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

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  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 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 = 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: Cẳ Aa Ar ẵ1 For flat-plate collectors with no reflectors, C = For concentrators, C is always greater than 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 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 ẳ 4R2 ịTs4 ẵ2 The fraction of radiation intercepted by the collector is given by: Fsr ẳ Aa 4D2 ẵ3 Thus the energy radiated from the sun and received by the concentrator is [1]: Qs−r ¼ Aa 4πR2 R2 T ẳ Aa Ts4 D 4D2 s ẵ4 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 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 ẳ Fr s R Ar ẵ6 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 sin ðθs Þ ½7Š A similar analysis for linear or two-dimensional concentrators gives: Cmax ẳ sins ị ẵ8 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 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, ẳ 216 sin16ị ẳ ẳ 46 747 sin 16ị For single-axis tracking : Cmax ẳ 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 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 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 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 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 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 d iat ion Insulation Reflector Figure Inverted flat-plate collector Low Concentration Ratio Solar Collectors 153 Insulation lar So t dia ing az Gl ion Reflector Figure Inclined flat-plate collector Y (a) Y (b) X X X X Y Y Figure 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 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 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 It is a linear two-dimensional concentrator consisting of two distinct parabolas A and B, the axes of which are inclined at angles Ỉθc 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 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 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 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 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 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  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 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 ẳ FR ẵSAa Ar UL Ti Ta ị ẵ10 S ẳ GB ; CPC c ; B CPC ; B B ỵ GD ; CPC c ; D CPC ; D D ỵ 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 ẳ GBn cosị if c ị tan ẵtanịcoszị ỵ c ị 8G D > if ỵ c ị < 90˚ < C  GD ; CPC ¼ G  > : D ỵ cosị if ỵ c ị > 90 C if ỵ c Þ < 90˚ 90 : 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 GD ẵ13 GCPC ẳ GB ỵ GD ẳ Gt GD ị ỵ GD ẳ Gt − 1− C C C It is convenient to express the absorbed solar radiation S in terms of GCPC in the following way:         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 C C Gt ẵ14 or S ẳ 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:   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]: e ẳ 44:86 0:0716c ỵ 0:005122c 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: CPC ẳ n ẵ18 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):   ART x2 cos ị n ẳ max C ; ẵ19 C 4T 21 ỵ sinịị where:  xẳ ỵ sinị cosị  1 = ! hT sinị ỵ ỵ cot ị 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 ẳ ỵ cosc ÞÞ α′ sinðθc Þ ½22Š f cosðθc Þ sin c ị ẵ23 ẳ hẳ T ẳ ẵ21 f sinT c ị sin T =2ị ẵ24 f cosT c ị sin T =2ị ẵ25 hT ¼ For a truncated CPC : C ¼ For a full CPC : C ẳ T ẵ27 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 sinc ị ẵ28 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:   T ART f cos=2ị ẳ ỵ ln cot ẵ29 c ỵ = 2 sin ðΦ=2Þ 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 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 curveị ị ẳ R; jj c ỵ i9 8h < ỵ c ỵ cos − θc Þ = π 3π − θc ρð ị ẳ R ; c ỵ : ; ỵ sin c ị 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 ẳ Rsin cos ẵ31 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 < 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] Kalogirou SA (2009) Solar Energy Engineering: Processes and Systems New York: Elsevier Science; Academic Press ISBN: 978-0-12-374501-9 Tabor H (1966) Mirror boosters for solar collectors Solar Energy 10(3): 111–118 Low Concentration Ratio Solar Collectors [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] 163 Garg HP and Hrishikesan DS (1998) Enhancement of solar energy on flat-plate collector by plane booster mirrors Solar Energy 40(4): 295–307 Tripanagnostopoulos Y, Souliotis M, and Nousia Th (2000) Solar collectors with colored absorbers Solar Energy 68(4): 343–356 Tripanagnostopoulos Y (2007) Aspects and improvements of hybrid photovoltaic/thermal solar energy systems Solar Energy 81(9): 1117–1131 Tripanagnostopoulos Y, Nousia Th, Souliotis M, and Yianoulis P (2002) Hybrid photovoltaic/thermal solar systems Solar Energy 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