Ideas

Ideas for a solar cooker with a conical concentrator

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Figure 1. Experimental conical reflectors in Korea, as shown in a 2018 science paper [1]. The design shown has the heat receiver along the axis of the cone, tracks the sun and has a 45° cone angle. The proposed design of this article makes the same three choices. The literature includes systems where these choices are different.

One attraction of a parabolic trough as a solar concentrator is that the reflector can be made by bending sheet material. This is in contrast to the parabolic dish where the reflector is curved in three dimensions and cannot be made from a sheet. However there is another shape that can be made by bending a sheet: the cone. This article refers to some of the literature, which shows that the conical solar reflector has been the subject of research for decades, and proposes some possible approaches for a home-made conical reflector.

Scientific and practical literature

The cone is always truncated, meaning that the reflector does not extend to the apex of a complete cone but stops at its own base, defined by a plane perpendicular to the axis (See Figure 3). The position of the base relative to the height of the cone varies. The system [1] shown in Figure 1 is an extreme case where there is almost no truncation.

In broad terms, there seem to be two different approaches. One assumes the axis of the cone is always pointing at the sun and analyses exactly how rays arrive on the target, after one reflection. In these the heat receiver or target is usually on the axis of the cone.

Figure 2. “Conical concentrator with its parameters as proposed by Schmidt-Kloiber et al.” - a figure and its caption in the review article [3]. (The original paper was not available on the open web in June 2024.) The figure is an example of the second kind of approach, with analysis of rays not parallel to the cone axis and with multiple reflections. The review refers to additional related papers.

The other approach tolerates some misalignment with the sun and hopes that most rays somehow arrive on the target, potentially after multiple reflections down the cone. In the research literature the heat receiver is often the entire base of the reflector. The cone is typically steeper than 45° (otherwise rays parallel to the axis would not continue down the cone after the first reflection).

In the first kind of approach, Cobble in a 1963 paper made a geometrical analysis based on the finite size of the sun to derive the maximum concentration obtainable from a conical reflector with the heat receiver being either cylindrical or conical and on the axis of the reflector cone. [2]

He found the cone angle for maximum concentration was 45°. For a cylindrical heat receiver maximum concentration is with truncation of the cone such that the ratio of the distance of the cone apex to the base of the reflector is ~0.873 times the distance of the cone apex to mouth of the reflector.

Table 1 shows the figures presented in his conclusions which noted that a conical reflector with either heat receiver was theoretically capable of higher concentration than the parabolic trough. “On this basis, it is theoretically the best type of singly curved concentrator that has appeared in the literature.”

Table 1: Maximum theoretical concentration of solar radiation given in [2] for four different concentrator configurations.
Configuration Max concentration
Parabolic trough, flat receiver ~107.3
Parabolic trough, cylindrical receiver ~68.7
Conical reflector, conical receiver ~212.6
Conical reflector, cylindrical receiver ~188.4

Figure 2 shows an example of the second kind of approach with misalignment and multiple bounces. Further references are not given here because the design here will use the first approach and track the sun.

Practical plans for conical reflector solar cookers on the web in 2023 included https://solarcooking.fandom.com/wiki/Conical_Solar_Cooker which included “It can be made in a few hours using cardboard and wrapping paper (Mylar) and, according to the designers, can achieve temperatures above 200°C (392°F) when using a cooking bag.”

There were several other designs using cones on the same website including one using sheet steel covered by reflecting foil at https://solarcooking.fandom.com/wiki/Conical_Cooker “When using a conical cooker with a diameter of 80 cm, 1 liters (0.3 gal.) liter of water can be brought to boiling in about 20 minutes.”

Possible design approaches and considerations

b h h
Figure 3. The outline of a solar kettle with a 45° conical reflector. The diagram shows a cross-section along the axis of the cone. Sunlight coming down the page is concentrated onto all sides of the bottle in the centre. The cone is truncated at the reflector's base, which has radius b. Sunlight falling onto the base is not caught. The effective receiving area normal to the sunlight is π(2b + h)h.

Figure 2 shows the outline of a 45° conical reflector. The size of the area receiving sunlight is the size of the area of the disc defined by the rim of the reflector minus the size of the area of the disc defined by its base.

A = π(h + b)2 - πb2 = πh(2b + h)

Power estimates

The parabolic trough described the earlier article [4] was found to heat about 350mL of water in a copper pipe in about 10 minutes with a total aperture of 0.81 square metre.

In a subsequent article [5] a double-walled glass bottle was heated using the same trough. This took 36 minutes to heat 410g of water from 30°C to 100°C. ([5], Figure 5). As calculated in that article, the effective aperture receiving sunlight for the bottle was (0.81 - 0.045)x0.21 = ~0.16 square metre.

If the same double-walled bottle were used here as the heat receiver, then with h = 0.21 to match the height of the bottle and with b = 0.6, by the expression above the effective aperture would be ~0.93 square metre.

Other things being equal, this area represents nearly 6 times the power applied to the same bottle, so we could hope for at least the corresponding factor reduction in heating time, possibly making the corresponding time around 6 minutes.

This aperture area would exceed the area in the original parabolic trough with the copper pipe. However the reflector would be relatively large, being 1.62m outside diameter.

Advantages of 45° cone angle

The 45° cone angle means that the rays would strike a cylindrical heat receiver perpendicular to its surface. In the case of a glass bottle this might minimise reflection from the glass. It also means that the diameter of the target can be changed experimentally without changing the amount of light intercepted.

Tracking the sun

The parabolic trough kettle described in [4] is focused by changing its angle of elevation but once this is done experience has confirmed that it does not need to be adjusted during the heating of a single batch of water, except early or late in the day when the sun is changing elevation more quickly.

So the parabolic trough has the advantage that no attention to tracking is required during each batch heating. However the design of [4] cannot be left unattended because when it boils it will eject the water from the pipe. This is potentially hazardous and means the water is lost. The pipe will then overheat, perhaps then causing unwanted oxidation (although this aspect has not been investigated).

So if you cannot go away and forget a kettle while it is heating, then there is not much additional overhead in having to manually adjust it to track the sun during the heating. This will be the approach used for the conical kettle. The usability of this remains to be empirically tested.

Amount of reflector material

The area of reflector material used is A√2. In other words it uses about 41% more reflector than its aperture.

For comparison the parabolic trough described in the earlier article had an aperture of 0.81m wide using reflector material 0.9m wide, meaning it used only about 11% more material than its aperture.

This means that the conical design uses about 27% more reflector material for a given aperture than that particular parabolic trough, although in general the amount used by a parabolic trough depends on how deep the trough is relative its focus.

In addition cutting the material for the cone, which means cutting part of a circle, is likely to result in off-cuts which cannot be used for anything else. In contrast the parabolic trough uses a rectangular shape which matches the kind of shapes material is usually supplied in. However, it might be possible to make the reflector of cheap film, as noted below.

Temperature inversion

A possible problem for the cone can be seen from Figure 3. The wider end of the reflector receives more sunlight than the other end because the circumference is larger. The wider end heats the top of the bottle and the narrower end heats the bottom of the bottle. If the bottle is a cylinder, having a uniform amount of water at each height, then water at the top will therefore become hotter than at the bottom. Unfortunately under these conditions there will be no convection and the hotter water will remain stratified at the top. Of course the situation is not as extreme as implied by a casual glance at Figure 3, because the cone will not be pointing directly upwards (at least, not in England). Nevertheless the hotter water in general will be nearer to top.

Possible solutions would be to use a heat receiver that is itself somewhat conical, so the amount of water could be proportional at each height to the circumference of the associated part of the reflector. However commonly found bottles and cans and other items that might be used experimentally as heat receivers are often cylindrical and rarely tapered, especially not wider at the top. So this approach might lose the advantage of being able to experiment with commonly found items. And it would mean radiation was no longer incident perpendicular to the walls, assuming a 45° cone.

Another possible mitigation might be to intermittently shake or invert the bottle by hand.

Another possible mitigation might be to make the bottle taller than the reflector. Then it could contain extra water at the top beyond where its walls are irradiated. (Those parts of the walls should instead be well insulated). We might then for example try to match the total received radiation per unit mass of water in some defined bottom part of the bottle to the total received mass of radiation per unit mass of water in the remaining top part of the bottle. Further analysis and/or empirical testing is needed to understand how this would affect the temperature profile along the entire length.

Possible construction materials

The reflector could be supported by two circular rings, one around the rim, and one around the base. For a design with h ~0.2m, the distance between the rings would be ~0.28m. With this distance being quite small, one possibility to explore is a low-cost reflector made of unsupported aluminised Mylar (PET) film stretched between the two rings. A way to attach the film to the rings would be necessary. Open questions are whether wind could damage the film or deflect it enough to reduce the optical efficiency.

For the rings themselves one possibility is tubular aluminium. In June 2024 UK company Gardening Naturally was advertising on its website “Round Hoops For Garden Tunnel Cloches” described as “semi-circular aluminium garden hoops” at https://www.gardening-naturally.com/round-aluminium-hoops . In photographs these looked semi-circular. Two of these would be joined to make a full circle.

There were two sizes, with the smaller of radius ~0.6m offered at £18.49 for two, and the larger of radius ~0.8m.

If the smaller hoop were used around the base of the reflector and the larger around the rim and the difference of 0.2m would suit the proposed height of the heat receiver.

An cheaper alternative might be to make hoops using MDPE (medium density polyethylene) water pipe which, coloured blue, is widely used in England for mains supply.

Terminology

CSC
Conical solar concentrator (used in [1])
PET
Polyethylene terephthalate

References

[1]

Design and Performance Analysis of Conical Solar Concentrator, Mun Soo Na, Joon Yeal Hwang, Seong Geun Hwang, Joo Hee Lee, Gwi Hyun Lee, Journal of Biosystems Engineering, 43(1):21-29. (2018. 3)

In March 2023 this was available on the web as a PDF with SHA256 hash 11656a4c2680f6834cff68bb404e06f04b67f852407821ae7ccb68ce3e0ed8b4

[2]

Analysis of a conical solar concentrator, M.H. Cobble, Solar Energy, Vol. 7, No. 2, 1963

In March 2023 this was available on the web as a PDF with SHA256 hash 1b2c7e9c2b26ffe398c912b42498cc3b11571c5ff46acede1ce575fbaf878701

[3]

Photovoltaic Concentration: Research and Development, Sarah El Himer, Salima El Ayane, Sara El-Yahyaoui, J. P. Salvestrini and Ali Ahaitouf. Energies, November 2020

In June 2024 this was linked from https://www.mdpi.com/1996-1073/13/21/5721 as a PDF with SHA256 hash 9f6efdd5c7ea7a355823441e66895dc638afcc83cb72ef100cade60a3d65f98b

[4]

A home-made solar kettle, its performance and its problems, Stephen Hewitt, 28 October 2022 (link below)

[5]

Higher net power from a solar kettle heating water in glass rather than copper, Stephen Hewitt, 29 March 2023 (link below)

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