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Heat transfer analysis ofunderground

U‑type heat exchanger ofground source

heat pump system

Guihong Pei and Liyin Zhang*

Background

As a building energy conservation technique, ground source heat pumps (GSHP) have

attracted considerable attention on the basis of rising energy prices and urgent environ-

mental pressure caused by excessive energy consumption. Bhutta etal. (2012) reviewed

CFD techniques and concluded that they are good tools to simulate heat exchanger

design. e geothermal heat exchangers (GHEs) are the basis for the normal opera-

tion of heat pump systems, and the thermal characteristics signiﬁcantly depend on the

rock-soil type and the longitudinal temperature distribution. In addition, heat transfer

with the surrounding rock-soil is a complicated and unstable process. ere has been

Abstract

Background: Ground source heat pumps is a building energy conservation tech-

nique. The underground buried pipe heat exchanging system of a ground source heat

pump (GSHP) is the basis for the normal operation of an entire heat pump system.

Methods: Computational-ﬂuid-dynamics (CFD) numerical simulation software,

ANSYS-FLUENT17.0 have been performed the calculations under the working condi-

tions of a continuous and intermittent operation over 7 days on a GSHP with a single-

well, single-U and double-U heat exchanger and the impact of single-U and double-U

buried heat pipes on the surrounding rock-soil temperature ﬁeld and the impact of

intermittent operation and continuous operation on the outlet water temperature.

Conclusions: The inﬂuence on the rock-soil temperature is approximately 13 %

higher for the double-U heat exchanger than that of the single-U heat exchanger.

The extracted energy of the intermittent operation is 36.44 kw·h higher than that of

the continuous mode, although the running time is lower than that of continuous

mode, over the course of 7 days. The thermal interference loss and quantity of heat

exchanged for unit well depths at steady-state condition of 2.5 De, 3 De, 4 De, 4.5 De, 5

De, 5.5 De and 6 De of sidetube spacing are detailed in this work. The simulation results

of seven working conditions are compared. It is recommended that the side-tube

spacing of double-U underground pipes shall be greater than or equal to ﬁve times of

outer diameter (borehole diameter: 180 mm).

Keywords: U-type ground tube, Numerical simulation, Heat transfer rate, Thermal

interference

Open Access

© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License

(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,

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indicate if changes were made.

RESEARCH

Pei and Zhang SpringerPlus (2016) 5:1863

DOI 10.1186/s40064‑016‑3548‑8

*Correspondence:

377231918@qq.com

School of Civil Engineering

and Architecture, Southwest

Petroleum University,

Chengdu 610500, People’s

Republic of China

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Pei and Zhang SpringerPlus (2016) 5:1863

signiﬁcant research into the heat transfer phenomena of GHEs which has been which

include experimentation, numerical simulation and theoretical analysis models (Bouha-

cina etal. 2015; Hu etal. 2013; Nam etal. 2008). Katsura (2008) proposed a method

to calculate the rock-soil temperature under a pipe-group heat extraction condition by

means of a temperature superposition based on linear heat source theory. Shang (2011)

predicted the rock-soil temperature variation between the operation and recovery

period of GSHPs by establishing a 3D model of a single-well, single-U heat exchanger

combined with multi-aperture theory. e results indicated that the soil properties have

a greater inﬂuence on the soil temperature recovery than environmental factors did.

Choi (2011) applied a CFD numerical simulation method to analyzing the inﬂuential

factors which contains shank spacing, borehole depth, ﬂow velocity and the diﬀerential

temperature of the inlet/outlet on the heat transfer rate of the GSHP. e results showed

that the borehole depth was found to be the most signiﬁcant factor aﬀecting the system

performance. Additionally, the impact of the saturated soil on the mean heat exchange

rate was higher than in unsaturated soil, at 40%. However, to facilitate the research, it is

assumed that the soil is homogeneous.

Generally, the drilling diameter is 100~300 mm (Zhao and Dai 2007). Among all

GSHP vertical ground heat exchangers, u-tubes, annular tubes and single tubes are most

commonly used. e U-tube is most common due to its simple construction, good heat

exchanger performance, high bearing, less tube joints, and unlikely leakage. e U-type

side tube spacing is small due to restraints imposed on the well drilling diameter. Due to

the existence of temperature diﬀerences, heat conduction will occur directly between the

two side-tubes, interfering with the ability of the soil to function as an eﬀective heat sink.

ermal interference seriously inﬂuences the underground heat exchange of U-type

tubes, decreasing the quantity of heat rejection for unit well depth by 20–40%. More

seriously, it will lead to a malfunction of the heat pump refrigerant-cycle system, which

can stop operation. It was found that increasing the pipe spacing, applying high ther-

mal conductivity backﬁll soil can enhance the performace of GSHP systems (Dehkordi

and Schincariol 2014). Shen (2007) uses a ﬁnite unit method to perform quantitative

analyses on the hystereses caused by thermal interference. Carli (2010) analyzed the

thermal interference in the drill holes by calculating the heat resistance, which makes

uses an electrical analogy with lumped capacitances. ese thermal resistances were

used to solve for the heat transfer in an unsteady state. For the vertical double U-type

ground tube, although the quantity of heat exchange for a unit well depth is larger than

the single U-type tube, for the same drilling area, thermal interference is more likely to

happen because the temperature of several side-tubes is diﬀerent. e rock-soil’s heat

equilibrium temperature not only aﬀects the underground rock-soil heat transfer rate,

but is also associated with normal operation and economy of heat pump systems. An

ideal temperature range ensures eﬃcient running of the system. In addition, appropri-

ate side-tube spacing not can enhance the heat exchanger eﬃciency but also can reduce

the required drilling diameter. erefore, this paper establishes a three-dimensional heat

transfer model for a single-well, double-U buried tube based on the rock-soil thermo-

physical properties. It also accounts for vertical temperature stratiﬁcation according to

underground heat transfer test experiment conditions, and carried out comparison of

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simulation results for soil temperature and U-tube water temperature are compared for

single U-type buried pipes and a double-U buried pipes for continuous operation over

7days. After that, the paper compares the outlet water temperature changes during the

time of continuous operation and intermittent operation for a double-U heat exchanger.

Eventually, the double-U buried pipe model was established of diﬀerent side-tube center

distance. ermal interference arising from temperature distribution variation for diﬀer-

ent side-tubes was also analyzed.

Methods

Governing equation

e process of ﬂuid ﬂow and heat conduction within U-type GHEs follows the law of

conservation laws of mass, momentum and energy. e mathematical description

of these laws is the controlling equation of the process. Since the Re is 18,116, we use

standard k-ε model to simulate the turbulent ﬂow, which has widely applicability, robust-

ness, and saves computation time. e general governing equation (Tu etal. 2009) is as

follows:

Continuity part

Momentum part

Energy part

Turbulent kinetic energy k and turbulent energy dissipationεpart

where u, v, w, stands for the velocity of x, y, z dimension, respectively. ν means kinematic

viscosity. t, T, ρ and p stands for time, temperature, density and pressure, respectively;

Pr is Prandtl number, which means the ratio of molecular momentum diﬀusivity and

molecular thermal diﬀusivity. Subscript T stands for turbulent ﬂow, P means the term of

turbulent kinetic energy production, and D means the term of turbulent energy dissipa-

tion. Constants for the turbulent model are observed as below (Launder and Spalding

1974):

(1)

∂φ

∂

t

+∂(uφ)

∂

x

+∂(vφ)

∂

y

+∂(wφ)

∂

z

=∂

∂

x

Gamma ∂φ

∂

x

+∂

∂

y

Ŵ∂φ

∂

y

+∂

∂

z

Ŵ∂φ

∂

z

+S

φ

φ

=

1

;

Ŵ

=

0

;

Sφ

=

0

φ

=u,v,w;Ŵ=ν+νT;Sφ=−

1

ρ

∂p

∂x

S′

u,−

1

ρ

∂p

∂y

S′

v,−

1

ρ

∂p

∂z

S′

w

φ

=T;Ŵ=

ν

Pr

+

νT

PrT

;Sφ=ST

;

φ

=k,ε;Ŵ=

ν

T

σk

,

ν

T

σε

;Sφ=P−D,

ε

k

(cε1P−cε2D

)

σk

=

1.0,

σ

ε

=

1.3, cε1

=

1.44, cε2

=

1.92

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Pei and Zhang SpringerPlus (2016) 5:1863

The geometric model

ANSYS-ICEM CFD (ANSYS I. C. 17.0 2016) pre-processing software to build the geo-

metric model of the single-U and double-U ground heat exchanger and mesh the model.

e simulated U-type tube is a DN25 HDPE tube, with the standard speciﬁcation, (Sun

etal. 2000) which has an outer diameter 25mm, inner diameter of 20.4mm, wall thick-

ness of 2.3mm, and a tube surface roughness of 0.01mm. According to the Prandtl–

Schlichting equation, the thickness of the viscous sublayer is 0.29mm which indicates

that the turbulence is in the hydraulic smooth wall region. e side-tube spacing is

75mm with drilling a diameter of 130mm. e ground far boundary semi-diameter is

2.5m, and the distance from the bottom surface to the pipe’s elbow is 1m. e embed-

ded depth of the tube is 80m and the tube’s center distance S equal 3 De. A schematic

diagram of geometric model is shown in Fig.1. Based on the basic model, we build the

geometric model of a single well double-U tube with S/De=2.5, 3, 4, 4.5, 5, 5.5, and 6.

e cross section is shown in Fig.2, and the units are mm.

Numerical calculation

ANSYS FLUENT 17.0 (2016) software is used to calculate the current numerical investi-

gation. A ﬁnite volume discretization is used in approximating the governing equations.

A double-precision and pressure-based solver is used in the numerical computation. A

non-slip boundary condition is adopted on pipe surface. e SIMPLE algorithm is used

for pressure–velocity coupling. A ﬁrst-order upwind scheme is adopted to the discre-

tization of all terms. e computation can be considered as converged when the normal-

ized residuals for mass, momentum and energy equations are less than 10−6, 10−6, 10−8,

respectively. e ﬁnal results are the dynamic simulation values with a time-step size of

30s for 7days of continuous/intermittent operation. e intermittent operation mode

process is within the speciﬁc time steps where the inlet velocity and ﬂow mode will go

Fig. 1 Schematic diagram of geometric model

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through periodical changes between 0.65m/s, standard k-ε mode and 0.0m/s, laminar

mode. e inlet temperature is set as 303K, during the shutoﬀ operation. e following

assumptions can be implemented:

1. Ignore the inﬂuence of surface temperature ﬂuctuations on the ground temperature.

2. Ignore the inﬂuence of the water migration in the soil.

3. Ignore the thermal contact resistance between U-type tube to backﬁll material, back-

ﬁll material to well wall, and well wall to the soil.

Grid generation

e single-U model in this work uses structured meshing while the double-U models all

use a combination of structured and non-structured meshing. In the simulation, struc-

tured meshing and non-structured meshing can provide the same precision (Shevchuk

etal. 2011). To meet the requirement of the turbulence model, we use a growing layer

ratio of 1.2 to satisfy the desired y+ value, dividing the prism into six layers where the

thickness of ﬁrst layer is 0.1mm in the radial direction and is adjacent to the interface of

the water domain. Because the entire model is a spindly structure, a mesh size of 100mm

is adopted in the longitudinal direction. e mesh size in the elbow of a U-type tube is

small approximately 2mm, due to centrifugal force. e meshes in the soil part gradually

sparse and their minimum size is 20mm in the radial direction. Various mesh elements

(approximately 25 million, 33 million and 40 million in single-U; approximately 30 mil-

lion, 45 million, and 50 million in double-U) are generated to pass a mesh independ-

ence test. e relative deviations of the average outlet temperature on both U-type tubes

between the last two sets of meshes are within 2%. To reduce the quantity of mesh, the

ﬁnal number of cells for the single-U and double-U type GHEs systems are 3297878 and

4522149, respectively. Pictures of the mesh are shown in Fig.3.

Fig. 2 Schematic diagram of the cross section with diﬀerent center distance and well

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Boundary conditions andmaterial’s physical property parameters

e computational domain material physical parameters are shown in Table1. Bound-

ary conditions are shown in Table2. e initial temperature of all domains and soil

boundary wall temperatures varies according to a quadratic function formula based on a

numerical ﬁtting of the experiment. ese were compiled by INIT macro and PROFILE

macro of UDF programs. Figure4 shows soil temperature changes.

Results anddiscussion

Simulation verication

Figure5 shows the test model of the working condition2 (S=3De). When operating

continuously for 12h, the temperature at the outlet of the U-type pipe changes with

time. Table3 is the comparison between the simulation value and the measured value.

e deﬁnition of heat transfer for a unit well depth of a U-type heat exchanger as follows:

(2)

q

l=

G

·

c

p·

(T

in −

T

out

)

H

Fig. 3 The mesh of cross-section (a–b), inlet of double-U (c), elbow (d–e)

Table 1 Material’s physical property parameter

ρ [kg/m3] cp [J/kg.k] λ [W/m.k] η [Pa.s]

Water 993.9 4147 0.6265 7.275e−04

HDPE pipe 950 2300 0.45

Backﬁll soil 1900 900 2.2

Rock-soil 2530 840 2.58

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Pei and Zhang SpringerPlus (2016) 5:1863

G is the mass ﬂow rate in kg/s. cp is speciﬁc heat in J/kg/K; Tin is the temperature of

water inlet in K. Tout is the temperature of water outlet in K. H is the drilling depth

in m.

Table 2 Boundary conditions

Boundary type Velocity (m/s) Temperature (K)

Fluid part

Inlet VELCITY_INLET 0.65 308

Outlet OUTFLOW

Solid part

Distant surface Gradually reduce from upper to bottom

Borehole wall Coupled wall

Pipe wall Coupled wall 289

Bottom surface Constant temperature

Top Heat insulation

Fig. 4 Distant surface and initial temperature of soil from upper to bottom

100 200300 400500 600700 800

29

30

31

32

33

34

35

36

100 200300 400500 600700 800

29

30

31

32

33

34

35

36

simulated(T

out

)

measured(T

out

)

measured(T

in

)

temperature (

o

C)

Time(min)

Fig. 5 Comparison of outlet temperature between experiment and simulation

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As shown in Fig.5, the outlet temperature is changing with time in agreement with

the experimental data from (Zhang etal. 2009). From Table3 we can see the simulation

value of u-tube heat transfer at a unit well depth is 102.8 w/m, and the measured value

is 108.975w/m, which is a fractional error of 6.175%. us the simulation results can be

observed as valid.

The temperature variation ofwater alongthe pipe androck‑soil

In this section, we analyzed the impact of a single-U heat exchanger and double-U heat

exchanger on the surrounding rock-soil temperature and ﬂuid temperature under a con-

tinuous operation mode and an intermittent operation mode. Figures6 and 7 show rock-

soil temperature changes under the condition of a single-U and double-U buried pipe

after running for 3 and 6days at r=0.078m along the depth direction and z=−40m

along the radial direction. Figure6 shows that the single-U heat exchanger raises tem-

perature of rock-soil by 6.91K and 8.0K on average at the edge of the borehole and

an average change of 38 and 44% was observed relative to the initial average tempera-

ture (291.31K). Furthermore, the double-U heat exchanger makes the temperature of

the rock-soil rise by 9.39 and 10.38K on average at the edge of the borehole. e aver-

age change rates have reached 51.7 and 57% compared with initial average tempera-

ture. From above we can see that temperature increase rate of the rock-soil gradually

decreases as the operation time increases. e impact of the double-U heat exchanger

on the initial temperature of the rock-soil is approximately 13% higher than that of

the single-U heat exchanger. From Fig.7 it can observed that the temperature of the

rock-soil from the far boundary of the drilling location presents an increasing inverse

Table 3 The comparison betweensimulation value andmeasured value

Mass ow

rate [kg/s] Tin [°C] Tout [°C] ΔT [°C] Q [KW] ql [w/m]

Experimental value 0.563 34.91 31.2 3.71 8.718 108.975

Simulation value 0.563 35 31.5 3.5 8.224 102.8

01020304050607080

289

290

291

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298

299

300

301

302

303

01020304050607080

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

temperature (k)

drilling depth (m)

initial

single U the 3rd day

single U the 6th day

double U the 3rd day

double U the 6th day

Fig. 6 Longitudinal temperature change of rock-soil at r = 0.078 m

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Pei and Zhang SpringerPlus (2016) 5:1863

proportional function. e inﬂuence of the double-U buried pipe radius is twice that of

the single-U tube. Consequently, it is suggested that the drilling spacing of the single-U

buried pipe should be reduced relative to the double-U buried pipe. Adopting a mixed

pipe laying form, the double-U buried pipes lay on the outermost layer. Figure8 indi-

cates the serious heat short-circuiting of the double-U buried pipe. e decreasing out-

let pipe water temperature is obviously higher than that of single-U buried pipe. e

mean temperature diﬀerence between the inlet and outlet of the single-U buried pipe

at the 3rd and 6th day are 4.01 and 3.85K. Consequently, the rates of heat transfer are

9.423 and 9.047kw and that of double-U buried pipe are 3.28 and 3.068K. e heat

transfer rates are 7.71 and 7.21kw, respectively.

Figure9a shows the average temperature changes of the outlet ﬂuid for double-U tube

running for 18h, stopping for 6h in intermittent operation and ﬁnishing with continu-

ous operation for 7days. e heat transfer rate for the two working condition is deter-

mined with Eq.(3) and is plotted in Fig.9b. Since intermittent operation can realize

cyclical recovery of the ground temperature, the water temperature at the outlet remains

at the initial stage and is always lower than the continuous operation mode. Although the

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

290

291

292

293

294

295

296

297

298

299

300

301

302

303

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

290

291

292

293

294

295

296

297

298

299

300

301

302

303

temperature (k)

radius (m)

initial

single-U the 3rd day

single-U the 6th day

double-U the 3rd day

double-U the 6th day

Fig. 7 Radial temperature change of rock-soil at Z = −40 m

01020304050607080

304.0

304.5

305.0

305.5

306.0

306.5

307.0

307.5

308.0

01020304050607080

304.0

304.5

305.0

305.5

306.0

306.5

307.0

307.5

308.0

temperature (k)

pipe depth (m)

single-U the 3rd day

single-U the 6th day

double-U the 3rd day

double-U the 6th day

Fig. 8 Average temperature variation within U-type pipe

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Pei and Zhang SpringerPlus (2016) 5:1863

-10010 20 30 40 50 60 70 80 90 100110 120130 140150 160

301.0

301.5

302.0

302.5

303.0

303.5

304.0

304.5

305.0

305.5

-10010 20 30 40 50 60 70 80 90 100110 120130 140150 160

301.0

301.5

302.0

302.5

303.0

303.5

304.0

304.5

305.0

305.5

temperature (k)

time (h)

continusous mode operation

intermittent mode operation

20 40 60 80 100120 140160

0

500

1000

1500

2000

2500

3000

3500

20 40 60 80 100120 140160

0

500

1000

1500

2000

2500

3000

3500

heat transfer rate (w)

time (h)

continusous operation mode

intermittent operation mode

ab

Fig. 9 a Outlet ﬂuid temperature variation and b heat transfer rate at continuous/intermittent operation

mode

operation time of the intermittent mode is lower than that of the continuous mode, the

extracted energy is 337.33kw·h, which is higher than the continuous mode (36.44kw·h)

based on Eq.(3). Figure10 is the temperature changes of the rock-soil at the radial posi-

tion (r=0.078m, r=1.4m) and longitudinal direction (Z=−70m, Z=−30m). It

is found that the temperature variation trend of the rock-soil at the edge of the bore-

hole (r=0.078m) is in keeping with the outlet ﬂuid temperature. e temperature will

go down rapidly when the GSHP system shutoﬀ, and increases quickly once the system

restarts operation. Interestingly, the rock-soil temperature at r=1.4m will not decrease

with the GSHP system shutoﬀ. e temperature at R=0.078m always greater than

R=1.4m because it continually receives the heat ﬂux from the heat source. is varia-

tion trend does not vary with longitudinal depth. e temperature distribution of nearby

soil at −40m during the operation and out of operation time of the ﬁrst day and the

sixth day are shown in Fig.11. It can be observed on the 1st day of the outage period, the

soil temperature along the depth direction around the buried pipes was obviously lower

than during the operational period. In the 6th day of intermittent operation, the change

became smaller, and the radius of inﬂuence on soil the temperature by the buried pipes

gradually increased. In addition, because the gradient of temperature rise of the continu-

ous operation mode at the same position is larger than that of the intermittent operation

mode as the operation time increases, the ground temperature in continuous operation

mode will be unable to recover, resulting in a much lower eﬃciency than the intermit-

tent operation mode. Under such operation, other auxiliary cooling and heat sources can

be adopted to recover the ground temperature at around the buried pipe area to ensure

long-term and eﬃcient running of the system.

where G is mass ﬂow rate in kg/s. Cp is speciﬁc heat, J/kg/K. Tin is the temperature of

water inlet in K. Tout is the temperature of water outlet in K and P is total extracted

energy in kW·h.

(3)

P

=

t

0

P(t)·dt =Cp·G

t

0

(Tout −Tin)·

dt

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Analysis onheat transfer characteristics ofdierent side‑tube spacing

It can be observed above that the interaction eﬀect of the double-U heat exchanger

branch pipe is more serious than the single-U model. However, the side-tube spacing

has a great impact on the heat transfer of the double-U buried pipe and the selection

of proper spacing to achieve economic requirements is worth studying. Under the con-

dition of a side-tube spacing that remains constant, if the tube diameter is bigger, the

thermal interference will become more noticeable. erefore, we use the S/De value to

describe the inﬂuence of side-tube spacing to heat transmission eﬀectiveness. Conse-

quently, the branch center distance has reached 2.5, 3, 4, 4.5, 5, 5.5 and 6De when the

heat transfer characteristics of the double-U buried pipe are at a thermal equilibrium

state. It is assumed that there is no thermal interference at an inﬁnitely far location,

under the circumstance that the temperature diﬀerence between inlet and outlet is 4.6K.

Table4 shows that the double-U heat exchanger heat transfer rate (Q) at seven working

conditions, and the ratio between the branch center distance and external diameter of

pipe (S/De) is represented by the corner marked i. e comparative calculation between

0102030405060708090100 110120 130140 150160 170

289

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0102030405060708090100 11 0120 130140 150160 170

289

290

291

292

293

294

295

296

297

298

299

300

301

302

temperature (k)

time

ab

(h)

continusous mode (R=0.078m)

intermittent mode (R=0.078m)

continusous mode (R=1.4m)

intermittent mode (R=1.4m)

0102030405060708090100 110120 130 140150 160170

291

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0102030405060708090100 110120 130 140150 160170

29

1

29

2

29

3

29

4

29

5

29

6

29

7

29

8

29

9

30

0

30

1

30

2

temperature (k)

time (h)

continusous mode (R=0.078m)

intermittent mode (R=0.078m)

continusous mode (R=1.4m)

intermittent mode (R=1.4m)

Fig. 10 Rock-soil temperature variation at Z = −70 m (a) and Z = −30 m (b)

Fig. 11 The temperature ﬁeld in the longitudinal direction running at t = 18 h (a) and t = 138 h (c); out of

operation at t = 24 h (b) and t = 144 h (d)

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Pei and Zhang SpringerPlus (2016) 5:1863

Table 4 Comparison ofheat transfer rate forseven working condition double-U pipe

S/DeΔT (K) Qi (kw) (Q∞−Qi)/Qi (%)

2.5 2.4 5.64 90.66

3 2.54 5.97 80.14

4 2.81 6.6 62.83

4.5 2.944 6.92 55.42

5 3.1 7.28 47.6

5.5 3.23 7.59 41.66

heat transfer rate with an inﬁnitely distant branch interval and heat transfer rate at the

working conditions is set up as the heat loss caused by tube pitch. Figure12 shows the

heat loss arising from tube spacing changes. From the ﬁgure, it can be observed that

when the side-tube spacing increases from S/De =2.5 to 6, the thermal loss factor

gradually decreases from 90.66 to 36.17% with an increasing inlet/outlet temperature

diﬀerential. When S/De is greater than 5, the downward gradient of thermal loss starts

decreasing slightly. Figure13 is the drilling surface temperature distribution at z=0.

e results show that the hot ﬂuid inside the U-tube has a great eﬀect on the tempera-

ture distribution of the soil around the tube. With the increasing of the tube spacing, the

thermal interference gradually weakens. It’s clear that when S/De is greater than ﬁve, the

backﬁll soil temperature around the outlet is lower than the outlet temperature, which

indicates that the ﬂuid at the outlet will not directly absorb heat from the inlet.

Figure14 is the heat exchange variation of a unit well depth under diﬀerent spacing

conditions. It can be observed from the ﬁgure that heat exchange amount rises with the

increasing side-tube spacing. From −80 to −20m, the heat ﬂux of unit well depth pre-

sents a linearly increasing trend. However, when S/De<5, the linearly increasing trend

tends to fall from −20 to 0m. However, when S/De≥5, it almost always presents an

increasing linear trend. When S/De increases from 4 to 5, the heat transfer amount at

2.02.5 3.03.5 4.04.5 5.05.5 6.06.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2.02.5 3.03.5 4.04.5 5.05.5 6.06.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

thermal loss fa ctor

S/D

e

Fig. 12 Thermal loss factor of each working condition

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Pei and Zhang SpringerPlus (2016) 5:1863

a unit well depth increased by 8.76%. While increasing from 5 to 6, the heat transfer

amount at a unit well depth increases by 8.69%.

Consequently, under a limited buried pipe area, for a double-U buried pipe system, S/

De is suggested to be 5 (with a drilling diameter of 180mm).

Conclusions

Based on a CFD numerical simulation method, we analyzed the inﬂuence of a GHEs

system of GSHP’s on the temperature of rock-soil under the working conditions of heat

removal and Studies were carried out on three aspects of performance, such as outlet

Fig. 13 Drill cross section temperature distribution at z = 0

0102030405060708090

70

75

80

85

90

95

100

105

110

115

120

125

130

135

0102030405060708090

70

75

80

85

90

95

100

105

110

115

120

125

130

135

ql (w/m)

(S/De=6)

(S/De=5.5)

(S/De=5)

(S/De=4.5)

(S/De=4)

(S/De=3)

(S/De=2.5)

drilling depth (m)

Fig. 14 Heat exchange amount of each working condition per unit well depth

Page 14 of 15

Pei and Zhang SpringerPlus (2016) 5:1863

ﬂuid temperature variation of the double-U buried pipe under continuous operation,

intermittent operation and thermal interference arising from diﬀerent branch pipe spac-

ing. e main conclusion is as follow:

1. After continuous operation for 6days, a single-well, single-U and double-U GHEs

makes the rock-soil temperature increase by 8.0 and 10.38K at the borehole. In addi-

tion, the increasing trend gradually slows down with increasing time. e impact of

the double-U buried pipe on the rock-soil temperature is approximately 13% higher

than that of the single-U buried pipe. e thermal interference generated among

side-U tubes of double-U buried pipe is 25.48% higher than that of the single-U pipe.

In addition, the impact increases over time. e inﬂuence radius of the double-U

heat exchanger is twice that of that of single-U heat exchanger.

2. For intermittent operation mode (running for 18h and shut down for 6h), the rock-

soil temperature obtained a cyclical recovery, and the extracted energy of intermit-

tent is 36.44kw·h higher than that of continuous mode, although the running time

is less than the continuous mode. It is recommended that other auxiliary cooling

and heat sources can be adopted during intermittent operation mode to recover the

ground temperature to ensure long-term and eﬃcient operation of the system.

3. e heat transfer rate of double-U heat exchanger at the side-U tube at a center dis-

tance of S/De as 2.5, 3, 4, 4.5, 5, 5.5 and 6 were compared. It can be observed that

when S/De is greater than 5, heat loss decreasing in a small amount. It is undesirable

to achieve zero loss from the perspective of economy. In order for this system to be

practical, it is suggested to adopt a center distance of S/De=5~6 (with drilling diam-

eter of 180~205mm) for single-well double-U buried pipe system

Abbreviations

GSHP: ground source heat pump; GHE: geothermal heat exchanger.

Authors’ contributions

GHP contributed to the analysis and drafted the manuscript. LYZ contributed to meshing generation and data acquisi-

tion. All authors read and approved the ﬁnal manuscript.

Acknowledgements

This study is ﬁnancially supported by Natural Science Foundation of China (Grant No. 51174170). The authors are grateful

to Professor Jianjun Liu for his constructive comments on this paper).

Competing interests

The authors declared that they have no competing interests.

Received: 9 May 2016 Accepted: 13 October 2016

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