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7/29/13 Power From The Sun :: Chapter 10

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10.__________________________

Central Receiver Systems

The central receiver concept for solar energy concentration and collection is based on a field of individuallysun-tracking mirrors (heliostats) that reflect the incident sunshine to a receiver (boiler) at the top of acentrally located tower. Typically 80 to 95 percent of the reflected energy is absorbed into the working fluidwhich is pumped up the tower and into the receiver. The heated fluid (or steam) returns down the tower

and then to a thermal demand such as a thermal electrical power plant or an industrial process requiringheat.

The basic difference between the central receiver concept of collecting solar energy and the trough or dishcollectors discussed previously is that in this case, all of the solar energy to be collected in the entire field, istransmitted optically to a small central collection region rather than being piped around a field as hot fluid.Because of this characteristic, central receiver systems are characterized by large power levels (1 to 500MW) and high temperatures (540 to 840C).

Central receiver technology for generating electricity has been demonstrated in the Solar One pilot power

plant at Barstow, California. This system consists of 1818 heliostats, each with a reflective area of 39.9 m2

(430 ft2) covering 291,000 m2(72 acres) of land. The receiver is located at the top of a 90.8 m (298 ft) high

tower and produces steam at 516C (960F) at a maximum rate of 42 MW (142 MBtu/h).

System design for a central receiver application is performed in a manner similar to that when other types ocollector are used. Basically, the thermal output of the solar field is found by calculating collection efficiencyand multiplying this by the solar irradiance falling on the collector (heliostat) field. The balance of the systemis then designed as discussed in the latter chapters of this book.

In this chapter we describe the components of a central receiver system and how they interact in aparticular field design. Then a computer model for collection efficiency is developed that can be used inconjunction with solar irradiance data and a system model such as SIMPLESYS to determine the systemsenergy delivery capabilities.

System Description

Heliostats

Receiver / Tower

Field Layout

System Thermal Performance

Energy Losses

System Performance Models

SCRAM

The reader should realize that the material presented below represents the state-of-the-art for central

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receiver systems in the early 1980s. Since then there have not been any new central receiver power plantsconstructed, however the Solar One prototype power plant in Barstow underwent major modifications totest a different concept of central receiver design.Renamed Solar Two, the facility at Barstow, CA was modified to test the concept of using molten salt as theheat transfer fluid rather than water/steam. A completely new receiver was installed, and the storage waschanged to a two-tank system. In addition a few newly designed heliostats were added. The Solar Twopower plant was operated for over a year with generally positive results. The reader is referred to the U.S.Department of Energy SunLab web site; http://www.sandia.gov/csp/csp_r_d_sandia.html for current

information on this technology. For international status of central receiver technology, the reader isencouraged to go to the International Energy Agency Solar PACES web site;http://www.solarpaces.org/CSP_Technology/csp_technology.htm .

10.1 System Description

10.1.1 Heliostats

Design. The heliostat used in Solar One is shown in Figure 10.1. The reflecting element of a heliostat istypically a thin, back (second) surface, low-iron glass mirror. This heliostat is composed of several mirrormodule panels rather than a single large mirror. The thin glass mirrors are supported by a substrate backing

to form a slightly concave mirror surface. Individual panels on the heliostat are also canted toward a pointon the receiver. The heliostat focal length is approximately equal to the distance from the receiver to thefarthest heliostat. Subsequent tuning of the closer mirrors is possible.
http://www.solarpaces.org/CSP_Technology/csp_technology.htmhttp://www.sandia.gov/csp/csp_r_d_sandia.html


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Figure 10.1 (a) Backside of the heliostat used at the Solar One central receiver pilot plant in Barstow, CA. (b) A photographof the front of a Solar One heliostat (Both are courtesy of Southern California Edison Co.)

Another heliostat design concept, not so widely developed, uses a thin reflective plastic membrane

stretched over a hoop. This design must be protected from the weather but requires considerable lessexpenditure in supports and the mechanical drive mechanism because of its light weight. Membranerenewal and cleaning appear to be important considerations with this design.

The reflective surface is mounted or supported on a pedestal that permits movement about the azimuth andelevation axis. Movement about each axis is provided by a fractional-horsepower motor through a gearboxdrive. These motors receive signals from a central control computer that accurately points the reflectivesurface normal halfway between the sun and the receiver. The equation for this half angle was developed inChapter 8 as Equation (8.49). The elevation and azimuth angles of a heliostat are given in Equations (8.52)and (8.53), respectively.

Heliostat Errors.A perfectly flat heliostat would produce an image on the receiver the size of the heliostat


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(projected normal to the heliostat-receiver direction) increased by the approximately 0.5 degree ofsunspread. For most applications, each mirror segment is concaved slightly and each mirror segment on aheliostat is canted toward a focal point. This produces a higher flux density at the aim point.

A number of factors tend to increase the image size from a particular heliostat. Mirror surface waviness isan important factor for heliostats as it is with parabolic collector surfaces. In addition, the gross curvatureerror of each mirror segment and the errors associated with accurate canting of each mirror segment onthe heliostat frame further increase the image error. This last source of error can be amplified by the effectsof differential thermal growth and gravity (heliostat position) on the heliostat frame. All of these errors add

up optically to produce a flux profile at the aim point (receiver) which has a distribution pattern similar to thatshown in Figure 10.2. The important heliostat performance parameter is the size of the isoflux contourcontaining 90 percent of the total reflected power.

Figure 10.2 Pattern of flux density arriving at the receiver from a typical heliostat.

In addition to producing a high flux density, the ability of the heliostat tracking system to position the centroidof the flux profile at the center of the receiver (aim point) is critical. Positioning errors may be caused byvertical and horizontal errors in the heliostat positioning or feedback mechanisms. In addition, wind canproduce structural deflections, causing position errors.

Most of the heliostat errors discussed become more significant (in terms of the flux spilled from thereceiver), the farther the heliostat is located from the receiver. However, the flux contour and positioningerrors are also critical for heliostats close to the tower because the projected area of the receiver is verysmall at that location. A more complete discussion of heliostat errors and error measurement may befound in King (1982).

Environmental Considerations. Probably the most important environmental design criterion that must bemet by a heliostat design is the wind condition. Typical requirements may be for the heliostat to meet itsoperating requirements in a 12 m/s (27 mph) wind, to survive a 22 m/s (49 mph) wind, and to continue tooperate or move to the stow position in a 40 m/s (89 mph) wind (a position usually horizontal with mirrorsface-up or face-down). Also, the ability to survive hail is important for any flat surface exposed to theelements. A typical hail survival criterion is 19 mm (0.75 in.) diameter hailstones impinging at 20 m/s (45


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Figure 10.4 A cavity type receiver design incorporating four apertures. It would operate in the 510 to 565oC (950 to 1050oFtemperature range with steam, molten salt or sodium (Battleson, 1981).

The aperture size is minimized to reduce convection and radiation losses without blocking out too much ofthe solar flux arriving at the receiver. The aperture is typically sized to about the same dimensions as thesuns reflected image from the farthest heliostat, giving a spillage of 1 to 4 percent. For a 380 MW (1.3109 Btu/h) plant design, the aperture width for the largest of the four cavities (the north-facing cavity) is 16

m (52 ft), and the flux at the aperture plane is four times that reaching the absorbing surface inside.

Heat Flux Considerations. The primary limitation on receiver design is the heat flux that can he absorbedthrough the receiver surface and into the heat transfer fluid, without overheating the receiver walls or theheat transfer fluid within them. A survey of typical design peak values is given in Table 10.1. The averageflux over the entire absorber wall is typically one-half to one-third of these peak values. Two other importantconsiderations are: (1) limiting the temperature gradients along the receiver panels and (2) the daily heat-

cycling of the receiver tubes.

Table 10.1 Typical Receiver Peak Flux Design Values

Heat Transfer Fluid Configuration Peak Flux

(MW/m2)Liquid sodium In tubes 1.5

Liquid sodium In heat pipes(transferring to air)

1.2

Molten nitrate salt In tubes 0.7Liquid water In tubes 0.7


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Steam vapor In tubes 0.5Air In metal tubes 0.22

Source; Battleson (1981).

Tower Design. The height of the tower is limited by its cost. The weight and windage area of the receiverare the two most important factors in the design of the tower. Seismic considerations are also important insome locations. The weight and size of a receiver are affected by the fluid choice as discussed previously.

Typical weights for a 380 MW (1.3 109Btu/h) receiver range from 250,000 kg (550,000 lb) for an external

receiver using liquid sodium to 2,500,000 kg (5,500,000 lb) for a cavity air receiver. These would be placed

at the top of a 140 to 170 m (460 to 560 ft) tower if a surrounding heliostat field is used.

Proposed tower designs are of either steel frame construction, using oil derrick design techniques, orconcrete, using smokestack design techniques. Cost analyses indicate that steel frame towers are lessexpensive at heights of less than about 120 m (400 ft) and that concrete towers are less expensive forhigher towers. The results of such a cost analysis described in Sterns Roger Engineering (1979) areshown in Figure 10.5.

Figure 10.5 Tower cost data for towers of different heights. The band reflects use of different receivers having differentwindage and weight. These designs were made to withstand a 40 m/s (90 mph) wind and a ground acceleration of 0.25 g

(Battleson, 1981).

Beam Characterization Targets. Prominent on any photograph or drawing of a central receiver tower are thewhite targets located just below the receiver. These are beam characterization system (BCS) targets usedto aid in periodic calibration and alignment of individual heliostats. They are coated with a diffusely reflectingwhite paint, and are not designed to receive the flux of more than one or two heliostats. Instrumentationwithin the target area is used to determine the centroid and flux density distribution of the beam from a


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selected heliostat. If the centroid of the beam is not located where the field tracking program predicts it to btracking program coefficients are modified appropriately.

Heat Transfer Fluids. The choice of the heat transfer fluid to be pumped through the receiver is determinedby the application. The primary choice criterion is the maximum operating temperature of the systemfollowed closely by the cost-effectiveness of the system and safety considerations. Five heat transfer fluidshave been studied in detail for application to central receiver systems. They are discussed separately in theparagraphs which follow.

The heat transfer fluids with the lowest operating temperature capabilities are heat transfer oils. Bothhydrocarbon and synthetic-based oils may be used, but their maximum temperature is around 425C(797F). However, their vapor pressure is low at these temperatures, thus allowing their use for thermalenergy storage. Below temperatures of about -10C (14F), heat must be supplied to make most of theseoils flow. Oils have the major drawback of flammable and thus require special safety systems when usedat high temperatures. Heat transfer oils cost about $0.77/kg ($0.35/lb).

Steam has been studied for many central receives applications and is the heat transfer fluid used in theSolar One power plant. Maximum temperature applications are around 540C (1000F) where the pressuremust be about 10 MPa (1450 psi) to produce a high boiling temperature. Freeze protection must beprovided for ambient temperatures less than 0C (32F). The water used in the receiver must be highlydeionized in order to prevent scale buildup on the inner walls of the receiver heat transfer surfaces.However, its cost is lower than that of other heat transfer fluids. Use of water as a high-temperaturestorage medium is difficult because of the high pressures involved.

Nitrate salt mixtures can be used as both a heat transfer fluid and a storage medium at temperatures of upto 565C (1050F). However, most mixtures currently being considered freeze at temperatures around 140to 220C (285 to 430F) and thus must be heated when the system is shutdown. They have a good storagepotential because of their high volumetric heat capacity. The cost of nitrate salt mixtures is around $0.33/kg($0.15/lb), making them an attractive heat transfer fluid candidate.

Liquid sodium can also be used as both a heat transfer fluid and storage medium, with a maximumoperating temperature of 600C (1112F). Because sodium is liquid at this temperature, its vapor pressureis low. However, it solidifies at 98C (208F), thereby requiring heating on shutdown. The cost of sodium-based systems is higher than the nitrate salt systems since sodium costs about $0.88/ kg ($0.40/lb).

For high-temperature applications such as Brayton cycles, it is proposed to use air or helium as the heattransfer fluid. Operating temperatures of around 850C (1560F) at 12 atm pressure are being proposed.Although the cost of these gases would be low, they cannot be used for storage and require very largediameter piping to transport them through the system.

10.1.3 Field Layout

Decisions regarding the best position for locating heliostats relative to the receiver and how high to place thereceiver above the field constitute a multifaceted problem, in which costs and heliostat lossmechanismsare the variables. We first discuss some of these loss mechanisms and then how they interact in shapingan optimum heliostat field.

Cosine Effect. The major factor determining an optimum heliostat field layout is the cosine efficiency ofthe heliostat. This efficiency depends on both the suns position and the location of the individual heliostatrelative to the receiver. The heliostat is positioned by the tracking mechanism so that its surface normalbisects the angle between the suns rays and a line from the heliostat to the tower. The effective reflectionarea of the heliostat is reduced by the cosine of one-half of this angle. This may be visualized byconsidering heliostats at two positions in a field as shown on Figure 10.6. Heliostat A has a small cosineloss since its surface normal is almost pointing toward the receiver. Heliostat B has a larger cosine lossbecause of the position it must assume in order to reflect the suns rays onto the receiver. Note that themost efficient heliostats are located opposite the sun.


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Figure 10.6 The cosine effect for two heliostats in opposite directions from the tower. For the noontime sun condition

shown, heliostat A in the north field has a much greater cosine efficiency than does heliostat B.

An expression for calculation of the cosine of this half angle has been developed as Equation (8.49).Incorporating the appropriate tower and heliostat position coordinates defined in Figure 8.20, we have

(10.1)

where andAare the suns altitude and azimuth angles, respectively, andz, e, andnare the orthogonal

coordinates from a point on the tower at the height of the heliostat mirrors as depicted in Figure 8.20.

Field cosine efficiency, calculated by using Equation (10.1), has been plotted in Figure 10.7 for three sunaltitude angles. This figure also shows that the heliostats opposite the sun are the most efficient. This iswhy most of the heliostats in a typical heliostat field (for an omnidirectional receiver) will be north of thetower. In the morning, heliostats west of the tower will have a high efficiency and those east of the tower, apoorer efficiency. The opposite occurs in the afternoon, giving the east and west fields an averageefficiency in between the high and the low.


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Figure 10.7 The cosine efficiency of heliostats at different field locations for three sun altitude angles.

Averaged over the entire year, the cosine efficiency of a field resembles that shown in Figure 10.8. Againthe north field dominance can be seen. In some de signs as Solar One in Barstow, California, the south fieldheliostats are used only to preheat the water, which is subsequently turned into superheated steam in therest of the receiver. This is done because of the reduced flux being reflected to this part of the receiver.

Figure 10.8 Annual average cosine efficiency at Barstow, CA (Holl, 1978).


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Shadowing and Blocking. In previous chapters we discussed the problem of one collector casting a shadowon an adjacent collector, thereby reducing the energy output of the shaded collector. For central receiversystems, there are two such interaction processes that reduce the amount of energy reaching the receiver.These are shadowingand blockingby adjacent heliostats.

Shadowing occurs at low sun angles when a heliostat casts its shadow on a heliostat located behind it.Therefore, not all the incident solar flux is reaching the reflector. Blocking occurs when a heliostat in front oanother heliostat blocks the reflected flux on its way to the receiver. Both processes are illustrated in Figure10.9. Blocking can be observed in a heliostat field by noting reflected light onthe backs of heliostats.

Figure 10.9 Shadowing and blocking loss of solar flux.

The amount of shadowing and blocking in a particular field layout is a function of the heliostat spacing, tower

height, and sun angle. Optimum field lay outs are made by use of ray tracing techniques in an extensivecomputer analysis. These programs study representative heliostats in a field and check them for bothblocking and shadowing by the heliostats in the two rows in front of the heliostat in question. Two centralreceiver performance programs that have this capability are HELIOS (Biggs and Vittitoe, 1979) andDELSOL2 (Dellin et al., 1981).

This type of analysis is beyond the scope of this book; however, some general field layout guidelines havebeen developed from these studies. It is generally best to arrange heliostats in a radial stagger pattern asshown in Figure 10.10. This pattern minimizes land usage as well as shadowing and blocking losses. Theheliostats are tightly packed near the tower but must be sufficiently separated to prevent mechanicalinterference. For heliostats located farther from the tower, the spacing increases in order to minimizeblocking of the reflected beams. Going out a long a radius, additional heliostats are added when spacingbecomes too great and a new stagger pattern is established.


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Figure 10.10 The radial stagger heliostat layout pattern developed by the University of Houston.

Heliostat packing density is the ratio of mirror area to field area. The average heliostat packing density fromoptimized ray trace analyses of shadowing and blocking is typically in the range of 0.2 to 0.25 (Battleson,1981).

Optimized heliostat layouts developed at the University of Houston (Lipps and Vant-Hull, 1978) haveproduced a means of determining spacing and average field density for preliminary field layouts. The radialspacing Rand the azimuthal spacing A, defined in Figure 10.10, are given by Dellin et. al. (1981) for high

reflectance heliostats (about 90 percent) in large fields as

(10.2)

and

(10.3)

whereHMandWMare the height and width of the heliostat, respectively as depicted in Figure 10.9. The

angle Lis the altitude angle to the receiver from the heliostat location of interest and may be calculated as


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(10.4)

where ris the normalized distance from the tower to the heliostat location measured in tower heights.

The local field density is the ratio of mirror area to land area at a particular point in the field. This may becalculated as

(10.5)

whereDM, the mirror density, is the ratio of mirror area to overall heliostat area.

The process of laying out a heliostat field consists of segmenting the land area around the tower into anumber of concentric zones. Equations (10.2) and (10.3) are used to determine the average or centralradial stagger pattern within these zones, and Equation (10.5) is used to calculate the local field density. Iflarge zones are selected, it may not be possible to maintain the azimuthal spacing defined in Equation(10.3) for all rings. Heliostats near the inner ring of the zone may produce mechanical interference orunacceptable blocking or shad owing. When this is the case, every fourth heliostat is normally removed

from a ring in what is called a slip plane and the radial stagger pattern is restarted.

Figure 10.11 shows the spacing predicted by Equations (10.2) and (10.3). Note that for the heliostats farthefrom the tower, the radial spacing increases dramatically, whereas the azimuthal spacing decreases to thepoint where the heliostats at a particular radial distance have one heliostat width between them (A = 2).

Figure 10.12 shows the decrease in local field density as distance from the tower increases.


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Figure 10.11 Heliostat spacing for a field using the radial stagger layout pattern.


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Figure 10.12 Local heliostat density as predicted by Equation (10.5) for radial-stagger field layouts.

Atmospheric Transmittance. Many factors in field layout suggest that the field should extend far to the northof a very high tower. One major limitation on the distance a heliostat is placed away from the tower is theattenuation of the reflected beam as it travels from the heliostat to the receiver.

Atmospheric transmittance has been approximated by Vittitoe and Biggs (1978) for a clear day (23-kmvisibility) and a hazy day (5-km visibility). For a clear day with 23-km visibility, the atmospherictransmittance is

(10.6)

where Sis the slant range from heliostat to receiver in kilometers. For a hazy day with only 5-km visibility,

the atmospheric transmittance is

(10.7)

Although these expressions were derived for a specific site altitude, they are strongly dependent on theaerosol distribution at ground level (visibility) and only slightly dependent on site altitude.

The effect of atmospheric attenuation is presented graphically in Figure 10.13. The maximum slant rangefor Solar One is 0.44 km (1440 ft); however, larger fields are envisioned in the near future whereatmospheric attenuation will be even more significant.


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Figure 10.13 Atmospheric transmittance for a clear and a hazy atmosphere.

Optimization Studies. A number of case studies have been performed that reflect optimum field layouts forthe components studied (Battleson, 1981). The shape of the optimum field depends on the power level ofthe plant. For small systems of less than 100 MW (thermal), single or multiple north fields appear to bemost economical. Any increase in power would require heliostats to be farther away from the tower. As thedistance from heliostat to tower increases, atmospheric attenuation reduces the efficiency of the far-fieldheliostats. This forces the placement of heliostats to the east and west of the tower in locations with lowercosine efficiency but less attenuation loss. For large plants with power levels above 500 MW (thermal), theoptimum field layout becomes a field surrounding the tower.

In addition to cosine loss and atmospheric attenuation, other performance tradeoffs are required to producean optimum field. These include spillage and receiver thermal loss as well as cost algorithms for the towerpiping, and receiver. The field designs resulting from these studies are shown in Figure 10.14. The height of

the receiver tower for these fields falls into a range such as that shown in Figure 10.15.


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Figure 10.14 Optimum field shape defined by cosine loss, atmospheric attenuation, tower cost, and other systemperformance parameters (Batt leson, 1981).

Figure 10.15 Range of optimum receiver tower heights for systems with different power levels (Battleson, 1981).


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Source: Design study f or a 380 MW (thermal) pow er plant (Sterns Rogers Engineering Company, 1979).

Field Losses. The energy losses associated specifically with the heliostat field include four of the fivegreatest sources of energy loss. Most of these have been discussed in detail in the previous section. Thelargest loss term is the cosine loss. As discussed in Section 10.1.3, cosine losses may be minimizedthrough proper field design; however, they still represent the single most important loss mode.

Following the cosine effect in importance is the mirror reflectance loss. Although new low-absorption glassmirrors can be made with a reflectance of about 94 percent, age and dust soon reduce this to an average

value of about 90 per cent. Keeping the mirrors washed, clean and in good repair is essential to maximizeannual energy output.

The third most important loss factor for the losses listed in Table 10.2 is the atmospheric attenuation. Asdiscussed in the previous section, atmospheric attenuation becomes significant for very large heliostatfields where the outer heliostats are far from the receiver. The value listed represents a large field havingabout 10 times the area of Solar One, where the atmospheric attenuation losses are estimated to be around3 percent (Coggi and Eden, 1981).

Blocking and shadowing represent the next most important loss factor in central receiver systemperformance. Although at noon, when the suns altitude is a maximum, there is usually no blocking orshadowing for a well designed field, significant blocking and shadowing does take place in the mornings and

afternoons, especially in the winter, when the sun is low in the sky. Because of this, the annual averageblocking and shadowing losses are also significant.

Defining each of these losses in terms of an efficiency, we express the field efficiency as

(10.9)

where cos, shadow, block, refland attenare efficiencies (i.e., 1 minus the fraction of

energy lost in the process) based on cosine, shadowing, blocking, mirror reflectance, and atmosphericattenuation losses, respectively.

One loss source, receiver spillage, is a function of both the heliostat field (heliostat beam focus anddistance from the tower) and the receiver (size of absorbing surface or aperture). We have arbitrarilychosen to include this factor with the receiver loss rather than with the field loss.

Receiver Losses.The remainder of the losses tabulated in Table 10.2 are associated with the receiver.The various modes of receiver loss are depicted in Figure 10.16.


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Figure 10.16 Receiver heat loss modes.

Receiver efficiency may be defined as the product of each loss mode efficiency.

(10.10)

where spill, absorp, rad, convandcondare efficiencies based on receiver spillage, absorption, radiation,

convection, and conduction losses, respectively.The important energy loss for the receiver originates from convection and radiation heat transfer to thesurroundings. These losses depend on the design of the receiver, whether it is a cavity or external receiver

its heated (or aperture) area, and its operating temperature. Additional factors include the local windvelocity, ambient temperature, and the orientation of the receiver.

Studies have been made on the combined radiation, free and forced-convection losses from large surfacesand tilted cavities. Siebers et al. (1982) have performed experiments on large vertical surfaces in horizontaf low, and their data are being used to predict losses from external receivers. Clausing (1981) hasdeveloped a method for predicting the natural convective loss from cavity receivers. A summary of thesestudies may be found in Siebers and Kraabel (1984).

Radiation and convection losses are primarily functions of the size of the receiver and the operatingtemperature of the system. For most currently conceived central receiver system designs, the receiveroperates at a constant temperature. Therefore, the rate of energy being lost from the receiver is essentially


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constant throughout the day (and year) and the percentage loss increases in the morning and evening. Thismakes the annual average percentage loss greater than the design point (noon) loss as indicated in Table10.2.

It is this constant receiver thermal loss rate that defines the operating threshold for the system. The systemwill operate only when the suns energy is sufficient to overcome the receiver heat loss. This thresholdusually occurs when the suns altitude angle is about 15 degrees. Operation at sun angles below this isalso constrained because of the rapid increase of heliostat blocking and shadowing.

Spillage lossor energy directed toward the receiver that does not fall on the absorbing area is a parameterof both the heliostat field and the receiver design. The heliostat surface accuracy, beam spread, mirrorcanting accuracy, and tracking accuracy all have a major effect on the flux distribution at the receiver and,therefore, on the spillage.

Spillage loss can be reduced by increasing the size of the receiver. The receiver is normally made largeenough to intercept most of the reflected irradiance from the heliostat field and to keep peak incident fluxvalues low enough for the heat transfer fluid. However, its size is limited because both radiation andconvection heat losses are directly proportional to the receiver area. Determination of the optimum receiversize requires numerous optimization studies with field receiver computer models.

In contrast to spillage, receiver absorptance is only a function of the type of coating on the absorbing

surface. Many current designs use a high-absorptance paint commercially marketed as Pyromark. Thispaint is formulated for high temperature surfaces and has an absorptance of approximately 0.95. If theabsorbing surface is inside a cavity, the effective absorptance (based on reflection back through the cavityaperture) increases to about 0.98.

The final receiver heat loss term represents the heat conducted away from the receiver. Most of this heat islost through the receiver supporting brackets that connect the receiver to the tower structure. This isnormally a small fraction of the total receiver heat loss and is kept small by minimizing the number and sizeof receiver attach points and using low thermal conductance metals such as stainless steels in theirconstruction.

10.2.2 System Performance Models

For accurate prediction of the thermal performance of a central receiver system, it is necessary to definethe flux profile produced on the receiver by a large number of representative heliostats throughout each dayof a typical year. This is done by the use of ray tracing and mathematical simulation techniques todetermine the overall optical performance fieldand the spillage spill, of the central receiver system.

Three generally available models of this type are discussed here. These were selected for their generalityand universal availability. Since they all require large, rapid computers for their operation, only a briefdescription is given here with references for further information.

HELIOS. The Helios optical behavior model was developed at Sandia National Laboratories in Albuquerque

as a general simulation model for the optical behavior of reflecting concentrators. The theoreticalfoundations on which this model is based are described in detail in Biggs and Vittitoe (1979).

The Helios model follows the incident solar irradiance through the system (including the interveningatmosphere) and includes all the factors that influence the optical performance of the collector. An

important output is the flux density pattern (W/cm2) at a grid of points on a surface (such as the receiver)and its integral over the surface.

The angular distribution of sun rays for the irradiance incident on a concentrator is modified by convolution,using a fast Fourier transform, to incorporate the effects of other nondeterministic factors such as suntracking errors, surface s lope errors, and reflectance properties. Other analytical methods are used forbeam statistics, off-axis reflecting optics, and atmospheric effects.


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An optical performance computer program called HELIOS uses the Helios optical behavior model to predictthe performance of real systems and is de scribed in Vittitoe et al. (1979). This program has been used forperformance predictions, safety studies, design tradeoffs, data analysis problems, specification andanalysis of concentrator quality, and the general understanding of solar concentrator technology.

MIRVAL. This computer model was developed to perform the same type of analyses as HELIOS, but usinga completely different optical modeling technique to perform its optical analyses. This gives it the potential

to analyze very complex but well defined systems. The MIRVAL routine is described in Leary and Hawkins(1979).

DELSOL2. The DELSOL2 computer program calculated collector field performance and performs fieldlayout and optimal system design for solar thermal central receiver plants. It is described in detail in Dellinet al. (1981). The code consists of a detailed model of the optical performance, a simpler model of the non-optical performance, an algorithm for field layout, and a searching algorithm for determination of the bestsystem design. The latter two features are coupled to a cost model of central receiver components and aneconomic model for calculating energy costs.

The code can handle flat, focused, and/or canted heliostats and external cylindrical, multi-aperture cavity

and flat plate receivers. The program optimizes the tower height, receiver size, field layout, heliostatspacing, and tower position at the user specified power levels subject to flux limits on the receiver and landconstraints for field layout.

10.2.3 SCRAM . An Approximation Model.

The overall thermal performance of a central receiver system can be predicted by using large, rapid,computer codes that require the specification of many design variables. Most of the computational effort isassociated with calculating blocking and shadowing losses. Bergeron and Chiang (1980) have developed amathematical approximation procedure that relies on data generated by the DELSOL2 code to determinemany of the field optical performance parameters but is simple, rapid, and accurate.

This program, called SCRAM,may be used to perform many design tradeoff optimization studies such asstorage sizing and load variation effects. It may also be used for predicting long-term system performancewhen combined with a system simulation mode l (such as SIMPLESYS developed in Chapter 2 of this text)and realistic weather data (i.e., the TMY tapes discussed in Chapter 4). The SCRAM model is simpleenough for use on a microcomputer and is a useful tool for learning about the performance characteristicsof a central receiver system. The SCRAM algorithm has been reprogrammed in BASIC by the authors, anda copy of the code is included in the Appendix.

Description. The approach used in developing this code was to make use of DELSOL2 to generate a largeamount of data that can be pictured as a surface in a multi-parameter space. A polynomial function is foundthat is a good approximation to this surface over the range of parameters of interest. The SCRAM program

then uses these polynomials along with field layout and solar irradiance data to predict overall systemperformance. The SCRAM approximation model can be considered an adjunct to DELSOL2.

The overall thermal energy collection efficiency of a point focus central receiver system, as defined byEquation (10.8), may be described in terms of the heliostat field efficiency and the receiver efficiency:

(10.11 )

where fieldwas defined in Equation (10.9) and receiverin Equation (10.10).

The SCRAM model accurately predicts the field efficiency and uses simple algorithms to determine receiveefficiency. This is done to simplify the mathematics and may be justified on the basis that the dominant


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losses are contained in the field efficiency and that the assumptions used to evaluate receiver thermalefficiency are less reliable. In the resulting model, receiver efficiency is computed directly and thealgorithms used may be modified as a clearer understanding of receiver thermal losses develops.

A major simplification is introduced by recognizing that all the terms in the field efficiency, scalegeometrically with tower height except for atmospheric attenuation, which is treated separately. Therefore,tower height is used as the unit length throughout the calculation until the final evaluation of the total powerreflected toward the receiver ismade.

Program SCRAM has been divided into two parts for operational ease. The first part, SCRAM1, generatesan arrayXijthat is done only once for a specific heliostat field, Program SCRAM1 writes the values of this

array on a disc naming the fileXFILE. Program SCRAM2 reads the data in XFILE along with sun angle andsolar irradiance data to calculate the overall system performance. This sequence is shown in Figure 10.17

Figure 10.17 Program configuration for SCRAM. Program SCRAM1 needs to be run only once for a particular heliostat field

Fixed Parameters. Both the heliostat design configuration and the method of field layout are fixed for theSCRAM model presented here. Modification of either of these would require multiple runs of DELSOL2 togenerate a new set of surface fit coefficients Ci,j,k, which are specified in program statements 4020 through

4100.

The heliostat specified in this model has a rectangular reflecting surface 7.4 m (24.3 ft) 7.4 m with

focused, canted mirrors. The mirrors do not have to cover the entire heliostat area. Tracking errors and


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foundation motion are both assumed to be 0.75 mrad, and mirror waviness and panel alignment errors areboth assumed to be 1.0 mrad. The canting and focusing values are the default values given in Section II ofDellin et al. (1981).

The field layout method specified for this model uses the radial stagger pattern with the University ofHouston spacing parameters defined in Equations (10.2) and (10.3). The size and shape of the field can bevaried.

SCRAM1 Input. The size and shape of the heliostat field must be defined in SCRAM1 in terms of radialsegments as shown in Figure 10.18. The field is divided into JMX segments with ANG(I) (in radians)specifying the azimuth of the center line of each segment from north. The distance from the tower to theinnermost ring of heliostats in tower heights is RI(I), and the distance to the outermost ring is RO(I). Table10.3 gives the program locations of these variables.

Figure 10.18 Heliostat field definit ion scheme for program SCRAM. The program variables defining a field are shown. Forthe field pictured, JMX =13.

Table 10.3. Input Parameters for Program SCRAM

Variable Units StatementSCRAM1


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Number of field segments JMX --- 210Field azimuth ANG(I) radians 260Inner radius RI(I) tower heights 300Outer radius RO(I) tower heights 340

Total heliostat area AM m2 180

Mirror reflectance MR --- 190Mirror density DM --- 200

Attenuation model A2TEN% 0=no, 1=yes 160

Spillage model SPILL% 0=no, 1=yes 170

SCRAM2Receiver absorptance ROPT --- 1040Receiver thermal loss RTHER W 1050

Sun zenith angle SPA degrees 1220Sun azimuth angle SAA degrees 1240Direct normal solar

irradianceDN W/m2 1260

Notes:

The dimens ion statement for JMX mus t be changed if more than 13 segments are used. An option is available (subroutine at statement 2000) to generate ANG(I), RI(I) and RO(I) for an eccentric circle field. For angle SAA, zero azimuth is due south in SCRAM (rather than due north) for programming convenience.

In addition to the heliostat field configuration, several variable characteristics of the heliostats must bedefined in SCRAM1. The reflectance of the heliostat mirrors is a variable and is specified as MR. Also, theratio of mirror area to the full heliostat area may be varied by modification of DM. The total mirror areacontained in the heliostat field, AM is the basic system sizing parameter and must be specified here.

The use of an atmospheric attenuation model and a receiver flux spillage model are both optional. Theoptical attenuation model is that given in Equation (10.6). As noted, this model represents the terrestrialpropagation loss for a clear day.

An approximate spillage model may also be used. This has been developed from DELSOL2 results ofoptimally designed fields. The receiver is a cylinder that has a diameter and height of 0.091 tower heights.The receiver spillage model is described in Appendix C of Bergeron and Chiang (1980).

SCRAM2. This portion of the program requires the input of receiver loss parameters, solar irradiance, andsun position data. Receiver loss is characterized by two variables, receiver absorptance ROPT and totalreceiver heat loss rate RTHER. Receiver absorptance depends on the radiation characteristics of thesurface or the cavity. A representative value of 0.87 is used in the listing of the program.

Because most receivers are designed to operate at constant temperature, the receiver heat loss isassumed constant throughout the day. As a first approximation, the receiver heat loss may be estimated by

(10.12)

where Ul,is approximately 35 W/m2K (6.2 Btu/h ft2F),Ar is the receiver surface area (or aperture area in

the case of a cavity receiver), and (Tout-Ta) is the temperature difference between the fluid outlet

temperature and the average daytime ambient temperature. If the receiver surface area is not known, itmay be roughly approximated by assuming that the system has a geometric concentration ratio of about250.

Solar position and solar irradiance data are also input to SCRAM2. The sun s zenith angle is input as SPAand the azimuth as SAA. For programming convenience, the azimuth zero is due south rather than due


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north as used throughout the remainder of this book. The direct normal solar irradiance in W/m2is input asDN. All of these parameters vary throughout the day and year; therefore, when configured for long-termperformance calculations, SCRAM2 would read these solar input parameters from a large array.

SCRAM2 Output. The important parameter calculated by SCRAM2 is the field efficiency (ETA/AM). This isdefined as the ratio of the radiant power incident on the receiver to the solar power incident normal to anarea equal to the mirror area. It should he emphasized that this efficiency is not based on the land areacovered, but on the total heliostat aperture area.

The total power reflected to the receiver (PWR) is simply the product of field efficiency, the total reflectivesurface area, and the direct normal solar irradiance. The total power output (POUT) to the working fluid isthen calculated by applying the receiver surface absorptance and total heat loss rate that had been inputinto the program. A collection efficiency (ECOL) equivalent to that discussed for other collectors iscalculated as the ratio of the power into the working fluid to the direct normal solar irradiance on theheliostats.

Example. The input data for an example case are contained in the program listing in the Appendix. The

case defined is for a heliostat field that has a total mirror area of 75,000 m2(246,000 ft2). The heliostatshave a reflectance of 89 percent, and mirror coverage (density) is 89.7 percent.

The heliostat field is defined by using the eccentric circle option with the outer circle having a radius of 5

tower heights. The inner circle has a radius of 0.5 tower heights with its center displaced to the south bytwo tower heights. This field configuration is pictured in the insert to Figure 10.19.


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The central receiver design described above was used along with typical meteorological year (TMY) data foAlbuquerque, New Mexico to illustrate the use of SCRAM1 and SCRAM2. Performance for one day (June20) near the summer solstice is shown in Figure 10.20. The rates of energy incident on the heliostats,reflected to the receiver, and entering the working fluid are shown. Field efficiency and system collectionefficiency are also shown for this case. If this computation is performed for every day of the year with theuse of TMY solar irradiance data, the total yearly thermal energy delivered by the system will be computed.This is the most important issue for the system designer.

Figure 10.20 System performance calculated by SCRAM2 for a 75,000 m2 centralreceiver system located inAlbuquerque, NM on June 20 using TMY solar irradiance data.

Program SCRAM2 may also be used as a subroutine to SIMPLESYS. In that case, SCRAM2 would replacestatements 420 through 550 of SIMPLESYS with QC (in SIMPLESYS) being set equal to POUT (inSCRAM2) and the final GOTO statement in SCRAM2 removed.

References

Battleson, K.W.(1981), Solar Power Tower Design Guide: Solar Thermal Central Receiver PowerSystems, A Source of Electricity and/or Process Heat, Sandia National Labs Report SAND81-8005, April.

Bergeron, K. D., and C. J. Chiang (1980), SCRAM: A Fast Computational Model for the OpticalPerformance of Point Focus Solar Central Receiver Systems, Sandia National Labs Report SAND80-0433April.

Biggs, F. and C. M. Vittitoe,(1979), The HELIOS Model for the Optical Behavior of Reflecting SolarConcentrators," Sandia National Labs Report SAND76-0347, March.

Clausing, A. M. (1981), An Analysis of Convective Losses from Cavity Solar Central Receivers, SolarEnergy 27(4), 295.

Coggi, J., and H. Eden (1981), Solar 10 Megawatt Pilot Plant Performance Analysis, The AerospaceCorporation, Report No. ATR-81 (7747)-1, February.

Dellin,T.A., M. J. Fish, and C. L. Yang (1981), A Users Manual for DELSOL2: A Computer Code for

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Calculating the Optical Performance and Optimal System Design for Solar Thermal Central ReceiverPlants, Sandia National Labs Report SAND81-8237, August.

Holl, R. J. (1978), Definition of Two Small Central Receiver Systems, Sandia National Labs ReportSAND78-7001, April.

King, D. L. (1982), Beam Quality and Tracking Accuracy Evaluation of Second Generation and BarstowProduction Heliostats, Sandia National Labs Report SAND82-0181, August.

Leary, P., and J. Hawkins (1979), A Users Guide for MIRVAL Computer Code for Comparing Designs ofHeliostat Receiver Optics for Central Receiver Solar Power Plants, Sandia National Labs Report SAND77-

8280, February.

Lipps, F. W., and L. L. Vant-Hull (1978), A Cellwise Method for the Optimization of Large Central ReceiverSystems, Solar Energy 30(6), 505.

Siebers, D. L., and J. S. Kraabel (1984), Estimating Convective Energy Losses from Solar CentralReceivers, Sandia National Labs Report SAND84-8717, April.

Siebers, D. L., R. G. Schwind, and R. J. Moffat (1982). Experimental Mixed Convection From a Large,Vertical Plate in a Horizontal Flow, in Proceedings of the Seventh International Heat Transfer Conference,Munich, vol. 3, pp. 477-482, September 6-10.

Sterns Roger Engineering Company (1979), Tower Cost Data for Central Receiver Studies, SandiaNational Labs Report SAND78 -8185, June.

Vittitoe, C. N., and F. Biggs (1978), Terrestrial Propagation Loss, paper presented at the AmericanSection, International Solar Energy Society Meeting, Denver, Colorado, August.

Vittitoe, C. N., F. Biggs and R. E. Lighthill (1979), HELIOS: A Computer Program for Modeling the SolarThermal Test Facility, A Users Guide, Sandia National Labs Report SAND76-0346, March.

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