An absorber captures radiant energy and makes that energy available in another form. In the context of this project, an absorber captures solar energy and makes it available as thermal energy.
As I worked with concentrating collectors, so much of the solar energy focused on the absorber was being lost by reflection that I needed to wear welding goggles to protect my eyes. This page describes the result of my effort to design an absorber so as to minimize reflection and re-radiation losses.
Solar energy is used here to refer the stream of photons emitted by the sun and impinging on the earth.
Absorption is the phenomenon that takes place when a photon impinges upon an atom, thereby increasing the atom's energy content.
Reflection is defined as the immediate re-emission of an absorbed photon.
Re-radiation is defined as the delayed emission of a previously absorbed photon.
Energy absorption can be improved by featuring a surface with V-shaped depressions in such a way as to increase the number of reflections at the surface of the absorber.
The method works on the principle that with each reflection, some of the incident energy is imparted to the reflecting surface, and that by increasing the number of reflections, the amount of absorbed energy is increased.
The efficiency of this method can be optimized by making V-shaped grooves adjacent to one another, by configuring the grooves with the smallest possible interior angle, and by configuring the grooves in such a manner that the bisector of the interior angle is directed along the path of the incident energy.
The maximum number of reflections can be determined by dividing the angular measure of a half-circle by the interior angle of the V-groove. For example, a 90-degree interior angle would produce two reflections, a 15-degree interior angle would produce twelve reflections, a ten-degree interior angle would produce eighteen reflections, and a one-degree interior angle would produce 180 reflections.
The simple geometry of this method results in the greatest number of reflections (with the largest incidence angles) taking place near the interior apex of the V-groove, which concentrates the heat energy there and so makes the method particularly useful for those applications for which it is desirable to harvest the incident energy – as in, for example, concentrating solar collectors using parabolic mirrors or heliostats using multiple mirrors. In shielding applications this behavior facilitates removal of the intercepted energy.
The method is applicable to all particles/waves to which the absorber material is non-transparent and, in the case of particles, will function best when the width of the V-groove opening is much larger than the greatest dimension of the incident particle – other than for this aspect, scale is not generally a consideration.
It’s immaterial how the V-grooves are produced – typical techniques might be extrusion, casting, molding, embossing, milling, sawing, etc. and will depend on the absorber material selected, the interior angle chosen, the depth/spacing of the V-grooves, the specific absorber shape, and production cost factors.
The method can readily be used in conjunction with other absorption techniques such as plating and selective coatings, and will have a multiplicative, rather than additive, effect on their efficacy.
The method is applicable to planar and non-planar surfaces, and the groove size may range from microscopic to "very large" to suit specific application design and production requirements.
History and Background
While designing flat solar heating panels, I began looking for ways to "game" the loss mechanisms (reflection, radiation, conduction, and friction) so as to use them to contribute to energy gain. Conventional wisdom dictated that absorber surfaces be flat black – but I observed that absorber surface and geometry could use reflectivity to produce gains instead of losses.
Later work with heat engines called for higher temperatures so I turned to parabolic trough concentrators. The initial trough was 44 inches wide and focused the incident light on a region approximately 3/8 inches wide on a pipe running along the focal line. During operation that target area received more than 100-sun solar intensity, and was so bright that welding goggles were required to protect vision.
That reflected light represented significant losses, and so I again worked to "game" the loss mechanisms to improve energy absorption. Drawing on insights gained from the flat panels, I looked for ways to maximize the number of times incident energy might be reflected before being lost to the environment.
Finding the solution was simply a matter of asking the right question. The immediate answer was a tapered, smooth-sided depression or a V-groove, and V-grooves seemed to be the most simple, effective, and manufacturable approach.
To verify my hypothesis that a V-shaped reflection cavity would behave as expected, I devised a simple, inexpensive experiment using an apparatus which permitted varying the internal angle of the V-shaped cavity and allowed me to observe and photograph how well (or not well) my method corresponded to real-world physics.
The sketch above illustrates the beam path expected within a V-shaped cavity with a 15-degree internal angle. If the cavity walls were sufficiently smooth reflectors, they should produce twelve reflections before the beam exited the cavity. I was interested in seeing how much of the beam might be absorbed by "ordinary" (unpolished) surfaces.
The experiment used a laser level equipped with a diffraction grating to project a vertical line, an aluminum base plate, two aluminum blocks, and a sheet of ordinary copy/printer paper.
The laser level was my (directed) light source, the two aluminum blocks were arranged to form the walls of a V-shaped cavity, and the sheet of typing paper allowed me (and the camera) to see the path taken by the laser beam. The aluminum base plate provided a flat, stable surface for the other components.
In the photo above, the camera looked directly down into the V-shaped cavity from close enough that the cavity walls could both be seen. The fan-shaped laser beam enters the V-shaped cavity from the left. The series of dots are an effect produced by the laser level's coarse plastic diffraction grating.
Although there is a certain amount of beam diffusion due to the unpolished surface of the cavity walls, the beam diminished in intensity with each reflection much more than can be attributed to diffusion effects alone.
Perhaps even more interesting is the fact that, no matter how I varied the internal angle, I was unable to produce more than three visible reflections, which may indicate that the rate of absorption was much higher than could be accounted for by diffusion alone (note the lack of general illumination from diffused light) and certainly much higher than I had expected.
I concluded that the hypothesis under test, that a V-shaped cavity could be used to make an improved energy absorber, was correct.
Implications for All Absorbers
In general this method can be classified as "imprecision tolerant" because the field of view of each V-groove overlaps that of adjacent V-grooves and is wider than that from the focus through the widest part of the V-groove aperture, as illustrated by
As a consequence, the absorber will add some measure of compensation for off-axis absorbers and distorted mirrors in applications like solar concentrators.
Implications for High-Temperature Absorbers
Radiation losses are minimized because much of the re-radiated energy will be directed toward adjacent absorber surfaces, rather than toward the environment.
Convection losses are minimized in atmospheric contexts because the air in the V-grooves will become increasingly viscous as the temperature of the absorber rises. This will tend to maintain the strongest possible boundary layer exactly where heat might otherwise be lost to the environment. Designers can take advantage of this characteristic by specifying the maximum width of the V-groove to be twice (or less) some fraction of the boundary layer thickness at the operating temperature.
Contrasting This Method with Prior Art
Prior art considers energy absorbed by the reflector and energy reflected by the absorber to be systemic losses, and so sought to minimize the number of reflections required to direct energy to absorbers (to minimize per-reflection absorption losses) and to minimize reflectivity of the absorber (to maximize absorption).
By making the reflector and absorber one and the same, and by maximizing the number of reflections at the absorber surface, this method converts those systemic losses to gains – and so makes possible unprecedented performance in combination with economy of material.
I've added two web pages to help design absorbers using this method. The first provides a program to approximate the efficiency of this method for a specified groove interior angle, and the second provides a program to calculate actual absorber geometry given the interior angle, groove depth, and target span angle. Both web pages include C-language source code and a link to an MS-DOS executable.
This method's usefulness is not restricted to cylindrical absorbers. I've added a page illustrating how this method can be used to similarly enhance performance of parabolic dish absorbers.