Linear Fresnel Solar Concentrator

The solar concentrator arrangement proposed for the factor e farm solar turbine implementation is of the linear fresnel type. Linear, as it's focus is a line as opposed to a point, and fresenl as it is made of many small reflectors as opposed to a monolithic parabolic trough.

This is a discussion of the theory of linear fresnel solar concentrators, and a justification of the design decisions siezed upon by the factor e farm team.

Estimating available energy
to be added soon. should cover:

1) total insolation

2) air mass losses

3) declination losses

Given an estimate of available energy for a particular day of the year, actual performance estimates can be made, and (once operable) efficiencies measured.

Implementation dependant losses and issues
In any orientation, the sun must be tracked minute by minute. The complexity of this tracking varies however with different orientations.

Also, since a linear focusing system tracks in only one dimension, it suffers losses due to rays parallel to the axis of the trough coming in at a shallow angle and (though hitting the mirrors) missing the collector. The efficency of a linear collector experiencing edge effects is given by e=(L-o)/L where L is the length of the collector and o is the average offset caused by the angled light. o is given by h*Tan(theta) where h is the average distance between the collector and the reflectors and theta is the angle of the incident light in the plane parallel to the axis of the reflectors.

Lastly, the effect of the mirrors not being perpendicular to the sun is a loss in flux reflected by the mirror. The effect varies with the half angle between the sun and the collector and the efficiency of light reflected is given as the cosine of the half angle (e= Cos(1/2 theta)

There a three common orientations:

1) polar

2) North-South axis

3) East-West axis

Each of these three possible orientations has associated tracking issues and also efficency losses specific to that orientation (end losses and half angle losses).

The Polar orientation focuses on a line parallel to the pole of the earths rotation, that is, inclined and running north-south. Tracking here is the simplest, as the mirrors need only rotate at half the angular speed of the earths rotation. However, due to the need to incline the absorber and reflectors, this orientation requires more structural considerations (and expenditures) than a flat (of the ground) approach. Thus, the Factor E farm team has decided against this.

The North-South orientation is similar to the polar orientation, but may be flat on the ground. Tracking may be as simple as in polar or it may have hidden complications (We don't know). Due to the latitude of the Factor E farm, the end losses associated with the shallowness of the suns angle parallel to the axis of the collector would be severe in winter if this orientation were laid flat on the ground. Since we do not wish to tilt the array towards the south for construction cost reasons (same as polar), and wish to collect energy during the winter, The factor E Farm team has shied away from this orientation as well. (calculations at Solar_Collector_Calculations

Also, the reflectors move between plus and minus 22.5 degrees of tilt from 9am till 3pm. Thus there will be a maximum half angle loss of cosine 22.5 and a total daily loss of the integral of cos (1/2 theta) from theta =-22.3 to 22.5

The East-West orientation offers possibly the most complex tracking. The angle of the mirrors is determined by the vector towards the sun projected onto the vertical axis running north-south. During the winter, the mirrors tilt down towards the south, coming up till noon and decreasing again. The severity of this angular adjustment decreases from winter solstice till equinox, when no angular adjustment is needed (the plane of the sun's motion is co-incident with the plane of the parabolic trough), and reverses direction during the summer, as the sun rises slightly north and comes slightly south by noon. This tracking will likely need to be accomplished by sensors rather than formulas.

End losses in the east west orientation are maximum in the morning and evening, with almost none at noon. But as the sun is not inclined to the axis of the trough more than 45 degrees during the time of useable insolation, these losses are never as severe as winter end losses in the north south arrangement (where the noon sun is lower than 30 degrees, and the pre and post noon sun even lower. Thus, this arrangement will perform most satifactorily of the three in a flat on the ground implementation.

As the exact tracking for this orientation is not known by us, the exact half angle losses cannot be calculated over a day. Over the year however, the noon time losses are much less than the north south orientation, as the sun only moves from -23 degrees to +23 degrees, giving a half angle change of -11 to +11 degrees.

Given this information, the factor e farm team has selected an east-west orientation.

wall vs field of slats
With many slats and a single absorber, the question comes up:
 * put the absorber high in the air, and put a field of slats near the ground to the south (and possibly also to the north), or
 * use the slats to cover a south-facing wall, like the slats of a window blind, and put the absorber to the south (possibly on the ground, or possibly high in the air -- but not so high it shadows the slats in the winter).

Mounting slats to a wall significantly reduces the cost of making the array hail-resistant or hail-proof. Mounting slats to a wall results in needing to clean the slats less often, because any given piece of dirt is more likely to fall off a near-vertical slat than a near-horizontal slat. Mounting slats to a south-facing wall seems like it would collect more sunlight in the winter.

Mounting the slats near ground level puts the moving parts where they are easier to access and repair. Mounting the slats near ground level requires less structure cost per slat (if you ignore the cost of hail-proofing). Mounting the slats near ground level works fine even near the equator.

For now we choose to put the absorber high in the air, and the slats near the ground, because that is a proven system.

Reflector Design
There are two possible materials from which to make the reflectors: glass mirrors or aluminized polymers (mylar, Reflect-tech).

Also, the reflectors could be many and flat, or fewer and curved reflectors.

Aluminized polymers have a short life (with reflect-tech claiming about a decade worth of usage), as they eventually succumb to Ultra Violet degradation and moisture wicked through the adhesives used to bind the polymer to a substrate. We have yet to find suitable backing for the thin films. We tried various wood products (oriented strand board, laminated medium density fiber board and thin ply wood). The Oriented strand board was not smooth enough to give an adequate reflection once the mylar (our cheap test for reflect-tech) was adhered to it, and there was general concern that the wood products would warp over the course of the years exposed to the elements. Tyvek house wrap was suggested but was not tried, though simulations with a tarp not adhered to the mylar gave decent results (is stretching of the film is adequate, which we found difficult to achieve). Reflect-tech advises the use of aluminum sheets (very expensive per square feet). Reflect-tech itself is expensive (2.00 per sqaure foot) given its relatively short life span, making the lifetime cost of a system prohibitive. Required maintenance may also be heavy, as dirt adheres readily to the surface, and care must be used when cleaning (mylar streaks easily we found)

Glass mirrors have a much longer life span than polymers (30+ years according to doug woods of Cassandra's Green Company). They may be curved to a focal length of 12 ft maximum and do not require a backing. We broke one mirror by over tensioning it, and though doug woods has left his systems in the elements for thrity years, we have some doubts about its durability in a sever hail storm or very severe winds. Cheap 1/8th inch glass mirrors can be bought at huge chain hardware stores for $1.50 a square foot. Low iron, silver palladium glass mirrors can be bought for 1.75 a square foot by the train car load. Possibly we could by small sets at a reasonable price from Mr. Woods.

As far as curvature goes, there are structural advantages to having fewer reflectors, each with a concentration ratio of 5 or so. Although a perfect parabola could have a concentration ratio of 50 or more, there are geometric limitations to a system which must track the sun. Also, we found a perfect parabolic shap difficult to achieve under non-tracking conditions. Our best results for curvature where with 2'x 1' panels of glass, with an image size of just under an inch and a half (concentration ratio of about 20), with about seven inches of unconcentrated light around the focus (ie: only 75% of the mirror assumed the curve, since the ends, for whatever reason, do not curve). image sizes of about 3 inches were achieved with mylar on thin plywood, but this could not be achieved over the entire length of the focus.

the limits of concentration
Focusable light in this system moves off axis in two dimensions, yielding two complications to a perfect focus over the course of the day and year.

Parallel-axis abberations

(illustration soon)

As light travels down different angles parallel to the axis of the concentrator, it travels different distances before reaching the absorber. Thus, if the array is in perfect focus at one angle, at another angle it will be out of focus. The percentage out of focus is inversely proportional to the amount of concentration possible. At twice the focal distance (%100 out of focus), the image is the same size as the width of the reflector. At 1.5 the focal length (%50), the image will be half the width of the reflector.

In an east-west axis system, the sun moves from 45 degrees at 9 am to 0 at noon to 45 again at 3 pm. If this system were perfectly in focus at noon, the extra path length of Square root of two (~1.4) in the morning and evening would correspond to %40 out of focus or 2.5 times concentration. The best achievable theoretical fix would be to have the system focused perfectly at 22.5 degrees, so that the absorber is too close at noon and too far at 3pm, but neither as badly as if the system were in focus at noon. This corresponds to a maximum concentration of 3.27 (change in path length is 1/cos45 - 1/cos22.5 = 1.41 - 1.08 = .33 -> % out of focus of .33/1.08= %30.5). since the sine changes quickly around 45 degrees, greater ratios could be obtained by sacrificing efficiency at the extremes.

A north south axis orientation will experience this distortion less severely due to the fact that the seasonal angular deviation of the sun is much less than its daily variation.

Perpendicular-axis abberations

There are (at least) two parabolas passing through a given point that will focus perfectly at one point. (illustration soon). The first is a parabola has its axis parallel to the sun's rays with the absorber at its focus. The second is one with its axis at the half angle between the absorber and sun, with a focal length such that the absrober lays on the focal plane of the parabola (a plane perpendicular to the parabola's axis and passing through the focus. The image created by a parabolic reflector is undistorted on this plane). This second parabola will be useful in analyzing this type of distortion (and is also easier to implement)

As the sun moves and the mirror moves to track it, the focal plane of our perfect reflector rotates around the reflector's pivot. thus, the absorber, once in the focal plane is there no longer. (illustration soon). The ideal focal length of our mirror would then be Cos(theta) of its previous value to maintain focus on the absorber. Because this effect depends upon the half angle, it is much less noticeable than the parallel axis phenomena. The maximum deviation in an east-west axis system is very small (1-Cos(11 degrees)=.018 or 1.8%), thus this effect is negligible in our system. It is more sever in the north-south system (1-cos(22.5) = 7.6%), but still hardly noticeable.

Recomendations
The conclusion of this report is that the Factor E farm linear fresenl collector should have an East-West axis and use 1/8th inch untempered glass mirrors. Mirrors closer to the absorber (<~14 ft) should be flat, whilst mirrors more distant should be curved so as to focus perfectly at ~11am half way between the equinox and the solstice. If at the time the mirrors are focused it happens to not be near that date, its alright because seasonal drift of the focus is minimal (1.8%).

Further steps
The use of a secondary reflector of the compound parabolic type would be highly beneficial, and inquiries should be made into its possible manufacture or purchase.

Estimations of available insolation should be made for several specific days throughout the year, and for noon time throughout the seasons.

Absorber height decided upon, which will be based upon available construction methods.

A site chosen and roughly surveyed. (general strike and dip of the working surface)

Details of the mirror row's positions should be sketched, with proper spacing for minimal shading in the winter with reasonably efficent land use for summer radiation considered.

Expected system performance estimated.

and on from there...


 * Wikipedia: Concentrating Linear Fresnel Reflector