Flawed experiments succeed at 12% efficiency

Today Elliot and I tested our solar oven.  As is often the case, we learned a lot, in this case that our original experiments were flawed.  Nonetheless we got some good data for establishing a baseline to be ready to improve our collector.

Let me reintroduce our situation.  We are currently using our modular solar oven that makes a clear distinction between the concentrator module and the frame module.  The frame module is based on a Dobsonian telescope frame.  It provides both a holder for the cooking chamber and place to bolt the concentrator such that the cooking chamber is held at the exit pupil of the concentrator.  The concentrator is a square (3d) compound parabolic collector, whose exit pupil is 9 square inches and input pupil is 144 square inches, providing a theoretic concentrating power of 16.

At present, our concentrator uses reflective panels made by gluing aluminum to poster board.  As such as it is a little flimsy, and visibly imperfect both in having wrinkles and not being perfectly parabolic.

Elliot with the Oven

Nonetheless, it concentrates sunlight well enough that is painful to hold the palm of your hand at the exit pupil for more than 15 or 20 seconds.

Today, we attempted to measure the ability and rate of heating a cup of water.  We darkened the water with food coloring, and placed it in a 1-quart Mason (canning) jar.  We poked a small hole in the lid, allowing us to insert an instant-read thermometer.  The jar could then be turned as if to rest on its side and placed in the frame module, forming a cooking chamber, with the thermometer easily readable from the outside.  The jar was backed by aluminum foil to reflect radiation back into the jar.

 

Thermometer stuck in the jar

 

Darkened water with thermometer inserted

Our initial experimental plan was to aim the oven at the sun and measure the temperature every 5 minutes.  Here are our results:

1. 0 minutes : 80 degrees F
2. 5 minutes : 130 degrees F
3. 10 minutes : 140 degrees F
4. 15 minutes : 153 degrees F
5. 20 minutes : 160 degrees F
6. 25 minutes : 163 degrees F
7. 30 minutes : 165 degrees F
8. 35 minutes : 180 degrees F
9. 40 minutes : 182 degress F
10. 45 minutes : 190 degrees F

We stopped the experiment there.  Between the 30 and 35 minute measurements we readjusted the oven to aim at the sun better.  This should NOT make a difference in a perfectly constructed CPC --- but our is not perfect, and it obviously matters.

This looks like a success.  Little did we realize that in fact our thermometer was NOT immersed in the water!  It is much easier to heat the tip of a thermometer than a cup of water.  This was a major flaw that invalidated most the of the experiment.  We measured the water temperature at 170 degrees F after the termination of the experiment.

So, of course, we attempted to repeat the experiment, making sure that our thermometer was fully immersed.  We also decided to take measurements every 2 minutes.

The oven in the Texas sun awaiting our tests

Here are our results:

1. 0 minutes : 80 degrees F
2. 2 minutes : 93 degrees F
3. 4 minutes : 99 degrees F
4. 6 minutes : 103 degrees F
5. 8 minutes : 108 degrees F
6. 10 minutes : 113 degrees F
7. 12 minutes : 118 degrees F
8. 14 minutes : 120 degrees F
9. 16 minutes : 121 degress F
10. 18 minutes : 122 degrees F
11. 20 minutes : 130 degrees F
12. 22 minutes : 132 degrees F
13. 24 minutes : 137 degrees F
14. 26 minutes : 138 degrees F
15. 28 minutes : 140 degrees F
16. 30 minutes : 141 degrees F
17. 32 minutes : 141 degrees F

This data is fairly "smooth" up to the stagnation temperature of 141 degrees F.  Unfortunately, it is also somewhat imperfect in the following way.  After the experiment (which was performed at 5:35 pm), the sun had gotten so low that the liquid was not very visible from the point of view of the sun.  That basically meant that most of the light was bouncing off the back reflector, rather than into our liquid!  Since our reflector was crinkly, some of energy did go into the liquid, and of course the jar itself was heated (even thought transparent), which would conduct some heat to the liquid.  This was our mistake in not observing that there was so little liquid that in pooling in the bottom of the jar it was mostly removed from the light of the exit pupil.

Nonetheless, there is nothing "invalid" about our second experiment, save that it measures an effect that we believe would be much greater if the sun was higher in the sky, or if our darkened object were a solid that would have stayed in the middle of our exit pupil.

Therefore, based on the data that we did collect, I have computed the wattage of our oven, and therefore its efficiency.

Here is my approach---if you see a flaw, please inform me.

A cup of water weighs 128 grams.  The temperatures was raised from 80 F to 137 F in 24 minutes. Converted to Celsius, this is 31.667 degrees of increase.  By the definition of calories, this is 128 * 31.667 = 4053.28 calories.  Converting to Joules, this is 16983.27 Joules.  Twenty-four minutes is 1,440 seconds.  Since a Watt is a unit of power expressed as Joules per second, the sun powered our oven at effectively 11.79 watts over this period of time to our water.

Taking as a general rule-of-thumb estimate a solar input of 100 watts per square foot, our oven therefore achieved an efficiency of about 12% during these 24 minutes.

This is modest, but I am very pleased by it.  We have achieved this with a concentrator we are pretty sure we can improve upon.  We have a established a baseline that will allow us to test this hypothesis.

It is possible that nobody has ever actually attempted to cook with a compound parabolic collector before.  It is therefore possible that we are doing something truly unique.

Perhaps more importantly, we have are getting close to be able to actually cook something.

One might look at all of our effort and ridicule how little we have accomplished, given that it is so easy to cook with charcoal, gas, or electricity.  However, I remained convinced that any increase in solar energy usage is a step forward for all mankind.  The possibility of using this on a personal level here in a America to replace the use of charcoal in outdoor barbecue grills seems like a worthy project, both in terms of reducing fossil fuel usage and carbon footprint and raising consciousness about the possibility of using solar energy more broadly.