三维快速多极边界元法分析地埋管群传热问题

宋子欣; 胡宗军; 胡斌; 牛忠荣

doi:10.21656/1000-0887.430210

三维快速多极边界元法分析地埋管群传热问题

doi: 10.21656/1000-0887.430210

合肥工业大学土木与水利工程学院, 合肥 230009

基金项目:

国家自然科学基金项目 11272111

详细信息

作者简介:
宋子欣(1997—)，女，硕士(E-mail: peytonsong@163.com)

通讯作者:
胡宗军(1975—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: huzongjun_1975@163.com)

中图分类号: O39
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- 被引次数: 0
出版历程
- 收稿日期: 2022-06-21
- 修回日期: 2022-10-13
- 刊出日期: 2023-07-01

3D Fast Multipole Boundary Element Method Analysis of Heat Exchange Performance of Buried Pipe Groups

College of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China

摘要

摘要: 基于三节点三角形线性单元，为克服单元跨叶子积分难题，将三维位势问题快速多极边界元法与几乎奇异积分的半解析算法相结合，实现了三维边界元法中几乎奇异积分的准确计算，该方法适用于U型地埋管薄体结构的换热分析. 在制冷、制热两种工况下研究了U型地埋管壁厚对换热量的影响，并进一步分析了管群间的热相互作用. 计算结果显示，当管壁导热系数一定时，管壁越厚，对管内流体和土壤之间的换热影响越大. 当钻孔间距一定时，管群中埋管数量越多，热干扰现象越强烈，提高管群换热量的主要措施是降低管群间热干扰. 因准确计算了几乎奇异积分，三维快速多极边界元法可以有效计算薄体和厚体耦合的三维热传导问题. 该文方法和分析结果可为地埋管换热器系统的工程应用提供参考.
- 地埋管群换热器 /
- 几乎奇异积分 /
- 薄体 /
- 传热 /
- 快速多极边界元法
Abstract: Based on the 3-node triangular linear element and to overcome the element cross-leaf integration problem, a new 3D fast method was formulated for 3D potential problems through combination of the fast multipole boundary element method (FMBEM) with the semi-analytical algorithm of nearly singular integral, to realize the accurate calculation of the nearly singular integral in the 3D boundary element method (BEM). This method is applicable to the heat exchange of thin-wall structures of U-type buried pipe groups. In the cooling and heating conditions, the effects of the wall thickness of the U-type buried pipe group were analyzed by means of the new FMBEM, and the thermal interaction between multiple buried pipes was discussed. The calculation results show that, for a constant thermal conductivity of the pipe wall, the thicker the pipe wall is, the greater the effect on the heat exchange between the pipe fluid and the soil will be. For a constant borehole spacing, the bigger the number of buried pipes in a group is, the stronger the thermal interference between the pipes will be. The main strategy to increase the heat exchange of the pipe group is to reduce the thermal interference between the heat exchange pipes. Due to the accurate calculation of the nearly singular integral, the proposed 3D FMBEM can effectively solve the 3D heat exchange problems of thin-thick coupled bodies. This method and the results for the provide references for the engineering application of buried pipe heat exchangers.
- U-type buried pipe heat exchanger /
- nearly singular integral /
- thin body /
- heat conduction /
- fast multipole boundary element method

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图 1 参考坐标系

Figure 1. Reference coordinate systems

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图 2 双层圆筒壁结构

Figure 2. The double cylinder wall structure

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图 3 双层圆筒壁网格模型

Figure 3. Double-layer cylindrical wall mesh models

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图 4 FMBEM在Z=10 mm处沿AB路径计算所得温度T_FMBEM及相对误差Δ

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. Temperature T_FMBEM and relative error Δ calculated with the FMBEM along the AB path at Z=10 mm

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图 5 U型管FMBEM网格模型

Figure 5. The U-tube FMBEM mesh model

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图 6 不同管壁厚度时FMBEM计算温度分布图

Figure 6. FMBEM calculated temperature distribution diagrams for different tube wall thicknesses

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图 7 4×4管群FMBEM单元模型

Figure 7. The 4×4 pipe system's FMBEM model

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图 8 4×4管群FMBEM计算温度分布图

Figure 8. The 4×4 pipe system's FMBEM calculated temperature distribution diagrams

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图 9 4×4地埋管群单位井深换热量对比

Figure 9. Comparison of heat transfer fluxes of 4×4 buried pipe groups

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表 1 地埋管换热器设计参数

Table 1. The U-tube buried pipe design parameters

number	parameter name	value	unit
1	borehole depth	50	m
2	borehole radius	75	mm
3	U-tube pipe outer radius	16	mm
4	U-tube pipe inner radius	13	mm
5	shank spacing	100	mm
6	soil radius	1.5	m
7	U-tube (PE pipe) thermal conductivity	0.4	W/(m·℃)
8	fill material thermal conductivity	2.4	W/(m·℃)
9	ground thermal conductivity	2.0	W/(m·℃)
10	inlet water temperature in summer	35	℃
11	outlet water temperature in summer	32	℃
12	inlet water temperature in winter	7	℃
13	outlet water temperature in winter	10	℃
14	undisturbed ground temperature	18	℃

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表 2 不同管壁厚度时地埋管单位井深换热量(单位: W/m)

Table 2. Heat transfer fluxes of buried pipes with different wall thicknesses (unit: W/m)

wall thickness	cooling			heating
wall thickness	Q_i	Q_o	Q=_i+Q_o	Q_i	Q_o	Q=Q_i+Q_o
0	-29.466	-17.230	-46.696	20.433	8.205	28.638
3	-28.081	-13.300	-41.381	20.061	5.300	25.361
6	-21.922	-15.910	-37.832	14.640	8.548	23.188
8	-18.118	-14.471	-32.589	11.826	8.147	19.973
10	-15.927	-13.017	-28.944	10.332	7.407	17.739

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表 3 壁厚3 mm时4×4管群单位井深换热量(单位: W/m)

Table 3. Heat transfer fluxes of 4×4 pipe groups for a wall thickness of 3 mm (unti: W/m)

heat exchange	cooling				heating
heat exchange	tube of №.①	tube of №.②	tube of №.③	tube of №.④	tube of №.①	tube of №.②	tube of №.③	tube of №.④
Q_i	-7.901	-10.999	-11.640	-14.856	6.055	8.218	8.390	10.352
Q_o	-1.530	-5.077	-5.637	-8.999	0.379	1.822	2.216	4.275
Q=Q_i+Q_o	-9.431	-16.076	-17.277	-23.855	6.434	10.040	10.606	14.627

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表 4 不考虑壁厚时4×4管群单位井深换热量(单位: W/m)

Table 4. Heat transfer fluxes of 4×4 pipe groups regardless of the wall thickness (unit: W/m)

heat exchange	cooling				heating
heat exchange	tube of №.①	tube of №.②	tube of №.③	tube of №.④	tube of №.①	tube of №.②	tube of №.③	tube of №.④
Q_i	-9.768	-14.009	-13.776	-17.944	7.966	10.579	10.447	13.002
Q_o	-0.519	-3.829	-4.128	-8.281	2.320	0.337	0.535	3.079
Q=Q_i+Q_o	-10.287	-17.838	-17.904	-26.225	10.286	10.916	10.982	16.081

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