## Last Single-Mirror Solar Oven Simulation Test

by Curlydock
Nov 24, 2007

In my previous couple of posts I showed some of the results of tests of a program I wrote to simulate what I call a “kaleidoscopic” type solar oven. In earlier posts I detail the actual oven I use to bake bread. I wanted to see how to build a better oven of this type, so I wrote the simulation for ray-tracing various reflector sizes, shapes, quantities and configurations.

This post will cover what I hope is the last of the one-reflector tests. I wish to begin tests of two-mirror simulations in the next post. Graph “nov1026a” shows the results of five runs with a single equilateral triangular reflector in the plane of the horizon. That reflector I frequently refer to as “R3”. Five sweeps of the sun from zero degrees (horizon) to 90 degrees (zenith) are shown, one sweep for each size of R3. The sides are all equal and are measured in cavity diameters. The smallest R3 is 2.0 and the largest is 8.0 cavity diameters on a side. The cavity bounding sphere is represented by the ball that is aways in the corner farthest from the sun when the sun is on the horizon.

Observe that the gain never exceeds 2.0 and never falls below 1.0. This is consistent with my expectations of what happens with only one mirror and increases my confidence in the simulator.

Rule 1026a

Also observe that the increment of improvement in gain decreases as R3 gets larger. Large mirrors increase the gain when the sun is at lower angles but the reflector has to get perhaps impractically large to produce these gains. At solar angles above about 20.0 degrees, it hardly seems worth having a floor reflector larger than 4.0 cavity diameters on a side. This is more than my prejudice up until now, which was that 3.0 cavity diameters on a side was the practical limit. The actual oven I made has only 3.0. So, the next time I build one of these ovens I will probably go with 4.0. It depends on what else we learn when more reflectors are in play.

“Rule 1026a” is, then: the triangular reflector always parallel with the plane of the horizon, that is the one the cavity is above, should be sized to about 4.0 cavity diameters on a side, physical practicality permitting, and probably not less than 3.0.

Now I combine this rule with rule 1010a from the previous post, which said the cavity should be elevated. That results in chart “1027a”: For this run I kept the mirror sized to 8.0 cavity diameters on a side and elevated the bottom of the cavity from just touching R3 to where the bottom of the cavity is 0.5 cavity diameters over R3. Otherwise the run and chart calibration are the same.

Again, the gain never exceeds 2.0 and never falls below 1.0, which is good.

Also note that elevating the cavity improves gain when the sun is at higher angles. This is consistent with what we learned in the prior post and was to be expected. The simulation still seems to work. For this configuration, with the cavity elevated, the range of sun angles with the maximum gain of 2.0 is much larger.

In a prior post I expressed some doubt about whether the simulation was following the ray trace through an arbitrary number of reflections or breaking off too soon. I later discovered that was indeed a problem. But it only affected simulations of more than one mirror, none of which I had published yet. I fixed the bug and am now confident that I am ready to do multi-mirror tests. In the next post we will see some results using two reflectors. Those reflectors are the ones I have named “R1” and “R2” in prior posts. They are linked by a vertical hinge and open like a book over the plane of R3. R3 will be put aside while we consider only R1 and R2 and will return probably much later when three-mirror tests begin.

Published in: on November 26, 2007 at 1:04 am  Comments (42) ## More Elementary Tests of a Solar Oven Simulation

by Curlydock

Nov 16, 2007

In the prior post I introduced a test of the simulation using only one plane of the “kaleidoscopic” type solar oven. So far, we have seen the bounding sphere of the oven cavity positioned over one triangular concentrator. That concentrator corresponds to the R3 reflector mentioned in other posts describing an actual oven that I have been using. The R3 reflector is in the plane that appears to be parallel with the earth’s surface and the cavity assembly rests on R3. In later posts we will be considering the effect of the other reflectors: R1, R2 and R4. This post is confined to more implications of the R3 reflector.

Diagrams “nov1007” and “nov1008” illustrate the oven cavity bounding sphere positioned at two different levels over the triangular reflector.

The red dots represent the absorption of a light ray on the surface of the bounding sphere. The blue dots represent rays reflected from the surface of the mirror that do not intercept the cavity. The shadow of the cavity can be seen on the mirror. The other dark spot on the mirror is that portion of the mirror where rays are reflected that do intercept the cavity.

This Test

The present question is how the height above the mirror affects the amount of solar flux gain the cavity will receive as the sun sweeps over an altitude angle from zero degrees on the horizon to 90 degrees at the zenith. Diagram “nov1010” shows the result of four simulated solar sweeps, one for each of four different heights of the oven cavity above mirror R3.

On Units

Unless otherwise noted in these posts, the units of distance measurement will be cavity diameters. I think that is more interesting and informative than using yards or meters, etc. So, no matter what the radius of the cavity is in feet, centimeters, inches or any other unit, it is always 0.5 in cavity diameters. When the cavity rests on the mirror the center of the cavity will be 0.5 cavity diameters from the surface. The lowest point on the cavity, in that case, will be zero cavity diameters from the mirror.

The triangular mirror, R3, seen in the above illustrations and used in this particular post, is equilateral and 3.0 cavity diameters on a side. The cavity CENTER heights used to generate the data for the chart “nov1010” are 0.5 (red), 1.5 (green), 2.5 (blue) and 3.5 (black) cavity diameters. There is one color coded sun altitude sweep for each cavity placement.

The Solar Sweeps

These “altitude sweeps” are not the natural movements of the sun, so don’t be confused. The sweeps begin at the lowest point on the horizon and end at the highest point in the sky, or the zenith, at 90 degrees. The point on the horizon, zero degrees, where the sweep begins, is always in a vertical plane that bisects an angle of the triangular reflector.

The reason for this type of sweep is to see how the more complicated mirror arrangements respond to different solar angles, all of which keep the sun in the plane that bisects the symmetry of the concentrator arrangement. The purpose was to have a standardized sweep with which to compare different arrangements under any solar angle that might happen no matter what the season, location on the earth, or time of day, given that one could always adjust the oven so the sun is in that bisecting plane. Such an adjustment would not change the fact that R3 is in the plane of the horizon; it would merely rotate R3 in that plane. The tests to see how the simulated oven responds to a natural solar transit will probably be some of the last tests.

Rule 1010a

Now back to chart “nov1010”.

Note that when cavity height is lowest, 0.5, which corresponds to touching the mirror, the gain never reaches the greater levels it does when the cavity is elevated from the mirror. This is the reason for placing the inverted glass bowl underneath the oven cavity assembly, as seen in my prior posts detailing an actual solar oven. The lower bowl elevates the whole assembly a bit. I was never quite sure just how much it should be elevated but now it seems my simulations may help to determine this.

So, Rule 1010a for building kaleidoscopic solar ovens is: elevate the cavity over the mirror that is parallel to the plane of the horizon instead of letting it rest on it.

Next, we see just how much elevation is best. The above graphs suggest that the best cavity elevation will depend on the solar altitude. The angle of the sun is constantly changing; so, if we can figure out a way to easily adjust the cavity elevation about every twenty minutes, that would optimize flux gain at all times. Such a rig might be more complicated than the extra flux gain is worth, however.

Diagram “rule1010a”, seen below, might be used in the design and operation of a one-triangular reflector solar oven with an equilateral shaped mirror three cavity diameters on a side. It probably would not work for baking because the flux gain would never exceed 2.0. It might be useful for proofing bread dough or keeping a plate warm. It might also apply to ovens with more reflectors, but we have to wait to see what more tests produce to be sure. This diagram allows us to determine the best cavity height above the reflecting plane for any given altitude angle of the sun. I gathered the data for the diagram from repeated runs with the simulation program. That these curves seem to make sense to me reinforces my confidence in the accuracy of the program so far (no guarantee, of course).

The runs show rather broad peaks. That suggests that a particular cavity elevation would work well for a wide range of solar angles without need to re-adjust the height. For that reason, the diagram “rule1010a” shows a region instead of a line. The acceptable region is in yellow-green between two limiting lines. The limiting lines represent the points where the solar flux gain has dropped to 0.9 times the peak value seen in the sweep. The graph seems to indicate that for solar angles below about 25 degrees there is no need to elevate the cavity at all. The flux gain might be very low, but elevating the cavity will not help.

How to Apply Rule 1010a

Here is an example of the use of diagram “rule1010a”:

Suppose the sun is at 70.0 degrees above the horizon. Find 70.0 degrees on the horizontal axis of the chart. Follow the vertical from 70 degrees up until it just reaches the green region (the first limiting line). Follow the horizontal from that point to read the cavity height. That yields about 0.70 cavity diameters.

Continue on the 70.0 degree vertical until the green region just ends (on the other limiting line). Following the horizontal from that point yields about 2.9 cavity diameters.

Therefore, the maximum gain will be when the BOTTOM (not the center) of the cavity is between 0.70 and 2.9 cavity diameters from the surface of mirror R3.

If the cavity is 12.0 inches in diameter then 0.70 cavity diameters represents 0.70 X 12.0 = 8.4 inches. Likewise, 2.9 cavity diameters X 12.0 inches per cavity diameter = 34.8 inches. At these points the gain will be about 9/10 what it would be at the peak.

To find the height corresponding to the actual peak, you can use the average. In this case, the average cavity height is (0.70 + 2.9) / 2.0 = 1.8 cavity diameters, and 1.8 X 12.0 = 21.6 inches.

In the morning and evening hours the sun is not so high and the cavity will not need so much elevation. Even if the cavity elevation is not optimum, the losses will not make the oven useless, it will probably just take a little longer to cook something. Also, when we start adding the other reflectors R1, R2 and R4, the gain will be considerably beyond 2.0, so some small maladjustments will be even less of a problem.

Published in: on November 18, 2007 at 5:15 pm  Comments (38) 