Heat transfer analysis of underground U-type heat exchanger of ground source heat pump system

Abstract

Background
Ground source heat pumps is a building energy conservation technique. 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 conditions 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).

Full text

Heat transfer analysis ofunderground
U‑type heat exchanger ofground 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 etal. (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,
provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and
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 etal. 2015; Hu etal. 2013; Nam etal. 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
7days. 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 etal. 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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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
etal. 2000) which has an outer diameter 25mm, inner diameter of 20.4mm, wall thick-
ness of 2.3mm, and a tube surface roughness of 0.01mm. According to the Prandtl–
Schlichting equation, the thickness of the viscous sublayer is 0.29mm which indicates
that the turbulence is in the hydraulic smooth wall region. e side-tube spacing is
75mm with drilling a diameter of 130mm. e ground far boundary semi-diameter is
2.5m, and the distance from the bottom surface to the pipe’s elbow is 1m. e embed-
ded depth of the tube is 80m 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
30s for 7days 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 0.65m/s, standard k-ε mode and 0.0m/s, laminar
mode. e inlet temperature is set as 303K, 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
etal. 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 0.1mm 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 100mm
is adopted in the longitudinal direction. e mesh size in the elbow of a U-type tube is
small approximately 2mm, due to centrifugal force. e meshes in the soil part gradually
sparse and their minimum size is 20mm 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 andmaterial’s physical property parameters
e computational domain material physical parameters are shown in Table1. Bound-
ary conditions are shown in Table2. 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. Figure4 shows soil temperature changes.
Results anddiscussion
Simulation verication
Figure5 shows the test model of the working condition2 (S=3De). When operating
continuously for 12h, the temperature at the outlet of the U-type pipe changes with
time. Table3 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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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 etal. 2009). From Table3 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 108.975w/m, which is a fractional error of 6.175%. us the simulation results can be
observed as valid.
The temperature variation ofwater alongthe pipe androck‑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. Figures6 and 7 show rock-
soil temperature changes under the condition of a single-U and double-U buried pipe
after running for 3 and 6days at r=0.078m along the depth direction and z=−40m
along the radial direction. Figure6 shows that the single-U heat exchanger raises tem-
perature of rock-soil by 6.91K and 8.0K 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 (291.31K). Furthermore, the double-U heat exchanger makes the temperature of
the rock-soil rise by 9.39 and 10.38K 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 betweensimulation value andmeasured 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
292
293
294
295
296
297
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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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. Figure8 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 3.85K. Consequently, the rates of heat transfer are
9.423 and 9.047kw and that of double-U buried pipe are 3.28 and 3.068K. e heat
transfer rates are 7.71 and 7.21kw, respectively.
Figure9a shows the average temperature changes of the outlet fluid for double-U tube
running for 18h, stopping for 6h in intermittent operation and finishing with continu-
ous operation for 7days. 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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-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 337.33kw·h, which is higher than the continuous mode (36.44kw·h)
based on Eq.(3). Figure10 is the temperature changes of the rock-soil at the radial posi-
tion (r=0.078m, r=1.4m) and longitudinal direction (Z=−70m, Z=−30m). It
is found that the temperature variation trend of the rock-soil at the edge of the bore-
hole (r=0.078m) 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=1.4m will not decrease
with the GSHP system shutoff. e temperature at R=0.078m always greater than
R=1.4m 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 −40m 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 onheat transfer characteristics ofdierent 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 6De 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 4.6K.
Table4 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
290
291
292
293
294
295
296
297
298
299
300
301
302
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
292
293
294
295
296
297
298
299
300
301
302
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 ofheat transfer rate forseven 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. Figure12 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. Figure13 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.
Figure14 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 −20m, 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 0m. 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 180mm).
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

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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 6days, a single-well, single-U and double-U GHEs
makes the rock-soil temperature increase by 8.0 and 10.38K 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 18h and shut down for 6h), the rock-
soil temperature obtained a cyclical recovery, and the extracted energy of intermit-
tent is 36.44kw·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~205mm) 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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