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

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

SA Kalogirou, Cyprus University of Technology, Limassol, Cyprus

© 2012 Elsevier Ltd All rights reserved

Nomenclature Qs radiation emitted by the sun (kJ)

n average number of reflections (–)

Q radiated energy (kJ)

Greek θs sun half-acceptance angle (degrees)

σ Stefan Boltzmann constant (=5.67
10−8 W m−2 K−4

θe effective incidence angle (degrees)

Glossary Concentrating collector A solar collector that uses

Evacuated tube collector A collector employing a glass Insolation A term applying specifically to solar energy

levels of effectiveness

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:

A

½1

Ar 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 ð4πR2ÞσT4

The fraction of radiation intercepted by the collector is given by:

A

4πD2 Thus the energy radiated from the sun and received by the concentrator is [1]:

A black body receiver, which is considered a perfect radiator and absorber, radiates energy equal to ArT4

r and a fraction of this reaches the sun, given by:

D

R

on earth

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

Ar

Aa

R2 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:

1

sin 2ðθsÞ

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

1

sÞ

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

sin 16ð ′Þ

1

sin 2ð16′Þ

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

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 diffuse

Flat-plate collector

reflector

Flat diffuse reflector

Flat-plate collector

Solar rays

Horizontal concrete roof

Flat diffuse reflector

Flat-plate collector

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

Insulation

Reflector

Glazing Solar r

adiation

Insulation

Reflector

Glazing Solar r

adiation

Y

Y

Y

Y

X

X

X

X

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

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 θc 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

(a) Solar radiation Glass cover

Insulation

Absorber Absorber

Casing

Involute reflector (b)

Aperture

Axis of parabola A Parabola B Focus of parabola A

CPC axis

θc θc

Sun ray

Receiver

Parabola A

Focus of parabola B

Aperture

B A C

P

D

G



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
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,

Qu

aGt

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]:

The absorbed radiation S is obtained from [14]:

S ¼ GB ; CPCτc ; BτCPC ; BαB þ GD ; CPCτc ; DτCPC ; DαD þ GG ; CPCτc ; GτCPC ; GαG ½11 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:

8

>GD

ifðβ þ θcÞ < 90˚

: GD 1 þ cosðβÞ ifðβ þ θcÞ > 90˚

8

cÞ > 90˚

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:

It is convenient to express the absorbed solar radiation S in terms of GCPC in the following way:

t

or

where αr is the absorptivity of the receiver and γ is the correction factor for diffuse radiation given by:

t

 

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]:

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:

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):

where:

!

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]:

α′

sinðθcÞ

f cosðθcÞ

sin 2ðθcÞ

f sinðΦT − θcÞ

sin 2ðΦT =2Þ

f cosðΦT − θcÞ

sin 2ðΦT =2Þ

αT

α

2α

θc

φ T

Axis of parabola

h

2αT

2α′





By replacing α from eqn [22]

1

c Þ 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:

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

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 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

Evacuated tube Absorber plate Heat pipe evaporator

Cross-sectional detail

Fluid flow Manifold