Report - Jan Hensen

Transcription

Report - Jan Hensen

Report
Old technology for new buildings, a study on earth-to-air heat exchangers
AO 4012.07
Wednesday, 30 April 2008
To my parents,
Student
J. van de Brake
0548779
Building Services
University of Technology Eindhoven
Den Dolech 2
Eindhoven
Company
Smits van Burgst BV
Raadgevend Ingenieursbureau
Baron de Coubertinlaan 8
2719 EL Zoetermeer
Counsellors from the university
Prof. Dr. Ir. J.A. Hensen
M. Trcka dipl. Ing
Counsellor from Smits van Burgst BV
Ir. J.G. Mast
Version
1.2
Document identification mark
12122007 Scriptie.doc
Date
30 April 2008
This report consists of 182 pages
-2-
Contents
Acknowledgements ................................................................................................................ 6
Abstract .................................................................................................................................. 7
Nomenclature ......................................................................................................................... 9
1
Introduction ........................................................................................................ 15
2
Thesis outline ..................................................................................................... 18
2.1
Relevance .......................................................................................................... 18
2.2
Working principle of an earth-to-air heat exchanger.......................................... 19
2.3
Research question ............................................................................................. 20
2.4
Delineation ......................................................................................................... 21
2.5
Research methodology ...................................................................................... 25
2.5.1
Literature review................................................................................................. 25
2.5.2
Modelling............................................................................................................ 25
2.5.3
Simulation .......................................................................................................... 26
3
Literature review................................................................................................. 27
3.1
Available models ................................................................................................ 27
3.1.1
The Elmer Schiller algorithm (Elmer and Schiller, 1981) ................................... 27
3.1.2
The Puri algorithm (Puri, 1984b;Puri, 1984a) .................................................... 30
3.1.3
The Boulard algorithm (Boulard, Razafinjohany et al., 1989b).......................... 32
3.1.4
The Santamouris algorithm (Mihalakakou, Santamouris et al., 1994a)............. 35
3.1.5
The Gautier algorithm (Gauthier, Lacroix et al., 1997) ...................................... 38
3.1.6
The Hollmuller algorithm (Hollmuller and Lachal, 1998).................................... 40
3.1.7
The Bojić algorithm (Bojic, Papadakis et al., 1999) ........................................... 42
3.1.8
The Zimmermann algorithm (Zimmermann and Huber, 2000) .......................... 44
3.1.9
The Hanby algorithm (Hanby, Loveday et al., 2005) ......................................... 49
3.2
Realized projects................................................................................................ 51
3.3
Model selection .................................................................................................. 51
3.4
Software selection.............................................................................................. 52
4
Selected algorithms............................................................................................ 56
4.1
Hollmuller algorithm ........................................................................................... 56
4.1.1
Mathematical algorithm ...................................................................................... 56
-3-
4.1.2
Alterations to the original script.......................................................................... 65
4.2
Santamouris algorithm ....................................................................................... 65
4.2.1
Mathematical algorithm ...................................................................................... 65
4.2.2
Alterations to the original script.......................................................................... 70
4.3
Comparison between Hollmuller and Santamouris model................................. 72
5
Verification ......................................................................................................... 73
5.1
Hollmuller model verification .............................................................................. 73
5.1.1
Verification methodology.................................................................................... 73
5.1.2
Results of verification ......................................................................................... 75
5.2
Santamouris model verification.......................................................................... 76
5.2.1
Verification methodology.................................................................................... 76
5.2.2
Results of verification ......................................................................................... 78
6
Sensitivity analysis ............................................................................................. 81
6.1
Basic set up........................................................................................................ 81
6.2
Soil and climate.................................................................................................. 82
6.2.1
Methodology....................................................................................................... 82
6.2.2
Results ............................................................................................................... 85
6.2.3
Discussion.......................................................................................................... 88
6.3
Pipe material ...................................................................................................... 89
6.3.1
Methodology....................................................................................................... 89
6.3.2
Results ............................................................................................................... 89
6.3.3
Discussion.......................................................................................................... 91
6.4
Diameter............................................................................................................. 92
6.4.1
Methodology....................................................................................................... 92
6.4.2
Results ............................................................................................................... 92
6.4.3
Discussion.......................................................................................................... 94
6.5
Length ................................................................................................................ 95
6.5.1
Methodology....................................................................................................... 95
6.5.2
Results ............................................................................................................... 95
6.5.3
Discussion.......................................................................................................... 97
6.6
Depth.................................................................................................................. 98
6.6.1
Methodology....................................................................................................... 98
6.6.2
Results ............................................................................................................... 99
6.6.3
Discussion........................................................................................................ 102
-4-
6.7
Volume flow...................................................................................................... 102
6.7.1
Methodology..................................................................................................... 102
6.7.2
Results ............................................................................................................. 102
6.7.3
Discussion........................................................................................................ 104
6.8
Moisture diffusivity............................................................................................ 104
6.8.1
Methodology..................................................................................................... 104
6.8.2
Results ............................................................................................................. 105
6.8.3
Discussion........................................................................................................ 107
7
Case studies .................................................................................................... 108
7.1
Town house (The Netherlands) ....................................................................... 108
7.2
Shopping mall “Vasco da Gama” (Portugal) .................................................... 114
7.2.1
Mall/promenade ............................................................................................... 116
7.2.2
Shops ............................................................................................................... 119
7.2.3
Restaurants...................................................................................................... 122
7.2.4
Savings ............................................................................................................ 125
8
Conclusions...................................................................................................... 130
Bibliography...................................................................................................... 134
A
Realised projects.............................................................................................. 139
B
Thermal properties used in verification Hollmuller algorithm ........................... 145
C
Properties used in verification Santamouris algorithm..................................... 148
D
Comparison predicted and calculated temperatures of the Santamouris model
151
E
Properties used in sensitivity analysis ............................................................. 157
F
Thermal properties of soil ................................................................................ 163
G
Surface temperatures and annual amplitudes ................................................. 165
H
Results of the soil and surface sensitivity analysis of the Rome ..................... 170
I
Results of the Santamouris model ................................................................... 173
J
Data CD ........................................................................................................... 181
-5-
Acknowledgements
I would like to express my thanks to Prof. Dr. Ir. J.A. Hensen and M. Trcka dipl. Ing, Unit
Building physics and systems at the University of Technology Eindhoven, for their help
without whom this study would not have been possible.
Also my thanks to Ir J.G. Mast of Smits van Burgst BV for his support and the opportunity to
do this study at his company. Besides my thanks to M. Eimermann, E. Ottes R. v.d. Nes
and C.W. Nuissl at Smits van Burgst for their help and moral support.
Mom and dad thanks for your support and your advice. And last but certainly not least
Stella many thanks to you for putting up with the late nights and you support.
Heerlen, Wednesday, 30 April 2008
Jacco van de Brake
-6-
Abstract
The consumption of fossil fuels today still increases all over the world. If this goes
unchecked the CO2 concentration in the air will increase with 50% in the next 25 years. To
counteract this prediction the Kyoto climate treaty was signed in 2002. For the Netherlands
this would mean a 6% reduction of the CO2 emissions compared with the 159.4 Mton CO2
emissions of 1990. The largest reductions can be realised in the Build environment and
Transport sector.
The total primary energy consumption for Dutch commercial buildings in 2000 was in the
excess of 306 Petajoule. The second largest energy consumer in this category is shops
with a total energy consumption of 1938 MJ m-2. But it is also likely that the energy
consumption of residential buildings will rise in the moderate climates. This is caused by
people getting more accustomed to higher comfort levels during the summer.
A possible way of reducing the energy demand of the Build environment is by applying an
earth-to-air heat exchanger. An earth-to-air heat exchanger dampens the effect of the
ambient temperature on the heating and cooling demands for ventilation. But unfortunately
not even <1% of the shopping malls and only a few residential project use this technology.
For this study the following research question was set up.
Can earth-to-air heat exchangers be applied to new shopping centres and houses in
Europe?
There are several algorithms that describe the physical process that occurs within an earthto-air heat exchanger. Nine algorithms for an earth-to-air heat exchanger were found during
the literature study. From these algorithms the Santamouris and Hollmuller algorithms were
selected to be used in this study. The selection was based on boundary conditions, multipipe configuration and validation published.
For this research TRNSYS IISIBAT 16 was selected for the modelling of the earth-to-air
heat exchanger. Because the original algorithms were written in TRNSYS and that it would
be to time consuming to rewrite them for another program.
The geographical location of an earth-to-air heat exchanger is a major factor to its
-1
applicabillety. The highest energy savings, 2257 kWh a , were obtained for a dry steppe
climate with 1 month with and average temperature lower then 0°C. The dry steppe
climates favour a climate with low temperatures. The most common climate in Europe is the
-7-
Mesothermal climate. This climate favours climates that have a high temperature and rain
in all the seasons of the year. The more important of those two criterions is the high
temperature. The Microthermal climate favours a climate with low temperatures.
For all the climates the largest energy savings are obtained with a soil with high thermal
conductivity, density and specific heat. Increasing the soils thermal conductivity gives the
largest boost, with a maximum of 79%, of the energy savings. An increase of the specific
heat of the soil will result in an increase of the energy savings of maximum 48%. The
smallest increase of energy savings, maximum of 33%, is obtained by increasing the
density of the soil. When all the soil parameters would be tackled simultaneously this would
result in a maximum increase of 120%.
The optimum design of an earth-to-air heat exchanger is an exchanger that consists of
short pipes, small diameters and low airspeed. But when designing it is essential to keep
the air flow turbulent and pressure loss low.
The effect of the material of the exchanger on the energy savings is minimal compared to
the other design criteria. It is better to select the material based upon practical design
considerations like groundwater level. The largest savings are obtained in the first two
meters in depth. After three meters the savings are minimal while the costs of digging
increase significantly.
The case study for the townhouse showed an average coverage between 6% and 8% of
the annual heating load. The system performers more efficiently in cooling mode resulting
in average coverage between 78% and 90%. The system is proofed to be effective for
houses regarding CO2 reduction. Nevertheless the nowadays costs for such a system
result in long pay back times. Possibly the initial costs will be reduced when applying these
systems on large scale systems. The obtained CO2 reduction is 5-6% and the calculated
payback time is 17-24 years excl. filter (44-81 years inclusive filter replacement).
On a large scale project as a shopping mall the performance is better but the initial costs
increase rapidly due to the need for special products. Therefore payback times between 88
and 338 years are found when including the replacement of the extra filters. Looking at the
energy coverage (55% of the heating and 21 % of the cooling loads are covered) and the
CO2 reduction (218,8 ton) the system makes sense after all. In order to make this system
more cost effectively there should be searched for cheaper pipe materials.
Based on the payback time, the coverage of the heating/cooling demand and
environmental savings the choice of applying this technology is not based on the financial
reasons but more on ideological and environmental reasons.
-8-
Nomenclature
As
Annual surface temperature amplitude
K
(UA)i
Coupling thermal conductance between the two parallel
W K-1
(UA)ij
Conductivity between two parallel pipes
W K-1
a
Absorbtivity for solar radiation
AHj,i
Temperature discretization coefficient for node i of pipe j
Aj,i
Ap
Area of pipe surface
m2
Ap,c
Area of the cross-section
m2
Ass,i
Area of the soil node side i
m2
Awat
Area of water surface inside the pipe
m2
BHj,i
Bij
Distance between pipe i and pipe j
Bj,i
CHj,i
Cj,i
CO2
CO2 emission
kg
cp,a
Specific heat of the air
J kg-1 K-1
cp,p
Specific heat of the pipe
J kg-1 K -1
cp,s
Specific heat of the soil
J kg-1 K-1
cp,vap
Specific heat of vapour
J kg-1 K-1
Cv
Volumetric heat capacity
J m-3 K-1
cv,s
Volumetric specific heat of soil
J m-3 K-1
d
Internal diameter of the pipe
m
DHj,i
Soil humidity discretization coefficient for node i of pipe j
Dj,i,seg
Temperature discretization coefficient for current segment
m
of node 2 of pipe j
Dt
Thermal moisture diffusivity
m2 s-1 K-1
Du
Isothermal moisture diffusivity
m2 s-1
Du,vap
Isothermal moisture diffusivity in vapour
m2 s-1
dw,p
Thickness of pipe wall
m
-9-
EHj,i
Ej,i
Eo
Solar radiation intensity
FHj,i
Fj,i
Ge
Electricity consumption saved
kWh
Gf
Fan electricity consumption
kWh
GHj,i
Gj,i
Gv
Gas consumption saved
m3
H
Volumetric enthalpy of air
J m-3
HLa
Mass transfer coefficient of the air
m2 s-1
HLp
Mass transfer coefficient of the pipe
m2 s-1
l
Pipe length
m
lg
Heat of evaporation of moisture
J kg-1
ln
Node width (along x,y or z axis)
m
ln,i
Node width neighbouring node (along x, y or z axis)
m
Mp
Water content pipe
kgwater kgpipe-1
mwat,in
Mass of water flowing into the node
kg
mwat,inf
Mass of water infiltrated into the node
kg
mwat,lat
Mass of water condensed or evaporated
kg
mwat,out
Mass of water flow out of node
kg
mwat,t-1
Mass of water in the node at last time step
kg
NOx
NOx emission
g
OHj,i
pe
Electricity price
€ kWh-1
Pfan
Fan power
W
pg
Gas price
€ m-3
Qfric
Energy lost due to friction
W
Qint
Energy loss to water inside the pipe
W
Qlat
Latent heat
W
qm,a
Mass flow of the air
kg s-1
qp’
Energy diffused per meter pipe
W m-1
Qs
Energy diffused by neighbouring nodes
W
J m-2
- 10 -
Qs,a
Energy diffused between soil and air
W
Qs,j
Energy diffused form pipe j to the soil
W
Qs,j,seg
Energy diffused to neighbouring nodes of pipe j current
W
segment
Qs,surf
Heat flux from the environment
W
Qs,u
Energy diffused in opposite direction of the x-axis
W
Qs,v
Energy diffused in opposite direction of the y-axis
W
Qs,w
Energy diffused in opposite direction of the z-axis
W
Qs,x
Energy diffused in direction of the x-axis
W
Qs,y
Energy diffused in direction of the y-axis
W
Qs,z
Energy diffused in direction of the z-axis
W
Qsbl
Sensible energy
W
qv,a
Volume flow rate of air
m3 s-1
qv,a,j
Volume flow rate of air of pipe j
m3 s
Qwat
W
r
Polar coordinate, radial distance from the tube axis
-,m
r0
Inner radius of the pipe
m
r1
Outer radius of the pipe
m
Ra
Heat resistance air
K W-1
Ra,p
Heat resistance air-pipe interface
K W-1
Re
Reynolds number
m
rn
Radius of soil layer
m
rp
Radius of the pipe
m
Rp,s
Heat resistance pipe-soil interface
K W-1
Rs
Heat resistance soil
K W-1
rs
Radius of soil cylinder
m
Rs,surf
Heat resistance soil surface
m2 K W-1
Rs,surf
Heat resistance soil-surface interface
K W-1
rzn
Distance temperature node from centreline of pipe
m
S
Source term
W m-3
SOx
SOx emission
g
t
Time
s
t0
Phase constant
h,d
Ta
Temperature of the air
°C
- 11 -
Ta,eahe,out
Temperature exiting the earth-to-air heat exchanger
°C
Ta,i
Air temperature in exchanger i
°C
Ta,i+1
Temperature of the air in next element
°C
Ta,ini
Initial temperature of the air
°C
Ta,seg
Temperature of the air current segment
°C
Ta,seg,in
Temperature of the air entering the segment
°C
Ta,seg,out
Temperature of the air exiting the segment
°C
Ta,seg-1
Temperature of the air previous segment
°C
Tamb
Temperature of the ambient air
°C
Tave,surf
Average surface temperature
°C
Tgfix
Temperature of the floor in the zone with fixed room
°C
temperature
Tgfree
Temperature of the floor in the zone with free floating room
°C
temperature
Tj,1,seg-1
Temperature of the air in previous segment of pipe j
°C
Tj,2,seg
Temperature for current segment of node 2 of pipe j
°C
Tj,3,seg,t-1
°C
previous time step
Tj,i,seg
Temperature for current segment of node i of pipe j
°C
Tj,i+1,seg,t-1
Temperature for current segment of node i+1 of pipe j
°C
previous time step
Tj,i-1,seg
Temperature for current segment of node i-1 of pipe j
°C
Toutlet
Exit temperature including increased air temperature due to
°C
heat of fan power
Tp
Temperature of the pipe
°C
Tp,i
Temperature of pipe i
°C
Tp,i,t
Temperature of pipe neighbouring node at current time step
°C
Tp,i-1
Temperature of the neighbouring node
°C
Tp,s
Temperature of pipe-soil interface
°C
Tp,seg
Temperature of the pipe current segment
°C
Tp,t-1
Temperature of node at the last time step
°C
Ts
Temperature of the soil
°C
Ts,i,t-1
Temperature of the neighbouring node last time step
°C
- 12 -
Ts,ini
Initial temperature of the soil
°C
Ts,surf
Temperature at ground level
°C
Ts,t-1
Temperature of the soil in last time step
°C
Tt-1
Temperature of the soil previous time step
°C
U
Heat transfer coefficient
W m-2 K-1
Ua
Heat transfer coefficient air
W m-2 K-1
Up
Heat transfer coefficient of the pipe
W m2 K-1
Us,a
Heat transfer coefficient soil-air
W m2 K-1
Uss,i
Heat transfer coefficient node side i
W m-2 K-1
Usurf
Heat transfer coefficient soil-environment
W m-2 K-1
va
Air speed
m s-1
va
Air speed
m s-1
Vp
Volume of pipe node
m3
Vs
Volume of soil node
m3
vwat
Velocity of water
m s-1
x
Cartesian coordinate
m
xa
Water vapour content in the air
kg kg-1
xp
Water vapour content pipe
kg kg-1
xs
Moisture content of soil
kg kg-1
y
Cartesian coordinate, polar coordinate, distance from the
m,m,m
inlet
z
Cartesian coordinate, depth below the surface
m
zi
Depth of pipe i below surface
m
zj
Depth of pipe j below surface
m
αsurf
Heat transfer coefficient soil-surface interface
W m-2 K-1
γ
Money savings
€
δi,j
Kronecker delta
Δp
Total pressure loss earth-to-air heat exchanger
Pa
ΔTf
Temperature increase due to fan
°C
ε
Temperature effectiveness
-
εw
Wall roughness
m
ηfan
Total fan efficiency
-
λ
Friction coefficient
-
λp
Thermal conductivity of the pipe
W m-1 K-1
- 13 -
λp,s
Thermal conductivity of the pipe-soil interface
W m-1 K-1
λs
Thermal conductivity of the soil
W m-1 K-1
ξ
Resistance coefficient
-
ρa
Density of the air
kg m-3
ρm
Density of moisture
kg m-3
ρp
Density of the pipe
kg m-3
ρs
Density of the soil
kg m-3
φ
Relative humidity
%
φa
Relative humidity of the air
%
Φcool,savings
Energy savings in cooling mode
W
Φeahe
Energy flux from the earth-to-air heat exchanger
W
Φheat,savings
Energy savings in heating mode
W
φs,,j,i
Relative soil humidity of node i of pipe j
%
φs,,j,i,t-1
Relative soil humidity of node i of pipe j previous time step
%
φs,,j,i+1,t-1
Relative soil humidity of node i+1 of pipe j previous time
%
step
φs,,j,i-1
Relative soil humidity of node i-1 of pipe j
%
φs,,j,i-1,t-1
Relative soil humidity of node i-1 of pipe j previous time
%
step
- 14 -
1
Introduction
The consumption of fossil fuels today still increases all over the world. If the inclination of
the consumption of fossil fuel is not moderated this inclination will result in an increase of
the CO2 concentration in the air of 50% in the next 25 years. To tackle this grim prediction
the Kyoto treaty was signed in 2002, this treaty discusses the emission of greenhouse
gasses. For the Netherlands this means that between 2008 and 2012 the CO2 emission
must to be reduced with 6% compared to 159.4 Megaton CO2 emission in 1990 (Milieu en
Natuur Planbureau, 2006). After this period the European Union has defined an ambition
for the industrialised countries stating that the CO2 emission in 2020 have to be reduced
with an average of 15 to 30% in relation to the CO2 emission of 1990. This ambition is in
line with the reduction target defined in the United Nations global climate treaty. The current
Dutch energy policy states the intention of reducing energy consumption with 500
Petajoule, this is 500.000.000.000.000.000 joule (140.000 GWh). This will be realized by
means of energy conservation and by replacing fossil fuels by renewable energy.
The total primary energy consumption for Dutch commercial buildings in 2000 was in
excess of 306 Petajoule. This is equal to 10% of the national consumption of energy
(SenterNovem, 2007). The second largest consumer, with an energy consumption of 1938
MJ m-2, within the commercial buildings category is shops.
Miscellaneous
29%
Heating 34%
Other building
bound uses 12%
Hot water 0%
Cooling 1%
Lighting 24%
Figure 1: Distribution of energy consumption for shops in the Netherlands
(SenterNovem, 2007)
- 15 -
The distribution of the energy consumption for shops is shown in Figure 1. But it is also
likely that the energy consumption of residential buildings will dramatically increase due to
air-conditioning in even the moderate climates. This is due to people getting more
accustomed to higher comfort levels during summer conditions. The energy consumption of
6 typical residential buildings are shown in
Table 1.
Kind of residential building
Town house
Town house (corner)
Semi-detached house
Detached house
Gallery flat
Apartment complex
Ventilation system
Energy consumption
[MJ m-2]
balanced
340
mechanical exhaust
359
balanced
383
mechanical exhaust
403
balanced
392
mechanical exhaust
401
balanced
418
mechanical exhaust
417
balanced
342
mechanical exhaust
351
balanced
337
mechanical exhaust
346
Table 1: Energy consumption of 6 kinds of residential buildings for the Netherlands
One of the possibilities of reducing or preventing a further growth in energy consumption and thus in CO2 emission- is applying earth-to-air heat exchangers. This technology can
preheat or precool the air before it enters the building and by doing so decrease the
demand for heating and cooling.
This research aims at assessing the applicability of the earth-to-air heat exchanger
technology for houses and shopping malls in Europe.
In Table 2 an overview is given where certain components of the research can be found.
- 16 -
Chapter
Chapter name
Content
Chapter 1
Introduction
An introduction to the research
The relevance of the study, a general principle of
Chapter 2
Study outline
an earth-to-air heat exchanger, delineation of the
problem, research question and the methodology
used in this study
An overview of the available algorithms,
Chapter 3
Literature study
publicized realized projects in the Netherlands
and surrounding countries, model and program
selection.
The mathematical models of the selected
Chapter 4
Selected algorithms
algorithms, the alterations to the original codes
and an overview of the differences between the
codes.
Chapter 5
Verification
The verification of the implementation of the
selected algorithms
The sensitivity of the selected algorithms to
Chapter 6
Sensitivity analysis
combinations of soil and climate, pipe material,
diameter of the tubes, length of the tubes, depth
of tubes, air velocity and diffusivities.
Chapter 7
Case studies
Chapter 8
Conclusions
The case studies of a house and the Vasco da
Gama shopping mall
Conclusions and recommendations based on this
study
Table 2: Bookmark anchor
- 17 -
2
Thesis outline
In the first part of this chapter the relevance of this research and the general principle of an
earth-to-air heat exchanger will be discussed. After which the boundaries of this study will
be set. Subsequently the main research question will be presented; this main research
question is divided in six sub questions. At the end of this chapter the research
methodology of this study is be addressed.
2.1
Relevance
As mentioned in the introduction the Dutch government has to reduce the national CO2
emissions with 6% compared to the CO2 emissions of 1990. The largest reduction of the
CO2 emissions can be realised in the build environment and transport sector (Ministerie van
Economische Zaken, 2005). Approximately one third of the total CO2 emissions are emitted
in the Build environment (Joosen, Harmelink et al., 2004).
An earth-to-air heat exchanger dampens the effect of the ambient temperature on heating
and cooling demands for ventilation. The green area’s of Figure 2 show which part of the
Trias energetica are used when applying an earth-to-air heat exchanger.
Figure 2: Effect of an earth-to-air heat exchanger on the Trias Energetica
But not even 1% of the shopping malls in the Netherlands are using this technology to
reduce their energy consumption. The earth-to-air heat exchanger technology is used in a
few residential buildings in the Netherlands.
- 18 -
The application of this technology can have advantages on different levels. For the central
government the application of this technology helps to reduce the CO2 emissions for the
build environment. As mentioned before an earth-to-air heat exchanger lowers the heating
and cooling demand for a building. Applying this technology helps the project developer to
meet the declining energy consumption demanded by the building code. Apart from the
benefit to the environment, the end-user will benefit financially by using this technology.
2.2
Working principle of an earth-to-air heat exchanger
The principle of using ground inertia for heating and cooling is not a new concept, but rather
a modified concept that goes back to the Ancients. This technology has been used through
out history from the ancient Greeks and Persians in the pre-Christian era until recent history
(Santamouris and Asimakopoulos, 1996). For instance the Italians in the Middle Ages used
caves, called colvoli, to precool/preheat the air before it entered the building.
The system which is used nowadays (Figure 3) consists of a matrix of buried pipes through
which air is transported by a fan. In the summer the supply air to the building is cooled due
to the fact that the ground temperature around the heat exchanger is lower than the
ambient temperature. During the winter, when the ambient temperature is lower than the
ground temperature the process is reversed and the air gets pre-heated.
- 19 -
Figure 3: Principles of ground cooling and heating
2.3
Research question
The aim mentioned in the introduction can be rewritten in to the following research
question:
Can earth-to-air heat exchangers be applied to houses and shopping centres in Europe?
- 20 -
To accomplish this research question the following sub questions have to be answered:
Which earth-to-air heat exchangers are available?
What are the experiences using earth-to-air heat exchangers so far?
Which factors are normative for earth-to-air heat exchangers?
Which model is best suited for the desired earth-to-air heat exchanger?
How does the performance of an earth-to-air heat exchanger relate to the
performance of a traditional system?
2.4
Delineation
Building
The buildings used in the case studies are simple building models using Vabi software
(Vabi, 2007).
Exchanger
This study assumes that it is always possible to place the earth-to-air heat exchanger
above the groundwater level. Furthermore that it is always possible to apply this
technology. The study will only use existing models that are published.
- 21 -
Savings
In this study the following kinds of savings are defined:
Energy savings
Φ heat , saving = qv ,a ρ a c p , a (Ta ,eahe,out − Tamb )
Φ cool , saving = qv ,a ρ a c p ,a (Tamb − Ta ,eahe,out ) + Φ lat
(1a)
(1b)
Where:
cp,a
Specific heat of air
J kg-1 K-1
qv,a
Volume flow
m3 s-1
Ta,eahe,out
Temperature air exiting the heat exchanger
°C
Tamb
Ambient temperature
°C
ρa
Density of air
kg m-3
Φcool,savings
Energy savings in cooling mode
W
Φheat,savings
Energy savings in heating mode
W
*
Φlat
*
W
Latent heat
Only used in the Hollmuller program
Equation 1: Energy savings obtained by earth-to-air heat exchanger
Environmental savings
CO2 = 1, 780Gv + 0,566Ge
(2a)
NOx = 0,55Gv + 0,15Ge
(2b)
SOx = 0, 016Gv + 0, 425Ge
(2c)
Where:
CO2
CO2 emission
kg
Ge
kWh
Gv
m3
NOx
NOx emission
g
SOx
SOx emission
g
Equation 2: Environmental savings (SenterNovem, 2006)
- 22 -
Financial savings
(3)
γ = Gv pg + Ge pe − G f pe
Where:
Gv
m3
Ge
kWh
Gf
Fan electricity consumption
kWh
γ
Money savings
€
pg
Gas price
€ m-3
pe
Electricity price
€ kWh-1
Equation 3: Emissions (SenterNovem, 2006)
Pressure loss
The pressure loss caused by friction in an earth-to-air heat exchanger is calculated is
written as:
Δp = λ
l
0,5 ρ a va 2 + ζ 0,5ρ a va 2
d
(4)
Where:
d
m
l
Pipe length
m
va
Air speed
m s-1
Δp
Pa
λ
-
ξ
Resistance coefficient
-
ρa
Density of air
kg m-3
Equation 4: Pressure loss in straight ducts (Roel, Aerts et al., 1993)
Because of the high turbulent air flow associated with earth-to-air heat exchangers a
standard Moody diagram can not be used. The friction coefficient has to be calculated
using Equation 5.
- 23 -
5,94 ⎞
⎛ ε
= −2 log ⎜ w + 0,901 ⎟
λ
⎝ 3, 72d Re
⎠
1
(5)
Where:
d
m
Re
Reynolds number
m
εw
Wall roughness
m
λ
-
Equation 5: Friction coefficient (Roel, Aerts, Bedeke, 't Hooft, Arkesteijn, Konings,
Vos, and Wiemer, 1993)
The wall roughness is dependent on which material the pipe is made from and how the pipe
was manufactured. The wall roughness for several kinds of materials and ways of
manufacturing are shown in Table 3.
Way of manufacturing
Seamless pipes
Stony pipes
material
Wall roughness
[mm/m]
Steel
0,045
Aluminium
0,045
Plastics
0,01
Concrete
2,0
Brick
3,0
Table 3: Wall roughness of different kind of pipes (Roel, Aerts, Bedeke, 't Hooft,
Arkesteijn, Konings, Vos, and Wiemer, 1993)
The resistance coefficients were determined using the general derived formula described in
Appendix A of Roels (1993). The extra needed fan power due to applying the earth-to-air
heat exchanger is determined using Equation 6.
- 24 -
Pfan =
qv , a Δp
(6)
η fan
Where:
Pfan
Fan power
W
qv,a
Volume flow air
m3 s-1
Δp
Pa
ηfan
Total efficiency of the fan
-
Equation 6: Fan power (Stichting ISSO, 2007)
2.5
Research methodology
2.5.1
Literature review
The literature study is comprised of three main components. The first step of the literature
study was to establish the state of the art in earth-to-air heat exchanger models. During this
phase the available earth-to-air heat exchanger models have been studied and an overview
is made of the available earth-to-air heat exchanger algorithms; how the algorithms were
validated and which boundary settings were used in developing the algorithms. In the
second part of the literature study and inventory was made of published projects in the
Netherlands and her surrounding countries, in which an earth-to-air heat exchanger was
applied.
In the final stage of the literature study a survey was made on how to select the proper
simulation tool for a project.
2.5.2
Modelling
Based on the data found in the desk research two models, the Santamouris model and the
Hollmuller model, of an earth-to-air heat exchanger and a software package, TRNSYSIISIBAT (Solar Energy Laboratory, 2005a), were selected. The Santamouris model was
rewritten and updated to the current version of TRNSYS-IISIBAT (Solar Energy Laboratory,
- 25 -
2005a) and the Proforma file1 were made for both models. To ensure the right
implementation of the algorithms verification has been carried out.
2.5.3
Simulation
The simulation process was done in two separate parts. In the first part of the simulation
process the earth-to-air heat exchanger was simulated as a stand alone model. At this
stage of the simulation process a sensitivity analysis was done. Also the sensitivity analysis
was broken down in to two sections.
The first section of the sensitivity analysis a study was done to asses the effect of climate
and soil on the energy savings. Europe was divided in to 11 climates based up on the
Köppen-scale. For the soil a general approach was chosen instead of using real soil data
found in literature. This approach used the maximum value, minimum value and a value in
between of the densities, specific heats and thermal conductivities found in literature. For
each climate one of those three values were varied resulting in 27 soil types.
In the second section of the sensitivity analysis the normative factors (Pipe material,
diameter, length, buried depth and air velocity) varied. During this part of the sensitivity
analysis only one factor was varied in each simulation run.
In the second part of the simulation process the earth-to-air heat exchanger was coupled to
a simple model of the Vasco da Gama shopping mall in Lisbon, Portugal, and to a simple
model of a standardized Dutch Town house (DGMR Bouw BV, 2006)
1
a Proforma file is the interface between the TRNSYS Studio and the FORTRAN source
code used within TRNSYS Studio, used in TRNSYS-IISIBAT (Solar Energy Laboratory,
2005a)
- 26 -
3
Literature review
In this chapter an overview is made of the available algorithms with which an earth-to-air
heat exchanger can be modelled. This overview consists of the mathematical algorithms,
the boundary conditions of these mathematical algorithms and how the algorithms are
validated. To get a clear view of the current state of the application of earth-to-air heat
exchanger a survey was made of publicized realised projects in the Netherlands and
surrounding countries. Subsequently a selection is made out of the overview of available
algorithms. Finally a software package is selected for this study based upon two decision
models and the selected algorithms.
3.1
Available models
3.1.1
The Elmer Schiller algorithm (Elmer and Schiller, 1981)
Heat and moisture model
The Elmer Schiller (1981) algorithm states, that the heat transfer for a single pipe earth-toair heat exchanger can be divided into two coupled thermal process. The first process is the
heat transfer through the cylindrical segments of the exchanger. The energy transfer to the
soil from each one meter segment is written as:
- 27 -
Φ eahe =
1
⎛
⎜
⎜⎛ 1
⎜ ⎜⎜ 2π r U
p p
⎜⎝
⎜
⎝
⎛ ⎛r ⎞
⎛ rs ,2 ⎞ ⎞ ⎞
⎜ ln ⎜ s ,1 ⎟ ln ⎜⎜
⎟ ⎟⎟
⎞ ⎛ dp ⎞ ⎜ ⎝ r ⎠
rs ,1 ⎠⎟ ⎟ ⎟
⎝
+
+
+
⎟⎟ ⎜⎜ 2π r λ ⎟⎟ ⎜ 2πλ
2πλs ,2 ⎟ ⎟
p p ⎠
s ,1
⎠ ⎝
⎜
⎟⎟
⎜
⎟⎟
⎝
⎠⎠
(T
a ,in
− Ts )
(7)
Where:
dp
m
rp
Radius of the pipe
m
rs,1
Radius of the inner soil cylinder
m
rs,2
Radius of the outer soil cylinder
m
Ta,in
°C
Ts
°C
Up
Heat transfer coefficient inside the pipe
W m-2 K-1
λs,1
Thermal conductivity of the inner soil cylinder
W m-1 K-1
λs,2
Thermal conductivity of the outer soil cylinder
W m-1 K-1
λp
W m-1 K-1
Φeahe
W
Equation 7: Energy flux into the soil per meter
Drying of the soil in the vicinity of the pipes of the heat exchanger is taken into account by
giving the inner soil cylinder a thickness of approximately 0,3 metres and a low thermal
conductivity. The second thermal process is the heat transfer through the pipe of the
exchanger. The exit temperature of each metre segment can be calculated by:
- 28 -
Ta ,out = Ta ,in −
Φ eahe
qm ,a * c p ,a
(8)
Where:
cp,a
J kg-1 K-1
qm,a
Mass flow rate of air
kg s-1
Ta,in
°C
Ta,out
Temperature of the air exiting the segment
°C
Φeahe
W
Equation 8: Exit air temperature segment
No moisture equations were incorporated into this model. The dehumidification of the air
was evaluated by comparing the exit temperature of each segment with the dew point
temperature.
Boundary conditions
The air inlet temperature is assumed to be constant throughout the calculation.
Furthermore the soil is represented as a homogeneous solid with no seasonal variation.
The undisturbed soil temperature is defined as:
Ts = Tave , surf − As e
−z
π
365*α
⎛ 2* π
π
*cos ⎜⎜
( t − t0 ) − z *
365*α
⎝ 365
⎞
⎟⎟
⎠
(9)
Where:
As
K
t
Time
d
t0
Phase constant
d
Tave,surf
°C
Ts
°C
z
Depth below the surface
m
α
Soil diffusivity
m2 d-1
Equation 9: Undisturbed soil temperature
- 29 -
Validation
The model was validated using data obtained from Cornell University (US). This validation
concluded, that the model did not predict accurate values for the inner surface of the pipe.
Also it was not possible to predict the dehumidification of the air inside the pipe.
3.1.2
The Puri algorithm (Puri, 1984b;Puri, 1984a)
Heat and moisture model
This algorithm was developed by Puri (1984b; 1984a) for TWODEPEP -a partial differential
solver from the International Mathematical and Statistical Library- as an implicit numerical
model for a single pipe earth-to-air heat exchanger, based on coupled and simultaneous
transfer into the soil and pipe. The following assumptions were made during the
development of the algorithms:
Pressure is constant throughout the transport process
Effect of gravity is negligible
The vapour-liquid interface is a function of temperature only
The soil is homogeneous and does not swell with changing moisture content.
These assumptions led to the following energy and moisture balance equations, in
cylindrical coordinates:
- 30 -
ρ s c p,s
∂Ts 1 ∂ ⎛
∂T
=
λs r s
⎜
∂t r ∂r ⎝
∂r
− lg ρ m
∂xs ⎞
1 ∂ ⎛
⎞ ∂ ⎛ ∂Ts ⎞
⎟ + y ⎜ λs y ⎟ − lg ρ m r r ⎜ Du ,vap r ⎟
∂ ⎝
∂ ⎠
⎠ ∂ ⎝ ∂ ⎠
(10a)
∂xs ⎞
∂ ⎛
⎜ Du ,vap
⎟
∂y ⎝
∂y ⎠
∂xs 1 ∂ ⎛
∂T
DT r s
=
⎜
∂t r ∂r ⎝
∂r
∂Ts
⎞ ∂ ⎛
⎟ + y ⎜ DT y
∂
⎠ ∂ ⎝
⎞ 1 ∂ ⎛
∂x
Du r s
⎟+
⎜
∂r
⎠ r ∂r ⎝
⎞ ∂ ⎛ ∂xs ⎞
⎟ + y ⎜ Du y ⎟
∂ ⎠
⎠ ∂ ⎝
(10b)
Where:
cp,s
J kg-1 K-1
Dt
m2 s-1 K-1
Du
m2 s-1
Du,vap
Isothermal moisture diffusivity in vapour
m2 s-1
lg
Moisture heat of evaporation
J kg-1
r
Polar coordinate, radial distance from the tube axis
-,m
Ts
°C
x
Moisture content of soil
kg kg-1
y
Polar coordinate, distance from the inlet
-,m
λs
W m-1 K-1
ρm
Density of moisture
kg m-3
ρs
Density of soil
kg m-3
Equation 10: Heat and moisture transfer equations
Boundary conditions
At a large distance from the exchanger, undisturbed conditions are assumed. At the outer
surface of the pipe the heat transfer through the soil equals the heat losses along the pipe.
There the pipe wall is impervious, so no moisture exchange exists between the air and the
soil. Furthermore there is no mass flow across the soil boundary. The total pressure in the
soil is approximated by the ambient air pressure.
Validation
No validation was shown in the papers.
- 31 -
3.1.3
The Boulard algorithm (Boulard, Razafinjohany et al., 1989b)
Heat and moisture transfer equations
In the paper of Boulard et al (1989b) a numerical model is suggested that calculates the
mass and heat transfer in a multi pipe earth-to-air heat exchanger. The mass and heat
transfer equations are broken down into four distinct domains:
Pipe domain
ρ pc p, p
∂Tp
∂t
(
)
= div λ p , s grad (Tp , s ) + U p Ap (Ta − Tp ) + lg ρ a HL p Awat ( xa ,eahe − x p )
Where:
Ap
m2
Awat
m2
cp,p
J kg-1 K -1
HLp
Mass transfer coefficient of the pipe
m2 s-1
lg
J kg-1
Ta
Temperature of air
°C
Tp
°C
Tp,s
Temperature of pipe-soil interface
°C
Up
W m2 K-1
xa
kg kg-1
xp
Water vapour content op the pipe wall
kg kg-1
λp,s
Thermal conductivity of the pipe-soil interface
W m-1 K-1
ρa
Density of the air
kg m-3
ρp
Density of the pipe
kg m-3
Equation 11: Pipe domain heat transfer equation
- 32 -
(11)
Water domain
ρp
∂M p
∂t
= ρ a HLp Awat ( xa − x p )
(12)
Where:
Awat
m2
HLp
Mass transfer coefficient pipe
m s-1
Mp
Water content pipe
kgwater kgpipe-1
t
Time
s
xa
Water vapour content air
kg kg-1
xp
Water vapour content pipe
kg kg-1
ρa
Density of the air
kg m-3
ρp
Density of the soil
kg m-3
Equation 12: Water domain moisture transfer equation
Soil domain
ρ s c p,s
∂Ts
= div ( λs grad (Ts ) )
∂t
(13)
Where:
cp,s
J kg-1 K-1
t
Time
s
Ts
°C
λs
Thermal conductivity of soil
W m-1 K -1
ρs
Density of soil
kg m-3
Equation 13: Soil domain heat transfer equation
- 33 -
Air domain
ρ a c p ,a va grad (Ta ) = U p Ap (Tp − Ta )
(14a)
ρ a va grad ( xa ) = ρ a HLa Awat ( x p − xa )
(14b)
Where:
Ap
m2
Awat
m2
cp,a
J kg-1 K -1
HLa
Mass transfer coefficient of the air
m2 s-1
Ta
Temperature of air
°C
Tp
°C
Up
W m2 K-1
va
Air speed
m s-1
xa
kg kg-1
xp
Water vapour content op the pipe wall
kg kg-1
ρa
Density of the air
kg m-3
Equation 14: Soil domain heat and moisture transfer equations
Due to the small temperature variation in the soil, the effect of water transfer on the heat
transfer coefficients is neglected.
Boundary conditions
Pipe domain
On the soil-pipe and air-pipe interfaces the Dirichlet boundary conditions are assumed.
Water domain
The diffusive term of moisture transport on the inner surface of the pipe is neglected.
Furthermore there is moisture transport between the soil and the pipe.
- 34 -
Soil domain
If the model is working in multi-pipe configuration the Neumann conditions -null flux- is
imposed at the mid-point between the pipes. As mentioned above the Dirichlet boundary
conditions are assumed, not only on the surface but also on the soil-pipe interface.
Air domain
On the air-pipe domain interface the Dirichlet boundary conditions are imposed.
Algorithm validation
The model was validated with experimental data, obtained from a greenhouse in the
Avignon area (Boulard, Razafinjohany et al., 1989a). The total validation time was set on 2
weeks. There is good agreement between the measured and the calculated data.
3.1.4
The Santamouris algorithm (Mihalakakou, Santamouris et al., 1994a)
Heat and moisture equations
This heat and moisture equations for this algorithm are the same as the algorithms, used in
the Puri model (Puri, 1984b;Puri, 1984a). The heat equations are also extended to
incorporate possibility for multi pipe configurations up to 4 pipes (Mihalakakou, Santamouris
et al., 1994b). This was done by superimposing the thermal behaviour of the single pipe
configuration.
- 35 -
(UA)ij =
2* π * l * λ p
(1 − δ )
⎞
(15a)
⎛ B 2 + 4* z * z
ij
i
j
⎟
ln ⎜
Bij
⎜
⎟
⎝
⎠
n
Qs , j
Q
Ta ,i − Tp ,i = s ,i + ∑
(1 − δ i, j )
(UA)i j =1 (UA)ij
i, j
(15b)
Where:
(UA)i
Coupling thermal conductance between the two parallel
W K-1
(UA)ij
Conductivity between two parallel pipes
W K-1
Bij
Distance between pipe i and pipe j
m
l
Pipe length
m1
Qs,i
Energy diffused from pipe i to the soil
W
Qs,j
Energy diffused form pipe j to the soil
W
Ta,i
Air temperature in exchanger i
°C
Tp,i
°C
zi
Depth of pipe i below surface
m
zj
Depth of pipe j below surface
m
δi,j
Kronecker delta
λp
W m-1 K-1
Equation 15: Superimposition of the thermal behaviour of a single pipe
- 36 -
Boundary conditions
r coordinate
Undisturbed soil temperatures and humidity are assumed at large distances from the
tube. The undisturbed soil temperature is calculated with:
−z
π
8760*α
⎛ ⎛ 2* π ⎞ ⎛
⎛ z ⎞ 8760 ⎞ ⎞
t
t
*cos ⎜ ⎜
−
−
⎜
⎟⎟
0
⎜ ⎟*
⎜ ⎝ 8760 ⎟⎠ ⎜
⎝ 2 ⎠ π *α ⎟⎠ ⎟⎠
⎝
⎝
(16)
Where:
As
K
t
Time
h
t0
Phase constant
h
Tave,surf
°C
Ts
°C
z
m
α
Soil diffusivity
m2 h-1
At the outer surface of the pipe the calculated heat flow from air to pipe equals the
heat flow into the soil.
The pipe is not pervious to water, so no moisture transfer takes place between pipe
and air.
At the start of the simulation the temperature of the air inside the tube equals to the
ambient temperature.
y coordinate
Undisturbed soil temperatures and humidity are assumed at large distances from
inlet and outlet of the pipe.
Validation
The algorithm is extensively validated in both single (Mihalakakou, Santamouris, and
Asimakopoulos, 1994a) and multi pipe (Mihalakakou, Santamouris, and Asimakopoulos,
1994b) configuration. Both validations show a very good agreement between the
experimental and simulated results.
- 37 -
3.1.5
The Gautier algorithm (Gauthier, Lacroix et al., 1997)
In this paper Gauthier et al. (1997) is proposing a numerical model to predict the thermal
behaviour of a multi pipe earth-to-air heat exchanger, aimed at reducing energy
consumption of greenhouses.
This model assumes that the thermo-physical properties of soil are constant and that they
are temperature independent. The model is developed for pipes with square cross-sections,
but pipes of circular cross-section can be modelled as pipes of square cross-sections of
equivalent areas. The energy conservation equations, used in this model, are based on the
following assumptions:
Conduction heat transfer is transient and fully three-dimensional in the soil.
Heat transfer, caused by moisture gradients in the soil, is negligible with respect to
that by temperature.
Heat transfer is dominated by convection in axial direction.
Condensation and evaporation are taken into account.
Based on these assumptions, the heat and moisture equations can be written as:
- 38 -
∂T ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞
= ⎜U
⎟ + ⎜U
⎟ + ⎜U
⎟+S
∂t ∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂z ⎝ ∂z ⎠
dx
dH
q'
=
− a ρ lg
dz va Ap ,c dz
(17a)
Cv
(17b)
Where:
Ap,c
Area of the cross-section
m2
Cv
J m-3 K-1
H
Volumetric enthalpy of air
J m-3
lg
Latent heat from evaporation of water
J kg-1
qp’
Energy diffused per meter pipe
W m-1
S
Source term
W m-3
T
Temperaturei
°C
t
°C
U
W m-2 K-1
va
Air speed
m s-1
x
m
xa
kg kg-1
y
m
z
m
ρa
Density of air
kg m-3
Equation 17: Heat and moisture equations
Boundary conditions
All underground external surfaces except the bottom are assumed to be adiabatic. The
bottom of the computational domain is set at 8°C. At the ground surface the soil
temperature is calculated by Equation 18.
- 39 -
λs
∂Ts
= U s ,a (Ts − Ts , surf
∂y
)
(18)
Where:
Ts
°C
Ts,surf
Temperature at ground level
°C
Us,a
W m-2 K-1
y
m
λs
W m-1 K-1
Equation 18: Surface temperature
The inlet enthalpy of the earth-to-air heat exchanger is provided by experimental data.
Validation
The validation of this model was done in two steps. In the first step of the validation process
the numerical data was compared to analytical solutions for one, two and three dimensional
conduction of heat. The last step in the validation process the obtained results were
compared to experimental data form an earth-to-air heat exchanger located in La Pocatière,
Quebec, Canada.
3.1.6
The Hollmuller algorithm (Hollmuller and Lachal, 1998)
This algorithm is based on the study, done by Boulard (1989b). It is one of the few available
models, that can predict sensible as well as latent heat transfer phenomena in an earth-toair heat exchanger. Beside this it also takes friction losses, water infiltration,
inhomogeneous soils, variation in flow rate and direction into account. This model was
developed for TRNSYS and can be used in a multi pipe configuration. For each of the cells
from the model the following heat and moisture balance is solved:
- 40 -
Qin = Qsbl + Qlat + Qs + Qwat
(19a)
mwat = mwat ,t −1 + mwat ,lat + mwat ,inf + mwat ,in + mwat ,out
(19b)
Where:
Qin
Energy rate of tube or soil internal gains
W
Qsbl
Energy rate of sensible air-tube heat exchange
W
Qlat
Energy rate of latent air-tube heat exchange
W
Qs
Energy rate of heat diffused by neighbouring nodes
W
Qwat
Energy rate of free water internal losses
W
mwat
Mass of free water
kg
mwat,t-1
Mass of free water previous time step
kg
mwat,lat
Mass of water condensed/evaporated
kg
mwat,inf
Mass of water infiltrating into node
kg
mwat,in
Mass of water flowing into node
kg
mwat,out
Mass of water flowing or ejected out of node
kg
Equation 19: Heat and moisture equation
Boundary conditions
In the Hollmuller Lachal algorithm the boundary conditions can be given the following
conditions:
Adiabatic boundary conditions
Transient temperatures
Static temperatures
Transient energy flows
Static energy flows
Validation
The algorithm was extensively validated on two greenhouses; each with 100 m2 ground
surface, a residential home and a commercial and industrial building. There was good
agreement between the simulated and measured values.
- 41 -
3.1.7
The Bojić algorithm (Bojic, Papadakis et al., 1999)
This earth-to-air heat exchanger algorithm, developed at the University of Kragujevac in
Yugoslavia, uses a finite volume approach and does allow for multi-pipe configuration. The
model uses a set of 8 steady state equations for calculating the temperature of the soil
around and the air inside the heat exchanger. The first six of those equations calculate the
heat exchange coming into/going out of the sides from each of the volumes:
⎛ 2λλ j (T j − Tini ) ⎞
⎟ bl
Qs , j = ⎜
⎜ λ Lj + λ j L ⎟ n
⎝
⎠
(20)
Where:
b
Node length of side j of the node
m
L
Parallel pipe-element dimension in the heat-flux direction
m
Lj
Parallel pipe-element dimension in the heat-flux direction
m
of side j of the node
ln
Node width of side j
m
Qs,j
Diffused energy through side j of the element
W
Tini
Initial temperature of the element
°C
Tj
Temperature of side j of the element
°C
λj
Thermal conductivity of side j
W m-1 K-1
λ
Thermal conductivity
kg
Equation 20: Energy transfer through sides of element
- 42 -
One equation describes the heat flux between the soil and the air:
Qs ,a = U s ,a Ap (Ta ,ini − Ts ,ini )
(21)
Where:
Ap
m
Qs,a
W
Ta,ini
Initial temperature of the air
°C
Ts,ini
Initial temperature of the soil
°C
Us,a
W m2 K-1
Equation 21: Heat transfer between soil and air
The last equation calculates the temperature of each element:
⎛ ( Qs , x + Qs , y + Qs , z + Qs ,u + Qs ,v + Qs , w + Qs , surf + Qs ,a ) ⎞
⎟ dt
Ts = Ts ,t −1 + ⎜
⎜
⎟
c p , sVs
⎝
⎠
(22)
Where:
cp,s
J kg-1 K-1
Qs,a
W
Qs,surf
Energy diffused to surface
W
Qs,u
Energy diffused in opposite direction of the x-axis
W
Qs,v
Energy diffused in opposite direction of the y-axis
W
Qs,w
Energy diffused in opposite direction of the z-axis
W
Qs,x
Energy diffused in direction of the x-axis
W
Qs,y
Energy diffused in direction of the y-axis
W
Qs,z
Energy diffused in direction of the z-axis
W
t
Time
s
T
°C
Tt-1
Temperature of the soil previous time step
°C
Vs
Volume of soil node
m3
Equation 22: Temperature of the elements
- 43 -
Boundary conditions
The boundary conditions of the soil are assumed to be adiabatic; except the soilenvironment interface. In Equation 23 is shown, how the boundary condition between the
soil and environment are calculated.
⎛
⎞
aEo
Qs , surf = U surf ⎜ Tamb +
− ts ,ini ⎟
⎜
⎟
U surf
⎝
⎠
(23)
Where:
a
Absorbtivity for solar radiation
Eo
Solar radiation intensity
J m-2
Qs,surf
Heat flux from the environment
W
Tamb
Ambient temperature
°C
Ts,ini
Initial soil temperature
°C
Usurf
Heat transfer coefficient soil-environment
W m-2 K-1
Equation 23: Soil-environment interface
Validation
In both the papers (Bojic, Trifunovic et al., 1997;Bojic, Papadakis, and Kyritsis, 1999) , in
which this algorithm is used, no validation is given for this model.
3.1.8
The Zimmermann algorithm (Zimmermann and Huber, 2000)
This algorithm states, that -due to the analogy between electricity and heat- the earth-to-air
heat exchanger can be represented as a resistance-capacity model, shown in Figure 4.
Figure 4: Graphical representation of the Zimmermann model
- 44 -
The heat transfer is divided into two sections:
Radial heat transport (Soil)
Axial heat transport (Air)
The algorithm uses the numerical implicit Cranck-Nicolson method to solve Equation 26
and Equation 27. The capacities and resistors used in this algorithm can be calculated
using Equation 24 and Equation 25.
C p = c p , p ρ pπ ( r12 − r0 2 )
Cs = c p , s ρ sπ ( rn − r
2
2
n −1
(24a)
)
(24b)
Where:
Cp
Capacity of the pipe
J K-1
cp,p
J kg-1 K-1
cp,s
J kg-1 K-1
Cs
Capacity of the soil
J K-1
r0
m
r1
m
rn
m
ρp
Density of the pipe
kg m-3
ρs
Density of the soil
kg m-3
Equation 24: Capacities used in the Zimmermann algorithm
- 45 -
Ra =
1
π * r0 * va * c p ,a * ρ a
Ra , p =
2
1
2* π * α * r0 * dl
+
(25a)
⎛r ⎞
1
ln ⎜ z1 ⎟
2* π * λ p * dl ⎝ r1 ⎠
(25b)
⎛ 1 ⎛ r1 ⎞ 1 ⎛ rz1 ⎞ ⎞
⎜ ln ⎜ ⎟ + ln ⎜ ⎟ ⎟
2* π * dl ⎜⎝ λ p ⎝ rz1 ⎠ λs ⎝ r1 ⎠ ⎟⎠
1
1 ⎛ rzn ⎞
ln ⎜
Rs =
⎟
2* π * dl λs ⎝ rzn −1 ⎠
Rp,s =
Rs , surf =
1
(25c)
(25d)
⎛r ⎞
1
ln ⎜ 3 ⎟ +
2* π * dl λs ⎝ rzn ⎠ 2* π * α surf * r3 dl
1
1
(25e)
Where:
cp,a
J kg-1 K-1
r0
m
r1
m
Ra
Heat resistance air
K W-1
Ra,p
K W-1
rn
m
r0
Inner radius of pipe
m
rn
m
Rp,s
Heat resistance pipe-soil interface
K W-1
Rs
Heat resistance soil
K W-1
Rs,surf
Heat resistance soil-surface interface
K W-1
rzn
Distance temperature node from centreline of pipe
m
αsurf
Heat transfer coefficient soil-surface interface
W m-2 K-1
λp
W m-1 K-1
λs
W m-1 K-1
ρa
Density of the air
kg m-3
Equation 25: Resistors used in Zimmermann algorithm
- 46 -
In the radial direction the Fourier equation has been used to calculate the soil
temperatures. It is assumed, that none of the radial branches interact with each other. The
Fourier can be rewritten as the following implicit function:
1
1
dt R j
dt R j +1
Tk +1, j −
Tk +1, j −1 − Tk +1, j ) −
(
(Tk +1, j +1 − Tk +1, j ) =
2 Cj
2 Cj
1
1
dt R j
dt R j +1
Tk , j +
Tk , j −1 − Tk , j ) −
(
(Tk , j +1 − Tk , j )
2 Cj
2 Cj
(26)
Where:
Cj
Capacity in radial direction
J K-1
Rk
Heat resistance in radial direction
K W-1
Rk+1
Heat resistance in radial direction next layer
°C
Tk
Temperature in current layer
°C
Tk+1
Temperature in next layer
°C
Tk-1
Temperature in previous layer
°C
Tk,t+1
Temperature in next time step
°C
Tk+1,t+1
Temperature in next layer in the next time step
°C
Tk+1,t-1
Temperature in previous layer next time step
°C
Equation 26: Heat equation in the radial direction
For the multi-pipe configuration two more branches need to be added; one which serves as
the link between the pipes and one that calculates the influences from the top.
- 47 -
In the axial direction the heat is only transferred by means of air. Because the algorithm
ignores the capacity of the air, the heat balance can be written as the following steady state
equation:
Ta , seg
⎛
⎞
⎛
1
1
⎜
⎟
⎜
Ra , p
Ra
⎜
⎟
⎜
= Ta , seg −1 * ⎜
+ Tp , seg * ⎜
⎟
⎛
⎞
⎛
⎜⎜ 1 + 1 ⎟⎟
⎜⎜ 1 + 1
⎜ ⎜ Ra Ra , p ⎟ ⎟
⎜ ⎜ Ra Ra , p
⎠⎠
⎝⎝
⎝⎝
⎞
⎟
⎟
⎞⎟
⎟⎟ ⎟⎟
⎠⎠
(27)
Where:
Ra
Heat resistance air
K W-1
Ra,p
K W-1
Ta,seg
Temperature of the air current segment
°C
Ta,seg-1
Temperature of the air previous segment
°C
Tp,seg
Temperature of the pipe current segment
°C
Equation 27: Heat equation in the axial direction
- 48 -
Boundary conditions
The algorithm can have the following boundary conditions:
Adiabatic temperature at the end of each of the electrical branches
Constant temperature if connected to a building
Undisturbed soil temperature:
−z
π
tt *α
⎛ 2π
*cos ⎜
⎝ tt
π
⎞
⎟t − z
α tt
⎠
(28)
Where:
As
K
t
Time
h
t0
Phase constant
h
Tave,surf
°C
Ts
°C
tt
Time period
h
z
m
α
Soil diffusivity
m2 h-1
Validation
No validation results were published for this model.
3.1.9
The Hanby algorithm (Hanby, Loveday et al., 2005)
In this study a single pipe earth-to-air heat exchanger is modelled in TRNSYS-IISIBAT
(Solar Energy Laboratory, 2005a), as a cross flow heat exchanger with an unmixed fluid.
The pipe of the exchanger is assumed to have a uniform cross-section and the material, of
which the pipe is made, has a negligible thermal resistance. The soil is modelled as a
concentric cylinder of earth with isotropic properties. Furthermore it is assumed, that the
soil has a homogeneous thermal conductivity.
- 49 -
No moisture equations were incorporated in this model. The outlet temperature in this
model is calculated by:
ε = 1− e
⎛ −U * Ap
⎜
⎜ qm ,a *c p ,a
⎝
⎞
⎟
⎟
⎠
(29a)
Ta ,eahe,out = Ta − (Ta − Ts ) * ε
ΔT f =
(29b)
Δp
(29c)
η fan * ρ a * c p ,a
(29d)
Toutlet = Ta ,eahe,out + ΔT f
Where:
Ap
Area pipe wall
m2
cp,a
J kg-1 K-1
qm,a
Mass flow of the air
kg s-1
Ta
°C
Ta,eahe,out
Exit temperature of earth-to-air heat exchanger
°C
Toutlet
Exit temperature including increased air temperature due
°C
to heat of fan power
Ts
°C
U
W m-2 K-1
Δp
Pa
ΔTf
Temperature increase due to fan
°C
ε
Temperature effectiveness
-
ηfan
Total fan efficiency
-
ρa
Density of air
kg m-3
Equation 29: Heat equation of the Hanby algorithm
Boundary conditions
The thermal effect of the heat exchanger is limited to a distance from the pipe wall, equal to
the radius of the pipe exchanger; from the point undisturbed soil is assumed.
The undisturbed soil temperature is calculated by Equation 16.The surface temperature of
the soil is approximated by ambient air temperature.
- 50 -
Validation
The model was validated against two experimental studies and one theoretical study
(Mihalakakou, Santamouris et al., 1995). The comparison with the two experimental studies
was done for one day. There is a good agreement between the results from the
experimental and the theoretical studies and the results obtained from this algorithm (Al
Ajmi, Loveday et al., 2006).
3.2
Realized projects
Not much is published about residential or commercial buildings, in which an earth-to-air
heat exchanger was installed. In the Netherlands and the surrounding countries only nine
projects were publicized. The publicized projects were five office buildings, two
manufacturing plants, a house and a university. The specifications of those earth-to-air heat
exchangers can be found in Appendix A.
3.3
Model selection
The selection of the models, used in this study, is based on four criteria.
1. Ability to use a multi pipe configuration
2. Multi pipe coupling has to be published
3. Algorithm has to be validated and the validation has to be published
4. Adiabatic or calculated soil boundary conditions
First of all, the algorithm has to be able to be suitable for using in a multi pipe configuration.
This criterion is based on the fact, that most of the realised projects have an earth-to-air
heat exchanger that uses a multi pipe configuration. In order to enable this, the coupling of
the multiple pipes in the algorithms has to be published.
Because there is neither time nor resources within this project to validate an algorithm, the
selected algorithm has to be validated by its author. Also this validation has to be
published, since this data has to be used for verification of the implementation of the
models in this study.
Because not many weather stations measure the temperature at various depths in the soil,
the soil temperature of the algorithm has either to be calculated by the model or adiabatic
boundary conditions have to be assumed.
- 51 -
Criterion
Algorithm
1
The Elmer Schiller algorithm (Elmer and Schiller, 1981)
2
3
4
*
The Puri algorithm (Puri, 1984b)
The Boulard algorithm (Boulard, Razafinjohany, and Baille, 1989b)
The Santamouris algorithm (Mihalakakou, Santamouris, and
Asimakopoulos, 1994a)
The Gautier algorithm (Gauthier, Lacroix, and Bernier, 1997)
The Hollmuller algorithm (Hollmuller and Lachal, 1998)
The Bojić algorithm (Bojic, Papadakis, and Kyritsis, 1999)
The Zimmermann algorithm (Zimmermann and Huber, 2000)
The Hanby algorithm (Hanby, Loveday, and Al Ajmi, 2005)
* Validation was done. But the validation showed that the program didn’t predict accurate values
Table 4: Algorithm selection
The Santamouris and Hollmuller algorithms were selected to be used in this study.
3.4
Software selection
For the simulation program selection two decision models, (Slater and Cartmell, 2003) and
(Hensen and Djunaedy, 2006;Djunaedy, Hensen et al., 2004) were used.
- 52 -
The first method determines which kind of software, that is required based on the kind of
ventilation system, is chosen and the degree of compliance to the building code.
Figure 5: Software selection schematic (Slater and Cartmell, 2003)
- 53 -
Due to the unknown effect, which the pipes of an earth-to-air heat exchanger have on each
other and on the surrounding soil, the model was categorized as innovative - unknown
conditions. According to the Slater-Cartmell software selection flowchart Figure 5 the model
needs a dynamic thermal simulation; this because of the fact, that the evaluated kinds of
buildings have well defined comfort conditions and the high capacity of the soil. The initial
selection of the kind of program was made according to the schematic in Figure 5.
It must be noted though, that (Djunaedy, Hensen, and Loomans, 2004) pointed out, that
this method lacked the option of coupled simulation and possibility of using different levels
of simulations. The decision model, presented in their paper Figure 6 does allow these
possibilities.
Figure 6: Advanced software selection schematic (Hensen and Djunaedy,
2006;Djunaedy, Hensen, and Loomans, 2004)
On Figure 6, it can be seen that also this method resulted in the selection of a building
energy balance model.
- 54 -
For this research the TRNSYS-IISIBAT (Solar Energy Laboratory, 2005a) program is
selected. The selection of this program is based on the fact that the algorithms were made
for this program and that it would be to time consuming to rewrite them for another
program.
- 55 -
4
Selected algorithms
The Hollmuller and Santamouris algorithms were selected to be used in this study.
To get a better understanding of the selected algorithms, the mathematical models of these
algorithms are discussed more detailed in this chapter. Also the alterations to the original
script will be explained.
4.1
4.1.1
Hollmuller algorithm
Mathematical algorithm
Air-tube interface
As is shown in Equation 19, the air-tube interface of the Hollmuller algorithm has two
components. Figure 7 illustrates the moisture balance of the air-tube interface.
Mwat,inf
Mwat,lat
Mwat,out
Mwat,inf
Mwat,in
Mwat,inf
Mwat,inf
Figure 7: Moisture balance air-pipe interface
There are two ways moisture can leave the earth-to-air heat exchanger it can either flow
through the exchanger or it can be ejected out of the exchanger straight away. If the water
- 56 -
flows through the exchanger the water flowing out of each pipe element can be calculated
using Equation 30.
mwat ,out = ( mwat ,t −1 + mwat ,in + mwat ,inf + mwat ,lat )
vwat Dt
Dln
(30)
Where:
ln
Node width (along x,y or z axis)
m
mwat,lat
kg
mwat,out
kg
mwat,t-1
Mass of water previous time step
kg
mwat,in
kg
mwat,inf
kg
t
Time
s
vwat
Velocity of water
m s-1
Equation 30: Mass exiting the pipe element, when water flows through the
exchanger
When the water is ejected straight away, then the water flowing out of can be written as:
mwat ,out = mwat ,t −1 + mwat .inf + mwat .lat
(31)
Where:
mwat,lat
kg
mwat,out
kg
mwat,t-1
Mass of water previous time step
kg
mwat,inf
kg
Equation 31: Mass exiting the pipe element when, water is ejected straight away
Depending on the flow of the water, the mass entering the pipe element is either zero or
equal to the mass exiting the previous element. The mass is zero when the water is ejected
out of the earth-to-air heat exchanger and equal to mass exiting previous element when
water flows through the pipe.
- 57 -
Due to the difference in temperature between the pipe wall and the air inside the exchanger
moisture can evaporate or condensate on the pipe wall. The amount of water that
evaporates or condenses can be calculated by:
(
mwat ,lat = xa (Ta , ϕa ) − x p (Tp , ϕ100 )
)
ApU a Dt
(32)
c p ,a
Where:
Ap
Area pipe surface
m2
cp,a
J kg-1 K-1
mwat,lat
kg
t
Time
s
Ta
°C
Ua
W m-2 K-1
xa
kg kg-1
xp
Water vapour content of the pipe
kg kg-1
φa
%
φ
Velocity of water
m s-1
Equation 32: Vapour transfer due to evaporation or condensation
Based on Equation 19 the relative humidity for the next pipe element can be calculated by
Equation 33.
ϕi +1 = ϕ −
mwat ,lat
(33)
ρ a Ap ,c va Dt
Where:
Ap,c
Tube cross section
m2
mwat,lat
kg
t
Time
s
va
Air speed
m s-1
ρa
Density of air
kg m-3
φa
%
Equation 33: Relative humidity next pipe element
- 58 -
The second component of the air-tube interface is depicted in Figure 8.
Q
s,2
Qlat
Qint
Qs,5
Qs,3
Qsbl
Qs,6
Qs,1
Qfric
Q wat
Qs,4
Figure 8: Energy balance air-pipe interface
The energy balance from Equation 19 for the air-pipe interface takes the following energy
flows into account:
Sensible energy
Qsbl = ApU a (Ta − Tp )
(34)
Where:
Ap
Area of tube surface
m2
Qsbl
Sensible energy
W
Ta
°C
Tp
°C
Ua
W m-2 K-1
Equation 34: Sensible energy
- 59 -
Latent energy
⎛m
⎞
Qlat = lg ⎜ wat ,lat ⎟
⎝ Dt ⎠
(35)
Where:
lg
J K-1
mwat,lat
Sensible energy
kg
Qlat
Latent heat
W
t
Time
s
Equation 35: Latent energy
Diffused energy
The diffused energy from the surrounding elements can be divided into two groups,
depending on the kind of element which adjourns the element in question. The
diffused energy from the elements -adjourning side 2, side 4, side 5 and side 6
(Figure 8)- can be calculated with Equation 36 using the heat transfer coefficient
calculated with Equation 36b. For the energy diffused from elements next to side 1
and side 2 of the pipe element in Figure 8 Equation 36c can be used for the heat
transfer coefficient.
- 60 -
Qs = ∑ Ass ,iU ss ,i (Ts ,i ,t −1 − Tp )
6
(36a)
i =1
1
U ss ,i =
d w, p
λp
U ss ,i =
Dln ,i
+ 2
(36b)
1
(36c)
λs ,i
Dln Dln ,i
2 + 2
λp
λp
Where:
Ass,i
m2
dw,p
m
ln
Node with (along x, y or z axis)
m
ln,i
Node width neighbouring node (along x, y or z axis)
m
Qs
W
Tp
°C
Ts,i,t-1
Temperature of the neighbouring node last time step
°C
Uss,i
Heat transfer coefficient node side I
W m-2 K-1
λp
W m-1 K-1
λs
W m-1 K-1
Equation 36: Diffused energy flow
Energy loss due to friction
Q fric = qv ,a Δp
(37)
Where:
Qfric
Energy lost due to friction
W
qv,a
Volume flow rate of air
m3 h-1
Δp
Pressure loss
Pa
Equation 37: Energy loss due to friction
- 61 -
Energy loss to water inside the exchanger
Qwat = c p , wat
mwat ,t −1 (Tp ,t −1 − Tp ) + mwat ,in (Tp ,i −1 − Tp )
( 33)
Dt
Where:
cp,wat
Specific heat of water
J kg-1 K-1
mwat,in
kg
mwat,t-1
Mass of water in the node at last time step
kg
Qwat
W
t
Time
s
Tp
°C
Tp,i-1
Temperature of the neighbouring node
°C
Tp,t-1
°C
Equation 38: Energy loss to water inside the pipe
Internal energy
Qint =
cv , pV p (Tp − Tp ,t −1 )
( 39)
Dt
Where:
cv,p
Specific heat of water
J kg-1 K-1
Qint
W
t
Time
s
Tp
°C
Tp,t-1
°C
Vp
Volume of pipe node
m3
Equation 39: Internal energy
- 62 -
Based on the energy balance, stated in Equation 19, the air temperature for the next pipe
element can be computed by:
Ta ,i +1 = Ta +
(c
Q fric − Qsbl
p ,a
+ ϕ c p ,vap ) ρ a Ap ,c va
(40)
Where:
Ap,c
Cross section of pipe
m2
cp,a
J kg-1 K-1
cp,vap
Specific heat of vapour
J kg-1 K-1
Qfric
Energy loss to friction
W
Qsbl
Sensible energy
W
Ta
°C
Ta,i+1
Temperature of the air in next element
°C
va
Air speed
m s-1
ρa
Density of air
kg m-3
φ
Relative humidity
%
Equation 40: Air temperature in the next element
Other soil interfaces
Depending on the kind of element adjourning the side of the Equation 41a (soil-soil),
Equation 41b (soil-tube) or Equation 41c (soil-surface) is used to calculate the energy
diffused to the element.
- 63 -
6
Qs = ∑ Ass
i =1
1
(T − T )
Dln Dln ,i s ,i ,t −1 s ,t −1
2 + 2
λs
6
Qs = ∑ Ass
i =1
6
i =1
λs
1
(Tp,i,t − Ts,t −1 )
Dln
2 + d w, p
(41b)
1
(Ts,surf ,i,t − Ts,t −1 )
Dln
2 +R
s , surf
(41c)
λs
Qs = ∑ Ass
(41a)
λp
λs
Where:
Ass
m2
dw,p
m
ln
Node with (along x, y or z axis)
m
Qs
W
Rs,surf
Heat resistance soil surface
m2 K W-1
Tp,i,t
Temperature of pipe neighbouring node at current time step
°C
Ts,i,t-1
Temperature of soil neighbouring node at last time step
°C
Ts,surf,i,t
Temperature on the surface of the soil of the neighbouring
°C
node at current time step
Ts,t-1
Sensible energy
W
λp
Thermal conductivity of pipe
W m-1 K-1
λs
W m-1 K-1
Equation 41: Diffused energy other interfaces
When the amount of diffused energy to all six sides of the soil element is known the new
soil temperature can be computed by Equation 42.
- 64 -
6
Ts = Ts ,t −1 +
∑Q
s
(42)
1
cv , s *Vs
Where:
cv,s
Volumetric specific heat of soil
J m-3 K-1
Qs
W
Ts
°C
Ts,t-1
Temperature of the soil in last time step
°C
Vs
Volume of soil node
m3
Equation 42: Soil temperature
Script
The script of the Hollmuller algorithm can be found on the CD in Appendix J.
4.1.2
Alterations to the original script
The original script of the earth-to-air heat exchanger developed by Hollmuller (1998) during
his PhD study was written for TRNSYS-IISIBAT version 15 and was updated to TRNSYSIISIBAT 16 by TESS in 2000. No Proforma-file was given with the supplied script, therefore
a Proforma-file was written. Instead of linking the external files in the Proforma file the
2
external files are linked with the deck file . This was done so that the external files can be
put in any folder instead of the prerequisite folder for the Proforma files.
4.2
4.2.1
Santamouris algorithm
Mathematical algorithm
Solver
The Santamouris model uses the Gauss-Seidel iterative method to solve the system of
differential equations, Equation 10, of which the earth-to-air heat exchanger is made.
2
A file listing the simulations settings, component models and their interactions
- 65 -
The Gauss-Seidel method is a technique for solving N equations of the linear system of
equations A * x =b one at a time; using previously calculated results as soon as they are
available.
Air node
The first node in the Santamouris algorithm is the air, which is inside the earth-to-air heat
exchanger. The temperature of the air in the first segment of the exchanger is set equal to
the ambient temperature. The consequent segments of the earth-to-air heat exchanger are
computed by Equation 43.
T j ,1, seg = T j ,1, seg −1 −
Qs , j , seg
(43)
qv , a , j * ρ a
Where:
Qs,j,seg
Energy diffused to neighbouring nodes of pipe j current
W
segment
qv,a,j
Volume flow rate of air of pipe j
m3 s
Tj,1,seg
Temperature of the air in current segment of pipe j
°C
Tj,1,seg-1
Temperature of the air in previous segment of pipe j
°C
ρa
Density of air
kg m-3
Equation 43: Air temperature in consequent segments
No moister transfer takes place at the air node because the pipe is assumed to be
impervious.
Tube node
The second node is situated on the outside of the pipe wall. At initialization the temperature
and moisture of the second nodes for all segments are set equal to the undisturbed soil
properties. The temperature and humidity on the outside of the pipe is calculated by:
- 66 -
T j ,2, seg =
B j ,2
ϕ s , j ,2 =
Fj ,2
Aj ,2
T j ,3, seg ,t −1 +
OH j ,2
C j ,2
Aj ,2
T j ,3, seg ,t −1 +
* T j ,1, seg +
G j ,2
OH j ,2
D j ,2, seg
T j ,1, seg +
(44a)
Aj ,2
DH j ,2
OH j ,2
−
E j ,2
OH j ,2
(44b)
T j ,2, seg
Where:
Aj,2
Temperature discretization coefficient for node 2 of pipe j
Bj,2
Cj,2
Dj,2,seg
Temperature discretization coefficient for current segment of
node 2 of pipe j
DHj,2
Soil humidity discretization coefficient for node 2 of pipe j
Ej,2
Fj,2
Gj,2
OHj,2
Tj,1,seg
°C
Tj,2,seg
°C
Tj,3,seg,t-1
Temperature for current segment of node 3 of pipe j previous
°C
time step
φs,,j,2
Relative soil humidity of node 2 of pipe j
%
Equation 44: Discretization equation for the soil temperature and humidity at pipe
wall
Nodes in between pipe and outer node
The initial soil temperature of the soil nodes is assumed to be equal to the undisturbed soil
temperature calculated by Equation 16. The humidity of the soil at the beginning of the
calculation is equal to the undisturbed humidity of the soil.
The temperature and humidity of the consequent soil layers between the pipe and the outer
node can be expressed as:
- 67 -
T j ,i , seg =
B j ,i
A j ,i
+
T j ,i +1, seg ,t −1 +
AH j ,i
A j ,i
C j ,i
A j ,i
ϕ j ,i ,t −1 −
T j ,i −1, j , seg +
CH j ,i
A j ,i
BH j ,i
A j ,i
ϕ j ,i +1,t −1 +
D j ,i , seg
A j ,i
(45)
ϕ j ,i −1,t −1
Where:
Aj,i
AHj,i
Bj,i
BHj,i
Cj,i
CHj,i
Dj,i,seg
Temperature discretization coefficient for current segment
of node 2 of pipe j
Tj,i,seg
°C
Tj,i-1,seg
°C
Tj,i+1,seg,t-1
°C
previous time step
φs,,j,i,t-1
Relative soil humidity of node i of pipe j previous time step
%
φs,,j,i-1,t-1
Relative soil humidity of node i-1 of pipe j previous time step
%
Equation 45: Discretization equation for the soil temperature soil nodes
- 68 -
The variation of the soil humidity over time is given by:
ϕ s , j ,i =
F j ,i
EH j ,i
−
T j ,i +1, seg ,t −1 +
E j ,i
EH j ,i
T j ,i , seg +
G j ,i
EH j ,i
GH j ,i
EH j ,i
T j ,i −1, seg +
FH j ,i
EH j ,i
ϕ s , j ,i +1,t −1 +
DH j ,i
EH j ,i
(46)
ϕ s , j ,i −1
Where:
DHj,i
Ej,i
EHj,i
Fj,i
FHj,i
Gj,i
GHj,i
Tj,i,seg
°C
Tj,i-1,seg
°C
Tj,i+1,seg,t-1
°C
previous time step
φs,,j,i
Relative soil humidity of node i of pipe j
%
φs,,j,i-1
Relative soil humidity of node i-1 of pipe j
%
φs,,j,i+1,t-1
Relative soil humidity of node i+1 of pipe j previous time
%
step
Equation 46: Discretization equation for the soil humidity soil nodes
Outer node
The temperature of the outer soil layer is set equal to the undisturbed soil temperature that
is calculated with Equation 16. Also the humidity at the outer soil layer is set equal to the
undisturbed soil humidity.
Script
The script and the discretization coefficients of the Santamouris model can be found on the
CD in the Appendix J.
- 69 -
4.2.2
Alterations to the original script
The earth-to-air heat exchanger which was developed by Santamouris (Mihalakakou,
Santamouris, and Asimakopoulos, 1994a) at the University of Athens was subdivided into
the following models:
Type 68 : Calculates the final soil temperature of five user defined soil nodes
Type 69 : Calculates the air temperature inside the pipe taking into account the
effect of other pipes using superposition
Type 70 : Converts the outlet temperature from degrees Fahrenheit to degrees
Celsius
Type 71 : The core algorithm that calculates the temperature, soil humidity for
for all nodes and heat losses for each segment of the pipe
Type 72 : Calculates the initial soil temperature for each soil node at the
beginning of the simulation
Type 73 : Calculates the thermal capacity of each of the nodes
Type 74 : Calculates the air properties of the air in the tube
Type 75 : Calculates the thermal conductance between the nodes and the
coefficients of the discretization equations.
Because the FORTRAN codes of these types were made for an outdated version of
TRNSYS, TRNSYS 13.1, the codes had to be rewritten completely, so that they can be
used for TRNSYS 16.00.0037. For the rewriting of these codes, the FORTRAN compiler of
Compaq (Hewlett-Packard Company, 2003) was used. The updated script still used the
modular approach, Figure 9, of the original program.
- 70 -
Figure 9: Updated modular approach
The Type 70 code had to be edited because that algorithm used its own output as the input
of the next time step. This combined with the Gauss-Seidel iterative method resulted in an
algebraic loop. This loop was broken by introducing delays for the temperature and soil
humidity arrays. At the start of each iteration the values of the temperature and soil
humidity array are being reset with the values of the secondary arrays. At the end of each
time step the secondary array gets updated with the values of the output.
When all sub models were updated to the TRNSYS 16.00.0037 (Solar Energy Laboratory,
2005a), all sub models were combined in one single type, being type 280. Combining all
the models greatly simplifies the program; it eliminates 1236 connections if the program is
used for its maximum capacity of four pipes. Furthermore the elimination of that many
connections reduces computer time to a great extend.
- 71 -
4.3
Comparison between Hollmuller and Santamouris model
Santamouris
Hollmuller
The same conditions across
Can be set for each outer
the outer shell
element
Coordinate system
Cylindrical
Cartesian
External heat transfer
Simple
Complex
Internal heat transfer
Complex
Simple
Latent heat transfer
No
Yes
Length of pipes
10 nodes
100 nodes
Number of pipes
4
20 per module
Number of soil nodes
8
800
Output variables
3
37
Boundary conditions
Table 5: Difference between Hollmuller and Santamouris model
- 72 -
5
Verification
Validation and verification is essential in modelling and simulation. In this study validation is
defined as substantiating that a model within its domain of applicability, behaves with
satisfactory results. Validation deals with building the right model for the given problem
(Balci, 1997). Verification is defined as substantiating that the model is transformed from
one form into another with sufficient accuracy, in other words building the model right
(Balci, 1997). The mathematical algorithms used in both the earth-to-air heat exchanger
algorithms are extensively validated against experimental studies and realised projects
(Mihalakakou, Santamouris, and Asimakopoulos, 1994a;Mihalakakou, Santamouris, and
Asimakopoulos, 1994b;Hollmuller and Lachal, 1998;Hollmuller and Lachal, 2001).
Although the algorithms are validated it is very important to verify the right implementation
of the algorithms in this study. This is because all kinds of errors can be made in creating
the FORTRAN codes and Proforma files. Therefore, a verification of the implementation of
the models’ algorithms used in this study is carried out in this chapter.
5.1
5.1.1
Hollmuller model verification
Verification methodology
The model was validated by comparing of the obtained results and the results published of
the original model (Hollmuller and Lachal, 1998). The total simulation time was set at 100
hours with a 12 minute time step. The temperature and humidity were constant throughout
the simulation at respectively 30°C and 50%. The layout of the publicized model is shown in
Figure 10.
- 73 -
x
y
z
z
Multizone building (Type56b)
Multizone building (Type56b)
Zone 2
(Constant temperature of 15ºC)
Zone 2
(Constant temperature of 15ºC)
Zone 1
(Free float)
Zone 1
(Free float)
Ambient
temperature
Ambient
temperature
Earth-to-air heat exchanger (type 260a)
Ambient
temperature
Ambient
temperature
Earth-to-air heat exchanger (type 260a)
Soil type 1
Soil type 2
Tube
Figure 10: Graphical representation of validation model
The building, modelled by the multizone building Type 56b, was stripped down to the bare
brick structure and comprised of two zones with no windows or infiltration. Both the zones
had an initial temperature of 15°C and an initial humidity of 50%. The coupling between the
building and the earth-to-air heat exchanger was achieved by using the boundary
temperatures, respectfully Tgfree and Tgfix, of the heat exchanger as the boundary
temperature of the floors of the building. The building in its turn supplies the boundary
values, energy flows from the two zones, to the earth-to-air heat exchangers.
The earth-to-air heat exchanger model existed out of two modules. The dimensions of the
cells in metres can be found in Figure 11.
- 74 -
0,4
0,2 0,2 0,2 0,2 0,2
0,4
0,2 0,2 0,2 0,2 0,2 0,4
0,4
Figure 11: Geometry of earth to air heat exchanger in metres
The modelled exchanger consisted of 14 pipes with a length of 5,95 metres. Two of those
pipes were cut axially in half due to the symmetry of the exchanger. The thermal properties
of the building and the earth-to-air heat exchanger can be found in Appendix B.
5.1.2
Results of verification
As is shown in Figure 12 there is a very good agreement between the obtained results and
the published results.
- 75 -
Relative deviation [%]
4,0%
3,0%
2,0%
1,0%
0,0%
-1,0%
0
10
20
30
40
50
60
70
80
90
100
60
70
80
90
100
Time [h]
35
Temperature [˚ C]
30
25
20
15
10
0
10
20
30
40
50
Time [h]
Ground temperature Zone 1
Air temperature after 1,33 m
Ground temperature Zone 2 (Hollmulller)
Air temperature after 2,66 m (Hollmuller)
Outlet temperature (Holmuller)
Ground temperature Zone 2
Outlet temperature
Ambient temperature (Hollmulller)
Air temperature after 4 m (Hollmuller)
Ambient temperature
Air tempature after 4 m
Ground temperature Zone 1 (Holllmuller)
Figure 12: Predicted and published temperatures
The two biggest abnormalities are the ground temperatures of the Type56b multi-zone
building. But after a swing-in period of 30 hours the deviation drops from 0,3°C to 0,09°C
and 0,08°C, respectfully the ground temperature of the free and fixed temperature zone of
the multi-zone building.
The differences in the air temperature in the earth-to-air heat exchanger did not exceed the
0,3%.
5.2
5.2.1
Santamouris model verification
Verification methodology
The Santamouris model was validated by comparing its results with the results from the
“Summer” example of the Earth program (Santamouris, Mihalakakou et al., 1996). This
- 76 -
program has the possibility to calculate the humidity of the soil, air temperature in the
exchanger and three soil nodes (Figure 13).
Z-Axis
XAx
is
Figure 13: Position of the soil nodes in the soil
The total simulation time was 48 hours, from 4968 until 5016, with a time step of 12
minutes.
The exchanger was configured as a single tube, made up by ten segments of 1 metre.
Each of the segments was defined by 10 nodes. The properties used for verification can be
found in Appendix C.
- 77 -
Results of verification
The results of the simulation were compared with the data from the Earth program
(Santamouris, Mihalakakou, and Klitsikas, 1996). Figure 14 shows the variation of the air
temperature in each segment of the heat exchanger. Also the relative deviation of those
temperatures between the model and the Earth program is shown in Figure 14. As can be
seen in the upper graph of Figure 14 the relative deviation of the Type 280 varies from
Relative deviation [%]
+0,5% to -0,9% deviation
1,00%
0,50%
0,00%
-0,50%
-1,00%
4968
4972
4976
4980
4984
4988
4992
4996
5000
5004
5008
5012
5016
4996
5000
5004
5008
5012
5016
Time [h]
31
29
Temperature [˚ C]
5.2.2
27
25
23
21
19
17
4968
4972
4976
4980
4984
4988
4992
Time [h]
Segment 1
Segment 5
Segment 9
Segment 3 Earth program
Segment 2
Segment 6
Segment 10
Segment 3
Segment 7
Segment 4
Segment 8
Figure 14: Predicted and calculated air temperature in each segment of the heat
exchanger
To asses if the model, Type 280, accurately predicts the air temperature throughout the
exchanger outlet temperatures of the Type 280 model and the Earth program
(Santamouris, Mihalakakou, and Klitsikas, 1996) are compared in Figure 15.
- 78 -
31
Temperature [˚C]
29
27
25
23
21
19
17
4968
4972
4976
4980
4984
4988
4992
4996
5000
5004
5008
5012
5016
Tim e [h]
Outlet Earth program
Outlet
Outlet temperature Earth program [˚C]
28
26
24
22
20
18
16
16
18
20
22
24
26
28
Outlet tem perature Type 280 [˚C]
Figure 15: Comparison between outlet temperature of Type 280 and Earth program
As shown in Figure 14 and Figure 15, there is very good agreement between the two
programs. The absolute difference between the program varies between -0,17°C and
- 79 -
0,1°C. The same agreement between the two programs exists for the other temperatures
(Appendix D).
- 80 -
6
Sensitivity analysis
In this chapter a sensitivity analysis has been done to asses the sensitivity of the two
selected models to main design parameters of earth-to-air heat exchangers. The first part
of the sensitivity analysis the effect of the different combination of soils and climate
combinations within Europe will be assessed. In the second section of the sensitivity
analysis of the principal design parameters will be done. The principal design parameters
found in literature (Hanby, Loveday, and Al Ajmi, 2005;Mihalakakou, Lewis et al.,
1996;Santamouris, Mihalakakou, and Klitsikas, 1996) are:
Buried depth
Diameter
Length
Pipe material
Volume flow
For the Santamouris model three extra soil properties (Thermal moisture diffusivity,
isothermal moisture diffusivity and isothermal moisture diffusivity in vapour) will be
evaluated.
To keep this report concise and because of the not realistic boundary conditions of the
Santamouris model only the results of the Hollmuller model are published in the results
sections. Results of the Santamouris model are published in Appendix I.
6.1
Basic set up
The basic configuration of the earth-to-air heat exchanger used in the sensitivity analysis is
comprised of a one pipe concrete heat exchanger at a depth of 3 meters. The exchanger
has a length of 10 meters, divided in 10 equal segments. The thermal properties of the tube
and soil as well as the node geometry can be found in Appendix E. The De Bilt climate file
is used as climate file for the basic set up. The swing-in period for each of the simulations is
set at one year. The savings of the earth-to-air heat exchangers are calculated when the
ambient temperature is either above 18°C or below 14°C.
- 81 -
6.2
6.2.1
Soil and climate
Methodology
Soil
Soil is a mixture of mineral particles, organic and inorganic materials, water, air and a large
number of organisms. The definition of the kind of soil type in this study depended on the
concentration of clay, sand and silt that are present in the soil.
For instance a soil comprised of 50% clay, 30 % silt and 20% can be defined as Clay
Figure 16.
Figure 16: Definition of the soil types (Arossi, 2007)
The properties of the soils depend on the moisture content of the soil and the air filled
porosity but for this study the properties were assumed to be constant (Gauthier, Lacroix,
and Bernier, 1997). The thermal properties for the different kinds of soil can be found in
Appendix F. Because if the energy savings were calculated for the soils in Appendix F
would get the energy savings for those specific soils a more general approach was chosen.
This approach uses the maximum, average and minimum values of the density, thermal
conductivity and heat capacity of the soils, Table 6, in Appendix F.
- 82 -
Density
Heat capacity
-1
-3
-1
[kg m ]
[J kg K ]
[W m-1 K-1]
Minimum
1160
846
0,89
3
Average
1460
2308
1,46
Maximum
2600
2934
3,57
Table 6: Thermal properties of soil
In each simulation only one value will be varied. This results in 27 “kinds” of soil for each
climate.
Climate
According to the Köppen scale Europe can be divided up into 11 sub climates. The division
of those climates is shown in Figure 17. For every climate a city, Table 7
Figure 17: Subdivision of climates in Europe
was chosen to represent that climate.
3
The average soil properties are not the mathematical mean
- 83 -
Scale
BSh
BSk
Cfa
Climate description (Wikipedia, 2007)
Dry steppe climate with average annual
temperature above 18°C
Dry steppe climate with 1 month with an
average temperature lower then 0°C
Mesothermal climate with rain in every season
and an average temperature above 22°C
City
Country
Murcia
Spain
Odessa
Ukraine
Venezia
Italy
De Bilt
The Netherlands
Reykjavik
Iceland
Rome
Italy
Porto
Portugal
Stockholm
Sweden
Sodankyläe
Finland
Mesothermal climate with rain in every season,
Cfb
an average temperature below 22°C and at
least 4 months above the 10°C
Mesothermal climate with rain in every season,
Cfc
an average temperature above 10°C and at
Csa
Mesothermal climate dry summers and an
average temperature above 22°C
Mesothermal climate with dry summers, an
Csb
average temperature below 22°C and at least
4 months above the 10°C
Microthermal climate with rain in every season,
Dfb
an average temperature below 22°C and at
Microthermal climate with rain in every season,
Dfc
an average temperature above 10°C and at
EH
Mountainous climate
Innsbrück
Austria
ET
Tundra climate
Utsjoki
Finland
Table 7: Definition of cities
Except Odessa-climate file, which was found at the website of US Department of Energy
(US Department of Energy, 2007), all the used climate files were from the expanded
weather data for TRNSYS-IISIBAT(Solar Energy Laboratory, 2005b). Because there was
an error in the Utsjoki-climate file, Tundra climate, and no replacement climate file could be
found this climate was excluded from this study. Except the climate data also the surface
temperature and the annual amplitude of the surface temperature were needed for the
- 84 -
Santamouris model. These data were not included in the climate files so they were
obtained from the NASA surface meteorology and solar energy project (NASA, 2007). This
site calculates these values from measurements done in space for a grid cell measuring 1
degree latitude and 1 degree longitude. The soil temperature and the annual amplitude of
the selected cities can be found in Appendix G.
Combined with the 27 soil types defined in the beginning of this paragraph this results in
270 simulations done for this part of the sensitivity analysis.
Results
Figure 18 illustrated the average energy savings for all the climates in Europe. In the same
figure also the spread of the energy savings for all 27 soil combinations is displayed.
2500
2000
Energy savings [kWh]
6.2.2
1500
1000
500
0
0
1 BSk
2
BSh
3
Cfa
4
Cfb
5
Cfc
6
Csa
7
Csb
8
Dfb
9
Dfc
10
EH
11
Climate
Figure 18: Minimum, average and maximum energy savings
As can be seen in Figure 18 the climate with the highest energy savings are realized by
Odessa in the BSk climate. There were discrepancies between the savings obtained by the
Hollmuller algorithm and the Santamouris algorithm. The areas of Europe where the same
trends in
- 85 -
Figure 19: Regions with the same trend in energy savings for the Hollmuller and
Santamouris algorithm
energy savings was seen for the Hollmuller and Santamouris algorithm is shown in Figure
19. The same trend in energy savings only exist for soils with the average and minimum
thermal conductivity. Figure 20, Figure 21 and Figure 22 show the influence of soil
properties on the energy savings for the Csa-climate.
- 86 -
Figure 20: Energy savings for Rome climate with a soil a specific heat of 2934 J kg-1 K-1
- 87 -
The graphs for the other soil and climate combinations for the Hollmuller and Santamouris
algorithms can be found on the CD in Appendix J. The graphs of the energy savings for
Rome for the different thermal conductivities are shown in Appendix H. The energy saving
graphs for Rome obtained with the Santamouris algorithm is depicted in Appendix I.
6.2.3
Discussion
All of the calculated combinations of soil and climate favour a soil with high conductivity,
specific heat and density. As can be seen in Figure 20 to Figure 22 the biggest influence of
the soil properties, an increase up to a maximum of 79% on the energy savings, on the
energy savings is the thermal conductivity of the soil. Increasing the density will lead to a
small, maximum of 33%, increase of the energy savings. An increase in specific heat will
resolve in to an improvement of maximal 48% on the energy savings. If one would improve
all the parameters all at once this would result in to a maximum increase of 127% of the
energy savings.
- 88 -
As can be seen in Figure 19 not every climate shows a good agreement between the
Hollmuller and Santamouris algorithm. This is caused by the difference in approach with
which an earth-to-air heat exchanger is modelled.
6.3
6.3.1
Pipe material
Methodology
Besides the thermal properties of the soil, the thermal properties of the tube are also
important for the heat transfer from the air inside the heat exchanger to the soil surrounding
the exchanger. As can be seen in Appendix I and in Santamouris (1996) modern earth-toair heat exchangers are made of plastics, concrete or steel. To asses the effect of material
selection on the outlet temperature a material, Table 8, is selected for each of the three
categories.
Density [kg m-3] 1
-1
-1 1
Thermal conductivity [W kg K ]
-1
-1 1
Specific heat [J kg K ]
Wall thickness [m]
1
Wall roughness [mm]
1
2
(Roel, Aerts, Bedeke, 't Hooft, Arkesteijn, Konings, Vos, and Wiemer, 1993)
2
Concrete
PVC
Steel
1800
1400
7800
1,15
0,2
45
1000
1470
505
0,02
0,01
0,005
2
0,01
0,045
(Stichting ISSO, 2007)
Table 8: Material properties
For all three materials the day with the highest and lowest temperature were evaluated.
6.3.2
Results
Figure 23 and Figure 24 illustrates the outlet air temperature through out the day with the
highest and lowest ambient temperature.
- 89 -
Outlet temperature [°C]
3
0
-3
-6
-9
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
-12
Time [h]
Ambient temperature
Concrete
PVC
Steel
Figure 23: Outlet temperature on January 11th for the selected materials
35
30
25
20
15
Time [h]
Ambient temperature
Concrete
PVC
Figure 24: Outlet temperature on July 20th for the selected materials
- 90 -
Steel
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
10
In Figure 25 the energy savings and pressure drop due to the selected material can be
1600
54
1400
53,5
1200
53
1000
52,5
800
52
600
51,5
400
51
200
50,5
0
Pressure drop [Pa]
seen.
50
Concrete
PVC
Steel
Material
Energy savings
Pressure drop
Figure 25: Energy savings and pressure drop for the selected materials
6.3.3
Discussion
As can be seen in Figure 25 the largest energy savings can be obtained by a steel tube.
The higher energy savings are thanks to the much higher thermal conductivity of steel
compared with the other two materials. The choice of tube material affects the outlet
temperature of the earth-to-air heat exchanger, Figure 23 and Figure 24, more in the winter
then during the summer. On average the outlet temperature is 1,05°C and 0,40°C higher
during the day with the coldest temperature then the temperatures for PVC and concrete.
For the day with the hottest temperature the average temperature only 0,55°C and 0,23°C.
The choice of tube material has a very limited effect, less the 1 Pa, on the pressure loss
caused by the earth-to-air heat exchanger. The larger pressure loss of the concrete tube,
Figure 25, is a result of a coarser surface of the tube compared with the other two
materials.
Often the selection of the tube material is based on practical criterions then on the thermal
properties (Steeman, 2004). For instance in the Netherlands there is a high ground water
level (Hameetman, Haas et al., 2006) it is much more important that the exchanger is
- 91 -
waterproof. From that point of view it would better to select the waterproof material PVC
instead of concrete that soaks up water. The saturation of concrete with ground water can
lead to the growth of moulds on the tube which results in a diminished air quality. Nor does
PVC corrode like the steel tubes. Another benefit of using PVC is that it is easier to work
with.
So it would be better to not only select a material on its thermal properties but also on other
like for instance the chance of growth of moulds and assembly time.
6.4
6.4.1
Diameter
Methodology
Three different tube diameters (0,15m, 0,3m, and 0,45m) were used to evaluate the impact
of the tube diameter on the thermal behaviour of the earth-to-air heat exchanger. The
enlarging and reducing of the diameter was counterbalanced by respectively reducing and
enlarging the first soil node. The other parameters were left equal to the basic
configuration.
6.4.2
Results
The variation of the outlet temperature of the three tube diameters through out January 11th
and July 20th are shown in Figure 26 and Figure 27. °C
- 92 -
6,00
3,00
0,00
-3,00
-6,00
-9,00
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
0:
00
-12,00
Time [h]
Ambient temperature
d = 0,15 m
d = 0,3 m
d = 0,45 m
Figure 26: Outlet temperature on January 11th for pipe with a diameter of 150, 300 and
450 mm
35
30
25
20
15
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
0:
00
10
Time [h]
Ambient temperature
d = 0,15 m
d = 0,3 m
d = 0,45 m
Figure 27: Outlet temperature on July 20th for pipe with a diameter of 150, 300 and
450 mm
- 93 -
The energy savings and the pressure loss of the three selected pipe diameters are shown
4500
4000
3500
3000
2500
2000
1500
1000
500
0
58
57
56
55
54
53
52
51
50
49
150
300
Pressure loss [Pa]
in Figure 28.
450
Diameter [mm]
Energy savings
Pressure loss
Figure 28: Energy savings and pressure drop for pipe with a diameter of 150, 300 and
450 mm
6.4.3
Discussion
As can be seen in Figure 26 and Figure 27 an inclination in tube diameter, and thus an
inclination of the wall area, will influence the thermal behaviour of the earth-to-air heat
exchanger in a negative way. By reducing the diameter of the basic configuration by half
the average difference between the ambient and outlet temperature on July 20th decreases
with 3,1°C. In heating mode, January 11th, this difference increases to 4,64°C. These
differences were caused by the declination of the heat transfer coefficient from 8,19 W m-2
K-1 to 7,13 W m-2 K-1 due to the fact that the air flow becoming less turbulent when the
diameter gets larger when the velocity stays the same. The opposite phenomenon is
observed with the pressure difference. A reduction in the pipe diameter will lead to an
increase of the pressure loss due to the earth-to-air heat exchanger.
So it would be better to split the needed volume flow over several smaller pipes then one
big pipe, but by decreasing the diameter accepting a higher pressure difference over the
pipe and higher energy consumption by the fan.
- 94 -
6.5
Length
6.5.1
Methodology
One of the most important design parameters for earth-to-air heat exchangers is the length
of the tubes of which the tubes are comprised. The sensitivity analysis of the pipe length
was done for 30, 50 and 70 meters. The rest of the parameters of the exchanger were kept
the same as in the basic setup defined in paragraph 6.1.
Results
12
9
6
3
0
-3
-6
-9
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
-12
0:
00
6.5.2
Time [h]
Ambient temperature
Undisturbed soil temperature
l = 30 m
l = 50 m
l = 70 m
Figure 29: Outlet temperature on January 11th of a tube with a length of 30 meter, 50
meter and 70 meter
Figure 29 shows the air temperature variation of the inlet and outlet for the three lengths of
the exchanger for January 11th.
- 95 -
35
30
25
20
15
10
0:
00
22
:0
0
18
:0
0
20
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
5
Time [h]
Ambient temperature
Undisturbed soil temperature
l = 30 m
l = 50 m
l = 70 m
Figure 30: Outlet temperature on July 20th of a tube with a length of 30 meter, 50
meter and 70 meter
The temperature distribution for the three pipe lengths during the day with the hottest
temperature is shown in Figure 30.
- 96 -
68
5000
66
4000
64
3000
62
2000
60
1000
58
0
Pressure drop [Pa]
6000
56
30
50
70
Length [m]
Energy savings
Pressure drop
Figure 31: Energy savings and pressure loss of a tube with a length of 30 meter, 50
meter and 70 meter
The energy savings and pressure drop for an earth-to-air heat exchanger with one pipe of
30, 50 and 70 meters is illustrated in Figure 31.
6.5.3
Discussion
As shown in this study and in the studies done by Mihalakakou (1994a; 1994b) and
Steemans (2004) the thermal behaviour of an earth-to-air heat exchanger benefits
significantly form adding more length to the exchanger. But the addition of more length can
not continue undefined, because the thermal benefits drops while the pressure difference
over the tube rises. This is due to the diminishing temperature difference between the air
inside the pipe and the undisturbed soil temperature. After 50 meters the increase/decrease
of temperature is minimal. Due to the fact that the biggest energy saving are earned in the
first 30 to 50 meters its better to design an earth-to-air heat exchanger with several shorter
pipes than one long one.
- 97 -
6.6.1
Depth
Methodology
One of the most important design criteria of an earth-to-air heat exchanger system is the
depth at which the exchanger is situated. The undisturbed soil temperature depends on the
kind of soil in which the exchanger is placed, the season of the year and its position on the
globe. Only the effect of the season on the soil temperature is not instantaneous but
somewhat delayed as is shown in Figure 32.
Undisturbed soil temperature [°C]
6.6
20
15
10
5
0
-5
0
876
1752
2628
3504
4380
5256
6132
7008
7884
8760
Time [h]
Depth 1 m
Depth 2 m
Depth 3 m
Depth 4 m
Depth 5 m
Depth 6 m
Figure 32: Undisturbed soil temperature in De Bilt, the Netherlands
To be able to make an assessment on the effect of the depth on the outlet temperature of
the heat exchanger three simulations, at depths of 1,2 meters, 2 meters and 3 meters, were
done.
The geometry of the soil nodes were adapted relatively to the depth of the tube, the
remainder of the parameters were set equal to the values of the basic set up.
- 98 -
Results
Figure 33 and Figure 34 show how the depth of the earth-to-air heat exchanger influences
the outlet temperature of the exchanger during January 11th and July 20th.
9
6
3
0
-3
-6
-9
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
-12
0:
00
6.6.2
Time [h]
Ambient temperature
Depth = 1,2 m
Depth = 2 m
Depth = 3 m
Figure 33: Outlet temperature on January 11th at a buried depth of 1,2 meter, 2 meter
and 3 meter
- 99 -
33
30
27
24
21
18
15
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
12
Time [h]
Ambient temperature
Depth = 1,2 m
Depth = 2 m
Depth = 3 m
Figure 34: Outlet temperature on July 20th at a buried depth of 1,2 meter, 2 meter and
3 meter
The cumulative distributions of the outlet temperature for the different depths are presented
in Figure 35.
- 100 -
100%
Cumulative distribution [%]
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
5
10
15
20
25
30
Ambient temperature
Depth = 1,2 m
Depth = 2 m
Depth = 3 m
Figure 35: Cumulative distribution of the outlet temperature at a buried depth of 1,2
meter, 2 meter and 3 meter
The effect of the burial depth of the earth-to-air heat exchanger is shown in Figure 36.
1450
1400
1350
1300
1250
1200
1150
1100
1050
1,2
2
Depth [m]
Figure 36: Energy savings for a pipe at 1,2, 2 and 3 meters depth
- 101 -
3
6.6.3
Discussion
The thermal behaviour of the earth-to-air heat exchanger, Figure 36, improves by
increasing the depth at which the exchanger is buried. This same effect was shown in
studies by Mihalakakou (1994a; 1994b) and Steemans (2004). This is a result of the
dampening effect of the soil. As result of the inclining depth, Figure 32, the amplitude of the
undisturbed soil temperature shall decrease and the extremes will occur later during the
year.
The largest savings are obtained in the first 2 meters of the soil. After the second meter the
savings to adding more depth the rate of energy saved diminishes. According to the study
done by Steemans (2004) the profits beyond 3 to 4 meters of depth are minimal while the
costs of digging increase significantly.
The Santamouris model shows a different trend in the outlet temperature of the earth-to-air
heat exchanger. This deviation of results for the results obtained with the Hollmuller
program and other studies is due to the boundary conditions set to the outer perimeter of
the soil. When determining the depth for an earth-to-air heat exchanger it is also important
to look at the water table of the location at which the earth-to-air heat exchanger will be
realized. For instance in the Netherlands where there is a relative high groundwater level is
possible that an exchanger at 1,5 meters will al ready be situated in ground water
(Hameetman, Haas, AA, Vries, and Kalkman, 2006).
6.7
6.7.1
Volume flow
Methodology
The last of the design parameters mentioned in literature is the volume flow of air through
the earth to air heat exchanger. To determine the influence of the volume flow on the
thermal behaviour of the earth-to-air heat exchanger a volume flow of 225 m3 h-1,
450 m3 h-1 and 675 m3 h-1 were simulated. The values of the basic configuration were kept
for all the other parameters.
6.7.2
Results
The variation of the outlet temperature during January 11th for the three volume flows is
shown in Figure 37.
- 102 -
6
3
0
-3
-6
-9
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
0:
00
-12
Time [h]
Ambient temperature
Volume flow = 225 m3/h
Figure 37: Outlet temperature on January 11th
Figure 38 illustrates the effect of the volume flow during a summer day.
35
30
25
20
15
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
10
Time [h]
Ambient temperature
Figure 38: Outlet temperature on July 20th
- 103 -
60
2000
58
1500
56
1000
54
500
52
0
50
225
450
Pressure drop [Pa]
2500
675
Volume flow [m3/h]
Energy savings
Pressure drop
Figure 39: Energy savings and pressure loss at 225, 450 and 675 m3 h-1
6.7.3
Discussion
Figure 37 and Figure 38 show that the inclination of the volume flow negatively influences
the thermal behaviour of the earth-to-air heat exchanger. This same trend was shown in
studies done by Mihalakakou (1994a; 1994b) and Tzafiris (1992). This negative influence of
the inclination of the volume flow is caused by the diminishing time spent in the exchanger.
(Tzaferis, Liparakis et al., 1992)
6.8
6.8.1
Moisture diffusivity
Methodology
The Santamouris model assumes that the isothermal diffusivity of moisture, isothermal
diffusivity of moisture in vapour form and the thermal diffusivity stay constant through out
the calculations. To asses the effect of diffusivities on the outlet temperature the diffusivities
- 104 -
were varied with plus and minus 10% of the values used, Table 9, in the Earth program
(Santamouris, Mihalakakou, and Klitsikas, 1996).
-9
-1
Isothermal diffusivity of moisture in vapour form x 10 (ft h )
-7
-1
Isothermal diffusivity of moisture x 10 (ft h )
-1
-1
Thermal diffusivity of moisture (ft h F )
90%
100%
110%
4,0365
4,485
4,9335
1,1934
1,326
1,4586
0,3024
0,336
0,3636
Table 9: Variation in isothermal diffusivity of moisture and moisture in vapour form
and thermal diffusivity of moisture
Results
The cumulative distributions for the different isothermals diffusivity of moisture in vapour
form, Du,vap, is shown in Figure 40.
6.8.2
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
5
10
15
20
25
30
Outlet temperature [oC]
Ambient temperature
Du,vap = 4,0365 *10^-9 ft/h
Du,vap = 4,485 *10^-9 ft/h
Du,vap = 4,9335 *10^-9 ft/h
Figure 40: Cumulative distribution of the isothermal diffusivity of moisture in vapour
form
In Figure 41 the cumulative distribution for the three values of the isothermal diffusivity of
moisture is depicted. Figure 42 illustrates the cumulative distribution of the thermal
diffusivity of moisture.
- 105 -
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
5
10
15
20
25
30
Ambient temperature
Du =1,1934 *10^-7 ft/h
Du = 1,326 *10^-7 ft/h
Du = 1,4586 *10^-7 ft/h
Figure 41: Cumulative distribution of the isothermal diffusivity of moisture
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
5
10
15
20
25
Ambient temperature
Dt =0,3024 ft/(h F)
Dt = 0,336 ft/(h F)
Dt = 0,3636 ft/(h F)
Figure 42: Cumulative distribution of the thermal diffusivity of moisture
- 106 -
30
6.8.3
Discussion
The thermal diffusivity, the isothermal diffusivity of moisture and the isothermal diffusivity of
moisture in vapour form can be assumed to be constant. The variations of diffusivities do
not influence the temperature at all, because of the model sensitivity on these values.
- 107 -
7
Case studies
In this chapter two designs are made to asses the applicability of the earth-to-air heat
exchanger technology for houses and large shopping malls. To assist in the preliminary
design an Excel-tool was made, based on the paper written by Paepe (2003). The tool is
incorporated on the CD in appendix J. The assessment of the applicability will be based
upon the payback time of the extra investment, coverage of the heating/cooling loads and
the reduction in greenhouse gas emissions.
7.1
Town house (The Netherlands)
Building description
The majority of residential buildings built in the Netherlands are terraced houses. The
biggest part of this majority is made up by houses of the mid-terrace town house variety.
The townhouse used in this study is based on the “Tussenwoning” from reference guide for
new residential buildings (DGMR Bouw BV, 2006) commissioned by the Ministry of
Housing, Spatial planning and the Environment of the Netherlands. The floor plan of the
town house is illustrated in Figure 43.
Ground floor
First floor
Figure 43: Floor plan "Tussenwoning" (DGMR Bouw BV, 2006)
- 108 -
Attic
The storey height of the ground and first floor is 2,6 meter. The temperature on those two
storeys is set at a uniform temperature of 20°C in the winter and 26°C in the summer. In
compliance with the Dutch building code (Ministerie van Verkeer Ruimtelijke Ordening
Milieu, 2007) , the total of the fresh air flow is 225 m3 h-1. The heat transfer coefficients of
the architectural construction of the town house can be found in Table 10.
Structure component
[W m-2 K-1]
Front door
2,00
Ground floor
0,32
Roof
0,24
Walls
0,32
Windows
2,00
Table 10: Architectural construction (DGMR Bouw BV, 2006)
The heat and cooling load of this building were calculated using Vabi VA114 (Vabi, 2007).
Earth-to-air heat exchanger description
The earth-to-air heat exchanger for the town house is designed based upon the
assumptions that it has to have an effectiveness of approximately 80% and that the
pressure loss due of the tube is equal to or less than 1,5 Pa m-1. The exchanger is made of
ULTRA-3® PVC sewage pipes. For this case study the following configurations of the
earth-to-air heat exchanger were evaluated:
Option 1: One pipe configuration
Option 2 : Three pipes configuration
Option 3 : Five pipes configuration
- 109 -
The technical deals of the three options are shown in Figure 44.
II
I
VI
I
VII
VII
VI
III
IV
X
Option 1
Option 2 and 3
1
Option 1
Option 2
Option 3
Fan efficiency
[-]
0,4
0,4
0,4
Number of tubes
[-]
1
3
5
[-]
F7
F7
F7
Total pressure loss 3
[Pa]
24
34
33
Extra fan power needed
[W]
4
5
5
Depth of the exchanger (I)
[m]
2
2
2
Diameter main supply/return manifold (II/X)
[m]
0,16
0,16
0,16
[m]
-
0,5
0,5
Space between pipes (IV)
[m]
-
1
1
Length earth-to-sir heat exchanger (VI)
[m]
20
13
10
Diameter earth-to-air heat exchanger (VII)
[m]
0,16
0,125
0,1
[m]
-
0,5
0,5
[m]
-
0,16
0,16
Filter class
2
Space between main supply manifold and
1st pipe (III)
Space between last pipe and main return
manifold (VIII)
Diameter supply/return manifold (V/IX)
1 (Knoll and Wagenaar, 1994)
2 (Ras, 2007)
3 Pressure loss calculation on CD in Appendix J.
Figure 44: Technical description earth-to-air heat exchangers for the Townhouse
The exchanger is situated in to a soil categorized as sand. The sand has the following
thermal properties (De Vries, 1963):
- 110 -
Density
: 1640 kg m-3
: 1,77 W m-1 K-1
Heat capacity
: 1758 J kg-1 K-1
Water content
: 0,38 m3 m-3
Savings
The total heating and cooling loads for the townhouse are 15547,1 kWh for heating and
36,9 kWh for cooling. Energy saving occurs when the amount of energy saved by the
exchanger is greater then the energy needed for the fan and there is a heating or cooling
demand from the building. Table 11 show the energy savings obtained by the three options
and how they cover the total heating and cooling loads.
Energy saved
Coverage
Heating
Cooling
Heating
Cooling
[kWh]
[kWh]
[%]
[%]
Option 1
894,3
28,7
6
78
Option 2
968,6
30,5
6
83
Option 3
1231,5
33,2
8
90
Table 11: The energy savings and coverage of heating\cooling loads by the options
The electricity and gas prices for households in the Netherlands for 2007 are € 0,22
(Goerten and Clement, 2007a) and € 0,58 (Goerten and Clement, 2007b). The central
heating system installed in the townhouse has got an overall efficiency of 80%. The
refrigerating machine has got a coefficient of performance of 3. Based on these
assumptions the annual money savings are:
Option 1
: € 72,52
Option 2
: € 77,36
Option 3
: € 99,35
The distribution of the money over the months can be seen in Figure 45 to Figure 47.
- 111 -
Annual savings earth-to-air heat exchanger : € 72,52
15%
19%
9%
11%
11%
12%
6%
4%
3%
4%
4%
2%
January
February
March
April
May
June
July
August
September
October
November
December
Figure 45: Distribution of the money savings option 1
16%
21%
9%
12%
10%
13%
6%
4%
2%
3%
1%
3%
January
February
March
April
May
June
July
August
September
October
November
December
- 112 -
20%
21%
10%
12%
12%
12%
4%
2%
2%
1%
2%
2%
January
February
March
April
May
June
July
August
September
October
November
December
Besides the reduction in heating and cooling costs also the environment benefits from the
application of earth-to-air heat exchangers. The reduction in greenhouse gas emissions for
each of the options can be seen in Table 12.
Gas
Electricity
[m3]
[kWh]
Reduction in emissions
CO2
SOx
NOx
[kg]
[g]
[g]
Option 1
127,15
9,56
231,7
6,1
71,4
Option 2
137,7
10,2
250,9
6,5
77,3
Option 3
175,1
11,6
317,9
7,5
98,0
Table 12: Greenhouse gas emission reduction
To asses if it’s financially attractive to incorporate an earth-to-air heat exchanger the
payback time of the initial extra investment was calculated.
- 113 -
Digging2
Material/
Assembling
Filter
Total cost
Savings
1
Payback
time
[€]
[€]
[€]
[€]
[€]
[yrs]
Option 1
267
840
57
1164
72,52
17
Option 2
540,52
1120
57
1717,52
77,36
23
Option 3
631,16
1320
57
1951,16
99,36
24
1
(Dyka BV, 2007)
2 (Plaisier Middenmeer, 2007)
Table 13: Cost overview and payback time
Table 11 shows that the payback for the initial extra investment for the three options varies
between the 17 and 24 years. But when applying this technology one has to bear in mind
that the filter needs to be changed at least once a year due to bacterial contamination. If
this would be taken into account the payback time would rise to:
Option 1
: 72 years
Option 2
: 81 years
Option 3
: 45 years
Based on the payback time, the financial and environmental savings the choice of applying
this technology is not justified by financial reasons but on ideological and environmental
ones. Possible ways to reduce the payback period are:
Discount on digging and materials/assembling by applying the technology on larger
developments
Applying for subsidies by the European and national governments..
Because the earth-to-air heat exchanger can cover up to 90% of the cooling loads the
comfort level of the occupants of the house is increased. Also no split units are needed to
obtain the same kind of comfort level.
7.2
Shopping mall “Vasco da Gama” (Portugal)
The Centro Vasco da Gama is situated on the Av D. Joao II in Lisbon Portugal.
- 114 -
Figure 48: The Vasco da Gama shopping mall (First Q, 2005)
The shopping mall was developed by Sonae Imobiliária and ING Real Estate in 1999. The
total area of the shopping mall is 161247 m2 divided over 4 floors. The Vasco da Gama
shopping mall consists of a mall/promenade, 36 restaurants, 11 anchor shops and 116
satellite shops (Sonae Imobiliária, 1999). For this study it’s assumed that the mall is opened
everyday between 8:00 and 19:00 and that the supply temperature of the HVAC units is
100
80
60
40
20
Hour of the day [h]
Figure 49: Fan control signal
- 115 -
24
22
20
18
16
14
12
10
8
6
4
2
0
0
Percentage of volume flow [%]
constant throughout the day.
The exchanger is situated in to a soil categorized as sand. The sand has the following
thermal properties (De Vries, 1963):
7.2.1
Density
: 1640 kg m-3
: 1,77 W m-1 K-1
Heat capacity
: 1758 J kg-1 K-1
Water content
: 0,38 m3 m-3
Mall/promenade
The mall and promenade (Figure 50) is conditioned by means of cooled air, which is
supplied into the mall by jet nozzles and grills in the ceiling of each floor.
Figure 50: Mall/promenade (First Q, 2005)
The air is climatized by means of 5 air-handling units. The technical details of the units can
be found in Table 14.
HVAC unit
Supply air capacity
3
Supply air temperature
-1
[m h ]
[ºC]
Mall 1
11900
12,9
Mall 2
41100
12,1
Mall 3
77200
11,7
Mall 4
38100
12,2
Mall 5
15600
12,6
Table 14: Air-handling units mall/promenade
- 116 -
Earth-to-air heat exchanger description
The earth-to-air heat exchangers for the mall/promenade are designed upon the
assumptions that it has to have an effectiveness of approximately 80% and that the
pressure loss due to the pipe is equal or less then 1 Pa m-1. The exchangers are made
from PE sewage pipe. The dimensions of the earth-to-air heat exchangers can be found in
Table 15 and Figure 51.
II
I
V
VII
XI
VI
XII
IV
XVI
XVII
III
X
XII
I
IX
III
XV
I
VII XV
XI V
XX
XIX
Figure 51: Graphical representation earth-to-air heat exchanger
- 117 -
Mall 1
Mall 2
Mall 3
Mall 4
Mall 5
[-]
0,85
0,85
0,85
0,85
0,85
[-]
8/7/8
13/12/1
13/12/1
13/12/1
13/12/1
3
3
3
3
[-]
F7
F7
F7
F7
F7
[Pa]
203
268
261
272
223
Depth of the exchanger level 1 (I)
[m]
2
2
2
2
2
Depth of the exchanger level 2 (XI)
[m]
3
3
3
3
3
Depth of the exchanger level 3 (XVI)
[m]
4
4
4
4
4
[m]
0,8
1,25
1,25
1,25
0,8
[m]
0,63
1
1
1
0,8
[m]
0,5
0,8
0,8
0,8
0,5
[m]
0,5
0,5
0.5
0,5
0,5
[m]
1
1
1
1
1
[m]
0,5
0,5
0,5
0,5
0,5
[m]
1
1
1
1
1
[m]
34
60
69
69
40
[m]
0,25
0,4
0,315
0,315
0,2
[m]
0,5
0,5
0,5
0,5
0,5
[m]
1
1
1
1
1
[m]
0,5
0,5
0,5
0,5
0,5
[m]
0,5
0,8
0,8
0,8
0,5
Fan efficiency
1
Number of tubes (level 1/level2/level3)
Filter class
2
Total pressure loss
3
Diameter main supply/return manifold level
1 (II/X)
2 (XII/XV)
3 (XVII/XX)
1st pipe level 1 (III)
1st pipe level 2 (XIII)
1st pipe level 3 (XVIII)
manifold level 1 (VIII)
manifold level 3(VIII)
2 (Ras, 2007)
3 Pressure loss calculation on CD in Appendix J.
Table 15: Technical description earth-to-air heat exchangers for the mall/promenade
- 118 -
7.2.2
Shops
As mentioned before the Vasco da Gama shopping centre has got 11 anchor shops and
116 satellite shops (Figure 52). Because of the wide variety of the kind of shops the shops
are conditioned using fan-coils connected to the chilled water installation, equipped with a
2-way control valve.
Figure 52: Shops (First Q, 2005)
An amount of 9 m3 h-1 m-2 is supplied to the shops by 5 air-handling units. The supply air
capacity and the inlet temperatures of these 5 air-handling units are gathered in Table 16.
HVAC unit
Supply air capacity
3
-1
[m h ]
[ºC]
Shop 1
20200
19,9
Shop 2
27100
19,5
Shop 3
20300
18,3
Shop 4
17000
19,5
Shop 5
15600
12,6
Table 16: Air-handling units shops
- 119 -
Earth-to-air heat exchanger descriptions
Each of the 5 air-handling units is equipped with one earth-to-air heat exchanger made of
PE sewage pipe. The design of the exchangers is based on an effectively of approximately
80% and a maximum pressure loss of 1 Pa m-1. The dimensions of the 5 earth-to-air heat
exchangers can be found in Figure 53 and Table 17.
II
I
V
VII
XI
VI
XII
IV
XVI
III
XVII
X
XII
X
I
IX
I
VII
I
VII XV
XI V
XX
XIX
- 120 -
Shop 1
Shop 2
Shop 3
Shop 4
Shop 5
[-]
0,85
0,85
0,85
0,85
0,85
[-]
13/12/13
13/12/13
13/12/13
13/12/13
13/12/13
[-]
F7
F7
F7
F7
F7
[Pa]
`229
324
231
239
214
[m]
2
2
2
2
2
[m]
3
3
3
3
3
[m]
4
4
4
4
4
[m]
1
1
1
0,8
0,8
[m]
0,8
0,8
0,8
0,8
0,8
[m]
0,63
0,63
0,63
0,63
0,63
[m]
0,5
0,5
0.5
0,5
0,5
[m]
1
1
1
1
1
[m]
0,5
0,5
0,5
0,5
0,5
[m]
1
1
1
1
1
[m]
50
53
50
40
39
[m]
0,25
0,25
0,25
0,2
0,2
[m]
0,5
0,5
0,5
0,5
0,5
[m]
1
1
1
1
1
[m]
0,5
0,5
0,5
0,5
0,5
[m]
0,63
0,63
0,63
0,63
0,63
Fan efficiency
1
Filter class
2
Total pressure loss
3
Diameter main supply/return manifold
level 1 (II/X)
level 2 (XII/XV)
level 3 (XVII/XX)
2 (Ras, 2007)
3 Pressure loss calculation on CD in J.
- 121 -
7.2.3
Restaurants
Besides the shops there are also a fair number of restaurants situated in the Vasco da
Gama shopping centre. The central restaurant area is conditioned by supplying cooled air
by means of induction diffusers. The air conditioning is realized by means of air-handling
unit Restaurant 1. Any additional cooling is supplied by auxiliary split units in the restaurant
itself.
Figure 54: Central restaurant (First Q, 2005)
The other restaurants are conditioned using fan-coils connected to the chilled water
installation, equipped with a 2-way control valve. The fresh air for the restaurants is
supplied by means of air-handling unit Restaurant 2.
The supply temperature and capacity of the air-handling units for the restaurants can be
found in Table 18.
Supply air capacity
3
-1
[m h ]
[ºC]
Restaurant 1
37700
12,2
Restaurant 2
32450
19,1
Table 18: Air-handling units restaurants
- 122 -
Earth-to-air heat exchanger descriptions
Both of the air-handling units are equipped with a 38 pipe PE earth-to-air heat exchanger.
The exchangers are designed to have an efficiency of approximately 80% and a pressure
loss of 1 Pa per meter tube.
II
I
V
VII
XI
VI
XII
IV
XVI
XVII
III
X
XII
I
IX
III
XV
I
VII XV
XI V
XX
XIX
- 123 -
Shop 1
Shop 2
[-]
0,85
0,85
[-]
13/12/13
13/12/13
[-]
F7
F7
[Pa]
`229
324
[m]
2
2
[m]
3
3
[m]
4
4
[m]
1,25
1,25
[m]
1
1
[m]
0,8
0,8
[m]
0,5
0,5
[m]
1
1
[m]
0,5
0,5
[m]
1
1
[m]
69
66
[m]
0,315
0,315
[m]
0,5
0,5
[m]
1
1
[m]
0,5
0,5
[m]
0,8
0,8
Fan efficiency
1
Filter class
2
Total pressure loss
3
level 1 (II/X)
level 2 (XII/XV)
level 3 (XVII/XX)
2 (Ras, 2007)
3 Pressure loss calculation on CD in J.
- 124 -
7.2.4
Savings
The total annual heating and cooling loads for the air-handling units are 624,9 MWh for
heating and 3489,6 MWh for cooling. The 13 earth-to-air heat exchangers can cover 55%
of the total annual heating load and 21% of the total annual cooling load. Energy saving
occurs when there is the amount of energy saved by the earth-to-air heat exchanger is
greater then the electrical energy consumed by the fan and that there is either an heating or
cooling demand by the air-handling unit. The energy savings and demand coverage for
each air-handling unit is shown in Table 20.
Energy needed
Mall/promenade
Restaurant
Shop
Energy saved
Coverage
Cooling
Heating
Cooling
Heating
Cooling
Heating
[MWh]
[MWh]
[MWh]
[MWh]
[%]
[%]
1
141,9
8,6
24,7
7,7
17
89
2
544,4
20,1
92,0
19,4
17
96
3
1075,5
30,5
179,4
30,2
17
99
4
498,3
19,6
89,1
19,2
18
98
5
192,9
9,8
35,5
9,4
18
98
1
493,0
19,4
88,6
19,0
18
98
2
133,8
159,5
58,8
59,6
44
37
1
69,6
118,6
34,7
40,4
50
34
2
101,8
146,5
43,0
47,2
42
32
3
97,8
83,8
40,1
35,6
41
42
4
63,9
91,9
27,5
30
43
33
5
76,7
60,2
29,2
25,0
38
41
Table 20: The energy consumption, savings and coverage of heating/cooling loads
by the air-handling units
It is assumed that the heating system has an overall efficiency of 80%. Also it is assumed
that the refrigerating system has got a coefficient of performance of 3. The energy prices in
Portugal for large consumers of energy in 2007 are € 7,76 per GJ for heating (Goerten and
Clement, 2007b) and € 8,60 per 100 kWh electricity (Goerten and Clement, 2007a). Based
on these assumptions the annual savings by applying this technology are:
- 125 -
Mall/promenade
: € 10.747,23
Restaurants
: € 5.356,70
Shops
: € 9.170,70
The distribution of the money savings can be seen in Figure 56 and Figure 58.
Money savings by earth-to-air heat exchanger
2%
2%
7%
8%
8%
4%
10%
11%
8%
15%
12%
13%
January
February
March
April
May
June
July
August
September
October
November
December
Figure 56: Distribution of the money savings Mall/promenade
- 126 -
9%
4%
8%
7%
8%
9%
4%
8%
8%
11%
12%
12%
January
February
March
April
May
June
July
August
September
October
November
December
Figure 57: Distribution of the money savings Restaurants
8%
12%
6%
7%
12%
8%
5%
4%
9%
7%
11%
11%
January
February
March
April
May
June
July
August
September
October
November
December
Figure 58: Distribution of the money savings Shops
- 127 -
Also the environment benefits from the application of earth-to-air heat exchangers. The
reduction in greenhouse gas emissions for the mall, restaurants and shops can be seen in
Table 21.
Gas
Electricity
[GJ]
[MWh]
Reduction in emissions
CO2
SOx
NOx
[ton]
[kg]
[kg]
Mall/promenade
386,1
140,2
101,1
27,7
59,8
Restaurant
353,3
11,1
47,7
13,5
21,1
Shop
801,5
25,3
70,0
22,7
25,1
Table 21: Greenhouse gas emission reduction Vasco da Gama
To asses if applying earth-to-air heat exchangers to shopping malls is financial attractive
the payback time for the initial extra investment are calculated in Table 22.
Digging2
Material/
Assembling
Mall/promenade
Restaurant
Shop
1
Filter
Total cost
Savings
1
Payback
time
[€]
[€]
[€]
[€]
[€]
[yrs]
1
58.825,00
15.840,00
453,60
75.118,60
976,40
77
2
200.045,00
43.520,00
1.512,00
245.077,00
2.231,50
110
3
333.382,00
96.560,00
2.872,80
432.814,80
4.324,95
100
4
165.551,00
48.280,00
1.360,80
215.191,80
2.201,15
98
5
40.007,79
24.480,00
604,80
65.092,59
1013,24
64
1
166.016,00
24.820,00
680,40
191.516,4
2.202,77
87
2
162.539,00
23.800,00
604,80
186.943,80
3.153,93
59
1
93.705,00
36.720,00
756,00
131.181,00
2.026,89
65
2
95.928,00
38.760,00
1.058,40
135.746,40
2.069,13
66
3
93.705,00
36.720,00
756,00
131.181,00
1.974,53
66
4
61.847,40
29.920,00
604,80
92.372,20
1.483,80
62
5
61.707.47
29.240,00
604,80
91.552,27
1.616,35
57
(Wavin, 2007) 2 (Plaisier Middenmeer, 2007)
Table 22: Cost overview and payback time Vasco da Gama
- 128 -
As is shown in Table 22 the payback periods of the initial costs vary between the 57 and
110 years. The reason for the high payback time for the earth-to-air heat exchanger of the
air-handling units 2,3 and 4 of the mall/promenade is caused by the use of special
products. Just like in the townhouse case study the filters of the earth-to-air heat
exchangers have to be replaced at least once a year. The replacing of the filters is needed
to prevent the contamination of the exchanger. If this is taken into account the payback
periods will increased to between 88 for shop 5 and 338 years for Mall/promenade 2.
- 129 -
8
Conclusions
The study presented in this report discusses the applicabillity of a earth-to-air heat
exchanger for both houses and large shopping malls. This in respect to the energy savings,
environmental saving and payback time.
The applicabillity has been researched with existing computational models. First of all a
literature study was preformed to analyse the existing models, design parameters and
realized projects. Although there are a lot of computer models available that are described
in literature there is little publizised about parameter analysis nor realized projects. It should
be mentioned that none of the publized parameter analysis has incorporated soil and
climate effects on the performance of earth-to-air heat exchangers.
From literature 9 models were pre-selected and described in this report, from which the
Santamouris and Hollmuller models satisfied the demands set in this study. Both the
models are written in Fortran code for use by the TRNSYS simulation engine. The
Santamouris model written for TRNSYS 13 was updated to version 16 to be able to be
used in this study. The Hollmuller model the source code was already written for version
16, there for it needed to be updated. The application of both models are verified and found
to be accurate within 1% of the publicised data. The study has proven that the Hollmuller
model is more suitable for this application. Based on the flexibility and accuracy of the
model. Where the Santamouris model uses 1 boundary condition for the complete outer
shell the Hollmuller model allows different boundary condition for each of the border nodes.
Meaning that the Santamouris model uses a 2 dimensional and the Hollmuller model a 3
dimensional heat transfer model. The Santamouris model neglects the vertical soil
temperature gradient. Furthermore the Hollmuller takes latent heat transfer into account.
Based on these facts its recommended to use the Hollmuller model for this kind of
applications.
The sensitivity analysis was performed in order to check the applicability of both models
and create a clear view of the principal design criteria. Below the most significant results
per component are shown.
- 130 -
Geographical location
The geographical location of an earth-to-air heat exchanger is a major factor to its
applicability. Europe is sub divided into four major climate groups according to the
Köppenscale. The most savings were obtained for a dry steppe climate (Odessa climate
file) with 1 month with an average temperature lower then 0°C.
The dry steppe climates (Odessa and Murcia) favour a climate with low temperatures.
The Mesothermal climates (Venezia, Rome, De Bilt, Porto and Reykjavik) favour a warm
climate with rain all year round. The more significant of these two criterions is the high
temperatures. In other words a warm dry climate gives more savings then a cool wet
climate. The Microthermal climate (Sodankylae and Stockholm) favour a climate with low
temperatures.
Soil types
All the climates favour a soil with a high thermal conductivity, density and specific heat. The
largest influence, a maximum increase of 79%, on the energy savings is thermal
conductivity. An increase of the specific heat will lead to an increase of 48%.Increasing the
density of the soil will lead to a small increase, maximum of 33%.
If one would improve all three properties all at once this would result in a maximum
increase of 120% on the energy savings.
Pipe material
The effect on the pressure loss of the selection of PVC, Steel or concrete as material for an
earth-to-air heat exchanger is minimal, less then 1 Pa. Steel has the best thermal
performance of the evaluated materials. Nevertheless it is better to base the selection of
the tube material on practical criterions, like for instance does the pipe need to be
waterproof, because the effect of the selected material on the energy savings is minimal.
Pipe diameter
The diameter is interdependent with the required volume flow and resulting velocity. The
energy savings obtained increase when the diameter of the tube is decreased. It is
recommended to split the needed volume flow over several smaller pipes then one big pipe,
but by decreasing the diameter accepting a higher pressure difference over the pipe and
higher energy consumption by the fan.
- 131 -
Pipe length
Adding more length to the tubes of an earth-to-air heat exchanger improves the thermal
performance. After approximately 50 meters the increase in savings is minimal while the
pressure loss increases. It is recommended to design an exchanger with multiple shorter
tubes then an exchanger with long pipes.
Buried depth
For a winter situation, heating, increasing the buried depth beyond 3 meters has got little
effect on the output temperature of the earth-to-air heat exchanger. In summer the “cooling
mode”, summer, 2 meters is sufficient.
After evaluating the different mathematical models and design parameters two case studies
were performed to asses the applicability of this technologie for houses and large shopping
malls. A standard townhouse in the Netherlands and a large shopping mall in Portugal were
assessed.
The case study for the townhouse showed an average coverage between 6% and 8% of
the annual heating load. The system performers more efficiently in cooling mode resulting
in average coverage between 78% and 90%. The system is proofed to be effectively for
houses regarding CO2 reduction. Nevertheless the nowadays costs for such a system
result in long pay back times. Possibly the initial costs will be reduced when applying these
systems on large scale systems. The obtained CO2 reduction is 5-6% and the calculated
payback time is 17-24 years excl. filter (44-81 years inclusive filter replacement).
On a large scale project as a shopping mall the performance is better but the initial costs
increase rapidly due to the need for special products. Therefore payback times between 88
and 338 are found when including the replacement of the extra filters. Looking at the
energy coverage (55% of the heating and 21 % of the cooling loads are covered) and the
CO2 reduction (218,8 ton) the system makes sense after all. In order to make this system
more cost effective cheaper pipe materials have to be found.
- 132 -
The overall conclusions that can be drawn upon the results presented in this report are:
The system can cover a large part of the heating and cooling load for both
townhouse and shopping mall;
Based on current payback times it’s not financial feasible to apply this technology;
The CO2 reduction when applying this technology to a townhouse is approximately
6% , which corresponds with the required reduction by the Kyoto agreement.
When applied in shopping malls the CO2 emissions are reduced by 218,8 ton.
Based on the payback time, the coverage and environmental savings the choice of applying
this technology is not justified by financial reasons but more on ideological and
environmental reasons.
- 133 -
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sensitivity of eight models to predict the performance of earth-to-air heat exchangers.
Energy Build. 18:35-43
US Department of Energy. Climate file Odessa. (Accessed 7-6-2007). 2007.
http://www.eere.energy.gov/buildings/energyplus/cfm/weather_data3.cfm/region=6_europe
_wmo_region_6/country=UKR/cname=Ukraine.
Vabi. Vabi UO. (2.20). 2007.
Wavin. Prices PE sewage pipe. 2007.
Wikipedia. Köppen climate classification. (Accessed 12-7-2007). 2007.
Zimmermann M, Huber A (2000) Detailed design tools for low energy cooling technologies.
In: Roel, H. (ed) Detailed design tools, Annex 28 edn. Internaional Energy Agency, Building
Research Ltd, p J-1-J-25 (De Paepe and Janssens, 2003)
- 138 -
A Realised projects
- 139 -
Deutschen Bahn Netz AG
Figure 59: Earth-to-air heat exchanger under construction, Deutschen Bahn Netz AG
(Fraunhofer Institute Solare Energiesysteme: 2006)
Location
Hamm (Germany)
Depth
2-4
m
Diameter
DN 200-300
mm
In use since
1999
Length of pipes
70-130
Number of pipes
26
Overall length
1800
Pipe material
PE
Total airflow
21000
m
m
3 -1
m h
Fraunhoffer ISE
Hübner production hall
Location
Freiburg (Germany)
Depth
2
m
Diameter
DN 250
mm
In use since
2001
Length of pipes
95
Number of pipes
7
Overall length
665
Pipe material
PE
Total airflow
9000
m
m
3 -1
m h
(Pfafferott, 2003)
- 140 -
Passive office Lamparter
Figure 60: Earth-to-air heat exchanger under construction, lamparter (Pfafferott,
2003)
Location
Weilheim (Germany)
Depth
2,8
m
Diameter
DN 350
mm
In use since
1999
Length of pipes
90
Number of pipes
2
Overall length
180
Pipe material
PE
Total airflow
1900
m
m
3 -1
m h
Omega Pharma office
Location
Nazereth (Belgium)
Depth
2,65-3
m
Diameter
DN 400
mm
In use since
Unknown
Length of pipes
65
Number of pipes
2
Overall length
130
Pipe material
PVC
Total airflow
8540
m
m
3 -1
m h
(Steeman, 2004)
- 141 -
Passive house Heusden
Location
Heusden (Belgium)
Depth
1,5-2,5
m
Diameter
DN 110
mm
In use since
2003
Length of pipes
40
Number of pipes
1
Overall length
40
Pipe material
HDPE
Total airflow
74
m
m
m3 h-1
(Steeman, 2004)
SD Worx
Location
Kortrijk (Belgium)
Depth PE
3
m
Depth concrete
3 and 5
M
Diameter
DN 400 (PE)
DN 800 (Concrete)
In use since
2000
Length of pipes
40
Number of pipes
Overall length
Pipe material
Total airflow
mm
M
6 PE
2 Concrete
320
M
PE
Concrete
5400 (summer)
3000 (winter)
(Steeman, 2004)
- 142 -
3 -1
m h
SurTec Factory
Figure 61: Earth-to-air heat exchanger under construction at the SurTec plant
Location
Zwingenberg (Germany)
Depth
4,3
m
Diameter
DN 600
mm
In use since
2000
Length of pipes
60
Number of pipes
5
Overall length
300
Pipe material
Concrete
Total airflow
16100
m
m
3 -1
m h
- 143 -
University of Bonn-Rhein-Sieg
Location
Sankt Augustin (Germany)
Depth
3,6
m
Diameter
DN 1700
mm
In use since
1997
Length of pipes
75
Number of pipes
3
Overall length
225
Pipe material
Concrete
Total airflow
50000
m
m
m3 h-1
Wagner
Figure 62: Configuration Wagner earth-to-air heat exchanger (Fraunhofer Institute
Solare Energiesysteme: 2006)
Location
Cölbe (Germany)
Depth
1,5
m
Diameter
DN 500
mm
In use since
1998
Length of pipes
32
Number of pipes
4
Overall length
128
Pipe material
Concrete
Total airflow
3000-6000
m
m
3 -1
m h
- 144 -
B Thermal properties used in verification Hollmuller algorithm
- 145 -
Building
Zone 1:
External wall (Brick)
: 1,887 W m-2 K-1
External wall surface
: 16 m2
Floor surface
: 8 m2
Heat transfer coefficient floor (Soil)
: 2,703 W m-2 K-1
Internal wall (Insulated brick)
: 0,33 W m-2 K-1
Internal wall surface
: 16 m2
Volume
: 16 m3
Zone 2:
External wall (Insulated brick)
: 0,33 W m-2 K-1
External wall surface
: 41 m2
Floor surface
: 12 m2
Heat transfer coefficient floor (Insulated Soil)
: 0,348 W m-2 K-1
Internal wall (Insulated brick)
: 0,33 W m-2 K-1
Internal wall surface
: 16 m2
Volume
: 39 m3
- 146 -
Earth-to-air heat exchanger
Soil:
Free water flow along the tubes
: None
Heat conductivity soil 1
: 5,4 kJ K-1 m-1
Heat conductivity soil 2
: 7,2 kJ K-1 m-1
Initial air temperature within the exchanger
: 10 ºC
: 15 °C
Volumetric heat capacity soil 1
: 100 kJ K-1 m-3
Volumetric heat capacity soil 2
: 100 kJ K-1 m-3
: None
Tube:
: 7,2 kJ K-1 m-1
Heat conductivity
: 10 ºC
Total airflow
: 1000 m3 h-1
Tube thickness
: 0,005 m
: 100 kJ K-1 m-3
Water infiltration
: None
- 147 -
C Properties used in verification Santamouris algorithm
- 148 -
Soil:
Density
: 2050 kg m-3
Specific heat
: 1841 J kg-1 K-1
: 0,52 W m-1 K-1
Tube
Density
: 1050 kg m-3
Radius
: 0,15 m
Specific heat
: 838 J kg-1 K-1
: 0,16 W m-1 K-1
Velocity
: 1,77 m s-1
Wall thickness
: 0,003 m
The initial values and depths of the nodes:
Depth
Initial temperature
Initial humidity
[m]
[°C]
[%]
Air
3,00
19,00
Impervious pipe
Tube wall (Outside)
3,15
12,07
40
Soil node 1
3,33
12,15
39,99
Soil node 2
3,68
12,42
39,98
Soil node 3
4,04
12,74
39,97
Soil node 4
4,40
13,03
39,96
Soil node 5
4,75
13,27
39,95
Soil node 6
5,11
13,44
39,94
Soil node 7
5,47
13,56
39,93
Soil node 8
5,82
13,62
39,92
Name
Table 23: Initial values of the nodes
- 149 -
32
Amplitude surface temperature variation : 30°C
30
: 13,6°C
Phase constant
: 240 h
Temperature [˚ C]
28
26
24
22
20
18
16
4969
4974
4979
4984
4989
4994
Time [h]
Figure 63: Ambient temperature
- 150 -
4999
5004
5009
5014
D Comparison predicted and calculated temperatures of the
Santamouris model
- 151 -
Segment 1 temperature Earth program [˚C]
28
26
24
22
20
18
16
16
18
20
22
24
26
28
Segment 1 temperature Type 280 [˚C]
Figure 64: Comparison between temperature segment 1 of Type 280 and Earth program
28
26
24
22
20
18
16
16
18
20
22
24
26
28
- 152 -
28
26
24
22
20
18
16
16
18
20
22
24
26
28
28
26
24
22
20
18
16
16
18
20
22
24
26
28
- 153 -
28
26
24
22
20
18
16
16
18
20
22
24
26
28
28
26
24
22
20
18
16
16
18
20
22
24
26
28
- 154 -
28
26
24
22
20
18
16
16
18
20
22
24
26
28
28
26
24
22
20
18
16
16
18
20
22
24
26
28
- 155 -
28
26
24
22
20
18
16
16
18
20
22
24
26
28
28
26
24
22
20
18
16
16
18
20
22
24
26
28
- 156 -
E Properties used in sensitivity analysis
- 157 -
Node geometry Hollmuller model
Tube
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
Soil
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
0,2659
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
0,2659
Figure 74: Z-Y cross section Hollmuller
- 158 -
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
Soil
1
1
1
1
1
Tube
0,2659
1
Figure 75: X-Y cross section Hollmuller model
- 159 1
1
1
1
1
1
Node geometry Santamouris model
Tube
Soil
0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562 0,3562
0,02
0,15
Figure 76: X-Z cross section Santamouris model
- 160 -
Tube
Soil
0,02
0,3
0,02
1
1
1
1
1
Figure 77: Y-Z Cross section Santamouris model
- 161 -
1
1
1
1
1
Soil:
Density
: 2600 kg m-3
: 3,57 W m-1 K-1
Specific heat
: 2934 J kg-1 K-1
: 7,2 kJ K-1 m-1
Total airflow
: 450 m3 h-1
Tube thickness
: 0,02 m
Tube:
Hollmuller
: 10 ºC
: 15 °C
: 10 ºC
: None
Water infiltration
: None
Santamouris
Amplitude of temperature wave
: 14.6°C
Mean annual surface temperature
: 8,73°C
Phase constant
: 744 h
Isothermal diffusivity of vapour
: 4,485*10-9 ft h-1
: 0,336 ft h-1
: 1,326*10-7 ft h-1 F-1
- 162 -
F Thermal properties of soil
- 163 -
Water content
Material
3
Clay1,3
Clay loam
Loam
2
3
5
Loamy sand
Sand3,4,5,7
Sandy clay
*Sandy loam6,7
6
Sandy clay loam
Silt
Silt clay loam5
Silt loam5,7
5
Silty clay
-
-3
Heat capacity (Cp)
Density (ρ)
-1
Thermal conductivity (λ)
-1
[kg m ]
[J kg K ]
[W m K ]
[m2 h-1]
-
1460
880
1,3
0,00364
0,3
1340
1732
1,34
0,00141
-
2600
846
3,57
0,00108
0,4
1400
1690
1,2
0,00183
0,4
1690
1778
1,59
0,00190
0,38
1640
1758
1,77
0,00225
0,25
1652
1250
1,14
0,00199
0,38
1600
1783
2,24
0,00282
-
1520
1848
2,90
0,00278
-
-
-
-
-
0,22
1440
1979
1,65
0,00208
-
1320
2258
1,7
0,00205
0,21
1400
2028
1,5
0,00190
-
-
-
-
-
0,59
1160
2934
1,09
0,00115
0,29
1300
1732
0,89
0,00142
0,3
1250
1802
1,13
0,00168
-
1200
2642
1,15
0,00131
0,3
1250
1802
0,9
0,00144
2 (Ochsner, Horten et al., 2001)
3 (De Vries, 1963)
et al., 2005)
- 164 -
4 (Abu-Hamdeh, 2003)
-1
5 (Sumber, 2000)
-1
Thermal diffusivity (α)
[m m ]
Not publicised 1 (Incropera and DeWitt, 2002)
-3
6 (Gao, Ren et al., 2006)
7 (Ochsner, Horten
G Surface temperatures and annual amplitudes
- 165 -
Murcia
Latitude
: 37° 59’ North (Google, 2007)
Longitude
: 1° 07’ West (Google, 2007)
Country
: Spain
Climate
: BSh
Annual average mean earth temperature
: 17,2°C (NASA, 2007)
Annual earth temperature amplitude
: 11,4°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
9,61
10,7
12,3
14,1
17.2
21,6
26,4
26,7
23,8
18,3
13,9
10,9
Table 24: Mean earth temperature (°C) (NASA, 2007)
Odessa
Latitude
: 46° 42’ North (Google, 2007)
Longitude
: 29° 45’ East (Google, 2007)
Country
: Ukraine
Climate
: BSk
: 8,25°C (NASA, 2007)
: 25,2°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-9,8
-5,04
2,73
10,2
15,8
20,0
23,0
22,8
16,6
8,44
-0,32
-6,4
Rome
Latitude
: 41° 53’ North (Google, 2007)
Longitude
: 12° 28’ East (Google, 2007)
Country
: Italy
Climate
: Csa
: 14,3°C (NASA, 2007)
: 14,7°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
5,4
6,36
9,22
12,1
16,2
19,9
24,6
25,0
20,8
15,9
10,3
5,87
- 166 -
Porto
Latitude
: 41° 09’ North (Google, 2007)
Longitude
: 8° 37’ West (Google, 2007)
Country
: Portugal
Climate
: Csb
: 14,1°C (NASA, 2007)
: 9,73°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
8,52
9,39
10,5
11,8
14,2
17,1
20,5
20,8
19,3
15,0
11,8
9,93
Venezia
Latitude
: 45° 26’ North (Google, 2007)
Longitude
: 12° 20’ East (Google, 2007)
Country
: Italy
Climate
: Cfa
: 7,39°C (NASA, 2007)
: 18,2°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-4,47
-1,6
3,04
7,36
12,1
15,3
18,5
18,3
13,9
8,63
1,06
-4,09
De Bilt
Latitude
: 52° 08’ North (Google, 2007)
Longitude
: 5° 09’ East (Google, 2007)
Country
: The Netherlands
Climate
: Csb
: 8,97°C (NASA, 2007)
: 14,6°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
0,9
1,15
4,5
7,38
11,6
14,5
17,2
17,2
14,1
10,4
5,31
2,58
- 167 -
Reykjavik
Latitude
: 64° 08’ North (Google, 2007)
Longitude
: 21° 55’ West (Google, 2007)
Country
: Iceland
Climate
: Cfc
: 3,18°C (NASA, 2007)
: 13,8°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-4,48
-2,6
-0,23
3,16
7,09
9,86
11,4
10,3
6,39
2,33
-1,81
-3,73
Stockholm
Latitude
: 59° 19’ North (Google, 2007)
Longitude
: 18° 03’ East (Google, 2007)
Country
: Sweden
Climate
: Dfb
: 4,33°C (NASA, 2007)
: 19,5°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-8,3
-6,81
-1,19
2,13
8,84
13,2
16,5
15,6
10,9
5,79
-0,89
-5,91
Sodankyläe
Latitude
: 67° 24’ North (Google, 2007)
Longitude
: 26° 35’ East (Google, 2007)
Country
: Finland
Climate
: Dfc
: -7,68°C (NASA, 2007)
: 31°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-28,8
-24,8
-15,1
-6,95
-0,72
11,6
14,6
11,3
4,29
-9,4
-21,5
-27,8
- 168 -
Utsjoki
Remark
: Removed from study due to an error in
the climate file
Latitude
: 69° 54’ North (Google, 2007)
Longitude
: 27° 01’ East (Google, 2007)
Country
: Finland
Climate
: ET
: -7,61°C (NASA, 2007)
: 29,5°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-26,0
-23,6
-16,4
-8,07
-2,48
10,5
14,1
10,6
3,91
-9,73
-20,1
-25,1
Innsbruck
Latitude
: 47° 15’ North (Google, 2007)
Longitude
: 11° 23’ East (Google, 2007)
Country
: Austria
Climate
: EH
: 5,84°C (NASA, 2007)
: 17,9°C (NASA, 2007)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
-5,39
-2,64
1,76
5,89
10,8
13,4
16,1
15,7
11,7
7,07
-0,3
-4,59
- 169 -
H Results of the soil and surface sensitivity analysis of the Rome
- 170 -
Rome
Figure 78: Energy savings with high specific heat
- 171 -
Figure 79: Energy savings with medium specific heat
Figure 80: Energy savings with low specific heat
- 172 -
I
Results of the Santamouris model
- 173 -
Soil-climate analysis
Rome
Figure 81: Energy savings with high specific heat
- 174 -
Figure 82: Energy savings with medium specific heat
Figure 83: Energy savings with low specific heat
- 175 -
Pipe material
35
30
25
20
15
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
10
Time [h]
Ambient temperature
Concrete
PVC
Steel
35
30
25
20
15
Time [h]
Ambient temperature
- 176 -
Concrete
PVC
Steel
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
0:
00
10
Diameter
6
3
0
-3
-6
-9
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
0:
00
-12
Time [h]
Ambient temperature
d = 0,15 m
d = 0,3 m
d = 0,45 m
35
30
25
20
15
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
10
Time [h]
Ambient temperature
d = 0,15 m
- 177 -
d = 0,3 m
d = 0,45 m
Length
9
6
3
0
-3
-6
-9
0:
00
8:
00
10
:0
0
12
:0
0
14
:0
0
16
:0
0
18
:0
0
20
:0
0
22
:0
0
6:
00
4:
00
2:
00
0:
00
-12
Time [h]
Ambient temperature
l = 30 m
l = 50 m
l = 70 m
35
30
25
20
15
Time [h]
Ambient temperature
- 178 -
l = 30 m
l = 50 m
l = 70 m
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
14
:0
0
12
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
10
Depth
3
0
-3
-6
-9
0
0:
0
22
:0
0
:0
0
20
18
:0
0
16
:0
0
:0
0
14
12
:0
0
0
10
:0
0
8:
0
6:
00
0
4:
0
0
2:
0
0:
00
-12
Time [h]
Ambient temperature
Depth = 1,2 m
Depth = 2 m
Depth = 3 m
35
30
25
20
15
0:
00
22
:0
0
20
:0
0
18
:0
0
16
:0
0
12
:0
0
14
:0
0
10
:0
0
8:
00
6:
00
4:
00
2:
00
0:
00
10
Time [h]
Ambient temperature
Depth = 1,2 m
- 179 -
Depth = 2 m
Depth = 3 m
Volume flow
4
2
0
-2
-4
-6
-8
-10
-12
0:
00
18
:0
0
20
:0
0
22
:0
0
12
:0
0
14
:0
0
16
:0
0
8:
00
10
:0
0
6:
00
4:
00
2:
00
0:
00
-14
Time [h]
Ambient temperature
4
2
0
-2
-4
-6
-8
-10
-12
0:
00
18
:0
0
20
:0
0
22
:0
0
12
:0
0
14
:0
0
16
:0
0
8:
00
10
:0
0
6:
00
4:
00
2:
00
0:
00
-14
Time [h]
Ambient temperature
- 180 -
J Data CD
The data cd contains :
Source codes of both algorithms
Pressure drop calculations
Soil analysis graphs of all the soils
- 181 -
- 182 -

Report - Jan Hensen

Transcription

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