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:




Special note to the reader:  The prototype hardware described in the sections below represents the state-of-the-art in the 1970´s and early 1980´s.  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.



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).



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.



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 Δr 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.




where p is the parabolic radius, n the number of standard deviations (i.e. defining the percent of reflected energy intercepted), and σtot  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 Δr ), 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 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 α and β are approximately 90 degrees.  Thus the projection of the image width onto the focal plane is




Substitution into Equation (8.44) yields




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 decreases because of the cosine ψ 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.





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)

σΒ  = Stefan-Boltzmann constant (5.6696 ×10-8 W/m2 K4 )

ε 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 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





εt =    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 ,r2see 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
(kair,) with Rayleigh Number (Ra) (at Ra = 794.33,
ke/kair, = 1.00000) (Eckert and Drake, 1972)












  20 ,000



































A review of Ratzel’s references yields the following as reasonable “nominal values” for the factors needed for evaluation of Equations (9.11) and (9.12).




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.



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 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




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 Δr.  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.


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.



Figure 9.8  Logic flow for receiver sizing algorithm.

The algorithm shown in Figure 9.8 predicts the energy intercepted by a receiver of specified size, from a concentrator with total error σtot.  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





  ρs = mirror surface specular reflectance

  α = receiver absorptance

  Γ = flux capture fraction (see Appendix G)

dΦ/dψ = from Equation (8.38a) or (8.38b)

  ΔΨ= incremental parabola angle defining strip or ring


The flux capture fraction  Γ, is defined as the fraction of reflected flux which will be intercepted by a receiver of width Δr (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 Γ 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.


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.



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 sun’s apparent motion does not result in the incident solar irradiance falling outside the CPC’s acceptance angle, the CPC’s aperture need not be tracked.  Typically, a CPC’s aperture need not be tracked on an hourly basis throughout a day since the sun’s 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.


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




where θaccept  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)













Number of


Time if Tilt


Time Average




Half -Angle

over Year

per Year


Every Day





















































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 ΔT/I curve for CPCs.  However, the Solar Energy Research Institute (Anonymous, 1979) has used the equation


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 (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 CPC’s 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.

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 engineer’s 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 motor-gearbox 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 one’s 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 - 2.0°C 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 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.



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 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 <2.5 mrad).



Figure 9.16  Stamped sheet metal parabolic trough structure.  Courtesy of Sandia National Laboratories.


Figure 9.17 shows a prototype parabolic trough concept in which the reflector panel is simply a parabolic glass mirror supported by two stamped sheet metal ribs.  This concept, referred to as the spaceframe concept, is potentially attractive since it reduces the reflector structure to the reflector itself with a minimum of other structural components.



Figure 9.17  Space-frame parabolic trough structure.  Courtesy of Sandia National Laboratories.


Performance - The thermal performance of the prototype trough is shown in Figure 9.18.  Since parabolic troughs tend to be used over a wide range of temperatures, the efficiency of the prototype trough is reported as a curve.  The efficiencies reported in Figure 9.18 are experimentally determined values (Thunborg, 1983).


Figure 9.18  Performance of prototype trough.


9.4   Prototype Parabolic Dishes


The parabolic dish has undergone far less development than the parabolic trough.  In this section two prototype parabolic dishes are discussed: the Shenandoah dish and the JPL Parabolic Dish Concentrator.  Both of these dishes are present first-generation designs.

9.4.1   Shenandoay Dish

The Shenandoah dish was designed for application to a solar thermal cogeneration project located at Shenandoah, GA (see Chapter 16).  The dish is designed to heat silicone oil in one pass to 400'C (750°F) with an inlet temperature of 260°C (500°F).  A sketch of the Shenandoah dish is shown in Figure 9.19.  The dish was designed by General Electric Corporation and was manufactured by Solar Kinetics, Inc.  The 7 m diameter parabolic reflecting dish is formed of 21 aluminum petals, covered on one side with FEK-244 reflective film and then die-stamped to the correct contour.  The petals are bolted to 21 supporting aluminum sheet metal ribs that are fastened to a fabricated steel central hub weldment.


Design - Many of the design tradeoffs discussed above for the prototype trough were also examined in the design of the Shenandoah dish.  Dish diameter, for example, results from a tradeoff involving the desire to maximize dish diameter in order to decrease the amount of field piping in a given-size field.  The difficulty (and thus expense) of constructing very large optical structures capable of withstanding the anticipated wind loads, however, limits the size of parabolic dishes.



Figure 9.19  Parabolic dish prototype use in the solar thermal cogeneration project at Shenandoah, GA.


The central steel hub of the dish is supported at the declination points by a concrete counterweighted yoke structure.  This yoke is held at an angle by two polar axis bearings that are, in turn, supported by a tubular steel tripod mount.  The mount rests on a triangular base that is bolted to the tops of three concrete pier foundations that have been cast into the ground.


Tracking and Control - Drive about the polar axis is accomplished by rotation of the yoke structure by two 75 W i.e. 1/10 horsepower motor-driven jack screws in series, at the rate of 15 degrees per hour.  A third jack screw of the same type pivots the dish on its yoke support points to provide for motion about the declination angle.


A microprocessor-based control unit mounted on each concentrator provides tracking and safety commands (e.g., defocus during high winds or overheating).  Coarse tracking is provided by a microprocessor ephemeris track.  Fine tracking is provided by nulling the output of two pairs of fiber optics sensors located on the receiver aperture, one pair for each axis of rotation.  A 17.5-mrad (1-degree) angular motion microprocessor limit prevents wandering of the concentrator, due to extraneous reflections.


Receiver - The cavity receiver (shown in Figure 9.2 and 9.3) is designed to heat the heat-transfer fluid, Dow Corning Siltherm-800®, to a maximum constant outlet temperature of 400°C. Fluid supply and return lines are directed along a receiver support strut.  Two sets of flexible hoses are required to compensate for differential movement of the dish receiver with respect to the fixed thermal distribution piping in the field.  One flexible hose permits movement about the declination axis, whereas the other flexible hose permits the daily tracking movement of the dish about the polar axis.  The flexible hoses are similar in construction to that shown in Figure 9.13.


As can be seen from the sketch in Figure 9.2, the receiver is an insulated, cylindrical container with a coil of tubing inside to carry the heat-transfer fluid. Concentrated light entering the cavity aperture strikes the tubes and is absorbed. Any light not absorbed on this first encounter with the tubing is reflected off the surface of the tube and strikes the coil of tubing in a different place, where it undergoes absorption again. Even if the absorptance of the tubing is only 0.6, over 98 percent of the radiation will be absorbed after three reflections within the cavity.


A photograph of the Shenandoah dish as it appears after installation is shown in Figure 9.20. The tested efficiency of the dish at its design conditions of 260°C (500°F) inlet, 400°C (750°F) outlet is about 61% (Kinoshita, private communication).  The efficiency of the dish is essentially constant with temperature as a result of the cavity receiver.



Figure 9.20  Photograph of parabolic dish installed at Shenandoah, GA.  Courtesy of Sandia National Laboratories

9.4.2   JPL Parabolic Dish Concentrator-1

The second parabolic dish discussed here is the JPL Parabolic Dish Concentrator-1 (PDC-1).  This concentrator consists of a dish designed by the Space Division of the General Electric Company and a receiver-power conversion cycle module designed by the Aeronautics Division of Ford Aerospace and Communications Corporation.  The concentrator is depicted in Figure 9.21.  The power conversion system is designed to operate at 400°C and to provide electrical power to the power distribution grid of a small community.  A description of the power conversion system is included in Chapter 12.



Figure 9.21  JPL Parabolic Dish Concentrator-1

Design - The 12 m diameter parabolic reflector surface consists of 12 gores (panels) made of fiberglass and balsa wood sandwich panels that are injection-molded to the correct contour.  This lightweight construction was selected because of the very large aperture (12 m diameter) of the PDC-1.  An aluminized polyester reflective film is then bonded to each panel.  Each gore is essentially an arc segment 3 m at its widest point and approximately 6 m in length.  The gores are attached to 12 front-bracing ribs, which supply support and alignment with minimal weight.  Note that the diameter of this dish is considerably larger than that of the Shenandoah dish.


The support structure of the PDC-1 is designed for azimuth-elevation tracking.  The dish is attached to a transverse semicircular truss and is pivoted at diametrically opposed points for a full 180-degree rotation.  The truss is attached to the receiver at one end and to the counterweight at the other.  The dish, truss, and pivots are supported by a lightweight space frame that rotates on wheels along a rolled I-beam circular steel track, which is supported from the ground by concrete piers.  The receiver is supported by three arms and one end point of the semicircular truss.


Tracking and Control - The semicircular truss is rotated by use of a cable-drum arrangement.  The cable rides in a channel in the semicircular truss from the receiver to the counterweight.  Azimuth rotation is provided by a drive wheel that moves with the base along the circular track.


The control system is a hybrid design similar in concept to that used with the parabolic trough system described earlier. A computed tracking angle is used for coarse tracking and fiber optic sensors located on the receiver are used for closed loop fine tracking.  The fiber optic sensors are located at the receiver aperture and provide feedback information to the tracking system to center the reflected beam on the cavity aperture area.


At the focus is a module containing a combined cavity receiver and Rankine power conversion cycle.  The cavity receiver is a direct-heated, once-through monotube boiler that uses toluene at supercritical pressure.  The cavity is formed by a cylindrical copper shell and backwall with stainless steel tubing brazed to the outside surface.  This core is surrounded by lightweight refractory insulation, load-bearing struts and an outer case. The aperture plate is made of copper to provide long life by conducting and reradiating heat and stray concentrated flux away from the aperture lip.  The power conversion cycle to be used with this dish is described in Chapter 12.


Performance Comparison - A comparison of prototype parabolic dish and troughs with flat plate collectors is shown in Figure 9.22.  Referencing Chapter 5 of this text, the below curves indicate the effects of operating temperature and solar radiation levels on the efficiency of the solar collector.  Of particular note is the low efficiency of the prototype parabolic dish which does not agree with that shown on Figure 5.8.  This is due to the low reflectance of the FEK-244 reflective plastic film used on the prototype dish.  The dish in Figure 5.8 used glass mirrors.



Figure 9.22  Comparison of experimentally measured ΔT/I curves with flat-plate collector performance


9.5   Other Concentrator Concepts

There have been a large number of line focus prototype collectors that do not employ simple parabolic reflectors.  Generally, the motivation for this is to provide a collector in which either the reflector surface or receiver does not move.  All the collector concepts discussed in this section have apertures fixed in space.  Although some fixed-aperture concentrators may incorporate seasonal or more frequent periodic adjustments (e.g., see discussion of compound parabolic concentrators), the aperture of the concentrator typically remains fixed in space and does not attempt to follow the relative hourly motion of the sun. 


Of the more common fixed-aperture concentrators, all except one (the compound parabolic concentrator) focus only the incident beam solar irradiance.  As a result, diffuse solar irradiance does not contribute significantly to the performance of these concentrators.  Since there must be a well-defined relationship among the angular position of the incident solar irradiance, the reflector surface, and the absorber, only beam solar irradiance can be concentrated by a focusing collector (see Chapter 8).


Of the two primary means of focusing light (refraction and reflection), only reflection is used in fixed-aperture concentrators.  This results from the strong off-axis aberrations associated with most lens systems.  Typically, lenses are used only when two-axis tracking is provided (see Chapter 8).  Since the apertures of fixed-aperture concentrators are not necessarily normal to the incident solar irradiance in the plane of curvature, spherical optics, as discussed in Chapter 8, dominate.

9.5.1   Fixed-Mirror Solar Collector (FMSC)

The term “fixed-mirror solar collector” (FMSC) is the generic term applied to the type of fixed aperture concentrator represented in Figure 9.23.  Direct solar irradiance incident on the collector aperture is concentrated on a linear receiver by reflection from fixed, linear mirror facets.  The mirror facets produce a line of concentrated light that moves along a circular path as the sun moves.  The mirror facets are mounted on a cylindrical support substrate as illustrated in Figure 9.24.  The focal line of the mirror facets also lies on this cylindrical contour.  The receiver tracks about the center of curvature of the cylindrical substrate to intercept the reflected beam solar irradiance.  Receiver positions at various times throughout the year are shown on Figure 9.24.



Figure 9.23  Fixed-mirror solar collector concept without receiver installed.  Courtesy of Sandia National Laboratories.


Figure 9.24  Fixed-mirror solar collector showing annual and daily positions of receiver in Albuquerque.


The alignment of an individual mirror facet on the cylindrical support substrate is a function of its position on the substrate (Russel et al., 1974).  The first step in determining the appropriate orientation of the individual mirror facets is to locate the so-called tangent mirror facet (see Figure 9.24).  The surface of this mirror facet is tangent to the surface of the cylinder defined by the gross contour of the mirror support substrate.  The normal to the surface of the tangent mirror facet, by definition, passes through the center of curvature of the mirror support substrate (and thus the axis of rotation of the receiver) as indicated in Figure 9.24. The orientation of the normal to any other mirror facet is uniquely related to its angular distance from the tangent mirror facet. 


As shown in Figure 9.25, the angle that the normal to any mirror facet M makes with the normal to the tangent mirror facet is equal to θM/4, where θM is the angular distance between the two mirrors as shown in Figure 9.25.


Figure 9.25  Determination of mirror facet tilts for FMSC on mirror substrate.


To illustrate these angular relationships, consider the situation in which beam insulation, in the plane of curvature, is incident parallel to the tangent mirror facet normal. This is the case illustrated in Figure 9.25.  Light incident on the tangent mirror facet will be reflected directly back through the center of curvature (i.e., the angle of incidence on the tangent mirror facet is zero).  The mirror located at position M must be oriented so that the incident beam solar irradiance will be reflected to the focal point as indicated.  If the angular distance between the normal to the tangent mirror facet and the mirror facet M is θM, the angular distance between the reflected beam from the tangent mirror facet (and thus the normal to the tangent mirror facet) and the beam reflected from the mirror facet M is equal to θM/2.


From the angular relationship of parallel lines, the angle between the incident solar irradiance and the reflected solar irradiance from the mirror M is also equal to θM./2.  Thus, since the angle of incidence equals the angle of reflection, the angle between the incoming beam solar irradiance and the normal to the mirror facet M is half θM/2, or θM/4.  Since the incident beam solar irradiance was assumed parallel in the plane of curvature to the normal to the “tangent sector,” θM /4 is also the angle between the normal to mirror M and the normal to the tangent mirror facet.  This uniquely defines the position of mirror M relative to the tangent mirror facet.  The positions of all other mirror facets are defined in this manner.


Typically, the tangent mirror facet for an E/W-oriented FMSC is positioned such that its normal is parallel to the direct normal solar irradiance at solar noon on the equinoxes (i.e., the normal to the tangent mirror facet is tilted down from the vertical by the latitude angle).  This is usually referred to as latitude tilt in the solar energy literature.  Latitude tilt tends to maximize yearly thermal energy production except in locations where seasonally dependent cloud cover would encourage maximization of either summer or winter performance.  With a latitude tilt, the solar declination, with respect to the FMSC aperture, varies 23.5 degrees either side of the solar equinoxes throughout the year (see Chapter 3).


If the FMSC is oriented N/S, it is placed horizontal on the ground with the normal to the tangent mirror facet set vertical to provide symmetrical morning and afternoon performance.  An FMSC concentrator is rarely tilted toward the south when deployed in a N/S orientation because of the expense of the structure required to support a long tilted structure.


Prototype Description - A photograph of an FMSC reflector substrate developed by the General Atomic Company is shown in Figure 9.23.  The cross section of the typical FMSC receiver developed by General Atomic (Russel et al., 1974) is shown schematically in Figure 9.26.  The primary support beam of the receiver was an extruded aluminum channel.  A rectangular receiver tube was contained within the channel, and silica foam insulation was used to reduce conductive thermal losses from the receiver. 


Figure 9.26  Receiver used in FMSC.


The receiver tube was coated with a black chrome selective coating to reduce radiative heat losses.  The absorber tube mounting allowed axial movement to compensate for thermal expansion and contraction of the receiver tube during the diurnal heating cycle of the receiver.  The side of the receiver tube exposed to the concentrated solar irradiance was covered with a transparent Teflon film to reduce convection heat losses.  An extruded compound parabolic concentrator (see the following paragraphs) was mounted at the entrance to the receiver cavity to provide secondary concentration.  Secondary concentration compensated for any slight inaccuracies in mirror facet mounting that would lead to broadening or inaccurate focus of the beam at the focal line.  The reflecting surface of the secondary concentrator was polished anodized aluminum sheet material.


Prototype Performance - The efficiency of a prototype FMSC module tested at Sandia National Laboratories (SNLA) is reported in Figure 9.27.  The concentrator was tested near noon to eliminate significant endloss and cosine effects.  There was, however, a small cosine effect since the tests were performed in late August and the fixed aperture of the FMSC could not be tilted to be normal to the incident direct normal solar irradiance.  In the case of the data presented in Figure 9.27, the tangent mirror facet normal was tilted 32 degrees with respect to the vertical (see Figure 9.24 for angle definitions.)


Figure 9.27  Performance test results for FMSC.


The solar noon sun elevation angle on August 17 (date of test start) is approximately 68 degrees in Albuquerque.  This means that the incidence angle that the beam solar irradiance made with the aperture of the FMSC was approximately 10 degrees, resulting in a cosine effect of about 0.99.  This cosine effect apparently was, not taken into account when Figure 9.27 was compiled (Workhoven and Dudley, 1978).  Although this is a small effect, it does point out the potential for systematic errors creeping into published performance data.  Such errors can sometimes be corrected, or at least compensated for, if known.  The reader should be reminded that, before test data are used for system design, it is imperative to read the accompanying test report and understand how the performance data were obtained.


The test results presented in Figure 9.27 also reveal the rather large impact that component degradation can have on collector performance.  The first series of tests were performed on a FMSC (curve 1 of Figure 9.27) having mirror facets whose specular reflectance had degraded to 0.88 from an initial specular reflectance of 0.92 before testing. Installation of new mirrors with a specular reflectance of 0.95 resulted in the sharp increase in collector efficiency reported in Figure 9.27 as curve 2.


Loss of fluid flow during testing with the new mirrors resulted in severe over heating of the receiver tube shortly after the testing with the new mirrors had started.  In order to continue the test series, a new receiver was installed on the FMSC test module even though it was not matched to the collector.  The net result, as evidenced by curve 3 in Figure 9.27, was a significant decrease in collector performance.  During testing with the new receiver, fluid flow was again lost, resulting in overheating of the new receiver tube. (The receiver temperature reached 550°C.) The resultant drop in collector efficiency (point 4 in Figure 9.27) was probably due to the partial decomposition of the black chrome selective coating.  The optical properties of black chrome are known to degrade rapidly if the coating is heated above 350-400°C (662-752°F) (Pettit and Sowel, 1983).

9.5.2   Moving Reflector Stationary Receiver (SLATS)

A collector concept that relies on individually movable linear mirror facets to focus the incident beam solar irradiance on a linear receiver is shown in Figure 9.28.



Figure 9.28  Photograph of SLATS collector.  Courtesy of Sandia National Laboratories.


This concentrator concept, generically termed moving reflector stationary receiver, is commonly referred to as SLATS, which is an acronym for solar linear array thermal system. Although the individual mirror segments (slats) rotate about linear axes to focus the incident beam solar irradiance on the stationary receiver, the frame (and thus the collector aperture as defined in this text) holding the mirror facets remains fixed in space.  Thus the concept may he considered a fixed aperture concentrator, where the aperture of the concentrator is defined by the rectangular reflector assembly frame.  As the individual mirror facets move in order to maintain the incident beam solar irradiance focused on the fixed receiver, the inter-slat shading and gaps that may occur between slats produce essentially the same net effect as the incident angle effects on a fixed flat plate tilted to the same angle. Thus, based on the area of the reflector assembly, a SLATS concentrator has incident on its aperture the same amount of beam solar irradiance as a flat plate or FMSC tilted at the same angle.


Prototype Description - The cross section of .an individual mirror facet of a SLATS concentrator tested at SNLA (Gerwin, 1979) is shown in Figure 9.29.  A typical collector consists of two bays of 10 mirror segments each.  Each mirror facet has a cylindrical contour.  The cylindrical contour is used since a mirror facet does not normally point directly at the sun in the plane of curvature.  Off-axis aberrations are reduced in cylindrical optics (see Chapter 8) since the beam solar irradiance incident from any direction sees the same curvature.  Since the absorber remains stationary, the normal to the aperture of each mirror facet must bisect the angle defined by the sun, the mirror facet, and the receiver.  This relationship defines the relative tilt of each mirror facet.  The relative positions of the mirror facets can be established by employing the concept of a tangent mirror facet as used earlier in the discussion of the FMSC.


Figure 9.29 Cross section of SLATS reflector assembly.


The tangent mirror facet for the situation shown in Figure 9.30 is slat A.  The angle between the incident beam solar irradiance and a line pointing to the receiver for, as an example, slat B will be θB as shown in Figure 9.30.  Since the normal to the aperture of slat B must bisect the angle θB, the angle that the normal to slat B must make with the normal with the collector apertures θB/2.  This defines the tilt of slat B with respect to the normal to the collector aperture.


Figure 9.30  Definition of relative slat tilts for SLATS collector.


Once this initial relationship has been defined for all mirror facets, the facets can be ganged together and driven as a unit.  If the component of the beam solar irradiance in the N/S plane changes by some angle, each mirror slat must be rotated by half that angle from its original position.  Typically, the mirrors are driven as an assembly by using a chain and gear mechanism.


The optics of a SLATS concentrator are interesting because each mirror facet is constructed with the same radius of curvature.  The effective focal line of each mirror facet is different.  Moreover, the focal line of each mirror facet moves during the day as the incidence angle of the sun changes.  During most time periods when solar energy is being collected, however, the spread of the SLATS composite focal line due to the varying focal lines of the individual mirror facets is small.  In practice, a concentration ratio of about 35 is achieved.


The receiver designed for use with the SLATS concentrator tested at SNLA (Dudley and Workhoven, 1978; Gerwin, 1979) is shown in Figure 9.31. The receiver was designed for operation with water up to 315°C (600°F).  As such, thick wall boiler tubing (4.78 mm thick) was used for the receiver tube.  The receiver was configured in a U shape.  The U bend was free to expand laterally, and thus no thermal expansion compensation was necessary.  The receiver tube was insulated on all sides except the side facing the mirror facets.  A glass plate covered the receiver aperture to reduce convection heat losses.



Figure 9.31  Cross section of SLATS receiver assembly.


Because of the thick walls of the receiver tube needed to withstand the pressure 10.6 MPa (1540 psia) of water at 3l5°C (600°F) and the inherent high heat capacity of water, the thermal mass of the receiver design shown in Figure 9.31 is very high.  Since the receiver cools to ambient temperatures every night, the energy needed to warm the receiver to operating temperature every day is lost.  This can act as a significant parasitic energy loss.  An additional problem with a receiver designed with water as the heat-transfer fluid is freezing.  Freeze protection was provided in the SLATS collector tested at SNLA by circulating warm water through the receiver whenever the ambient temperature dropped below the freezing point. This resulted in significant thermal losses. A rather complete evaluation of the SLATS collector concept is presented in Gerwin (1979).


Prototype Performance - The thermal performance of a SLATS prototype module tested at SNLA (Dudley and Workhoven, 1978; Gerwin, 1979) is reported in Figure 9.32.  Initial testing prompted the installation of new glass mirrors, resulting in an improvement in optical efficiency (i.e., the efficiency axis intercept in Figure 9.32) from 0.63 to near 0.70.  Note that the slope of the ΔT/I curve changed between the two tests (old mirrors vs. new mirrors).  The reason for this change was not discussed in the test report.  Changing of the mirrors should not have significantly affected the SLATS overall heat loss coefficient (i.e., the slope of the ΔT/I curve).


Figure 9.32  Performance test results for SLATS.


Given the rather large scatter in the test data points, the slopes of the two lines could, within experimental error, be the same.  In addition, test data were obtained on different days because of the nature of the test procedures, and mirror realignment was necessary several times during the test series.  These considerations, together with significant data scatter, indicate the importance of understanding the validity of reported test data.  Read the entire test report when using test data!  Do not simply pick up test data such as that reported in Figure 9.32 and use it blindly.

9.5.3   Fixed Mirror Distributed Focus (FMDF)

The fixed mirror distributed focus (FMDF) concentrator concept is shown in Figure 9.33. For obvious reasons, this concept is frequently referred to as the "solar bowl" concept as well as the FMDF concept.  The acronym FMDF derives from the fact that the mirror substrate is a fixed spherical bowl focusing the incident radiation, as described in Chapter 8, to a focal line passing through the center of the sphere and pointing at the sun.  Figure 8.9 is reproduced here as Figure 9.34 to facilitate discussion.



Figure 9.33  Fixed-mirror distributed focus (bowl) concentrator.  Courtesy of Sandia National Laboratories.


Figure 9.34  Characteristics of spherical optics.


Receiver - As discussed in Chapter 8 and illustrated in Figure 9.34, the beam solar irradiance entering the aperture of a spherical reflector will be reflected to a line drawn through the center of curvature and pointing at the sun.  Thus the receiver must be configured to intercept the energy passing through the focal line.  In addition, since the focal line moves as the sun’s relative position changes, the linear receiver must be able to move with two degrees of freedom.  Typically, movement of the receiver is accomplished by pivoting the receiver structure about the center of curvature as indicated in Figure 9.35. 


Figure 9.35  Receiver movement in the FMDF concept.


Tracking and Control - Two types of tracking strategy can be employed. The receiver can be tracked by using an az-el tracking mode or a polar tracking strategy.  Both tracking strategies are discussed in some detail in Chapter 4.


The az-el tracking mode is usually dependent on interaction with a computer that calculates the instantaneous solar azimuth and elevation angles and then drives the receiver to point in that direction.  In a polar tracking scheme, the receiver is rotated about an axis parallel to the earth’s polar axis at the constant speed of 15 degrees per hour to compensate for the earth’s rotational speed.  The tilt of the linear receiver with respect to the earth’s polar axis is adjusted daily, if needed, to compensate for changes in the sun’s declination.  The tilt of the, receiver structure, with respect to the horizontal, is equal to the sun’s elevation angle.  Both types of tracking strategy are in use with FMDF concentrators.


Prototype Description - The FMDF concentrator shown in Figure 9.33 is part of a project planned for construction in Crosbyton, Texas.  The concentrator is currently being used to generate steam at 5l0°C (950°F) to test the FMDF concentrator’s potential application to electric power generation.  The receiver is comprised of helically wound ribbons consisting of 20 individual tubes per ribbon bundle as shown in Figure 9.36.  Since the focal line of a spherical bowl extends only halfway up the radius line (see Figure 9.35), the tube bundles comprising the receiver go only halfway to the pivot point of the receiver support structure.  The receiver structure was originally tapered, as shown, by 1 degree.


Figure 9.36  Schematic diagram of the receiver for FMDF collector.


Now it is felt that the cost of manufacturing a tapered receiver may out weigh any resultant small gain.  In operation, as envisioned at Crosbyton, the inlet water temperature would be about 38°C (100°F), and the outlet steam temperature would be 540°C (1000°F) at about 6.2 MPa (900 psia).


The flux distribution along the receiver is not uniform, as shown in Figure 9.37.  This type of flux distribution gives rise to the temperature profile along the receiver shown in Figure 9.39.  The temperature profile shown in Figure 9.39 is for a specific test, as indicated, but the temperature profile is typical and nicely illustrates the three heat-transfer regions of the receiver-preheat, boiling, and superheat.  Note that when compared with the flux distribution shown in Figure 9.38, the boiling region of the receiver occupies one of the regions of greatest flux.  This is where the highest heat-transfer coefficients are and most of the heat input occurs as a result of phase change taking place. The boiling region of the receiver is thus nicely compatible with the flux distribution on the receiver. There is a small region of superheating near the end of the receiver.



Figure 9.37  Flux distribution along the receiver of the FMDF collector.  (Length = 1.0 is the bottom of the receiver.)



Figure 9.38  Temperature distribution along the receiver of the FMDF collector.

Since the FMDF receiver serves as a boiler, treated water must be supplied to the receiver.  The steam exiting the receiver would, in an actual power generation application, be fed directly to a steam turbine.


Prototype Performance - Although the FMDF concentrator has not been subjected to the variable-temperature testing that many of the line focus concepts have, it is possible to estimate the shape of the ΔT/I efficiency curve.  The optical efficiency of the FMDF prototype concentrator module at Crosbyton, Texas has been reported to be 67 percent (i.e., the efficiency axis intercept of the ΔT/I vs. efficiency curve is 0.67) and the value of the overall heat-loss coefficient of the receiver (i.e., the slope of the ΔT/I-efficiency curve) has been estimated to be 0.43 (Kinoshita, 1983).  This yields the efficiency curve shown in Figure 9.39.


Figure 9.39    Predicted performance of the FMDF collector


Since the temperature of the receiver does not increase linearly with receiver length as a result of the phase change (see Figure 9.38), the average temperature of the receiver is not simply the average of the receiver inlet and outlet fluid temperatures. A reasonable approach to computing the average receiver temperature is to first calculate the average temperature of the receiver preheat, boiling, and super heat regions individually.  These average temperatures, weighted by the length of the respective receiver regions, are then used to compute an overall receiver average temperature (see Figure 9.38).

9.6   Prototype Performance Comparisons

The daily energy collection performance of each prototype collector concept, for a typical meteorological year (TMY) in Albuquerque, NM, is summarized in Figure 9.40.  The CPC was treated as an E/W-oriented single-axis tracking aperture.  All performance was computed by use of the COLECTK routine.  The average daily energy collected, averaged over the year, is shown by the symbols on the right hand side.



Figure 9.40  Annual performance summary of flat-plate, parabolic trough and parabolic dish collectors.


Figure 9.41  Annual performance summary of the collector concepts discussed above.




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