热弥散对地埋管换热器全尺度传热的影响

doi:10.11949/0438-1157.20201220

摘要/Abstract

摘要：

开展地埋管换热器的传热研究是增强其传热性能以及提高热泵系统能效比的关键，现有的地埋管换热器传热模型多忽略了由地下含水层空间非均质性而产生的热弥散传热。因此，基于渗流影响下的全尺度模型和求解热弥散系数的速度一次方模型，提出了考虑热弥散影响的地埋管换热器全尺度传热模型。研究表明此模型所适用的地下水渗流速度范围为1×10^-8~1×10^-6 m/s；热弥散效应主要在中长时间尺度下体现，渗流速度、热弥散度以及孔隙率是影响传热过程的主要因素。地下水渗流速度和热弥散度越大，孔隙率越小，热弥散效应越强。综合考虑三类影响因素，渗流速度对钻孔传热的影响最大，热弥散度次之，孔隙率的影响最弱；对钻孔群而言，热弥散对上游钻孔传热过程的影响最大，中游次之，下游最小；在所研究的参数范围内，热弥散可使钻孔稳态传热能力提升5.52%~49.93%。

关键词: 地源热泵, 地埋管换热器, 地下水渗流, 全尺度传热, 热弥散

Abstract:

Research on the heat transfer of borehole heat exchanger (BHE) is the key to enhance the heat transfer efficiency of the ground source heat pump(GSHP) system. Most of the BHE models proposed in the current literature ignore the influence of thermal dispersion, which is caused by spatial heterogeneity of underground aquifer. In order to consider thermal dispersion effect, an improved full-scale heat transfer model is developed by including thermal dispersion coefficient. The main findings are summarized as follows. The appropriate range of seepage velocity applied in the model is from 1×10^-8 m/s to 1×10^-6 m/s. The thermal dispersion effect is mainly reflected in the medium and long time scale. Seepage velocity, thermal dispersivity and porosity are the main factors affecting the heat transfer process. High values of the seepage velocity and thermal dispersivity of groundwater, as well as low values of the porosity, may lead to strong thermal dispersion effect. Seepage velocity has the strongest impact on the overall heat transfer around boreholes, followed by the thermal dispersivity, and the porosity has the weakest effect. As far as the borehole group is concerned, thermal dispersion has the greatest impact on the heat transfer process of the upstream borehole, followed by the middle reaches, and the downstream is the least. Within the parameters studied in this paper, thermal dispersion can increase the steady-state heat transfer capacity of the borehole by 5.52% to 49.93%.

Key words: ground source heat pump, borehole heat exchangers, groundwater seepage, full-time scale heat transfer, thermal dispersion

中图分类号:

TK 521.2

李晓宇, 徐宏阳, 代敏, 蔡姗姗. 热弥散对地埋管换热器全尺度传热的影响[J]. 化工学报, 2021, 72(5): 2547-2559.

LI Xiaoyu, XU Hongyang, DAI Min, CAI Shanshan. Impact of thermal dispersion on full-scale heat transfer of borehole heat exchangers[J]. CIESC Journal, 2021, 72(5): 2547-2559.

图/表 13

表1 用于预测钻孔壁温度的G函数

Table 1 G functions for predicting the wall temperature of borehole

模型	G函数
ILS	$G I L S t = 1 4 π λ ∫ r b 2 4 a t ∞ e x p ? - u u d u = 1 4 π λ E 1 r b 2 4 a t$	(1)
FLS	$G F L S t = 1 4 π H λ ∫ 0 H d z ∫ 0 H e r f c r b 2 + z - l 2 2 a t r b 2 + z - l 2 - e r f c r b 2 + z + l 2 2 a t r b 2 + z + l 2 d l$	(2)
MILS^[19]	$G M I L S t = 1 4 π 2 λ ∫ 0 π e x p P e 2 R' c o s φ ∫ 0 P e 2 F o / 4 1 ψ e x p - ψ - P e 2 R' 2 16 ψ d ψ d φ$	(3)
MFLS^[19]	$G M F L S t = 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ$ $f R, F o, P e = 1 4 R e x p - P e 2 R e r f c R - P e × F o 2 F o + e x p P e 2 R e r f c R + P e × F o 2 F o$	(4)
CMLS	$G C M L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u$ $φ = a * k * J n u r b J n' a * u r b - J n' u r b J n a * u r b$ $ψ = a * k * J n u r b Y n' a * u r b - J n' u r b Y n a * u r b$ $f = a * k * Y n u r b J n' a * u r b - Y n' u r b J n a * u r b$ $g = a * k * Y n u r b Y n' a * u r b - Y n' u r b Y n a * u r b$	(5)
CMLS-MFLS	$G C M L S - M F L S t = G C M L S t + G M F L S t - G I L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u + 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ - 1 4 π λ ∫ r b 2 4 a t + ∞ e x p - u u d u$	(6)

表1 用于预测钻孔壁温度的G函数

Table 1 G functions for predicting the wall temperature of borehole

模型	G函数
ILS	$G I L S t = 1 4 π λ ∫ r b 2 4 a t ∞ e x p ? - u u d u = 1 4 π λ E 1 r b 2 4 a t$	(1)
FLS	$G F L S t = 1 4 π H λ ∫ 0 H d z ∫ 0 H e r f c r b 2 + z - l 2 2 a t r b 2 + z - l 2 - e r f c r b 2 + z + l 2 2 a t r b 2 + z + l 2 d l$	(2)
MILS^[19]	$G M I L S t = 1 4 π 2 λ ∫ 0 π e x p P e 2 R' c o s φ ∫ 0 P e 2 F o / 4 1 ψ e x p - ψ - P e 2 R' 2 16 ψ d ψ d φ$	(3)
MFLS^[19]	$G M F L S t = 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ$ $f R, F o, P e = 1 4 R e x p - P e 2 R e r f c R - P e × F o 2 F o + e x p P e 2 R e r f c R + P e × F o 2 F o$	(4)
CMLS	$G C M L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u$ $φ = a * k * J n u r b J n' a * u r b - J n' u r b J n a * u r b$ $ψ = a * k * J n u r b Y n' a * u r b - J n' u r b Y n a * u r b$ $f = a * k * Y n u r b J n' a * u r b - Y n' u r b J n a * u r b$ $g = a * k * Y n u r b Y n' a * u r b - Y n' u r b Y n a * u r b$	(5)
CMLS-MFLS	$G C M L S - M F L S t = G C M L S t + G M F L S t - G I L S t = 1 2 π λ b ∑ n = - ∞ + ∞ ∫ 0 + ∞ 1 - e x p - u 2 a b t × J n u r' φ g - ψ f J n u r A + J n u r B 2 u φ 2 + ψ 2 d u + 1 4 π 2 λ ∫ 01 d Z ∫ 0 π 2 e x p P e 2 R' c o s φ ∫ 01 f R, F o, P e d Z' - ∫ - 1 0 f R, F o, P e d Z' d φ - 1 4 π λ ∫ r b 2 4 a t + ∞ e x p - u u d u$	(6)

图1 地埋管换热器传热模型关系

Fig.1 The heat transfer models of borehole heat exchanger

图2 钻孔群的立面（a）与平面（b）示意图

Fig.2 Elevation (a) and plane (b) diagram of borehole group

表2 单钻孔地埋管换热器运行参数

Table 2 Operation parameters of single hole buried pipe heat exchanger

相关参数	取值
单位长度热量(q_l)	28.85 W/m
U型管热导率(λ_p)	0.42 W/(m·K)
土壤热扩散率(a)	1.33 $×$ 10^-6 m²/s
回灌材料热扩散率(a_b)	4.84 $×$ 10^-6 m²/s
U型管内水流量(?)	0.563 kg/s
竖直钻孔长度(H)	100 m
U型管间距(x_u)	0.026 m
U型管内管径(r_i)	0.016 m
U型管外管径(r_o)	0.02 m
渗流速度(u_d)	1×10^-7 m/s
钻孔半径(r_b)	0.065 m
土壤初始温度(T₀)	15 $℃$
热弥散度(α_L)	0.5 m

表2 单钻孔地埋管换热器运行参数

Table 2 Operation parameters of single hole buried pipe heat exchanger

相关参数	取值
单位长度热量(q_l)	28.85 W/m
U型管热导率(λ_p)	0.42 W/(m·K)
土壤热扩散率(a)	1.33 $×$ 10^-6 m²/s
回灌材料热扩散率(a_b)	4.84 $×$ 10^-6 m²/s
U型管内水流量(?)	0.563 kg/s
竖直钻孔长度(H)	100 m
U型管间距(x_u)	0.026 m
U型管内管径(r_i)	0.016 m
U型管外管径(r_o)	0.02 m
渗流速度(u_d)	1×10^-7 m/s
钻孔半径(r_b)	0.065 m
土壤初始温度(T₀)	15 $℃$
热弥散度(α_L)	0.5 m

图3 基于热弥散的解析解模型与数值解模型对比

Fig.3 Comparisons between analytical and numerical models considering thermal dispersion

图4 单位负荷下两类模型在不同渗流速度下流体温升预测曲线(a) ud =5×10-9 m/s; (b) ud =1×10-8 m/s; (c) ud =1×10-7 m/s; (d) ud =1×10-6 m/s; (e) ud =3×10-6 m/s

Fig.4 The prediction curve of fluid temperature response at different seepage velocity under unit load in two types of model

图5 不同渗流速度下的流体温升

Fig.5 Temperature response of fluid at different seepage velocities

图6 不同热弥散度下的流体温升

Fig.6 Temperature response of fluid with different thermal dispersivity

图7 不同孔隙率下的流体温升

Fig.7 Temperature response of fluid with different porosity

图8 不同渗流速度下钻孔群内的流体温升

Fig.8 Temperature response of fluid in borehole group at different seepage velocities

图9 不同热弥散度下钻孔群内的流体温升

Fig.9 Temperature response of fluid in borehole group with different thermal dispersivity

图10 不同孔隙率下钻孔群内的流体温升

Fig.10 Temperature response of fluid in borehole group with different porosity

图11 影响因素变化率相同时钻孔内的流体温升

Fig.11 Sensitivity analysis of impact factors on the fluid temperature response in the borehole

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