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SIMULATION OF A DOMESTIC GROUND SOURCE HEAT PUMP SYSTEM
USING A TRANSIENT NUMERICAL BOREHOLE HEAT EXCHANGER MODEL
Miaomiao He, Simon Rees, and Li Shao
Institute of Energy and Sustainable Development
De Montfort University
Leicester, LE1 9BH, UK
Tel: +44 (0) 116 2551 511 ext 6856
mhe@dmu.ac.uk
ABSTRACT
Common approaches to the simulation of Borehole
Heat Exchangers (BHEs) assume heat transfer in
circulating fluid and grout to be in a quasi-steady
state and ignore fluctuations in fluid temperature due
to transport of the fluid around the loop. However, in
domestic ground source heat pump systems, the heat
pump and circulating pumps switch on and off during
a given hour; therefore the effect of the thermal mass
of the circulating fluid and the dynamics of fluid
transport through the loop has important implications
for system design. This may also be important in
commercial systems that are used intermittently. This
paper presents transient simulation of a domestic
Ground Source Heat Pump (GSHP) system with a
single BHE using a dynamic three-dimensional
numerical borehole heat exchanger model.
INTRODUCTION
The Climate Change Act 2008 has set the target for
2050 that the UK should reduce emissions of the
carbon dioxide and the other greenhouse gases at
least 80% by 2050 relative to the 1990 baseline. The
UK residential sector accounts for around 30% of
total final energy use and more than one-quarter of
total CO2 emissions; therefore, reducing energy
consumption and CO2 emission in the domestic
sector can be significant (Kannan and Strachan,
2009). Ground Source Heat Pump (GSHP) systems,
due to their higher coefficients of performance (COP)
and lower CO2 emissions, have been proposed as
sustainable systems for domestic buildings to provide
heating and hot water in the UK. A recent study
shows that a suitably sized GSHP system could
achieve almost 40% CO2 savings when compared to
a conventional gas boiler (Jenkins et al., 2009). Even
though GSHP systems have well established in North
America and many parts of Europe, there are still
relatively a few systems installed in the UK.
However, because of their potential to reduce energy
consumption and CO2 emissions, GSHP systems are
receiving increasing interest.
Pipes formed in a ‘U’ loop and grouted into vertical
boreholes are probably the commonest form of
ground heat exchanger found in GSHP systems,
known as Borehole Heat Exchangers (BHEs). Their
careful design is critical to the long-term
performance of the heat pump system. A horizontal
cross-section of half of a typical BHE is shown in
Figure 1. BHEs of this type are not only used in
conventional building heating and cooling systems
but also in large thermal storage schemes. BHEs can
not be designed on the basis of steady-state
calculations but require application of dynamic
thermal models that are able to take account of the
heat transfer inside the borehole as well as the
surrounding soil/rock formation. The purpose of the
model developments discussed here is to:
• Investigate the effects of the dynamics of
the fluid transport along the pipe loop;
• Investigate the three-dimensional
characteristics of heat transfer around the
borehole;
• Develop insight into the limitations of two-
dimensional models and suggest ways in
which they can be improved.
In this paper, development of the numerical model is
described in brief and results of application of the
model in building heating system simulations are
presented.
Figure 1 A half cross-section of a Borehole Heat
Exchanger.
HEAT EXCHANGER MODELS
Models of BHEs have three principle applications:
1. Design of BHEs. This means sizing the
borehole depth, number of boreholes etc.
2. Analysis of in-situ ground thermal
conductivity test data.
3. Integration with building system simulation
i.e with the model coupled to HVAC system
Eleventh International IBPSA Conference
Glasgow, Scotland
July 27-30, 2009
- 607 -
and building heat transfer models to study
overall performance.
Analytical models have been developed by making a
number of simplifying assumptions and applied to
both the design of BHEs and analysis of in-situ test
data. The analytical Cylinder Source solution
presented by Carslaw and Jaeger (1947) has been
applied by treating the two pipes as one pipe coaxial
with the borehole. Further simplifying the pipe and
the borehole as an infinitely long line source, the line
source solution (Ingersoll et al., 1954) can also be
used and is commonly done so in the analysis of in-
situ thermal conductivity test data.
Although analytical solutions require less computing
effort, they are less suited to design and simulation
tasks where one would like to take account of time
varying heat transfer rates and the influence of
surrounding boreholes on long time scales. A number
of approaches that have combined analytical and
numerical methods have been developed with design
tasks in mind. Eskilson (1987), and later Helstrom
(1991) developed a response factor approach – using
so called g-function - to design BHEs for thermal
storage applications. Response to heat flux over
timescales of approximately one month to more than
ten years can be derived from application of these
models and integration of the response according to
the number of boreholes and the relationship to those
neighbouring. The response can be normalised and so
applied to ranges of BHE configurations.
Analytical models such as the line source approach
and also the g-function models make simplifications
about the grout and pipes within the borehole. The
common assumption is that the relationship between
the fluid and the borehole wall temperatures can be
defined by a thermal resistance i.e. a coaxial pipe
without thermal mass. The fluid temperature is one
representative of the loop inlet and outlet
temperatures (often their average). The borehole
thermal resistance then becomes an important
quantity for design purposes. There are a number of
ways of calculating this resistance that take some
account of pipe size and spacing. The most rigorous
method is the multipole method (Bennet et al., 1987)
which represents the pipes in the circular borehole
using a series of line heat sources or sinks.
Application of models for system simulation tasks –
unlike design tasks – requires the ability to operate at
much shorter timescales than one month. The
dynamic response of the grout material inside the
borehole should also be considered. Yavuzturk and
Spitler (1999) extended the g-function model to short
time steps to be considered by applying the finite
difference method on a two-dimensional radial-axial
coordinate system to solve the partial differential heat
conduction equation. This short time step g-function
has been implemented in EnergyPlus and validated
by Fisher et al. (2006). Also, Hellstrom developed
the DST model (1991) to simulate BHEs using a one-
dimensional radial mesh to calculate the thermal
resistance of a borehole by approximating the steady-
state heat transfer in a borehole. Likewise, the DST
model has been implemented in TRNSYS (SEL,
1997).
Two-dimensional numerical models that discretise
the material inside and outside the borehole (e.g. that
of Yavuzturk) can be used to calculate the dynamic
properties of all BHE components – pipes, grout and
rock. Borehole resistance is calculated explicitly.
Young (2004) has recently used such a model to
include the fluid and the effect of its thermal mass.
Such two-dimensional models avoid some of the
simplifications of other models and can distinguish
between different pipe and grout properties and
geometry. However, as variation in fluid temperature
with depth can not be considered explicitly, some
assumption has to be made – as it does with simpler
models – about the fluid temperatures in the two
pipes and the associated boundary conditions. For
example, both pipes could be assumed to be at a
temperature equivalent to the average of the inlet and
outlet temperatures. An alternative is to assume one
pipe temperature is the same as that of the inlet and
the other is at the outlet temperature. We discuss the
significance of these assumptions later. These
assumptions can be avoided in a three-dimensional
numerical model.
In this study, we have applied a three-dimensional
finite volume model. Several three-dimensional
models have been developed to simulate BHEs
(Bandyopadhyay et al., 2008; Lee and Lam, 2008;
Zeng et al., 2003). The advantages of a three-
dimensional model include:
• Fluid transport along the pipe loop and the
dynamics of the fluid can be represented;
• Fluid, borehole and ground temperature
variation along the borehole depth can be
modelled;
• Different layers of rock and soil can be
explicitly represented;
• Climate dependent boundary conditions at
the surface can be applied;
• Heat transfer below the borehole can be
explicitly considered;
• Initial vertical ground temperature gradients
can be applied.
Two-dimensional models may now be
computationally efficient enough for practical design
and simulation purposes. Three-dimensional models
offer most generality and most accurate
representation of heat transfer and so are useful for
detailed studies like that presented here but are not
yet suited to practical simulation of annual or super
annual performance.
- 608 -
MODEL DEVELOPMENT
A dynamic three-dimensional BHE numerical model
has been developed that is built upon a finite volume
solver known as GEMS3D (General Elliptical Multi-
block Solver). This has been developed to simulate
the dynamic response of the circulating fluid and
transient heat transfer in and around BHEs. The
GEMS3D model applies the finite volume method to
solve the general advection-diffusion equation on
three-dimensional boundary fitted grids. The
approach is similar to that described by Ferziger and
Peric (2002). The multi-block structured mesh allows
the complex geometries around the pipes in BHEs to
be explicitly represented (Figure 2).
A three-dimensional representation that includes cells
representing the fluid means that transport of fluid
along the pipe, down and up the borehole, allows the
variation of fluid, grout and borehole temperatures
with depth to be considered. This also and perhaps
more importantly, allows the effects of the delayed
response of the outlet to variations in inlet
temperature to be studied.
Figure 2 A cross-section of boundary fitted grid
showing the pipe and grout region. Symmetry allows
only half the borehole geometry to be included.
Precisely the same numerical method has been
implemented in a two-dimensional version of the
code (GEMS2D). The two-dimensional model can
also be considered equivalent to a three-dimensional
model of one cell depth (1m). This two-dimensional
implementation has been used here to highlight the
differences between model predictions that are due
solely to three-dimensional effects and dynamic fluid
transport. The two-dimensional model necessarily
employs some of the simplifications of other existing
models. One important issue in defining a two-
dimensional model is relating the model boundary
conditions to the inlet and outlet fluid temperatures.
In this case, one pipe of the model is assumed to have
a temperature the same as the inlet. The temperature
boundary condition applied to the second pipe is
calculated in an iterative manner so that the total
ground heat transfer rate is consistent with the fluid
heat balance.
There is no analytical solution for three-dimensional
heat transfer in a borehole geometry that can be
applied to try to validate the numerical model. It is
useful however to show some validation using a two-
dimensional calculation of borehole thermal
resistance. Numerical values can be compared with
the multi-pole analytical solution method (Bennet et
al., 1987). This is done by making a two-dimensional
steady-state calculation of the heat flux for a given
fluid and far field temperature.
Assuming the heat transfer of BHEs is in steady-
state, the total amount of heat flux between the fluid
and the ground can be expressed as:
(1)
where Q is the total heat flux, Tf is the fluid
temperature, Tborehole is the borehole wall temperature,
and R is the borehole thermal resistance, which
includes the convective resistance between the fluid
and the inner side of the pipe, the conductive
resistance of the pipe, and the conductive resistance
of the grout.
Two different types of grout have been used in the
validation study, one with the thermal conductivity of
0.75 W/mK, and the other one with the thermal
conductivity of 1.5 W/mK. For the grout with the
thermal conductivity equal to 0.75 W/mK, the
borehole thermal resistance calculated by the
numerical model was 0.1821K/W while by the
multipole model is 0.1823K/W. In addition, for the
grout thermal conductivity equal to 1.5 W/mK, the
borehole thermal resistance by the numerical model
was found to be 0.1157 K/W while by the multipole
model is 0.1158 K/W. The model can be seen to be
capable of matching analytical values extremely
closely. Variation of mesh density by a factor of five
(the mesh in Fig. 2 is in the middle of the range)
showed variation of the calculated borehole thermal
resistance of less than 0.4%. In practice calculation,
using courser meshes to reduce computation times
would be reasonable.
Fluctuations in fluid temperature due to transport of
the fluid through the loop are usually ignored in
common approaches to model BHEs. In situations
where the heat pump and circulating pumps switch
on and off during a given hour, and in situations
where the building loads have noticeable peaks, the
dynamic response of the circulating fluid is of great
importance. The effect of the thermal mass of the
circulating fluid and the dynamics of fluid transport
through the loop is to damp out fluctuations in the
outlet temperature of BHEs, which has important
implications for system design.
Using a layer of cells inside the pipe allows the fluid
to be discretised along the length of the borehole.
Fluid velocity is imposed in these cells and the
transport of heat from one cell to the next along the
pipe is then represented by a convection term in the
- 609 -
temperature differential equation being solved. Each
finite volume cell can be considered as a well-mixed
node that is defined by a single temperature T, and is
transported at velocity V (Figure 3).
Figure 3 Diagram of fluid transport model.
The fluid cells in the model can be considered similar
to a Compartments-In-Series model (Wen and Fan,
1975) . Fluid transport models of this type have been
widely used in process engineering and their
characteristics are well known. Thermal response of
the pipe inside the borehole will be different from
this simple model by virtue of heat transfer to the
pipe wall. However, it is worth testing the model
without this heat transfer for the purposes of
validation. The transporting properties inside pipes
(be it heat or a chemical species that travels along the
pipe) can be thought of in terms of Residence Time
Distribution (RTD). The RTD is considered as the
fraction of fluid, which undergoes a step change at
the inlet, appears in the outgoing fluid at time t, and it
is represented by the function F(t), illustrated in a F-
Diagram. The analysis is simplified by using
dimensionless time given by,
(2)
where: : volume flow rate, m3/s
: system volume, m3
The actual shape of the F-Diagram depends primarily
on the velocity profile, in which case the faster-
moving elements near the centreline will arrive at the
end of the pipe more quickly than the average. Fluid
undergoes a diffusion process so that step changes in
inlet condition are smoothed. Hanby et al. (2002)
examined the Compartments-in-Series model and
found it performed well but the solution was not
independent of the number of compartments. They
made comparisons with an analytical solution for the
RTD in turbulent flow. The results indicated that the
optimum number of nodes is 46, but given
computational constraints, 20 nodes give a
reasonable approximation. Figure 4 shows the F-
Diagram generated by GEMS3D using 40 cells
compared with the analytical solution (Bosworth,
1949) and the results indicate the dynamics of fluid
transport predicted by the GEMS3D model
satisfactorily matches the analytical solution.
The delayed response to transient variations in inlet
temperature is of significance in that GSHP system
designs (i.e. choice of borehole depth) are sometimes
constrained by peak load conditions. In these cases,
selection of too small a BHE could result in fluid
temperatures close to or outside the operating range
of the heat pump for short periods. Two-dimensional
models (numerical or analytical) are not able to
consider the effects of fluid transport in the pipe.
Figure 4. F-Diagrams by GEMS3D model compared
with the analytical solution.
The significance of the transient fluid transport can
be investigated by applying step changes in borehole
inlet temperature. This has been done using step
changes that might be typical of a domestic GSHP
system and the on-and-off operating intervals of the
heat pump operation. The heat pump cycles twice per
hour (on for 15 min and off for 15 min, and then on
for another 15 min and off for another 15 min), and
when the heat pump is on, the inlet temperature of
the BHEs maintains at 20 °C , and when it is off, the
inlet temperature maintains at 10 °C. The initial
ground temperature is 10 °C, and the fluid only
circulates along the pipe loop when the heat pump is
on.
A calculation using the two-dimensional model has
been carried out for the purposes of comparison. In
this model, the fluid outlet temperature necessarily
shows an instant response to changes in inlet
temperature. This is not only true of the GEMS2D
two-dimensional model but is also true of all models
that are formulated on a two or one-dimensional
basis. The results of the simulations by the two
models are shown in Figure 5.
Figure 5 Fluid temperature variations due to step
changes in inlet temperature predicted by two and
three-dimensional numerical models.
- 610 -
At the start of each step increase in inlet temperature
the 2D model shows an instant change in outlet
temperature. Responses predicted by the 3D model
show little change in the predicted outlet temperature
until after three or four minutes (the nominal loop
transit time is 200 s).
SYSTEM SIMULATION
The simulation of GSHP systems have been
implemented in different building simulation tools,
for example, HVACSim+ (Clark, 1985), TRNSYS
(SEL, 1997), and EnergyPlus (Crawley et al., 2001).
Both HVACSim+ and EnergyPlus use the short time
step g-function model developed by Yavuzturk and
Spitler (1999) to simulate BHEs, while TRNSYS
uses the duct storage (DST) model by Hellstrom
(1991). Both the g-function model and the DST
model neglect the dynamics of fluid transport in the
pipe loops. A new dynamic BHEs model has been
implemented in TRNSYS by Wetter and Huber
(1997), which takes into account those dynamics.
Kummert and Bernier carried out a study of
residential GSHP systems and compared steady-state
and dynamic model predictions of operating
behaviour and performance. Their findings indicate
that steady-state models can lead to overestimating
the energy use by as much as 75% in extreme cases,
because they predict quick temperature drops in the
ground return temperature that prevents the heat
pump from operating in heating mode (Kummert and
Bernier, 2008).
In this study, a GSHP system with a BHE has been
simulated using the short time step g-function model
implemented in EnergyPlus., The results are to
compared with those by the two and three-
dimensional models (GEMS2D and GEMS3D).
Building Simulation
A typical UK two-storey domestic building with a
GSHP system has been modelled using EnergyPlus.
This has been done to derive fluid temperatures more
typical of a building than step changes. The system
simulation also allows transient heat transfer rates to
be compared and differences in overall efficiency to
be evaluated.
The building has been modelled in two zones, one is
the living zone at the ground floor and the other is the
bedroom zone at the first floor. The internal gains are
modelled as a typical family of four. The heating
floor area is 102 m2 and the heating volume is 272
m3. The heating period is from January to May, and
then from September to December. The heating set
point is 21 °C and the heating load is about 5.6
MWh/y. The annual building load profile is shown in
Figure 6.
Figure 6 Building Load of a typical domestic
building in the UK.
Heat Pump Model
A ground source water-to-water heat pump is used to
provide the heating of the house. Hot water is
delivered to the low temperature radiators installed in
both zones. A simple water-water heat pump
equation fit model (Tang, 2005) implemented in
EnergyPlus is chosen to simulate the heat pump in
this study. This model uses four non-dimensional
equations or curves to predict the heat pump
performance in cooling and heating mode. The
methodology involved using the generalized least
square method to generate a set of performance
coefficients from the catalogue data at indicated
reference conditions. Then the respective coefficients
and indicated reference conditions are used in the
model to simulate the heat pump performance. In this
case, the output of the heat pump is proportional to
the building load during the operation. Cyclic
operation of the heat pump is not modelled.
The only variables that influence the water-to-water
heat pump performance are load side inlet water
temperature, source side inlet temperature, providing
the source side water flow rate and load side water
flow rate are constant. The EnergyPlus model allows
the characteristics to vary according to both flow
rates and temperatures but, as the manufacturer’s
data is only available for single design flow rate, the
model can be defined solely in terms of load and
source side inlet temperatures. The governing
equations for the heating mode are consequently
simplified and can be described as follows.
(5)
(6)
where:
C1-D3: Equation coefficients for the heating mode
Tref : Reference temperature (283K)
- 611 -
TL,in,: Entering load side water temperature, K
TS,in : Entering source side water temperature, K
Qh : Load side heat transfer rate (heating), W
Powerh : Power consumption (heating), W.
The model coefficients have been derived from data
for the Viessmann Vitocal 200-G Type BWP 106
water-to-water heat pump, which has a 6kW rated
capacity.
Borehole Heat Exchanger Model
The BHE has been designed using the GLHEPro tool
(IGSHPA, 2007) based on the simulated heat pump
monthly and peak loads. A single borehole with a
diameter of 150 mm and a depth of 100 m is chosen
and the configurations and thermal properties of the
borehole are shown in Table 1. The spacing between
pipes is the end-to-end distance. Three models have
been applied to simulate the BHE, including the g-
function model, the GEMS2D model, and the
GEMS3D model.
Table 1 Configurations and thermal properties of the
domestic building BHE.
Borehole Diameter
D
150
mm
Pipe Inner Diameter
Din
26.2
mm
Pipe Outer Diameter
Dout
32
mm
Spacing between pipes
Ls
32.2
mm
Conductivity
kf
0.6
W/mK
Fluid
Thermal Capacity
ρcp
3.59
MJ/m3K
Conductivity
kpipe
0.39
W/mK
Pipe
Thermal Capacity
ρcp
1.77
MJ/m3K
Conductivity
kgrout
0.75
W/mK
Grout
Thermal Capacity
ρcp
3.9
MJ/m3K
Conductivity
ksoil
2.5
W/mK
Soil
Thermal Capacity
ρcp
2.5
MJ/m3K
Fluid Flow Rate
m
0.4
kg/s
Convective Coefficient
H
2280
W/m2K
Initial Ground Temp
T
10
°C
RESULTS AND DISCUSSION
The simulation of the GSHP system has been carried
out in EnergyPlus with 10 min time steps for one
year, using the existing g-function model
implementation (Fisher et al., 2006) to simulate the
BHE.
The simulation results have been used in two ways.
Firstly, we take the borehole inlet temperatures
calculated in the course of the annual simulation and
use these as boundary conditions in the two and
three-dimensional numerical models implemented in
GEMS2D and GEMS3D respectively. The second
way in which the annual simulation results have been
used is to take the calculated building heating loads
and use these as boundary conditions in simulations
integrating the numerical borehole models with the
heat pump model. This allows the overall effect of
the different heat transfer rates and dynamic response
to be evaluated.
Predicted fluid temperatures
The BHE inlet fluid temperatures (heat pump source-
side outlet temperature) obtained from EnergyPlus
have been used in the first comparison of alternative
models. The resulting outlet temperatures predicted
using the two and three-dimensional models and
using twenty hours of inlet temperature data are
shown in Figure 7. In addition, the results from the
28 hour to the 48 hour are shown in Figure 8. The
simulations ran using 1-minute time steps.
Figure 7 Comparison of outlet temperatures by g-
function model, GEMS2D and GEMS3D model.
Figure 8 Comparison of outlet temperatures by g-
function model, GEMS2D and GEMS3D model from
28 hour to 48 hour.
Over this long period of operation the outlet
temperature predicted by the GEMS3D model is only
slightly lower than that predicted by the two-
dimensional GEMS2D model, but is slightly higher
than the temperature predicted by the EnergyPlus g-
function model. The effect of the dynamic response
of the GEMS3D is demonstrated during the first 10
min running of the heat pump. Heat transfer rates
calculated over the same period are shown in Figure
9. The patterns of the heat transfer rate for the g-
function model and the GEMS2D model are similar.
The main things to note are that heat transfer rates
are higher in the GEMS3D model at the start of
operation, and are otherwise slightly lower than the
GEMS2D two-dimensional model.
- 612 -
Figure 9 Comparison of heat transfer rates by g-
function mode (EnergyPlus) , GEMS2D model and
GEMS3D model.
Integrated system simulation results
In realistic simulation of GSHP system behaviour,
the appropriate boundary conditions are the ones of
building heating loads rather than inlet fluid
temperatures. Ground loop conditions are dependent
on heat pump characteristics as well as the BHE
performance. To simulate loop and heat pump
operation building heating loads and load-side inlet
temperatures calculated from the annual simulation
using EnergyPlus have been imposed on the load-
side of the heat pump. Heat transferred to the ground
loop then depends on the heat pump Coefficient of
Performance (COP) that, in turn, is dependent on
ground loop temperature.
The inlet and outlet temperatures of the BHE
calculated by the GEMS2D and GEMS3D models
during 24 hours simulation are shown in Figure 10.
The three-dimensional model shows relatively higher
heat transfer rates and delayed response at the short
period when the heat pump starts. After slightly more
than an hour, the fluid temperatures predicted by the
three-dimensional model are lower than those
predicted by the two-dimensional model are. This is
consistent with previous results (Figure 9).
Differences in dynamic behaviour at sudden changes
in inlet temperature do not seem significant over an
operating period like that shown. However, Kummert
and Bernier (2008) showed dynamic fluid transport
could significantly change overall system behaviour
when interaction with the heat pump control system
(i.e. cycling) was considered.
Apparently high heat transfer rates at the start of heat
pump operation are to be expected if the dynamics of
the fluid in the borehole are considered. Heat transfer
at a particular point down the borehole cannot be
expected to be fundamentally different when three-
dimensional effects are considered. However, the
delay in transport of the initial cold fluid entering the
loop means that, for a short period, the outlet
temperature does not change and so a heat balance
calculated using the inlet and outlet temperatures
shows a high overall heat transfer rate.
The predicted ground loop temperatures are lower
when the three-dimensional model is applied in this
heating case. This indicates that the temperature
difference between the borehole and the surrounding
ground is larger. This corresponds to a lower
predicted heat transfer rate over longer periods.
Higher heat transfer can be expected in a two-
dimensional model in that the temperature of the
pipes is assumed to be the same along their whole
length. The pipe temperatures in the two-dimensional
model are the same as the inlet and outlet
temperatures. These temperatures are higher and
lower than the mean pipe temperatures predicted by
the three-dimensional model. It may be more
accurate to say then, that the two-dimensional model
tends to over-predict the heat transfer rate.
Figure 10 BHE temperature variance in 24 hours.
CONCLUSIONS AND FUTURE WORK
A three-dimensional numerical model, which can
simulate the fluid transport along the pipe loop as
well as heat transfer with the ground, has been used
to study the dynamic response of a Borehole Heat
Exchanger. The model has been validated by
reference to analytical models of borehole thermal
resistance and also fluid transport inside the pipe. It
has been possible to compare predicted outlet
temperature with those of a similar two-dimensional
model and an implementation of a short time step g-
function model.
The results show that delayed response associated
with the transit of fluid around the pipe loop, is of
some significance in moderating swings in
temperature during the short period when the heat
pump starts to operate. The GEMS3D three-
dimensional model of the BHE shows a lower heat
transfer rate will occur over longer periods of
operation when compared to two-dimensional
models. This is due to the mean temperature
differences between the fluid and the ground being
lower in the three-dimensional model – this seems
more realistic.
- 613 -
A simple heat pump model has been used in this
study and cannot simulate the on-and-off dynamic
characteristics of a typical domestic heat pump. A
more detailed dynamic heat pump model may be
applied in further work to investigate system
performance and control system operation.
Study of characteristics of BHEs using this detailed
three-dimensional model should give insights into the
limitations of two-dimensional models and highlight
ways in which they may be improved. Implications
for design methods are also to be investigated.
ACKNOWLEDGEMENTS
This work is sponsored by De Montfort University.
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