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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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Conductive Heat Flows To and Between

Pipes In a Composite Cylinder, University

of Lund, Sweden.

Bosworth, R.C.L., 1949. Phil. Mag., 39: 847-850.

Carslaw, H.S. and Jaeger, J.C., 1947. Conduction of

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