thesis - Pavel Kopecký

Transkript

ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ V PRAZE
Fakulta stavební
Doktorský studijní program: STAVEBNÍ INŽENÝRSTVÍ
Studijní obor: Pozemní stavby
Ing. Pavel Kopecký
HYGRO-THERMAL PERFORMANCE OF EARTH-TO-AIR
HEAT EXCHANGERS
numerical model, analytical and experimental validation,
measurements in-situ, design
TEPELNĚ VLHKOSTNÍ CHOVÁNÍ ZEMNÍCH VÝMĚNÍKŮ TEPLA
numerický model, analytická a experimentální validace, měření in-situ, navrhování
DISERTAČNÍ PRÁCE K ZÍSKÁNÍ AKADEMICKÉHO TITULU Ph.D.
Školitel: Prof. Ing. Jan Tywoniak, CSc.
Praha, březen 2008
Preface
This report documents the work conducted in my study for PhD degree at the
Czech Technical University in Prague. My involvement in earth-to-air heat exchangers
began in 2003, when my supervisor Jan Tywoniak gave me a chance to participate in
the design of ecology centre Sluňákov. The large earth-to-air heat exchanger plays an
important role in this fascinating building.
The PhD study was financed by several grants. I acknowledge the support of
doctoral grant 103/03/H089 and participation within the CIDEAS research centre
1M0579. Without this support, the PhD would have never been conducted.
During autumn 2004, I carried out a stay at the Danish Technical University in
Lyngby under my supervisor Prof. Stephen Emmitt. This stay was made possible by
Socrates Erasmus scholarship and Prof. Emmitt himself. Two courses were carried out
at DTU. Mr. Carsten Rode introduced me the mysterious field of numerical methods
(Numerical Methods for Building Energy Technology). His personality and the way of
thinking was inspiration for me. The course, Ventilation and Climatic Systems, at
famous International Centre for Indoor Environment and Energy with course manager
Mr. Arsen Melikov gave me a good opportunity to spend nice weeks within the team of
international students.
I thank my supervisor Prof. Jan Tywoniak for all discussions and an
encouragement. I also thank Prof. Petr Hájek who ensured the support of doctoral grant
103/03/H089 and CIDEAS research centre.
I thank my colleagues at the department, PhD students from the group of
building physics, for their every-day support and discussions.
I thank Mr. Martin Jindrák for support and monitoring collaboration. The
monitoring on Rychnov family house was made possible by research cooperation
between CTU Prague and a company ATREA (http:/www.atrea.cz).
I thank Tereza Nováková for some necessary language and text correction.
-i-
Last but not least, I want to thank my wife Anežka for all the support she has
provided me. No doubt, I want to thank her for great help with German language
course.
Pavel
March 2008
- ii -
Abstract
The thermal comfort requirements and cooling energy demand have significantly
increased during the last twenty years. Air heating and/or cooling in earth-to-air heat
exchanger is a possible approach for reduction of ventilation heat loss and for
improvement of thermal comfort in a building. The earth-to-air heat exchanger is a pipe
buried in the ground through which the air is sucked into a building.
The general aim of this work is to contribute to the evaluation of hygro-thermal
performance of earth-to-air heat exchangers. The overall performance of the earth-to-air
heat exchanger may be understood as a bundle of particular components which interact
with each other. For instance, the local thermal process (air-to-ground heat transfer near
the pipe), the influence of neighbouring pipes, latent heat transfer inside pipes
(condensation or evaporation), and thermal coupling with the ground surface can be
mentioned.
This research on earth-to-air heat exchangers was the combination of a
theoretical study and experimental measurements. The theoretical predictions of the
hygro-thermal model developed for simulation of the earth-to-air heat exchangers were
compared with a) analytical solution for cylindrical heat exchanger and b) in-situ
measurements on real-size earth-to-air heat exchangers connected with mechanical
ventilation in two low-energy family houses.
The model showed perfect agreement with the analytical solution and
satisfactory agreement with experimental data. The validated model was then submitted
to series of simulations resulting in the straightforward parametric analysis. Moreover,
the evaluation of some measured data on real-size earth-to-air heat exchanger collected
during 2006 and 2007 was performed.
A deeper understanding of heat and moisture dynamics in the earth-to-air heat
exchanger is required for the proper design of the earth-to-air heat exchanger. A design
methodology was developed in order to facilitate the design of earth-to-air heat
exchangers using knowledge gained through both theoretical and experimental work.
- iii -
The model and long-term monitoring provides information about processes
which take place during earth-to-air heat exchanger operation and reveals limitations
and energy saving potential of the earth-to-air heat exchanger with respect to building
ventilation.
Keywords: passive cooling, earth-to-air heat exchanger, hygro-thermal simulation,
analytical validation, experimental validation, long-term monitoring, design
- iv -
Abstrakt
V poslední době je snahou snižovat spotřebu energie na provozování budov.
Požadavky na tepelný komfort vnitřního prostředí budov naopak stále rostou. Pro
předehřev a chlazení čerstvého vzduchu přiváděného do budovy může být v domech
větraných pomocí systému nuceného větrání využito zemních výměníků tepla (ZVT).
ZVT je potrubí, zakopané v určité hloubce pod povrchem země, přes které je do budovy
nasáván čerstvý vzduch.
Tato práce je kombinací teoretického zkoumání s měřením na reálných ZVT.
Teoretické předpovědi vyvinutého modelu ZVT byly porovnávány s a) analytickým
řešením a b) měřením in-situ na dvou skutečných ZVT. Takto validovaný model byl
potom podroben parametrické analýze. Částí této práce je i vyhodnocení měřených dat
z reálného ZVT (zejména měřená data z roku 2006) a vývoj metodiky pro návrh
dimenzí ZVT.
Porovnání mezi měřením a simulací ZVT sice neukázalo absolutní shodu, avšak
matematický model a později i dlouhodobé sledování reálných ZVT poskytují jasnou
informaci o procesech vyskytujících se během provozování ZVT a odkrývají tak
potenciál využití ZVT ve spojení s větráním budov.
Klíčová slova: zemní výměník tepla, tepelně vlhkostní simulace, analytická validace,
experimentální validace, monitoring
-v-
Table of contents
Preface ...............................................................................................................................i
Abstract .......................................................................................................................... iii
Abstrakt............................................................................................................................v
Table of contents.............................................................................................................vi
Nomenclature..................................................................................................................xi
1
2
Introduction ............................................................................................................1
1.1
General context ...............................................................................................1
1.2
Earth-to-air heat exchanger .............................................................................3
1.3
Literature review .............................................................................................5
1.4
Objectives........................................................................................................7
1.5
Scientific methods...........................................................................................8
1.6
Outline of the work .........................................................................................9
Model for simultaneous heat and moisture transfer in EAHX........................11
2.1
Fundamentals ................................................................................................12
2.1.1
Heat transfer ......................................................................................12
Conduction ......................................................................................................... 12
Convection.......................................................................................................... 13
2.1.2
Moisture transfer ...............................................................................14
Diffusion............................................................................................................. 15
Convection.......................................................................................................... 16
2.1.3
Direct link between heat and moisture transfer.................................16
Generation of latent heat..................................................................................... 17
2.1.4
Analytical solutions for semi-infinite body.......................................17
Harmonic oscillation of surface temperature...................................................... 17
Approximate calculation of soil thermal diffusivity........................................... 18
2.1.5
2.2
Natural thermal regime of shallow subsurface..................................19
Theoretical analysis.......................................................................................20
2.2.1
Problem definition.............................................................................20
- vi -
2.2.2
Heat transfer...................................................................................... 21
Convective heat transfer coefficient................................................................... 22
2.3
2.2.3
Moisture transfer............................................................................... 24
2.2.4
Coupled heat and moisture transfer .................................................. 26
Numerical solution........................................................................................ 26
2.3.1
Stage of operation ............................................................................. 26
Calculation of new air temperature (step 1a)...................................................... 27
Calculation of new water vapour concentration and moisture flux (step 1b) ..... 27
Calculation of new temperature in the soil (step 2)............................................ 28
Calculation of new pipe surface temperature (step 3) ........................................ 31
2.4
3
2.3.2
Stage of natural soil recovery ........................................................... 31
2.3.3
Flow diagram .................................................................................... 32
2.3.4
Stability and accuracy....................................................................... 33
Summary....................................................................................................... 35
Model validation .................................................................................................. 37
3.1
3.2
Flat-plate heat exchanger.............................................................................. 37
3.1.1
Problem definition ............................................................................ 37
3.1.2
Numerical solution............................................................................ 38
3.1.3
Test of longitudinal heat conduction ................................................ 40
3.1.4
Phase-shifting phenomenon.............................................................. 40
3.1.5
Summary........................................................................................... 45
Verification exercises ................................................................................... 45
3.2.1
Test of undisturbed soil temperature calculation.............................. 45
3.2.2
Test of hygrothermal calculations..................................................... 49
Step change of inlet relative humidity................................................................ 50
Periodic inlet signals .......................................................................................... 51
3.3
3.4
Analytical validation..................................................................................... 55
3.3.1
Analytical solution............................................................................ 55
3.3.2
Simulation......................................................................................... 55
3.3.3
Comparison analytical vs. numerical................................................ 58
3.3.4
Summary........................................................................................... 60
Experimental validation................................................................................ 60
3.4.1
Long-term thermal simulation .......................................................... 60
Measurement in-situ........................................................................................... 60
Simulation .......................................................................................................... 61
Sensitivity analysis............................................................................................. 62
Comparison simulation vs. measurement........................................................... 65
- vii -
Continuous mode................................................................................................ 67
Intermittent mode ............................................................................................... 67
Conclusions ........................................................................................................ 68
Summary ............................................................................................................ 69
3.4.2
Short-term hygro-thermal simulation................................................70
Measurement in-situ ........................................................................................... 70
Simulation .......................................................................................................... 70
Comparison simulation vs. measurement ........................................................... 70
Conclusions ........................................................................................................ 73
Summary ............................................................................................................ 73
3.5
3.6
4
Parametric analysis........................................................................................73
3.5.1
Simulation .........................................................................................73
3.5.2
Input parameters................................................................................75
3.5.3
Monitored outputs .............................................................................75
3.5.4
Results ...............................................................................................76
3.5.5
Conclusions .......................................................................................78
Summary .......................................................................................................78
Measurements in situ ...........................................................................................81
4.1
Introduction ...................................................................................................81
4.2
Soil ................................................................................................................83
4.3
4.4
4.2.1
Thermal properties ............................................................................83
4.2.2
Soil temperature ................................................................................84
4.2.3
Approximate calculation of soil thermal diffusivity .........................84
External environment ....................................................................................85
4.3.1
Ambient air temperature....................................................................85
4.3.2
Ambient air water vapour concentration...........................................86
4.3.3
Tendency of EAHX to condensation ................................................87
Earth-to-air heat exchanger ...........................................................................88
4.4.1
Example of measured data ................................................................88
4.4.2
EAHX operation................................................................................90
Pre-heating mode................................................................................................ 90
Cooling mode ..................................................................................................... 91
Annual statistic ................................................................................................... 91
4.5
4.4.3
Outlet air temperature........................................................................92
4.4.4
Moisture balance ...............................................................................93
4.4.5
Energy performance ..........................................................................94
Conclusions ...................................................................................................97
- viii -
4.6
5
Dimensioning of EAHXs ..................................................................................... 99
5.1
5.2
6
Summary....................................................................................................... 97
Theory........................................................................................................... 99
5.1.1
Outlet air temperature ....................................................................... 99
5.1.2
Temperature efficiency ................................................................... 100
5.1.3
Pressure loss.................................................................................... 101
5.1.4
Cooling power................................................................................. 102
5.1.5
Hollmuller design rules................................................................... 103
Simulations ................................................................................................. 103
5.2.1
Hollmuller design rules................................................................... 104
5.2.2
Constant NTU ................................................................................. 104
5.2.3
Constant Va/A.................................................................................. 105
5.2.4
Distance between pipes................................................................... 106
5.2.5
Role of pipe material....................................................................... 106
5.3
Design methodology................................................................................... 107
5.4
Examples..................................................................................................... 109
5.4.1
EAHX for family house.................................................................. 109
5.4.2
EAHX for larger building ............................................................... 110
5.5
Conclusions................................................................................................. 110
5.6
Summary..................................................................................................... 111
Conclusions......................................................................................................... 113
6.1
Results......................................................................................................... 113
6.2
Final remarks and recommendations for further research .......................... 114
Appendices................................................................................................................... 117
A1
Derivations and solutions ........................................................................... 117
Equation 2.30 ................................................................................................... 117
Equation 2.39 ................................................................................................... 118
FPHX with adiabatic boundary – analytical solution ....................................... 118
A2
Explicit finite difference method for transient heat conduction ................. 120
A3
House W ..................................................................................................... 122
Basic information ............................................................................................. 122
List of sensors .................................................................................................. 123
A4
Passive family house in Rychnov ............................................................... 124
Basic information ............................................................................................. 124
- ix -
List of sensors................................................................................................... 125
Ventilation modes............................................................................................. 126
Air flow rates.................................................................................................... 127
Auxiliary energy............................................................................................... 127
A5
Thermal properties of soils and rocks .........................................................128
References ....................................................................................................................130
Publications written in context with the thesis .........................................................135
Other publications.......................................................................................................137
-x-
Nomenclature
The following list of symbols is not complete. However, all the symbols used
within the thesis are explained in the place where they appear so that their meaning
should be already clear from the text. Abbreviation EAHX, appearing throughout the
following text, denotes earth-to-air heat exchanger. Similarly, FPHX denotes flat-plate
heat exchanger.
symbol
latin letters
as
bs
cp
deq
dp
eAeahx
eVaAeahx
gv
ha
l
ne
va
q
rh
t
tp
x, y, z
explanation
unit
thermal diffusivity of soil
thermal effusivity of soil
specific isobaric thermal capacity
equivalent diameter
periodic penetration depth
specific energy injected to
surrounding soil related to
exchange surface A
specific energy injected/extracted
to/from surrounding soil (related
to exchange surface A and air
flow rate Va)
vapor flux
convective heat transfer
coefficient
latent heat of
condensation/evaporation
air change rate
air velocity
heat flux
relative humidity
time
period
spatial coordinates
[m2/s]
[Ws0.5/(m2.K)]
[J/(kg.K)]
[m]
[m/period]
[Wh/(m2.period)]
- xi -
[(Wh/period)/(m2.m3/period)
= Wh/m5]
[kg/(m2.s)]
[W/(m2.K)]
[J/kg]
[1/h]
[m/s]
[W/m2]
[%]
[s]
[s]
[m]
r
z
A
B
Dchar
E
L
Nu
NTU
Pr
Q
QEAHX
Qcooling
G
Va
W
radial coordinate
depth
area, exchange surface
thickness of the plate
characteristic dimension
energy
length of EAHX
Nusselt number
number of transfer units
Prandtl number
heat flow
heat flow injected/extracted
to/from soil by EAHX
cooling power of EAHX
convective moisture flow
volumetric air flow rate
width of the plate for FPHX
[m]
[m]
[m2]
[m]
[m]
[kWh/period]
[m]
[-]
[-]
[-]
[W]
[W]
thermal conductivity
thermal conductivity of pipe
material
water vapour transfer coefficient
(vapor concentration as driving
potential)
temperature
density
partial density of water vapour
(vapor concentration)
temperature efficiency of EAHX
friction pressure loss in a straight
pipe
[W/(m.K)]
[W/(m.K)]
[W]
[kg/s]
[m3/s]
[m]
greek letters
λ
λp
βρ
θ
ρ
ρv
ηEAHX
∆pfric
subscripts
a
conv
in
out
rec
s
air, ambient
convection
inlet
outlet
recovery
soil or surface
- xii -
[m/s]
[°C]
[kg/m3]
[kg/m3]
[-]
[Pa]
sat
v
i
i, j, k
superscripts
a
dry
moist
ol
cl
saturation
vapour
internal
indexes (counters)
amplitude
simulation with absolutely dry air
simulation with moist air
open loop of EAHX (direct suction of ambient air)
closed loop of EAHX (circulation between internal environment
and EAHX)
- xiii -
Introduction
1 Introduction
The chapter will focus on the background of earth-to-air heat exchangers and a
basic literature review. Furthermore, the emphasis is put on the introduction of thesis
objectives and the scientific methods used in the thesis.
1.1 General context
We live in time when global warming becomes more and more apparent
(see Figure 1.1). Most of the observed increase in global average temperatures since the
mid-20th century is very likely caused by observed increase in anthropogenic
greenhouse gas concentrations (IPCC report, 2007). Consequently, and amongst others,
longer and more intense heat wave periods and heavy precipitation events will very
likely occur in the 21st century. European countries could already notice extremely hot
summer in 2003 and 2006 (see Figure 1.2), and extraordinarily mild autumn 2006 (see
Oldenborgh, 2006).
The amount of any fossil fuel under the ground worldwide is finite. Therefore,
fossil fuels will be more expensive in the future due to their successive depletion. For
instance, (Cílek and Kašík, 2007) report that the worldwide maximum in oil production
(peak oil) will likely occur between 2008 and 2015. Thus, problems with oil availability
and related price increase should be already expected in the following decade.
In developed countries, approximately 40 % of total primary energy is consumed
in buildings and approximately 25 % of the green house gas emissions (CO2 in
particular) are building-related. Therefore, a future strategy focuses on: a) low energy
and passive buildings (energy efficiency), and b) use of renewable energy sources for
heating and cooling of buildings and electricity production. The technical measures are
already available on the market. But more is required than pure increase in energy
efficiency of buildings. The future development will have to focus on zero-energy
buildings (Voss and Kramp, 2007), and the energy-independent buildings.
-1-
Chapter 1
40
40
fourier (N=5)
35
35
30
30
25
25
frequency
frequency
fourier (N=5)
20
15
20
15
10
10
5
5
0
1800
1850
1900
year
1950
2000
0
1800
1850
1900
year
1950
2000
Figure 1.1: Left - absolute frequency of daily ambient air temperature maximums sorted
by the year of their record. Right – absolute frequency of daily ambient air temperature
minimums sorted by the year of their record. Data from Prague Klementinum (1775 2006)
2001
1991
2001
1991
1981
1971
1961
1951
1941
1931
1921
1911
1901
0
1981
5
1971
10
1961
15
1951
20
5th degree polynomial
1941
25
90
80
70
60
50
40
30
20
10
0
1931
30
2006
1921
2003
1911
5th degree polynomial
1901
35
Figure 1.2: Left - number of tropical days (θambient > 30 °C). Right – number of summer
days (θambient > 25 °C). Data from Prague Klementinum (1900 – 2006)
The thermal comfort requirements and cooling energy demand have significantly
increased during the last twenty years. Production of coldness by a “traditional”
compressor cooling consumes a lot of electricity. Countries with high penetration of airconditioning, such as the USA or Canada, have serious problems with very high
demand during summer temperature peaks. Therefore, the substantial reduction of heat
gains (prevention and protection) and short-term storage of heat gains in building
components (modulation of heat gains) should be considered to be important issues of
building-energy concept. Alternative (often called passive) cooling techniques could be
used for heat rejection, if necessary. Ventilation by cold night air and using coldness of
ground (earth-to-air or earth-to-fluid heat exchangers) are standard examples of passive
cooling techniques. Some promising cooling techniques are still under scientific
investigation, see e.g. (Hollmuller et al, 2006) and (Arkar and Medved, 2007).
-2-
Introduction
1.2 Earth-to-air heat exchanger
Air heating and/or cooling in earth-to-air heat exchanger is a possible approach
for reduction of ventilation heat loss and for improvement of thermal comfort in a
building. The earth-to-air heat exchanger is a pipe buried in the ground through which
the air is sucked into a building. Such device is considered to be both renewable energy
source and a technique for reduction of building heat use and cooling energy demand.
Using soil for heat dissipation is a traditional principle. Because of high soil
thermal capacity, the temperature in sufficient depth under upper soil surface remains
stable, oscillating roughly around annual mean ambient temperature. Hence, the
ambient air sucked through the pipe is either cooled down or heated up. The principle
had already been known by ancient Persian and Greeks (Santamouris et al, 1996).
Nowadays, with rising energy costs and higher requirements on thermal comfort, the
utilization of earth-to-air heat exchangers is slowly coming back. Its simplicity, high
cooling potential, low initial, operational and maintenance costs are presented as the
advantages of the earth-to-air heat exchanger. In many cases, well designed earth-to-air
heat exchanger together with efficient overall concept of a building may eliminate the
need for mechanical air conditioning (Pfafferot, 2004).
The setup of a simple earth-to air heat exchanger is depicted in Figure 1.3. The
system typically consists of an inlet shaft with filters and a pipe buried in the ground.
The pipe is connected to a mechanical ventilation system using T-fitting with damper.
The damper controls whether air is sucked through the earth-to-air heat exchanger or is
directly sucked through a facade inlet.
Ventilation
system
Figure 1.3: EAHX linked to a building (open loop mode)
-3-
Chapter 1
An alternative setup of the earth-to-air heat exchanger has been developed by the
Czech company ATREA (http://www.atrea.cz). The layout (Figure 1.4) allows air
circulation between building and the earth-to-air heat exchanger (closed loop system).
In order to switch over operational modes the system needs a special damper placed in a
chamber somewhere near an air handling unit.
Ventilation
system
Figure 1.4: Alternative setup of EAHX (closed loop mode)
What is the current state-of-the-art in the Czech Republic? The earth-to-air heat
exchanger has become quite popular when small one-pipe exchangers are widely used
in low-energy family houses. Even multi-pipe exchangers have been built, e.g.
kindergarten in Ostrava Proskovice (Kramoliš, 2002) or Ecological Education Centre
Sluňákov near Olomouc (Hofmeister et al, 2007). However, such systems are still rare
and perceived as partially experimental.
Figure 1.5: Left – EAHX in Ostrava Proskovice. Right – EAHX Sluňákov near Olomouc
-4-
Introduction
1.3 Literature review
Heat conduction in the ground has traditionally been a domain of researchers
from the northern European countries. Because of the cold climate, they are more
attracted by the field of foundation design, soil freezing, ground heat storage, and air
pre-heating in earth-to-air heat exchangers. Researchers of the southern European
countries often examine cooling potential of earth-to-air heat exchangers. The most
recent research perhaps comes from Switzerland and Germany. The valuable
information is often found in books or papers dealing with ground heat storage
(e.g. Hellstrom, 1991) or thermo-active components (e.g. floor heating, radiant cooling
ceilings).
The references dealing with earth-to-air heat exchangers may be further divided
into:

Modelling issue (analytical, numerical or mixed models) – (Claesson, 1983),
(Nilsson, 1991), (Mihalakakou et al, 1994), (Stahl, 2002), (Hollmuller, 2005a),
(Hollmuller, 2003), (Hollmuller, 1998)

Comparative analysis between predicted and measured data – (Nilsson, 2001),
(Hollmuller, 2001), (Mihalakakou et al, 1994)

Evaluation, design, and operational experience of real examples – (Pfafferott,
2003), (De Paepe, 2003), (Herkel, 2002), (Fink et. al, 2002)
One of the first investigations of heat extraction from the ground was launched
by (Claesson, 1983). Mathematically focused publication employed analytical solutions
for heat conduction equation with different boundary conditions. The analysis was
based on the technique of superposition, when the complex thermal process in the
ground was considered to be superposition of the elementary ones.
In his doctoral thesis, (Nilsson, 1991) dealt with pre-heating of ambient air by a
system of earth-tubes as primary energy source for a heat pump. His work also
employed an analytical approach and special attention was paid to latent heat effects in
the soil (soil freezing). The theoretical analysis was compared with in-situ measurement
of pre-heating system located in northern Sweden.
(Mihalakakou et al, 1994) introduced a numerical model of the EAHX. The
model was compared with an experimental setup of EAHX. (Mihalakakou et al, 1996)
used the model to describe the thermal influence of design variables – pipe length, pipe
-5-
Chapter 1
radius, air flow rate and pipe depth. In (Mihalakakou, 2003), a neural network was used
for to estimate the thermal performance of a single pipe exchanger. Another neural
network approach was discussed in (Kumar, 2006).
(Santamouris, 1995) developed a method for estimation of the EAHX
contribution to the reduction of building cooling load.
(Stahl, 2002) shortly discussed the moisture consequences of EAHX operation.
High relative humidity level of outlet air during summer operation was shown; it was
further stated that high air humidity near the pipe outlet might result in mould growth
inside the pipe.
In his doctoral thesis, (Hollmuller, 2002) dealt with earth-to-air heat exchanger.
He developed a numerical simulation model, and analyzed the monitored data from real
scale installations. (Hollmuller, 2003) introduced an analytical solution for cylindrical
air-to-soil heat-exchanger with either external adiabatic or isothermal boundary. In
parallel, it was mentioned that a special setup of EAHX (special combination of
geometry, exchanger operational parameters, and periodical input signal) will lead to
the outlet phase-shifting almost without amplitude-damping. The guideline for the
combination of inputs in order to reach this performance was also proposed. Heating as
well as cooling potential of one commercial building was evaluated by (Hollmuller,
2001) by means of his numerical simulation model and the evaluation of the monitored
data.
(Pfafferott, 2003) evaluated three EAHXs for office buildings. A general method
for comparison of EAHXs in operation was introduced.
(De Paepe and Janssens, 2003) developed a simple design tool of EAHX which
was based on thermo-hydraulic performance optimization.
Even though many publications are available in this research field, other
research topics which have not been well explored, yet, can be deduced:

The moisture consequences: Except for Hollmuller’s numerical model, existing
mathematical models don not take humidity of air into account. Are really latent
heat effects inside pipes so important (e.g. unwanted heating due to the release of
condensation heat, positive effect of the water vapour evaporation, consequent
mould growth in pipes)?.
-6-
Introduction

A comparative analysis between simulation and measured data: (Hollmuller,
2002) made careful analysis between monitored data of real scale exchangers and
his mathematical model. It was stated that water infiltration due to leaky pipe wall
can significantly affect the air heat balance. The model developed by
(Mihalakakou, 1994) was compared to experimental short-term measurement.
Still, there is a lack of measured data, especially monitoring of real size
installations would be a valuable contribution.

The evaluation of EAHX’s total effect with regard to the ventilated zone:
(Pfafferott, 2003) evaluated the operation of real size earth-to-air heat exchangers,
but the contribution of the exchanger to overall building energy balance was not
discussed. The contribution to the overall building energy balance was discussed
by (Hollmuller, 2001), who pointed out the fundamental difference between preheating and pre-cooling mode of the EAHX. The air pre-heating lowers building
energy demand; however, there is competitive relationship of EAHX with heat
recovery because the EAHX “steals” energy which could otherwise be recovered.
Hence, the total effect of the EAHX in series with heat recovery is not
significantly higher than the effect of heat recovery itself, especially for very high
efficiency of heat recovery (assuming very tight building envelope). The air precooling may dampen the daily temperature peaks below the comfort threshold.
However, the amount of heat which is removed from the building is strongly
dependent on the air-flow rate and current soil temperature.

The comparison between closed loop mode and open loop mode of EAHX has
not been performed, yet. Is a closed loop setup more effective for cooling than
open loop system? What is the difference between closed loop and open loop
mode from moisture point of view?
1.4 Objectives
Development of hygro-thermal model for simulation of the earth-to-air heat
exchangers is the main objective of this work. It is believed that through theoretical
work the main tendencies in heat and moisture transfer in the earth-to-air heat
exchanger will be explored. However, reality is always much more complicated than
any complex model could be. Therefore, a reasonable model complexity should be kept
in mind.
-7-
Chapter 1
Since the model is a pure mathematical representation (i.e. simplification) of the
physical reality, validation and/or verification of the model will be another objective
of this work. Since experimental validation is conditioned by good quality of
experimental data, long-term monitoring of real-size earth-to-air heat exchanger and
evaluation of the measured data will be the next part of this work.
A complex modeling is not always required to answer simple question.
Therefore, a method for design of EAHX dimensions should be developed. The result
of this part should make possible to design EAHX quickly and easily without loosing a
physical background.
1.5 Scientific methods
The research method was a combination of a theoretical study and the
experimental measurements performed on two real size EAHXs.
The theoretical chapters used logical methods (mainly abstraction, analysis and
synthesis) which complemented each other. The analysis was used for development of
the simulation model for earth-to-air heat exchanger when complex problem of
simultaneous heat and moisture transfer was divided into particular components. On the
other hand, the synthesis put the components together when interrelations between
components were studied. The model was developed by a step-by-step procedure when
the first version of the algorithm included only heat transfer and was tested on simpler
case of the flat-plate heat exchanger. Subsequently, the basic routine (dealing with heat
transfer only) for the earth-to-air heat exchanger was developed adjusting the model of
the flat-plate heat exchanger (pipe, two-dimensional calculation of heat conduction,
boundary nodes). The moisture transfer and influence of latent heat on air balance were
added later.
The long-term monitoring was performed on two low-energy family houses
ventilated by mechanical ventilation equipped with heat recovery and real size earth-toair heat exchangers. Monitoring on real size systems has two important advantages.
First, the simulation can be compared with measurement so that the relation between
reality and the model can be studied. Second, the measurement provides authentic
information about EAHX real operation and about link between house ventilation
system and the earth-to-air heat exchanger.
-8-
Introduction
The process of thesis development may be represented via the following flow
diagram (Figure 1.6).
Theoretical analysis of physical processes in
EAHX
The development of a mathematical model for
hygro-thermal simulation of the earth-to-air heat
exchangers + validation
The measurement on real size exchangers, data
evaluation, measurement vs. simulation
Figure 1.6: The thesis - flow diagram
1.6 Outline of the work
Chapter 1: The chapter focuses on the background of earth-to-air heat
exchangers in the Czech context and a basic literature review (state-of-the-art).
Furthermore, the emphasis is put on the introduction of thesis objectives and the
scientific methods used in the thesis.
Chapter 2: The hygro-thermal model of the earth-to-air heat exchanger will be
described in this chapter. The emphasis is put on the introduction of physical processes
which may take place in earth-to-air heat exchangers and the presentation of developed
model.
Chapter 3: The developed hygro-thermal model of the earth-to-air heat
exchanger will be validated in this chapter. An analytical validation and experimental
validation are introduced here. Finally, the hygro-thermal performance of the validated
model is evaluated by a parametric analysis.
Chapter 4: The results from long-term monitoring on passive family house in
Rychnov will be introduced in this chapter. The presentation will focus on the EAHX
performance.
Chapter 5: The chapter will focus on the development of a simple method for
design of optimal dimensions of EAHXs.
Chapter 2, 3, 4, 5 are considered to be the body of the work.
-9-
Chapter 1
- 10 -
Model for simultaneous heat and moisture transfer in EAHX
2 Model for simultaneous heat and
moisture transfer in EAHX
The hygro-thermal model of the earth-to-air heat exchanger will be described in
this chapter. The emphasis is put on the introduction of physical processes which may
take place in earth-to-air heat exchangers and the presentation of developed model.
The overall performance of the earth-to-air heat exchanger may be understood as
a bundle of particular components which interact with each other (Figure 2.1). For
instance, the local thermal process (air-to-ground heat transfer near the pipe), the
influence of neighbouring pipes, latent heat transfer inside pipes (condensation or
evaporation), and coupling with the ground surface (long-term behaviour of the
exchanger) can be mentioned. Another complication of the computational analysis is the
time scale of thermal process; even very short extraction or injection pulses take place
during the operation of the exchanger (see chapter 4.4.2).
short-wave
radiation
rain
wind
ambient temperature
long-wave
radiation
cond./evap.
heat λs, as
conduction
cond./evap. in
the pipe, latent
heat of phase
change
ground water table
Figure 2.1: Boundary conditions for earth-to-air heat exchanger
- 11 -
Chapter 2
2.1 Fundamentals
This part will deal with several heat and mass transfer topics. The emphasis is
placed on the description of mathematical formulae. The sub-chapter focuses on the
physical processes taking place in the earth-to-air heat exchanger. The main references
for this introductory theoretical chapter are (Hagentoft, 2001) and (Hens, 2007).
2.1.1 Heat transfer
Heat transfer is the process by which energy is transported as a result of
temperature difference. The heat can be transferred by following mechanisms:
•
Conduction
•
Convection
•
Radiation
The heat conduction is the most important transport process in solids, radiation
or convection are usually minor. On the contrary, convection and radiation are the most
important transport processes in gases and liquids, e.g. air gap embedded in solid
material.
Conduction
The heat flux q [W/m2] in homogenous and isotropic material is expressed by
Fourier’s law which says that the heat flux is proportional to the gradient of temperature
and is flowing in the opposite direction of gradient temperature vector:
q = −λ
∂θ
∂x
(2.1)
where: λ is thermal conductivity of material [W/(m.K)], θ is temperature [K].
The energy conservation law says that energy can not disappear. This general
law is used to describe the thermal balance of a control volume. The inflow of heat
[W/m3] minus outflow [W/m3] has to be equal to heat stored [W/m3] in the control
volume per time step:
−
∂q
∂h
=ρ
∂x
∂t
(2.2)
- 12 -
where: ρ is density of material [kg/m3], h is specific enthalpy [J/kg]. By
inserting transport equation (2.1) to equation (2.2) is obtained:
−
∂ ⎛
∂θ ⎞
∂h
⎜ −λ
⎟=ρ
∂x ⎝
∂x ⎠
∂t
(2.3)
The relationship between change of specific enthalpy h (J/kg) and temperature
change in a certain material is:
∂h = c p ∂θ
(2.4)
where: cp is specific thermal capacity [J/(kg.K)]. By inserting the equation of
state (2.4) to continuity equation (2.3), transient heat conduction equation is obtained:
−
∂ ⎛
∂θ ⎞
∂θ
⎜ −λ
⎟ = ρc p
∂x ⎝
∂x ⎠
∂t
(2.5)
In case of constant λ and ρcp equation (2.5) can be rearranged into the following
form:
∂θ
∂ 2θ
=λ 2
∂t
∂x
ρc p
(2.6)
Thermal diffusivity a (m2/s) is the ratio:
a=
λ
ρc p
(2.7)
The equation for heat conduction in two dimensions can be written as:
ρc p
⎛ ∂ 2θ ∂ 2θ
∂θ
= λ⎜ 2 + 2
⎜ ∂x
∂t
∂y
⎝
⎞
⎟⎟
⎠
(2.8)
Convection
The convective heat transfer is caused by fluid flow. The convective heat flow
Qconv [W] is:
Qconv = ma caθ a
(2.9)
where: ma is air (fluid) flow rate [kg/s], ca is specific thermal capacity of air
(fluid) [J/(kg.K)] and θa is air (fluid) temperature [K]. If fluid flows along a surface and
the difference between fluid and surface temperature exists, the convective heat transfer
will occur. The convective heat flux qconv (W/m2) is expressed as a function of the
- 13 -
Chapter 2
convective heat transfer coefficient ha [W/(m2.K)] and the difference between fluid and
surface temperature:
qconv = ha (θ a − θ s )
(2.10)
Convection caused by a pump or a fan is called forced convection. Convection
caused by density differences in the fluid is called natural convection.
The flow in pipes can be classified as either laminar or turbulent. No mixing of
the fluid occurs in the laminar flow. The flow velocity and direction of flow in a certain
point remains constant over time. In the turbulent flow the fluid is completely mixed,
the flow velocity and direction of flow in a certain point is not constant over time. Due
to the mixing, the temperature in the channel becomes almost uniform.
Reynold’s number may characterize the flow: in straight pipes, at Re ≤ 2300 the
flow is considered to be laminar and at Re ≥ 10000 the flow is considered to be
turbulent. Between 2300 and 10000 the flow is in transition state (neither laminar nor
turbulent).
2.1.2 Moisture transfer
The moisture transfer is the process by which mass (vapour or water) is
transported as a result of difference in vapour concentrations (or partial vapour
pressures). The moisture can be transferred in porous materials by the following
mechanisms:
•
Diffusion
•
Convection
•
Capillary suction
•
Special types (thermo-diffusion)
For the earth-to-air heat exchanger, all types of moisture transfer are important.
The convective vapour transfer occurs between air and inner surface of pipes. Water
vapour is transferred by diffusion through the wall of pipes. Convection and capillary
suction may take place in the surrounding soil.
- 14 -
Diffusion
The water vapour flux gv [kg/m2s] is expressed by Fick’s law which says that
vapour flux is proportional to the gradient of a driving potential and flows in the
opposite direction of gradient vector. Either water vapor concentration or partial
pressure of water vapor can be chosen as the driving potential:
g v = −δ ρ
∂ρv
∂x
(2.11)
g v = −δ p
∂pv
∂x
(2.12)
where: δρ is water vapour permeability in [m2/s] (when ρv is driving potential),
δp is water vapour permeability in [kg/(m.s.Pa)], (when pv is driving potential), ρv is
water vapour concentration [kg/m3], pv is partial pressure of water vapour [Pa].
The equation of state for water vapour expresses the relationship between partial
pressure and water vapour concentration under isothermal conditions:
pv = Rv ρvθ
(2.13)
where: Rv is gas constant for water vapour (Rv = 461.5 J/kg.K). Therefore, the
relationship between water vapour permeability δp and δρ is:
δp =
δρ
(2.14)
RvT
The mass conservation law says that mass can not disappear. This basic law is
used to describe the moisture balance of a control volume. The inflow of moisture
[kg/(m3.s)] minus outflow [kg/(m3.s)] has to be equal to moisture stored [kg/(m3.s)] in
the control volume per time step:
−
∂g v
∂u
=ρ
∂x
∂t
(2.15)
The relationship between change of moisture content u (kg/kg) and partial
vapour pressure change in a certain material can be described by using the slope of the
sorption isotherm ξ and saturated water vapour pressure psat:
∂pv psat ∂u
=
ξ ∂x
∂x
(2.16)
- 15 -
Chapter 2
By inserting the equation of state (2.16) to continuity equation (2.15), transient
equation for moisture transport under isothermal conditions is obtained:
∂u ∂ ⎛ psatδ p ∂u ⎞
= ⎜
⎟
∂t ∂x ⎝ ρξ ∂x ⎠
(2.17)
Convection
Convective moisture transfer is caused by air flow. The convective moisture
flow G [kg/s] is:
G = Va ρv
(2.18)
where: Va is air flow rate in [m3/s].
If the air flows along a surface and there is the difference between water vapour
concentration in flowing air and water vapour concentration in air close to the surface,
the convective vapour transfer will occur. Analogously to heat transfer, the water
vapour flux gv (kg/(m2.s)) is expressed as a function of the transfer coefficient βρ and
the difference between air and the surface water vapour concentration:
g v = β ρ ( ρv − ρv ,s )
(2.19)
The mass transfer coefficient can be calculated from the heat transfer coefficient
according to Lewis formula:
βρ =
ha
ρ a ⋅ ca
(2.20)
2.1.3 Direct link between heat and moisture transfer
Heat and moisture transfer are processes which are linked together. The moisture
transfer influences the heat transfer in the following ways:
•
Generation of latent heat
•
Thermal conductivity of wet materials is increased
•
Thermal capacity of wet materials is increased
- 16 -
Generation of latent heat
For the earth-to-air heat exchanger, the generation of latent heat is considered to
be important because the periods of condensation on the inner surface of the pipe and/or
evaporation of the water vapour from the inner surface of the pipe can occur. If the
water vapour condenses on the inner surface of the pipe, heat will be released; therefore,
the air temperature will increase1. Consequently, increased air temperature increases the
temperature of the pipe, and the condensation rate is reduced (a reverse link). The
evaporation has an inverse effect.
The generation of latent heat ql [W/m2, condensation (+), evaporation (-)] is
defined as:
ql = l ⋅ gv
(2.21)
where: l is latent heat of condensation [2.5*106 J/kg], gv is condensing (+) or
evaporating (-) flux in [kg/(m2.s)].
2.1.4 Analytical solutions for semi-infinite body
An analytical solution of the general heat conduction equation (2.6) is to be
found for semi-infinite medium. The harmonic oscillation of surface temperature is an
important case of boundary temperature input.
Harmonic oscillation of surface temperature
Semi-infinite body is submitted to a harmonic oscillation of the surface
temperature with period tp. The surface temperature oscillation θs may be defined by
sinus function:
⎛ 2π t ⎞
⎟
⎜ tp ⎟
⎝
⎠
θ S (t ) = θ MEAN + θ A sin ⎜
(2.22)
where: θMEAN is mean surface temperature, θA is the amplitude of surface
temperature, and t is time. The formula for temperature oscillation inside semi-infinite
slab (in the depth z [m]) is given as:
1
One might also imagine a thin film of water on the pipe surface which decreases the value of
the heat transfer coefficient and reduces heat transfer between flowing air and the pipe.
- 17 -
Chapter 2
θ ( z, t ) = θ MEAN + θ A exp
−z
dp
⎛ 2π t z ⎞
−
sin ⎜
⎟
⎜ tp dp ⎟
⎝
⎠
(2.23)
The response is linearly shifted, and the amplitude is exponentially dampened.
The heat flow rate is given as:
−z
⎛ 2π t z π ⎞
Aλ 2
d
−
+ ⎟
Q( z , t ) =
θ A exp p sin ⎜
⎜ tp dp 4 ⎟
dp
⎝
⎠
(2.24)
At the boundary (z = 0):
Q(0, t ) =
⎛ 2π t π ⎞
Aλ 2
θ A sin ⎜
+ ⎟
⎜ tp
dp
4 ⎠⎟
⎝
(2.25)
where: dp is periodic penetration depth [m].
dp =
at p
(2.26)
π
Approximate calculation of soil thermal diffusivity
The approximate calculation of soil thermal diffusivity as can be based on
measured soil temperature profiles in several depths; see e.g. (Verhoef et al., 2002). The
method is based on the analytical solution for a semi-infinite slab comparing the
amplitudes and/or phase shifts of signals in different depths. If the soil surface
temperature oscillation was compared with temperature oscillation in depth z, the
method would be expressed by the following formulas:
π⎛
⎞
z
as = ⎜⎜
⎟⎟
t p ⎝ ln ( dampening ) ⎠
as =
π⎛ z ⎞
2
(2.27)
2
(2.28)
⎜
⎟
t p ⎝ shift ⎠
where: dampening is the amplitude dampening [-] in depth z, shift is the phase
shift [rad] and tp is the period of the oscillation [s]. If the signals from two different
depths were compared, z would denote the difference between the depths.
- 18 -
2.1.5 Natural thermal regime of shallow subsurface
The estimation of natural soil thermal regime may be quite complicated and
dependent on many circumstances. Generally, the heat transfer in soils has conductive
character. The most important factors for thermal regime of soil layer near the earth
surface (depth < 15 m) are ambient air temperature, incoming solar radiation,
vegetation, and snow cover (especially for northern countries with many days with
snow cover). However, closer to the earth surface some other factors may play a
significant role, e.g. latent heat of condensation or evaporation, subsurface freezing or
thawing, evapotranspiration, subsurface moisture transfer, and heat transfer by long
wave radiation between soil surface and surrounding surfaces (the sky in particular).
“The interaction of all these variables over short and long time scales determines the
temperature of the ground as a complex (i.e. nonlinear) and complicated series of
processes”, (Beltrami, 2003). Understanding the thermal regime of soil is not important
only for the earth-to-air heat exchangers, but it can provide valuable information about
the Earth. “Temperature-depth profiles contain a robust signal of the long-term surface
temperature history”, (Beltrami, 2001). For instance, the phenomenon of global
warming has been studied with help of geothermal data.
A potential time behavior of the temperature in shallow subsurface is depicted in
Figure 2.2. The temperature of the ground two meters in depth under the surface is a
harmonic oscillation with the maximum approximately in September and minimum
approximately in March.
25
20
[°C]
15
10
5
0
-5
0
30
60
90
120
150
θ
a
180
210
θ
1.0
240
270
300
330
360
θ
2.0
Figure 2.2: Daily means of ambient air temperature θa and soil temperature in depths
1.0 m and 2.0 m (θ1.0, θ2.0); based on measured data provided by the Geophysical Institute
in Prague (http://www.ig.cas.cz/)
- 19 -
Chapter 2
Geothermal heat flow (steady state heat flow from the Earth’s interior towards
the ground) in depths usual for horizontal pipes (several meters) can be neglected, for
this heat flow is very weak (typical temperature gradient 0.3 K/100 m), compared with
much stronger vertical heat flow through the surface. The temperature in ground in
depth > 15 m is often estimated by the following linear dependence:
θ ( z ) = θ MEAN +
qg
λ
z
(2.29)
where: qg is the estimated or measured value of geothermal heat flow [W/m2], λ
is the estimated mean thermal conductivity of ground [W/m.K], θMEAN is mean surface
temperature [°C], and z is depth under the ground [m].
Moreover, the exchanger may be influenced by the level of underground water
which might extract significant portion of heat because of the horizontal water flow.
2.2 Theoretical analysis
2.2.1 Problem definition
The geometrical setup of EAHX used in the model is depicted in Figure 2.3 and
Figure 2.4.
Figure 2.3: Axonometric view of EAHX
- 20 -
Figure 2.4: Longitudinal and transversal section of EAHX
2.2.2 Heat transfer
Generally, the convective heat flow along the pipe has to be balanced with
conductive heat flow in soil. The heat transfer processes in the earth-to-air heat
exchanger may be described by three differential equations. The differential equation
(2.30) describes the heat balance of flowing air when latent heat generation is taken into
account (Figure 2.5):
∂θ a ha 2π r0
h 2π r
g l 2π r0
+
θa − a 0 θs − v
=0
∂x
ma ca
ma ca
ma ca
(2.30)
where: θa is temperature of air in the pipe [°C], θs is temperature of internal
surface of the pipe [°C], gv is condensing (+) or evaporating (-) amount of water vapour
[kg/(m2s)], these variables differ in length of the exchanger and in time; ha is air-to-pipe
convective heat transfer coefficient [W/(m2.K)], ma is air flow rate [kg/s], these
variables vary in time; l is latent heat of condensation [J/kg], ca is specific thermal
capacity of air [J/(kg.K)]; they are assumed to be constant, and ro is internal radius of
the pipe [m]. The differential equation (2.31) is the continuity (balance) equation
describing heat conduction around the pipe:
ρc p
⎛ ∂ 2θ ∂ 2θ
∂θ
= λ⎜ 2 + 2
⎜ ∂y
∂t
∂z
⎝
⎞
⎟⎟
⎠
(2.31)
where: θ is temperature of the soil [°C], ρcp is volumetric heat capacity of the
soil [J/(m3.K)], and λ is thermal conductivity of the soil [W/(m.K)]. The longitudinal
component of heat flow (along the pipe) can be neglected. A test on the influence of
longitudinal heat conduction is performed in chapter 3.1.3. The moisture transfer in
surrounding soil was neglected. Differential equations (2.30) and (2.31) are linked
together by the heat balance of internal surface (si):
- 21 -
Chapter 2
ha (θ a − θ s ) = −λ
∂θ
∂r
(2.32)
si
Figure 2.5: Heat balance on longitudinal control volume
Convective heat transfer coefficient
The earth-to-air heat exchanger usually employs longer horizontal pipes with
aspect ratio length-to-diameter in the order of hundreds. The convective heat transfer
coefficient depends on the velocity and the character of fluid flow, temperature and
geometrical conditions. Using dimensionless Nusselt number Nu [-], the heat transfer
coefficient can be calculated from the well-known formula:
ha =
Nu ⋅ λa
Dchar
(2.33)
where: λa is thermal conductivity of air [W/(m.K)], Dchar is characteristic
dimension, in this case diameter of the pipe [m]. Nusselt number for forced flow in a
long circular pipe can be calculated according to the following formula (Ashrae, 2001):
Nu = C Rem Pr n
(2.34)
where: constant C, exponents m and n are determined from experimental
measurements, Re is Reynolds number [-], and Pr Prandtl number [-]. For common
circular pipes, constant C and exponents m and n are: C = 0.023, m = 0.8, n = 0.4 for
heating, n = 0.3 for cooling. Reynolds number Re represents the ratio between inertial
and viscous (frictional) forces in the fluid:
Re =
ρ a va Dchar
µa
(2.35)
where: ρa is the density of air [kg/m3], va is average flow velocity in the pipe
[m/s], and µa is dynamic viscosity [kg/(m.s)]. Prandtl number Pr is calculated as the
- 22 -
ratio of two transport coefficients (kinematic viscosity υa [m2/s] and thermal diffusivity
aa [m2/s]):
Pr =
νa
aa
=
µ a ca
λa
(2.36)
According to (Ashrae, 2001), formula (2.34) is a good approximation in
turbulent range of 10 000 < Re < 120 000, 0.7 < Pr < 120, and L/D > 60. Thermophysical properties of air are shown in Table 2.1.
T (°C)
-10
0
10
20
30
λa
ρa
cpa
[J/kg.K]
[W/m.K]
0.023
0.024
0.025
0.026
0.026
µa
3
[kg/m ]
1.343
1.293
1.247
1.205
1.165
1005
1005
1006
1006
1007
[kg/m.s]
1.673*10-5
1.723*10-5
1.772*10-5
1.821*10-5
1.868*10-5
υa
[m2/s]
1.246*10-5
1.332*10-5
1.421*10-5
1.511*10-5
1.604*10-5
Pr (-)
0.72
0.72
0.72
0.72
0.71
Table 2.1: Thermo-physical properties of air
The value of Prandtl number is almost independent on temperature; therefore,
the influence of temperature on the value of Nusselt number can be neglected. The
values of the heat transfer coefficient are depicted in Figure 2.6 and Figure 2.7 (the air
properties were chosen for temperature 10 °C).
35
ha [W/m2.K]
30
25
20
15
150mm - c
150mm - h
200mm - c
200mm - h
250mm - c
250mm - h
10
5
100 200
300
400
500 600 700
V [m3/h]
800
900 1000
Figure 2.6: Convective heat transfer coefficient ha with respect to air flow rate and pipe
diameter; c denotes cooling, h denotes heating
- 23 -
Chapter 2
35
ha[W/m2.K]
30
25
20
150mm - c
150mm - h
200mm - c
200mm - h
250mm - c
250mm - h
15
10
5
1
2
3
4
5
6
va [m/s]
7
8
9
10
Figure 2.7: Convective heat transfer coefficient ha with respect to velocity and pipe
diameter; c denotes cooling, h denotes heating
As seen from Figure 2.7, the heat transfer coefficient is almost linear function of
the velocity. The following approximate relation (Hollmuller, 2002) could be used:
h a = 3va + 3
(2.37)
The velocity in a pipe related to air flow rate and pipe diameter is depicted in
Figure 2.8.
va [m/s]
15
150 mm
200 mm
250 mm
10
5
100
200
300
400
500 600 700
V[m3/h]
800
900 1000
Figure 2.8: The velocity va with respect to air flow rate and pipe diameter
2.2.3 Moisture transfer
The description of moisture transfer in EAHX was simplified; variations of
moisture content and latent heat effects in surrounding soil were not taken into account.
- 24 -
Basically, it is assumed that water vapour concentration in flowing air is a constant
value:
ρv = ρv,in
(2.38)
where: ρv is water vapour concentration of air in EAHX [kg/m3], ρv,in is water
vapour concentration of air at the inlet of the exchanger [kg/m3]. If the pipe is made of
plastic material with tight joints and no condensation or evaporation from wet pipe
surface occurs, the assumption (2.38) will be valid. However, if water vapour condenses
or evaporates, air will be either dehumidified or humidified. The resulting moisture
balance (Figure 2.9) on the longitudinal element is set up analogously to the heat
balance:
β 2π r0 θ s
∂ρ v β ρ 2π r0
ρv − ρ
ρ
+
=0
v , sat
Va
Va
∂x
(2.39)2
where: Va is air flow rate [m3/s], ρv,sat is saturated water vapour concentration (a
function of internal pipe surface temperature θs) a βρ is moisture transfer coefficient
[m/s].
Figure 2.9: Moisture balance on longitudinal control volume
Furthermore, it is advantageous to introduce some simplifications and
limitations:

the pipe can be wet only as a consequence of previous condensation3

water in the pipe does not move (water stays in the same longitudinal control
volume as it has condensed) and the surface of the pipe is moist uniformly4
2
If formula (2.20) was added to (2.39) the equation analogous to (2.30) would be obtained.
3
In reality, an important phenomenon might be the constant infiltration of moisture from the soil
into the pipe because of leakage in the pipe wall, (Hollmuller, 2001).
- 25 -
Chapter 2

air moistening is limited by saturated water vapour concentration
ρv ≤ ρ θa
(2.40)
v , sat
where: ρv,sat is saturated water vapour concentration (a function of air
temperature in the pipe θa).
2.2.4 Coupled heat and moisture transfer
The thermal balance of flowing air in the pipe is influenced by heat connected
with a change of phase. The thermal effect of condensation or evaporation is covered by
the last term in the differential equation (2.30).
2.3 Numerical solution
The following system of indexes is introduced: i - x axis index (along the length
of the exchanger), j – y axis index, k – z axis index, and t – time step index. Index (t - 1)
denotes previous values (preceding time step).
Basically, the exchanger may work in the following operation modes:
•
ma ≠ 0; heat exchanger is in operation, air is sucked through the pipe
•
ma = 0; heat exchanger is not in operation, and this stage is called the
natural soil recovery5
2.3.1 Stage of operation
Generally, the solution procedure within one time step of the operational stage is
divided into three sub-steps:
•
1a) the explicit calculation of new air temperature and 1b) the explicit
calculation of new water vapour concentration in air, condensing and/or
evaporating amount, and accumulated water in the exchanger
•
4
2) the explicit calculation of new soil temperature
In reality, the pipe is often sloped and water can move.
5
On the contrary, the forced soil recovery might occur when the exchanger will be operated
during a summer night (soil is cooled down by relatively cold night air).
- 26 -
•
3) the calculation of new pipe surface temperature
Calculation of new air temperature (step 1a)
The analytical solution of (2.30) can be written as:
(
)
θ a (i ,t ) = θ s ,eqv i ,t −1 + θ a(i −1,t ) − θ s ,eqv( i ,t −1) exp
(
)
−
ha 2π r0
∆xi
ma ca
(2.41)
θ s ,eqv( i ,t −1) = θ s ,mean( i ,t −1) + ∆θ s ,lat ( i ,t −1)
(2.42)
where: θs,mean is mean surface temperature in the pipe [°C] and θs,eqv is equivalent
surface temperature containing the thermal contribution of condensation or evaporation
∆θs,lat [°C].
∆θ s ,lat( i ,t −1) =
g v ( i ,t −1) ⋅ l
(2.43)
ha
1
14
2
ha [W/(m K)]
12
10
8
2
6
3
4
4
2
4
6
2
gv [g/(m s)]
5
8
67
-3
x 10
Figure 2.10: ∆θs,lat [°C] as a function of water vapor flux gv and convective heat transfer
coefficient ha
Calculation of new water vapour concentration and moisture flux (step 1b)
The analytical solution of (2.39) can be written as:
(
)
ρv (i ,t ) = ρv,sat i ,t −1 + ρv( i −1,t ) − ρv,sat(i ,t −1) exp
(
)
−
β ρ 2π r0
Va
∆xi
The possibilities which can occur are summarized in the Table 2.2.
- 27 -
(2.44)
Chapter 2
Moisture flux
Water vapour
concentration
Condition
Condensation
ρv (i −1,t ) > ρvθ,ssat (i ,t −1)
Evaporation
Dry surface
ρv (i −1,t ) < ρvθ,ssat (i ,t −1)
ρv (i −1,t ) < ρ vθ,ssat (i ,t −1)
and
Gacu (i ,t −1) > 0
and
Gacu (i ,t −1) = 0
*
ρv (i ,t ) = according to (2.44)
ρv (i,t ) = according to
(2.44)
g v (i ,t ) =
ρv (i ,t ) ≤ ρvθ,asat ρ
v (i ,t ) = ρ v (i ,t )
ρv (i ,t ) > ρvθ,asat
( ρv(i−1,t ) − ρv(i,t ) )Va
2π r0 ∆xi
g v (i ,t ) =
ρv (i ,t ) = ρvθ,asat
ρv (i ,t ) = ρv (i −1,t )
**
( ρv(i−1,t ) − ρv(i,t ) )Va
2π r0 ∆xi
g v (i ,t ) = 0
g v (i ,t ) = 0
**
Table 2.2: Condensation and evaporation in the model

* The surface of pipe is wet; Gacu is accumulated moisture [kg].

** The relative humidity must not exceed 100 %. Even if the pipe is wet,
evaporation will not occur (air is fully saturated).
Calculation of new temperature in the soil (step 2)
Soil temperature is calculated in perpendicular planes to the length of the
exchanger as shown in Figure 2.11. As a result, the 3D temperature field is calculated
using calculation in 2D. The calculation mesh is automatically generated by developed
function, denser near the pipe and the ground surface with an expansive factor towards
other boundaries.
- 28 -
Figure 2.11: Perpendicular sections along length of the exchanger.
The explicit finite difference method is used for the solution of equation (2.31).
The method is based on the calculation of new temperatures from previous temperatures
(fully explicit scheme for a discretization in time), and it is briefly introduced in
appendix A2 using the information gathered in (Rode, 1997).
A special attention has to be aimed to set up the heat balance of boundary nodes:
Pipe-to-soil boundary: mean air temperature θa,mean and the value of convective
resistance is used for constructing air/pipe-to-soil boundary condition6. Mean air
temperature in each longitudinal control volume is calculated as:
6
The approximation of air temperature in a longitudinal element by mean temperature need not
be always accurate. If one dealt with a theoretical case of very high (e.g. closed to infinity) air-to-pipe
convective heat transfer coefficient, the approximation would lead to the overestimation of heat flow
- 29 -
Chapter 2
θ a ,mean( i ,t ) =
θ a( i −1,t ) + θ a( i ,t )
(2.45)
2
The pipe is approximated by an equivalent square with a perimeter which equals
to the perimeter of the pipe. The thermal resistance of the pipe is calculated according
to (2.46).
Figure 2.12: Replacement of the pipe by an equivalent square.
R pipe
⎛
⎞
rpipe
2 D pipe ln ⎜
⎜ rpipe − t pipe ⎟⎟
⎝
⎠
=
π ⋅ λ pipe
(2.46)
The boundary at the ground surface: ambient air temperature, global solar
radiation on a horizontal plane, convective surface thermal resistance Ra (the influence
of wind), and inserted additional thermal resistance Rs representing the influence of soil
cover (vegetation, snow, defined by user) are used for constructing ambient air-toground boundary condition (Figure 2.13). Undoubtedly, the soil surface boundary
condition should also consider many other factors (see section 2.1.5). Perhaps, except
for the heat transfer via radiation, these factors influence a few upper centimeters of soil
only, for they are based on daily time scale (e.g. morning condensation followed by
evaporation). Therefore, when one deals with horizontal pipes placed in depth of several
meters under the ground, it should be possible to leave out short time scale factors
(short-term air-soil temperature coupling) out of balancing the upper soil surface
boundary condition. Their influence on the exchanger is probably minor.
between air and the ground. However, the approximation is accurate for real cases of low values of
convective heat transfer coefficient. For details see chapter 3.1.
- 30 -
Figure 2.13: The ground boundary condition.
The remaining walls of the rectangle: the vertical sides of the rectangle are
usually assumed to be adiabatic. The adiabatic boundary condition may be placed at the
bottom side of the rectangle. In some cases, this boundary may be assumed to be
isothermal (e.g. with annual mean ambient temperature).
Calculation of new pipe surface temperature (step 3)
The surface temperature of the pipe is calculated by setting up the heat balance
for the inner surface of a fictitious pipe.
2.3.2 Stage of natural soil recovery
For this mode, air in the pipe is assumed to be still. The calculation follows up
the calculation of the operation stage. The initial values of soil temperature are taken
from the previous time step (the last time step of the operation). Again, explicit finite
difference method is used for the calculation of soil temperature.
- 31 -
Chapter 2
2.3.3 Flow diagram
A flow diagram of the basic algorithm is depicted in Figure 2.14. The calculation
routine has been developed within MATLAB environment.
start
read
initial
values
list of
inputs
pipe surface temperature
soil temperature
time = 1,t
yes
ma > 0
1a, 1b
2
stage of
operation
2
natural soil
recovery
3
3
print
outputs
end
Figure 2.14: Flow diagram of the algorithm
- 32 -
2.3.4 Stability and accuracy
Using previous values for the calculation of new ones brings also some stability
problems. Except for possible numerical instability of used explicit finite difference
method, which is controlled by using stable time step (reasonably dense mesh), there is
a stability problem due to the use of old temperatures and old condensation rates
(explicit coupling in (2.41) and (2.44)).
Using preceding pipe surface temperatures may influence air temperatures in a
few time steps after the stage of natural soil recovery. Using preceding moisture fluxes
may overestimate or underestimate the latent heat of condensation with the impact on
new air temperatures. These oscillations can be limited via a calculation which repeats
basic algorithm several times per one time step (Figure 2.15). The inserted iteration loop
involves some other computational operations in the algorithm; therefore, it influences
the speed of the calculation. Generally, the iteration is appropriate to be used for
calculations of several time steps after the stage of natural soil recovery only and
perhaps for cooling calculations when latent heat effects play more important role.
The density of the mesh is also of vital importance since it influences the speed
of the calculation, accuracy, and stability of heat conduction calculation. The denser
mesh is the shorter time step we need and the longer calculation is performed.
The difference between the properties of air inside the pipe (insulation without
thermal capacity) and soil properties (a good conductor with high thermal capacity)
causes the problem with stability of heat conduction calculation during the stage of
natural soil recovery. A very short time step is necessary in order to achieve stability;
therefore, the calculation might be time consuming. The possible solution could be
either the calculation of heat conduction using the implicit method, or replacement the
inner volume of air in the pipe by soil in order to preserve the explicit calculation. The
latter way is used in the MATLAB routine.
- 33 -
Chapter 2
time = 1,t
ma > 0
θa,new
1
gv,new
θnew
2
2
natural soil
recovery
θs,new
3
3
i=1
stage of
operation
old = new
i=i+1
θa,new = f(θs,old, gv,old)
1
gv,new
2 θnew
3
θs,new
|θa,new - θa,old| < ε
v
i>n
yes
i>n
yes
print
mistake
Figure 2.15: Alternative flow diagram – iterative procedure for stage of operation
- 34 -
2.4 Summary
Based on the theory described in this chapter, a series of computer codes written
in MATLAB environment (Figure 2.16) was developed in order to deal with the
simulation of EAHXs. The main features of the model can be described as follows:

Heat transfer: The model is based on: a) the analytical solution of differential
equation describing heat balance of the exchanger longitudinal control volume of
the exchanger (sensible and latent heat is taken into account) and b) the numerical
solution of two-dimensional transient heat conduction in soil around the pipe. The
algorithm allows the calculation of air and pipe surface temperature profiles along
the exchanger, temperatures within the soil as well as extracted/injected heat
from/to soil for different inlet temperature signals and different boundary
conditions.

Moisture transfer: The model is based on the analytical solution of the
differential equation (analogy with heat transfer) describing moisture balance of
the exchanger longitudinal control volume. The moisture transfer within soil is not
included. The algorithm allows the calculation of moisture flux (condensation or
evaporation amount in the pipe), accumulated moisture in the pipe, and outlet air
relative humidity and water vapour concentration.

Coupled heat and moisture transfer: The effect of latent heat (condensation on
the pipe surface or evaporation from already wet surface) on the air balance may
be taken into account.
Automatic
grid
generator
Inputs
Input
m-file
With expansive
mesh from pipe and
the ground towards
other boundaries
From hourly
Weather data data
interpolation
Solution loop
Results
Control
schedules
Routine
Operation
Air flow rate
Figure 2.16: Structure of the calculation routine
- 35 -
Chapter 2
- 36 -
Model validation
3 Model validation
An analytical and experimental validation of the model will be introduced in this
chapter.
3.1 Flat-plate heat exchanger
The subchapter will illustrate development of the EAHX model. In fact, a
routine for the flat-plate heat exchanger (FPHX) was developed earlier than already
thoroughly described model for a simulation of EAHXs. The model of the FPHX is
simpler (but similar in principle) than more complex case of the EAHX. The study of
the FPHX surprisingly provides a good physical insight into the dynamical performance
of air-to-mass heat exchangers.
Especially, air-to-mass convective coupling was tested with the FPHX. Besides,
some other tests were performed: a) the effect of heat conduction parallel with
longitudinal axis was studied; b) the phenomenon of phase-shifting almost without
amplitude dampening was studied. The goal was to verify whether longitudinal heat
flow component is negligible or not and to verify the phenomenon of phase-shifting.
3.1.1 Problem definition
The flat-plate heat exchanger is a device depicted in Figure 3.1 and Figure 3.2. It
consists of two mass panels with vertical adiabatic sides and a gap which allows airflow
parallel with x-axis.
Figure 3.1: Axonometric view of the flat-plate heat exchanger
- 37 -
Chapter 3
Figure 3.2: Longitudinal and transversal section of the flat-plate heat exchanger
A few changes compared to the model of the EAHX have to be made in order to
describe heat transfer in the FPHX. The heat balance of the longitudinal control volume
has a similar form to equation (2.30):
∂θ a ha 2 B
h 2B
θa − a θ s = 0
+
ma ca
∂x ma ca
(3.1)
where: θa is temperature of air in the exchanger [°C], θs is temperature of
internal surface of the exchanger [°C], ha is convective (air-to-plate) heat transfer
coefficient [W/(m2.K)], ma is air flow rate [kg/s], ca is specific thermal capacity of air
[J/(kg.K)], B is width of the plate [m]. Because of the adiabatic boundary on both
vertical sides, the differential equation describing heat conduction in the panel does not
contain the y component:
ρc p
⎛ ∂ 2θ ∂ 2θ
∂θ
= λ⎜ 2 + 2
⎜ ∂x
∂t
∂z
⎝
⎞
⎟⎟
⎠
(3.2)
where: θ is temperature of the panel [°C]. These two differential equations are
linked together by the heat balance of the internal surface (si):
ha (θ a − θ s ) = −λ
∂θ
∂z
(3.3)
si
3.1.2 Numerical solution
The algorithm is similar to the already described procedure for earth-to-air heat
exchangers (see chapter 2.3); only a few changes have to be made. The temperature of
air along the pipe (the analytical solution of equation (3.1)) is calculated as:
θ a ( i ,t ) = θ s
( i ,t −1)
h 2B
− a
∆ xi
⎞ exp ma ca
+ ⎛⎜ θ a
− θs
⎟
( i ,t −1) ⎠
⎝ ( i −1,t )
- 38 -
(3.4)
Model validation
where: i is x axis index, and t – time step index. The analysis of the exponent7 in
the equation (3.4) reveals two limit cases:

If NTU is infinite, term (e-∞) will equal to zero. Such situation would refer either
to infinite convective heat transfer coefficient ha or infinite exchange surface
(infinite length or radius) or zero air flow rate ma. The solution (3.4) will be
reduced to the following form:
θout = θ s

(3.5)
If NTU is equal to zero, term (e0) is equal to one. Such situation would refer either
to zero exchange surface or zero convective heat transfer coefficient ha or infinite
air flow rate ma. The solution (3.4) will be reduced to the following form:
θout = θin
(3.6)
The temperature of the panel may be calculated in two ways: either 1D
calculation (heat flow component parallel with x axis is neglected) or 2D calculation
can be utilized. In the first case, plane xz is divided into the stripes which are separated
from each other by an adiabatic layer (Figure 3.5).
Figure 3.3: FPHX – the longitudinal control volume and 1D heat conduction in the panel
7
The exponent is called number of transfer units (NTU) in standard terminology of heat
exchangers.
- 39 -
Chapter 3
3.1.3 Test of longitudinal heat conduction
The heat flow component parallel with x axis was neglected from the analysis of
the EAHX. The test with a step change of inlet air temperature had been performed with
the model of the FPHX in order to prove such simplification.
Let no air flows through a concrete FPHX longer time. The panel has length
L = 20 m, thickness W = 1.0 m, width B = 0.3 m, cavity 0.05 m between panels, and the
isothermal boundary condition at the external surface of both panels with temperature
0 °C. The initial temperature of the panel is 0 °C. At time zero, there is a sudden change
of the inlet air temperature; the inlet air temperature is changed to 10 °C and the air flow
rate is maintained at 125 m3/h. The convective heat transfer coefficient is calculated
according to equation (2.37).
As shown in Figure 3.4, the influence of longitudinal heat flow component is
very weak. The difference of the outlet air temperature between 1D and 2D calculation
was in order of 10-4 (negligible).
x 10
10
5
7.5
4
[°C]
[°C]
-4
5
3
2
θ
2.5
in
1
θ1D
out
0
2
4
6
8
[days]
10
12
14
0
0
diff
2
4
6
8
[days]
10
12
14
Figure 3.4: Left - temperature of inlet (θin) and outlet air (θout ); right - the difference
between 2D and 1D calculation of heat conduction in the panel, diff = θout2D - θout1D
3.1.4 Phase-shifting phenomenon
The characteristic phenomenon of phase-shifting almost without amplitudedampening of input harmonic signal was most probably first formulated by (Hollmuller,
2003). A rather special combination of input harmonic oscillation, thin mass layer, large
exchange surface, external adiabatic boundary, and high convective heat transfer lead to
such dynamical balance. This phenomenon might be used as a cooling technique for
buildings in a climate with strong daily oscillation of ambient air temperature (e.g. mild
climate). (Hollmuller, 2006) dealt with a laterally insulated rectangle box filled with
- 40 -
Model validation
thermal mass through which air is sucked in order to delay input harmonic oscillation
almost without dampening. A developed analytical model is compared with
experimentally monitored performance of the material stored in the box (e.g. ceramic
balls, ceramic slabs, perforated ceramic bricks, gravel). The effort was aimed at
calibration of the analytical model and development of real-size installation for a house
(so called cool shifter).
This chapter compares the numerical simulation performed with the numerical
model of the FPHX with an analytical solution of the FPHX (Hollmuller, 2003). The
goal was to make another cross comparison and understand more deeply the dynamics
of air-to-mass heat exchangers. The analytical solution of the FPHX with harmonic
input (see appendix A1) has similar form as the analytical solution for cylindrical heat
exchanger (3.12). A small MATLAB routine was written in order to calculate the
analytical output. Different setups of the FPHX (see Table 3.1) were simulated:
•
setups with low values of convective heat transfer
•
setups with high values of convective heat transfer
•
extreme setups with very high convective heat transfer (~ closed to infinity)
Each setup (Table 3.1) was defined by a combination of dimensionless numbers
with prescribed value of the convective heat transfer coefficient. Dimensionless
numbers are defined as:
∆R0 =
W
dp
(3.7)
S
S =
Sd p
(3.8)
h
ha = a
hd p
(3.9)
where: W is thickness of the plate [m], dp is daily penetration depth [m/day],
Sdp is associated characteristic surface [m2], ha is convective heat transfer coefficient
[W/(m2.K)], hdp is conductance between inner surface of panel and penetration depth
[W/(m2.K)].
Sd p =
ma ca
hd p
(3.10)
- 41 -
Chapter 3
λ = 1,6 W/m2.K
ρ = 2300 kg/m3
Material properties
Length L [m]
Width B [m]
Discretization
c = 840 J/kg.K
ρc = 1,93 MJ/m3.K
2,0 m
0,25 m
30 control volumes
20 control volumes
60 s
z axis
x axis
Time step
ha [W/m2.K] W [m] Va [m3/h]
DAM
10,6
10,6
10,6
10,6
0,15
0,15
0,15
0,15
4
8
16
32
1
1
1
1
8
4
2
1
1
1
1
1
PS
PS 8
PS 4
PS 2
PS 1
10,6
10,6
10,6
10,6
0,03
0,03
0,03
0,03
4
8
16
32
0,2
0,2
0,2
0,2
8
4
2
1
1
1
1
1
DAM
DAM 8
DAM 4
DAM 2
DAM 1
106
106
106
106
0,15
0,15
0,15
0,15
4
8
16
32
1
1
1
1
8
4
2
1
10
10
10
10
PS
PS 8
PS 4
PS 2
PS 1
106
106
106
106
0,03
0,03
0,03
0,03
4
8
16
32
0,2
0,2
0,2
0,2
8
4
2
1
10
10
10
10
DAM
DAM 8
DAM 4
DAM 2
DAM 1
1060
1060
1060
1060
0,15
0,15
0,15
0,15
4
8
16
32
1
1
1
1
8
4
2
1
100
100
100
100
PS 8
PS 4
PS 2
PS 1
1060
1060
1060
1060
0,03
0,03
0,03
0,03
4
8
16
32
0,2
0,2
0,2
0,2
8
4
2
1
100
100
100
100
low ha
DAM 8
DAM 4
DAM 2
DAM 1
high ha
very high ha
∆R0 [-] S [-] ha [-]
PS
setup
Table 3.1: Simulated setups of FPHX; DAM denotes dampening setup, PS denotes
phase-shifting setup
As shown in Figure 3.5, the numerical simulation precisely matched the
analytical results of the case with low convective heat transfer. The simulation also
- 42 -
Model validation
~
matched the analytical results of the case with high convective heat transfer with S = 1
~
or S = 2 , Figure 3.6. However, the numerical simulation did not match the analytical
results of the case with very high convective heat transfer. In the latter case, the
performance of the exchanger seems to be flow rate independent and exchanger
geometry independent (Figure 3.7). Hence, the numerical algorithm (especially the
thermal link between air and mass) has to be reviewed again in order to make such
discrepancy clear. The numerical algorithm first calculates the mean value of the air
temperature from input and output temperature of the longitudinal control volume (see
Figure 2.11). Then, the mean air temperature together with convective resistance form
the boundary condition (coupling with mass) assigned to the longitudinal control
volume. Using the mean air temperature to construct the thermal link between air and
panel is rather a good approximation for low convective heat transfer. However, if very
high convective heat transfer occurs, the heat flow injected to panel will not be
calculated correctly. Instead of the mean air temperature with convective resistance, it
would be better to construct the thermal air-to-mass link as a boundary with heat flux
driven by temperature difference between input and output of the longitudinal control
volume. In latter case, the energy balance will always be correct.
10
7.5
5
2.5
0
-2.5
-5
-7.5
-10
0
0.5
input
1
output numerical
1.5
anal#PS1
2
anal#PS2
2.5
anal#PS4
3
anal#PS8
10
7.5
5
2.5
0
-2.5
-5
-7.5
-10
0
input
0.5
1
output numerical
1.5
anal#DAM1
2
anal#DAM2
2.5
anal#DAM4
3
anal#DAM8
Figure 3.5: Low ha – comparison of the numerical simulation (grey) with analytical
solution
- 43 -
Chapter 3
10
7.5
5
2.5
0
-2.5
-5
-7.5
-10
0
0.5
1
output numerical
input
1.5
anal#DAM1
2
anal#DAM2
2.5
anal#DAM4
3
anal#DAM8
10
7.5
5
2.5
0
-2.5
-5
-7.5
-10
0
0.5
input
1
output numerical
1.5
anal#PS1
2
anal#PS2
2.5
anal#PS4
3
anal#PS8
Figure 3.6: High ha - comparison of the numerical simulation (grey) with anal.
solution
10
7.5
5
2.5
0
-2.5
-5
-7.5
-10
0
input
0.5
1
output numerical
1.5
anal#DAM1
2
anal#DAM2
2.5
anal#DAM4
3
anal#DAM8
10
7.5
5
2.5
0
-2.5
-5
-7.5
-10
0
0.5
input
1
output numerical
1.5
anal#PS1
2
anal#PS2
2.5
anal#PS4
3
anal#PS8
Figure 3.7: Infinite ha - comparison of the numerical simulation (grey) with anal.
solution
- 44 -
Model validation
3.1.5 Summary
The simulation of the FPHX was presented. First, the comparison between the
simulation routines of the FPHX led to the conclusion that the heat conduction parallel
with longitudinal axis of air-to-mass heat exchangers is negligible. This finding was
reflected in the formulation of the model of the EAHX. Next, the results from
simulation of several FPHX setups were compared with the results calculated via
analytical solution of the FPHX. The comparison showed the imperfection of the
numerical algorithm which caused the incorrect results for theoretical cases with very
high convective heat transfer.
Further research perspectives:

It might be interesting, particularly from theoretical point of view, to deal with a
harmonic oscillation at the external boundary of the FPHX. Two driving input
signals and their conductive interaction with the mass of panels somehow form the
oscillation of the output

It might be interesting to deal with a coupled system of a solar air collector with a
storage masonry wall (FPHX). The wall is the component of a house. The
interaction of the energy producer with the wall is one problem. The interaction of
the storage wall with internal environment of the house is another complication in
analysis.
3.2 Verification exercises
3.2.1 Test of undisturbed soil temperature calculation
The calculation of natural temperature stratification in soil is partial and difficult
component of the earth-to-air heat exchanger simulation. A test of the algorithm ability
for calculation the temperature of soil was performed with weather data for Holzkirchen
(Figure 3.8; downloaded from http://www.wufi.de).
First, the soil thermal diffusivity was determined by a cross comparison between
three temperature signals (see chapter 2.1.4): i) the temperature of the surface, ii) the
temperature of the ground 0.5 m in depth under the surface, iii) the temperature of the
ground 1.0 m in depth under the surface. These signals were decomposed into annual
harmonic pulses (Figure 3.9) so that the amplitude, the phase of each pulse, yearly
- 45 -
Chapter 3
penetration depth, and thermal diffusivity of soil were determined (Table 3.2). The
range of calculated thermal diffusivities indicates that the ground was not perfectly
homogenous in the vertical direction. However, the decrease of thermal diffusivity with
depth is not standard situation since the porosity of upper layer (< 0.5 m) is typically
higher than pressed bottom layers. Therefore, the calculation of thermal diffusivity from
annual harmonics seems inaccurate.
40
35
30
25
20
[°C]
15
10
5
0
-5
-10
-15
-20
0
30
60
90
120
150
θ
180
θ
e
210
240
θ
s
270
300
330
360
θ
0.5
1.0
Figure 3.8: Holzkirchen, weather data - θe is ambient air temperature, θs is the
temperature of the ground surface, θ0.5 and θ1.0 are temperatures 0.5 m and 1.0 m in depth
under the surface
20
[°C]
15
10
5
0
-5
0
30
60
90
120
150
θ
s
180
210
θ
0.5
240
270
300
330
360
θ
1.0
θ0.5 vs. θs
θ1.0 vs. θs
θ1.0 vs. θ0.5
Phase shift
[rad]
Comparison
between
signals
Amplitude
damping [-]
Figure 3.9: Holzkirchen – decomposition of weather data into harmonics
0.8629 0.1494
Penetration depth dp
[m/year]
from
from phase
damping
shift
3.39
3.35
Thermal diffusivity as
[m2/s]
from
from
damping phase shift
1.15*10-6 1.11*10-6
0.7094 0.3506
2.91
2.85
0.85*10-6
0.81*10-6
0.8221 0.2012
2.55
2.49
0.65*10-6
0.62*10-6
mean value of soil thermal diffusivity as [m2/s]
0.86*10-6
Table 3.2: Amplitude dampening and phase shift of harmonics – calculated values
of yearly periodic penetration depth and thermal diffusivity
- 46 -
Model validation
Next, the simulation of undisturbed soil temperature was performed; the time
step of the simulation was 1200 seconds. A calculation domain was 10 m stripe (1D
heat conduction) divided into 36 control volumes (denser grid near the ground). The
bottom boundary was assumed to be isothermal with temperature equal to the annual
mean temperature of ambient air on site (6.4 °C). Soil properties were assumed as
follows: subsurface 0.5 m thick layer with thermal conductivity 2.7 W/mK and
volumetric heat capacity 2.4 MJ/m3K; remaining soil with thermal conductivity
1.5 W/mK and identical volumetric heat capacity as sub-surface layer. The balance of
the upper plane surface was set up by ambient air temperature, global solar radiation on
a horizontal plane (absorptivity α according to Figure 3.11), convective surface thermal
resistance Ra (the influence of wind, set to be constant value 0.04 m2K/W), and inserted
additional thermal resistance Rs representing the influence of soil cover (vegetation or
snow, inserted between the ground surface and the first soil node). It was supposed that
[m2K/W] or [-]
the ground was covered by snow between 21st November and 1st March.
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
30
60
90
120
150
α
180
210
240
Rs
Ra
270
300
330
360
Figure 3.10: Holzkirchen - surface resistances Rs, Ra, and absorptivity α used in the
simulation
Despite many uncertainties in input parameters (soil properties, soil cover) and
some bugs evident in measured data (sudden discontinuities in soil temperature time
profile), the trends of all simulated cases correspond with the trends of measured data,
as shown e.g. in Figure 3.11. Basic statistics of the difference (numerical - measured)
are given in Table 3.3. The temperature profile in depth of 1 m was calculated with
better accuracy than the profile closer to the surface. Probably, the closer to the surface,
the more uncertain the calculation was.
- 47 -
Chapter 3
20
[°C]
15
10
5
0
0
30
60
90
120
150
180
simulated
1.0
210
240
270
measured
1.0
θ
300
330
360
θ
Figure 3.11: Holzkirchen - comparison between numerical simulation and
measured soil temperature in depth of 1.0 m; from hourly values
20
[°C]
15
10
5
0
0
30
60
90
120
150
180
measured
0.5
210
240
270
simulated
0.5
θ
300
330
360
θ
Figure 3.12: Holzkirchen - comparison between numerical simulation and
measured soil temperature in depth of 0.5 m; from hourly values
30
25
20
[°C]
15
10
5
0
-5
-10
0
30
60
90
120
150
180
θ - simulated
s
210
240
270
θ - measured
s
300
330
360
Figure 3.13: Holzkirchen – daily means of soil surface temperature, the
comparison between numerical simulation and measured data
numerical - measured max mean min
std
from
18.66 1.53 -15.38 4.42 hourly means
θs
θ0.5
θ1.0
4.86
1.46
-2.96
1.55 hourly means
3.79
1.20
-0.76
0.96 hourly means
Table 3.3: Basic statistics of the difference (numerical – measured)
- 48 -
Model validation
Two typical situations of the ground heat balance are depicted in Figure 3.14.
The heat flux through the ground surface is depicted in Figure 3.15.
Figure 3.14: The ground heat balance; left – typical winter situation, right – typical
summer situation
40
30
[W/m2]
20
10
0
-10
-20
-30
0
30
60
90
120
150
180
210
240
270
300
330
360
Figure 3.15: Daily means of heat flux through the ground surface (q1); positive
values denote the gain (soil is heated up), negative values denote the loss (soil is cooled
down); the mean value of q1 is closed to zero
3.2.2 Test of hygrothermal calculations
Simulations presented in this chapter are supposed to examine some moisture
calculations with the model. Generally, it is better to focus on trends of output
parameters (which are expected) rather than on absolute values of output parameters
(which are uncertain). The case of dry air provides a basic case. If moist air is sucked
through the exchanger, the basic case will be deformed due to the release of latent heat
of condensation and/or consequent evaporation. Generally, the magnitude of such
deformation depends on: inlet air temperature and relative humidity, pipe surface
temperature, air flow rate, pipe length and depth, and soil properties.
A calculation domain was a block 2 m (width) x 2 m (height) x 30 m (length of
the pipe). The domain was divided into 17 x 17 x 120 control volumes. All external
- 49 -
Chapter 3
walls of the rectangle were assumed to be adiabatic. The pipe (external diameter
200 mm) was approximated by an equivalent square with perimeter which equals to
perimeter of the pipe. The time step of all simulations was 300 seconds. The soil was
assumed to have properties λ = 1.9 W/(m.K) and ρcp = 1.9 MJ/(m3.K).
Step change of inlet relative humidity
Let no air flows through the pipe longer time. The temperature of the block is
constant (13 °C). At time zero, there is a sudden change of the inlet air temperature and
relative humidity; the inlet air temperature is changed to 30 °C and relative humidity is
changed to 50 %. The air flow rate is maintained at 250 m3/h.
Figure 3.17 shows the expected performance. Warm and humid air passing
through the pipe is cooled down. Initially, water vapour condensation prevails, but the
pipe and surrounding soil are consequently warmed up. Next, evaporation prevails over
condensation until condensation fully diminishes and finally all water in tubes
evaporates.
30
[°C]
25
20
θ
out
15
θ
10
θdry
0
in
out
0.5
1
1.5
[day]
2
2.5
Figure 3.16: Temperature of inlet (θin) and outlet air (θout); index dry denotes the
simulation with dry air. The reason for the instability visible near the initial step of inlet
air temperature was described in section 2.3.4
- 50 -
Model validation
750
Gacu
[g]
500
250
0
0
0.5
1
1.5
[day]
2
2.5
Figure 3.17: Total accumulated moisture Gacu [g] in the pipe; a marker shows the
point when condensation stopped
dG
[g/timestep]
15
10
5
0
0.5
1
1.5
[day]
2
2.5
[control volumes
Figure 3.18: Moisture rate dG = Gcond + Gevap [g/timestep]; if positive, condensation
rate Gcond prevails; if negative evaporation rate Gevap prevails
100
75
50
25
0
0.5
1
1.5
[day]
2
2.5
Figure 3.19: Number of control volumes with water (120 control volumes within
the pipe)
Periodic inlet signals
Let no air flows through the pipe longer time. The temperature of the block is
constant (13 °C). At time zero, the inlet air temperature and relative humidity started to
pulsate with daily frequency as shown in Figure 3.20 and in Figure 3.21 respectively.
The air flow rate is maintained at 250 m3/h.
- 51 -
Chapter 3
θ
30
θ
[°C]
25
out
in
θdry
out
20
15
10
0
0.5
1
1.5
[day]
2
2.5
Figure 3.20: Temperature of inlet (θin) and outlet air (θout); index dry denotes the
simulation with dry air
[%]
90
80
70
rhout
60
0
rhin
0.5
1
1.5
[day]
2
2.5
Figure 3.21: Relative humidity of inlet (rhin) and outlet air (rhout)
cout
[g/m3]
17.5
cin
15
12.5
10
7.5
0
0.5
1
1.5
[day]
2
2.5
Figure 3.22: Water vapour concentration in inlet (cin) and outlet air (cout)
- 52 -
Model validation
1500
Gacu
[g]
1000
500
0
0
0.5
1
1.5
[day]
2
2.5
[g/timestep]
Figure 3.23: Total accumulated moisture Gacu [g] in the pipe
20
10
0
-10
-20
0.5
1
1.5
[day]
2
dG
2.5
Gcond(+)
Gevap(-)
[control volumes]
Figure 3.24: Moisture rate dG = Gcond + Gevap [g/timestep]; if positive, condensation
rate Gcond prevails; if negative evaporation rate Gevap prevails
75
50
25
0
0.5
1
1.5
[day]
2
2.5
Figure 3.25: Number of control volumes with water (120 control volumes within
the pipe)
The temperature of air along the pipe for three selected steps of simulation
(step 130, step 193, and step 240) is depicted in Figure 3.26, Figure 3.27, and Figure
3.28. During the simulation, the following cases occurred: a) only condensation took
place (step 130), b) only evaporation took place (step 240), and c) when both
condensation and evaporation took place (step 193).
- 53 -
Chapter 3
[g/control volume]
[°C]
30
Step 130
θmoist
a
θdry
a
25
20
15
0
0.4
5
10
15
20
25
5
10
15
20
25
30
0.3
0.2
0.1
0
0
[m]
30
Figure 3.26: Temperature of air along the pipe and condensed amount in each
control volume
[°C]
30
Step 240
25
θmoist
a
θdry
a
20
[g/control volume]
15
10
0
5
10
15
20
25
5
10
15
20
25
30
-0.25
-0.5
-0.75
-1
0
[m]
30
Figure 3.27: Temperature of air along the pipe and evaporated amount in each
control volume
[g/control volume]
[°C]
30
Step 193
θmoist
a
25
θdry
a
20
15
0
5
10
15
20
25
5
10
15
20
25
0.1
0
-0.1
-0.2
-0.3
-0.4
0
30
[m]
30
Figure 3.28: Temperature of air along the pipe, condensed and evaporated amount
in each control volume (condensation simultaneous with evaporation)
- 54 -
Model validation
3.3 Analytical validation
3.3.1 Analytical solution
The analytical solution for cylindrical heat exchanger with external adiabatic
boundary condition (Figure 3.29) and harmonic oscillation at the input was used for a
comparison with numerical calculation. The analytical output was calculated using
Excel routine designed by (Hollmuller, 2005).
Figure 3.29: Cylindrical air-to-mass heat exchanger with adiabatic boundary
The analytical solution for harmonic input with angular frequency ω
θin (t ) = θ0 cos (ωt )
(3.11)
is described by formula:
⎛ ⎛
Sh ⎞
x⎞
Sk ⎞
⎟⎟
⎟ cos ⎜⎜ ω ⎜ t − ⎟ −
⎝ ma ca ⎠
⎝ ⎝ va ⎠ ma ca ⎠
⎛
θ a ( x, t ) = θ 0 exp ⎜ −
(3.12)
where: S is heat exchange surface [m2] from the inlet to distance x, h is total
(air/pipe + soil) amplitude-dampening exchange coefficient [W/(m2.K)],
k is total
(air/pipe + soil) phase-shifting exchange coefficient [W/(m2.K)], t is time [s]. Term x/va
is time in which air flows from the inlet to distance x from the inlet (transit time).
Details to derivation of the analytical solution and the calculation of both exchange
coefficients can be found in (Hollmuller, 2003).
3.3.2 Simulation
The comparative analysis was performed for three different setups of the
cylindrical exchanger (Table 3.4). These setups cause different kinds of outlet air
temperature modulation:
- 55 -
Chapter 3

annual dampening

daily dampening

annual phase-shifting
In parallel, the choice of these setups provides a cross comparison between the
developed model and respected numerical model which was examined by identical
validation process (see Hollmuller, 2005).
Setup
Annual dampening
Daily dampening
Annual phase-shifting
r0 [m]
0.125
0.125
0.125
rad [m]
2.0
0.6
0.6
L [m]
50
50
400
External boundary
adiabatic
adiabatic
adiabatic
Table 3.4: Setups of cylindrical heat exchanger
The inlet air temperature was determined by standard annual meteorological data
for Geneva and was fully decomposed into a complete sum of harmonic pulses (4380
frequencies) through Fourier series. The setups were submitted to constant air flow rate
162.5 m3/h (200 kg/h) which induced the value 4.13 W/(m2.K) of the convective heat
transfer coefficient. Soil properties were considered to be λs = 1,9 W/(m.K),
ρcp = 1,9 MJ/(m3.K).
Two numerical calculation routines were used for the numerical simulation.
Both routines use the identical basic calculation procedure described in chapter 2.3.
They differ in the calculation of heat conduction in the cylinder. While the first routine
uses one-dimensional implicit calculation of the heat conduction within radial
coordinate r, the second routine is based on two-dimensional explicit calculation within
rectangular control volumes. In the latter case, the pipe was approximated by an
equivalent square with perimeter 4deq which equals to perimeter of the pipe 2πr0. The
equivalent square for external adiabatic boundary was derived from the condition of
identical surface areas:
d ad ,eq = rad π
(3.13)
- 56 -
Model validation
r0
rad
deq
dad,eq
Figure 3.30: Replacement of the cylinder by equivalent squares
The mesh for 2D calculations was generated so it was possible to simulate all
setups with time step of one hour. Although such time step implies rather coarse mesh
(Table 3.5), utilization of this time step is intentional for studying the influence of the
coarse grid on the accuracy of calculation.
1D radial model
Annual
dampening
Daily
dampening
number of radial control 30 (∆r = 0,067
volumes
m)
number of longitudinal 25 (∆L = 2 m)
25 (∆L = 2 m)
control volumes
2D model
Annual
dampening
y 14
z 14
number of
rectangular control
volumes
number of longitudinal 25 (∆L = 2 m)
control volumes
0.1963
deq [m]
dad,eqv [m]
3.5449
Annual phaseshifting
30 (∆r = 0,02m)
Daily
dampening
7
7
25+15 (the first 200
m ∆L = 8 m )
Annual phaseshifting
7
7
25 (∆L = 2 m)
50 (∆L = 8 m)
0.1963
0.1963
1.0635
1.0635
Table 3.5: Specification of simulations
- 57 -
Chapter 3
30
[°C] Annual dampening
1D radial model
20
20
15
10
analytical
3.3.3 Comparison analytical vs. numerical
10
0
5
-10
30
50
100
150
200
250
300
350
0
numerical
0
1D radial model
[°C] Daily dampening
20
20
15
10
5
10
5
10
5
10
15
20
analytical
0
10
0
5
-10
0
30
50
100
150
200
250
300
[°C] Annual phase-shifting
350
numerical
0
1D radial model
15
20
analytical
0
20
20
15
10
10
0
5
numerical
-10
0
50
Tinletmax
100
Tinletmin
150
num Toutletmax
200
250
num Toutletmin
300
anal Toutletmax
350
0
0
anal Toutletmin
daily min
15
20
daily max
Annual dampening
from daily min
200
100
50
100
150
200
250
300
350
0
-0,3-0,2-0,1 0 0,1 0,2 0,3
Daily dampening
from daily min
200
[1/year]
from daily max
100
from daily max
50
100
150
200
250
300
350
0
-0,3-0,2-0,1 0 0,1 0,2 0,3
200
[1/year]
0.3
0.2 [°C]
0.1
0
-0.1
-0.2
-0.3
0
0.3
0.2 [°C]
0.1
0
-0.1
-0.2
-0.3
0
0.3
0.2 [°C]
0.1
0
-0.1
-0.2
-0.3
0
[1/year]
Figure 3.31: 1D radial model – comparison with analytical; Left - comparison
between numerical simulation (grey thick) and analytical solution (black thin) for
different configurations of cylindrical heat exchanger with external adiabatic boundary
conditions – daily values of maximal and minimal inlet and outlet temperatures; Right –
scatter plot numerical vs. analytical (from daily maximal and minimal values)
100
50
100
150
200
250
300
350
0
-0,3-0,2-0,1 0 0,1 0,2 0,3
Figure 3.32: 1D radial model - comparison with analytical; Left – error
propagation during the year, error is defined as: err = (numToutlet - analToutlet); Right –
histogram of error’s frequency (grey – error calculated from daily maximums; black –
error calculated from daily minimums)
- 58 -
[°C] Annual dampening
30
2D model
analytical
Model validation
20
20
15
10
10
0
5
numerical
-10
30
60
90
120
150
180
210
240
270
300
360
2D model
[°C] Daily dampening
30
330
0
0
5
10
5
10
5
10
15
20
analytical
0
20
20
15
10
10
0
5
numerical
-10
30
60
90
120
150
180
210
240
270
300
[°C] Annual phase-shifting
30
330
360
2D model
0
0
20
20
15
10
15
20
analytical
0
10
0
5
numerical
-10
0
30
60
Tinletmax
90
Tinletmin
120
150
180
num Toutletmax
210
240
num Toutletmin
270
300
anal Toutletmax
330
360
0
0
anal Toutletmin
15
daily min
20
daily max
[°C]
100
50
from daily min
60
90
120
150
180
210
240
270
300
330
360
Daily dampening
0
-1
150
100
-0,5
0
0,5
1
-0,5
0
0,5
1
0
0,5
1
[1/year]
0
30
0.5
0.4 [°C]
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0
30
0.5
0.4
[
°C]
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0
30
Annual dampening
from daily max
50
60
90
120
150
180
210
240
270
300
330
360
0
-1
100
50
60
90
120
150
180
210
240
270
300
330
360
0
-1
[1/year]
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
[1/year]
Figure 3.33: 2D model; Left - comparison between numerical simulation (grey
thick lines) and analytical solution (black thin lines) for different configurations of
cylindrical heat exchanger with external adiabatic boundary conditions – daily values of
maximal and minimal inlet and outlet temperatures; Right – scatter plot numerical vs.
analytical (from daily maximal and minimal values)
-0,5
Figure 3.34: 2D model - comparison with analytical; Left – error propagation
during the year, error is defined as: err = (numToutlet - analToutlet); Right – histogram of
error’s frequency (grey – error calculated from daily maximums; black – error calculated
from daily minimums
- 59 -
Chapter 3
3.3.4 Summary
The comparison between numerical simulation and analytical solution
demonstrated the perfect agreement of numerical simulation with analytical model.
Even if quite a coarse mesh was used in the 2D routine, high accuracy was achieved.
This confirmed that the basic part of the algorithm (local heat transfer near pipe) works
properly.
The third setup of the exchanger (400 m pipe length and 0.60 m soil radius)
resulted into an atypical performance. The outlet air temperature was dampened
similarly to daily dampening setup (50 m length and 0.60 m soil radius), but the output
signal was shifted much more. Probably, such strong phase-shifting was firstly
introduced in (Hollmuller, 2003). The phenomenon also has more realistic daily mode
(not so long tube) and it is intended to use it for cooling of buildings (Hollmuller, 2005).
3.4 Experimental validation
The capability of the model will be demonstrated by its application on
simulation of two monitored real-size EAHXs. First, the long-term thermal simulation
will be compared with basic measurement on a low-energy house. The sensitivity
analysis will be performed as a part of simulation. Second, the short-term hygro-thermal
simulation will be compared with measured data on passive house in Rychnov.
3.4.1 Long-term thermal simulation
Measurement in-situ
A low-energy family house equipped with mechanical ventilation, heat recovery,
and a simple earth-to-air heat exchanger has been monitored since the end of summer
2004. The description of the house is to be found in appendix A3. The scheme of the
monitored system with placement of sensors is shown in Figure 3.35. Table 3.6
provides a basic description of the EAHX.
- 60 -
Model validation
Figure 3.35: House W – the scheme of ventilation system with placement of sensors
Number of pipes
1
Air flow rate
[m3/(h.pipe)]
100 – 350, higher
values for summer
ventilation
Length of pipe [m]
21
Soil
Diameter [mm]
200
Control strategy
Depth [m]
1,9
Location
no data
According to θa and Velké Popovice,
link with actual mode central Bohemia,
of the ventilation near Prague
unit*
Table 3.6: House W - description of the EAHX
* In reality, the operation of the EAHX is not only the function of the ambient
air temperature, but it also depends on the actual ventilation mode. The ventilation
system in house W may be operated in five basic modes, see (Tywoniak et al, 2007).
Simulation
A calculation domain was a block 8 m (width) x 5 m (height) x L (length of the
pipe). The domain was divided on 17 x 15 x 21 control volumes. The pipe was
approximated by an equivalent square with perimeter which equals to perimeter of the
pipe. The material of the pipe was neglected. The upper edge of the equivalent square
had distance Zp from the upper side of the rectangular section (soil surface). The
simulations were performed according to a schedule as shown in Table 3.7; the time
step of the simulation was 1200 seconds. The influence of the inlet shaft was not
simulated; the inlet air temperature was equal to measured ambient air temperature. The
inlet air was assumed to be absolutely dry. A boundary condition for soil surface was
set up by ambient air temperature, global solar radiation on a horizontal plane (assumed
constant 80% absorptivity for solar radiation), convective surface thermal resistance
(the influence of wind, assumed to be constant value 0,04 (m.2K)/W) and inserted
- 61 -
Chapter 3
additional thermal resistance Rs representing the influence of soil cover (vegetation,
snow, determined by user defined function). Other walls of the rectangle were assumed
to be adiabatic.
Ini*
start
30.8. 2004
125
1.1.
125
25.2.
125
7.3.
0
25.5.
350
1.6.
0
25.7.
350
finish
23.8. 2005
0
Table 3.7: The specification of the simulation
* Ini denotes the initiation of the simulation. The initiation period is the
simulation of two years without the influence of the EAHX. Thus, soil temperature field
is influenced only by upper soil surface boundary; geothermal heat flow was omitted,
too. The main purpose of the initiation is to build up the undisturbed soil temperature
field as accurately as possible. The blue fields in Table 3.7 denote the intermittent
operation of the EAHX; suction of air through the EAHX was started when ambient air
fell below 0 °C, and disrupted when ambient air temperature exceeded 5 °C. The orange
fields denote the identical EAHX operation as monitored. The number in the frame is
the air flow rate in (m3/h).
Sensitivity analysis
Sensitivity analysis is the important part of the model validation. The analysis
should help to identify input parameters to which the model outputs are particularly
sensitive and to get parameters to which the outputs are not sensitive. It is especially
important to identify sensitive input parameters with high uncertainty.
The method of Differential Sensitivity Analysis (Lomas, Eppel, 1992) was used.
The method is based on varying just one input parameter for each simulation while
remaining inputs stay fixed at their most likely base case values (BC). The range of
input parameter represents input uncertainty. The change in predicted output parameter
∆pi represents an effect of uncertainty in i - th input parameter:
∆pi = pi − pBC
(3.14)
First, the sensitivity of the annual soil temperature amplitude θsoilA (°C) to
uncertainty in input parameters (parameters 1 to 6 in Table 3.8) was studied. The soil
temperature is monitored in the first soil control volume above the equivalent pipe
during the second year of the initiation. Such soil temperature represents undisturbed
- 62 -
Model validation
soil temperature during a year in depth closed to the place where the EAHX is buried.
Next, the sensitivity of the total energy Eeahx (kWh/a) delivered to and extracted from
soil during the simulated period (30.8.2004 – 23.8.2005) to uncertainty in all input
parameters (Table 3.8) was studied. The effect of spatial and time discretization was not
studied; it was assumed that the grid was generated dense enough to produce correct
results.
1 λs [W/mK]
2 ρcp [MJ/m3K]
b
-1.0
BC
1.5
a
+1.0
note
range of common soils
-1.5
3.0
+1.5
range of common soils
+0.2
3 θin
[°C]
-0.2
from measurement
4 Ig
[W/m2]
-3 %
from measurement
5 Rs
[m2K/W]
-50 %
UDF
6 Zp
[m]
-0.25
2.0
7 L
8 Va
[m]
[m3/h]
9 ha
[W/m2K]
-3.0
-25
-50
-25 %
21
125
350
calculation
Nu
measurement
uncertainty
+3 % measurement
uncertainty
+50 % UDF is user defined
function, guess
+0.25 pipe slope
+3.0
+25
+50
from +25 %
pipe length
pre-heating guess
cooling
guess
Table 3.8: Uncertainties in input parameters
λs
ρ
cp
ρcp
as*10-6 bs
[W/mK]
1.5
2.5
0.5
1.5
1.5
[kg/m3]
2000
2000
2000
2250
1500
[J/kgK3]
1500
1500
1500
2000
1000
[MJ/m3K1]
3.0
3.0
3.0
4.5
1.5
[m2/s]
0.50
0.83
0.17
0.33
1.00
[Ws0,5/m2K]
2121
2739
1225
2598
1500
SC1 2.5
2250
2000
4.5
0.56
3354
SC2 0.5
1500
1000
1.5
0.33
866
BC
1a
1b
2a
2b
Table 3.9: Soil properties in simulation. SC denotes superior case
Soil temperature calculated during the initiation of simulations is depicted in
Figure 3.36. The effect of input uncertainties monitored on the value of the annual soil
amplitude (4.7 °C for BC) is illustrated in Figure 3.37, left. Uncertainties assumed in
soil properties (Table 3.9) have the strongest impact; the undisturbed soil temperature
- 63 -
Chapter 3
strongly depends on the value of the soil thermal diffusivity and resulting upper soil
surface temperature.
25
θsoil [°C]
20
15
10
5
30.8.2004
0
23.8.2005
30
60
BC
90
1a
120
1b
150
2a
180 210
t [days]
2b
6a
240
270
300
330
6b
4o
5o
6o
357
Figure 3.36: Soil temperatures θsoil (°C) calculated during initiation of the
simulation; 4o is BC without solar radiation; 5o is BC with Rs assumed to be a constant
value 1.0 m2KW-1; 6o is BC with pipe buried in depth 0.5 m
a
b
+2.0
+1.5
+20
∆Eeahx [kWh/a]
+0.5
4.9
a
∆θsoil [°C]
+1.0
-0.5
-1
451
-20
-40
-60
-80
-1.5
-2
a
b
+40
-100
λs
1
ρ cp
θin
Ig
Rs
Zp
2
3
4
5
[input parameters]
6
λ s ρ cp θin Ig Rs Zp L
1 2 3 4 5 6 7
[input parameters]
Va ha
8
9
Figure 3.37: The effect of uncertainties in inputs monitored on the annual soil
temperature amplitude θasoil (left) and total energy delivered to or extracted from soil
(right)
The effect of input parameters uncertainties monitored on the value of total
energy injected and extracted from the soil (451 kWh for BC) is shown in Figure 3.37,
right and in Figure 3.38. The positive and negative changes to the input parameters do
not affect the predicted value Eeahx by similar amount. The model (i.e. the earth-to-air
heat exchanger) behaves as a nonlinear system. The reaction of the model to change of
soil properties is strongly non-linear. The reaction of the model to change of length, air
flow rate, and depth is weakly non-linear.
- 64 -
Model validation
Although the undisturbed soil temperature is the most stable in case 1b (the
lowest value of the soil thermal diffusivity), this particular advantage does not
overweight poor thermal transport near the pipe. The performance of cases 2a and 1a
need another comment. Although the value of the soil thermal conductivity of case 2a is
lower than in case 1a, case 2a shows the overall thermal performance better than case
1a. Both cases have similar soil thermal effusivity; however, case 2a has the value of the
soil thermal diffusivity much lower than case 1a. Thus, the undisturbed soil temperature
of case 2a is more dampened than in case 1a, and this particular advantage is probably
the most decisive. Conclusively, a relatively thin cylinder surrounding the pipe having
high thermal conductivity combined with semi-infinite body having low thermal
diffusivity could lead to some improvement of EAHX.
500
[kWh/year]
400
300
200
100
0
BC
1a
1b
2a
2b
SC1
SC2
Figure 3.38: House W - the effect of uncertainties in soil properties monitored on
the value of total energy injected and extracted from the soil (451 kWh for BC)
The non-linear reaction of the model to uncertainties in the inlet air temperature
(cases 3a, 3b) is not caused by non-linear effects of the model. The temperature of the
inlet air is a parameter which governed whether the EAHX was turned on, or turned off.
As a result, the different operation patterns were executed, and consequently, the
different portion of heat was extracted from and injected to soil.
Comparison simulation vs. measurement
Several measurement data can be used for a comparison with the model
prediction. The following time intervals with characteristic pulses (intermittent
operation of EAHX) were chosen in order to compare the simulation with measured
data: a) 25.2. – 6.3.2005, and b) 25.7. – 31.7.2005. The first interval is the last term of
- 65 -
Chapter 3
air pre-heating during winter 2004/2005, and the second interval is the second hot spell
of summer 2005 (air cooling). The comparison of measured outlet air temperature with
simulated values is in Figure 3.39 and in Figure 3.40. The results of variants with the
most significant uncertainties are depicted too. Those variants form the interval in
which all simulation results were found.
8b
5
θ (°C)
0
1b
-5
-10
25.2
26.2
27.2
28.2
θ
in
1.3
θ
2.3
out
3.3
BC
4.3
1b
5.3
6.3
8b
Figure 3.39: 25.2. – 6.3.2005; measured inlet (θin) and outlet (θout) air temperatures
vs. simulated outlet air temperature (BC, 1b, 8b); no suction if θin = θout
θ (°C)
30
1b
25
7a
20
15
25.7
26.7
27.7
θ
in
28.7
θ
out
29.7
BC
30.7
1b
31.7
7a
Figure 3.40: 25.7. – 31.7.2005; measured inlet (θin) and outlet (θout) air
temperatures vs. simulated outlet air temperature; no suction if θin = θout
- 66 -
Model validation
Continuous mode
The continuous mode of the operation (suction over all year) is studied with
different values of air flow rate (125 and 350 m3/h). The influence of the continuous
operation of the EAHX on the soil temperature may be significant, especially during
winter (Figure 3.41). If the inlet air temperature is lower (cooling season) or higher
(pre-heating season) than actual soil temperature, the recovery of soil induced by air
flow rate (forced soil thermal recovery) takes place. The forced soil recovery is more
common during summer. The soil near the pipe is cooled down by suction of colder
night air or during colder spells in summer. Therefore, the soil temperature remained
oscillating roughly around the undisturbed soil temperature profile in summer season.
20
θ (°C)
15
10
5
0
30.8.2004
30
23.8.2005
60
90
120
θ
150
180
(BC)
undisturbed
210
θ350
soil
240
270
θ125
300
330
357
soil
Figure 3.41: Continuous operation - soil temperature in the reference point;
θundisturbed(BC) is temperature calculated during initiation of BC simulation, θsoil350 is soil
temperature in the reference point - air flow rate 350 m3/h, θsoil125 is soil temperature in the
reference point - air flow rate 125 m3/h; the reference point is located 0.5 m from the inlet
in depth of 1.9 m – the first control volume above the pipe
Intermittent mode
The process of natural soil recovery in intermittent mode is quite rapid,
especially immediately after turning the exchanger off (Figure 3.42). The effect of such
recovery is surprisingly comparable with the effect of recovery induced by air flow.
Roughly, majority of a thermal pulse is removed in period four times longer than the
length of pulse. During spring or autumn, when no air is sucked through EAHX, the soil
temperature is progressively restored to undisturbed profile, as shown in Figure 3.42
(seasonal heat storage is ineffective).
- 67 -
Chapter 3
20
θ (°C)
15
10
5
0
30.8.2004
30
23.8.2005
60
90
120
θ
150
180 210
θ (BC)
(BC)
undisturbed
soil
240
270
on/off
300
330
357
Figure 3.42: Intermittent operation - soil temperature in the reference point;
θundisturbed(BC) is temperature calculated during initiation of BC simulation, θsoil(BC) is soil
temperature in the reference point (BC simulation, intermittent operation according to
Table 3.7);the reference point is located 0.5 m from the inlet in depth of 1.9 m – the first
control volume above the pipe
The example with more significant thermal charge of soil (no suction within the
interval of ambient air temperature between 5 °C and 19 °C) illustrates previous
conclusion (Figure 3.43).
20
θ (°C)
15
10
5
30.8.2004
0
30
23.8.2005
60
90
120
θ
150
180 210
θ
(BC)
undisturbed
soil
240
270
on/off
300
330
357
Figure 3.43: Intermittent operation, more significant thermal charge - soil
temperature in the reference point; θundisturbed(BC) is temperature calculated during
initiation of BC simulation
Conclusions
On the basis of presented results, the following conclusions were formulated:
- 68 -
Model validation

Because of relatively low air-to-soil heat flows and the intermittent pattern of
operation, the accurate simulation of the EAHX is rather difficult. The relative
error of the model prediction can be high.

The quality of the model prediction is dependent on the accurate estimation of the
natural thermal stratification in soil during the initiation of the simulation. The
natural thermal performance of shallow subsurface governs the long-term thermal
performance of the EAHX. The operation of the EAHX disturbs the natural
thermal stratification of soil and governs the short-term thermal performance of
EAHX (heat injection/extraction, natural soil recovery).

The accuracy of the numerical model was rather destroyed by uncertainties in
several input parameters (primarily soil properties and the air flow rate which are
almost always uncertain). Even more simplified models might be suitable for the
simulation of the EAHX. Perhaps, they will not be so sensitive to input parameters
uncertainties. Despite of their simplicity, they could be sufficiently accurate.

The numerical model brings clear information about processes which take place
during the operation of EAHX and allows rather detailed analysis. The perfect fit
between measured data and simulation results is not from this point of view so
important.

Rather good accuracy of the numerical simulation was achieved, as shown in
comparison with measured data. However, such comparison is not considered to
be a sufficient experimental validation of the model because the air flow rate was
not directly measured (the value in simulation of BC was tuned).
Summary
The long-term simulation of a simple real-size EAHX was presented in the
chapter. Measured data of ambient air temperature, solar radiation and EAHX operation
served as input parameters to series of simulations. First, the simple differential
sensitivity analysis of the model was performed. Next, the comparison of the measured
data with simulation was done. Then, the thermal charge of soil as a result of different
operation modes (continuous, intermittent mode) was discussed. Finally, principal
conclusions regarding to the accuracy of performed numerical simulation were
presented.
- 69 -
Chapter 3
3.4.2 Short-term hygro-thermal simulation
Measurement in-situ
For details about measurement see chapter 4 and also appendix A4.
Simulation
The simulation performed with the developed numerical model focuses on
hygro-thermal performance of the open loop mode during a) ten-day summer term from
13.6.2006 to 22.6.2006 (term 1) and b) three-day summer term from 15.7.2007 to
17.7.2007 (term 2). The terms are typical by very high ambient air temperature and
intensive EAHX operation during daytime periods.
The inlet air temperature and relative humidity were equal to measured values in
the inlet shaft (position 2, Figure 4.1). One pipe of the exchanger only was simulated.
The thermal influence of the neighbouring pipe was not included into the simulation.
The time step used for the simulation was 5 minutes. Although moisture flows were
calculated, generation of latent heat was not considered.
Term 1: A calculation domain was a soil block 1.18 m (width) x 1.18 m
(height) x 23 m (length of the pipe) with external adiabatic walls. The block was
divided into 17 x 17 x 46 control volumes. The initial soil temperature was assumed
8.5 °C in all control volumes of the block (the value was tuned).
Term 2: A calculation domain was a soil block 2 m (width) x 5 m (height) x
23 m (length of the pipe). The block was divided into 20 x 38 x 46 control volumes. The
bottom and vertical boundaries were assumed to be adiabatic. The upper boundary was
formed by measured values of soil temperature in depth of 1 m. The initial soil
temperature matrix was built up by the numerical simulation (the initiation of the
simulation).
Comparison simulation vs. measurement
The output parameters from the short-term simulation were compared with
measured parameters. The correspondence of the model prediction with measurement is
obvious (Figure 3.44 to Figure 3.49).
- 70 -
Model validation
θout [°C]
relative frequency [%]
17
simulated
16
15
14
13
12
11
12.5
10
7.5
5
2.5
11 12 13 14 15 16 17
measured
-2
-1
0
+1 +2
numerical-measured
Figure 3.44: Term 1 - outlet air temperature θout. Left - scatter plot measured vs.
simulated. Right – relative frequency of difference between simulated and measured
values
3
ρ v,out [g/m ]
14
simulated
13
12
11
10
9
8
8
12.5
10
7.5
5
2.5
9 10 11 12 13 14
measured
-1.5 -1 -0.5 0 +0.5+1+1.5
numerical-measured
Figure 3.45: Term 1 - outlet air water vapor concentration ρv,out. Left - scatter plot
measured vs. simulated. Right - relative frequency of difference between simulated and
measured values
dG [g/(min.pipe)]
15
simulated
10
5
0
-5
-5
0
5
10
measured
12.5
10
7.5
5
2.5
-4 -3 -2 -1 0 +1+2+3+4
numerical-measured
15
Figure 3.46: Term 1 - overall moisture rate dG. Left - scatter plot measured vs.
simulated. Right - relative frequency of difference between simulated and measured values
- 71 -
Chapter 3
20
19
18
17
16
15
14
13
12
11
simulated
θout [°C]
12.5
10
7.5
5
2.5
11 12 13 14 15 16 17 18 19 20
measured
-2
-1
0
+1 +2
numerical-measured
Figure 3.47: Term 2 - outlet air temperature θout. Left - scatter plot measured vs.
simulated. Right – relative frequency of difference between simulated and measured
values
3
15
14
13
12
11
10
9
8
simulated
ρ v,out [g/m ]
8
12.5
10
7.5
5
2.5
9 10 11 12 13 14 15
measured
-1.5 -1 -0.5 0 +0.5+1+1.5
numerical-measured
Figure 3.48: Term 2 - outlet air water vapor concentration ρv,out. Left - scatter plot
measured vs. simulated. Right - relative frequency of difference between simulated and
measured values
dG [g/(min.pipe)]
15
simulated
10
5
0
-5
-5
0
5
10
measured
12.5
10
7.5
5
2.5
15
-4 -3 -2 -1 0 +1+2+3+4
numerical-measured
Figure 3.49: Term 2 - overall moisture rate dG. Left - scatter plot measured vs.
simulated. Right - relative frequency of difference between simulated and measured values
- 72 -
Model validation
Conclusions
On the basis of the presented results, the following conclusions were formulated:

The accuracy of moisture calculations is very dependent on the accurate
calculation of heat transfer.

Although the absolutely perfect agreement was not achieved, the model shows
good consistency (the trends are similar).

The influence of latent heat transfer due to condensation and/or evaporation inside
the pipe is still unclear. As shown by both measurement and simulation,
condensation and consequent evaporation evidently occur inside the pipe.
However, the measured outlet air temperature tended to be lower than simulated
when latent heat was taken into account.
Summary
The short-term simulation of a simple real-size EAHX was presented in the
chapter. Measured data of inlet air temperature, soil temperature and EAHX operation
served as input parameters to series of simulations. The comparison between simulation
and measurement serves as an experimental validation of the model.
3.5 Parametric analysis
The hygro-thermal performance of the validated model is evaluated by a
parametric analysis. The method is based on varying just one input parameter (see Table
3.10) for each simulation while remaining inputs stay fixed (at so called base case). The
analysis should help to identify input parameters to which the model outputs are
sensitive and demonstrate the model reaction on change of input parameters.
3.5.1 Simulation
A simple (and therefore predictable) basic situation, the step-change of inlet air
temperature or humidity, was simulated. At time zero, there is a sudden change of the
inlet air temperature (θin) or inlet air humidity (ρv,in). A calculation domain was a block
(1 + deq) m x (1 + deq) m x L m (length of the pipe). All external walls of the block were
assumed to be adiabatic. The block was assumed to have thermal conductivity λs and
- 73 -
Chapter 3
volumetric heat capacity ρcp. The initial temperature of the block (θini) was constant.
The pipe (with wall thickness tp and thermal conductivity λp) was approximated by an
equivalent square with perimeter which equals to perimeter of the pipe. The time step of
all simulations was 300 seconds.
Two types of simulation were performed:

Latent heat was not considered. Although moisture flows were calculated,
generation of latent heat was not considered.

Latent heat was considered. Generation of latent heat affects the thermal
performance of EAHX. Because of latent heat release, condensed amount is lower
(reverse link) compared to the latter type of simulation.
Figure 3.50 shows the typical situation during five days (simulation period) after
initial step-change (see also chapter 3.2.2). Initially, water vapour condensation
prevails, but the pipe and surrounding soil are consequently warmed up. Next,
evaporation prevails over condensation (“evap over cond”) until condensation fully
diminishes (“cond stop”). Finally, all water in tube evaporates (“evap stop”).
3000
2000
↑ Gacu,cond
evap over cond
cond stop
[g]
1000
← Gacu
evap stop
0
-1000
← Gacu,evap
-2000
-3000
0
1
2
3
4
5
[days]
Figure 3.50: Total accumulated water Gacu [g] in the pipe
Gacu = Gacu ,cond + Gacu ,evap

(3.15)
where: Gacu,cond is cumulative total condensed amount of water vapour [kg],
Gacu,evap is cumulative total evaporated amount of water vapour [kg] and Gacu is
total accumulated water in the pipe [kg].
- 74 -
Model validation
3.5.2 Input parameters
The range of climate input parameters (θin, ρv,in, θini) covers likely situation in
summer. For instance, the range of inlet water vapour concentration could be typical in
summer for climate of middle Europe (Czech Republic, Germany, Austria, etc.). The
range of initial block temperature covers summer soil temperature increase typical for
depth of two meters. The range of soil input parameters (λs, ρcp) covers all soil types
(lower values for dry soils, higher for moist soils, for details see appendix A5). The
range of exchanger key design parameters (air flow rate Va, length L) covers some
design alternatives, i.e. from undersized (L = 10 m, Va = 400 m3/h) to slightly oversized
alternatives (L = 40 m, Va = 100 m3/h). The range of two remaining design parameters
(diameter d0, thermal conductivity of pipe material λp) was chosen so as to cover
standard diameters and materials (thermal conductivity of PVC is approximately
0,10 W/(m.K)).
exchanger
2
climate
inlet
soil
1
3
4
5
6
7
8
9
λs
ρcp
θini
θin
ρv,in
d0
Va
L
λp
10 tp
unit
[W/(m.K)]
lower
-67 % -1,0
BC
1,5
upper
+1,0 + 67 %
step
0,25
[MJ/(m3.K)] -50 %
-1,0
2,0
+1,0
+50 %
0,5
[°C]
-25 %
-3,0
12,0
+3,0
+25 %
1,0
[°C]
-20 %
-5,0
25
+5,0
+20 %
2,5
[g/m3]
-11 %
-1,5
14,0
+1,5
+11 %
0,5
[m]
[m3/h]
[m]
[W/(m.K)]
-25 % 0,15
-60 % -150
-60 % -15
-67 % -0,1
0,20
250
25
0,15
0,25
+150
+15
+0,1
+25 %
+60 %
+60 %
+67 %
0,05
50
5
0,05
[m]
-
-
0,005 +0,005 +100 % 0,005
Table 3.10: Perturbation of input parameters; BC denotes base case
3.5.3 Monitored outputs
The following outputs from simulation were monitored:

Energy injected through exchange surface A to surrounding soil block per period
of simulation in [kWh/period]
Eeahx = ∫ Qeahx dt

(3.16)
Specific energy injected to surrounding soil block (related to exchange surface A)
per period of simulation in [kWh/(m2.period)]
- 75 -
Chapter 3
A
=
eeahx

Eeahx
A
(3.17)
Total condensed amount per period of simulation in [kg/period]
Gcond ,tot = max ( Gacu ,cond )
(3.18)
3.5.4 Results
The values of monitored inputs and outputs were relativized (related to BC
simulation) in order to allow direct comparison. Both sensitivity and non-linearity may
be evaluated. Sensitivity is defined as the first order derivative of sensitivity curve (the
steeper curve, the higher sensitivity). Non-linearity is defined as curvature of sensitivity
curve.
The effect of perturbation of input parameters on the value of energy injected to
rel. change in output parameter [%]
the surrounding soil block is shown in Figure 3.51.
+50
λs
ρcp
+25
θini
θin
0
ρv,in
d0
L
Va
-25
-50
λp
-50 -25
0 +25 +50
rel. change in input parameter [%]
tp
BC
Figure 3.51: Eeahx – parametric study. Dotted curves denote the cases when latent
heat was taken into account
The most sensitive input parameters are inlet air temperature and actual soil
temperature (initial temperature of simulation). These parameters are influenced by
climatic locality and therefore cannot be designed. Length and air flow rate are the most
sensitive design parameters. The remaining design parameters (diameter, thermal
conductivity of pipe wall, soil properties) are less sensitive. For instance, the effect of
pipe thermal conductivity difference is rather small and almost negligible (keeping in
mind low pipe wall thickness for BC).
- 76 -
Model validation
The effect of perturbation of input parameters on the value of specific energy
injected to the surrounding soil block is shown in Figure 3.52. The relation to the
exchange surface was used because the value of specific energy evaluates the design
effectiveness (i.e. taking into account the material spent on). As seen in Figure 3.52,
length and diameter perform inversely compared to the latter case (Figure 3.51).
+50
λs
ρcp
+25
θini
θin
0
ρv,in
d0
L
Va
-25
-50
Figure 3.52:
λp
-50 -25
0 +25 +50
eAeahx
tp
BC
– parametric study. Dotted curves - latent heat taken into
account
The parametric analysis also identified input parameters to which condensed
amount (moisture performance) of EAHX is particularly sensitive. The effect of
perturbation of input parameters on the value of total condensed amount is shown in
Figure 3.53.
λs
+700
ρcp
+600
θini
+500
+400
θin
+300
ρv,in
+200
d0
+100
L
Va
0
-50
λp
-50 -25
0 +25 +50
tp
BC
Figure 3.53: Gcond,tot – parametric study. Dotted curves - latent heat taken into
account
- 77 -
Chapter 3
The moisture performance is much more sensitive to change of input parameter
than thermal performance. The most sensitive parameters, which dominantly influence
moisture performance, are instantaneous soil temperature (initial temperature of
simulation) and temperature and humidity of inlet air. Therefore, risk of water vapour
condensation is higher during spring when soil is cooled down after winter season. Low
inlet air temperature leads to lower outlet air temperature and thus to higher risk of
condensation. High air humidity is also a very important factor, especially
simultaneously with low inlet air temperature.
3.5.5 Conclusions
Because EAHX performance is nonlinear, it is easier to deteriorate the
performance (inherently) than to improve. Moisture performance of EAHX is inherently
linked with thermal performance, i.e. air temperature drop (saturation limit) is related to
instantaneous humidity of inlet air. Daily oscillation of ambient air temperature and
humidity, instantaneous soil temperature (link to annual soil temperature oscillation and
EAHX previous operation), configuration of the pipe (diameter, length, air flow rate),
and thermal properties of soil near pipe plays an important role role. It seems that
condensation inside EAHX might occur rather frequently in climate of middle Europe
and probably can not be absolutely eliminated by EAHX design. Therefore, the
inspection of real size EAHXs with a camera and some microbial investigations would
be very valuable. Mould growth inside pipes should be still questionable, although the
several existing studies, e. g. (Fluckiger, 1999), have not confirmed any hygienic
problems.
3.6 Summary
The chapter dealt with model validation. First, some verification exercises were
performed. The aim of these tests was to validate two basic parts of the model: air-toground heat transfer near the pipe and coupling with the ground surface. Then, the
model predictions were compared with:

the analytical solution for cylindrical heat exchanger

the measured data on two monitored real-size EAHXs
- 78 -
Model validation
The model showed perfect agreement with the analytical solution and
satisfactory agreement with experimental data. Finally, the validated and verified model
was submitted to series of simulation leading to straightforward parametric analysis.
- 79 -
Chapter 3
- 80 -
Measurements in situ
4 Measurements in situ
The aim of this chapter is the evaluation of some measured data collected during
year 2006 and 2007 and subsequent generalization.
4.1 Introduction
The passive family house (see appendix A4) ventilated by mechanical
ventilation equipped with heat recovery and a simple earth-to-air heat exchanger is
being monitored since summer 2005. The scheme of the ventilation system is displayed
in Figure 4.1. Table 4.1 provides a basic description of EAHX. The extensive
monitoring is primarily aimed at operating the ventilation system linked with EAHX.
Measured data are collected in the main data logger (measuring step 1 min) and
three other independent data loggers (measuring step 5 min). The first one is placed
directly in the inlet shaft (position 2 in Figure 1); the second one is a living room data
logger collecting parameters of indoor air (temperature, relative humidity, and CO2
concentration). The third data logger collects undisturbed soil temperature from several
depths under the surface (5, 30, 62, 105 cm). For the list of sensors see appendix A4.
Figure 4.1: The scheme of ventilation system with position of sensors; the closed
loop mode of EAHX (circulation of internal air through the EAHX)
- 81 -
Chapter 4
Number of pipes
2
Air flow rate [m3/h]
115 – 410, higher
values for summer
ventilation
Length of pipe [m]
23
Soil
Clay*
λs = 1,39 W/(m.K)
ρcp = 2,23 MJ/(m3.K)
Diameter [mm]
200
Control strategy
According to
ambient air
temperature and
link with the actual
mode of the
ventilation unit
Depth [m]
1.0 and 2.0
Place
Rychnov near
Jablonec nad
Nisou, North
Bohemia
Table 4.1: The description of EAHX; *Homogenous moist clay; the thermal properties are
based on samples taken from a borehole drilled to depth of one meter
The mechanical ventilation system offers five ventilation modes divided into
two air flow rate levels and three special modes switched on by external signals (e.g. by
usage of W.C., bathroom, cooking in a kitchen). The more detailed description of the
ventilation system is presented in (Tywoniak et al, 2007).
EAHX may be operated in two principally different modes:

Circulation of air between the ventilated zone and the EAHX (closed loop mode,
experimentally used for cooling, see Figure 4.2, left).

Direct suction of air through the EAHX (open loop mode, usual option used for air
pre-heating and cooling, Figure 4.2, right).
The closed loop mode of the exchanger was experimentally installed by placing
a removable elbow (from 11.7.2006 to 10.9.2006).
elbow
datalogger
Figure 4.2: The inlet shaft; Left – the closed loop mode with a removable elbow;
Right – open loop mode
The short step of measurement allows the accurate determination of the
ventilation mode. Therefore, it allows the precise determination of time intervals when
EAHX was in operation and the determination of corresponding value of the air flow
- 82 -
rate. The monitoring of air relative humidity also allows the determination whether air
flowing through the pipe was moistened (the moisture deficit indicates that
condensation within the pipe prevailed).
4.2 Soil
4.2.1 Thermal properties
The three soil samples from different depths were taken during installment of
temperature sensors in the borehole (18.12.2006).
Figure 4.3: Installment of soil temperature sensors in the borehole
The thermal parameters of samples were measured by a portable heat transfer
analyzer ISOMET. The results are shown in Table 4.2. It is recognizable that the value
of thermal diffusivity slightly increases with depth. This should be caused by higher
porosity of upper soil layers.
sample
depth
30 cm measurement 1
measurement 2
50 cm measurement 1
II.
measurement 2
95 cm measurement 1
III.
measurement 2
mean values
I.
λ [W/(m.K)] ρcp [MJ/(m3.K)]
1,26
1,43
2,29
1,23
1,61
1,41
1,39
2,45
2,26
2,18
2,06
2,33
2,06
2,23
as [m2/s]
0,51*10-6
0,63*10-6
1,05*10-6
0,59*10-6
0,69*10-6
0,68*10-6
0,62*10-6
Table 4.2: Thermal properties of soil samples; the first measurement of sample 2
was excluded from calculation of the mean values
- 83 -
Chapter 4
4.2.2 Soil temperature
30
25
[°C]
20
θs2.0m
15
10
5
0
-5
0
30
60
90
θa
120
150
0.05m
θs
180
0.3m
θs
210
240
270
0.6m
θs
300
330
360
1.0m
θs
Figure 4.4: Soil temperatures in 2007 – depths 0.05, 0.3, 0.6, 1.0 m are measured
values. Temperature in depth of 2 m was calculated using measured temperature in depth
of 0.3, 0.6, 1.0 m (grey stripe represents uncertainty of calculation).
4.2.3 Approximate calculation of soil thermal diffusivity
The soil thermal diffusivity was also calculated by comparison of daily
amplitudes between measured temperature signals in depth of 5 cm and 30 cm. The
temperatures from March 2007 to May 2007 (Figure 4.5) were used for the analysis.
The soil thermal diffusivity calculated by this method is shown in Figure 4.6.
θ
θ [°C]
20
θ
5 cm
30 cm
15
10
5
0 1.3.07
0
1.4.07
31
[days]
1.5.07
61
Figure 4.5: Soil temperatures measured from 1.3.2007 to 1.5.2007
- 84 -
92
-6
x 10
as
mean
as [m2/s]
1
0.75
0.5
0
0
1.3.07
1.4.07
31
1.5.07
61
[days]
92
Figure 4.6: Soil thermal diffusivity as calculated from amplitude damping
4.3 External environment
4.3.1 Ambient air temperature
The daily and night ambient air temperature overlaps (Figure 4.7 and Figure 4.8)
illustratively show three hot spells during summer. The overlaps clearly illustrate the
potential duration of air cooling in the EAHX which might occur for up to 10 hours
assuming cooling set point 24 °C.
12
10
6 - 18 h
>24 °C
>28 °C
>32 °C
[hours]
8
6
4
2
V.
VI.
VII.
VIII.
IX.
Figure 4.7: Daily temperature overlaps (6 – 18 h) over the period (V. – IX.2006)
The night temperature overlaps show up to 4 hours of possible air cooling
assuming cooling set point 24 °C. On the other side, ambient air temperature below
16 °C is rare during hot nights so that the potential of direct night cooling (i.e. open
window) is quite low in hot days.
- 85 -
Chapter 4
12
18 - 6 h
>16 °C
>20 °C
>24 °C
10
[hours]
8
6
4
2
V.
VI.
VII.
VIII.
IX.
Figure 4.8: Night temperature overlaps (18 – 6 h) over the term (V. – IX.2006)
Assuming pre-heating set point temperature 0 °C, the occurrence of ambient air
temperature lower than pre-heating set point leads to approximately 1500 hours suitable
for air pre-heating. Assuming cooling set point temperature 24 °C, air cooling would be
useful for approximately 500 hours (see Figure 4.9).
30
[°C]
20
Pre-heating
10 potential
~ 1500 h
Cooling
potential
~ 500 h
0
-10
θ sorted
a
-20
cooling setpoint
pre-heating setpoint
10
20
30
40
50
60
70
duration [%], 100 % = 8220 h
80
90
Figure 4.9: Sorted ambient air temperature (from 2006)
4.3.2 Ambient air water vapour concentration
The daily overlaps of ambient air water vapour concentration shows that the
absolute humidity of air is the highest during hot spells (i.e. in time when cooling of air
in EAHX might be needed).
- 86 -
12
6 - 18 h
3
>10 g/m
10
3
>12 g/m
3
[hours]
8
>14 g/m
6
4
2
V.
VI.
VII.
VIII.
IX.
Figure 4.10: Daily ambient air water vapour concentration overlaps (6 – 18 h) over
the term (V. – IX.2006)
4.3.3 Tendency of EAHX to condensation
Due to damping of soil mass, soil temperature is substantially lower than
ambient air temperature in summer. Simultaneously, absolute humidity of air is the
highest during summer. The tendency to condensation was evaluated with measured
data, see Figure 4.11 and Figure 4.12.
17.5
15
ρv,a
ρv,sat(θs,depth)
↓ 1.0m
3
[g/m ]
12.5
10
7.5
5
↑ 2.0m
← daily mean
ρv,a > ρv,sat(θs,2.0m)
2.5
V.
VI.
VII.
VIII.
07
07
[V. - IX. ]
IX.
Figure 4.11: Water vapour concentration of ambient air ρv,a and saturated water
vapour concentration ρv,sat as a function of soil temperature θs,depth, measured data in 2007
Condition ρv,a > ρv,sat occurred roughly 1300 h (~54 days) for depth of 2 m, and
613 h (~25 days) for depth of 1 m. As seen in Figure 4.12, evaporation (negative deficit)
cannot frequently occur during hot days of summer term (condition θa > 24 °C). It
means that during hot spells (air is sucked through EAHX) moisture will tend to
accumulate in the exchanger.
- 87 -
Chapter 4
12.5
θa>24°C
10
7.5
5
2.5
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
3
deficit [g/m ]
Figure 4.12: Relative frequency of difference between water vapour concentration
of ambient air and saturated water vapour concentration for soil temperature in depth of
2 m (measured data May – September 2007), deficit = ρv,a - ρv,sat(θs,2.0m)
4.4 Earth-to-air heat exchanger
4.4.1 Example of measured data
The example of time daily profiles measured on EAHX is depicted in Figure
4.13. The left column shows day 20.6.2006 with open loop mode of EAHX, the right
column shows day 19.7.2006 with closed loop mode of EAHX.
The performance of the open loop mode (Figure 4.13, left column) shows a quite
significant (and surprising) cooling effect of the inlet shaft itself; the response of the
outlet air temperature on the change of air flow rate is also visible, but not so evident.
Since the value of the convective heat transfer coefficient is only slightly non-linear
function of the air velocity (in the expected range of air flow rates), the cooling effect in
case of doubled value of air flow rate is, from the short-term perspective, only slightly
reduced (see Figure 4.13, left column). The difference between the inlet air water
vapour concentration and outlet air water vapour concentration indicates prevailing
condensation within pipes. The amount of condensed water is in order of several
kilograms per day. Because of the lower soil temperature and consequent higher
temperature drop of outlet air, the pipe buried in depth of two meters tends to stronger
condensation than the upper pipe.
- 88 -
θ
25
θ
θ
30
shaft,2
out,3
25
out,1
θ [°C]
θ [°C]
30
θ
θ
ambient
20
15
θ
θ
θ
ambient
shaft,2
out,3
in,1
20
15
200 m3/(h.pipe)
111 m /(h.pipe)
401 m3/(h.pipe)
221 m3/(h.pipe)
3
0
8
12
[hours]
16
20
24
0
4
v,ambient
12
[hours]
16
20
24
8
12
[hours]
16
20
24
8
12
[hours]
16
20
24
v,ambient
ρ
13
ρ
16
ρ
12
ρ
15
ρ
v,shaft,2
v,out,3
v,out,1
14
13
11
v,shaft,2
v,out,3
ρ
v,in,1
10
9
12
8
11
0
8
ρ
ρ
ρ [g/m3]
v
ρ [g/m3]
v
17
4
4
8
12
[hours]
16
20
24
0
4
14
-2
-4
10
dG [g/min]
dG [g/min]
12
8
6
-6
-8
-10
4
2
0
dG3
-12
dG1
-14
4
8
12
[hours]
16
20
24
0
dG(1+3)
4
Figure 4.13: The measured temperature θ, water vapour concentration ρv and
corresponding overall moisture rate dG during two selected days; the overall moisture
rate is the sum of condensation and evaporation rate within the whole pipe (positive value
denotes prevailing condensation within the pipe); the left column represents day 20.6.2006
(open loop mode), the right column represents day 19.7.2006 (closed loop mode), the
values measured by logger placed in the removable connection elbow (position 2) are
influenced by unwanted air suction due to the leaky wall of elbow (e.g. see measured
profile ρv,shaft,2)
The example of closed loop mode (Figure 4.13, right column) leads to totally
different moisture performance than the open loop mode. Although the outlet air
temperature is similar to the case of open loop mode, there is a negative moisture
- 89 -
Chapter 4
balance between inlet and outlet. The difference between inlet air (the air sucked from
the building) and outlet air water vapour concentration indicates prevailing evaporation
within pipes. The moisture present in the pipes is likely the result of previous open loop
mode operation (prevailing condensation). The movement of water towards the inlet
shaft is probably quite slow due to the surface tension so that some water stays inside
the pipes and only a limited amount of water is drained into the inlet shaft. The rate of
water uptake (evaporation) is lower in comparison to condensation rate. Probably, this
might occurs due to the active area which is limited to thin stripe of water at the bottom
of the pipe.
4.4.2 EAHX operation
EAHX operation pattern is important for understanding time scales of thermal
process. The pattern is rather important for a correct choice of the simulation time step.
The operation pattern of EAHX is driven by the following:

Ambient air temperature drives the position of EAHX damper (before entering air
handling unit).

An algorithm of control system drives the ventilation mode (see appendix A4,
Table A5).
Two typical days of EAHX operation based on the monitoring of the family
house in Rychnov are depicted in Figure 4.14 (14.1.2007, pre-heating mode) and in
Figure 4.15 (20.6.2007, cooling mode).
Pre-heating mode
Generally, there is a tendency to ventilate as less as possible with respect to the
desired reduction of ventilation heat loss and the acceptable level of air internal relative
humidity during winter time (not to extract too much moisture from the internal air).
The ventilation, however, should be sufficient respecting necessary supply of fresh air.
Therefore, the typical operation of EAHX in pre-heating mode is very intermittent. The
vertical stripes represent the feature of automatic cyclic ventilation (order of minutes
per hour) of the house in the night. The EAHX operation visible near the noon is the
ventilation induced by preparation of lunch. The evening operation represents the
ventilation due to presence of people in the house.
- 90 -
The average air change rate (over 14.1.2007) was 30 m3/h (0,12 1/h) only. The
air flow rate seems rather low. However, assuming certain value of air infiltration and
intermittent occupation of the house (4 persons, each 12 hours per day) the air flow rate
related to one person is 20 m3/h approximately.
1
0
0
4
8
12
"14.1.2006"
16
20
24
Figure 4.14: Intermittent pattern of operation typical during heating period
The intermittency of the operation could cause some problems to simulation. If
one wanted to be correct, it would be necessary to use very short time step of the
simulation (approximately 5 min for simulation of pre-heating mode). However, the
shortest thermal pulse lasts a few minutes and the pulse is followed by soil thermal
recovery which is much longer than the pulse itself. Therefore, the thermal impact on
the surrounding soil of such pulses should be negligible.
Cooling mode
The operation in cooling mode is not as intermittent as in the pre-heating mode.
It is usually concentrated on daytime during a hot spell. Generally, there is a tendency to
ventilate as much as possible with respect to desired reduction of cooling load.
1
0
0
4
8
12
"20.6.2006"
16
20
24
Figure 4.15: Typical pattern of operation during cooling period
Annual statistic
The daily sum and monthly sum of operation hours as measured during 2006 are
depicted on Figure 4.16 and Table 4.3.
- 91 -
Chapter 4
24
missing
data
[hours/day]
20
closed
loop
16
12
open
loop
8
preheating
4
1.12.2006
1.11.2006
1.10.2006
1.9.2006
1.8.2006
1.7.2006
1.6.2006
1.5.2006
1.4.2006
1.3.2006
1.2.2006
1.1.2006
0
Figure 4.16: Daily hours of operation (2006)
month [h/month]
1
2
3
4
5
6
7
8
9
10
11
12
pre-heating
open loop
148.5
140.1
164.7
64.6
5.1
2.4
0
0
0
3.9
48.1
200.5
cooling
open loop
0
0
0
0.1
2.8
120.8
29.4
0
23.1
0
0
0
cooling
closed loop
0
0
0
0
0
0
124
3.9
0
0
0
0
missing
data
1.1
179.4
45.6
2.0
81.6
2.1
0.2
69.3
133.1
0.5
0.1
32.1
TOTAL [h/year]
778
176
128
547
Table 4.3: Monthly hours of operation (2006)
4.4.3 Outlet air temperature
The temperature plot (Figure 4.17) illustrates the long-term temperature
dynamics of EAHX. The profile of outlet air temperature is similar to theoretical
undisturbed soil temperature profile. Because of to the link with the upper plane surface,
the temperature slowly decreases during winter and slowly increases during summer.
- 92 -
30
10
θ [°C]
θout [°C]
20
ol
ol
cl
0
30
θa
20
θs
10
0
-10
-10
-20
-20
-20 -10
0 10 20 30
θin [°C]
2.0m
0
50 100 150 200 250 300 350
t [days]
Figure 4.17: Left - scatter plot inlet air temperature θin vs. outlet air temperature
θout; right – outlet air temperature compared to ambient air temperature θa (hourly
means) and undisturbed soil temperature in depth of 2 m θs2.0m (see chapter 4.2.2); the
values of outlet air temperature are daily means over the EAHX operation (ol – open loop
(bottom pipe, see Figure 4.1), cl - closed loop); based on measured data in 2006
When evaluating outlet air temperature (EAHX cannot reach efficiency over
100 %), one has to consider the inaccuracy of daily mean values. One reason for the
inaccuracy is the following. Because of very short ventilation pulses taking place during
winter (see Figure 4.14) and the inertia of temperature/humidity sensors, daily mean
values of outlet air temperature are overestimated during winter.
4.4.4 Moisture balance
The outlet air water wapour concentration illustrates the long-term moisture
dynamics of EAHX. As seen in Figure 4.18 and Figure 4.19, no condensation or
evaporation takes place during winter period of air pre-heating; the pipe is perfectly dry.
During summer the outlet air water vapour concentration (Figure 4.18) is often lower
than inlet air water vapour concentration since condensation occurs.
Since the closed loop mode was used in the second half of summer, the outlet air
temperatures were higher than during open loop mode operation as the outlet air
temperature follows the undisturbed soil temperature profile (link with the upper plane
surface). The tendency to condensation was the strongest at the beginning of summer
when the soil is cold.
- 93 -
Chapter 4
20
ol
ol
cl
ρ v,a
ρ v,sat(θs,2.0m)
15
3
ρ v [g/m ]
15
3
ρ v,out[g/m ]
20
10
10
5
5
0
0
5
10
15
3
ρ v,in [g/m ]
20
0
0
50 100 150 200 250 300 350
t [days]
Figure 4.18: Left – scatter plot inlet air water vapour concentration ρv,in vs. outlet
air water vapour concentration ρv,out; right – outlet air water vapour concentration
compared to ambient air water vapour concentration ρv,a (hourly means) and saturated
water vapour concentration as a function of soil temperature in depth of 2 m ρv,sat(θs,2.0m)
2
10
ol
ol
cl
1
0
-1
dG(1+3) [kg/day]
3
3
ρ v,in - ρ v,out [g/m ]
4
7.5
ol
ol
cl
5
2.5
-2
0 2 4 6 8 10 12 14 16
3
ρ v,in [g/m ]
0
0 2 4 6 8 10 12 14 16
3
ρ v,in [g/m ]
Figure 4.19: Left – water vapour concentration in the inlet air ρv,in vs. the
difference between inlet and outlet water vapour concentration (ρv,in - ρv,out), the positive
values denote prevailing condensation within the pipe; right – water vapour concentration
in the inlet air ρv,in vs. overall moisture rate dG (if positive, condensation prevails within
the pipe); all depicted values are daily means over the EAHX operation
4.4.5 Energy performance
Energy injected to/extracted from soil Eeahx is depicted in Figure 4.20. Moreover,
for terms I. – IV., and X. – XII., there is depicted the energy recovered by heat recovery
Erec (calculated for the assumption of efficiency 85 % and balanced air flows), and
energy of additional heating Eheat in order to heat up air to 23 °C (assumed interior
temperature).
The control system of ventilation system restrains air flow rate during winter in
order to overcome too dry air inside. As mean ambient air absolute humidity rises
- 94 -
during spring the control system enhances ventilation. Thus, as seen in Figure 4.20,
ventilation heat loss was higher during spring than during winter.
cooling (+)
ol
15
Eeahx
10
Eeahx
E [kWh/day]
cl
Erec
5
Eheat
0
no data
-5
-10
-15
heating (-)
0
30
60
90
120 150 180 210 240 270 300 330 360
t [days]
Figure 4.20: Daily energy balance (2006); energy to cover ventilation heat loss Ev =
Eeahx + Erec + Eheat, Eeahx – contribution of the EAHX (energy injecteded to/extracted from
soil), Erec – contribution of heat recovery, Eheat – necessary contribution of additional
heating; superscript ol an cl denotes open loop and closed loop
5
2
1.75
1
0.75
0
-1
0.5
-5
2
3
1.25
20
15
1.5
ol
ol
cl
surface fit
10
VaA [(m /day)x m ]
Eeahx [kWh/day]
x 10
5
0.25
-20
-15
-10
-5
0
5
(θin - θout) [°C]
10
15
20
Figure 4.21: Daily energy Eeahx injected to (+)/extracted from (-) soil sorted by difference
between inlet and outlet air temperature (θin - θout) and parameter VaA (daily sum of air
flow times exchange surface), points denote measured values, contour lines estimate a
surface on a 2d grid (based on scattered data, smoothed)
The thermal performance of the EAHX could be further evaluated by specific
energy injected/extracted to/from surrounding soil (related to exchange surface A (here
34 m2 including the inlet shaft) and air flow rate Va). Unit may be defined in the
following way [(Wh/period)/(m2.m3/period) = Wh/m5], or in [J/m5]. The quantity
includes information about exchanger design (exchange surface consists of pipe length
- 95 -
Chapter 4
and diameter) and exchanger operation (daily sum of air flow) as well. It is the measure
of how large exchange surface and high air flow rate is paid for release of energy per
period of time. The parameter might allow a comparison between different EAHXs
cooling
5
pre-heating
-20
-10
0
10
(θin - θout) [°C]
VaA
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
eeahx [Wh/m ]
VaA
5
eeahx [Wh/m ]
(based on monitored data or simulation).
ol
ol
cl
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
cooling
pre-heating
-20
-10
0
10
(θin - θsoil) [°C]
20
ol
ol
cl
20
Figure 4.22: Specific energy sorted by difference between inlet and outlet air temperature
(left) and by difference between inlet air and undisturbed soil temperature (right). Outlet
air temperature from autumn 2006 was excluded from this analysis due to obvious
inconsistency (see Figure 4.17, right)
The value of cooling power is of particular interest (building cooling load is
3100 W). Cooling power typically varied between 700 W and 1500 W depending
strongly on the value of air flow rate (see Figure 4.23 and Figure 4.24). Cooling energy
should not be confused with energy injected to soil. Although the air may be cooled
down in EAHX, the instantaneous temperature in a building θi could be even lower than
the outlet air temperature and therefore cooling of building would not occur.
1500
Qcooling [W]
1250
1000
27.6. - 221m3/h
26.6. - 401 m3/h
750
500
250
0
25
26
[°C]
θTi i[°C]
27
Figure 4.23: Cooling power of EAHX sorted by internal air temperature θi in two
days of summer 2006 (26.6 and 27.6) for two air flow rate levels
- 96 -
1500
Qcooling [W]
ol
cl
no data
1000
500
V.
VI.
VII.
VIII.
IX.
Figure 4.24: Cooling power of EAHX during summer 2006; calculated for
θi = 26 °C
4.5 Conclusions
The impact of air pre-heating in EAHX on ventilation heat loss is not high,
especially compared to energy which may be recovered by heat recovery. However, the
EAHX serially connected with mechanical ventilation system equipped by heat
recovery will protect heat recovery from ice formations occurring in colder climates
(Heidt et al, 2002).
The impact of air cooling on internal environment may be substantial. Cooling
power of EAHX is the matter of dimensioning. However, in this small family house, the
value of air flow rate and thus cooling power is very limited by available fun power
(400 m3/h). Therefore, the value of cooling load should be primarily reduced by
building-energy concept.
Monitoring on real-size EAHX in Rychnov is still ongoing. There is still some
work to be done. Since only some measured data were evaluated, generalization of
measured data was not performed perfectly and knowledge is still rather dispersed.
4.6 Summary
The chapter dealt with measurements in-situ performed on real-size EAHX.
First, measured soil temperatures and thermal properties of soil were analyzed. Then,
the tendency to condensation in EAHX was shown using measured soil temperature and
ambient air temperature and humidity. Finally, the measured data on earth-to-air heat
exchanger were evaluated.
- 97 -
Chapter 4
- 98 -
Dimensioning of EAHXs
5 Dimensioning of EAHXs
The following chapter focuses on development of a simple method for design of
optimal dimensions of EAHXs. The characteristic problem of the EAHX design is
whether the extension of the pipe and/or addition of another pipe (decrease of air flow
rate per one pipe) will lead to the thermal improvement which will balance the increase
of investment costs. Therefore, a design methodology will be developed in order to
facilitate the design of EAHX.
The length of the pipe, diameter of the pipe, and the number of pipes are the
main design parameters. The air flow rate is not typical design parameter because the
maximal value is usually known before. The highest value of air flow rate is usually
needed during summer in order to release sufficient cooling power of EAHX. The
design value of air flow rate can be derived from standard calculation of building
cooling load or it is the value which can be realized by the ventilation system.
5.1 Theory
5.1.1 Outlet air temperature
Assuming constant surface temperature along the length of exchanger, the outlet
air temperature may be calculated as:
θout = θ s + (θin − θ s ) exp − NTU
(5.1)
where: NTU (number of transfer units) is dimensionless parameter defined as:
NTU =
ha 2π r0 L
ma c a
(5.2)
where: ha is air-to-pipe convective heat transfer coefficient [W/(m2K)], see
chapter 2.2.2, ma is air flow rate [kg/s], ca is specific thermal capacity of air [J/(kg.K)],
ro is internal radius of the pipe [m], and L is length of pipe [m].
- 99 -
Chapter 5
The thinner pipe leads to moderate increase of NTU (i.e. increase of thermal
efficiency)8, for the enhanced convective heat transfer coefficient prevails over the
reduction of diameter. The statement may be proved by analysis of formula (5.2).
Increase in air flow rate does not decrease the value of NTU considerably (see
Figure 5.1). An increase in air flow rate and/or reduction of diameter increase the value
of convective heat transfer coefficient, which compensates, to certain extent, the
influence of air flow rate increase on NTU parameter. However, an increase in air flow
rate and/or reduction of diameter increases pressure loss extensively. Therefore, as a
general rule, it is convenient to split air flow rate into more pipes with minimal diameter
and length leading to the sufficient thermal efficiency, reasonable pressure loss, and
desired value of cooling power. On the contrary, the higher number of pipes is in
conflict with economical restrictions and often with space restrictions of the building
site.
3
100 m /h
3
5
5
500 m /h
3
1000 m /h
4
NTU [-]
NTU [-]
4
3
3
2
2
1
1
5
10
15
20
L = 5m
L = 25m
L = 50m
25 30
L[m]
35
40
45
50
100 200 300 400 500 600 700 800 900 1000
3
Va [m /h]
Figure 5.1: Parameter NTU as a function of length L and air flow rate Va
5.1.2 Temperature efficiency
The temperature efficiency of EAHX ηEAHX shows how far the temperature of
the outlet air came close to the pipe surface temperature θs:
η EAHX =
θin − θ out
θin − θ s
(5.3)
Adding formula (5.1) to formula (5.3) the following formula is obtained:
8
This conclusion is valid as far as semi-empirical calculation of convective heat transfer
coefficient is accurate.
- 100 -
η EAHX = 1 − exp − NTU
(5.4)
1,0
0,9
0,8
ηEAHX [-]
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5
NTU [-]
5
Figure 5.2: Thermal efficiency of EAHX ηEAHX as a function of NTU
As seen in Figure 5.2, the higher NTU, the higher efficiency will be achieved.
The combination of low air flow rate with a very long pipe maximizes the value of
NTU. However, from certain value of NTU (approximately 2.0 – 2.5), the efficiency
curve rapidly flattens. Therefore, the parameter NTU should not exceed 2.5. However,
NTU is a “static” parameter which does not reflect the transient nature of EAHX - the
thermal saturation of surrounding soil due to the operation of EAHX and consequent
decrease of efficiency. Especially, high air flow rates combined with too short pipes
could lead to quick thermal saturation of the pipe surrounding and consequent loss of
1,0
1,0
0,9
0,9
0,8
0,8
0,7
0,7
0,6
0,6
ηEAHX [-]
ηEAHX [-]
thermal efficiency.
0,5
0,4
0,3
0,3
3
0,2
500 m /h
0,1
3
1000 m /h
5
0,4
3
100 m /h
0,2
0,5
10 15 20 25 30 35 40 45 50
L [m]
0,1
L = 5m
L = 25m
L = 50m
100 200 300 400 500 600 700 800 900 1000
3
Va [m /h]
Figure 5.3: Efficiency as a function of length L and air flow rate Va
5.1.3 Pressure loss
The pressure loss in a straight pipe may be calculated as:
- 101 -
Chapter 5
∆p fric = ξ
v2
L
ρa a
2r0
2
(5.5)
where: va is mean air velocity [m/s], ρa is density of air [kg/m3], ξ and is friction
factor in a hydraulic smooth pipe which may be calculated as (De Paeppe, Janssens,
2003):
−2
ξ = (1.82log Re− 1.64 ) for Re > 2300
(5.6)
5.1.4 Cooling power
Although the air may be cooled down in EAHX, the instantaneous temperature
in a building θi could be even lower than the outlet air temperature and therefore
cooling of building would not occur. Thus, heat flow QEAHX injected to soil can not
substitute the cooling power Qcooling.
The heat flow QEAHX is defined as:
QEAHX = ma ca (θin − θ out )
(5.7)
Adding formula (5.1) to formula (5.7) the following formula is obtained:
QEAHX = ma ca (θin − θ s )η EAHX
(5.8)
The cooling power of EAHX (having θi temperature of internal air) is defined
as:
Qcooling = ma ca (θi − θ out )
(5.9)
3
Qcooling [W]
2000
100 m /h
2500
3
500 m /h
3
2000
1000 m /h
Qcooling [W]
2500
1500
1000
500
1500
1000
500
0
0
-500
-500
5
10 15 20 25 30 35 40 45 50
L [m]
L = 5m
L = 25m
L = 50m
100 200 300 400 500 600 700 800 900 1000
3
Va [m /h]
Figure 5.4: Cooling power as a function of length L and air flow rate Va. Cooling
power was calculated for the following boundary conditions: θin = 32 °C, θs = 16 °C
(constant over the length of exchanger), θi = 26 °C and r0 = 0,1 m. The negative values of
θcooling denote heating of the zone (θi < θout)
- 102 -
5.1.5 Hollmuller design rules
In his doctoral thesis, (Hollmuller, 2002) recommends to meet the following
conditions (Table 5.1).
va [m/s]
daily dampening
annual dampening
2
3
2
1,0
1m for 10 m /h (Va/A = 10) 1m for 5 m3/h (Va/A = 5)
2,0
1m2 for 15 m3/h (Va/A = 15) 1m2 for 7 m3/h (Va/A = 7)
4,0
1m2 for 20 m3/h (Va/A = 20) 1m2 for 10 m3/h (Va/A = 10)
Table 5.1: Hollmuller’s design rules (Hollmuller, 2002)
Daily dampening denotes dampening of daily ambient air temperature oscillation
which occurs naturally during summer. Annual dampening denotes dampening of
annual ambient air temperature oscillation. If a design for long-term air heating (e.g.
seasonal pre-heating of air for an air-to-fluid heat pump) is intended, the rules for
annual dampening should be applied. The rules are also depicted as the bottom line in
Figure 5.11.
5.2 Simulations
Some simulations were performed in order to study several special setups of
EAHX, i.e. simulations testing a) Hollmuller design rules, b) dimensioning according to
curve of constant NTU, c) dimensioning according to line of constant Va/A. Moreover,
the distance between pipes for case of standard summer EAHX operation and the
influence of pipe wall material on thermal performance of EAHX was studied.
A calculation domain was a block 1 m (width) x 1 m (height) x L m (length of
the pipe). The domain was divided into 19 x 19 x 25 control volumes. All external walls
of the rectangle were assumed to be adiabatic. The pipe (external diameter 200 mm)
was approximated by an equivalent square with perimeter which equals to perimeter of
the pipe. The time step of simulation was 600 seconds. The soil was assumed to have
properties λ = 1.5 W/(m.K) and ρcp = 2.0 MJ/(m3.K). The initial temperature of the
block was constant (16 °C). At time zero, there was a sudden change of the inlet air
temperature; the inlet air temperature was changed to 24 °C and started to oscillate
periodically with amplitude 8 °C and period of 1 day. An intermittent operation of
EAHX was assumed when the air was sucked through the exchanger if θin > 24 °C
(12/12 h).
- 103 -
Chapter 5
5.2.1 Hollmuller design rules
alternative
1
2
3
3
Va [m /h]
100 200 400
va [m/s]
1.0 2.0 4.0
L [m]
17.0 22.6 33.9
3
2
Va/A [m /h/m ] 10
15
20
Table 5.2: Hollmuller design rules – simulation alternatives (for internal diameter
do = 188 mm, i.e. DN 200)
θin
θ [°C]
30
θout,1
θout,2
25
θout,3
20
15
1
2
3
4
5
t [days]
Figure 5.5: Hollmuller design rules – the inlet θin and outlet θout air temperature
5.2.2 Constant NTU
alternative
1
2
3
4
Va [m /h]
100 200 300 400
L [m] for NTU = 2.0 22.2 25.5 27.7 29.3
3
Table 5.3: Constant NTU – simulation alternatives
θin
θ [°C]
30
θout,1
θout,2
25
θout,3
θout,4
20
15
1
2
3
4
t [days]
Figure 5.6: Constant NTU – the inlet θin and outlet θout air temperature
- 104 -
5
5.2.3 Constant Va/A
alternative
1
2
3
4
Va [m /h]
100 200 300 400
L [m] for Va/A = 15 11.3 22.6 33.9 45.2
3
Table 5.4: Constant Va/A – simulation alternatives
θin
θ [°C]
30
θout,1
θout,2
25
θout,3
θout,4
20
15
1
2
3
4
5
t [days]
Figure 5.7: Constant Va/A – the inlet θin and outlet θout air temperature
Following the constant NTU curve (see Figure 5.8) leads to the deterioration of
thermal performance. The constant NTU curve is insufficiently steep. Following the
constant Va/A = 15 line (see Figure 5.8) leads to the inverse performance regarding the
previous case of constant NTU. The line is steep enough to dampen the outlet air
temperature more in cases with higher air flow rates. Conclusively, the design should be
a compromise between too steep line of constant Va/A = 15 and too flat curve of
constant NTU = 2.0.
40
DN 200
Va/A = 10
35
L [m]
30
NTU = 2.5
NTU = 2.0
25
NTU = 1.5
20
15
100
Va/A = 15
Va/A = 20
150
200
Hollmuller
250
300
Va [m3/h]
350
400
Figure 5.8: Display of NTU curves, lines of constant Va/A and Hollmuller design
rules for DN 200 (points according to Table 5.2)
- 105 -
Chapter 5
5.2.4 Distance between pipes
Three distances between pipes (0.3 m, 0.55 m, 0.8 m) are simulated. The pipe
material is neglected. The length of EAHX is assumed L = 25 m; the air flow rate is
maintained at 250 m3/h.
θ [°C]
30
25
θin
θout(Yp = 0,3 m)
θout(Yp = 0,55 m)
θout(Yp = 0,8 m)
20
15
1
2
3
4
5
t [days]
Figure 5.9: Different distances between pipes – the inlet θin and outlet θout air
temperature; Yp denotes horizontal distance between pipes
As seen in Figure 5.9, the minimal horizontal distance between pipes is in order
of several tens of centimeters, because of the intermittent character of summer cooling
(12 h pulse/12 h soil recovery). Three times the value of daily penetration depth 3dp
(Yp > (0.4 – 0.55) m depending on the soil type) should be a safe value.
5.2.5 Role of pipe material
Three real materials are studied: PVC with λ = 0,15 W/(m.K), PP with λ = 0,22
W/(m.K), and PP AWADUCT Thermo with λ = 0,27 W/(m.K). Thickness of pipe wall
is assumed tp = 5 mm; the length of EAHX is assumed L = 25 m. The air flow rate is
maintained at 250 m3/h.
- 106 -
θin
30
insul
θ [°C]
PVC
θout
25
PP
θout
AWA
θout
20
15
Rpipe = 0
1
2
3
4
5
t [days]
Figure 5.10: Different thermal conductivities of pipe material - the inlet θin and
outlet θout air temperature; insul denotes 5 mm thick material with thermal conductivity
0.04 W/(m.K); Rpipe = 0 denotes infinite thermal conductivity of pipe
As seen in Figure 5.10, the difference between different materials (PVC, PP, and
AWADUCT Thermo) is rather small (order of tenths °C) and almost negligible. The
increase of material costs will not be balanced by the increase of thermal efficiency.
However, the foam wall pipe (marked as a case “insulation”) deteriorates the thermal
performance considerably and therefore should be avoided. Moreover, a poor thermal
contact of soil with the pipe (i.e. low quality of work) has similar effect as a thin layer
of insulation. Thermal resistance of 5 mm thick air gap is the same magnitude as 10 mm
thick foam core.
5.3 Design methodology
Using already known (maximal) value of the air flow rate, a combination of
design parameters (length of EAHX L, internal diameter of the pipe 2r0, and number of
pipes np) should be identified so that the following aspects will be considered:

Sufficient efficiency of EAHX. The setup of one pipe, i.e. the relationship
between air flow rate per one pipe, internal diameter, and length, manages thermohydraulic efficiency. A range in which EAHX reaches sufficient efficiency is
depicted in Figure 5.11 (design for air cooling). The lower bounds are lines
originating from Hollmuller design rules for daily amplitude dampening. The
upper bounds are NTU curves (NTU = 2.5, i.e. theoretical efficiency 92 %).
Generally, a thinner pipe is advantageous because of both thermal efficiency and
material costs. In reality, three pipe diameters are applicable. Diameter DN 160 is
limited to air flow rate 250 m3/(h.pipe), DN 200 up to 400 m3/(h.pipe), and DN
- 107 -
Chapter 5
250 up to 600 m3/(h.pipe) which is va ≈ 4 m/s. Higher air flow rates should be split
into more pipes in order to ensure reasonable pipe pressure loss.
Figure 5.11: A range in which EAHX reaches sufficient efficiency (design for air
cooling)

Total pressure loss of EAHX (including filters, the inlet drill, elbows and other
additional resistances) should not be too high. The limit value has to be
determined by a designer of the ventilation system. The value depends on the type
of ventilation unit (available fan power) and the pressure loss of the building
ductwork.

Sufficient cooling power of EAHX with respect to the value of cooling load. The
number of pipes manages the total cooling power of EAHX. However, the design
of EAHX for removal of total cooling load need not be always effective. It could
be a good practice to design EAHX so that it removes a significant part of total
cooling load (e.g. one half). The value of cooling load should be primarily reduced
by building-energy concept, of course. A good thermal stability of a building is
crucial for design of realistic EAHX and effective cooling. For instance, cooling
power of EAHX (usual size for family house) is so limited that one south oriented
roof window may affect significantly the ratio cooling power of EAHX vs.
cooling load of building.
- 108 -
40
35
35
30
30
25
20
DN 200
Qcooling
L [m]
L [m]
40
DN 160
Qcooling
1000 W
25
20
500 W
500 W
15
15
200 W
200 W
50
100
150
3
Va [m /h]
200
250
100
150
200
250
300
3
Va [m /h]
350
400
Figure 5.12: Approximate cooling power of EAHX; calculated for the following
boundary conditions: θin = 32 °C, θs = 16 °C (constant over the length of exchanger), and
θi = 26 °C

Reasonable investment costs. The limit should be agreed by a designer of the
ventilation system together with investor. The important part of EAHX budget is
cost of excavation cut. Therefore, EAHX should be designed together with
building design; important savings may be achieved by integration of work on
excavation cuts.

Fulfillment of other boundary conditions. The space restrictions of building site
and other conditions should be considered (e.g. length limit, limit on number of
pipes, radon risk at the site, or the type of soil). The outlet air temperature should
be higher than minimal value (thermal comfort criterion).
5.4 Examples
5.4.1 EAHX for family house
The first example shows dimensioning of EAHX for cooling of a passive family
house with theoretical cooling load 2900 W (960 W are internal heat gains) and design
air flow rate 400 m3/h. Some variants are shown in Table 5.5.
diameter number air flow length approx.
of
rate
per of
cooling
pipes
one pipe
pipe
power
DN 160
DN 160
2
3
200 m3/h
133 m3/h
23 m
18 m
> 1 kW
- 109 -
pressure costs for
drop
one
meter of
pipe
(approx.)
22 Pa
175,-/m
8 Pa
175,-/m
total costs
(PVC)
8050,9450,-
Chapter 5
DN 200
DN 200
DN 250
1
2
1
400 m3/h
200 m3/h
400 m3/h
34 m
23 m
33 m
36 Pa
7 Pa
12 Pa
275,-/m
275,-/m
500,-/m
9350,12650,16500,-
Table 5.5: Family house - design alternatives
5.4.2 EAHX for larger building
The second example shows dimensioning of EAHX for cooling of larger
building with theoretical cooling load 15000 W and design air flow rate 3000 m3/h.
Some variants are shown in Table 5.6. All design variants lead to similar cooling power.
However, the space necessary for pipe placement, pipe costs and pressure drop is
different.
diameter number air flow length
of
rate
per of
pipes
one pipe
pipe
DN 160
DN 160
DN 200
DN 200
DN 250
12
18
8
12
5
250 m3/h
167 m3/h
375 m3/h
250 m3/h
600 m3/h
27 m
21 m
35 m
26 m
41 m
approx.
cooling
power
> 8 kW
pressu
re loss
38 Pa
15 Pa
33 Pa
12 Pa
31 Pa
costs per
one meter
of
pipe
(approx.)
175,-/m
175,-/m
275,-/m
275,-/m
500,-/m
total costs
of
pipe
material
(PVC)*
56700,66150,77000,85800,102500,-
Table 5.6: Larger building - design alternatives
* Not only material costs play role, but the cost of excavations and human work
should be considered.
5.5 Conclusions
During design of EAHX dimensions, a combination of design parameters (length
of EAHX, internal diameter of the pipe, and number of pipes) should be identified for
design air flow rate. As a general rule, it is convenient to split design air flow rate into
more pipes with minimal diameter and length leading to the sufficient temperature
efficiency, reasonable pressure loss, and desired value of cooling power. The placement
of more pipes into one excavation cut is suitable as an economical possibility (keeping
in mind the minimal distance between pipes, see 5.2.4).
Dimensioning should not be confused with the performance prediction
(i.e. simulation). The cooling power depicted in Figure 5.12 should be understood as an
- 110 -
approximate maximal achievable value. The designer should keep in mind the boundary
conditions for which the cooling power was calculated.
The effectiveness of the design and/or operation of EAHX could be evaluated by
a parameter called COP (coefficient of performance), i.e. the ratio between the expected
cooling power and the electric power needed for transport of air through the exchanger.
For instance, the cooling power of EAHX monitored on the passive house in Rychnov
(see chapter 4.4.5) was approximately 1500 W with necessary electric power of 150 W,
i.e. COP equal to 10. In this way, EAHX could be assumed to be more effective than
standard air conditioning by SPLIT units, which reach mean COP roughly equal to 3.
5.6 Summary
The chapter dealt with dimensioning of EAHXs. First, the relationship between
key design parameters (air flow rate, length, diameter, and number of pipes) was
studied. Then, a set of simulations was performed in order to study several special
setups of the pipe. Finally, a simple design methodology was developed in order to
facilitate the design of EAHX.
- 111 -
Chapter 5
- 112 -
Conclusions
6 Conclusions
In this final chapter, the review of results and final remarks and
recommendations for further research will be stated. Conclusions are presented in each
chapter at the end.
6.1 Results
The earth-to-air heat exchanger was studied by means of numerical simulation
and long-term monitoring on real-size systems. The work presents a contribution to
understanding the hygro-thermal performance of EAHXs. The main steps and
achievements are summarized below.
1) Hygro-thermal model for simulation of the earth-to-air heat exchangers.
A numerical model was developed for simulation of EAHXs. The model utilizes a) the
analytical solution of differential equation describing heat and moisture balance of the
exchanger longitudinal control volume (sensible and latent heat is considered) and
b) the numerical solution of two-dimensional transient heat conduction in soil
surrounding the pipe (explicit finite difference method), see chapter 2.3. The solution
procedure (algorithm) utilizes fully explicit scheme for a discretization in time, see
chapter 2.3.3. Since this approach suffers from stability problems, an alternative
iterative procedure suppressing the instability was proposed (chapter 2.3.4).
2) Validation of the model. The model was validated against both the analytical
solution and measured data on real size systems. The model showed perfect agreement
with the analytical solution for an externally insulated exchanger with harmonic
oscillation at the input (chapter 3.3). Furthermore, the model was compared with
detailed measurement on real-size EAHX (chapter 3.4). The simulated outlet air
temperature, outlet air water vapour concentration and overall moisture rate were rather
close to measured values. The validated model was finally submitted to series of
simulations leading to straightforward parametric analysis (chapter 3.5). The sensitivity
of all input parameters was identified.
- 113 -
Chapter 6
3) Long-term monitoring of real-size earth-to-air heat exchanger and
evaluation of the measured data. The results of measurement showed the hygro-
thermal performance of real-size EAHX. Plots of outlet air temperature, outlet air water
vapour concentration, energy gain, and cooling power were presented (chapter 4.4). The
general tendency to condensation in EAHX (the attribute of climatic locality) was
shown using measured soil temperature and ambient air temperature and humidity
(chapter 4.3.3).
4) Simple method for design of EAHX dimensions was developed using
a) design rules founded in the literature and b) theoretical relations between design
parameters (length and air flow rate in particular) and performance indicators
(e.g. temperature efficiency and cooling power). The method was presented as a stepby-step procedure stressing all aspects which should be considered during design
process (chapter 5.3).
6.2 Final remarks and recommendations for
further research
Based on some research results, recommendations for further research can be
made:
1) The EAHX model could be further extended, e.g. considering the neglected
physical phenomena.

Instead of air, heat carrier could be water or anti-freeze fluid (EWHX, earth-towater heat exchanger). It might be interesting to compare thermal performance of
EAHX with EWHX. Water as heat carrier fluid will achieve much higher values
of convective heat transfer coefficient than air systems. On the contrary, higher
thermal capacity of water will cause slower tendency to heat up/cool down the
fluid (compared to air as heat carrier). Generally, the principles of the EWHX
model will be the same as the principles of the EAHX model. Only temperature
dependency of fluid thermo-physical properties (impact on viscosity and thus on
convective heat transfer) is not probably negligible.

Based on monitored data, the thermal influence of the inlet shaft was considered to
be significant. This surprising observation could lead to conclusion that air cooling
due to the suction through a vertical short shaft or water well (e.g. a 2 m deep
- 114 -
Conclusions
shaft connected to a building by rather short pipe) will be sufficient in some cases.
Therefore, the inlet shaft should be also modeled (in case there is any inlet shaft).
A CFD analysis would be valuable.

The EAHX model neglected all kinds of moisture transfer through soil. However,
the flow of underground water table may have significant influence on soil
temperature. Therefore, the bottom boundary condition should be formulated with
respect to defined underground water flow. Moreover, the shallow subsurface is
influenced by precipitation.
2) As shown by parametric analysis of the model, soil temperature is one of the
key factors for hygro-thermal performance of EAHX. Soil temperature could be
intentionally influenced by the specific arrangement of soil surface (see Figure 6.1) or
the specific arrangement of soil layers. The thermal influence of a building on soil
temperature is another problem.
30
[°C]
25
20
asphalt - 0,5m
bare soil - 0,5 m
31.07.06
26.07.06
21.07.06
16.07.06
11.07.06
06.07.06
01.07.06
15
Figure 6.1: Measured soil temperature on the site of Geophysical Institute in Prague
(http://www.ig.cas.cz/) in depth of 0.5 m (two kinds of soil surface)
3) The emphasis on component modeling should be shifted to overall cooling
efficiency. Therefore, this work should be extended by simulations of a building/room
model coupled with the EAHX model. The general idea is that the EAHX model could
become a part of the International Building Physics Toolbox, see (Kalagasidis et al,
2007). The Simulink block could be developed in the same manner like floor heating
module (Weitzmann, 2002), using so-called S-function (Mathworks, 2005).
- 115 -
Chapter 6
4) Due to the presence of water in pipes, mould growth is still questionable.
Therefore, the inspection of real size installations with a camera and some microbial
investigations would be also very valuable.
5) Useful information could be gained by a simple computational
experimentation with the model of flat-plate heat exchanger (for geometry of FPHX see
Figure 3.1 and Figure 3.2). One case, which could be modeled, using an adjusted model
for FPHX, is the phase change material (PCM) heat exchanger. The plate of the
exchanger is not made of ordinary storage material, but is made of PCM. Such
exchanger could be used for cooling of ambient or internal air (melting process of
PCM). During night, when cold ambient air is sucked through the exchanger, the
reverse process (solidification) will maintain thermal balance of PCM. The problem of
phase change may be modeled by standard heat conduction equation assuming
temperature dependent thermal capacity and thermal conductivity.
6) The thermal phase-shifting (Hollmuller et al, 2006 and Hollmuller et al, 2007)
is a promising technique for cooling of buildings. The important problem of a phaseshifter is equalization of flow in the exchanger and precise dimensioning. The
performance of the phase-shifter is very dependent on the value of convective heat
transfer coefficient which is quite uncertain. The model of the flat-plate heat exchanger
could be used in order to study this phenomenon thoroughly. A CFD analysis and
experimental work would be also valuable.
- 116 -
Appendices
Appendices
A1 Derivations and solutions
Equation 2.30
Heat flows according to Figure 2.5:
Qin = ma caθ a
[W]
(A.1)
[W]
(A.2)
Qs = ha (θ a − θ s ) 2π r0∂x
[W]
(A.3)
Qlat = g vl 2π r0∂x
[W]
(A.4)
Qout = ma ca (θ a + ∂θ a )
Heat balance according to Figure 2.5:
Qin − Qout − Qs + Qlat = 0
(A.5)
− ma ca ∂θ a − haθ a 2π r0∂x + haθ s 2π r0∂x + g vl 2π r0∂x = 0
⎛
1 ⎞ ⎛ 1 ⎞
/× ⎜ −
⎟ /× ⎜ ⎟ (A.6)
⎝ ma ca ⎠ ⎝ ∂x ⎠
∂ θ a ha 2π r0
h 2π r0
g l 2π r0
+
θa − a
θs − v
=0
∂x
m a ca
m a ca
m a ca
(A.7)
Differential equation (2.30) has the form:
y′ + p × y = q
(A.8)
The solution is the superposition:
y = yH + yP
(A.9)
where yH is the solution of the homogenous differential equation (the equation
without right side) obtained by the separation of variable and yP is the particular solution
of the original equation, for details see (Bartsh, 1971).
- 117 -
Appendices
Equation 2.39
Moisture flows according to Figure 2.9:
Gin = Va ρv
[kg/s]
(A.10)
Gout = Va ( ρv + ∂ρv )
[kg/s]
(A.11)
Gs = g v 2π r0∂x
[kg/s]
(A.12)
[kg/(m2.s)]
(A.13)
where:
g v = β ρ ( ρv − ρ v,sat )
gv (+) denotes condensation, gv (-) denotes evaporation
Moisture balance according to Figure 2.9:
Gin − Gout − Gs = 0
(A.14)
−Va ∂ρv − β ρ ρv 2π r0∂x + β ρ ρ v,sat 2π r0∂x = 0
⎛ 1 ⎞ ⎛ 1 ⎞
/× ⎜ − ⎟ /× ⎜ ⎟ (A.15)
⎝ Va ⎠ ⎝ ∂x ⎠
β 2π r0 θ s
∂ρ v β ρ 2π r0
+
=0
ρv − ρ
ρ
v , sat
Va
Va
∂x
(A.16)
The solution is performed by identical procedure as described for
equation (2.30).
FPHX with adiabatic boundary – analytical solution
Based on (Hollmuller, 2003) and material sent by Mr. Hollmuller via email.
Input:
θin (t ) = θ 0 cos (ωt )
(A.17)
Output:
⎛ ⎛
Sh ⎞
x ⎞
Sk ⎞
⎟⎟
⎟ cos ⎜⎜ ω ⎜ t − ⎟ −
⎝ ma ca ⎠
⎝ ⎝ va ⎠ ma ca ⎠
⎛
θ a ( x, t ) = θ 0 exp ⎜ −
(A.18)
where S is heat exchange surface [m2] from the inlet to distance x, h is total
(air/pipe + soil) amplitude-dampening exchange coefficient [W/(m2.K)],
k is total
2
(air/pipe + soil) phase-shifting exchange coefficient [W/(m .K)], t is time [s]. Term x/va
is time for which air flows from the inlet to distance x from the inlet (transit time).
- 118 -
Appendices
S = 2 Bx
h=
k=
ha ( hs + ik s )
ha + ( hs + iks )
ha ( hs + ik s )
ha + ( hs + ik s )
(A.19)
(A.20)
Re
(A.21)
Im
where hs and ks are values for infinite ha.
⎛
W ⎞
sinh ⎜ (1 + i )
⎟⎟
⎜
d
λ
p
⎝
⎠
hs + ik s =
(1 + i )
dp
⎛
W ⎞
cosh ⎜ (1 + i ) ⎟
⎜
d p ⎟⎠
⎝
- 119 -
(A.22)
Appendices
A2 Explicit finite difference method for transient
heat conduction
The numerical treatment is based on discretized form of equation (2.31) in time
and space. The heat balance of a control volume (Figure A1:) is expressed as:
( ρ c p ) jk ∆y j ∆zk (θ j,k new − θ old
j ,k ) = ( qW − qE + qS − q N ) ∆t
(A.23)
where heat flow components are:
qW =
(θ j−1,k − θ j,k ) ∆zk
∆y j −1
2λ j −1,k
qE =
qN =
2λ j ,k
(θ j,k − θ j+1,k ) ∆zk
∆y j
2λ j ,k
qS =
+
(A.24)
∆y j
+
(A.25)
∆y j +1
2λ j +1,k
(θ j,k −1 − θ j,k ) ∆y j
(A.26)
∆zk −1
∆zk
+
2λ j ,k −1 2λ j ,k
(θ j,k − θ j,k +1 ) ∆y j
(A.27)
∆zk
∆zk +1
+
2λ j ,k 2λ j ,k +1
Figure A1: Heat balance of control volume
- 120 -
Appendices
After some rearrangements equation (A.23) takes shape:
(
)
(
)
(
)
(
)
(
HO jk θ j,k new − θ old
j ,k = HY jk θ j −1,k − θ j ,k + HY j +1,k θ j +1,k − θ j,k + HZ jk θ j,k −1 − θ j,k + HZ j ,k +1 θ j ,k +1 − θ j ,k
) (A.28)
where: HOjk, HYjk, HYj+1,k, HZjk and HZj,k+1 are helping functions defined as:
HO jk =
HY jk =
( ρ c p ) jk ∆y j ∆zk
∆zk
∆y j −1
2λ j −1,k
HY j +1,k =
HZ jk =
(A.29)
∆t
+
(A.30)
∆y j
2λ j ,k
∆zk
∆y j
∆y j +1
+
2λ j ,k 2λ j +1,k
(A.31)
∆y j
(A.32)
∆zk −1
∆zk
+
2λ j ,k −1 2λ j ,k
HZ j +1,k =
∆y j
∆zk
∆zk +1
+
2λ j ,k 2λ j ,k +1
(A.33)
Finally, temperatures on the right side of equation (A.28) are considered to be
old (already calculated or initial) and unknown (new) temperature is placed on the left
side of the equation:
(
)
old
old
old
old (A.34)
HOjkθj,knew = HYjkθold
j−1,k + HYj+1,kθj+1,k + HZjkθj,k−1 + HZj,k+1θj,k+1 + HOjk − HYjk −HYj+1,k − HZjk − HZj,k+1 θj,k
The advantage of explicit method is its simplicity; the disadvantage is that the
method is not always numerically stable. The computational time step has to fulfill the
criterion of the stability ∆t < ∆tcrit; the requirement can be derived from following
condition:
( HO jk − HY jk − HY j +1,k − HZ jk − HZ j,k +1 ) ≥ 0
( ρ c p ) ∆y j ∆zk
∆t =
crit
HY jk + HY j +1,k + HZ jk + HZ j ,k +1
- 121 -
(A.35)
(A.36)
Appendices
A3 House W
Basic information
Description
Single family wooden based house
(system two-by-four) with floor and
attic, without cellar.
Calculated heat use: 44 kWh/(m2.a)
20 km south of Prague, Velké Popovice
Location
Gypsum board
Wall
2
U = 0.19 W/m .K Wooden grill filled by mineral wool
Built in 2003
40 mm
Water vapor barrier (polyethylene foil)
Mineral wool between load bearing timber frame
140 mm
OSB plate
Wooden grill filled by mineral wool
60 mm
Diffusion open membrane
Ventilated air cavity
Wooden cladding
Gypsum board
Roof
2
U = 0.17 W/m .K Wooden grill filled by mineral wool
60 mm
Mineral wool between rafters
180 mm
Ventilated air cavity + roof cladding
Floor layers
Ground floor
2
U = 0.25 W/m .K Concrete slab
50 mm
Expanded polystyrene with ventilation ducts
130 mm
Ground water insulation (bitumen membrane)
Concrete slab on ground
150 mm
2
2
Wooden frame U = 1.7 W/m .K, Glazing U = 1.1 W/m .K
Windows
Heat storage (915 l) heated by electricity and solar system (roof
Heating
solar collectors 8.4 m2). Heat from the storage is used for heating
up of ventilation and circulation air and for hot water preparation.
Additional heat source is a wood burning stove (7 kW) in living
room.
Mechanical ventilation with heat recovery and EAHX
Ventilation
Table A1: Basic information about house W
- 122 -
Appendices
List of sensors
Nr.
1
2
3
4
5
6
Purpose
Temperature of ambient air
Outlet air temperature
Temperature of circulation air
Temperature (circulation +
fresh air)
Temperature of waste air (after
heat recovery)
Internal air temperature (in
staircase)
Signal
Type
Table A2: List of sensors on house W
This monitoring had several imperfections. The interval of the measurement
(20 min, later changed to 5 min) was too long, the air flow rate was not measured
directly, and the relative humidity of inlet and outlet air was not measured. Therefore,
the ventilation mode (current state of the ventilation unit) was often difficult to figure
out from measured data.
- 123 -
Appendices
A4 Passive family house in Rychnov
Basic information
Description
Single family wooden
based house (panel
system) with floor and
attic, without cellar.
Calculated heat use:
14 kWh/m2.a
Location
Built in
Wall
U = 0.10 W/m2.K
Rychnov near Jablonec nad Nisou
2004
Gypsum board 2x
120 mm
Gypsum board
Thermal insulation (mineral wool) between load 240 mm
bearing timber frame (I profiles)
Gypsum board
Thermal insulation (expanded polystyrene)
60 mm
Plaster
Roof
U = 0.11 W/m2.K
Gypsum board 2x
Mineral wool
Mineral wool between rafters
Ventilated air cavity
Roof cladding
60 mm
240 mm
170 mm
Slab on ground
U = 0.18 W/m2.K
Windows
Heating
Ventilation
Wooden frame, Glazing heat mirror U = 0.62 W/m2.K
Heat storage (615 l) heated by electricity and solar system (roof
solar collectors 5.34 m2). Heat from the storage is used for
heating up of ventilation and circulation air and for hot water
preparation.
Mechanical ventilation with heat recovery and earth-to-air heat
exchanger in closed loop mode.
Table A3: Basic information about house in Rychnov
- 124 -
Appendices
List of sensors
Nr.
Purpose
Signal
Main datalogger: COMET MS3+
1
Temperature + relative
DC (4 – 20 mA)
humidity
3
DC (4 – 20 mA)
humidity
5
Temperature – circulation air
DC (4 – 20 mA)
6
Air flow rate – circulation fan
AC 0 – 400V
7
Air flow rate – exhaust fan
AC 0 – 400V
8
Flap position
DC 0 – 10V
Data logger in the inlet shaft: COMET S3631
2
humidity
4
Temperature
Data logger – soil: COMET S0141
s1
Temperature – 5 cm
s2
s3
s4
Data logger – living room:
LR1
humidity
CO2_LR CO2 concentration – living
room
CO2_C1 CO2 concentration – circulation
air
Type
NH 421.65
NH 421.65
Pt 1000
module E3
module E3
module D2
embedded in the logger
Pt 1000 (external)
Pt 1000 (external)
Pt 1000 (external)
Pt 1000 (external)
Pt 1000 (external)
embedded in the logger
external, SIEMENS
external, SIEMENS
Table A4: List of sensors on house in Rychnov
- 125 -
Appendices
err1
err2
Ventilation modes
0
1 NORM 2 NORM 3 NORM 4 NORM 5
MAX
MAX
no ventilation
missing data
e1
e1
i1
i1
ventilation
with heat
recovery
heating +
ventilation
with heat
recovery
i2
e1
c1
i1
i1
c2 + e2
NORM
MAX
i2
e1
c1
e2
MAX
i2
i2
trace error
MAX
c2
heating or
cooling
(circulation
between
building
and
EAHX)
modes
2a, 2b,
5a
e2
e2
night
ventilation
external
signals
cooling
(suction
through
EAHX)
enhanced
ventilation
induced
by
external
signals
Table A5: Definition of ventilation modes
The ventilation system installed in the house utilizes five basic ventilation modes
(Table A5). Each mode is defined by the combination between fan operation and the
position of circulation damper (Table A6). Some other ventilation modes (marked 2a,
2b, 5a) are induced by external signals (cooking, use of shower or WC).
Ventilation mode
0
1
2
3
4
5
fans
circulation damper
Mc Mv closed e1 between closed c1
off
0
0
0
0
0
ventilation
1
1
0
0
1
circulation + ventilation 1
1
0
1
0
circulation
1
0
1
0
0
under pressure
0
1
0
0
1
over pressure
1
0
0
0
1
Table A6: Ventilation modes - basic combinations (1 – yes, 0 – no), Mc denotes circulation
fun, Mv denotes ventilation fan
- 126 -
Appendices
Air flow rates
The average velocity of air flow was measured at each outlet drill of the house
for each ventilation mode. Thus, each of ventilation modes was assigned with the value
of air flow rate through EAHX.
0
0
0
0
0
109 296
26
213 224 401
0
0
5a
4MAX
0
5MAX
4NORM
0
115 198 115 115 198 198
5NORM
3MAX
2b
2a
2MAX
1MAX
3NORM
0
2NORM
mode
open
loop
closed
loop
1NORM
off
Figure A2: Simple velocity (air flow rate) measurement on site (September 2006)
221 401 415
0
0
0
Table A7: Air flow rates in [m3/h] assigned with ventilation modes. Mc denotes circulation
fun; Mv denotes ventilation fan
1NORM
1MAX
2NORM
2MAX
2a
2b
3NORM
3MAX
4NORM
4MAX
5NORM
5MAX
5a
fun
Mc
Mv
off
Auxiliary energy
0
0
29
39
68
80
71
39
162
39
71
80
162
80
71
0
162
0
0
39
0
80
68
0
158
0
158
80
Table A8: Electric inputs assigned with ventilation modes (according to provided
information from manufacturer and measurement of air flow rates). Mc denotes
circulation fun, Mv denotes ventilation fan
- 127 -
Appendices
A5 Thermal properties of soils and rocks
A few references related to soil properties have been found. (Sundberg, 1989)
introduced typical thermal properties of some soils (CLAY, SILT, SAND, PEAT).
(Fink et al, 2002) provided data for three soil types (moist soil, dry soil, clay soil). The
software GAEA (Heidt et al, 1997) and software Awadukt Thermo (provided by
company Rehau) contain similar databases of soil thermal properties, but the source of
their information is unknown. (Janssen, 2002) comprehensively defined four main soil
types (SAND, SILT, LOAM, CLAY) and three extreme soil types using textural
triangle defined by United States Department of Agriculture (USDA). The thermal
properties (thermal conductivity, volumetric thermal capacity) were presented
graphically as a function of moisture content.

The thermal conductivity of dry soils varies between 0.3 and 1.0 W/(m.K). The
thermal conductivity of moist soils typically varies between 0.9 and 2.5 W/m.K.
Thermal conductivity rises fast at lower moister content, and then the curve
flattens. Thermal conductivity of frozen soil is substantially higher than thawed
soil (thermal conductivity of ice = 2.2 W/(m.K)). Dependence of thermal
conductivity on soil type is significant. Because of high quartz content, sand is the
best conductor whereas clay is the worst (Janssen, 2002, page 158, Figure 7.17).
Silt and loam are located in between.

Volumetric heat capacity typically varies between 1.0 and 3.0 MJ/(m3.K), higher
values for water saturated soils. Dependence of volumetric heat capacity on soil
type is very weak; the dominant factor is moisture content (linear function of
moisture content).

The thermal diffusivity of soils is typically in order of 10-7 m2/s.
Thermal properties of soils and rocks are listed below, based on several
information sources.
The measurement of several soil samples taken from the site should be
preferably used for the estimation of soil thermal properties (λ, ρcp), since the guess of
the thermal properties may be rather inaccurate.
- 128 -
Appendices
ρ
soil type
"Rehau Awadukt Thermo"
"EN
ISO
"AEE
Intec" 13370
"
"GAEA"
source
english
coarse gravel
calcareous
loamy soil
moist loamy soil
sand
dry sand
sandy ground
sandstone
clay
clay
gravel
homogenous rock
moist soil
dry soil
cp
ρcp
german
λs
[kg/m3] [J/kg.K] [MJ/m3.K] [W/m.K]
Grobkiesig
2000
1840
3,68
0,52
Kalkhaltige Erde
1670
2230
3,72
0,71
Lehmboden
1650
2850
4,70
2,30
lehmig feucht
1800
1340
2,41
1,49
Sand
1780
1390
2,47
0,93
Sand trocken
1500
920
1,38
0,70
Sandboden
1520
1650
2,51
1,24
Sandstein
2250
710
1,60
1,87
Tonboden
1500
880
1,32
1,28
Ton (ISO 13370)
3,00
1,50
Kiesig (ISO 13370)
2,00
2,00
Felsen (ISO 13370)
2,00
3,50
Erde, feucht
1800
1260
2,27
2,50
Erde, tonig
1500
1080
1,62
1,51
Erde, trocken
1500
840
1,26
0,35
Quarzsand, trocken (Darby 1978)
1650
1,32
0,27
Quarzsand, 8% Feuchte (Darby 1978)
1750
1,77
0,59
Sand trocken (Karl 1965)
1650
1,38
0,70
Sand, 15% Feuchte (Darby 1978)
1780
2,46
0,92
Sandboden, 9% Feuchte (Neiss 1977)
1440
2,17
0,98
Sandboden, 13% Feuchte (Neiss 1977)
1600
2,88
1,50
trockener Sand (ISO 13370)
1998
4,94
1,60
Sand feucht (Jager 1981)
1500
1,80
1,88
Sand/Kies (EN 12524)
1950
2,05
2,00
nasser Sand (ISO 13370)
2166
6,52
2,10
Erdreich, grobkiesig (VDI 1984)
2000
3,69
0,52
Erde, kalkhaltig (Darby 1978)
1670
3,72
0,71
Lehm feucht (Cube 1977)
1800
2,41
1,45
Lehmboden, 36% Feuchte (Neiss 1977)
1650
4,69
2,30
Lehm gesätigt (Jager 1981)
1800
2,57
2,90
Ton (ISO 13370)
1820
5,74
1,20
Ton boden (VDI 1984)
1500
1,32
1,28
Ton/Schlick/Schlamm (EN 12524)
1500
3,15
1,50
Schluff (ISO 13370)
1920
5,64
1,50
Sandstein (VDI 1974)
2250
1,60
1,90
Granit (EN 12524)
2600
2,60
2,80
Felsen (ISO 13370)
2500
6,25
3,50
Torf (ISO 13370)
1500
5,83
0,35
Table A9: Thermal properties of soils
- 129 -
as
bs
[m2/s]
1,4E-07
1,9E-07
4,9E-07
6,2E-07
3,8E-07
5,1E-07
4,9E-07
1,2E-06
9,7E-07
5,0E-07
1,0E-06
1,8E-06
1,1E-06
9,3E-07
2,8E-07
2,0E-07
3,3E-07
5,1E-07
3,8E-07
4,5E-07
5,2E-07
3,2E-07
1,0E-06
9,8E-07
3,2E-07
1,4E-07
1,9E-07
6,0E-07
4,9E-07
1,1E-06
2,1E-07
9,7E-07
4,8E-07
2,7E-07
1,2E-06
1,1E-06
5,6E-07
6,0E-08
[Ws0,5/m2.K]
1383
1626
3289
1896
1517
983
1763
1728
1300
2121
2000
2646
2381
1564
664
591
1019
984
1509
1458
2078
2811
1839
2023
3701
1385
1629
1869
3286
2728
2625
1300
2174
2908
1742
2698
4677
1429
References
References
1)
Ashrae: Ashrae Handbook of Fundamentals, American Society of Heating,
Refrigerating and Air Condition Engineers, 2001.
2)
Arkar, C., Medved, S.: Free cooling of a building using PCM heat storage
integrated into the ventilation system, Solar Energy 81, 2007.
3)
Bartsch, H., J.: Matematické vzorce, SNTL, Praha, 1971.
4)
Beltrami, H.: Inference of climate change from geothermal data, Global and
Planetary Change 29, 2001.
5)
Beltrami, H., Kellman, L.: An examination of short- and long-term air-ground
temperature coupling, Global and Planetary Change 38, 2003.
6)
Benkert, St., Heidt, F., D., Schöler, D.: Calculation tool for earth-to-air heat
exchangers GAEA, Building Simulation, Prague, 1997.
7)
Cílek, V., Kašík, M.: Nejistý plamen. Dokořán, Praha, 2007.
8)
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Publications written in context with the
thesis
[1] Kopecký, P.: Numerical modeling of the flat-plate heat exchanger, Sborník
konference Tepelná ochrana budov, Štrbské Pleso, Vysoké Tatry, 2005.
[2] Kopecký, P.: Numerické modelování zemních výměníků tepla, Sborník konference
Budova a Energia, Podbanské, Vysoké Tatry, 2005.
[3] Kopecký, P., Tywoniak, J.: Pre-heating and pre-cooling of fresh air in the earth-to-
air heat exchanger (EAHX) – Simulation and monitoring of a simple EAHX in lowenergy family house, Proceedings of conference CISBAT 2005, Lausanne,
Switzerland, 2005.
[4] Kopecký, P.: Zemní výměník tepla – matematický model, In: Tepelná ochrana budov
6/2005.
[5] Kopecký, P.: Zemní výměník tepla – matematický model, validace, experimentální
měření, simulace, Dílčí výzkumná zpráva pro výzkumné centrum CIDEAS, 2005.
[6] Kopecký, P.: Pokročilá simulace zemních výměníků tepla – srovnání simulace a
experimentálních dat z měření, konference Tepelná ochrana budov, Praha, 2006.
[7] Kopecký, P., Tywoniak, J.: Hygro-thermal numerical simulation model for earth-to-
air heat exchangers: validation process and the example of simulation, Proceedings
of conference Advance Engineering Design 2006, Praha, 2006.
[8] Kopecký, P.: Zemní výměník tepla: model a validace, In: Vytápění, Větrání,
Instalace 4/2006.
[9] Kopecký, P.: K energetickému přínosu zemního výměníku tepla, Sborník konference
Pasivní domy 2006, Brno, 2006.
[10] Kopecký, P.: Matematický model pro simulaci zemních výměníků tepla –
experimentální validace, Sborník konference Simulace budov a techniky prostředí
2006, Praha, 2006.
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[11] Kopecký, P.: K návrhu dimenzí zemních výměníků tepla I., Dílčí výzkumná zpráva
pro výzkumné centrum CIDEAS, 2006.
[12] Kopecký, P., Tywoniak, J.: Advanced simulation of the earth-to-air heat
exchangers – a comparison between simulation and measured data, Proceedings of
conference 12. Bauklimatische Symposium, Dresden, 2007.
[13] Tywoniak,
J.,
Morávek,
P.,
Kopecký,
P.:
Zur
Wohnungslüftung
in
Niedrigstenenergiehäusern in Tschechien, 2007.
[14] Kopecký, P.: Pasivní dům v Rychnově – vyhodnocení některých měřených dat za
rok 2006, Sborník konference Tepelná ochrana budov, Štrbské Pleso, Vysoké Tatry,
2007.
[15] Kopecký, P.: Hygro-thermal performance of earth-to-air heat exchanger: long-
term data evaluation and short-term simulation, Proceedings of conference
CISBAT 2007, Lausanne, Switzerland, 2007.
[16] Kopecký, P.: Zemní výměník tepla – vyhodnocení měřených dat a tepelně
vlhkostní simulace, Sborník konference Pasivní domy 2007, Brno, 2007.
[17] Kopecký, P.: Earth-to-air heat exchanger: hygro-thermal performance,
Proceedings of conference Passivhaustagung 2008, Nuremberg, 2008.
[18] Kopecký, P.: Návrh dimenzí zemních výměníků tepla, In: Vytápění, Větrání,
Instalace 2/2008.
- 136 -
Other publications
[1] Tywoniak, J., Morávek, P., Kopecký, P., Kramoliš, P.: Příklad stavebně energetické
koncepce budovy, Sborník konference CEERES 2003, Praha, 2003.
[2] Kopecký, P.: Integrace solárních systémů do obvodových konstrukcí budov, Sborník
konference Juniorstav 2004, Brno, únor 2004.
[3] Kopecký, P.: Vliv zadní izolace na tepelný zisk integrovaného neprovětrávaného
kolektoru, Sborník konference Tepelná ochrana budov 2004, Praha, 2004.
[4] Adamovský, D., Brázda, P., Kopecký, P., Nováček, J., Tencar, J.: Ideové řešení
rekonstrukce obvodového pláště budov FSv ČVUT v Praze, Sborník konference
Tepelná ochrana budov 2004, Praha, 2004.
[5] Hofmeister, O., Kopecký, P., Tywoniak, J.: Připravovaný projekt střediska
ekologické výchovy Sluňákov, Sborník konference Tepelná ochrana budov 2004,
Praha, 2004.
[6] Kopecký, P., Vonka, M.: Návrh rekonstrukce obvodového pláště budovy stavební
fakulty a fakulty architektury v Praze v širších environmentálních souvislostech, In:
Tepelná ochrana budov 4/2004.
[7] Vonka, M., Mukařovský, J., Kopecký, P.: Pasivní domy – Krems an der Donau
2004, In: Stavba 4/2004.
[8] Hofmeister, O., Kopecký, P., Tywoniak, J.: Sluňákov Ecological Education Centre
– Basic Information, Proceedings of conference Central Europe towards Sustainable
Building 2007, Prague 2007.
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