A Solar Collector Based on a

High Aspect Ratio Conical Frustum

The Concept:

This concentrator is in the form of a high aspect ratio right conical frustum (HARF).

A conical collector works when a reflective inner face concentrates rays parallel to the axis of the cone on to the axis of the cone. This is most effective when a right angle cone is used.

What is a High Aspect Ratio Frustum:

A frustum is what is left of a cone when a smaller cone is cut from the top. The aspect ratio refers to the relative thickness of the frustum compared to its diameters, and a high aspect ratio implies a large difference. In this case a much larger diameter than thickness.

In a high aspect ratio frustum collector most of the cone is cut away to improve the concentration ratio at the focus, which works because a circle’s area increases by a square of its radius.

This means, for example, that the outer 50% of a circle's area occurs in the last 29.3% of the radius and the outer 25% of area in the last 13.4% of the radius. By contrast the inner 25% of the radius only accounts for 6.25% of the collector area, or 1/7 of the outer 25%.

Using a right angle cone, in which the focal interval necessarily equals the radius of the base, each 25% of the focal interval will collect, from point to base, incident radiation in the proportions 6.25%, 18.75%, 31.25% and 43.75% respectively.

The principal of the HARF is to exploit this geometrical feature to maximise the concentration ratio, keeping the form and structure simple and allowing higher receiver temperature or more optimal use of concentrator photo voltaic cells.

History:

Conical collectors are not common but are not new. They are mentioned generically on p335 of Solar Engineering of Thermal Processes (Duffie and Beckman, 2^nd Edition, Wiley) and have been used in practice as described in Revisiting Solar Power's Past By Charles Smith which is published widely on the Internet and can be found at http://www.coronatech.net/History of Solar Power.htm amongst other locations.

The images below are of late 19^th century French and early 20^th century American designs described in Smith's article.

How to generate a HARF:

A cone can be fashioned from a sector, ie. that part of a circle bounded by two radii and the included arc.
A right cone is fashioned from a sector with an included angle of (approx) 254.56°.

Taking an annulus of this sector will produce a frustum.

This is a simple form to generate, lay out and produce.

Why a High Aspect Ratio Frustum:

A HARF provides higher concentration than a parabolic trough and is simpler to construct than a parabolic dish. Like a parabolic trough a conical frustum’s reflecting surface is only curved in one plane and can be simply generated by bending. A HARF, like a parabolic dish, requires two axis tracking but the shape has advantages among which are that it is self draining and the surface easy to maintain.

As explained earlier, using a thinner annulus produces a higher relative concentration ratio due to disproportionate shortening of the receiver. Annuli of the order of 20% or less produce very effective concentration ratios that should, say, produce superheated steam with much less difficulty than parabolic troughs and much less expense than parabolic dishes.

Concentration ratios comparable to parabolic dishes can be achieved using a curved secondary reflector or a conical secondary reflector and Fresnel lens combination.

Good results can be obtained for an annulus as large as 25% of the major radius.

That is the ratio used in the experimental solar oven below which achieved sustained temperatures of 190° Celsius in full sun, despite the low ratio and relatively unsophisticated collector and receiver.

Building a Simple Solar Concentrator using a

High Aspect Ratio Frustum

A WARNING:

Concentrating sunlight is potentially hazardous.

The dangers of fire, burns and eye damage are real and appropriate precautions must be taken whenever the device is exposed to sunlight.

The Experimental Solar Oven:

The collector area is 0.25 square metres and therefore delivers approximately 250 watts in full sun.
The receiver is a cylinder of 7 cm diameter and 10 cm length having an area of 220 square cm.
This gives a concentration ratio of 11.36 to 1.

The original collector was started a few years ago to prove the HARF concept, using avmat engineering, that is, whatever was at hand. In this case plywood, a space blanket and glues various. It is all pretty basic and rough but it is of interest as to how much can be done with so little.

It has undergone several transformations which accounts for its slightly Byzantine appearance. It was initially fitted with an un-shrouded copper tube receiver circulating water to a home made calorimeter. The results were just as the textbook predicted so work was begun on a one square meter collector which is ongoing.

Spotting a large unused glass jar lying around in the kitchen was the inspiration for re-cycling the prototype into a mini oven.

The Collector:

The reflector is aluminised mylar (Space Blanket) on an adhesive plastic substrate (Contact) glued to a frustum of laminated cellulose fibre (3 ply - not a brand name). It is a fairly important component so I will go into some detail about it.

The plywood frustum surface is coarse and the aluminised mylar very thin so some self adhesive plastic sheet (brand name Contact) serves as an inter medium. The mylar is metal sprayed on one side only and the coating is fragile. It will not weather and to avoid the adhesive effecting the silvering, the uncoated side was married to the adhesive side of the plastic sheet, producing a fairly smooth robust reflective surface. Contact adhesive (brand name Selleys I suspect) was used to stick the reflective sheet to the ply wood frustum.

The result was effective beyond reasonable expectations as the aluminium coating is a low quality reflector, it is not truly 'specular' when it reflects. A simple test is to use a laser pointer to see what happens to the reflected beam. In the case of the mylar the laser 'spot' becomes a fuzzy blur about 2 cm across. This restricts the minimum size of the receiver and therefore the maximum concentration ratio.

I have since discovered that a better technique would be to use a sheet metal or plastic frustum and to 'stick' the aluminised side to the metal with (say) automotive grease or Vaseline and tape the edges. This method is simpler and the reflective surface will weather better.

The best technique is to use a purpose made adhesive reflective film. I am using ReflecTech solar film for my next project. It is highly specular and weather resistant and is being tested with favourable results, its working life is currently estimated at ten years. (www.reflectechsolar.com). I expect to get much higher effective concentration using this material.

The frustum is attached to a stable base (more 3 ply) and the whole affair is mounted on horizontal trunnions.

The base is stabilised with intersecting ribs that leave an opening in the centre for mounting receivers and running tubes and/or wires.

The use of plywood for the frustum was an unfortunate choice as its 'grain' became obvious as soon as it was curved. Extensive ribbing was required to correct the distortions. Again, a better choice of material would have been sheet metal or plastic.

The trunnion arms are mounted on a tricycle undercarriage where the 'front' wheel is set at right angles to the axle of the 'rear' wheels. The result is that the base pivots around a vertical axis providing azimuth to the trunnions elevation. The elevation is motorised, as will the be the azimuth by way of the 'front' wheel of the base. This is a work in progress.

The elevation was motorised first as a proof-of-concept of sun tracking circuitry and because it was a huge nuisance trying to hold it 'on sun' in elevation. The drive has a small drum on the output shaft and simply winches the collector up and down.

The Tracker:

The inspiration for the tracker was taken from the archives of Duane C Johnson on his remarkable website www.redrok.com.
Duane has published several circuits using LED sensors and a couple of these were hybridised to get the result required.

The tracker uses green LEDs as detectors and a few transistors to switch a pair of double pole double throw relays. Between them the relays provide the three output states (forward/off/reverse) for the small motor/gearbox. The choice of drive was inspired by a Renew article of several years ago that pointed to small battery powered rotisserie motors as excellent candidates for use in flat panel trackers. These little guys are cheap, nasty and basic. They are driven by a 1.5 volt motor, have a 1200:1 reduction gear train and a robust alloy output shaft. They have a single D cell holder built in and when fired up give the impression could turn a spit for quite a while.

The trackers performance exceeded expectations, being stable and sensitive to between one and two degrees of sun movement. The results are achieved in part by 'shading' the sensors using reasonably long gnomon of about 120 mm.

The motor sized current requirements are delivered by the on-board 'D' cell. The control circuit requires about 5 or more volts but only modest current to drive the relays so to remove the need for a dual voltage power supply the circuit is powered by a small array of photo voltaic cells set around the top edge of the collector. It was just as easy to do that as cobble together a battery pack and it has a gee-whiz factor. There are enough cells to power the motor also but that will require some additional circuitry to manage the start up current draw. This is also pending work.

The Receiver:

The receiver is a a thin wall tube of copper shim with an untreated surface. Notice how the copper has started to change colour where the concentrated light strikes it.

The tube end is sealed with an insulating lid and the whole is insulated with a still air gap, courtesy of the aforementioned, generously proportioned, glass jar.

The receiver assembly is shown with the less-than-perfect reflector behind it. In hindsight a can of similar dimensions would have worked as well given a coating of copper plating or matte black.

Testing the Contraption:

Preliminary runs had boiled a small container of water but this test was to determine the maximum achievable temperature.
The test was done mid afternoon on a bright Autumn day. The temperature was in the low 30's Celsius and the humidity around 20%. The digital thermometer's ball sensor was inserted in the 'oven' space through a small hole in the base.

Nothing fancy was attempted.

Once the tracker was switched on it moved straight on sun and azimuth was adjusted via gentle big-toe-nudges.

Some condensation appeared inside of the glass and was wiped out without producing blisters (it was reasonably warm by this time). The digital camera worked overtime as the temperature reading climbed to ever dizzying heights until it became apparent that, as the sun dropped lower, the best result had been and gone. Temperatures between 180°C and 190°C were maintained for about an hour and a maximum temperature of 190.4°C was achieved on this occasion.

What's Next:

The plywood wonder was slated to be replaced by a one square metre collector with a higher aspect ratio based on acrylic mirror. While the mirror itself has excellent reflective and mechanical properties (aside from being difficult to work) the first attempt at a space frame support sent us back to the drawing board. There are also questions about the long term stability of acrylic when used outdoors. Apparently it is hygroscopic and prone to warping when exposed to weather.

Space frames are fiddly and labour-intensive and I have always been partial to the effectiveness of fastening large sheets and strips of stuff along their edges so a monocoque solution has hit the conceptual runway and a 0.3 square metre prototype using clear pvc sheet and ReflecTech film is under construction.

Come the Revolution:

When the HARF collector was first conceived it was to power a heat engine.

I consulted a photo-voltaics expert who told me that current cell technology could not sustain even modest concentrations, the best being the product used in orbital satellite's solar arrays, which I knew from my own reading had to be rated at about four times terrestrial cells.

It was few years later that concentrator photo-voltaic (CPV) appeared on the edge of the radar.

Manufacturers now seems to be leap-frogging each other, and at writing the good offerings are rated around 30% efficient at a hundred or more suns and there are already a couple of commercial offerings based on this technology nearing general availability.

These great numbers also mitigate against the high cost of the energy inputs that silicon cells have always been burdened with. I was once told, smugly, by a pro-nuclear advocate that mono crystalline silicon PV took more energy to make than it could capture in its working life. Enter concentrator PV, which could presage a true 'solar electric' revolution.

copyleft © Feb 2006 I Sykes.