Volume 3 solar thermal systems components and applications 3 05 – low concentration ratio solar collectors

3.05

Low Concentration Ratio Solar Collectors

SA Kalogirou, Cyprus University of Technology, Limassol, Cyprus
© 2012 Elsevier Ltd. All rights reserved.

3.05.1
3.05.1.1
3.05.2
3.05.3
3.05.4
3.05.4.1
3.05.5
3.05.6
References

Introduction
Maximum Concentration Ratio
Flat-Plate Collectors with Diffuse Reflectors
Reverse Flat-Plate Collectors
Compound Parabolic Collectors (CPC)
Optical and Thermal Analysis of CPCs
Concentrating Evacuated Tube Collectors
Integrated Collector Storage Systems

Nomenclature
Aa absorber area (m2)
Ac total collector aperture area (m2)
Ar receiver area (m2)
C collector concentration ratio (=Aa/Ar) (–)

D sun–earth distance (m)
F view factor (–)
FR heat removal factor (–)
G incident radiation (kJ m−2)
n average number of reflections (–)
Q radiated energy (kJ)

Greek
α absorptivity (–)
β collector slope (degrees)
γ correction factor for diffuse radiation (–)
θ angle of incidence (degrees)
θc collector acceptance half-angle for CPC collectors
(degrees)
θe effective incidence angle (degrees)

Subscripts

Qs radiation emitted by the sun (kJ)
Qu useful energy collected (kJ)
R sun radius, receiver radius (m)
S absorbed solar radiation per unit area (kJ m−2)
Ta ambient temperature (°C)
Ti collector inlet temperature (°C)
Tr receiver temperature (°C)
Ts apparent black body temperature of the sun (∼6000 K)
UL solar collector heat transfer loss coefficient (W m−2 °C)

θs sun half-acceptance angle (degrees)
η efficiency (–)

ρ specular reflectivity (–), distance in Figure 17
σ Stefan–Boltzmann constant (=5.67 Â 10−8 W m−2 K−4)
τc transmittance of CPC cover (–)
τCPC transmissivity of the CPC to account for reflection
loss

n normal
r receiver
R reflector
s sun
t total
T truncated
u useful

a aperture
B beam
c cover
D diffuse
G ground reflected
max maximum

Glossary
Collector Any device which can be used to gather the
sun's radiation and convert it to a useful form of
energy.
Concentration ratio Ratio of aperture to receiver area of a
solar collector.

Comprehensive Renewable Energy, Volume 3

150
150
151
152
153
154
158
159
162

Concentrating collector A solar collector that uses
reflectors or lenses to redirect and concentrate the solar
radiation passing through the aperture onto an observer.
CPC collector Compound parabolic concentrator. It is a
non-imaging collector consisting of two parabolas one
facing the other.

doi:10.1016/B978-0-08-087872-0.00305-X

149


150

Components

Evacuated tube collector A collector employing a glass
tube with an excavated space between the tube and the
absorber and using a heat pipe for energy collection.
Heat pipe A passive heat exchanger employing principles

of evaporation and condensation to transfer heat at high
levels of effectiveness.

Insolation A term applying specifically to solar energy
irradiation (J/m2)
Integrated collector storage A solar heating system in
which the solar collector also functions as the storage
device.

3.05.1 Introduction
This chapter deals with low concentration solar collectors. These are collectors that apply some form of concentration but their
concentration ratio (C), defined as the ratio of the aperture area to the absorber area, is not more than about 10. According to the
concentration ratio, these collectors are usually steady (C < 2), or if tracking is applied (for the higher concentration ones), this is
intermittent and not very accurate. Fixed concentrators are very important because of the practical advantages enjoyed by fixed solar
systems. By increasing the concentration ratio, the frequency of tracking increases. Thus a collector with C = 3 needs only biannual
adjustment, whereas a collector with C = 10 requires almost daily adjustment [1]. Generally speaking, the higher the concentration
ratio, the higher the temperature a collector can attain but the higher the tracking requirements. Because of the low concentration
ratio, these collectors usually collect both direct and diffuse solar radiation as opposed to the high concentration ones that collect
only direct solar radiation.
Generally, concentrating collectors can be classified into nonimaging and imaging depending on whether the image of the sun is
focused on the receiver or not. The representative types of concentrators belonging to the first category are the reverse flat-plate
collector and the compound parabolic collector (CPC).

3.05.1.1

Maximum Concentration Ratio

In equation form, the concentration ratio (C), defined as the ratio of the aperture area to the receiver/absorber area, is given by:
C¼

Aa
Ar

½1Š

For flat-plate collectors with no reflectors, C = 1. For concentrators, C is always greater than 1. It is required to define the maximum
possible concentration ratio that a concentrator can achieve based on the limitations of the laws of thermodynamics. In this
analysis, a circular (three-dimensional) concentrator with aperture Aa and receiver area Ar located at a distance D from the center of
the sun is considered, as shown in Figure 1. The sun is a sphere of radius R; therefore, as seen from the earth, the sun has a half-angle
θs, which is called the sun acceptance half-angle, and this angle is used for the calculation of the maximum concentration. If both the
sun and the receiver are considered to be black bodies at temperatures Ts and Tr, respectively, the amount of radiation emitted by the
sun is given by [1]:
Qs ¼ ð4πR2 ÞσTs4

½2Š

The fraction of radiation intercepted by the collector is given by:
Fs−r ¼

Aa
4πD2

½3Š

Thus the energy radiated from the sun and received by the concentrator is [1]:
Qs−r ¼ Aa

4πR2 4
R2
σT ¼ Aa 2 σTs4

D
4πD2 s

½4Š

A black body receiver, which is considered a perfect radiator and absorber, radiates energy equal to ArTr4 and a fraction of this
reaches the sun, given by:
Qr − s ¼ Ar Fr − s σTr4

R

D

Sun

Figure 1 Schematic of the sun and a concentrator on earth.

θs

½5Š

Aa
Ar
Concentrator
on earth


Low Concentration Ratio Solar Collectors

151

Under this idealized condition, the maximum temperature of the receiver is equal to that of the sun. According to the second law of
thermodynamics, this is true only when Qr–s = Qs–r. Therefore, from eqns [4] and [5]:
D2
Aa
¼ 2 Fr − s
R
Ar

½6Š

Since the maximum value of Fr–s is equal to 1, the maximum concentration ratio for three-dimensional concentrators, and
considering that sin(θs) = R/D, is:
Cmax ¼

1
sin 2 ðθs Þ

½7Š

A similar analysis for linear or two-dimensional concentrators gives:
Cmax ¼

1
sinðθs Þ

½8Š

As seen from the earth, the angle 2θs of the sun is equal to 0.53° (or 32′), so θs, the sun half-acceptance angle, is equal to 0.27°
(or 16′). The sun half-acceptance angle denotes the coverage of one-half of the angular zone within which radiation is accepted by

the concentrator’s receiver. Radiation is accepted over an angle of 2θs because radiation incident within this angle reaches the
receiver after passing through the aperture. This angle describes the angular field within which radiation can be collected by the
receiver without having to track the concentrator [1].
Equations [7] and [8] define the upper limit of concentration that may be obtained for a given collector viewing angle. For a
stationary CPC, the angle θs depends on the motion of the sun in the sky. For example, for a CPC having its axis in a north–south
direction and tilted from the horizontal such that the plane of the sun’s motion is normal to the aperture, the acceptance angle is
related to the range of hours over which sunshine collection is required, for example, for 6 h of useful sunshine collection, and as the
sun travels 15° h−1, 2θs = 90°. In this case, Cmax = 1/sin(45°) = 1.41.
For a tracking collector, θs is limited by the size of the sun’s disk, small-scale errors, irregularities of the reflector surface, and
tracking errors. For a perfect collector and tracking system, Cmax depends only on the sun’s half-acceptance angle. Therefore,
1
¼ 216
sinð16′Þ
1
¼
¼ 46 747
sin 2 ð16′Þ

For single-axis tracking : Cmax ¼
For full tracking : Cmax

It can therefore be concluded that the maximum concentration ratio for two-axes tracking collectors is much higher. However, high
tracking accuracy and careful construction of the collector are required with increased concentration ratio as θs is very small and a
possible small error will focus the sun beam away from the receiver. In practice, due to various errors, much lower values than the
above maximum ones are employed [1].
In this chapter, only low concentration ratio collectors are considered with C ≤ 10. These are two-dimensional concentrators and
the relation considered for Cmax is eqn [8].

3.05.2 Flat-Plate Collectors with Diffuse Reflectors
The first type of a solar concentrator examined in this chapter, shown in Figure 2, is effectively a flat-plate collector fitted with simple

flat diffuse reflectors. This can markedly increase the amount of direct radiation reaching the collector. This is in fact a concentrator
because the aperture is bigger than the absorber but the system is stationary. This simple enhancement of flat-plate collectors was
initially suggested by Tabor [2]. A comprehensive analysis and a model of such a system are presented by Garg and Hrishikesan [3].

Sun rays

Flat-plate
collector
Flat diffuse
reflector
Figure 2 Flat-plate collector with flat diffuse reflectors.


152

Components

Solar rays
Flat-plate
collector

Flat-plate
collector
Flat diffuse reflector

Flat diffuse reflector
Horizontal concrete roof
Figure 3 Flat-plate collectors with sawtooth reflectors.

The model facilitates the prediction of the total energy absorbed by the collector at any hour of the day for any latitude for random

tilt angles and azimuth angles of the collector and reflectors.
Individual flat-plate collectors can be equipped with flat reflectors in the way shown in Figure 2; however, for multirow collector
installations, a sawtooth arrangement shown in Figure 3 can be used. In both cases, the use of simple flat diffuse reflectors can
significantly increase the amount of direct radiation reaching the collector.
The expression ‘diffuse reflector’ denotes a material which is not a mirror, thus avoiding forming an image of the sun on the
absorber, which will create uneven radiation distribution and thermal stresses. Diffuse reflectors are usually made from galvanized
or stainless steel sheets, and their cost is usually a fraction of the cost of the collector. This is the reason why this type of
enhancement is considered as one of the most effective. Extensive, mostly experimental, studies on this type of systems are
presented by Tripanagnostopoulos et al. as part of their studies with collectors employing color absorbers [4] and hybrid PV/T
systems [5, 6].

3.05.3 Reverse Flat-Plate Collectors
In an attempt to extend the operation of flat-plate collectors to medium temperatures, many researchers investigated a type of
system called reversed or upside down absorber plate configuration. Kienzlen et al. [7] were the first who investigated this type of
system. On these systems, radiation is directed on the underside of the plate by a stationary concentrator of the shape shown in
Figure 4. The shape of this type of collector is like a CPC described in more detail in the next section. Heat losses from the absorber
are significantly reduced as the upper side of the plate is well insulated, and as the plate is upside down, there is little convective
motion in the air layer just below the plate. Another type is the inclined design shown in Figure 5. Compared with a normal
flat-plate collector, the reverse plate design has lower optical efficiency (maximum efficiency the collector can attain at inlet fluid
temperature equal to ambient temperature) due to the scattering losses in the reflector.
An extension of the concept is the double-sided flat-plate collector investigated by Goetzberger et al. [8] and
Tripanagnostopoulos et al. [9]. These are called bifacially irradiated solar flat-plate collectors because the absorber is a flat plate
and they have the advantage that they are illuminated at both sides of the absorber. In the design presented by Goetzberger et al. [8],
the absorber is ‘insulated’ at all sides with a transparent insulation (TI), whereas in the design presented by Tripanagnostopoulos

ing
az
Gl

So

lar

ra
d

iat
ion

Insulation

Reflector
Figure 4 Inverted flat-plate collector.


Low Concentration Ratio Solar Collectors

153

Insulation

lar
So
t
dia
ra

ing
az
Gl

ion

Reflector

Figure 5 Inclined flat-plate collector.

Y

(a)

Y

(b)

X

X

X

X

Y

Y
Figure 6 Cross section of a (a) CPC collector with one mirror–absorber unit and (b) CPC collector with three mirror–absorber units. Modified from
Tripanagnostopoulos Y, Yianoulis P, Papaefthimiou S, and Zafeiratos S (2000) CPC solar collectors with flat bifacial absorbers. Solar Energy 69(3): 191–203.

et al. [9], a simple glazing is used either in one mirror–absorber unit or in three mirror–absorber units as shown in Figures 6(a) and 6(b),

respectively, which are adapted from Reference [9] with many design details removed from the original figures for clarity.

3.05.4 Compound Parabolic Collectors (CPC)
CPCs are nonimaging concentrators. These have the capability of reflecting to the absorber all of the incident radiation within wide
limits. Their potential as collectors of solar energy was pointed out by Winston [10]. The necessity of moving the concentrator to
accommodate the changing solar orientation can be reduced by using a trough with two sections of a parabola facing each other, as
shown in Figure 7.
Compound parabolic concentrators can accept incoming radiation over a relatively wide range of angles. By using multiple
internal reflections, any radiation that is entering the aperture, within the collector acceptance angle, finds its way to the absorber
surface located at the bottom of the collector. Generally, CPCs are characterized by a relatively high average number of reflections,
ranging in most of the cases between 1.1 and 1.6, determined by ray tracing, so that if the reflectivity of the concentrating surface is
not high, optical losses may be significant [11]. The absorber of a CPC can take a variety of configurations. As can be seen in
Figure 7, it can be flat, bifacial, wedge, or cylindrical.
Two basic types of CPC collectors have been designed: the symmetric, shown in Figure 7, and the asymmetric, which have shapes
similar to the ones shown in the figures of the previous section. CPCs usually employ two main types of absorbers: fin type with
pipe and tubular absorbers. The fin type can be flat, bifacial, or wedge as shown in Figure 7 for the symmetric type and can be single
channel or multichannel.


154

Components

CPCs should have a gap between the receiver and the reflector to prevent the reflector from acting as a fin conducting heat away
from the absorber and this is more important for flat receivers. As the gap results in a loss of reflector area with a corresponding loss
of performance, it should be kept small.
Depending on the acceptance angle of the CPC, the collector can be stationary or tracking. When tracking is used, this is very
rough or intermittent as concentration ratio is usually small and radiation can be collected and concentrated by one or more
reflections on the parabolic surfaces. For higher temperature applications, a tracking CPC can be used.
CPCs can be manufactured either as one unit with one opening and one receiver (see Figure 7) or as a panel as shown in Figure 8(a).

When constructed as a panel, the collector looks like a flat-plate collector as shown in Figure 8(b).
In the following section, the optical and thermal analysis of CPCs is presented.

3.05.4.1

Optical and Thermal Analysis of CPCs

The optical analysis of CPC collectors concerns mainly the way to construct the collector shape. A CPC of the Winston design [12] is
shown in Figure 9. It is a linear two-dimensional concentrator consisting of two distinct parabolas A and B, the axes of which are
inclined at angles Æθc with respect to the optical axis of the collector. The angle θc is called the collector half-acceptance angle and is
defined as the angle through which a source of light can be moved and still converge at the absorber. CPCs have a constant
acceptance angle over the entire aperture area [11].
The Winston-type collector is a nonimaging concentrator with a concentration ratio approaching the upper limit permitted by
the second law of thermodynamics as explained in Section 3.05.1.1.
The receiver of the CPC does not have to be flat and parallel but as shown in Figure 7 can be bifacial, wedge, or cylindrical. In
Figure 10, a cylindrical receiver collector is shown. In this collector, the lower portion of the reflector (AB and AC) is circular while
the upper portions (BD and CE) are parabolic. In this design, the requirement for the parabolic portion of the collector is that at any
point P, the normal to the collector must bisect the angle between the tangent line PG to the receiver and the incident ray at point P
at angle θc with respect to the collector axis. The side wall profile of fully developed CPCs terminates when it is parallel to the optical
axis so that very little concentration is lost by truncating these devices by some fraction, usually about 0.6–0.9 of their full height
[11]. Therefore, as the upper part of a CPC contributes little to the radiation reaching the absorber, it is usually truncated, thus
forming a shorter version of the CPC. Truncation affects little the acceptance angle but results in considerable material saving and
changes the height-to-aperture ratio, the concentration ratio, and the average number of reflections. CPCs are usually covered with
glass to avoid dust and other materials from entering the collector, thus reducing the reflectivity of its walls.
These collectors are more useful as linear or trough-type concentrators. The orientation of a CPC collector is related to its
acceptance angle (2θc, in Figures 9 and 10). The two-dimensional CPC is an ideal concentrator, that is, it works perfectly for all rays
within the acceptance angle 2θc. Also depending on the collector acceptance angle, the collector can be stationary or tracking. A CPC
concentrator can be orientated with its long axis along either the north–south or the east–west direction, and its aperture is tilted

Flat absorber

Wedge absorber
Figure 7 Various absorber types for CPCs.

Bifacial absorber

Tube absorber


Low Concentration Ratio Solar Collectors

Solar radiation

(a)
Glass cover

Casing

Absorber

Absorber

Insulation
Casing

Involute reflector

(b)

Figure 8 Panel CPC collector with cylindrical absorbers. (a) Schematic diagram. (b) Photo of a CPC panel collector installation.

Aperture
CPC
Sun axis
ray

θc

θc

Axis of
parabola A

Parabola A

Parabola B
Focus of
parabola A

Focus of
parabola B
Receiver

Figure 9 Construction of a flat receiver CPC.

Aperture

D

E

2θc

G
P

B A C
Figure 10 Schematic diagram of a CPC collector.

155


156

Components

directly toward the equator at an angle equal to the local latitude. When orientated along the north–south direction, the collector
must track the sun by turning its axis so as to face the sun. As the acceptance angle of the concentrator along its long axis is wide,
seasonal tilt adjustment is not necessary. It can also be stationary but radiation will only be received during the hours when the sun
is within the collector acceptance angle [1].
When the concentrator is orientated with its long axis along the east–west direction, with a little seasonal adjustment in tilt angle, the
collector is able to catch the sun’s rays effectively through its wide acceptance angle along its long axis. The minimum acceptance angle in
this case should be equal to the maximum incidence angle projected in a north–south vertical plane during the times when output is
needed from the collector. For stationary CPC collectors mounted in this mode, the minimum acceptance angle is equal to 47°. This
angle covers the declination of the sun from summer to winter solstices (2 Â 23.5°). In practice, bigger angles are used to enable the
collector to collect diffuse radiation at the expense of a lower concentration ratio. Smaller (less than 3) concentration ratio CPCs are of
greatest practical interest. These according to Pereira [13] are able to accept a large proportion of diffuse radiation incident on their
apertures and concentrate it without the need of tracking the sun. Finally, the required frequency of collector adjustment is related to the
collector concentration ratio. Thus for C ≤ 2, the collector can be steady, whereas for C = 3, the collector needs only biannual adjustment,
while for C close to 10, it requires almost daily adjustment and these systems are also called quasi-static [1].

Concentrators of the type shown in Figure 7 have an area concentration ratio, which is a function of the acceptance half-angle θc.
For an ideal linear concentrator system, this is given by eqn [8] by replacing θs with θc.
The instantaneous efficiency η of a CPC is defined as the useful energy gain divided by the incident radiation on the aperture
plane, that is,
η¼

Qu
Aa Gt

½9Š

In eqn [9], Gt is the total incident radiation on the aperture plane. The useful energy Qu is given by an equation similar to that of a
flat-plate collector, by using the concept of absorbed radiation, as [1]:
Qu ¼ FR ½SAa − Ar UL ðTi − Ta ފ

½10Š

S ¼ GB ; CPC τ c ; B τ CPC ; B αB þ GD ; CPC τ c ; D τ CPC ; D αD þ GG ; CPC τ c ; G τ CPC ; G αG

½11Š

The absorbed radiation S is obtained from [14]:

where τc is the transmittance of the CPC cover and τCPC is the transmissivity of the CPC to account for reflection loss.
The various radiation components in eqn [11] refer to radiation falling on the aperture within the acceptance angle of the CPC
and are given from the following relations:
GB ; CPC ¼ GBn cosðθÞ if ðβ − θc Þ ≤ tan −1 ½tanðΦÞcosðzފ ≤ ðβ þ θc Þ
8G
D
>

if ðβ þ θc Þ < 90˚
<
C

GD ; CPC ¼ G  1
>
: D
þ cosðβÞ
if ðβ þ θc Þ > 90˚
2 C
8
if ðβ þ θc Þ < 90˚
<0 

GG ; CPC ¼ GG 1
−cosðβÞ
if ðβ þ θc Þ > 90˚
:
2 C

½12aŠ
½12bŠ

½12cŠ

In eqns [12a]–[12c], β is the collector aperture inclination angle with respect to the horizontal. In eqn [12c], the ground-reflected
radiation is only effective if the collector receiver ‘sees’ the ground, that is, (β + θc) > 90˚.
It has been shown by Rabl et al. [15] that the insolation GCPC of a collector with a concentration C can be approximated very well
from:



1
1
1
GD
½13Š
GCPC ¼ GB þ GD ¼ ðGt − GD Þ þ GD ¼ Gt − 1−
C
C
C
It is convenient to express the absorbed solar radiation S in terms of GCPC in the following way:


 
 


1
1 GD
S ¼ GCPC τ c τ CPC αr ¼ Gt − 1−
GD τ c τ CPC αr ¼ Gt τ c τ CPC αr 1− 1−
C
C Gt

½14Š

or
S ¼ Gt τ c τ CPC αr γ
where αr is the absorptivity of the receiver and γ is the correction factor for diffuse radiation given by:



1 GD
γ ¼ 1− 1−
C Gt

½15Š

½16Š


Low Concentration Ratio Solar Collectors

157

The factor γ given by eqn [16] accounts for the loss of diffuse radiation, which is outside of the acceptance angle of the CPC with a
concentration C. The ratio GD/Gt varies from about 0.11 on very clear sunny days to about 0.23 on hazy days.
It should be noted that only part of the diffuse radiation effectively enters the CPC and this is a function of the acceptance angle.
For isotropic diffuse radiation, the relationship between the effective incidence angle and the acceptance half-angle is given by [16]:
θe ¼ 44:86 − 0:0716θc þ 0:00512θ2c − 0:000 02798θ3c

½17Š

The effective transmissivity τCPC of the CPC accounts for reflection loss inside the collector. The fraction of the radiation passing
through the collector aperture and eventually reaching the absorber depends on the specular reflectivity, ρ, of the CPC walls and the
average number of reflections, n, expressed approximately by:
τ CPC ¼ ρn

½18Š

This equation can also be used to estimate τCPC,B, τCPC,D, and τCPC,G for use in eqn [11], which are usually treated as the same. Values of the

average number of reflections, n, for full and truncated CPCs can be obtained from [17] (the subscript T is for the truncated CPC design):


1
ART x2 − cos 2 ðθÞ
n ¼ max C
−
; 1−
½19Š
C
4αT 2ð1 þ sinðθÞÞ
where:

x¼

1 þ sinðθÞ
cosðθÞ


1 = 2 !
hT
−sinðθÞ þ 1 þ cot 2 ðθÞ
h



½20Š

ART is the reflector area for the truncated CPC (m2).
As noted before, the upper ends of CPCs contribute little to the radiation reaching the receiver and usually CPCs are truncated for

economic reasons. As can be seen from eqn [19], the average number of reflections is a function of concentration ratio C and the
collector acceptance half-angle θc. For a truncated concentrator, the value (1 – 1/C) can be taken as the lower bound for the number
of reflections for radiation within the acceptance angle.
The following equations can be used to design a CPC. The various symbols used in the following equations are shown in Figure 11.
The following equations apply for a full and truncated (subscript T) CPC [18]:
f ¼ α′ð1 þ cosðθc ÞÞ
α′
sinðθc Þ

½22Š

f cosðθc Þ
sin 2 ðθc Þ

½23Š

α¼
h¼
αT ¼

½21Š

f sinðΦT − θc Þ
−α′
sin 2 ðΦT =2Þ

½24Š

f cosðΦT − θc Þ
sin 2 ðΦT =2Þ

½25Š

hT ¼

For a truncated CPC : C ¼
For a full CPC : C ¼

α
α′

αT
α′

½27Š

2α

θc

Axis of
parabola
2α T
h
hT

½26Š

φT

2α ′
Figure 11 A truncated CPC – its height-to-aperture ratio is about one-half of the full height CPC.


158

Components

By replacing α from eqn [22]
C¼

1
sinðθc Þ

½28Š

which is the same as eqn [8] with the use of θc instead of θs. The reflector area per unit depth of a truncated CPC is given by:



 
ΦT
ART
f cosðΦ=2Þ
Φ


¼
þ ln cot
½29Š

θc þ π = 2
2 sin 2 ðΦ=2Þ
4
2αT


For eqn [29] if ΦT = 2θc, then ART = AR.
It should be noted that the above equations can be replaced by graphs, which can be found from the original paper of Rabl [19].
Eames and Norton [20] presented a detailed parametric analysis of heat transfer in CPC solar energy collectors, whereas in a
second paper [21] they presented the thermal and optical consequences of the introduction of baffles into compound parabolic
concentrating solar collector cavities, used to reduce the internal convection, thereby reducing thermal losses, with a consequent
small reduction in the optical efficiency.

3.05.5 Concentrating Evacuated Tube Collectors
The benefits of the simple flat-plate solar collectors that are developed for use in sunny and warm climates reduce greatly when
conditions become unfavorable during cold, cloudy, and windy days. Evacuated tube solar collectors operate differently, usually
consisting of a heat pipe inside a vacuum-sealed tube, as shown in Figure 12. To increase the heat collection area, many tubes are
connected to the same manifold as shown in the figure.
Evacuated tube collectors (ETCs) have demonstrated that the combination of selective surface and the effective convection
suppressor can result in good performance at high temperatures. The vacuum envelope reduces convection and conduction losses,
so the collectors can operate at higher temperatures than flat-plate collectors. Like flat-plate collectors, they collect both direct and
diffuse radiation, but their efficiency is higher at low incidence angles. This effect tends to give ETCs an advantage over flat-plate
collectors in day-long performance [1].
ETCs use liquid–vapor phase change materials to transfer heat at high efficiency. These collectors usually feature a heat pipe
placed inside a vacuum-sealed tube. The pipe, which is a sealed copper pipe, is then attached to a black copper fin that fills the
tube (absorber plate). Protruding from the top of each tube is a metal tip attached to the sealed pipe, which acts as a condenser.
The heat pipe contains a small amount of volatile fluid that undergoes an evaporating–condensing cycle. Solar heat evaporates
the liquid, and the vapor due to lower density rises to the heat sink region where it condenses and releases its latent heat. The

Heat pipe condenser
Manifold
Fluid flow

Evacuated tube
Absorber plate
Heat pipe evaporator

Cross-sectional detail

Figure 12 Schematic diagram of an ETC.


Low Concentration Ratio Solar Collectors

159

condensed fluid due to gravity returns back to the solar collector and the process is repeated. When these tubes are mounted,
the metal tips up into a manifold as shown in Figure 12. Water, or water–glycol mixture, flows through the manifold and picks up
the heat from the tubes. The heated liquid circulates through a heat exchanger and gives off its heat to a process or to water that is
stored in a storage tank.
Because no evaporation or condensation above the phase change temperature is possible, the heat pipe offers inherent
protection from freezing and overheating. This self-limiting temperature control is a unique feature of the evacuated heat pipe
collector [1].
A large number of absorber shape variations of ETCs exist in the market. One such design consists of an all-glass Dewar-type ETC.
In this, two concentric glass tubes are used and the space between the tubes is evacuated creating a vacuum jacket. In this type of
ETC, the selective coating is deposited onto the outside surface of a glass tube domed at one end. This tube is then inserted into a
second larger diameter domed glass tube and the tubes are joined at the open end. The advantage of this design is that it is made
entirely of glass and it is not necessary to penetrate the glass envelope in order to extract the heat from the tube; thus, leakage losses
are eliminated and it is cheaper than the single-envelope system [1]. This type is also called a wet-tube ETC. A variation of the

wet-tube ETC is a normal single-glass ETC in which water (or any other fluid) flows through the collector in either a U-tube or a
coaxial pipe.
Evacuated tubes with external or internal (inside the glass tube) reflectors are also commercialized by several manufacturers.
A diffuse reflector (reflectivity, ρ = 0.6) mounted behind the tubes spaced one tube diameter apart, as shown in Figure 13, increases
the absorbed energy in each tube by more than 25% for normal incidence. This system presents also a 10% increase in energy
collection over a full day because of incidence angle effects.
CPC reflectors can also be used either externally or internally, which increases the effectiveness of ETCs. A better enhancement
per tube can be achieved by using CPC-type reflectors as shown in Figure 14. In this design, the number of tubes is decreased and
they use reflectors to concentrate the solar radiation onto the tubes. Evacuated tube arrays with stationary concentrators may have
stagnation temperatures exceeding 300 °C.
When the reflector is installed inside the tube, the system is called integrated compound parabolic collector (ICPC). This is an
ETC in which at the bottom part of the glass tube, a reflective material is fixed [22]. In this case, either a CPC reflector, shown in
Figure 15(a), or a cylindrical reflector, shown in Figure 15(b), is used. The latter does not achieve the concentration of the shaped
reflector but has a very low manufacturing cost. In this way, the collector combines into a single unit the advantages of vacuum
insulation and nonimaging stationary concentration. In another design, a tracking ICPC is developed, which is suitable for
high-temperature applications [23].
ETCs are produced in a variety of sizes with outer diameters ranging from 30 mm to about 100 mm. The usual length of these
collectors is about 2 m.

3.05.6 Integrated Collector Storage Systems
Integrated collector storage (ICS) system is a water heating method that uses the hot water storage as part of the collector, that is, the
storage tank is used also as the collector absorber. As in all other systems, to improve stratification, the hot water is drawn from the
top of the tank and cold make-up water enters the bottom of the tank on the opposite side. Usually, the coating of the storage tank
surface is selective to minimize heat loss.
Solar radiation

ETC

Flat diffuse reflector
Figure 13 ETCs with external flat diffuse reflector.

Solar radiation
ETC

Reflector
Figure 14 ETCs with external CPC-type reflectors.

ETC


160

Components

(a)

(b)

Solar radiation

Solar radiation

Finned absorber

Figure 15 Integrated CPC tubes. (a) Internal compound parabolic. (b) Circular reflector with finned absorber.

Details of an ICS unit developed by the author are presented here [24]. The system employs a nonimaging CPC cusp-type collector.
A fully developed cusp concentrator for a cylindrical receiver is shown in Figure 16. The particular curve illustrated has an acceptance
half-angle, θc, of 60° or a full acceptance angle, 2θc, of 120°. Each side of the cusp has two mathematically distinct segments smoothly
joined at a point P related to θc. The first segment, from the bottom of the receiver to point P, is the involute of the receiver’s circular

cross section. The second segment is from point P to the top of the curve, where the curve becomes parallel to the y-axis [25].
With reference to Figure 17, for a cylindrical receiver with radius R and acceptance half-angle, θc, the distance, ρ, along a tangent
from the receiver to the curve is related to the angle θ between the radius to the bottom of the receiver and the radius to the point of
tangency, T, by the following expressions for the two sections of the curve [25]:
π
ðthe involute part of the curveÞ
ρðθÞ ¼ Rθ; jθj ≤ θc þ
2
i9
8h
π
< θ þ θc þ − cosðθ − θc Þ =
π
3π
2
− θc
ρð θ Þ ¼ R
; θc þ ≤ θ ≤
:
;
1 þ sinðθ − θc Þ
2
2

½30Š

The two expressions for ρ(θ) are equivalent for the point P in Figure 16, where θ = θc + π/2. The curve is generated by incrementing θ
in radians, calculating ρ, and then calculating the coordinates, X and Y, by:
X ¼ Rsin θ − ρcos θ
½31Š

Y ¼ −Rcos θ − ρsin θ
Figure 16 shows a full untruncated curve, which is the mathematical solution for a reflector shape with the maximum possible
concentration ratio. The reflector shape shown in Figure 16 is not the most practical design for a cost-effective concentrator, because
Y

θc
H

θc

X

θc + π/2

P
Figure 16

P

Fully developed cusp.

Y

T
R

X

θ
ρ

(X,Y)

Figure 17 Mirror coordinates for ideal nonimaging cusp concentrator.


Low Concentration Ratio Solar Collectors

161

Y
70°
Truncation

75°

X

Figure 18 Truncation of nonimaging concentrator.

Total height < 1 m

IC

S

co

lle

ct

Hot water supply

or

Cold water supply
Collector inclined
at local latitude

Roof slab
Figure 19 The complete solar ICS hot water system.

reflective material is not effectively used in the upper portion of the concentrator. As in the case of the CPC, a theoretical cusp curve
should be truncated to a lower height and slightly smaller concentration ratio. Graphically, this is done by drawing a horizontal line
across the cusp at a selected height and discarding the part of the curve above the line. Mathematically, the curve is defined to a
maximum angle θ of value less than 3π/2 – θc. The shape of the curve below the cut-off line is not changed by truncation, so the
acceptance angle used for the construction of the curve (using eqn [30]) of a truncated cusp is equal to the acceptance angle of the
fully developed cusp from which it was truncated.
A large acceptance angle of 75° is used in this design so that the collector would be able to collect as much diffuse radiation as
possible [24]. The fully developed cusp together with the truncated one is shown in Figure 18. The receiver radius considered in the
construction of the cusp is 0.24 m. The actual cylinder used is only 0.20 m. This is done in order to create a gap at the underside of
the receiver and the edge of the cusp in order to minimize the optical and conduction losses.
The final design is shown in Figure 19. The collector aperture is 1.77 m2, which in combination with the absorber diameter used
gives a concentration ratio of 1.47 [24]. It should be noted that the collector axis is east–west and as shown in Figure 19, the system
is inclined at the local latitude in order to work effectively.
The main disadvantage of ICS systems is the high thermal losses from the storage tank to the surroundings since most of the
surface area of the storage tank cannot be thermally insulated as it is intentionally exposed so as to be able to absorb solar radiation.
In particular, the thermal losses are greatest during the night and overcast days with low ambient temperature. Due to these losses,
the water temperature drops substantially during night time especially during the winter. Various techniques have been used to
avoid this from happening. Tripanagnostopoulos et al. [26] presented a number of experimental units in which the reduction of

thermal losses was achieved by considering single and double cylindrical horizontal tanks properly placed in truncated symmetric
and asymmetric CPC reflector troughs. Two such designs are shown in Figure 20 adapted from [26], with many design details
removed from the original figures for clarity.
Another possibility considered in the design shown in Figure 19, in view of the findings of Eames and Norton [21] on the use of
baffles to reduce the thermal losses, is the insertion of a second cylinder of smaller diameter in the space between the main cylinder
and the glass cover and using a small piece of insulation at the point of contact between the two cylinders and between the
secondary cylinder and the glass cover as shown in Figure 21. This modification offers a number of advantages: storage capacity
increased by 30%, top cylinder provides some sort of insulation (for radiation heat loss) as the main cylinder does not see the sky


162

Components

Y

X

X

O

Y
Y

X

X
O

Y
Figure 20 Cross section of two ICS unit designs with a partial protection of the storage tank. Modified from Tripanagnostopoulos Y, Souliotis M, and
Nousia Th (2002) CPC type integrated collector storage systems. Solar Energy 72(4): 327–350.

Cold water supply

Glass cover
Insulation

Hot water supply

Secondary cylinder
Main cylinder

Insulation
Secondary cylinder

Main cylinder

Figure 21 Basic system modification.

directly, the top cylinder creates a restriction to the flow of the convection currents (just like the baffle does), and finally, the
secondary cylinder is used as a preheating for the main one and thus the draw-off characteristics of the whole unit improved
considerably, as the cold make-up water does not enter into the main cylinder directly. The extra cylinder increased the cost of the
ICS system by 8%, whereas the performance of the system increased by about 7% [27].
Alternatively, if a 24-h hot water supply is required, these systems can be used only for preheating and in such a case must be
connected in series with a conventional water heater [1].

References
[1]

[2]

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Tabor H (1966) Mirror boosters for solar collectors. Solar Energy 10(3): 111–118.


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[3]
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