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Power From The Sun :: Chapter 9

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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:

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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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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 i...