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9._________________________ Concentrating Collectors The optical principle of a reflecting parabola (as discussed in Chapter 8) is that all rays of light parallel to its axis are reflected to a point. A parabolic trough is simply a linear translation of a two-dimensional parabolic reflector where, as a result of the linear translation, the focal point becomes a line. These are often called line-focus concentrators. A parabolic dish (paraboloid), on the other hand, is formed by rotating the parabola about its axis; the focus remains a point and are often called point-focus concentrators. If a receiver is mounted at the focus of a parabolic reflector, the reflected light will be absorbed and converted into heat (or directly into electricity as with a concentrating photovoltaic collector). These two principal functions, reflection to a point or a line, and subsequent absorption by a receiver, constitute the basic functions of a parabolic concentrating collector. The engineering task is to construct hardware that efficiently exploits these characteristics for the useful production of thermal or electrical energy. The resulting hardware is termed the collector subsystem. This chapter examines the basic optical and thermal considerations that influence receiver design and will emphasize thermal receivers rather than photovoltaic receivers. Also discussed here is an interesting type of concentrator called a compound parabolic concentrator (CPC). This is a non-imaging concentrator that concentrates light rays that are not necessarily parallel nor aligned with the axis of the concentrator. To complete this section we describe engineering prototype concentrators that have been constructed and tested. Parabolic concentrators that are not commercial products were chosen for discussion. This allows free discussion without concern for revealing proprietary information. In addition, the prototype concentrators discussed are representative of the parabolic concentrators under development for commercial use, and considerable design information is available. Performance data from some early prototypes are presented. The development includes the following topics: Receiver Design Receiver Size Receiver Heat Loss Receiver Size Optimization Compound Parabolic Concentrators (CPC) Prototype Parabolic Troughs Sandia Performance Prototype Trough Prototype Parabolic Dishes Shenandoah Dish JPL PDC1 Other Concentrator Concepts Fixed-Mirror Solar Collector (FMSC) Moving Reflector Stationary Receiver (SLATS) Fixed-Mirror Distributed Focus (FMDF) (spherical bowl) Page 1 of 47 Power From The Sun :: Chapter 9 7/17/2011 http://www.powerfromthesun.net/Book/chapter09/chapter09.html

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9._________________________ Concentrating CollectorsThe optical principle of a reflecting parabola (as discussed in Chapter 8) is that all rays of light parallel to its axis are reflected to a point. A parabolic trough is simply a linear translation of a two-dimensional parabolic reflector where, as a result of the linear translation, the focal point becomes a line. These are often called line-focus concentrators. A parabolic dish (paraboloid), on the other hand, is formed by rotating the parabola about its axis; the focus remains a point and are often called point-focus concentrators. If a receiver is mounted at the focus of a parabolic reflector, the reflected light will be absorbed and converted into heat (or directly into electricity as with a concentrating photovoltaic collector). These two principal functions, reflection to a point or a line, and subsequent absorption by a receiver, constitute the basic functions of a parabolic concentrating collector. The engineering task is to construct hardware that efficiently exploits these characteristics for the useful production of thermal or electrical energy. The resulting hardware is termed the collector subsystem. This chapter examines the basic optical and thermal considerations that influence receiver design and will emphasize thermal receivers rather than photovoltaic receivers. Also discussed here is an interesting type of concentrator called a compound parabolic concentrator (CPC). This is a non-imaging concentrator that concentrates light rays that are not necessarily parallel nor aligned with the axis of the concentrator. To complete this section we describe engineering prototype concentrators that have been constructed and tested. Parabolic concentrators that are not commercial products were chosen for discussion. This allows free discussion without concern for revealing proprietary information. In addition, the prototype concentrators discussed are representative of the parabolic concentrators under development for commercial use, and considerable design information is available. Performance data from some early prototypes are presented. The development includes the following topics:

z

z z

z

z

Receiver Design { Receiver Size { Receiver Heat Loss { Receiver Size Optimization Compound Parabolic Concentrators (CPC) Prototype Parabolic Troughs { Sandia Performance Prototype Trough Prototype Parabolic Dishes { Shenandoah Dish { JPL PDC1 Other Concentrator Concepts { Fixed-Mirror Solar Collector (FMSC) { Moving Reflector Stationary Receiver (SLATS) { Fixed-Mirror Distributed Focus (FMDF) (spherical bowl)

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z

Prototype Performance Comparisons

Special note to the reader: The prototype hardware described in the sections below represents the state-of-the-art in the 1970s and early 1980s. For updates on current status of solar concentrator hardware, the reader is referred to the web site of The SunLab (combined efforts of Sandia National Labs and the National Renewable Energy Laboratory web site: http://www.sandia.gov/csp/csp_r_d_sandia.html and the International Energy Agency web site: http://www.solarpaces.org/CSP_Technology/csp_technology.htm. Readers are also encouraged to access the web sites of different hardware manufacturers.

9.1 Receiver Design The job of the receiver is to absorb as much of the concentrated solar flux as possible, and convert it into usable energy (usually thermal energy). Once converted into thermal energy, this heat is transferred into a fluid of some type (liquid or gas), that takes the heat away from the receiver to be used by the specific application. Thus far we have concentrated our attention on reflection of incident solar energy and not been concerned with the geometry of the receiver. There are basically two different types of receivers - the omnidirectional receiver and the focal plane receiver. Rather than deal in complete generality and talk about the many possible types of receivers that could fall into these two categories, we discuss only two widely used receivers, the linear omnidirectional receiver and the point cavity receiver. This will not artificially limit the applicability of the development of the following paragraphs but will provide a nice focus to the discussion. Figure 9.1 is as photograph of a linear omnidirectional receiver used with parabolic troughs. It consists of a steel tube (usually with a selective coating; see Chapter 8) surrounded by a glass envelope to reduce convection heat losses. As the name omnidirectional implies, the receiver can accept optical input from any direction.

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Figure 9.1 Linear omnidirectional receiver, (a) photograph of operational receiver; (b) sketch of receiver assembly cross-section. Courtesy of Sandia National Laboratories.

Figure 9.2 is a sketch of a cavity receiver. This is clearly not an omnidirectional receiver since the light must enter through the cavity aperture (just in front of the inner shield for this receiver) to be absorbed on the cavity walls (coiled tubes in this case).

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Figure 9.2 Cavity (focal plane) receiver. Courtesy of Sandia National Laboratories.

Typically, the plane of the cavity aperture is placed near the focus of the parabola and normal to the axis of the parabola. Thus such a receiver is sometimes called a focal plane receiver. Although the cavity could be linear and thus used with a parabolic trough, a cavity receiver is most commonly used with parabolic dishes. Figure 9.3 is a photograph of this same parabolic dish cavity receiver.

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Figure 9.3 Photograph looking into the cavity aperture of the receiver of Figure 9.2. Courtesy of Sandia National Laboratories

9.1.1 Receiver Size Omnidirectional Receivers - The appropriate size for an omnidirectional receiver was developed in Chapter 8. The diameter of a tube receiver is r as defined in Equation (8.44) (and 2r1 as shown in Figure 9.1b). A receiver of this size intercepts all reflected radiation within the statistical error limits defined by n. This equation is reproduced here as an aid to the reader. (8.44) where p is the parabolic radius, n the number of standard deviations (i.e. defining the percent of reflected energy intercepted), and tot the weighted standard deviation of the beam spread angle for all concentrator errors, as developed in Section 8.4 and defined by Equation (8.43). As will be described below, the value of n (i.e. the number of standard deviations of beam spread intercepted by a receiver of size r ), is determined in an optimization process based on balancing the amount of intercepted radiation and amount of heat loss from the receiver. Put in simplified terms, a

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larger receiver will capture more reflected solar radiation, but will loose more heat due to radiation and conduction. Cavity Receivers - The appropriate size of the cavity opening (i.e. its aperture) is determined using the same optical principles used in the development of Equation (8.44) but then projecting the reflected image onto the focal plane where the receiver aperture will be located. If the beam spread due to errors is small in Figure 9.4, the angles and are approximately 90 degrees. Thus the projection of the image width onto the focal plane is (9.1) Substitution into Equation (8.44) yields (9.2)

Figure 9.4 Sizing of cavity aperture considering beam spreading due to errors.

Selection of Concentrator Rim Angle - It is interesting to study the impact of receiver type on the preferred concentrator rim angle. The whole idea of a concentrator is to reflect the light energy incident on the collector aperture onto as small a receiver as possible in order to minimize heat loss. Figure 9.5 is a plot of the relative concentration ratios for both cavities and omnidirectional receivers as a function of rim angle. The concentration ratio for the two concepts is the ratio of the collector aperture area divided by the area of the image at the receiver as defined by Equations (8.44) and (9.2), respectively. Note that the curve for the omnidirectional receiver increases uniformly up to 90 degrees, whereas the curve for the focal plane receiver increases up to a rim angle of about 45 degrees and then

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decreases because of the cosine term in the denominators in Equations (9.9) and (9.10).

Figure 9.5 Variation of geometric concentration ratio with rim angle.

The impact of this phenomenon is that most concentrators with an omnidirectional receiver have rim angles near 90 degrees. On the other hand, concentrators with focal plane receivers have rim angles near 45 degrees. The curves show only trends for each receiver type, and their magnitude relative to each other as shown in Figure 9.5 is not correct. 9.1.2 Receiver Heat Loss Linear Omnidirectional Receivers - The heat loss rate from a linear omnidirectional receiver of the type shown in Figure 9.1 is equal to the heat loss rate from the outside surface of the glass tube. This can be calculated as the sum of the convection to the environment from the glass envelope plus the radiation from the glass envelope to the surroundings.

(9.3) where: hg = convective heat-transfer coefficient at outside surface of glass envelope (W/m2 C) Ag = outside surface of glass envelope (m2) Tg = outside surface temperature of glass envelope (K) Ta = ambient temperature (K) = Stefan-Boltzmann constant (5.6696 10-8 W/m2 K4 ) g= emittance of the glass Fga = radiation shape factor Ts = sky temperature (K) (typically assumed to be 6 Kelvins lower than ambient temperature) (Treadwell, 1976) If all the variables can be evaluated, the heat-loss rate from the receiver under study can be determined. Unfortunately, it is not that easy. The glass envelope temperature Tg is a function of the

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receiver tube temperature and the resultant rate of thermal energy exchange between the receiver tube and the glass envelope. Treadwell (1976) presents the following simplified equation where the temperature of the glass envelope can be determined by equating (at steady state) the glass envelope heat-loss rate of Equation (9.3) with the receiver tube heat-loss rate

(9.4)

where: t = emittance of the receiver tube Tt = surface temperature a of receiver tube (K) At = surface area of receiver tube (m2) lt = length of receiver tube (m) r1 ,r2= see Figure 9.1b (m) ke = effective thermal conductance (includes convection) across the annulus (W/m K) The problem with using Equation (9.4) is to assign a value to ke. The development of the heat-transfer equations required in evaluating the conduction and convection heat transfer across the annulus from the receiver tube to the glass envelope is outside the scope of this book. Ratzel (1979a, 1979b) and Ratzel and Simpson (1979) review in detail the heat-transfer equations involved and correlate the results of their analytical analyses with experimental results. If you wish to delve into this area, it is recommended that you obtain all three references as the latter references build on the prior. Treadwell (private communication) states that a typical value for ke is 0.046 W/m K (0.027 Btu/h ft F). This value for ke corresponds to a 1.0-cm annulus (r2 - r1) with a Rayleigh number of 3000-4000. Table 8.3 lists values of ke/kair (kair = conductance of air) for various values of Rayleigh number. Kreith (1973) provides values for the conductance of air at various temperatures. Typically, the mean between the receiver tube and glass envelope temperatures is used to evaluate kair. Note that if an evacuated annulus receiver were employed, the second term of Equation (9.4) would be zero, leaving only the radiation loss term. Table 8.3. Variation of Ratio of Effective Conductance of Annulus Gap ke to Conductance of Air (kair,) with Rayleigh Number (Ra) (at Ra = 794.33, ke/kair, = 1.00000) (Eckert and Drake, 1972) Ra 1000 2000 3000 4000 5000 6000 7000 8000 9000 (ke/kair) 1.01859 1.10965 1.19208 1.27489 1.34809 1.40982 1.46467 1.51655 1.56918 Ra 10,000 20 ,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 (ke/kair) 1.62181 1.99668 2.25495 2.45820 2.62840 2.77617 2.90756 3.02640 3.13525 3.23594

A review of Ratzels references yields the following as reasonable nominal values for the factors needed for evaluation of Equations (9.11) and (9.12).

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where the units of temperatures are (K) and of r2 (m). Note that these are nominal values. Ratzel discusses effects such as temperature on these factors. The solution to the coupled equations, Equations (9.11) and (9.12), is easily addressed using an iterative computer program. One conceptually simple program is outlined in Figure 9.6. This program starts with a known receiver tube temperature. This starting point was chosen since a common statement of the collector heat-loss problem is: given the collector operating temperature (i.e., the fluid or receiver temperature), what is the associated heat loss." Although it is assumed that the fluid and receiver wall temperatures are the same here, this is not necessarily true. In fact, if not designed properly, the receiver wall temperature can be considerably higher than the fluid temperature.

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Figure 9.6 Logic flow for computing receiver heat loss - glass envelope.

As a starting point in the calculation, the glass envelope temperature is assumed equal to the average of the receiver tube and ambient temperatures. The heat loss is then computed by using Equation (9.3). Equation (9.4) is then used to calculate the heat loss from the receiver tube to the glass envelope. This heat loss must equal the heat loss from the glass envelope to the environment i.e. Equation (9.3) at steady state. If the two heat-loss quantities do not agree, a new glass envelope temperature is assumed as indicated in Figure 9.6 and the calculations are repeated. This iteration is continued until the two heat-loss quantities agree to within some predetermined limits (noted here as 5 percent). This same basic procedure can be used for any receiver consisting of an exposed receiver surrounded by a glass

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envelope. Cavity Receivers - Heat loss from a cavity receiver of the type shown in Figure 9.2 can be computed similarly. The general idea of a cavity receiver is to uniformly distribute the high flux incident on its aperture over the large internal surface area of the cavity in order to reduce the peak flux absorbed at any one point. Ideally, in a well insulated cavity, the cavity temperature is reasonably uniform and heat loss occurs primarily by convection and radiation from the cavity aperture. Thus Equation (9.3) is rewritten in terms of the characteristics of a cavity. For example, Ag becomes Acav the area of the cavity opening. Rewritten, Equation (9.3) would appear (9.5) where the subscript "cav" refers to the cavity. Since the opening of a cavity can be quite small compared to the surface area of an omnidirectional receiver, the heat loss is greatly reduced. In a typical calculation, the cavity temperature Tcav is assumed uniform and heat loss is computed as a function of this cavity temperature. Use of Equation (9.5) implies that heat loss through the insulation is zero. Although this is, strictly speaking, false, a well -insulated cavity receiver will lose most of its heat through the cavity aperture. In more complex models of cavity receivers, however, conduction heat loss through the insulation and through the receiver support structure is computed. Siebers and Kraabel (1984) review advanced techniques for computing convective heat loss from cavity receivers. 9.1.3 Receiver Size Optimization

At this point, we turn our attention to the factors involved in determining the size of a receiver (and therefore the concentration ratio). As described in Section 8.4.3, our knowledge of the optical quality of a concentrator is statistical in nature. Equation (8.44) describes the width of the reflected beam if we wish to ensure that a certain percentage of the reflected beam falls within r. We now address the issue of what is the proper percentage of reflected beam to capture. Figure 9.7 illustrates the design tradeoffs involved. As the receiver size increases, the amount of intercepted energy increases. However, all else remaining constant, as the receiver size increases, the heat loss from the receiver increases. The sum of the energy intercepted by the receiver and the heat loss (a negative number) from the receiver will show a maximum at some optimum receiver size. This will be the design point for sizing the receiver. Since heat loss is a function of the receiver design, we reconsider the two most common receiver types as examples to illustrate the design considerations.

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Figure 9.7 Optimization of the collector receiver size.

We now have all the elements needed for computing the optimum receiver size. Once again, to focus the discussion, we use the two common examples discussed above - the linear parabolic trough omnidirectional receiver shown in Figure 9.1 and the cavity receiver shown in Figure 9.2. The logic flow for a computer program to aid in selecting the optimum receiver size is shown in Figure 9.8. The basic idea is to compute, the optical energy intercepts and the heat lost by a series of different size receivers. A curve similar to that shown in Figure 9.7 can be constructed and the designer can select the optimum size.

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Figure 9.8 Logic flow for receiver sizing algorithm.

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The algorithm shown in Figure 9.8 predicts the energy intercepted by a receiver of specified size, from a concentrator with total error tot. The mirror surface is divided into incremental strips (or rings in the case of a dish), and the energy reflected from a strip and intercepted by the receiver is calculated as (9.6)

where: s = mirror surface specular reflectance = receiver absorptance = flux capture fraction (see Appendix G) d/d = from Equation (8.38a) or (8.38b) = incremental parabola angle defining strip or ring The flux capture fraction , is defined as the fraction of reflected flux which will be intercepted by a receiver of width r (or aperture diameter wn). It can be calculated by finding the fraction of the normal curve area within n/2 of the mean. A polynomial approximation of as a function of n is given in Appendix G to permit its computation within a computer code. The algorithm in Figure 9.8 requires the logic described in Figure 9.6 to compute the rate of heat loss when a receiver within a glass envelope is being evaluated. Otherwise, Equation (9.5) is used to compute the rate of heat loss from a cavity. 9.2 Compound Parabolic Concentrators (CPC) CPC Design Concepts - An interesting design for a concentrating collector makes use of the fact that when the rim of a parabola is tilted toward the sun, the rays are no longer concentrated to a point, but are all reflected somewhere below the focus. The rays striking the half of the parabola which is now tilted away from the sun are reflected somewhere above the focus. This can be seen on Figure 8.10 (repeated below as Figure 9.9 ) where the rays on the right-hand side are reflecting below the focus and the rays on the left-hand side are reflecting above the focus. If the half parabola tilted away from the sun is discarded, and replaced with a similarly shaped parabola with its rim pointed toward the sun, we have a concentrator that reflects (i.e. traps) all incoming rays to a region below the focal point.

Figure 9.9 Off-axis light reflection from parabolic mirror.

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Since the rays are no longer concentrated to a single point, this design is called a non-imaging concentrator. A receiver is now placed in the region below the focus and we have a concentrator that will trap sun rays coming from any angle between the focal line of the two parabola segments. Receivers can be flat plates at the base of the intersection of the two parabola, or a cylindrical tube passing through the region below the focus. The basic shape of the compound parabolic concentrator (CPC) is illustrated in Figure 9.10. The name, compound parabolic concentrator, derives from the fact that the CPC is comprised of two parabolic mirror segments with different focal points as indicated. The focal point for parabola A (FA) lies on parabola B, whereas the focal point of parabola B (FB) lies on parabola A. The two parabolic surfaces are symmetrical with respect to reflection through the axis of the CPC.

Figure 9.10 The compound parabolic concentrator (CPC).

The axis of parabola A is also shown in Figure 9.10 and, by definition, passes through the focal point of parabola A and the axis of parabola B likewise passes through the focal point of parabola B. The angle that the axes of the parabola A and B make with axis of the CPC defines the acceptance angle of the CPC. Light with an incidence angle less than one-half the acceptance angle will be reflected through the receiver opening (see Figure 9.11a). Light with an incidence angle greater than one-half the acceptance angle will not be reflected to the receiver opening (Figure 9.11b) and will, in fact, eventually be reflected back out through the aperture of the CPC.

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Figure 9.11 Light reflection from the CPC. a) Incidence angle less than acceptance angle; b) Incidence angle greater than acceptance angle.

The concentrating ability of the CPC can be understood through the use of ray tracing diagrams. The off-axis optics of parabolic troughs were discussed briefly in Chapter 8. That discussion is expanded here in order to explain the concentrating ability of the CPC. If beam solar irradiance parallel to the axis of parabola A were incident on the CPC shown in Figure 9.10, the light would be perfectly focused (ignoring the 0.5 degree solar degree-width and any mirror inaccuracies) to point FA, the focal point of parabola A. The behavior of beam solar irradiance not parallel to the axis of parabola A is shown in Figure 9.9. Note that all of the solar irradiance incident on the right half of the parabola is reflected such that it passes beneath the focal point between the focal point and the surface of the parabolic mirror. If the right half of the parabola in Figure 9.9 is tilted up to angle one-half the acceptance angle in order to approximate the orientation of parabola A in Figure 9.10, the situation would be analogous to that depicted in Figure 9.11a. All incident beam solar irradiance that is inclined to the right of the axis of the parabola in Figure 9.9 would he reflected by the right hand segment of the parabola beneath the focal point. Thus such solar irradiance would enter the receiver opening of an equivalent CPC. The converse situation is true where the angle of incidence is greater than one-half the acceptance angle. This situation is represented by the left half of the parabola in Figure 9.9. In this situation, all the incident beam solar irradiance is reflected above the focal point of the parabola and would not, as indicated in Figure 9.11b, enter the receiver opening of an equivalent CPC. In operation, the CPC is usually deployed with its linear receiver aligned along an E/W line. The aperture of the CPC is typically tilted toward the south so that the incident solar irradiance enters within the acceptance angle of the CPC. Provided the suns apparent motion does not result in the incident solar irradiance falling outside the CPCs acceptance angle, the CPCs aperture need not be tracked. Typically, a CPCs aperture need not be tracked on an hourly basis throughout a day since the suns declination does not change more than the acceptance angle throughout a day. However, the tilt of the CPC may have to be adjusted periodically throughout the year if the incident solar irradiance moves outside the acceptance angle of the CPC.

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The geometric concentration ratio of a CPC is related to the acceptance angle by (9.7)

where accept is the acceptance angle of the CPC. As the concentration ratio of the CPC is increased in an attempt to increase performance at elevated temperatures, the acceptance angle of the CPC must be reduced. The narrowing of the acceptance angle results in a requirement for increasing the number of tilt adjustments of the CPC throughout the year. Table 10.1 lists the number of tilt adjustments needed for CPC collectors with various concentration ratios. Cosine effect changes due to these adjustments are not included on this table.Table 10.1. Tilt Requirements of CPCs with Different Acceptance Angles (Rabl, 1980)

Acceptance Half -Angle 19.5 14 11 9 8 7 6.5 6 5.5

Collection Time Average over Year (h/day) 9.22 8.76 8.60 8.38 8.22 8.04 7.96 7.78 7.60

Number of Adjustments per Year 2 4 6 10 14 20 26 80 84

Shortest Period Without Adjustment (days) 180 35 35 24 16 13 9 1 1

Average Collection Time if Tilt Adjusted Every Day (h/day) 10.72 10.04 9.52 9.08 8.82 8.54 8.36 8.18 8.00

Prototype Performance - The performance of the Concentrating Parabolic Concentrator (CPC) varies with the acceptance angle. An acceptance angle of 180 degrees is equivalent to a flat-plate collector, and an acceptance angle of 0 degrees is equivalent to a parabolic concentrator. There has not been extensive performance testing of the CPC concept. As a result, there is to the authors knowledge no published T/I curve for CPCs. However, the Solar Energy Research Institute (Anonymous, 1979) has used the equation (9.8) where the variables are defined as in Chapter 5. This equation is for a CPC with a concentration ratio of 5, resulting in an acceptance angle of about 19 degrees. Sharp (1979) has evaluated this equation and found it to be equivalent to that of a good parabolic trough. However, Sharp has pointed out that parasitic losses associated with pumping the heat-transfer fluid through the small tubing typically used in CPC receivers could be a major problem. Unfortunately, there is, as stated previously, a general lack of published test data. It might be pointed out that computation of the CPC thermal energy production with the use of Equation

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(9.8) is straightforward if one assumes that the CPC tracks the sun about one axis. This is essentially what results from the multiple tilt adjustments given in Table 10.l. Since there is a general lack of data on the angular dependence of diffuse solar irradiance about the beam solar irradiance, Sharp (1979) suggests use of the beam solar irradiance in computing CPC performance in clear climates even though a fraction of the diffuse solar irradiance is captured. If data were available, the diffuse solar irradiance falling within the CPCs acceptance could be included in Equation (9.8). 9.3 Prototype Parabolic Trough Within the range of concentrating collector concepts, parabolic troughs are perhaps the most highly developed. Several generations of parabolic troughs have been built, tested, and deployed in prototype operating systems such as that located at Coolidge, AZ. 9.3.1 Sandia Performance Prototype Trough The parabolic trough chosen for examination is one developed at Sandia National Laboratories in conjunction with industry. The trough was assembled from pieces that were manufactured by private industry using techniques typical of mass production. The trough is typical of a high-performance parabolic trough and was chosen for discussion because of the availability of design and test data at the time of this writing. It is termed a "prototype" trough because, although it is not a commercially available product, it does contain features of many of the commercial troughs currently under development. For ease of reference throughout the book, this trough is referred to as the prototype trough. Drive String - A sketch of the prototype trough subsystem is presented in Figure 9.12. The sketch shows half of what is typically referred to as a drive string. A collector drive string is comprised of multiple parabolic trough reflector-receiver assemblies ganged together and driven by a single drive motor-gearbox unit. The drive motor-gearbox unit is located in the center of the drive string. The parabolic trough subsystem illustrated in Figure 9.12 is constructed from parabolic trough reflector panels 1.0 m long with an aperture width of 2.0 m. Six 90 rim angle reflector panels are then mounted on a steel torque tube 6.0 m in length, and the torque tube, in turn, is mounted on steel pylons.

Figure 9.12 Parabolic trough subsystem - half drive string. Courtesy of Sandia National Laboratories.

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The 6.0 m span for the torque tube was chosen to minimize the effect of sag of the structure between the pylons on the optical performance of the trough. The torque tube size (i.e., diameter and wall thickness) is determined by the anticipated maximum wind loads on the structure. The basic tradeoff involved in choosing the torque tube length is to minimize field construction costs (e.g., reduce the number of concrete foundations needed) while keeping the structure optically rigid by using a reasonable diameter (i.e., cost) torque tube. Depending on the engineers assessment of these costs, the basic length of the reflector module may vary. The various parabolic troughs produced commercially have varying-length reflector modules indicating the uncertainty in evaluating these costs and effects. As indicated in Figure 9.12, one drive motor-gearbox unit is used to drive four reflector modules for a total length of 24 m of collector structure. The length of collector structure driven by one drive motorgearbox unit is again determined by a tradeoff analysis. To reduce the costs, a collector designer would like to drive a very long length of collector with one drive motor-gearbox unit. As the collector structure length increases, however, the size of the drive motor and gearbox must increase as a result of the increasing torsional loads. Depending on ones assessment of these loads (predominantly loads due to the need to drive the collector to stow in high winds), the drive string will be either longer or shorter than the 24 m of the prototype shown in Figure 9.12. Wind tunnel analyses of the loads suggest that drive string lengths of 24-48 m may be reasonable. Once again, because of the uncertainties in the loads, various length parabolic trough collector drive strings are being developed by the commercial manufacturers of parabolic trough solar thermal energy systems. Delta-T string - The drive string is the basic module, or building block, of a field of parabolic trough collectors. The number of drive strings connected serially will be determined by the desired increase in temperature of the heat-transfer fluid. This serial connection of drive strings is termed a delta-T string. Choice of the proper heat-transfer fluid temperature increase and hence length of the delta-T string depends on the application serviced by the solar thermal system. This is discussed in Chapter 14. The temperature increase of the heat-transfer fluid per unit length of parabolic trough collector is determined by the heat-transfer fluid, collector design, and the need to provide turbulent flow within the receiver to allow good heat transfer. As such, the temperature rise of the heat-transfer fluid per unit length of the collector is a collector design parameter and is usually defined by the collector manufacturer. A reasonable value for a parabolic trough similar to the prototype shown in Figure 9.12 is a 1.0 - 2.0C rise in temperature per meter length of trough for an oil heat-transfer fluid. Receiver - The receiver tube of the prototype trough (see Figure 9.1) consists of a steel tube surrounded by a glass envelope to suppress convection heat losses. The steel tube is 31.57 mm outside diameter (OD) and was sized to intercept most of the reflected radiation and still minimize thermal losses. The receiver tube is coated with a black chrome selective coating to reduce radiation heat losses at elevated temperatures. Although not observable in Figure 9.1, o-rings near the ends of the glass envelope seal the annulus between the receiver tube and the glass envelope to prevent entry of dirt into the annulus. A reflective metal band (i.e., the hose clamp shown in Figure 9.1) protects the o-ring from concentrated solar radiation, which accelerates aging of rubber. The pivoting support mechanism illustrated in Figure 9.12 is also partially observable in Figure 9.1. The pivot compensates for expansion as the receiver temperature increases from ambient to operating temperature. The o-ring, which seals the annulus between the glass envelope and the receiver tube, also allows relative movement between the receiver tube and the glass envelope. This relative movement is needed to compensate for the difference in thermal expansion between the steel tube and the glass envelope. Although the annulus between the receiver tube and the glass envelope is not evacuated, evacuated receiver annuli have been proposed. The tradeoff involved is to provide a durable, vacuum tight seal for a cost less than the anticipated benefit in overall collector performance. The gain in collector efficiency and thus energy production anticipated from use of an evacuated annulus receiver tube is about 5 - 10 percent (Ratzel, 1979a) if a vacuum of 0.1 Pa or better can be maintained. Experience has shown that it

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is very difficult to maintain this level of vacuum. The alkali-borosilicate glass envelope around the receiver tube in the prototype trough has an antireflection coating. The surface was prepared by etching the glass surface as described in Chapter 8. Since the receiver in the prototype trough shown in Figure 9.12 moves with respect to the collector field thermal transport piping (i.e., the inlet and outlet manifolds), a flexible hose is provided. The structure of a typical flexible hose shown in Figure 9.13, consists of a thin metal bellows surrounded by a wire braid to protect the bellows from mechanical damage.

Figure 9.13 Structure of flexible metal hose. Courtesy of Sandia National Laboratories.

The back of a 100 m long delta-T string consisting of four individual drive strings is shown in Figure 9.14. There is a flexible hose at the end of each drive string. This is done (see Figure 9.15) to decouple the motion of each drive string from its neighbor to eliminate the need to synchronize the action of one drive motor with the next and is shown in Figure 9.15.

Figure 9.14 Photograph of 100-meter parabolic trough delta-T string. Courtesy of Sandia National Laboratories.

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Figure 9.15 Use of flexible metal hoses to decouple motion of adjacent drive strings. Courtesy of Sandia National Laboratories.

Control and tracking - Control and tracking of the delta-T string is provided by a hierarchical control system (Boultinghouse, 1983). A central field controller monitors overall collector field conditions and computes the instantaneous tracking angles for the troughs as discussed in Chapter 4 and communicates this information to the delta-T string. Local microcomputers resident on each drive string employ information from electro-optical sensors mounted on the receiver tubes to fine tune the tracking of the individual drive strings. The sensors are two matched nickel wires mounted on either side of the receiver tube. Reflected solar irradiance heats each wire, thus changing its respective resistance. Differences in the electrical resistances of the two wires are used to fine-tune the trough tracking. With perfect tracking, both wires should experience the same reflected flux and achieve the same resistance. Reflectors - Perhaps the component most unique to the parabolic trough subsystem shown in Figure

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9.12 is the reflector panel. The challenge is to produce a structure with an accurate parabolic contour and high specular reflectivity. One of the many possible designs for the reflector panels is shown in Figure 9.16. This panel exploits the mass-production-oriented technology of stamped sheet metal ribs to provide a rigid parabolic substrate onto which a glass reflector is bonded. Prototype reflector panels have been manufactured commercially with high contour accuracy (slope errors of