Solar Thermal Collectors at High Latitudes

Solar Thermal Collectors at High Latitudes
Comprehensive Summaries of Uppsala Dissertations
from the Faculty of Science and Technology 697
_____________________________
_____________________________
Solar Thermal Collectors at High Latitudes
Design and Performance of Non-Tracking Concentrators
BY
MONIKA ADSTEN
ACTA UNIVERSITATIS UPSALIENSIS
UPPSALA 2002
Dissertation for the Degree of Doctor of Technology in Engineering Science presented at
Uppsala University in 2002
ABSTRACT
Adsten, M. 2002. Solar thermal collectors at high latitudes -Design and performance of nontracking concentrators. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala
Dissertations from the Faculty of Science and Technology 697. 78 pp. Uppsala. ISBN 91-5545274-4
Solar thermal collectors at high latitudes have been studied, with emphasis on concentrating
collectors. A novel design of concentrating collector, the Maximum Reflector Collector
(MaReCo), especially designed for high latitudes, has been investigated optically and
thermally. The MaReCo is an asymmetrical compound parabolic concentrator with a bi-facial
absorber. The collector can be adapted to various installation conditions, for example standalone, roof- or wall mounted. MaReCo prototypes have been built and outdoor-tested. The
evaluation showed that all types work as expected and that the highest annually delivered
energy output, 340 kWh/m2, is found for the roof MaReCo. A study of the heat-losses from
the stand-alone MaReCo lead to the conclusion that teflon transparent insulation should be
placed around the absorber, which decreases the U-value by about 30%.
A method was developed to theoretically study the projected radiation distribution incident
on the MaReCo bi-facial absorber. The study showed that the geometry of the collectors
could be improved by slight changes in the acceptance intervals. It also indicated that the
MaReCo design concept could be used also at mid-European latitudes if the geometry is
changed.
A novel method was used to perform outdoor measurements of the distribution of
concentrated light on the absorber and then to calculate the annually collected zero-loss
energy, Ea,corr, together with the annual optical efficiency factor. A study using this method
indicated that the absorber should be mounted along the 20° optical axis instead of along the
65° optical axis, which leads to an increase of about 20% in Ea,corr. The same absorber
mounting is suggested from heat loss measurements. The Ea,corr at 20° absorber mounting
angle can be increased by 5% if the absorber fin thickness is changed from 0.5 to 1 mm and
by 13% if two 71.5 mm wide fins are used instead of one that is 143 mm wide. If the Ea,corr for
the standard stand-alone MaReCo with 143 mm wide absorber mounted at 65° is compared to
that of a collector with a 71.5 mm wide absorber mounted at 20°, the theoretical increase is
38%.
Monika Adsten, Department of Materials Science, The Ångström Laboratory, Uppsala
University, Box 534, SE-751 21 Uppsala, Sweden
© Monika Adsten 2002
ISSN 1104-232X
ISBN 91-554-5274-4
Printed in Sweden by Uppsala University, Tryck & Medier, Uppsala 2002
2
This thesis is based on work conducted within the
interdisciplinary graduate school Energy Systems. The
national Energy Systems Programme aims at creating
competence in solving complex energy problems by
combining technical and social sciences. The research
programme analyses processes for the conversion,
transmission and utilisation of energy, combined together in
order to fulfil specific needs.
The research groups that participate in the Energy Systems Programme are the Division of Solid State
Physics at Uppsala University, the Division of Energy Systems at Linköping Institute of Technology,
the Department of Technology and Social Change at Linköping University, the Department of Heat
and Power Technology at Chalmers Institute of Technology in Göteborg as well as the Division of
Energy Processes and the Department of Industrial Information and Control Systems at the Royal
Institute of Technology in Stockholm.
3
www.liu.se/energi
PUBLICATIONS INCLUDED IN THE THESIS
I.
Adsten M., Helgesson A. and Karlsson B. (2001). Evaluation of asymmetric CPCcollector designs for stand-alone, roof- or wall integrated installation, submitted to
Solar Energy
II.
Adsten M., Wäckelgård E. and Karlsson B. (2002). Calorimetric measurements of heat
losses from a truncated asymmetric solar thermal concentrator, Submitted to Solar
Energy
III.
Adsten M., and Karlsson B. (2002). Annually projected solar radiation distribution
analysis for optimum design of asymmetric CPC, submitted to Solar Energy
IV.
Adsten M., Hellström B.and Karlsson B. (2001) Measurement of radiation distribution
on the absorber in an asymmetric CPC collector, submitted to Solar Energy
V.
Adsten M., Hellström B. and Karlsson B. (2002).Comparison of the optical efficiency
of a wide and a narrow absorber fin in an asymmetric concentrating collector, in
manuscript
VI.
Adsten M., Perers B. and Wäckelgård E. (2002), The influence of climate and location
on collector performance, J. Renewable Energy, Volume 25, Issue 4, April 2002,
Pages 499-509
VII.
Adsten M. and Perers, B. (1999), Simulation of the influence of tilt and azimuth
angles on the collector output of solar collectors at northern latitudes, Proceedings
North Sun conference 1999, Edmonton Canada
VIII.
Hellström B., Adsten M., Nostell P., Wäckelgård E. and Karlsson B. (2000), The
impact of optical and thermal properties on the performance of flat plate solar
collectors, Proceedings Eurosun 2000, Denmark
IX.
Rönnelid M., Adsten M. Lindström T. Nostell P. and Wäckelgård E. (2001), Optical
scattering from rough aluminum surfaces, J. Applied Optics, 40, pp 2148-2158
X.
Adsten M., Joerger R., Järrendahl K. and Wäckelgård E. (2000) Optical
characterization of industrially sputtered nickel-nickel oxide solar selective surface,
Solar Energy 68, 325-328.
Comments on my participation
I-VII
VIII
IX
X
Major part of calculations/experimental work and writing
Part of simulations, part of writing
Part of optical measurements and writing
Part of optical measurements
4
PUBLICATIONS NOT INCLUDED IN THE THESIS
Wäckelgård E, Adsten M and Joerger R (1998). Optical characterization of industrially
sputtered nickel-nickel oxide solar selective surface, Proceedings of EuroSun 1998,
Portoroz, Slovenia
Adsten M and Wäckelgård E (1999). Solar energy-cost effective for the Navestad
residential area, Arbetsnotat nr 6, Program Energisystem, ISSN 1403-8307
Adsten M and Perers B (1999). Influence on solar collector output by annual climate
variation, internal report, Uppsala University Department of Materials Science
Adsten M and Perers B (2000). Influence of climate variation on collector output,
Proceedings of World Renewable Conference 2000, Brighton UK
Adsten M and Karlsson B (2001). Measurement of radiation distribution on the
absorber in an asymmetric CPC collector, Proceedings of ISES Solar World
Conference, Adelaide, Australia
Hellström, B., Adsten, M., Nostell, P., Wäckelgård, E. and Karlsson B. (2002), The
impact of optical and thermal properties on the performance of flat plate solar
collectors, accepted to Renewable Energy
5
CONTENTS
1
INTRODUCTION................................................................................................... 1
2
THEORETICAL BACKGROUND AND EXPERIMENTAL METHODS .......... 3
2.1 Collector analysis................................................................................................. 3
2.1.1 The solar collector ........................................................................................ 3
2.1.2 Introduction to optics.................................................................................... 4
2.1.3 Introduction to thermal radiation.................................................................. 7
2.1.4 Characterisation of solar collector components ........................................... 8
2.1.5 Instruments for optical characterisation ..................................................... 13
2.1.6 Collector heat losses................................................................................... 14
2.1.7 Characterisation of the collector................................................................. 20
2.2 Collector simulations ......................................................................................... 21
2.2.1 Introduction ................................................................................................ 21
2.2.2 The MINSUN program .............................................................................. 22
2.3 Optical characteristics of nonimaging concentrating collectors........................ 23
2.3.1 Introduction ................................................................................................ 23
2.3.2 Description of the Maximum Reflector Collector, MaReCo ..................... 25
2.3.3 MaReCo prototypes.................................................................................... 26
2.3.4 Characterisation of concentration distribution on the absorber fin ............ 29
2.3.5 Annually collected energy and optical efficiency factor............................ 30
2.4 Projection of solar radiation............................................................................... 32
2.4.1 Introduction ................................................................................................ 32
2.4.2 Horizontal system....................................................................................... 33
2.4.3 Rotated system ........................................................................................... 34
2.4.4 Projection angles ........................................................................................ 35
2.4.5 Radiation distribution diagrams ................................................................. 35
3
RESULTS AND DISCUSSION ........................................................................... 39
3.1 The MaReCo...................................................................................................... 39
3.2 Flat plate collectors............................................................................................ 52
3.3 Component studies............................................................................................. 60
4
CONCLUSIONS AND SUGGESTION FOR FUTURE WORK......................... 64
5
SUMMARY OF APPENDED PAPERS............................................................... 68
6
ACKNOWLEDGEMENTS .................................................................................. 73
7
REFERENCES ...................................................................................................... 75
6
NOMENCLATURE
A(λ,θ)
Aabs
Ac
Ai
As, Ap
b0
c
Ci
Ceff
d
E(λ,θ)
Ea
Ea,corr
Einterval
Etot
F’
F’av
F’c(x)
F’c,a
F'(τα)b
F'(τα)d
F'UL1
F'UL2
Fij
F12
G
G(θ)
Gb
Gd
Gtotal
h
hsun
h1
h2
h3
h4
hr
Ib(λ,T)
Ib
Ie
Isol(λ)
k
kb
kc
Kτα
L
(mC)e
n
N
q(θ)
qcorr(θ)
Qi
Absorptance at wavelength λ and angle θ [-]
Area of absorber [m2]
Collector aperture area [m2]
Area of surface i [m2]
Amplitude of incoming radiation for s- and p polarised light respectively [-]
Incidence angle modifier coefficient [-]
Speed of light [m/s]
Area concentration [-]
Effective concentration [-]
Thickness [m]
Emittance at wavelength λ and angle θ [-]
Annually collected zero-loss energy not corrected for F’c[x] [a.u.]
Annually collected zero-loss energy corrected for F’c[x] [a.u.]
Annual energy available within acceptance interval [kWh/m2]
Total annual energy incident on surface [kWh/m2]
Collector efficiency [-]
Mean temperature collector efficiency factor [-]
Local optical efficiency factor distribution [-]
Annual optical efficiency factor [-]
Zero Loss efficiency for beam radiation [at normal incidence] [-]
Zero Loss efficiency for diffuse radiation [in collector plane] [-]
First order heat loss coefficient [W/m2K]
Temperature dependence in heat loss coefficient [W/m2K2]
Exchange factor [-]
View factor between surfaces 1 and 2 [-]
Direct solar irradiance [kWh/m2]
Annually projected solar radiation distribution [-]
Annual beam radiation [kWh/m2]
Annual diffuse radiation [kWh/m2]
Annual total radiation [kWh/m2]
Planck constant [Js]
Solar height in the horizontal system [°]
Internal convection coefficient [W/m2K]
Plate to cover radiation coefficient [W/m2K]
External convection coefficient [W/m2K]
External radiation coefficient for clear sky conditions [W/m2K]
Radiation heat transfer coefficient [W/m2K]
Blackbody radiation wavelength distribution [-]
Total amount of energy emitted [WK2/m2]
Applied electric current [A]
Incident solar radiation distribution [W/m3]
Extinction coefficient [-]
Boltzmann constant [J/K]
Insulation conductivity [W/mC]
Incidence angle modifier [-]
Insulation thickness [m]
Effective thermal capacity for the collector [J/m2K]
Optical refractive index [-]
Complex refractive index [-]; number of intervals/surfaces [-]
Collected zero-loss energy not corrected for F’c[x] [a.u.]
Collected zero-loss energy corrected for F’c[x] [a.u.]
Amount of energy exchanged through radiation by surface i [W]
7
qu
Qu
rs, rp
G
r
R
R(λ,θ)
Rs , Rp
Rsol
S
G
s
Sc(x)
t
Ta
Tf
Ti
Tin
Tout
Tpm
Tsol
Tt(λ,θ)
(UA)edge
Ub
Ue
UL
U Llab
Ut
U1
U2
V
Ve
x
zi
αsol
β
δ
δrms
∆T
ε
εi
εtherm
φ
γs
η0b
η0d
λ
µ
θ
θc
θl
θt
ρ
ρd
σ
ω
Useful delivered energy output [kWh/m2]
Useful delivered energy output [kWh]
Ratio between reflected and incoming light for s-and p polarised light [-]
Position vector [-]
Reflectance amplitude [-]
Reflectance intensity at wavelength λ and angle θ [-]
Amplitude of reflected radiation for s- and p polarised light respectively [-]
Solar reflectance [-]
Radiation absorbed by the collector [kWh/m2]
Unit vector in the direction of the wave propagation [-]
Concentration distribution on the absorber [-]
Time [s]
Ambient temperature [°]
Mean fluid temperature in the collector [K]
Temperature of surface i [°]
Temperature of water out of the collector [°C]
Temperature of water into the collector [°C]
Mean absorber plate temperature [°]
Solar transmittance [-]
Transmittance at wavelength λ and angle θ [-]
Edge loss coefficient-area product [W/K]
Back loss coefficient [W/m2C]
Edge loss coefficient [W/m2C]
Collector overall heat loss coefficient [W/m2C]
Laboratory U-value [W/m2C]
Top loss coefficient [W/m2C]
First order heat loss coefficient [W/m2K]
Second order heat loss coefficient [W/m2K2]
Volume [m3]
Applied electric voltage [V]
Location on absorber [m]
Distance from mean surface level [m]
Solar absorptance of the absorber [-]
Aperture tilt [°]
Phase change [-]
rms-value [m]
Temperature difference between Tf and ambient temperature [K]
Dielectric permeability [-]
Emittance of surface i [-]
Thermal emittance [-]
Angle [°]
Solar azimuth [°]
Beam zero-loss efficiency [-]
Diffuse zero-loss efficiency [-]
Wavelength [m]
Magnetic permeability [-]
Angle [°]
Acceptance half angle [°]
Longitudinal projected angle of incidence [°]
Transversal projected angle of incidence [°]
Density [kg/m3]
Reflectance of a cover system for diffuse radiation incident from the bottom side [-]
Stefan Boltzmann constant [W/m2K4]
Angular frequency [1/s]
8
1 INTRODUCTION
Using solar thermal collectors is an environmentally friendly way of producing energy
for space heating and/or domestic hot water since it causes no carbon dioxide
emissions. The energy source is practically inexhaustible but the Swedish climate
limits the use of solar collectors to late spring, summer and early fall. An auxiliary
heating system is needed to cover the heating and domestic hot water load in the
building all year round. The solar thermal systems are normally designed to barely
cover the summer load in order not to over-size the system and thus make it as cost
effective as possible. There is also a possibility of building systems with seasonal
storage, but the storage space needs to be substantial to reduce the losses. This is only
of interest for very large solar collector fields.
There are about 200 000 m2 of installed solar collectors in Sweden. The major part of
these installations consists of flat plate solar collectors. The market involves mainly
small manufacturers and a large fraction of the production is manual. With a small
market and mainly manual production the cost of solar energy is in most cases too
high to compete with other energy supplies. There are generally speaking two ways to
reduce the cost per produced kWh; either by increasing the efficiency at a moderate
extra cost or to reduce the investment cost significantly without reducing the delivered
energy output too much.
The primary aim of this work was to obtain more knowledge about solar thermal
collectors and their components to be able to reduce the cost of energy produced with
solar thermal collectors. The main part of the work was focused on studying a
concentrating collector called the Maximum Reflector Collector, MaReCo, where the
cost of solar energy heating is reduced by replacing part of the expensive absorber area
with inexpensive reflector area and concentrate the incoming solar radiation.
The MaReCo has an asymmetrical design to fit the asymmetrical solar radiation
distribution in Sweden. Different types of MaReCo have been developed for standalone, roof or wall mounting. The delivered energy output of the MaReCo is in general
lower per aperture area than that of the flat plate collector. The purpose of the studies
of the MaReCo concept was to optimise the design, increase the efficiency and further
reduce the costs of the components in the collector to increase the benefit/cost ratio.
Prototypes of MaReCo for stand-alone, roof and wall mounting were built and
outdoor-tested at the Vattenfall Laboratory in Älvkarleby, Sweden. Hot-box
measurements were performed to study heat losses for different collector component
configurations in the stand alone MaReCo. To optimise the design of the geometry of
the reflectors, detailed studies of the annual solar radiation distribution at different
angles of incidence have been made to maximise the concentration ratio and still
collect a high percentage of the available solar radiation.
Part of the work has concerned simulations of flat plate collectors. The flat plate solar
thermal collector is by far the most common collector type on the market. Even though
1
the technology is well known there is still a lot that can be done to improve the
efficiency of the flat plate collectors and to obtain more knowledge about the
performance of flat plate collectors. For example not all roofs have the optimum tilt
and azimuth. This initiated a study of how the delivered energy output from different
flat plate solar collectors is affected by changes in tilt and azimuth. Another study
presented in this work concerns the variation in delivered solar collector energy output
with annual climate variations and how the delivered energy output varies with latitude
in Sweden. The possibility of increasing the efficiency by optimising the material
properties of the collector components was also investigated.
Two collector components, the reflector and the absorber have been studied in detail.
A study of the scattering properties of two different reflector materials was made to
investigate if a rough material can be used as a reflector in a solar collector. A
spectrally selective Sunstrip absorber was investigated and one of the layers in the
coating was analysed to optimise the absorbing properties.
This thesis involves studies from the material properties of the collector components to
performance analyses of the whole collector. It is important to have knowledge about
the components to be able to optimise the system. The work was carried out at the
division of Solid State Physics, department of Materials Science, The Ångström
Laboratory, Uppsala University. Traditionally this division studies the materials optics
of solar collector components but through the involvement in the Energy Systems
Programme some system studies have started. The Energy Systems Programme is a
Swedish research school funded by the Foundation for Strategic Research, SSF, the
Swedish Energy Agency, STEM, and Swedish industry.
2
2 THEORETICAL BACKGROUND AND EXPERIMENTAL
METHODS
2.1 Collector analysis
The delivered energy output from the solar collector depends on the optical and
thermal properties of the collector. This chapter contains a theoretical background of
the parameters used to characterise the collector optically and thermally. Two methods
to characterise the collector optically are presented. The first is to measure the optical
properties of the absorber and the glazing and then calculate the zero loss efficiency
and the incidence angle modifier. The second is through outdoor measurements where
the optical and thermal properties of the collector are determined simultaneously by
fitting to a collector model. Another method for thermal characterisation is also
presented, indoor hot-box measurements. The components of the solar collector are
presented.
2.1.1 The solar collector
Two different collector types have been studied in this work, concentrating collectors
and flat plate collectors. The major part has been focused on concentrating collectors,
shown in a general sketch in Fig. 1.
Fig. 1 Sketch of a concentrating collector.
The incoming light is reflected in the concentrating reflectors and then impinges on the
absorber where it is transferred to the heat carrying medium. Because of the
concentration the hot absorber area is reduced compared to that of the flat plate
collector. The light is concentrated according to
Ci =
Aabs
Ac
(1)
where Aabs is the absorber area and Ac is the aperture area.
3
In flat plate collectors, seen in Fig. 2, the absorbers are placed in an insulated collector
box with a sealed glazing on top to reduce heat losses and to protect the absorber from
rain and wind. An optional transparent insulation material (TIM) can be placed
between the glass cover and the absorber to decrease heat losses by convection and
radiation. In Fig. 2 a teflon film is shown. There are also more complex structures that
can be used, for example honeycomb transparent insulation which consists of small
plastic cells that are added together forming a honeycomb structure.
Teflon
Cover glass
Collector
box
Absorber
Fig. 2 Sketch of a flat plate solar collector.
The efficiency of a flat plate solar collector depends on its optical and thermal losses
according to the basic energy balance equation (Duffie and Beckman 1991) in Eq (2).
Qu is the useful output, Ac is the collector area, S is the radiation absorbed by the
collector per unit area of collector (incorporating the optical losses), UL is the overall
loss coefficient, Tpm is the mean plate temperature and Ta is the ambient temperature.
Qu = Ac [ S − U L (Tpm − Ta )]
(2)
Optical losses originate from reflection of the solar radiation in the cover glass, the
transparent insulation and the absorber surface. For the concentrating collector losses
are added due to reflection losses and optical errors in the reflectors. Thermal losses
are due to thermal conduction, convection and radiation. If the optical and thermal
characteristics of the different components are known, collector parameters can be
calculated and used in simulations to find the annual collector performance. The
following sections describe the optical and thermal characterisation that is needed for
this purpose.
2.1.2 Introduction to optics
The optical performance of a material depends on the wavelength of the incident light.
The interaction of electromagnetic radiation with matter is described by the Maxwell
equations (Wangsness 1986). In these equations electricity and magnetism are unified
into electromagnetism. A propagating plane wave is described by
E = E0e
n G G k G G

 i ( ω t − c ω r ⋅s ) − c ω r ⋅ s 


(3)
4
G
G
where r is the position vector and s is the unit vector describing the direction of wave
propagation in the chosen co-ordinate system. The optical refractive index, n, is the
ratio of the speed of radiation (as light) in vacuum to that in the medium. The
extinction coefficient, k, is a measure of the rate of extinction of transmitted light via
absorption in the medium. The numerical values of n and k vary with material and
wavelength. The quantities n and k define the complex refractive index and describe
the optical behaviour of the electromagnetic radiation according to
N=n+ik
(4)
The Fresnel equations describe the reflection and transmission of light when passing
from one medium to another. The ratio between the reflected and the incoming
radiation, the amplitude reflectance, is for a bulk material described by
rp =
rs =
N 2 cosθ1 − N 1 cosθ 2
N 2 cosθ1 + N 1 cosθ 2
(5)
Rs N 1 cosθ1 − N 2 cosθ 2
=
As N 1 cosθ1 + N 2 cosθ 2
(6)
Rp
Ap
=
where p indicates p-polarised light and s indicates s-polarised light, index 1 refers to
the medium before the interface and index 2 to the medium after the interface. Angles
θ1, angle of incidence, and θ2, angle of refraction, are formulated in Snell’s law
N 1 sin θ1 = N 2 sin θ 2
(7)
For incident unpolarised light the amounts of s- and p-polarised light are equal, and the
reflectance is found as
2
R=
rp + rs
2
(8)
2
In solar energy materials a thin film is often applied on a substrate to obtain the desired
optical properties. Such a case is sketched in Fig. 3. The arrows indicate the direction
of light reflected from and transmitted through the film.
5
Fig. 3 Geometry used for describing the optics of a thin film on a substrate. f-front, b-back, dfilm thickness. After Granqvist (1991).
Using the Fresnel’s relations the amplitude reflectance for the film, r2, is obtained from
(Born and Wolf 1980).
f
2s,p
r
=
rs12, p + rs23, p e 2iδ
(9)
1 + rs12, p rs23, p e 2iδ
The measurable light intensity is denoted R and is given by
2
R2fs,,bp = r2fs ,,bp
(10)
This can be generalised into multiple layer films using matrix formalism further
explained in for example Born and Wolf (1980). Each single layer is characterised by
a matrix m
 m11
m =
 m21
m12 

m22 
(11)
The elements in the matrix are
m11 = m22 = cos[
m12 = −i sin[
2πn( λ )d cos θ
]
(12)
]/ P
(13)
λ
2πn( λ )d cos θ
λ
2πn( λ )d cos θ
]
m21 = −iP sin[
λ
ε
P=
(s-polarised)
µ
P=
(14)
(15)
µ
(p-polarised)
ε
(16)
6
N(λ) is the complex refractive index, d is the thickness of the single layer and θ is the
angle of incidence. The matrices of the single layers 1 to N are then multiplied using
matrix multiplication to obtain the matrix M for the stack of layers
M = m1 ⋅ m2 ...⋅m N
(17)
The reflectance of the coating with multiple layers is found from the matrix elements
in M according to
 ( M 11 + M 12 PN +1 ) P0 − ( M 21 + M 22 PN +1 ) 

R=
 ( M 11 + M 12 PN +1 ) P0 + ( M 21 + M 22 PN +1 ) 
2
(18)
P0 and PN+1 denote the quantity P in Eq. (15) or (16) for the medium of incidence and
the substrate respectively.
2.1.3 Introduction to thermal radiation
Thermal radiation is electromagnetic radiation described in Eq. 3 and travels at the
speed of light. All bodies emit radiation according to their temperature, the blackbody
is a perfect absorber and absorbs 100% of the incoming radiation and it is also a
perfect emitter of thermal radiation. Planck’s law (Nordling and Österman 1987) gives
the wavelength distribution of the emitted radiation
2πc 2
I b (λ , T ) = 5
λ [exp(hC0 / λk b T ) − 1]
(19)
The location of the maximum in the energy density is found through differentiating the
Planck distribution and equating to zero. This relation is called Wien’s displacement
law (Duffie and Beckman 1991)
λ max T = 2897.8µmK
(20)
For solar collector purposes the radiation distributions of the sun and the blackbody
are important. Their maxima are separated according to Wien’s displacement law.
Before the solar radiation reaches the earth it is attenuated due to scattering and
absorption in the atmosphere. Fig. 4 shows the solar radiation distribution with air
mass 1.5 and a blackbody radiation distribution for a body of temperature 100°C.
7
3
Radiation distribution solar/blackbody [W/m ]
1.2 10
9
1 10
9
8 10
8
6 10
8
4 10
8
2 10
8
0
Solar radiation distribution
Blackbody radiation distribution
1
10
Wavelength (um)
Fig. 4 Incident solar radiation distribution with air mass 1.5 according to the ISO standard
9845-1 (1992) (dotted) and blackbody radiation distribution for a temperature of 100°C.
If Planck’s distribution is integrated over all wavelengths the total amount of energy
emitted by the blackbody is obtained (Duffie and Beckman 1991)
∞
I b = ∫ I b ( λ , T )dλ = σT 4
(21)
0
where σ is the Stefan-Bolzmann constant equal to 5.6697 ×10-8 W/m2K4.
2.1.4 Characterisation of solar collector components
2.1.4.1 Introduction
A thorough analysis of the optical properties of the components in the solar collector,
such as reflector, absorber and glazing, is needed to understand the optical
performance of the collector. Since the optical properties of the materials are
wavelength dependent the optical characterisation has to be made in the appropriate
wavelength range. For solar energy materials in low temperature solar collectors these
are the solar spectral range 0.3 to 2.5 µm and the infrared wavelength range up to
about 50 µm. The solar collector characterisation parameters can be obtained through
various methods. The frequently used method in this work is based on spectral optical
measurements.
Once the spectral reflectance and/or transmittance are known, the components can be
characterised. The relation between the absorptance, transmittance and reflectance is
A( λ ,θ ) + Tt ( λ ,θ ) + R( λ ,θ ) = 1
(22)
Using Kirchoffs law a relation between the light that is absorbed and emitted is found
A( λ ,θ ) = E ( λ ,θ )
(23)
8
2.1.4.2 Reflectors
A reflector material is characterised by the solar reflectance, Rsol.
2 .5
Rsol =
∫I
sol
( λ ) R( λ ,θ )dλ
0 .3
(24)
2 .5
∫I
sol
( λ )dλ
0 .3
R(λ,θ) is the spectral reflectance of the material at a certain incidence angle θ and
Isol(λ) is the incident solar radiation distribution from Fig. 4.
The reflector quality is of great importance for the optical efficiency of the solar
collecting device. High total reflectance in the solar wavelength range is important.
Aluminium is often used in solar energy applications. If it is protected with an
anodised layer it has a specular reflectance of approximately 80% and a total
reflectance of 85% (Nostell et al 1997). If it is instead covered with a polyvinyl difluoride lacquer the corresponding values are around 75 and 83% (Nostell et al 1998).
Silver has a significantly higher solar reflectance, but is also more expensive. Glass
covered with a thin silver film has a specular reflectance of roughly 95%, depending
on the glass (Paper VIII).
The surface roughness of the reflector determines how the reflected light is scattered.
A measure of the surface roughness is the root mean square (rms) value, δrms
δ rms =
1
N
N
∑z
i =1
2
i
(25)
where N is the number of measurement points and zi is the distance from the mean
surface level. Light that is reflected by a surface as shown in Fig. 5 can be divided in
three types. The specularly reflected light (a) is the light that is scattered within a small
solid angle around an angle equal to the angle of incidence. To obtain specularly
reflected light the surface must be smooth, i.e. the rms value is much smaller than the
wavelength of the light incident on the surface. Isotropically scattered light is found
for rough samples with no preferential structure leading to an equal scattering in all
directions as in case (b). General scattering, (c), is found for surfaces with some
preferential surface structure. A solar reflector generally exhibits anisotropical
scattering with a specular component and a general component.
9
(a)
(b)
(c)
Fig. 5 Reflection from surfaces of different surface roughnesses from Duffie and Beckman
(1991).
Most often high specular reflectance is preferable, but this is not always necessary.
Low-concentrating devices, such as compound parabolic concentrators (CPC) are less
sensitive to scattering of the incident radiation than high-concentrating devices such as
parabolic troughs or dishes. Furthermore, if the non-specular radiation is scattered in
linear corrugations with a particular geometry or unidirectional rolling grooves, this
can be beneficial for certain concentrator geometries (Rönnelid and Karlsson 1998,
1999, Perers et. al 1994). Since rolled aluminium is cheap compared to other reflector
materials, it can be a cost-effective and suitable material for certain solar energy
applications. It is therefore of interest to characterise reflectance and light scattering
from rolled aluminium of different surface roughness in order to evaluate their
feasibility as reflector materials. If a rough material with rolling grooves is studied the
scattering from the material shows a very characteristic pattern, depending mainly on
the orientation of the rolling grooves. A very large part of the reflected radiation is
scattered as in one-dimensional reflection gratings.
Angle resolved scattering, ARS, were performed to obtain more information about the
optical scattering of the reflectors. A method to characterise and evaluate the scattering
properties was developed in Paper IX, based on adding ARS-data together in different
regions according to:
Specular reflectance, SR- The radiation reflected between |φ|<3° and |θ|<3°
Low –Angle Scattered Light in the Scatterband, LAS-B- The radiation reflected within
the angular range 3°<|φ|<9° and 3°<|θ|<9° within the scatterband
Low-Angle Scattered light, LAS- The radiation reflected between |φ|<9° and |θ|<9°
excluding the radiation found in SR and LAS-B
High-Angle Scattered Light in the Scatterband, HAS-B- The radiation reflected
between |φ|>9° and |θ|>9° within the scatterband
High-Angle Scattered Light, HAS- The radiation reflected between |φ|>9° and |θ|>9°
that is not included in HAS-B
The angle φ refers to the angular deviation from the specular direction in the direction
perpendicular to the plane created by the surface normal and the incoming beam
(azimuthal angle). θ is the deviation from the specular spot in the direction parallel to
the plane created by the surface normal and the incoming beam. A feasible reflector
10
should have a large part of the reflected radiation within the SR region, especially if
the material is used as an internal reflector, like for example in a compound parabolic
concentrator.
9
1 10
9
8 10
8
6 10
8
4 10
8
0.4
2 10
8
0.2
0
0
1
0.8
3
radiation (W/m )
1.2 10
0.6
0.5
1
Wavelength (µm)
5
Reflectance
Spectral distribution solar/blackbody
2.1.4.3 Absorbers
To investigate how much of the radiation that will be absorbed and thermally reemitted, the spectral reflectance can be recorded in the solar wavelength interval,
approximately 0.3 to 2.5 µm and in the infrared interval, approximately 2.5 to 20 µm..
In Fig. 6 the reflectance curve for a spectrally selective absorber is shown together
with the spectral distribution of solar radiation (dotted) and the spectral distribution of
blackbody radiation for a surface with T=100°C from Fig. 4.
10
Fig. 6 Incident solar radiation distribution with air mass 1.5 according to the ISO standard
9845-1 (1992) (dotted), blackbody radiation distribution for absorber plate temperature
100°C and measured reflectance for a sputter deposited spectrally selective solar absorber.
In order to obtain the solar absorptance and thermal emittance, the measured spectral
reflectance is weighted against the solar spectrum and a thermal spectrum,
respectively. The spectral distribution of the solar radiation depends on which air mass
is chosen. For an opaque object Eq. (22) and (23) leads to the relation
A( λ ,θ ) = E ( λ ,θ ) = 1 − R( λ ,θ )
(26)
The solar absorptance is found through
2 .5
α sol =
∫I
sol
( λ )(1 − R( λ , θ )dλ
0.3
(27)
2 .5
∫I
sol
( λ )dλ
0. 3
where R(λ,θ) is the reflectance distribution.
11
The hemispherical thermal emittance of the absorber at temperature T is found through
20
ε therm =
∫ [1 − R(λ ,θ )]I
b
( λ , T )dλ
2 .5
(28)
20
∫I
b
( λ , T )dλ
2 .5
where Ib(λ,T) is the spectral distribution of blackbody radiation at temperature T from
Eq (19).
Typical values of αsol and εtherm for a spectrally selective absorber are 0.93-0.96 and
0.05-0.25 respectively. The spectrally selective absorber shown in Fig. 6 is
characterised by αsol=0.95 and εtherm=0.10. Further reading on spectrally selective
absorbers is found in Wäckelgård et al (2001) or Granqvist (1991). If the absorber is
non-selective, as ordinary black paint, αsol and εtherm have about the same value, around
0.95. An ideal spectrally selective absorber would have R(λ,θ) equal to zero
throughout the whole solar spectrum and equal to unity in the thermal range, but this is
not possible with the materials known today.
2.1.4.4 Glazing
The solar transmittance is found by integrating the transmittance of the material with
the solar spectrum at each wavelength and incidence angle according to (Duffie and
Beckman 1991)
2 .5
Tsol =
∫I
sol
( λ )Tt ( λ ,θ )dλ
0.3
(29)
2 .5
∫I
sol
( λ )dλ
0 .3
where Tt(λ,θ) is the transmittance distribution at angle θ.
Typical values of solar transmittance are for ordinary float glass 83-85% and for low
iron glass 90% (Nostell et al 1999). Low iron glass is the most frequently used glass
for solar collector covers, and the transmittance is fairly constant over the solar
spectrum. Ordinary float glass has a more wavelength dependent transmission. Teflon
film used in solar collectors has a solar transmittance of 96% (Rönnelid and Karlsson
1996). Honeycomb (HC) transparent insulation material has a Tsol that depends on the
material and the geometry. Poly-carbonate HC with a cell size 3.5x3.5 mm of
thickness 50 mm and 100 mm and have a diffuse Tsol of 81% and 75% respectively.
12
2.1.5 Instruments for optical characterisation
The spectral measurements were in general obtained with a spectrophotometer
equipped with an integrating sphere in the 0.3-2.5 µm region and an FTIR (Fourier
Transform Infra Red) spectrophotometer in the 2.5-20 µm region. One example of
such a measurement is found in Fig. 6 were the reflectance for a spectrally selective
absorber is shown. The measured spectral reflectance was then used to determine the
integrated values Rsol, αsol, εtherm and Tsol in a numerical integration routine.
Absolute measurements of spectral specular reflectance and transmittance at different
angles of incidence were performed in a non-standard spectrophotometer equipped
with an integrating sphere as detector. The sample is placed in the centre of a
horizontal ring, in a holder, which can rotate around its vertical axis. The detector can
be swept around the ring then allowing for measuring the specular reflectance and
transmittance at different angles of incidence. Description in detail of this measuring
system is published in Roos (1997).
Profilometry was used to investigate the surface roughness of reflector materials. In
this case white light optical microscopy was used, a WYKO NT-2000 interference
fringe microscope with a Mirau interferometer. This was used to obtain the surface
root mean square height and slope and the power spectral density function.
Angle resolved scattering, ARS, was measured with a set up shown in Fig. 7. A red
He-Ne laser (633 nm) was used as a light source. The sample could be tilted to vary
the angle of incidence on the sample. The detector was placed on a device that could
move over the sphere in angles θ and φ (defined in Fig. 7) allowing it to measure the
intensity in three dimensions. The distance between the measurement points was
determined by the intensity of the signal; shorter steps were taken when the signal
level was high.
Fig. 7 Schematic drawing of the ARS measurement equipment. Pi, incident beam; Ps,
scattered intensity; P0, the specular component. Angles θ and φ are the in-and out-of-plane
scattering angles, respectively.
Spectral measurements were also made with total integrated scattering, TIS, in the
region 0.37-0.97 µm (Rönnow and Veszelei 1994). With TIS a focusing half-sphere
with the detector placed in the focal point is used. Due to the focusing properties very
13
low intensities can be detected. To validate the ARS-measurements screens were used
that covered parts of the half-sphere in fixed angular intervals (Rönnow 1997).
2.1.6 Collector heat losses
2.1.6.1 Introduction
In a solar collector, energy is lost through radiation, convection and conduction.
Losses through thermal radiation introduced in section 2.1.3 are significant in the case
of a solar collector since the total energy transfer is low and thereby the radiation
losses are a large part of the total losses. This chapter reviews selected parts of the heat
transfer that is important in a solar collector starting with radiation heat transfer and
then proceeding with a short section on convection and conduction. These losses are
usually added together in one quantity, the overall loss coefficient UL of the collector,
and includes the top, bottom and edge losses.
The heat losses of a solar collector can be experimentally determined in a number of
ways, for example through hot-box measurements or outdoor/solar simulator collector
tests. They can also be determined through theoretical calculations. Two of these
methods have been used in the work presented in this thesis; hot-box measurements
and outdoor collector tests.
2.1.6.2 Radiation heat transfer
When N surfaces are facing each other a radiation exchange takes place. The amount
of energy that surface i exchanges pair wise with the N-1 other surfaces, Qi, depends
on the emittance of the surfaces, εi & εj, exposed area of surface i, Ai, total exchange
factor, Fij , and temperature difference between the surfaces according to Eq. (30)
(Duffie and Beckman 1991). The exchange factor depends on how the surfaces emit
radiation, if there is a specular component or if the radiation is diffuse and the view
factor. If the reflected radiation from the surface lacks a specular component the
exchange factor is reduced to the view factor. The assumptions that are made are that
the surface is grey (radiation properties are independent of wavelength), diffuse or
specular-diffuse, has a uniform temperature difference and that the incident energy
over the surface is uniform.
N
Qi = ∑ ε i ε j Ai Fij σ (T j4 − Ti 4 )
(30)
j =1
A large part of the heat transfer problems in solar energy applications involve radiation
between two surfaces. Eq. (30) is then simplified to
Q1 = − Q2 =
σ (T24 − T14 )
(31)
1 − ε1
1− ε2
1
+
+
ε 1 A1 A1 F12 ε 2 A2
Two special cases of this relation are useful:
14
1. Two infinite parallel surfaces, i.e. a flat plate collector, where the areas are equal
and the view factor is unity:
(T24 − T14 )
Q = Aσ
1
1
+
−1
ε1
(32)
ε2
2. The radiation exchange between the sky and a collector, the sky is considered a
blackbody radiator with sky temperature Ts. In this case the collector is considered
small compared to the surrounding sky (A1/A2→0) and the view factor is unity.
The relation is simplified to
Q = ε 1 A1σ (T2 4 − Ts4 )
(33)
To simplify to linear relations in Eq. (31) the radiation heat transfer coefficient, hr, is
introduced according to
Q = A1hr (T2 − T1 )
(34)
where
hr =
σ (T22 − T12 )(T2 + T1 )
(1 − ε 2 ) A1
1 − ε1
1
+
+
F12
ε1
ε 2 A2
(35)
2.1.6.3 Convection heat transfer
Heat is also transferred through natural convection in the solar collector. The air that is
closest to the hot surface is heated and the density is lowered. This causes the hot air to
rise and cold air to fall and a flow of air is created. The rate of heat transfer is
described with the Nusselt-, Rayleigh- and Prandtl number. These quantities are
dimensionless and depend on material properties, temperature difference between the
surfaces and spacing. They are further described, for example, in Duffie and Beckman
(1991). The natural convection can be suppressed through transparent insulation in the
spacing, for example a single teflon sheet or a honeycomb structure.
2.1.6.4 Conduction heat transfer
When two media are in contact heat is transported from the hot medium to the cold by
transferring kinetic energy from one molecule/atom to an adjacent molecule/atom. The
amount of energy that is transferred is dependent on temperature difference, contact
area and heat conductivity in the participating materials. Conduction can occur for
example through the insulation in the collector box.
15
2.1.6.5 Collector overall loss coefficient
The collector overall loss coefficient UL is used to characterise the heat losses in Eq.
(2). UL is the sum of the heat losses from top, back and edges:
U L = Ut + Ub + Ue
(36)
The major part of the heat losses escapes through the top of the collector. According to
Morrison (2001) the back and edge losses are of the order of 10% and 5% respectively
of the top losses.
If the sky temperature is approximated with the ambient temperature; the top loss
coefficient is found as (Morrison 2001):
Ut =
1
(37)
1
1
+
h1 + h2 h3 + h4 '
where:
h1
h2
Internal convection coefficient, 3-5 W/m2K
Plate to cover radiation coefficient, 6-8 W/m2K for εp=1.0 and 0.6-0.8
W/m2K for εp=0.1 (Calculated with Eq. 35)
External convection coefficient, 5.8 W/m2K for V=1 m/s and 8.8 for V=2
m/s
External radiation coefficient for clear sky conditions, 5-6 W/m2K
h3
h4
The use of a spectrally selective absorber thus reduces the heat losses significantly
compared to using a black painted absorber since h2 is decreased with a factor of 10.
The heat losses can also be reduced by including some kind of convection suppression,
for example teflon film or honeycomb transparent insulation which reduces the
internal convection coefficient and the radiation losses.
The back losses depend on the insulation thickness, L, and conductivity, kc, according
to (Duffie and Beckman 1991)
Ub =
kc
L
(38)
The edge losses depend on the edge loss coefficient-area product and the collector area
(Duffie and Beckman 1991):
Ue =
(UA) edge
(39)
Ac
16
When characterising a collector experimentally the temperature dependence of the
collector overall loss coefficient can be assumed to be linear (Duffie and Beckman
1991)
U L = U 1 + U 2 (Tpm − Ta )
(40)
Where U1 is the first order heat loss coefficient and U2 the second order heat loss
coefficient that determines the temperature dependence in the overall loss coefficient.
2.1.6.6 Heat loss collector characterisation methods
Two methods of characterising heat losses have been used in this work, the hot-box
method and the outdoor test method.
The major draw back with the hot-box method is that the obtained U-value is not
directly applicable for outdoor conditions but rather a laboratory U-value, since wind
and sky effects are not taken into account. Another difference is that in the hot-box
measurement only the absorber plate is heated while in a collector placed outdoors the
whole collector is heated. This difference is especially important for a concentrating
collector where the absorber area is smaller than the aperture area. Corrections are
needed to compensate for these differences before the values are used to estimate an
annual delivered energy output with simulations. The advantages are that no real
prototype is needed, only a simplified collector construction can be used. It is also
possible to study the materials in the collector one by one in a standardised equipment
that facilitates comparison measurements.
The thermal parameters obtained with the outdoor test method are directly applicable
in collector simulations to get an estimate of the annual performance of the collector
and not only laboratory U-values. Another advantage with this method is that the
thermal and optical performance are obtained simultaneously. With this method a
collector prototype needs to be built and it is harder to evaluate the materials in the
collector separately.
The hot-box method
The regular absorber is replaced by an electrically heated absorber plate simulating the
warm absorber. This method was used to characterise the heat losses in a stand alone
MaReCo in Paper II.
To measure the U-value with the hot box method thermocouples are attached to
measure the temperature of the heated absorber plate, Tpm, and the ambient, Ta. The
laboratory collector overall loss coefficient is then calculated through:
U Llab =
Ve I e
Ac (Tpm − Ta )
(41)
where Ac is the aperture area, Ve is the applied voltage and Ie is the current. Steady
state is in general reached after several hours, depending on the thermal inertia of the
17
collector. The hot-box method can be used for flat plate and concentrating collectors
and also to test the thermal properties of materials like for example transparent
insulation. In the latter case the electrically heated absorber is placed in a well
insulated box and the material to be investigated is placed covering the top of the box.
If the applied electric power is varied a series of U-values at different temperature
differences between the absorber and the ambient is obtained as seen in Fig. 8. The
linear relation was suggested in Eq. (40), and a linear fit is therefore indicated by the
solid line in Fig. 8.
2.6
2
U-value (W/m K)
2.4
2.2
2
1.8
10
20
30
40
50
60
70
T -T (K)
pm
a
Fig. 8 U-value as a function of temperature difference between absorber and ambient for a
stand-alone MaReCo with spectrally selective, vertical absorber and open ventilation
channels. The solid line indicates a least square fit of the measurements.
The hot-box technique can also be used to study the temperature distribution within
the collector. It is especially important if temperature sensitive materials such as polycarbonate transparent insulation is used in the collector. In this case thermocouples are
placed at the points of interest in the collector box and then the applied power is
varied.
Outdoor collector efficiency tests
The test site for outdoor measurements described in this thesis is situated at the
Älvkarleby Laboratory and it has the capacity to evaluate up to 15 collectors at the
same time. It has two main systems, one in which the inlet temperature at each
collector can be controlled in order to get a variety of operating conditions and one
system where all collectors are connected in series with a common flow, facilitating
comparison measurements. In the common flow system, which was used in the
evaluation in Paper I, the water is cooled after each collector to get the same inlet
temperature for all collectors. With this arrangement, where all collectors have the
same water flow, possible uncertainties in flow measurements have no effect on the
comparison measurements. The collector inlet and outlet temperatures were registered
together with the flow of water/glycol. The ambient temperature and solar radiation
(global and diffuse) measured both on a horizontal surface and in the collector plane
were recorded. The radiation was also measured with a sun tracking pyranometer and a
18
tracking pyrheliometer. The diffuse radiation was measured by using a shadow ring on
the pyranometer. All data were sampled with a Campbell Scientific data logger every
10:th second and the sampled values were stored as 10 minutes mean values.
Flow, temperatures and irradiation were measured during a number of days with
various combinations of irradiation and collector temperatures. From these data, the
energy output, qu, was calculated according to
qu = ρVcp(Tout-Tin)/Ac
(42)
where ρ represents density, V volume, cp heat capacity, Tout temperature out of the
collector, Tin temperature into the collector and Ac aperture area.
The incidence angle for beam radiation in the collector plane and the measured- and
the estimated output from the prototypes were calculated from the measured data. The
collector parameters in Eq (43) were then determined with the method of dynamic
testing using Multiple Linear Regression, MLR, on measured data. With the dynamical
testing method collectors can be evaluated not only during perfectly clear days but also
during partly cloudy days. The method is further described in Perers (1993 and 1997)
and Perers and Walletun (1991). The dynamic testing model has been compared to
other test methods and is considered theoretically complete taking almost all effects
into account (Nayak and Amer 2000). The parameters obtained with the dynamic
testing model are: beam zero loss efficiency, F’(τα)b, diffuse zero loss efficiency,
F’(τα)d, first order heat loss coefficient, F'UL1, second order heat loss coefficients,
F'UL2, collector thermal capacitance, (mC)e, incidence angle modifier, Kτα.The
incidence angle modifier can be expressed either as the incidence angle modifier
coefficient, b0, or by an incidence angle dependence matrix. These parameters are
further described in section 2.1.7.
In order to verify the parameters determined by the dynamic testing model different
diagrams are drawn. In a daily diagram the measured and the modelled output are
compared during a whole day. An example of this is found in Fig. 9, where it can be
seen that the agreement between the model and the measured data is very good. The
diagram also shows the daily irradiation. The energy output obtained with the dynamic
testing method follows the measured output even if there are sudden changes in
irradiation, e.g. rapidly passing clouds as seen in Fig. 9. In a model/measurementdiagram, the simulated output is plotted versus the measured output. This is shown in
Fig. 10. Ideally the dots should form a straight line y=x. The parameters obtained from
the dynamic testing-model are then fed into a simulation program to get an estimate of
the annually delivered energy output.
19
Itot
Pmeasured
Pdyn. model
800
600
400
200
0
00:00
600
Modelled power (W/m2)
Power (W/m2)
1000
500
400
300
200
100
04:00
08:00
12:00
16:00
20:00
100
Time of day
200
300
400
500
600
700
2
Measured power (W/m )
Fig. 9 Daily diagram from August 28th 2000
showing global radiation, modelled power
from the dynamical testing model and
measured power in W/m2 for the
concentrating collector.
Fig. 10 Modelled power as a function of
measured power in W/m2 for the roof mounted
MaReCo. The solid line indicates a linear fit
of the data.
2.1.7 Characterisation of the collector
The useful delivered energy output of a collector working under steady-state
conditions is given by (Perers 1995)
qu=F’(τα)bKταb(θ)Gb+ F’(τα)dKταd(θ)Gd- F'UL1∆T- F'UL2(∆T)2-(mC)edTf/dt (43)
The collector efficiency factor, F’, accounts for the temperature variation over the
absorber, the fins have a higher temperature than that of the heat carrying medium.
The value of F’ depends on the ability of the absorber to transfer the energy that is
absorbed in the fin to the riser tube.
The (τα)-product takes into account that some of the radiation that is reflected from
the absorber is then in turn reflected in the glazing back to the absorber (Duffie and
Beckman1991)
(τα ) =
τ sol α sol
1 − (1 − α ) ρ d
(44)
where Tsol is the solar transmittance of the glazing from Eq. (29), αsol is the solar
absorptance of the absorber from Eq. (27) and ρd is the reflectance of a cover system
for diffuse radiation incident from the bottom side.
The product of the fin efficiency and the (τα)-product is also denoted the zero-loss
efficiency, η0, and describes the efficiency of the collector when it is operating at
ambient temperature when no thermal losses are obtained.
20
The angular dependence of the solar collector is characterised by the incidence angle
modifier, Kτα (Duffie and Beckman 1991)
Kτα =
(τα )
(τα ) n
(45)
The index n indicates normal incidence. A general empirical expression that is widely
used for flat plate collectors incorporating the incidence angle modifier coefficient, b0
is (Duffie and Beckman 1991)
Kτα = 1 + b0 (
1
− 1)
cosθ
(46)
The angular dependence of the beam and the diffuse radiation are handled separately.
For the beam radiation the angle of incidence of the beam radiation is used for θ in Eq.
(46) and for the diffuse radiation an effective angle of incidence obtained for example
from Duffie and Beckman (1991) is used.
The loss coefficients UL1 and UL2 are found by dividing U1 and U2 from Eq. (40) by
the fin efficiency F’. The term (mC)e describes the thermal inertia of the collector. Part
of the absorbed energy is lost to heating the collector in the morning when the
collector starts to operate and then partly regained in the afternoon before the collector
is turned off. (mC)e also describes how the collector reacts with rapid changes in solar
radiation and wind.
2.2 Collector simulations
2.2.1 Introduction
Computer based model simulations of solar collectors are frequently used methods of
deriving the delivered energy output from the collector. Alterations in the collector are
easily made and evaluated and compared to other simulated results or measurements.
The number of solar collector models is of the same order as the number of people
who do collector simulations. All these programs have their own specialities, but can
roughly be divided into five groups, starting with the most simple “program”, the
nomogram and ending with very complex programs studying very specific parts of the
collector. A short review is given below.
1. Nomograms where the output can be determined by following some simple steps.
These nomograms are based on either calculations or measurements. As an
example the solar heating nomogram made by Bengt Perers, Vattenfall Utveckling
AB can be mentioned. This was compiled within the CEC Thermie B Project: Solar
Heating in Northern and Central Europe. In only a couple of minutes it is possible
to get the estimated delivered energy output.
21
2. Correlation based programs with long time steps, often daily time steps. They are
often built on a large number of detailed sub-simulations made with another
program. Running time typically about 1 minute. An example of this kind of
program is the F-Chart.
3. Programs with hourly time steps in climate data and components based on physics,
taking first order effects into account. MINSUN is one example of this kind of
program, and has an executing time of less than a minute. TRNSYS is probably a
better known example, with a running time of less than 15 minutes. TRNSYS is
perhaps the most frequently used simulation program used today (2002). The
largest advantage with TRNSYS is that it is flexible, since it is module based.
Different modules can be put together to simulate all sorts of complex systems.
4. Very detailed models on a component level. Time steps are normally less than one
hour and they are typically designed to investigate a very particular effect for a
certain collector type. These are not commercial programs, but often written by a
PhD-student for very specific cases.
5. Programs based on finite element methods designed to investigate problems on the
level of basic physics, for example convection. Very computer power demanding
and no commercial programs available.
For the type of simulations used in this thesis, programs from group 3 are the most
suitable. The MINSUN program was chosen because it is very easy to learn and has a
rather advanced collector model that is well validated with experimental data. It can
also be used to simulate a whole building, but that option is not used here.
2.2.2 The MINSUN program
The MINSUN simulation program was originally developed to speed up simulations
of large solar energy systems with seasonal storage. The program consists of two parts,
the solar collector array model and the system model including storage, district-heating
net, heat loads, and domestic hot water loads (Chant, 1985). Since the first MINSUN
version, the collector array model has been further developed with additional
correction terms and functions using experience from solar collector testing (Perers
1993a,b).
In this thesis only the collector array part was used. The collector array part of the
MINSUN simulation program was chosen here because no knowledge about the
system outside the collector array is needed, for example heat loads, tank sizes etc.
Instead of detailed system information the program uses a fixed average operating
(heat carrier fluid) temperature, ([Tin+Tout]/2). Five different average operating
temperatures can be simulated at once
The well-defined operating conditions make a comparison between different collectors
more straight forward, since no system effects are included. If the operating
22
temperature is varying within relatively small limits, this approximation is valid even
for a collector in a system.
In the solar collector model hourly steps are used in the calculations. The useful
energy output, qu, of the collector is calculated with the MINSUN program by the
energy balance in Eq (43).
The collector parameters zero-loss efficiency (beam and diffuse)η0b and η0d, loss
coefficients UL1 and UL2, (mC)e and b0 together with the collector tilt and azimuth are
fed into the program together with hourly climate data with beam and global radiation
and ambient temperature. The output from the program is presented in three different
files. A log-file with a presentation of the collector parameters and then a summary
with monthly/annual mean values of beam and total radiation, ambient temperature,
collector energy output and operating time at different operating temperatures is the
most frequently used. The other two files contain hourly values of the above
mentioned parameters together with various information on for example solar height,
azimuth etc.
The delivered collector output obtained with the MINSUN program can then be used
to analyse for example the collector dependency on tilt and azimuth for various
collectors (Paper VII), the impact of material properties on the collector energy output
(Paper VIII), the influence of annual climate variations on collector energy output
(Paper VI) or the expected annual energy output for a collector in an outdoor test
(Paper I).
2.3 Optical characteristics of nonimaging concentrating collectors
2.3.1 Introduction
If part of the expensive absorber area is replaced by cheap reflectors the cost of the
energy produced with solar collectors is reduced. The thermal losses are in general
lowered if the light is concentrated since a smaller area of hot absorber is required to
produce a certain amount of heat. The reduced losses also make it possible to reach
higher absorber temperatures than those obtained with flat plate solar collectors.
There are a number of ways to obtain the concentration of the light; for example with
reflectors and lenses. Concentrators are treated in two main groups, imaging and
nonimaging. In a nonimaging collector all radiation that impinges on the aperture,
beam and diffuse, that is within a certain angular interval is reflected onto the receiver.
These collectors function seasonally with minimum or no requirements of tracking.
The concentrators studied in this work are all nonimaging.
The most common nonimaging concentrator is the compound parabolic concentrator,
the CPC, with the original concept developed by Hinterberger and Winston (1966).
Since then the concept has been further developed by for example Rabl (1976) and
23
Mills and Giutronich (1978). The CPC-collector is described in more detail in for
example Welford and Winston (1989), Duffie and Beckman (1991) or Winston (2001).
The basic CPC concept with a cross section of a symmetrical nontruncated CPC is
shown in Fig. 11 (Duffie and Beckman 1991). The collectors are mainly used as linear
or trough-like concentrators.
Fig. 11 Cross section of a symmetrical nontruncated CPC (from Duffie and Beckman 1991).
The acceptance interval defines the angular interval within which all radiation is
transferred from the aperture to the receiver, and the acceptance half-angle shown in
Fig. 11 is half of the acceptance interval. For a full CPC, the collector height defined
in Fig. 11 tends to be long. The height of the CPC is often truncated by cutting the
reflectors to a shorter length. This saves reflector area with a small reduction in
performance.
The area concentration factor for a concentrating collector is defined as the ratio of the
aperture area to the receiver area according to Eq. (1). For an ideal two-dimensional
non-truncated CPC this is given by (Duffie and Beckman 1991)
Ci =
1
sin θ c
(47)
A number of concentrating collector types are denoted CPC-collectors even though
they have other reflector geometries than the parabolic.
24
2.3.2 Description of the Maximum Reflector Collector, MaReCo
The MaReCo is an asymmetrical truncated trough-like CPC collector designed for
high latitudes. It is non-tracking, has a bi-facial absorber and can be designed for
various system conditions, for example stand alone mounting on ground or roof
integrated. The aim is to design a low cost solar collector without reducing the
performance too much compared to a flat plate collector. Expensive absorber area is
replaced by cheap reflector area.
Several other studies of asymmetric concentrating collectors have been reported by,
for example, Tripanagnostopoulos et al. (1999 and 2000), Norton et al. (1991),
Welford and Winston (1989), Mills and Giutronich (1978) and Rabl (1976). A study of
ultra flat concentrators suitable for building integration has been made by Chaves and
Collares-Pereira (2000). Three large stand-alone ground mounted MaReCo systems
have been constructed and are described in Karlsson and Wilson (1999).
A CPC trough according to Fig. 12 is designed with two parabolas with their optical
axes given by the lower and upper acceptance angles. The reflector consists of three
parts. Part C is a lower side parabola extended between points 1 and 4 in Fig. 12. This
parabola has its optical axis directed towards the upper acceptance angle and focus on
the top of the absorber. Part B is a circular part between points 1 and 2. This circular
part transfers the light onto the absorber. It replaces a second absorber fin that
otherwise would have been needed between focus and point 2 (indicated by a dotted
absorber between points 2 and 5 in Fig. 12). The lower tip of the absorber can be
placed anywhere along the circle sector between points 1 and 2. Part A is a parabolic
upper reflector between the points 2 and 3 in Fig. 12. This parabola has its optical axis
along the lower acceptance angle and its focus at point 5.
A
β
ϕ
B
C
Fig. 12 Sketch of the basic MaReCo design. Part A is the upper parabolic reflector extended
from points 2-3, Part B is the connecting circular reflector extended from points 1-2, Part C
is the lower parabolic reflector extended from points 1-4. The cover glass is found between
points 3 and 4. The position of the cover glass varies along the extended parabola depending
on the truncation. β is the aperture tilt and ϕ is the absorber inclination angle.
The position of the cover glass (i.e. the position of points 3 and 4 along the extended
parabolas in Fig. 12) is determined by varying the position of the reflector along the
extended parabolas to find the position where maximum annual irradiation onto the
25
aperture is obtained. When designing the collector prototypes this was made by sliding
a reflector sheet of a certain length along the parabola/circle form shown in Fig. 12 and
measuring the distance between point 3 and 4 in Fig. 12, i.e. the width of the cover
glass, and the aperture tilt, β, defined in Fig.12. The glass width and the aperture tilt
angle were fed into the MINSUN simulation program together with the collector
parameters to calculate the expected annual delivered energy. The configuration with
the highest annual output is the optimum position of the reflector sheet in the
parabola/circle shape. For Stockholm conditions an optimum of 30° aperture tilt was
found. The non-symmetrical distribution of the annual irradiation leads to a lower
reflector that is longer than the upper reflector.
2.3.3 MaReCo prototypes
Prototypes of MaReCo for stand-alone, wall and roof installation designed for
Stockholm climatic conditions were built and tested at the Vattenfall Laboratory in
Älvkarleby, Sweden. The designs were based on solar radiation distribution diagrams
from Rönnelid and Karlsson (1997). The evaluation of the prototypes is described in
Paper I.
2.3.3.1 The stand-alone MaReCo
The stand-alone MaReCo for Stockholm conditions has a cover glass tilt of 30° from
the horizontal. The collector is shown in Fig. 13. The upper acceptance angle is 65°
and the lower is 20° with an area concentration of Ci=2.2. This collector is designed
for stand-alone mounting on ground in large collector fields connected to a district
heating system. The average operating temperature in a MaReCo field installed in a
small district heating system in Torsåker, Sweden is 65°C.
Fig. 13 Section of the stand-alone MaReCo for Stockholm conditions. Aperture tilt 30°.
Optical axes 20 and 65° defined from the horizon.
2.3.3.2 The roof integrated MaReCo
The roof integrated MaReCo shown in Fig. 14 has a smaller collector depth than the
stand-alone MaReCo in order to fit on a roof connected to a heating and/or hot water
system in a building. Basically the collector is designed by letting the cover glass start
where the circular part of the MaReCo ends; i.e. the glass is between point 2 and 4 in
Fig. 12. No upper reflector is used and the absorber is placed just underneath the
26
cover. The whole design is then tilted to the roof angle. All radiation from 0 to 60°
angle of incidence from the cover glass normal is accepted by the reflector. The angle
60° is determined by the roof angle and the reflector thus accepts radiation from the
horizon to the normal of the glass. Above 60° the collector works similar to a flat plate
collector with an absorber area of 1/3 of the aperture area (the front side of the
absorber). With a 30°-roof tilt the area concentration Ci is 1.5.
Fig. 14 Section of the roof integrated MaReCo design for a roof angle of 30°. Optical axis 90°
from the cover glass.
2.3.3.3 The east/west MaReCo
All roofs in existing buildings are not aligned in the east/west direction with the roofs
facing south. An alternative for roofs facing east or west is to use a specially designed
roof MaReCo. In this case the reflector axis is placed in the east/west direction, tilted
along the roof as shown in the photo in Fig. 15. The east/west MaReCo accepts
radiation in the interval 20 to 90° from the cover glass normal as seen in Fig. 16. The
area concentration is 2.0.
Fig. 15 Photo of a MaReCo designed for Fig. 16 Section of the east/west roof MaReCo
east/west-facing roofs. The white arrow designed for a roof facing west. Optical axis
indicates the south direction.
70° from the cover glass.
27
2.3.3.4 The spring/fall MaReCo
Another special case of the roof integrated MaReCo is the spring/fall MaReCo. In this
case a high solar fraction in the heating system over the whole year is the objective.
The geometry of the collector is designed to have a high efficiency during spring and
fall when the heating demand is high and a low efficiency during summer when the
heating demand is low. The latter condition prevents over-heating in the system during
summer. The optical axis is tilted compared to the ordinary roof MaReCo, as can be
seen in Fig. 17. Beam radiation hitting the reflector at an angle smaller than 15° from
the aperture normal will be reflected out of the collector. The absorber is placed just
underneath the cover glass and it is working for all angles of incidence and not only
within the acceptance interval. An area concentration of Ci=1.8 is found for the
spring/fall MaReCo. Another study of a season adapted concentrating collector has
been made by Nordlander and Rönnelid (2001).
Fig. 17 Section of the spring/fall MaReCo designed for a roof tilted 30°. Optical axis at 45°
from the horizon.
2.3.3.5 The wall MaReCo
The wall MaReCo is an alternative to the east/west MaReCo or the spring/fall
MaReCo. It can be mounted wall integrated. The concentration is Ci=2.2 if both sides
of the absorber are considered. The acceptance angle interval is from 25 up to 90°
from the horizon as seen in Fig. 18. The absorber is placed just underneath the cover
glass.
Fig. 18 Section of the wall MaReCo designed for a south facing wall. Optical axis at 25° from
the horizon.
28
2.3.4 Characterisation of concentration distribution on the absorber fin
The radiation distribution on the absorber in a concentrating collector is in general
uneven compared to the radiation distribution in a flat plate collector where the
radiation is distributed evenly on the absorber. The theoretical approach to study the
radiation distribution on the absorber is through ray tracing, which is described for
example in Benitez et al. (1999). In Paper IV an experimental approach is suggested
and a method using outdoor measurements is developed.
A monitoring device was constructed with a photo diode sliding on a potentiometer,
allowing both the irradiation and position of the diode along the absorber width to be
registered on a computer controlled logger. A reference photo diode was placed on the
aperture of the collector. The monitoring device measured the radiation on one side of
the absorber at a time. By normalising the signal from the monitoring device diode to
the signal from the reference diode the actual concentration is obtained for the
measured positions along the absorber width. An example of such a measurement is
shown in Fig. 19 below for normal incidence (on cover glass) solar radiation. The
concentration distribution, Sc(x), shown in Fig. 19 is then measured for a series of
solar radiation angles of incidence within the acceptance interval.
Fig. 19 Concentration of normal incidence (on cover glass) radiation, on the absorber of a
stand-alone MaReCo as a function of location of the radiation impact for absorber angle 45°.
Lower side indicates facing lower reflector and upper side indicates facing upper reflector. A
sketch of the absorber is drawn at zero concentration. Aperture tilted 30°.
Another method to study the radiation distribution using outdoor measurements is
suggested in Smyth et al. (1999) where thermocouples are attached along the width of
the absorber. Fendt and Wenzel (1999) used a radiometer to study the radiation
distribution on a cylindrical absorber.
29
2.3.5 Annually collected energy and optical efficiency factor
The annually collected zero-loss energy for a concentrating collector can be estimated
from the concentration distribution. In an asymmetrical concentrating collector like the
MaReCo the radiation is distributed unevenly on the absorber, which makes it very
important to study the absorber’s ability to transport the heat from the fin to the tube.
If an absorber with a low efficiency is used, part of the radiation concentrated close to
the edge of the absorber will be lost. To describe the efficiency of the fin in a
concentrating collector the optical efficiency factor is introduced (Hellström 2001).
This entity depends on the geometry and material properties of the absorber, the
distance from the radiation impact to the tube and the collector overall loss coefficient.
The annual optical efficiency factor can be determined from the annually collected
zero-loss energy.
A method to study the annually collected energy and the annual optical efficiency
factor, F'c,a in a MaReCo is developed in Paper IV. The first step is to obtain the
concentration distribution, Sc(x), on the absorber at different angles of incidence for
example from outdoor measurements as described in the previous section.
The concentration distribution is then multiplied by a local optical efficiency factor,
F’c(x). F’c(x), gives the fraction of locally absorbed heat which is conducted to the heat
carrying fluid. An example of a local optical efficiency factor distribution is shown in
Fig. 20 for a stand-alone MaReCo with a fin thickness of 0.5 mm.
1
0.95
c
F' (x)
0.9
0.85
0.8
0.75
0
0.05
0.1
0.15
Location on absorber, x, [m]
Fig. 20 The local optical efficiency factor F’c(x), as a function of location x on an aluminium
absorber of 0.5 mm fin thickness and a width of l=143 mm for a stand-alone MaReCo with an
assumed value of UL=13 W/m2K (U-value per absorber area, not aperture area) and for
water at 50°C with turbulent flow as the heat carrying medium.
In order to obtain a measure of the total energy irradiated on the surface, a numerical
rectangular method integration was performed on the irradiation data. The integration
was made with and without correction for F'c(x) since both are needed for the
calculation of the annual optical efficiency factor. The numerical integration was made
for each solar angle of incidence and absorber inclination angle at a time according to:
30
qcorr(θ) = ∑F’c(x)Sc(x)∆x
(48)
q(θ) = ∑Sc(x)∆x
(49)
This numerically integrated and F’c(x)-weighted energy qcorr is shown in Fig. 21 as the
sum of the corrected energy collected from the upper and lower sides. q, is the
uncorrected energy collected.
0.4
Energy q
corr
[a.u.]
0.35
0.3
0.25
0.2
0.15
20
30
40
50
60
Solar angle
Fig. 21 Integrated and F’c(x)-weighted energy qcorr at different projected solar radiation
angles of incidence for absorber angle 45° for an absorber fin thickness of d=0.5mm. The
effective concentration is obtained if the values is divided by the absorber width l=0.143.
The next step is to obtain a measure of the annually collected energy. In order to
weight the energy at the different solar angles of incidence, knowledge of the annual
irradiation distribution in the interval 20-65° of the meridian plane is required. This
was obtained from Paper III where hourly solar beam radiation data was sorted into
different angle of incidence intervals according to projected angles of incidence: the
incoming energy was divided into two components, one in the north-south plane,
orthogonal to the studied surface (transversal component), and one in the east-west
plane, parallel to the studied surface (longitudinal component). The energy in the
transversal component was sorted and summed according to projected angle into
angular intervals of 2.5° width. They were connected to the measured angle of
incidence with one interval on each side of the measured angle to a total width of 5°
with an exception at the angular limits of the acceptance angle interval that are only
2.5° wide since no radiation is accepted outside these angles. The relative distribution
within the interval 20-65°, G(θ), is shown in Fig. 22.
31
Relative energy content, G( θ)
0.3
0.25
0.2
0.15
0.1
0.05
0
20
30
40
50
60
Proj. solar angle of incidence interval
Fig. 22 Relative distribution of annually projected irradiation G(θ) on a 30°-tilted plane
within the interval 20- 65° in the vertical-south plane.
Then the integrated energy is weighted by multiplying the energy at each angle shown
in Fig. 21 with the relative distribution of projected annual irradiation G(θ) in Fig. 22
and a measure of the annually F’c-corrected collected energy, Ea, corr and the annually
collected un-F'c corrected energy Ea, are obtained.
E a ,corr =
Ea =
∑ G (θ )q (θ )
∑ G (θ )
corr
(50)
∑ G(θ )q (θ )
∑ G(θ )
(51)
These data can then be used to calculate the annual value of the optical efficiency
factor, F’c,a
F 'c ,a =
E a ,corr
(52)
Ea
A typical value of F’c,a is around 0.88 for a stand-alone MaReCo with 0.5 mm thick
absorber. With the same method it is also possible to calculate annual values of the
concentrating collector efficiency for the incoming radiation angle by angle.
2.4 Projection of solar radiation
2.4.1 Introduction
For a flat plate collector it is possible to rotate the collector 90 degrees around the
collector normal and still have the same available incoming solar radiation. For a
concentrating trough-like collector this is not the case since the concentrator is
designed for a certain orientation. One method to study the radiation incident on an
arbitrarily oriented concentrating collector is to project the solar radiation as is
described in Paper III. Related work has been done for example by Rönnelid and
Karlsson (1997), Pinazo et al (1992) and McIntire and Reed (1983).
32
The solar radiation incident on the concentrator aperture can be projected into two
components; one that is in a plane created by the concentrator axis and the normal of
the cover glass, the longitudinal plane, and one component that is orthogonal to this
plane, the transversal plane (Duffie and Beckman 1991). The longitudinal component
of the solar radiation is parallel to the aperture area and will therefore not contribute to
the energy gain of the collector. The transversal component of the solar radiation will
contribute to the energy gain if the projected transversal angle of incidence is within
the acceptance interval of the solar concentrator. The method starts with calculating
the solar radiation component co-ordinates in the horizontal system and then the
system is rotated to fit the arbitrarily oriented concentrator. Finally the projection
angles in the rotated system are calculated.
Combining the method of calculating projection data with measured/calculated solar
radiation data introduces the possibility of making radiation distribution diagrams,
showing the available solar radiation within each projected angle of incidence interval.
2.4.2 Horizontal system
The radiation components in the horizontal system X0Y0Z0, seen in Fig. 23, are found
through the solar azimuth, γs, and solar height, hsun, according to Duffie and Beckman
(1991).
Fig. 23 Horizontal co-ordinate system, solar height and solar azimuth.
The solar radiation co-ordinates are then transformed from spherical to Cartesian coordinates, x0, y0 and z0:
x0=cos(hsun)cos(γs)
(53)
(54)
y0= cos(hsun)sin(γs)
(55)
z0= sin(hsun)
The co-ordinate system is placed on the concentrator with the Y0-axis along the
concentrator axis as seen in Fig. 24.
33
Z0
EN-01
© ADST
Fig. 24 Description of horizontal co-ordinate system placement on concentrator.
2.4.3 Rotated system
A rotated co-ordinate system is placed with the Y-axis, Yrot, placed along the
concentrator axis according to Fig. 25.
Z rot
X rot
Yrot
1
N-0
TE
DS
A
©
Fig. 25 Description of co-ordinate system position on a concentrator for a rotated system.
The rotations used here are A degrees around the X-axis, B degrees around the Z-axis
and C degrees around the Y-axis, as seen in Fig. 26. The order of rotation is around X,
Z and finally Y. If the concentrator is to be placed on a roof the orientation of the roof
might not be exactly the optimum. With the freedom of rotating around all three axes
all possible concentrator orientations can be studied.
34
Fig. 26 Definition of rotation angles from the horizontal system.
In order to obtain the radiation component on an arbitrarily oriented surface the coordinates in the horizontal system are transformed using a rotation matrix:
 x rot 
 
 y rot  =
 z rot 
cos C cos B cos C sin B cos A + sin C sin A cos C sin B sin A − sin C cos A  x 0 

 
cos B cos A
cos B sin A
 − sin B
  y o  (56)
 sin C cos B sin C sin B cos A − cos C sin A sin C sin B sin A + cos C cos A  z 0 
2.4.4 Projection angles
The solar radiation projection angles θl (longitudinal) and θt (transversal) are defined
in Fig. 27.
Z
Sun
θt
X
Sun
Z
θl
Y
Fig. 27 Definition of solar radiation projection angles θl and θt.
The projection angles in the rotated system are found from the solar radiation coordinates in the rotated system:
 x rot 

 z rot 
(57)
 y rot 

 z rot 
(58)
θ t = arctan 
θ l = arctan 
2.4.5 Radiation distribution diagrams
The first step to obtain a radiation distribution diagram for a surface is to calculate the
solar position in the original horizontal co-ordinate system for the climate data. The
earth turns 15 degrees per hour, causing large movements also in the projected angles
during an hour. The hourly climate data is therefore interpolated linearly, dividing
35
each hour into ten intervals with constant radiation. With an improved resolution a
smoother radiation distribution is obtained. The solar position co-ordinates in the
original system are then used to calculate the co-ordinates in a rotated system, the
projection angles and the beam radiation incident on a rotated surface. Finally the
beam radiation is sorted into different projection angle intervals in 5-degree steps. An
example of such a radiation distribution diagram is shown in Fig. 28 for a surface tilted
30° and facing south. The calculations in Fig. 28 were also made with 200 W
subtracted from each hour, which is approximately the radiation needed to balance the
heat losses in a concentrating collector.
100
Stockholm
00_00_30
All rad.
200W subtr.
2
Incident energy (kWh/m a)
120
80
60
40
55 60
50 55
45 50
40 45
35 40
30 35
25 30
20 25
15 20
10 15
05
5 10
-5-0
-10-5
-15-10
0
-90-15
20
Proj. angle of incidence
Fig. 28 Solar beam radiation distribution on a south-facing surface that is tilted 30° in
Stockholm. Rotations A=0°, B=0° and C=30°. 200 W was subtracted from each hour in the
radiation raw data in the black bars.
At high latitudes a large part of the annual projected solar radiation in the transversal
plane is concentrated near a peak in the radiation distribution diagram around the
summer solstice as seen in Fig. 28. The summer solstice peak is located at 5.6° solar
radiation angle of incidence in the co-ordinate system that is rotated 30° around the Yaxis. At lower latitudes two peaks are found in the radiation distribution; one at the
summer solstice and one at the winter solstice as shown by Rönnelid and Karlsson
(1997). The loss of the winter solstice peak at high latitudes is due to large solar zenith
angles for direct radiation during the winter months causing high absorption of the
direct radiation in the atmosphere (Rönnelid et al 1996). When designing an
asymmetric CPC solar thermal collector at high latitudes this means that the collector
can have a small acceptance half angle covering an angular interval around the
summer solstice peak, leading to a high area concentration factor according to Eq.
(47).
Radiation distribution diagrams can then be used to design the acceptance interval of a
CPC-collector. The same method can be used to design concentrators for PV-cells.
There are several ways of designing the acceptance interval from the radiation
distribution diagrams, depending on the desired properties of the concentrator. The
overall principle is that adjacent projection angle energy intervals are added until the
optimisation condition is fulfilled. For example the roof MaReCo described in section
2.3.3.2 has a lower acceptance angle defined by the horizon. The upper acceptance
36
angle is then found by adding the intervals from the horizon and upwards together
until a maximum in the effective concentration is found. The effective concentration is
a measure of the amount of energy reaching the absorber and is defined by:
Ceff = Ci
E int erval
E tot
(59)
Ci is the area concentration, Einterval is the fraction of energy within the summed
interval, and Etot is the total amount of energy incident on the aperture plane. The
effective concentration for different half acceptance angles is shown in Fig. 29 for the
roof MaReCo.
1.4
1
Ceff
0.8
1
tot
0.4
/E
0.6
interval
0.6
0.8
E
Effective concentration
1.2
0.4
0.2
0.2
Einterval/Etot
0
0
10
20
30
40
50
60
0
Acceptance half-angle
Fig. 29 Effective concentration as a function of half acceptance angle for a surface tilted 30°
and facing south. The lower acceptance angle is 60 degrees in the rotated system
characterised by A=0°, B=0° and C=30° (the horizon in the horizontal system).
The radiation distribution diagram can also be separated into different months to find
the monthly distribution of the solar radiation at different projected angles of incidence
as shown in Fig. 30. Note that Fig. 30 is the same case as Fig. 28 except it is divided
into different periods of the year.
The monthly radiation distribution diagram can be used to determine the annual
operation interval of the concentrator. As an example the roof MaReCo can be
designed for a low performance during summertime to prevent overheating, the
spring/fall MaReCo described in section 2.3.3.4. In this case the lower acceptance
angle is the horizon in the horizontal system and the upper acceptance angle is
determined from the distribution in Fig. 30 to 10°, creating a collector that reflects the
major part of the radiation in May-July. The collector is still working during this part
of the year since the absorber placed just underneath the cover glass is still active for
the radiation hitting the absorber directly. This reduces the energy production by a
factor of 3 during May-July.
37
Another use for the monthly radiation distribution diagrams is for design of solar
shades for windows. In this case a distribution for a 90°-tilted surface facing the same
orientation as the window is needed. An example of such a distribution is shown in
Fig. 31 for a south facing vertical surface in Stockholm, Sweden. The length of the
solar shade is then determined from the monthly distribution, depending on during
which period of the year that the incoming radiation will cause over heating. To avoid
the solar radiation in May-July that might cause over heating solar radiation with
projected angles of incidence over 45° should be avoided. This means that if
horizontal solar shades are to be installed they should have a width equal to the height
of the window in Stockholm.
60
50
40
Incident energy (kWh/m 2a)
May-July
Aug,
April
Sept,
March
Oct-Feb
2
Incident energy (kWh/m a)
60
30
20
10
0
-20
0
20
40
Projected angle of incidenceθ
40
30
20
10
0
60
Oct-Feb
March
Sept.
April
August
May-July
50
0
20
40
60
80
Projected angle of incidence θt
t
Fig. 31 Monthly distribution of the incident
energy (beam radiation) for different
projected angles of incidence for Stockholm
on a vertical south facing surface. Projected
angles defined from the horizon.
Fig. 30 Monthly distribution of the incident
energy (beam radiation) for different
projected angles of incidence for Stockholm
on a surface tilted 30° and oriented towards
south (A=0°, B=0° and C=30°). 200 W
subtracted from the radiation data for each
hour.
38
3 RESULTS AND DISCUSSION
3.1 The MaReCo
3.1.1 Evaluation of MaReCo prototypes
A total of six prototypes designed for various installation conditions were built and
connected to an outdoor testing system. The tests were made according to the dynamic
testing model described in section 2.1.6.6. The parameters obtained from the testing
are shown in Table 1. The annually delivered energy output for each collector was
simulated at an operating temperature of 50°C.
Table 1 Estimated outputs for 50°C average operating temperature calculated with the
MINSUN simulation program and investment cost per annually produced kWh for all six
evaluated MaReCos.
MaReCo
Type
Stand-alone
Stand-alone
Teflon
Roof integr.
East
West
Spring/fall
Q50°
kWh/m2
253
282
Cost
η0b
€/kWha 0.61
0.59
0.55
0.64
η0d
b0
-
-
0.37
0.36
336
135
174
199
0.46
1.15
0.87
0.78
0.56
0.25
0.35
0.31
0.23*
0.27
Wall
142
1.09
*evaluated for summer months
0.69
0.58
0.60
0.56
0.34*
0.61
0.37
0.46
F’UL1
W/m2K
2.4
2.2
(mC)e
J/m2K
2980
3380
0.29
0.13
0.16
0.41
0.23*
0.22
2.4
2.0
2.0
2.6
2.0*
2.0
1950
6250
4890
2230
3800*
1130
The study showed that all collectors have low U-values, somewhere between 1.7 and
3.2 at 50°C operating temperature depending on the type of the collector according to
Table 1. This is explained by the small absorber surface compared to the total glazed
area. The corresponding U-value for a flat plate collector with selective absorber is
approximately from 4 W/m2K and up. An attempt was also made in the evaluation to
find the second order heat loss coefficients for the collectors, but the parameter fits
were better if only the first order loss coefficient was identified. The effective thermal
capacitance, (mC)e is low in most cases. This is in part explained by the low collector
weight due to the low material content.
Including a teflon convection suppression film significantly reduces the losses,
especially at high temperatures. The annual increase in delivered energy when
including a teflon film in the stand-alone MaReCo is 29 kWh/m2 at Top=50°C.
The roof mounted MaReCo obtained the highest annual output, 336 kWh/m2 at an
operating temperature of 50°C. This design can be mounted on roofs with inclination
30 ° and lower, which is an advantage compared to flat plate collectors that have an
39
optimum tilt of 45° for Swedish conditions. Not many roofs have a tilt of 45° in
Sweden, but rather 30° or lower. The output of a flat plate collector in Sweden is
around 15% higher than the output of the roof MaReCo.
The expected annual output of the east/west facing roof MaReCo is rather low. If it is
facing west the annual output is however higher than that of the wall MaReCo facing
south. The evaluation showed a large difference between an east/west MaReCo facing
east and west. The solar radiation is symmetric around noon, but the losses are in
general smaller in the afternoon since the ambient temperature is higher in the
afternoon.
It is difficult to make the spring/fall MaReCo cost effective, since the material in it is
the same as in the standard roof integrated MaReCo but the output is about 20% lower
than the standard roof integrated version. This collector can however be used if the
aim rather is a high annual solar fraction than a commercial system.
The wall MaReCo has a low annual output, only 142 kWh/m2, which is about 30%
lower than that of a flat plate collector mounted on a wall. The delivered energy output
is lower for any wall mounted collector but the annual distribution of the energy fits
the load distribution better since the solar height is low when the demand is high.
Another advantage with any wall mounted collector is that they have no problems with
stagnation. The wall-MaReCo has a very special design that is appreciated by some
architects.
The maximum reflector collector is designed to provide energy at a low cost. This is
achieved by replacing the expensive absorber with cheap reflectors. The investment
cost of the stand-alone MaReCo field shown in Fig. 32 was approximately 160 €/m2.
The material content is approximately the same for all MaReCo designs even though
the stand-alone MaReCo has a somewhat larger reflector area and has a need for
ground supports. Using the same investment cost for all the prototypes and the outputs
for Top=50°C in Table 1, the cost per annually produced kWh is calculated and found
in Table 1. As seen in Table 1 the ordinary roof integrated MaReCo is the most cost
efficient. A financial model, for example the annuity model, must be applied to obtain
the energy cost per produced kWh. If an annuity of 0.1 is used, the cost is 0.05 €/kWh
for energy produced with a roof MaReCo. This is cost effective at least compared to
heat produced with electricity in Sweden, which is around 0.09 €/kWh excluding fixed
costs and including tax for a household (2002). For a flat plate collector the cost per
produced kWh is around 0.07 €/kWh (excluding system costs).
40
Fig. 32 A field of 500m² stand-alone MaReCo collectors constructed 1999 in front of the bio
fuel burner in Torsåker, Sweden. Each collector has a length of 40 meter.
The results brought up new ideas for continued research on the MaReCo:
• A more sophisticated model for the incidence angle dependency must be used. In
this evaluation only the incidence angle modifier coefficient, b0, was identified,
which is insufficient for very asymmetric collectors, such as the MaReCo. In this
study b0 values of up to 0.51 are found according to Table 1, which is a bit too high
to be realistic. An attempt to solve this problem using a bi-axial incidence angle
modifier for the incidence angle dependency based on outdoor test data has been
made by Helgesson and Karlsson (2001).
• The collectors studied here were designed from a diagram showing the energy
distribution in various incidence angle intervals on a one-axis tracking south facing
surface from Rönnelid and Karlsson 1997. A further study of the radiation
distribution on the actual surfaces is required to investigate more accurate
acceptance intervals. This study was also expanded to cover other latitudes than
Swedish ones to investigate if the same concept can be used at lower latitudes. This
study is described in section 3.1.3.
• Because of the asymmetry an uneven distribution of radiation is incident on the
absorber. To get a high energy yield from the collector an absorber with high
collector efficiency is required. A more detailed study of the radiation distribution
on the absorber for various angles of incidence and absorber angles has been made
in order to find a mounting with a more even radiation distribution, making the
collector less dependent on the fin efficiency. This study is described in section
3.1.4.
3.1.2 The influence of collector components on heat losses
A study of the influence of collector components on heat losses in a stand-alone
MaReCo was initiated to get more information on how to design the MaReCo as cost
effectively as possible. The details of the study are found in Paper II. The study
comprised absorbers with different thermal emittance, reflectors with different thermal
emittance, external ventilation channels in the expanded polystyrene (EPS) and teflon
film as internal convection suppression. It was also investigated if the absorber should
be mounted horizontally or vertically, and the influence of having open or closed
41
ventilation channels in the EPS support of the reflector. The measurements were made
indoors with a hot box technique as described in section 2.1.6.6. The temperature was
recorded at several places in the collector box with different combinations of
components. A reference collector was chosen, with a selective absorber aligned
vertically, open ventilation channels, high emitting reflector, no teflon and with EPSinsulation. The most important results of the investigation are reported below.
The experiments showed measurable changes in U-value between all configurations.
They also showed that the temperatures within the collector depend strongly on the
actual component choice. Fig. 33 shows the influence of making one modification in
the collector compared to the reference. Experiments were also made where several
measures were combined, for example teflon wrapping of the absorber and a high
emitting absorber.
4
HighE abs.
No EPS
Reference
LowE refl.
Ch. cov.
LowE abs.
Hor. abs.
Teflon
2
U-value (W/m K)
3.5
3
2.5
2
1.5
1
10
20
30
40
50
60
70
80
90
T -T
pm
a
Fig. 33 U-value as a function of temperature difference between absorber and ambient for all
measures. The lines show least square fits of the measurements.
Adding teflon convection suppression reduces the U-value by about 30% depending
on what other modification is made at the same time. Introducing teflon is the single
measure that leads to the largest improvement in U-value. Teflon film is rather cheap,
6-12 €/m2, the only problem is to design a mounting that will keep the film in position
with a suitable distance to the absorber. In the MaReCo with a hot absorber area of
25% compared to that of a flat plate collector with equal aperture area, the amount of
teflon needed is only half of that required in a flat plate collector. The absorber
temperature is also higher than that in a flat plate collector because of the
concentration.
If the absorber is placed horizontally a lower U-value is obtained compared to that
obtained with a vertical mounting. The U-values are lowered by 4 to 22% with a
horizontal absorber depending on what other simultaneous modification is made in the
collector components. Placing the absorber horizontally leads to practically no extra
costs, except for some extra supports for the absorber that might be needed to keep the
absorber straight. Despite the improvement in U-value with a horizontal absorber a
vertical absorber was chosen in the installed collector fields (Karlsson and Wilson
1999). One of the conclusions of this study was therefore that further investigations are
42
needed to find the optimal absorber angle when both optical and thermal properties are
considered. This study has been made in Paper IV and is reported on in section 3.1.4.
The idea behind the ventilation channels is to reduce the risk of the EPS melting in
case of stagnation. With the ventilation channels blocked the U-value was decreased
by between 7 and 25% of the value obtained with open channels at 50°C temperature
difference between absorber and ambient and the temperature in the upper part of the
channel increased by 6°C. The channels should be designed to prevent airflow at low
temperatures and reinforce the flow at stagnation temperatures since the airflow at low
temperatures only causes unnecessary losses.
Using expanded polystyrene is an inexpensive way of getting the reflector in the
desired geometry. It has low weight, which is an advantage especially for roof
mounting and also for the transportation. A problem with EPS is that it cannot
withstand high stagnation temperatures since it is only long term stable for
temperatures of up to 60°C. It is also brittle and is easily damaged during
transportation and installation of the collector. The measurements showed that the
insulating properties of the EPS-block are not that important in the MaReCo. The
increase in U-value when removing the EPS was in the interval 6 to 14% at ∆T=50°C.
If the EPS was removed from the base case the U-value at ∆T=50° was increased by
8%.
A change in the collector configuration influences the temperature distribution in the
collector. R1 to R4 are positions on the reflector, C1 is in the ventilation channel and
A1 to A3 are air temperatures inside the collector cavity according to Fig. 34. The
results are seen in Fig. 35.
C1
R1
A1
Reflector
A2
A3
R2
R4
R3
Vent. Ch.
Fig. 34 Locations of investigated temperature distributions.
43
25
Hor. abs.
High E abs.
No EPS
Base case
Teflon
15
T-T
amb
(C)
20
Ch. cov
10
5
0
R1
R2
R3
R4
C1
A1
A2
A3
Location
Fig. 35 Distribution of temperatures (adjusted for ambient temperature) at various locations
in collector for a temperature difference of 50°C between absorber and ambient.
According to Fig. 35 the highest temperatures are found in the space in the centre of
the collector cavity at location A2 in Fig. 34. Covering the ventilation channels
significantly increases the temperatures in the collector but they are still below what
the EPS insulation can withstand on a long-term basis according to the measurements
performed here.
The stagnation temperature can be estimated from the linear loss relation in Eq. (40). If
a linear fit obtained from the measurements is used for absorber temperatures above
the range that is reported on here, estimated stagnation temperatures can be calculated
for the different cases. It is found that in order to avoid reflector temperatures above
60°C an estimated stagnation absorber temperature for the reference configuration of
150°C and for the case with ventilation channels covered 110°C is allowed. Long term
(two years) outdoor tests have shown that the EPS could endure stagnation for short
periods without visible damage in spite a maximum absorber stagnation temperature of
approximately 210°C. There is also some uncertainty if a linear fit from measurements
in a substantially lower temperature range is valid in the stagnation region.
If teflon convection suppression is introduced the temperatures outside the teflon
device are lowered. If another way of mounting the teflon would be used, the reflector
temperature at the bottom of the collector could be raised. In many MaReCo
installations with teflon convection suppression the teflon is mounted in a reversed Vshape over the absorber with no teflon underneath the absorber.
To summarise the results, the MaReCo should be designed with a teflon convection
suppression device around the absorber. If teflon is used, a spectrally selective
absorber with thermal emittance around 0.10 is quite sufficient. Horizontal absorber
mounting should be used. The ventilation channels significantly change the U-value of
the collector and can help to keep the reflector temperature down to protect the EPS in
case of stagnation.
44
3.1.3 Theoretical optimisation of optical MaReCo design
As mentioned above one of the conclusions of the evaluation of the prototypes was
that a more thorough study of the optical design was desired. The prototypes were
designed from one-axis tracking south facing radiation distribution diagrams made by
Rönnelid and Karlsson (1997). The new study found in Paper III featured radiation
diagrams for non-tracking surfaces facing the same orientation as the apertures of the
collectors. The method of obtaining the radiation distribution diagrams is described in
section 2.4.5 as well as the optical optimisation procedure to design the acceptance
intervals of the MaReCos.
The results of the study showed that radiation distribution diagrams is a convenient
way to estimate the acceptance interval for the design of a CPC-collector. Table 2
shows the suggested acceptance intervals for different types of MaReCos for
Stockholm and also the acceptance intervals of the evaluated prototypes from section
2.3.3. Note that the angles in Table 2 are defined in different co-ordinate systems
according to the method described in section 2.4.3. If a detailed study of the energy
accepted by the concentrator is the aim a more accurate method, for example ray
tracing, is required.
Table 2 Acceptance angle intervals, received energy and effective concentration for different
designs and cities. Note that the angles are defined in different co-ordinate systems for the
various MaReCo types according to the method described in section 2.4.3.
Lower
Upper
acc. angle acc. angle
Theoretical study
0
South facing 30° inclination, 40
stand alone MaReCo
0
South facing 30° inclination, 60
standard roof MaReCo
10
South facing 30° inclination, 60
spring/fall MaReCo
15
West facing 30° inclination 90
South facing, wall
-5
-90
Lower acc. Upper
angle
acc. angle
Prototypes
40
-5
60
0
60
15
90
20
-25
-90
When the MaReCo design obtained with the radiation distribution diagrams is compared
to the prototypes built and tested in Paper I it is found that some corrections of the
acceptance angles are needed to achieve the optimum design.
The highest effective concentration is found for the stand alone application since it has
two reflectors which facilitates the option to choose both limits of the acceptance angle
interval. For the stand alone MaReCo a slightly smaller acceptance interval is suggested,
which would increase the concentration slightly. The prototype has an acceptance
interval of –5° to 40° and the radiation distribution diagrams suggest 0° to 40°. With the
45
0° to 40° interval the collectable energy is reduced from 90 to 85% compared with the –
5° to 40° interval.
The spring/fall MaReCo where the summer energy production is suppressed has a
prototype designed with a slightly narrower acceptance interval, 15° to 60°, than that
suggested by the radiation distribution diagrams, 10° to 60°. If the interval is increased
more radiation in April and August, which is useful for heating, could be accepted
without getting too much of the radiation in May-July, which causes over heating. With
the broader acceptance interval the available solar radiation is increased from 42 to 53%.
It is also suggested that the acceptance interval of the east/west MaReCo should be
expanded slightly to increase the collectable energy. The prototype had an acceptance
interval of 20° to 90° and the radiation distribution diagrams suggest 15-90°, causing an
improvement from 70 to 77% in the collectable radiation.
A large increase in the acceptance interval of the wall MaReCo is suggested by the
radiation distribution diagrams. An upper acceptance angle of -5° instead of -25° would
increase the collectable energy significantly from 65 to almost 100%. It would also
expand the operating season because lower solar heights are accepted.
The alterations in geometry mentioned above can be made without increasing the costs
of the collector. The method of designing the acceptance interval of a collector does not
say anything about the geometry of the collector, only the acceptance interval is
determined.
Two other latitudes were also studied theoretically, Madrid, Spain, (40.4°N, 3.4°W) and
Munich, Germany, (48.1°N, 11.2°E). The study showed that the MaReCo design
concept can be used also for these latitudes. The acceptance intervals need to be
changed and the effective concentrations are in general lower compared to those for
MaReCos in Stockholm. The exception is the wall MaReCo that has a higher effective
concentration for the lower latitudes.
3.1.4 The annually collected energy (zero loss)
The heat loss study in section 3.1.2 indicated that the U-value of the collector could be
significantly decreased with an absorber aligned with the 20°-optical axis instead of
the 65°-optical axis. A study, described in Paper IV and V, was initiated in order to
find the optimum absorber angle from an optical point of view by studying the
annually collected energy. As mentioned in section 2.3.2 the lower tip of the absorber
in the stand-alone MaReCo can be placed anywhere between the optical axes. The
study was made with regard to the annual solar radiation distribution to obtain the
maximum energy output from the collector over the year.
A stand-alone MaReCo was constructed and the radiation distribution on the absorber
was obtained with the outdoor measurement method described in section 2.3.4. The
radiation distribution on the absorber for projected solar angles of incidence within the
46
acceptance interval, 20-65° was measured. Three different absorber inclination angles
were measured, 20°, 45° and 65° from the horizon. All measurements were corrected
for the optical efficiency factor and the annually collected energy was calculated
according to section 2.3.5. The same set of radiation distribution measurements were
used for the calculations in Papers IV and V.
In Paper IV calculations were made with absorber fins of thickness 0.5 and 1 mm and
also with a 0.5mm thick fin with teflon convection suppression around the absorber.
Increasing the thickness of the fin increases the optical efficiency factor. For the case
with teflon convection suppression the radiation data was multiplied by 0.96 to
account for the decreased transmission and the overall loss coefficient per single sided
absorber area was decreased from 13 to 8 W/m2K. The results are found in Table 3.
Table 3 Annually collected energy Ea, corr in arbitrary units for absorber inclination angles 20,
45 and 65° with absorber thickness d=0.5 mm, d=1 mm, d=0.5 mm with teflon convection
suppression film added.
Absorber
angle
20°
45°
65°
Annually collected energy, Ea,corr [a.u.]
d=0.5 mm
d=1 mm
teflon, d=0.5 mm
0.32
0.34
0.32
0.30
0.32
0.30
0.26
0.28
0.27
As seen in Table 3 the maximum amount of solar radiation is collected with 20°
absorber inclination angle for all three calculated cases. The amount of collected
energy is increased by 18-23% with 20° absorber angle compared to that with 65°
absorber angle. This result agrees with the results from the heat loss measurements in
Paper II- a horizontal absorber is preferable. Increasing the absorber fin thickness from
0.5 mm to 1 mm increases the collectable energy by 6-8%. Including a teflon film
around the absorber does not significantly improve the collectable energy. The reduced
U-value that improves the optical efficiency factor balances the transmission loss in
the teflon. The collected energy with losses considered would however be improved
with the teflon.
Preliminary measurements in a solar simulator showed no significant difference
between the two mounting angles, but this might be caused by the two absorber sides
not having the same absorptance. New solar simulator measurements are suggested
with an absorber having equal absorptance on both sides.
Another study using the annually collected energy was made in Paper V to investigate
the importance of the fin width and collector geometry. Three different combinations
of absorber width and collector geometry shown in Fig. 36 were investigated for
absorber inclination angles 20° and 65°. The study was initiated to investigate the
potential improvement with a new absorber width supplied by Sunstrip AB in Sweden.
Previously a 143 mm wide absorber has been the standard, but recently a narrow fin,
71.5 mm wide, was released.
47
62
0m
Glass
62
0m
m
m
E
D
C
62
0m
m
A
Absorber
Reflector
B
Fig. 36. Sketch of the three studied collector geometries
Configuration (C) was the standard collector also used in the study described above.
Configuration (D) was a standard reflector cavity and the absorbing surface consisted
of two narrow absorber fins (half of the width used in the standard collector) of
thickness 0.5 mm in parallel. The two absorbers are denoted A and B where A is
closest to the cavity centre. The last configuration (E) consisted of a two-unit reflector
cavity with one narrow absorber of thickness 0.5 mm placed in each reflector trough.
Configuration (E) was less deep than the other two. All configurations have the same
absorber and aperture areas. The results of the calculations of the annually collected
zero-loss energy are seen in Table 4.
Table 4 Annually collected energy Ea, corr in arbitrary units for absorber inclination angles 20
and 65° for the three configurations: standard wide absorber and standard reflector cavity, 2
narrow absorbers side by side in a standard reflector cavity and a 2-unit less deep reflector
cavity with one narrow absorber in each cavity.
Absorber
angle
20°
65°
Annually collected energy, Ea,corr [a.u.]
C
D
Standard
absorber 2 narrow absorbers
standard cavity
standard cavity
0.32
0.36
0.26
0.29
E
1 narrow absorber less
deep cavity
0.36
0.29
The configurations with narrow fins (D) and (E) collect 13% more energy at 20°
absorber inclination angle compared to the standard configuration (C). The installed
MaReCo systems have had the standard configuration (C) with the absorber mounted
65° from the horizon. If instead configuration (D) or (E) had been used with a 20°
mounted absorber the annually collected (zero-loss) energy would have increased by
38%.
A more detailed investigation was made for configuration (D) to analyse the relative
distribution of annually collected energy on the upper- and lower sides of the two
absorbers A and B in Fig. 36. The upper side of the absorber is facing the upper
reflector and the lower side is facing the lower reflector. The results of the calculations
are shown in Table 5.
48
Table 5 Relative distribution of annually collected energy on the upper- and lower sides of the
two absorbers in configuration (D). Absorber A is placed closest to the collector cavity centre
as seen in Fig. 36.
Absorber
Abs. A upper
inclination angle 29.8 %
20°
Sum 59.4 %
Absorber
Abs. A upper
inclination angle 25.8 %
65°
Sum 63.5 %
Abs. A lower
29.6 %
Abs. A lower
37.7 %
Abs. B upper
19.4 %
Sum 40.6%
Abs. B upper
14.6 %
Sum 36.5 %
Abs. B lower
21.2 %
Abs. B lower
21.9 %
As seen in Table 5 the largest part of the radiation is collected by absorber A for both
absorber inclination angles. According to Table 5 the collected energy is more evenly
distributed with the 20°-mounted absorber. This leads to lower thermal losses if the
absorbers are connected in parallel. If the absorbers are connected in series an uneven
distribution can be an advantage. The system is then designed to first letting the water
flow through the absorber with a low annually collected energy to preheat the water
and then through the absorber with high annually collected energy. If one side of the
absorbers in configuration (D) was to be covered by a solar cell to create a PV/thermal
hybrid the 65° mounting should be used and the cell should be placed on the lower
side of absorber A. This is the position receiving the maximum annual radiation.
3.1.5 Annual optical efficiency factor
The annual optical efficiency factor, F’c,a, for the stand-alone MaReCo configuration
was calculated. The method of calculating the optical efficiency factor is described in
section 2.3.5. The same measurements and radiation distribution data as in section
3.1.4 was used.
In Paper IV the influence of fin thickness and teflon on the annual optical efficiency
factor was investigated for three absorber inclination angles, 20°, 45°and 65°.
Calculations were made for three configurations with absorber fins of thickness 0.5
and 1 mm and finally with a 0.5 mm thick fin with teflon convection suppression
around the absorber. For the case with teflon convection suppression the radiation data
was multiplied by 0.96 to account for the transmission through the teflon film and the
overall loss coefficient per single sided absorber area was decreased from 13 to 8
W/m2K. The results are found in Table 6.
49
Table 6 The annual concentrating collector efficiency F’c,a for a stand-alone MaReCo with
absorber inclination angles 20, 45 and 65° with absorber thickness d=0.5 mm, d=1 mm and
d=0.5 mm with teflon convection suppression film added.
Absorber
angle
20°
45°
65°
Annual average optical efficiency factor, F’c,a
d=0.5 mm
d=1 mm
teflon, d=0.5 mm
0.87
0.92
0.92
0.88
0.92
0.92
0.88
0.92
0.92
As seen in Table 6 the F’c,a is rather independent of absorber inclination angle.
Increasing the absorber fin thickness or including a teflon film around the absorber
increases the F’c,a by 5-6% depending on absorber inclination angle.
The influence of absorber width and collector geometry on the optical efficiency factor
was investigated in Paper V. Three different combinations of absorber width and
collector geometry shown in Fig. 36 were investigated for absorber inclination angles
20° and 65°. The configurations are denoted (C), (D) and (E) and are described in
section 3.1.4. The results are found in Table 7.
Table 7 Annual optical efficiency factor, F’c,a, in arbitrary units for absorber inclination
angles 20 and 65° for the three configurations: standard wide absorber and standard
reflector cavity, 2 narrow absorbers side by side in a standard reflector cavity and a 2-unit
less deep reflector cavity with one narrow absorber in each cavity.
Absorber
angle
20°
65°
Annual average optical efficiency factor, F’c,a
C
D
Standard
absorber 2 narrow absorbers
standard cavity
standard cavity
0.87
0.97
0.88
0.97
E
1 narrow absorber less
deep cavity
0.97
0.97
According to Table 7 the two configurations with narrow absorber have an annual
average optical efficiency factor that is around 10% higher than that of the standard
configuration with a standard absorber.
The annual optical efficiency factor can also be calculated angle by angle, F’c(θ), as
seen in Fig. 37. This information can be used for example if the efficiency in a certain
angle interval is important such as in the spring/fall MaReCo, where the collector with
20° absorber inclination has a higher annual optical efficiency factor, especially below
35°.
50
0.91
0.9
0.89
20
45
65
c
F' (θ)
0.88
0.87
0.86
0.85
0.84
0.83
20
30
40
50
60
Projected angle of incidence
Fig. 37 Angle dependent average optical efficiency factor F’c(θ) for different projected angles
of incidence for the MaReCo for an absorber with fin thickness 0.5 mm at different absorber
inclination angles.
3.1.6 The influence of reflector performance on delivered energy output
In Paper VIII simulations of MaReCos with two different reflector materials were
performed to investigate the influence of reflector performance on delivered energy
output. In the collector fields that have been installed so far anodised aluminium
reflectors have been used.
The MaReCo collector simulated in this study has an antireflection treated cover
glazing and a selective absorber covered by a teflon film. The reflector in the reference
MaReCo collector consisted of anodised aluminium with a total solar reflectance, Rt,
of 0.85 and a specular solar reflectance, Rs, of 0.80 at 60° angle of incidence. An
improved version with a silvered glass reflector with Rt=Rs=0.95 was also simulated.
A maximum solar acceptance angle of 65° and a minimum acceptance angle of 20°
were used in the simulations. The results are listed in Table 8.
Table 8 Annual energy output and relative improvements for the MaReCo collector with a
silver reflector, compared to an anodised aluminium reflector at different operating
temperatures.
Op. temp. (°C) Anod. Al output
kWh/m2
30
377
50
317
70
269
Ag output
kWh/m2
440
377
328
Relative diff. Aganod. Al (%)
16.7
18.9
21.9
The MaReCo collectors built today can be improved by 19%, if the anodised
aluminium reflector is replaced by a silvered mirror. The major problem with the glass
51
protected silver mirror is that if it is used in the curved MaReCo geometry the glass
needs to be shaped before it is coated with silver, otherwise the glass will break.
3.2 Flat plate collectors
Three studies concerning flat plate collectors have been made within this thesis. The
first results originate from a study on how annual variations in solar radiation and
ambient temperature in Sweden affect the delivered energy output from a flat plate
collector. The second section describes how the delivered energy depends on the tilt
and orientation of the flat plate collector in Sweden. Finally results from a study
concerning the impact of the optical properties of collector components on the
delivered energy output is described.
3.2.1 Impact of annual climate variations and location on delivered energy
output
A comparative study of simulated annual delivered energy output from a solar
collector using climatic data for three locations in Sweden for a sixteen year period
from 1983 to 1998 was conducted in Paper VI. The aim was to elucidate the impact of
climatic variations such as annual global irradiation and ambient temperature. A
comparison with a synthetic year produced with Meteonorm has also been included in
the study. Two different collector types were simulated, a flat plate and a vacuum tube
collector. Climate data from three Swedish cities with approximately 5°-steps in
latitude, Lund, Stockholm and Luleå, were used in the simulations. The simulation
program MINSUN was used to perform the calculations.
Fig. 38 shows the deviation in delivered energy output from the 1983-1998 average for
the flat plate collector at 50°C average operating temperature and the total radiation
incident on a 45°-tilted surface and a horizontal surface for Stockholm.
Flat plate collector
2
Deviation [kWh/m a]
150
100
q(50°C)
g(45°)
g(0°)
50
0
-50
-100
-150
83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 M
Year
Fig. 38 Simulated solar collector output and solar irradiation on horizontal and 45°-inclined
surface compared to the average output for 1983 to 1998 and a synthetic year produced with
the Meteonorm weather simulation program (M) for a) a flat plate collector with high Uvalue for Stockholm, 1983-1998.
52
As seen in Fig. 38 the variations between the individual years can be rather large, the
maximum deviation from the mean value is around 20% for the flat plate collector.
The synthetic data obtained with the Meteonorm climate data simulation program
overestimates the solar radiation compared to the 1983-1998 average, but the
simulated delivered energy output is only slightly above the average. Table 9 shows
average- and extreme values and standard deviations of annual solar irradiation,
temperature and delivered collector energy output for collector simulations for the
three Swedish cities Lund, Stockholm and Luleå.
Table 9 Average- and extreme values and standard deviations of annual solar irradiation,
temperature and collector energy output for collector delivered energy simulations for three
Swedish cities. The numbers within brackets indicate the relative deviation from the mean.
Lund (55.72º N)
Average
Annual 1124
irradiation on 45°-tilted
surface (kWh/m2a)
Span insol. (kWh/m2a) +113 (+10%)
Relative highest lowest -103 (-9%)
insol.
Standard
deviation 69 (6%)
2
(kWh/m a)
Average
annual 13.4
temperature (°C) for
(G(45°)>300 W/m2)
Temperature span (°C) +2.1 (+16%)
Relative highest and -3.3 (-25%)
lowest
Standard deviation (°C) 1.3 (10%)
Flat plate Vacuum
781
Average
Top=25°C 610
annual
675
Top=50°C 337
collector
141
564
Top=75°C
energy
output
(kWh/m2a)
Span
in Top=25°C -73 +84
-79 +85
–61
+65
output
-77 +83
Top=50°C -36 +36
(kWh/m2a) Top=75°C
-59 +78
Relative
highest and
lowest
Standard
Top=25°C 57 (9%) 55 (7%)
deviation
Top=50°C 45 (13%) 54 (8%)
(kWh/m2a) Top=75°C 25 (18%) 53 (9%)
Stockholm (59.33º N) Luleå (65.55º N)
1113
1077
+115 (+10%)
-144 (-13%)
+146 (+14%)
-126 (-12%)
77 (7%)
80 (7%)
13.6
9.8
+1.8 (+13%)
-4.1 (-30%)
+1.4 (+14%)
-1.7 (-17%)
1.4 (10%)
Flat plate
603
337
145
1.1 (11%)
Flat plate
543
298
124
Vacuum
772
668
559
-103 +113 -111 +114 -96 +91
–71 +76 –108
–67 +59
-39 +40
+112
-38 +29
-99 +105
Vacuum
733
631
526
-98 +109
–95 +103
-88 +94
57 (9%) 59 (8%) 55 (10%) 61 (8%)
42 (12%) 58 (9%) 37 (13%) 59 (9%)
24 (16%) 55 (10%) 19 (16%) 54 (10%)
53
According to Table 9 the estimated annual energy outputs for collectors placed in
Lund and Stockholm are of the same order, but a collector placed in Luleå has a
significantly lower expected energy output. This stresses the importance of using local
climate data for the prediction of expected energy output through simulations in order
not to over/under estimate the collector system.
An attempt was also made to find a simple linear model, which can be used to estimate
the annual collector yield, qu from the global irradiation on a horizontal surface, G(0°)
at constant operation temperature, T (given in degrees Celsius):
qu=aG(0°)+bT
(60)
The constants a and b are found from double-linear regression from the 1983-1998
energy output simulation data. All parameters are presented in Table 10, together with
the standard deviation for each of the parameters, the R2 value and the standard
deviation for the whole model. R2 is the coefficient of determination, a value between
one and zero. For perfect correlation between model output and the simulated or
measured values the R2-value is equal to one.
Table 10 Multiple linear regression to obtain parameters for qu=aG(0°)+bT, where G is the
global horizontal irradiation in [kWh/m2] and T is the average collector temperature in [°C].
Regression was performed using simulated collector delivered thermal energy data for two
different solar collectors with climate data for three Swedish cities, Luleå, Stockholm and
Lund from 1983 to 1998.
Coll.
City
a
[-]
Flat plate Luleå
0.86
Stockholm 0.88
Lund
0.85
All three 0.86
cities
Vacuum Luleå
0.98
tube
Stockholm 0.95
Lund
0.92
All three 0.94
cities
sda
[-]
0.011
0.010
0.010
0.008
b
[kWh/m2°C]
-8.36
-9.13
-9.36
-8.82
sdb
[kWh/m2°C]
0.183
0.179
0.176
0.142
R2
[-]
0.98
0.98
0.98
0.97
sdmodel
[kWh/m2]
26
26
25
35
0.010
0.008
0.007
0.008
-4.22
-4.31
-4.36
-4.15
0.157
0.135
0.118
0.129
0.95
0.97
0.97
0.91
22
19
17
32
Fig. 39 shows a comparison between the energy outputs obtained with simulations
with the MINSUN-program from climate data 1983-1998 and the proposed model
from Eq (60) for the flat plate collector.
54
Flat plate collector
800
Annual output
2
[kWh/m ]
Sim.25°C
Mod. 25°C
Sim. 50°C
Mod. 50°C
Sim. 75°C
Mod. 75°C
600
400
200
0
825
875
925
975
Annual insolation [kWh/m2]
1025
Fig. 39 Simulated, (Sim) and calculated, (Mod), solar collector thermal energy output vs.
annual horizontal irradiation for a flat plate collector with high U-value. Three different
average collector temperatures were simulated and calculated for Stockholm 1983 to 1998.
The delivered energy obtained with the simulated result and the double linear
regression equation (Eq 51) show good agreement as can be seen in Fig. 39.
Deviations are found for example for years with extreme ambient temperatures or with
a very high or low beam radiation content in relation to the horizontal global solar
radiation. An example of the latter is Stockholm 1992 with a high horizontal global
irradiation, G(0°)=978 kWh/m2a (average 926 kWh/m2a), and low beam radiation,
Gbeam=881 kWh/m2a (average 972 kWh/m2a), resulting in a too high energy output
with the regression model compared to the MINSUN model. When studying Table 10
it is found that the a-coefficients (from Eq. 51) are quite close to 1, so a deviation in
solar irradiation of 100 kWh leads to a change of about 100 kWh in collector delivered
energy.
3.2.2 Impact of collector tilt and orientation on the delivered energy output
When installing solar collectors on existing buildings it is of practical importance to
know how the annual performance depends on tilt- and azimuth angle. In order to
obtain a reliable estimate of the expected output of a solar collector system, it is
important to distinguish between the output claimed by the manufacturer, valid for a
certain tilt- and azimuth angle, and the output for the actual case. In Paper VII
diagrams, which can help the user to make this distinction, are developed. Different
solar collectors have a different dependence on tilt- and azimuth angle. The collectors
simulated were six flat plate collectors and one vacuum tube collector. Simulations for
two of these collectors are presented here, one flat plate with selective absorber, low
iron glass, low U-value and one vacuum tube collector of through flow type.
To investigate the influence of tilt and azimuth on collector output, a number of
simulations were performed with the MINSUN program in 10° steps for tilt angles
55
1,0
1,0
0,9
0,9
0,8
0,8
Relative output
Relative output
ranging from 0 to 90° (horizontal to vertical) and in 30° steps for azimuth angles
between +90° and -90° (west to east). Additional calculations were performed for a tilt
angle of 45°, since that is often the tilt angle used by the manufacturer when predicting
the performance of the collector in Sweden. The average collector temperature used
was 50°C. Climate data for Stockholm, a reference year based on SMHI (Swedish
Meteorological and Hydrological Institute) measurements 1983-1992, was used in the
simulations. The International Energy Agency, Solar Heating and Cooling programme
compiled this reference year. The Hay and Davies (Duffie and Beckman 1991) model
was used for the diffuse solar radiation. Stockholm is situated on latitude 59° north and
longitude 18° east. The results are found in Fig. 40 a and b.
0,7
0,6
90
60
30
0
-30
-60
-90
0,5
0,4
0,3
0
10
0,7
90
0,6
60
0,5
0
30
-30
0,4
-60
-90
0,3
20
30
40
50
60
70
80
0
90
10 20 30 40 50 60 70 80 90
Tilt
Tilt
Fig. 40 a) Relative energy output for a flat
plate collector with selective absorber, low Uvalue and low iron glass with tilt Average
collector temperature 50°, maximum output
423 (kWh/m2, year).
Fig. 40 b) Relative energy output for a
vacuum tube solar collector of through flow
type with tilt angles 0 to 90° and azimuth
angles –90 to 90°. Average collector
temperature 50°C, maximum output 666
(kWh/m2, year).
There is a difference in dependence on tilt- and azimuth angle for the various
collectors as seen in Fig. 40. In general non-advanced collectors have a stronger
dependence on tilt- and azimuth angle and the vacuum collector, has a weaker
dependency. With vacuum tube collectors there is also the possibility of tilting the
absorber inside the tube during manufacturing to improve the performance for a
certain tilt- and azimuth angle. Not only do the curves in Fig. 40 begin and end at
different values; but the shape of the curves is also different. More advanced
collectors, such as the vacuum tube collector, have a flatter structure than the simple
collectors do. Optimum tilt is dependent on azimuth angle, especially for the more
advanced vacuum collector. The shape of the curves and the location of the optimum
tilt depend on climate and latitude.
The output for the collectors is not east- west symmetric; the output for the positive
azimuth angles is slightly higher. This behaviour is more pronounced for the simple
56
collectors, as can be seen when comparing Fig. 40 a and b. The difference is also
larger for higher azimuth angles (positive and negative) and the maximum difference
is found at the optimum tilt according to Fig. 40. With the weather data used here the
asymmetry is too small to be caused by variations in the radiation, but rather due to
higher thermal losses in the morning due to low ambient temperatures and thermal
capacity losses.
3.2.3 The influence of collector materials on delivered energy output
The impact of the materials properties on the energy output of solar collectors is not
always well known, but with this knowledge it is possible to give priority to the most
cost effective improvements. The aim of this study described in Paper VIII was to
investigate the impact of material improvements of different collector components on
the delivered energy output. Starting with the energy output from a “reference
collector”, the impact on the energy gain due to improved absorber emittance and
absorptance, adding of transparent insulation and antireflection treatment of the cover
glass were evaluated. The impact of adding external or internal booster reflectors was
also studied.
The calculations of the annually delivered heat were performed using the collector
array model in the MINSUN simulation program. The collector parameters used in the
model, for the different cases, were mainly obtained from a model based on heat
transfer that calculates the temperature dependent heat loss coefficients as well as the
incidence angle dependent optical efficiencies for the glazing. The model has been
verified through laboratory measurements.
The reference solar collector was a flat plate collector with a spectrally selective
absorber and a single glass pane with Tsol=0.90. For the absorber, εtherm=0.10 and
αsol=0.95 was chosen. No transparent insulation was included.
Eight changes from the reference case are treated (reference values within brackets):
1.
2.
3.
4.
5.
6.
7.
8.
ε=0.05 (0.10)
α=0.97 (0.95)
ε=0.05 and α=0.97, cases 1 and 2 combined
Teflon film added
Teflon honeycomb added
Cover glass with structure facing the absorber
Antireflection cover glass, τ=0.94 (0.90)
Optimised collector, cases 3, 5, and 7 combined
The results and the input parameters from the MINSUN simulations are presented in
Table 11.
57
Table 11 Absolute and relative annual energy gains (kWh/m2) from changes in the collector
parameters for different operating temperatures and MINSUN parameters for each case.
Case
1
2
tm
referenc ε=0.05 α=0.97
(°C) e
collector
Annual
30
608
620
621
collector
40
523
538
536
energy
50
447
464
459
output
60
377
396
388
(kWh/m2) 70
313
333
324
Relative
30
2.0
2.1
difference 40
2.9
2.5
collector- 50
3.8
2.7
reference
60
5.0
2.9
(%)
70
6.4
3.5
MINSUN F’(τα 0.809
0.813 0.824
parameters )b
(-),
F’(τα 0.721
0.725 0.734
(W/m2K)
)d
(W/m2K2) F'U1 3.42
3.22
3.43
F'U2 0.0113 0.0106 0.0113
3
ε=0.05
/
α=0.97
634
552
477
408
344
4.3
5.5
6.7
8.2
9.9
0.828
4
teflon
film
5
teflon
hc
6
7
8
struct. AR
Optim.
glazing glazing
606
536
472
412
357
-0.3
2.5
5.6
9.3
14.1
0.788
619
558
501
449
399
1.8
6.7
12.1
19.1
27.5
0.814
594
511
435
367
305
-2.3
-2.3
-2.7
-2.7
-2.6
0.809
639
553
476
404
338
5.1
5.7
6.5
7.2
8.0
0.843
672
612
557
505
455
10.5
17.0
24.6
34.0
45.4
0.868
0.738
0.680
0.669
0.721
0.751
0.712
3.23
2.69
2.22
3.42
3.42
2.11
0.0106 0.0082 0.0062 0.0113 0.0113 0.0055
The presented simulations show that several improvements can be achieved for solar
thermal collectors. The largest efforts should be put on the improvements that lead to
the largest increase in the annually delivered energy output per cost unit. Some of the
presented improvements already exist for commercial collectors, such as teflon films
and antireflection treated glass. Whereas other improvements, such as an absorber
simultaneously having an absorptance of α=0.97 and a hemispherical emittance of
ε=0.05, are difficult to achieve to a reasonable cost.
By increasing the absorptance from 0.95 to 0.97 the annual energy output increases by
6% at an operating temperature of 50°C. Decreasing the emittance from 0.10 to 0.05
leads to an increase of 4% for the same operating temperature. The improvements in
either absorptance or emittance for the solar absorber are realistic to obtain; some of
the new commercial absorbers already exhibit these characteristics. Improvements in
absorptance and emittance are possible through optimisations in the existing
manufacturing process. The use of the versatile sputter depositing technique in the
absorber manufacturing process increases the flexibility in comparison to previous
deposition methods. It is therefore conceivable to alter the absorber coating
performance without large investments.
Antireflection treated glass is commercially available for an additional cost of less than
10 €/m2. The presented simulations indicate an increase of 6% when an antireflection
treated glazing, with 4% higher solar transmittance than an untreated one, is used in a
collector operating at 50°C. The investigation of the structured glass, with the structure
58
facing the absorber, resulted in a deteriorated performance compared to the reference
collector with a plane glass. In spite of this relatively poor performance, the structured
glass is frequently used in Swedish solar collectors. Switching from a structured glass
to a plane glass would increase the output by approximately 2%.
Including a teflon film leads to a performance increase of 6% and a teflon honeycomb
to an increase of 12% at 50°C operating temperature. Including a flat teflon sheet is
cost effective, especially at high latitudes and high operating temperatures. If a
honeycomb of teflon is used instead the cost is too high to be cost effective, since the
amount of material required is about 10 times higher than that used for a flat single
film.
Adding a booster reflector in front of the collector was also investigated. In Table 12
the results from MINSUN simulations for a reference collector with a flat booster
reflector are shown. Three different commercially available booster reflectors were
considered; polyvinyl di-fluoride (PVF2) coated aluminium (PVF2), anodised
aluminium (Anod. Al), and silver coated glass (Ag).
Table 12 Annual energy output for the reference collector with a flat booster reflector,
absolute and relative difference due to addition of a booster reflector.
Op.temp.
(°C)
Annual energy output 30
(kWh/m2)
50
70
Relative improvement 30
with
addition
of 50
reflector (%)
70
PVF2
720
558
421
15.6
19.9
25.7
Anod.
Al
770
605
465
21.0
26.1
32.7
Ag
799
633
492
23.9
29.4
36.4
If the reference collector is combined with a flat booster reflector having an area twice
of the collector area, an increase of 20-29% at 50°C depending on the reflector
material being used is obtained. The relative improvement increases with increasing
operating temperatures.
The contribution from the reflector is proportional to its specular reflectance. A second
surface silver mirror is almost an ideal reflector material, with a 95% reflectance
resulting in a 30% output increase. It is also relatively cheap, around 10 €/m2. The
sheet of glass is however very thin, it might therefore suffer from insufficient
mechanical strength. Anodised aluminium is optically fairly good with a 26% increase
in output, but the long-term stability in outdoor applications is limited to about 5 years,
after which the specular reflectance decreases rapidly with time. The PVF2 coated
sheet aluminium is a commercially produced roofing material. It is long-term stable,
has good mechanical strength, and is practical to install, but has a low specular
reflectance.
59
3.3 Component studies
Detailed studies were performed for two of the components in the solar collector. The
first study was focused on the reflector. In this case the scattering properties of two
different reflector materials were studied to investigate if a low quality cheap reflector
could be used as concentrating element. The second component that was studied was
the absorber. The optical constants of the absorbing layer in a Sunstrip spectrally
selective absorber were investigated. If the optical constants of the layer is known it is
easier to improve the coating.
3.3.1 Optical scattering from rough rolled aluminium surfaces
The main reason for using external booster reflectors is to reduce the cost of energy
produced with solar energy. If a cheap reflector material can be used, the system gets
even more cost effective. High total reflectance in the solar wavelength range is
important, and therefore aluminium and silver are the most common reflector materials
used in solar energy applications. Anodised aluminium is a reflector material that is
often used. High quality reflectors are specular but rather expensive compared to
rolled more rough aluminium. Low-concentrating devices, such as compound
parabolic concentrators (CPC) are less sensitive to scattering of the incident radiation
than high-concentrating devices such as parabolic troughs or dishes. Furthermore, if
the non-specular radiation is scattered in linear corrugations with a particular geometry
or unidirectional rolling grooves, this can be beneficial for certain concentrator
geometries.
The aim of the study in Paper IX was to examine the scattering properties of two types
of cheap industrial aluminium samples with surface roughnesses originating from the
cold rolling process. The first sample was sheet aluminium that looked almost
completely diffuse. The second sample was an aluminium foil with quite specular
appearance. The major optical difference between the two samples was the angular
distribution of light scattered from the two surfaces.
The surfaces were analysed using white-light interferometry. A scan perpendicular to
the rolling grooves for the sheet and the foil is shown in Fig 42.
1.5
Sheet sample,
perpendicular scan
1
Height variation [µm]
Height variation [µm]
1.5
0.5
0
0.5
0
-0.5
-0.5
-1
-1.5
Foil sample,
perpendicular scan
1
0
0.2
0.4
0.6
Scan length [mm]
0.8
1
-1
-1.5
60
0
0.2
0.4
0.6
Scan length [mm]
0.8
1
Fig. 42 Line profiles of the aluminium sheet and foil taken with an interference fringe
microscope.
As seen in Fig. 42 the roughness of the sheet is significantly higher than that of the
foil. This is manifested in a three times larger rms height for the sheet (0.6 µm) than
for the foil (0.2 µm). The rms slopes were found to be gentle for both samples, thereby
corresponding to large radii of surface curvature when comparing with the wavelength
of the light used in the optical measurements.
The angular resolved scattering properties of the two samples were measured using
ARS and TIS described briefly in section 2.1.5. The sheet was found to scatter more at
higher scatter angles than the foil, as expected from the white light interferometry.
Both samples have a distinct narrow band of scattered light of higher intensity
extending in two directions from the specular peak. It originates from scattering by the
unidirectional rolling grooves and appears as a straight line perpendicular to the
grooves when these are oriented perpendicularly to the plane of the incident light. For
other groove orientations with respect to the incident plane and non-normal incident
light, the scatter band is bent into an arc like shape.
Using the data from the angular resolved measurements, the scatter intensity was
divided into different regions according to the method of summation of scattering
patterns described in section 2.1.4.2. A summary of the results is found in Table 13.
Table 13 Scattered radiation in various angular regions (described in section 2.1.4.2). The
samples are characterised by angle of incidence to the surface normal, angle of rolling
grooves from the incident plane (0° parallel and 90° perpendicular) and polarisation of light
(s- or p polarised).
Sample
Foil:
60°,0°,p
60°, 0°,s
60°,40°,p
60°,40°,s
60°,90°,,p
60, 90°,s
0°,-,un-pol
60°,90°,un-pol,
(green)
Sheet:
60°,0°,p
60°,0°,s
60°,90°,p
60°,90°,s
0°,-,p
SR
%
LAS-B
%
LAS
%
HAS-B
%
HAS
%
Extension
(band)
86.6
83.0
84.7
86.8
73.0
75.4
74.5
75.0
7.2
8.8
9.3
8.4
19.3
16.2
14.9
18.5
2.8
3.3
1.2
1.2
1.8
1.8
2.8
1.1
0.3
0.9
1.8
1.3
4.5
3.0
3.6
2.8
3.1
4.4
2.2
2.3
1.4
3.9
4.2
2.6
-11°
-13°
-19°
-15°
-23°
-19°
-23°
-19°
---------
+11°
+13°
+15°
+13°
+19°
+17°
+23°
+17°
49.6
50.2
28.7
30.6
26.6
36.7
36.4
37.2
37.8
32.0
1.6
1.5
0.6
0.7
1.6
9.1
9.3
29.1
27.7
34.1
3.0
2.6
4.4
3.2
5.7
-21°
-21°
-45°
-41°
-41°
------
+21°
+23°
+29°
+27°
+41°
61
An example of the angular distribution of scattered intensity from the sheet with light
of 60° angle of incidence is seen in Fig. 43. The rolling grooves are perpendicular and
parallel, respectively, to the incoming light in Fig. 43.
Fig. 43 Two examples of the scattering pattern from p-polarised light with a 60° incidence
angle on the aluminium sheet. Grooves parallel and perpendicular respectively to the incident
plane.
The rolled aluminium sheet, after etching, with a near normal hemispherical solar
reflectance of 0.88 has a much lower specular reflectance. According to Fig. 43 it
scatters almost 90% of all reflected radiation within the angular interval |φ| < 9°, |θ| <
9° with rolling grooves parallel to the incident plane. With groove orientation
perpendicular to the plane of the incident light or normal angle of incidence the
specular and low angle scattering is considerably lower, about 65%. A large fraction,
about 30%, is confined to the scatter band for higher angles, |φ| < 9°, |θ| < 9°. This
implies that an aluminium reflector with such a rough surface as the sheet will not
perform well in a concentrating reflector application but might be acceptable as a
planar booster reflector in front of flat plate solar collectors, i.e. with grooves oriented
in the north south direction. As the main part of the high angle scattered light is
collected in the scatter band, it will be bent downward onto the collector and will
therefore give less reflectance losses than an isotropically scattering surface having the
same rms height. Ray-tracing calculations for specific reflector-solar collector
configurations will reveal what can be gained by using reflectors with such
pronounced rolling grooves.
62
3.3.2 Optical characterisation of the absorbing layer in a nickel/nickel
oxide solar selective surface
The sputter deposited Sunstrip absorber (Wäckelgård and Hultmark 1998) has been
investigated in detail in Paper X. The coating shown in Fig. 41 consists of three layers,
starting with a nickel barrier layer deposited on the aluminium reflector, followed by
an absorbing graded index nickel-nickel oxide layer and finally an anti-reflection
layer. The optical constants (n and k) of the absorbing graded index layer were
determined from reflectance, transmittance and ellipsometry data.
Fig. 41 A model of the Sunstrip absorber in cross section showing AR-coating, absorbing
coating and reflector.
The investigated absorbing coating was deposited on a glass substrate to facilitate
measurements of reflectance and transmittance of the coating. The spectral specular
reflectance and transmittance were measured in a custom built spectrophotometer
described in Roos (1997). These data were then fitted using a least-square method
where the n- and k-values were fitted simultaneously. A two-layer structure was used
in the model. This is a too simple model for a graded index coating, but provides some
information about the optical constants of the base and top parts of the coating.
It was found that the top part of the graded index layer has a refractive index that
increases monotonically from n=1.7 to n=2.5 and a constant extinction coefficient of
k=0.5 over the measured spectral range. The base part of the graded index layer has a
metallic behaviour with higher n- and k-values than the top part and they were found
to increase with wavelength. A further optimisation of the sputter deposition process is
taking place at the moment but without the participation of the author.
63
4 CONCLUSIONS AND SUGGESTION FOR FUTURE WORK
The thesis comprises system aspects on solar collectors and how system performance
is linked to thermal and optical properties of the materials in the collector components.
The MaReCo design has the potential to provide energy at a low cost, achieved by
replacing the expensive absorber with cheap reflectors. A large part of the available
solar radiation can be collected without the need for tracking, which would increase
the investment and maintenance costs. The MaReCo design concept is flexible and can
be adapted to various installation conditions. The evaluation of the prototypes in Paper
I shows that all MaReCo types function as expected. The highest annually delivered
energy output was found for the roof mounted MaReCo. Based on this evaluation an
estimated investment cost of 0.46 € per annually produced kWh for the roof integrated
MaReCo and an annuity of 0.1, leads to an energy cost of 0.05 €/kWh. This is cost
effective in Sweden, at least compared to the electricity price, which is around 0.09
€/kWh including tax for a household (excluding fixed costs). The cost effectiveness
can be further increased through the results found in this thesis.
The major suggested improvements in components and system performance to
increase the performance are listed in the following:
• Paper I, Paper II and Paper IV show that the use of teflon is recommended in the
MaReCo since the absorber temperature is significantly higher than that of a flat
plate as an effect of the concentration
• The studies of the absorber inclination angle all show that the absorber should be
mounted along the 20°-optical axis both from a thermal and an optical point of
view. The installations so far have been made with the absorber mounted along the
65°-optical axis. Further studies of this are suggested, for example an outdoor test
with two identical prototypes but with different absorber inclination angle.
• An improvement in the geometry of the MaReCo is possible through a slight
correction of the acceptance interval compared to the prototypes as shown in Paper
III. For the wall MaReCo a change in the lower acceptance angle from 25° from
the horizon to 5° would increase the collectable fraction of the incoming solar
radiation from 65% to almost 100%.
• In a non-imaging concentrator a reflector material that is not completely specular
might be used. Paper IX involves a study of an aluminium foil laminated with
plastic, which might be a good enough reflector for the MaReCo. It is cheaper than
the anodised reflector most frequently used in the MaReCo. A study linking Paper
IX with Paper IV is therefore suggested where the radiation distribution on the
absorber is studied for a MaReCo with a reflector of foil laminated with plastic. A
rougher sheet metal was also studied in paper IX, but it was concluded that this
material scattered too much to be used in internal reflectors in concentrating
64
collectors but could be used in external booster reflectors for flat plate collectors.
Another way to increase the delivered energy output is to increase the solar
reflectance of the reflector. As mentioned in Paper VIII the delivered energy output
is significantly increased if the anodised aluminium is replaced by silvered glass.
• The ventilation channels investigated in Paper II can prove to be important in case
of stagnation for the MaReCo with EPS-insulation. The reflector is resting on the
EPS-insulation, which is not long-term stable for temperatures above 60°C. The
channels significantly help to lower the reflector temperature.
• A thicker absorber fin is suggested from measurements and calculations of the
annual incident solar radiation on the absorber in a stand-alone MaReCo. With an
absorber fin of 1 mm thickness instead of 0.5 mm 5% more energy is collected. If
the narrow absorber fin of width 71.5 mm is used instead of the standard absorber
(143 mm) 13% more energy can be collected at absorber inclination angle 20°. If
the standard configuration used in the present installations with 143 mm wide
absorber and 65° absorber angle is compared to using the narrow 71.5 mm
absorber mounted at 20°, 38% more energy can be collected.
A method to obtain an estimate of the acceptance interval for the design of a CPCcollector from radiation distribution diagrams was developed. The method worked
very well for the MaReCo and it is also applicable for the design of the acceptance
interval of any CPC-collector.
The method of measuring the concentration distribution on the absorber of a
concentrating collector and then calculating the collected energy and annual optical
efficiency factor developed in Paper IV worked very well. The method does not
require sophisticated equipment and a lot of information about the collector can be
obtained from one set of measurements. In the measurements described in Papers IV
and V angles within the acceptance interval were investigated. If angles outside the
acceptance interval were measured the incidence angle dependency of the collector
could be obtained. The major part of the energy is within the acceptance interval, but
some radiation is also accepted outside the acceptance interval.
The simulations of annual performance of flat plate collectors were performed to
investigate the impact of tilt, azimuth and annual climate variations on collector
performance. When solar collectors are tested at the Swedish National Testing and
Research Institute, SP, the results are valid for the optimum tilt (45°) and azimuth (0°)
and simulated with a standard climate for central Sweden. According to Paper VII
there is a large variation in delivered collector energy output for different tilts and
azimuths. If the roof tilt is within 30-60° and the azimuth within ±30° the delivered
collector energy output is at least 90% of that for the optimum conditions according to
Paper VII. Advanced collectors, such as vacuum tube collectors, depend less on tilt
and azimuth compared to less advanced collectors such as a flat plate collector with a
non-selective absorber. There is also a large variation in delivered collector energy
output between southern/central and northern Sweden according to Paper VI. Owing to
65
these factors the amount of energy that the individual owner gets from his solar
collector can therefore be significantly different from the test results. The annual
climate variations have a large impact on the solar collector as found in Paper VI. If a
16-year average in collector delivered energy obtained from simulations with
measured climate data is compared to the maximum and minimum annual energy
production, deviations of up to 100 kWh/m2 are found. There is also a large difference
between the estimated average delivered energy output between northern Sweden and
mid/southern Sweden. For a flat plate collector with selective absorber, a collector
placed in Luleå has an estimated delivered energy output that is 88% of that of a
collector placed in mid/southern Sweden.
The investigations of the impact of the materials in the collector components on the
delivered energy output showed that a lot of improvements are possible. It is especially
important to link the performance increase with the cost of the improvement. The
study in Paper VIII showed that using anti reflective treated cover glass, including
teflon and adding a flat external booster reflector are measures that are cost effective
for flat plate solar collectors.
Finally, it is of interest to compare the MaReCo with the flat plate collector. The
simulated flat plate collector is a large area collector with teflon and a low U-value,
η0b=0.75, η0d=0.60, F’U1=3.5 W/m2K, F’U2=0.002 W/m2K2, b0=0.19 and (mC)e=6
J/m2K. The present MaReCo is approximately the stand-alone MaReCo from the
prototype evaluation in Paper I except the b0 value is decreased from 0.37 to 0.30. A
future MaReCo with some of the improvements suggested in this thesis is introduced.
The process of obtaining the parameters for the future MaReCo is described below.
(mC)e =3 J/m2K, b0 =0.30 and F’U2=0 are assumed to be the same for the present and
the future MaReCo. The relative decrease in the real U-values is assumed to be the
same as that for the laboratory value and the increase in F’ is assumed to be the same
as that of F’c,a.
The present MaReCo:
η0b=0.60
η0d=0.40
F’U1=2.4
1. Introducing teflon. The laboratory U-value is lowered from 2.4 to 1.5 according to
Paper II. The transmittance is decreased with 0.96. The annual optical efficiency
factor, F’c,a, is increased from 0.88 to 0.92 according to Table 6. The collectable
energy is increased from 0.26 to 0.27 a.u. in Table 3, the same increase is assumed
for η.
η0b=0.60x0.96x(0.27/0.26)
=0.60
η0d=0.40x0.96x(0.27/0.26) F’U1=2.4x(1.5/2.4)x(0.92/0.88)
=1.6
=0.40
2. Changing the absorber inclination angle to 20°. The decrease in laboratory Uvalue is from 1.5 to 1.4 from Paper II. The F’c,a is the same according to Table 6.
The collectable energy is increased from 0.27 to 0.32 a.u. in Table 3.
F’U1=1.6x(1.4/1.5)
η0d=0.40x(0.32/0.27)
η0b=0.60x(0.32/0.27)
=1.5
=0.71
=0.47
66
3. Using two narrow absorber fins instead of one wide. Configuration D in section
3.1.4 is used, the heat losses are assumed not to be affected. Changing to a narrow
absorber increases the F’c,a from 0.87 to 0.97 according to Table 7. This is without
teflon, so the F’c,a is instead approximated to increase from 0.92 to 0.97. The
increase in η is assumed to be the same as the increase in F’c,a.
η0b=0.71x(0.97/0.92)
=0.75
η0d=0.47x(0.97/0.92)
=0.50
F’U1=1.5x(0.97/0.92)
=1.6
Table 14 shows simulations made with the MINSUN program of the annually
delivered energy output of a flat plate collector and a stand-alone MaReCo.
Table 14 Annually delivered energy output for a flat plate collector and a MaReCo.
Temperature Flat Plate Present
[kWh/m²] MaReCo
[kWh/m²]
25°
579
378
50°
401
289
75°
271
224
Ratio
Pres. MaReCo/
Flat Plate
0.65
0.72
0.83
Future
MaReCo
496
411
348
Ratio
Fut. MaReCo/
flat plate
0.86
1.02
1.28
According to Table 14 the performance of the flat plate collector is higher than that of
the present MaReCo. The low U-value of the MaReCo is an advantage especially at
high temperatures as seen in Table 14, the ratio between the performances of the two
collectors increases with temperature. For the future MaReCo the performance is
higher than that of the flat plate for operating temperatures of 50° and 75°. The
parameters used in the simulation are obtained in a theoretical study, and the
interaction of some of the improvements is not known. It does, however, show that
there is a potential for improvement to a performance that is in the same range as the
flat plate collector at 50° operating temperature and perhaps an even better
performance at higher temperatures.
The MaReCo has a lower investment cost compared to the flat plate collector. There is
also a potential for further cost reduction for the materials in the MaReCo, especially
the reflector. The MaReCo design is flexible with possibilities to design the collector
for various installation conditions or special demands. Examples of this are the
east/west MaReCo and the spring/fall MaReCo. Because of the low materials content,
the MaReCo is light, which is an advantage for roof mounting. As of today, the roof
MaReCo has a larger collector depth than the flat plate, but this can be reduced with
the use of the new 71.5 mm wide absorber. The same principle of MaReCo design can
be used for thermal and PV applications. The particular design of the MaReCo might
be a problem from an aesthetic point of view, some architects like it and others do not.
The major advantages with the flat plate collector is its higher performance and that it
is well established among manufacturers and customers. There is also plenty of
experience of the long-term performance of the flat plate collector.
67
5 SUMMARY OF APPENDED PAPERS
Paper I Evaluation of asymmetric CPC-collector designs for stand-alone,
roof- or wall integrated installation
The Maximum Reflector Collector, MaReCo, is a heavily truncated and nonsymmetric compound parabolic concentrator (CPC) extended in the east-west direction
with a bi-facial absorber optimised for northern latitudes. The MaReCo concept is
flexible and can be used for different applications. In this paper MaReCos for standalone, roof and wall mounting are studied. Prototypes of six different MaReCos have
been built and outdoor-tested. The evaluation gave the highest annual energy output
for the roof mounted MaReCo, 336 kWh/m2 and the stand-alone MaReCo with teflon
282 kWh/m2 at an operating temperature of Top=50°C. A special design for roofs
facing east or west was also investigated, and gave an annual energy output of 135
(east) and 174 (west) kWh/ m2 at Top =50°C. If a high solar fraction over the year is
the objective a MaReCo with a high output during spring/fall and a low output during
summer can be used. Such a collector had an output of 199 kWh/ m2 at Top=50°C.
Finally a MaReCo for wall mounting was evaluated, with an expected output of 142
kWh/ m2a at Top=50°.
Paper II Calorimetric measurements of heat losses from a truncated
asymmetric solar thermal concentrator
Indoor heat loss measurements have been performed on a truncated asymmetric
compound parabolic concentrating collector with concentration C=2.2. An electrically
heated flat bi-facial absorber aligned in the east-west direction was used. Geometrical
and material properties that affect the heat losses were investigated. The reference
configuration was a collector with polystyrene insulation, anodised aluminium
reflector, acrylic plastic cover and a vertically mounted selective absorber. The
components in the reference configuration were then modified. The modifications
were high-emitting black painted non-selective absorber, low-emitting un coated
aluminium absorber, adding teflon transparent insulation, low-emitting aluminium
reflector, placing the absorber in horizontal position, covering ventilation channels in
the polystyrene insulation and removing the back insulation. The measurements show
significant differences in U-value for almost all configurations. Adding a teflon film is
the single modification that causes the largest improvement in U-value, 35-55%,
mounting the absorber horizontally instead of vertically lowered the U-value by up to
22%, replacing the selective absorber by a high-emitting absorber increases the Uvalue by 73%, and using a low-emitting absorber lowers the U-value by 11%
compared to the selective absorber. All values presented at ∆T=50°. The ventilation
channels constructed to protect the insulating block from overheating increases the Uvalue by 7-22%. The variations in collector temperature distribution when the material
and geometrical properties were altered were also studied.
68
Paper III Annually projected solar radiation distribution analysis for
optimum design of asymmetric CPC
A method to study the projected solar radiation angle of incidence distribution on an
arbitrarily oriented surface is suggested. The method is based on a projection of the
incident solar radiation onto two orthogonal planes, one created by the concentrator
axis and the normal of the cover glass and one created by the orthogonal of the
concentrator axis and the cover glass normal. For a two-dimensional concentrator the
component orthogonal to the concentrator axis is the only component of interest since
the other component is parallel to the cover glass. Solar radiation distribution diagrams
are made for three cities, Madrid Spain, Munich Germany and Stockholm Sweden for
four different surface orientations. The radiation distribution diagrams can be used to
roughly design the acceptance interval of a solar concentrator. This method is used to
design the acceptance interval of the Maximum Reflector Collector, MaReCo, a twodimensional asymmetric CPC specially designed for high latitudes (Stockholm). It can
be designed for various installation conditions, on ground, roof or wall. Prototypes of
the MaReCo have previously been built and tested. In this work it is investigated if the
prototype designs are consistent with the designs obtained from the radiation
distribution diagrams. The existing prototypes could, with the exception of the roof
MaReCo, be improved with slightly changed acceptance intervals. It is also
investigated if the same design principle can be used for somewhat lower latitudes, i.e.
Munich and Madrid. The study shows that the MaReCo design principle can be used
for lower latitudes with a small decrease in the concentration factor.
Paper IV Measurement of radiation distribution on the absorber in an
asymmetric CPC collector
A method to estimate the annually collected energy and to calculate the annual average
optical efficiency factor is suggested. The radiation distribution on the absorber of an
asymmetric CPC collector with a flat bi-facial absorber is measured for three different
absorber inclination angles using a photo diode. The annually collected energy and
annual optical efficiency factors are determined for collectors with absorber fin
thickness 0.5 mm and 1 mm and for a collector with a teflon convection suppression
film mounted around the absorber. With the local optical efficiency factors and the
annual incident solar energy distribution considered, the energy gain without losses for
a mounting angle of 20° is 21-22% higher than for a collector with 65° absorber
inclination angle. The annually collected energy is increased with 6-8 % if the
absorber fin thickness is increased from 0.5 to 1 mm. The annual average optical
efficiency factor is relatively independent of absorber inclination angle. It was found
to be 0.87-0.88 for a collector with a 0.5 mm thick absorber fin and 0.92 for a collector
with a 1 mm thick absorber fin or for a collector with 0.5 mm thick absorber fin with a
teflon convection suppression film added.
69
Paper V Comparison of the optical efficiency of a wide and a narrow
absorber fin in an asymmetric concentrating collector
For a compound parabolic concentrating collector with a certain design a wider
absorber leads to a larger collector depth. The aim of this study was to investigate the
optical efficiency of three different combinations of absorber width and reflector
cavity depths for an asymmetrical truncated concentrating thermal collector designed
for ground mounting. Outdoor measurements of the radiation distribution on the
absorber fin are used to calculate the zero-loss annually collected energy and average
optical efficiency factor. Three different configurations of reflector geometry/absorber
width were investigated: A reference case with a standard fin and one deep reflector
cavity, (C), two narrow fins side by side and one deep reflector cavity, (D), and finally
two less deep reflector cavities with one narrow absorber fin each, (E). Two different
absorber mounting angles were investigated, 20 and 65° from the horizon. The
calculations show that with the absorber mounted 20° from the horizon the annually
collected energy (zero-loss) increases by 13% if any of the configurations (D) or (E)
with narrow fins are used. The annual average of the optical (zero-loss) efficiency
factor increases by approximately 11% for both the configurations (D) and (E) with
narrow fins, compared to the reference case (C). If the collected energy with
configuration (C) with 65° absorber angle, which has been used in installed collector
systems of this kind, is compared to that of configurations (D) or (E) with 20° absorber
angle, an increase of 38% is found.
Paper VI The influence of climate and location on collector performance
The influence of annual climate variations on the performance of solar thermal
collectors in the northern part of Europe has been investigated. The annual solar
collector energy output has been calculated with the MINSUN simulation program
using hourly, measured climatic data for the years 1983 to 1998 for three cities
situated in the south (Lund), central (Stockholm) and north (Luleå) of Sweden. A
synthetic year created with the Meteonorm weather simulation program was also used
in the simulations. Two solar thermal collectors were modelled: a flat plate solar
collector and a tubular vacuum collector, both of commercial standard. The annual
average energy delivered from the flat plate collector was 337 kWh/m2 for Stockholm
(337 for Lund and 298 for Luleå), and from the vacuum tube collector 668 kWh/m2 for
Stockholm (675 for Lund and 631 for Luleå) at an operating temperature of T=50°C.
Maximum deviations from the average value for this sixteen year period are around
20% for the flat plate and 15% for the vacuum tube collector, at T=50°C. The relation
between global irradiation on a horizontal surface and the annually collected thermal
energy at a constant operating temperature could be fitted to a linear equation:
qu=aG(0°)+bT. qu is the energy output from the collector, G(0°) the global irradiation
at a horizontal surface, T the average temperature of the collector fluid and a and b
fitting parameters in a double linear regression analysis.
70
Paper VII Simulation of the influence of tilt and azimuth angles on the
collector output of solar collectors at northern latitudes
For solar collector systems it is important to estimate the energy gain of the system for
an actual case from the specification provided by the manufacturer, valid for a certain
tilt- and azimuth angle. The performance for tilt angles between 0 and 90° and azimuth
angles between +90 and –90° (west to east) in steps of 10° have been simulated. The
simulation tool used is the MINSUN model (Chant 1985). Weather data for Stockholm
were used. Different solar collectors have a different dependence on tilt angle and
azimuth angle. In general a more advanced solar collector has a weaker dependence on
tilt- and azimuth angle since the thermal losses are smaller. According to the
simulations presented here the flat plate with non selective absorber has the strongest
dependence on tilt- and azimuth angle and the vacuum tube collector of the through
flow type has the weakest dependence. If the roof tilt is within 30-60° and the azimuth
within ±30° the delivered collector energy output is at least 90% of that for the
optimum conditions.
Paper VIII The impact of optical and thermal properties on the
performance of flat plate solar collectors
The impact of the optical properties on the annual performance of flat plate collectors
in a Swedish climate has been estimated with the MINSUN program. The collector
parameters were determined with a theoretically based calculation program verified
from laboratory measurements. The importance of changes in solar absorptance and
thermal emittance of the absorber, the addition of a teflon film or a teflon honeycomb,
antireflection treatment of the cover glazing and combinations of these improvements
were investigated. The results show that several improvements can be achieved for
solar thermal absorbers. A combined increase in absorptance from 0.95 to 0.97 and a
decrease in emittance from 0.10 to 0.05 increase the annual performance with 7% at
50°C operating temperature. The increase in performance by installing a teflon film as
second glazing was estimated to 6% at 50°C. If instead a teflon honeycomb is
installed, a twice as high performance increase is obtained, 12%. Antireflection
treatment of the cover glazing increases the annual output with 6% at 50°C. A
combination of absorber improvements together with a teflon honeycomb and an
antireflection treated glazing results in a total increase of 25% at 50°C. Including
external booster reflectors increases the expected annual output at 50°C to 20-30%
depending on reflector material.
71
Paper IX Optical scattering from rough aluminum surfaces
Bi-directional, angular resolved scatterometry were used in order to evaluate the
feasibility of rolled aluminium as reflectors in solar thermal collectors and solar cells.
Two types of rolled aluminium with different surface roughness were investigated.
The results show that the smoother of the two samples (rms height of (0.20 ± 0.02)
µm) can be used as a non-imaging, concentrating reflector with moderate reflection
losses compared to optically smooth aluminium reflectors. The sample with the
rougher surface (rms height (0.6 ± 0.1) µm) is not suitable as a concentrating element
but can be used as planar reflectors. The orientation of the rolling grooves is then of
importance in order to minimise reflection losses in the system.
Paper X Optical characterization of industrially sputtered nickel-nickel
oxide solar selective surface
Tandem absorbers are often used in the design of solar absorbers for photo thermal
conversion. They consist of a thin coating, selectively absorbing in the wavelength
range of the solar spectrum, on a metal substrate. The optical performance of a tandem
absorber depends on the optical constants and thickness of the absorbing coating and
also the reflectivity of the underlying metal. A very high solar absorptance is achieved
when the coating has a non-uniform composition in the sense that the refractive index
is highest closest to the metal substrate and then gradually decreases towards the front
surface. This type of composition suppresses coating interference and gives a low front
surface reflection if also the refractive index at the front surface is low. We report on
optical analysis of a solar absorber with a graded index coating of sputtered
nickel/nickel oxide deposited on aluminium. The optical constants have been
determined from reflectance, transmittance and ellipsometry data by fitting the data to
a two-layer model of the coating. The optical constants of the two layers can be
regarded as effective optical constants for the lower and upper part of the graded index
coating respectively. It is found that the effective refractive index of the top layer is
somewhat lower than for the base layer. The extinction coefficient is higher in the
lower part of the coating. Both effective refractive index and extinction coefficient of
the base layer increase monotonically with increasing wavelength as for metallic
materials.
72
6 ACKNOWLEDGEMENTS
The work has been carried out under the auspices of The Energy Systems Programme,
which is financed by the Swedish Foundation for Strategic Research, the Swedish
Energy Agency and Swedish industry. Vattenfall Utveckling AB provided very
important input to this work; supervision from their experienced staff and access to
their solar collector laboratory.
During my years as a PhD-student I have been supported and supervised by a number
of people that I would like to thank. Ewa Wäckelgård has been my main supervisor
during the whole period. She has been an excellent supervisor and friend who has
provided good comments and advise to my work as well as my personal questions. My
co-supervisor has been Björn Karlsson from Vattenfall Utveckling AB. He has
provided me with interesting projects and infected me with his MaReCo enthusiasm. If
I add together all the hours that I have been waiting for him personally or for him to
comment my work it would come to a lot of hours, but Björn is definitely worth
waiting for. On a personal level I would also like to thank Björn for always being very
considerate and frank. Arne Roos has made a tremendous work in correcting the
English in all my publications and I consider him as my co-co-supervisor. He is also a
very good travel mate and bought me colourful pills when I was feeling bad in
Australia. During my work with flat-plate collectors I got a lot of help and advise from
Bengt Perers at Vattenfall Utveckling AB. Thank you Claes-Göran Granqvist for being
my professor and for signing all those letters of recommendation for my scholarship
applications that made it possible for me to go to lots of interesting conferences.
In general the Solid State Physics group and the Ångström laboratory is full of nice
persons providing the important social environment needed to do a good job, thank
you all! I would especially like to thank the lunch gang for all these interesting lunch
discussions during these years, AnnaKarin, Anna-Lena, Arne, Annette, Barbara, CG,
Kristina, Maria, Richard, Solveig, Tobias and Tuquabo. CG is also a kind of sensible
person on duty that gives advice in various areas, from physics to housebreaking. My
ex-roommates Monica and Andreas are acknowledged for great discussions about life
in general and food in particular. Monica and Maria are special friends that I
appreciate very much. Fika is not the same without AnnaKarin. Kristina is a very good
friend and sort of my “plastic little sister”. Annette is also a very good friend and
advisor in spiritual and chemical matters. Joakim is my fellow energy systems PhD
and we’ve had a lot of good talks on trains together. Life would not be the same
without the e-mails with advice in various areas from Lisen. Thank you Tuquabo for
introducing Eritrean food to me.
I would also like to acknowledge Anders Boulogner at the Communications
Department for his expected and unexpected appearances at the lab and elsewhere.
Ingrid Ringård is acknowledged for having the answers to all possible questions.
Bengt H and Per are acknowledged for being good co-writers and keeping the spirit up
even during late hours. Mats R is acknowledged for being a great person and for his
73
interesting work on concentrators. Normally acknowledgements are about the past, but
I would also like to thank the new PhD-students at Solid State Physics for their
enthusiasm that ensures that the traditions of the department will continue.
My husband Björn and my family are also entitled to an acknowledgement. Thank you
Björn for loving me and taking care of me. I would also like to express my gratitude to
my family for supporting me.
74
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