（BE2020038）
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