First Multi-Mirror Solar Oven Simulations

by Curlydock
Nov 27, 2007

nov1039a.jpg

Results published in previous posts increased confidence in my solar oven simulation program. Those tests were confined to the single-mirror configuration. By keeping things simple, results were intuitively judged. Now it gets more interesting as we encounter kaleidoscopic multi-mirror configurations with results that may challenge intuition but that are, nevertheless, we hope, still accurate.

The number of variables that define the problem make closed form expression prohibitive, at least for me. Thus, my use of simulation.

HERE IS A LIST OF THOSE VARIABLES:

The oven seems simple enough in that it is composed of two sets of hinged mirrors and a sphere called a “bounding sphere” that stands for the oven cavity. The oven cavity is the part of the oven that gets hot enough to cook food. It is constructed like a small green house, but we need not concern ourself with those details.

The bounding sphere is all we need to know about the oven cavity. The center of the sphere gives the CAVITY LOCATION in EXTENSION and ELEVATION from the “origin”, the lowest point on the vertical R1-R2 hinge. The cavity location is always in the bisecting plane of the oven’s bilateral symmetry.

The radius of that sphere gives the SIZE OF THE CAVITY. Now, to make results easier to compare across simulations, I have normalized all units of distance to the diameter of the oven cavity. So, instead of inches, feet, meters, etc, all lengths are in units of cavity diameters.

I have named the four mirrors of concern: R1, R2, R3 and R4. Hinged on a vertical axis are R1 and R2. R3 and R4 are hinged horizontally. So, we have the two angles: R1–R2 ANGLE and R3–R4 ANGLE.

We will also be concerned with where the sun is in respect to our oven, so we have: SOLAR ALTITUDE ANGLE or elevation; zero degrees on horizon and 90.0 degrees at zenith, and SOLAR AZIMUTH ANGLE. In all runs I presently contemplate, the azimuth will not change, confining the sun to the plane that bisects the symmetry of the oven.

We also have to be concerned with R1 WIDTH and R1 HEIGHT. R2 is always identical to R1 in width and height.

Since R3 and R4 are hinged horizontally, it is confusing to speak of their width and height, so I define the dimension R4 RATIO, the length of the horizontal hinge, as a portion of the opening of R1-R2.

R3 is always parallel to, or in the plane of, the horizon. R1-R2 sits on R3 like an open book with the bottom two corners on the axis of the R3-R4 hinge. Because of this configuration, the reflective part of R3 will always be a triangle with size and shape determined by the width of R1, R2 and the R1-R2 angle. The other mirrors are always square or rectangular.

R4 EXTENSION is how far R4 extends from the horizontal hinge.

Also an input variable is the QUANTITY OF REFLECTIVE PLANES. I can consider four possibilities: R3 only; R1 and R2; R1, R2 and R3; as well as all four mirrors.

I think that about covers the input variables. So far I have not concerned myself with losses based on reflective angles, surface imperfections, convection, conduction, mass, re-radiation, transmission distances, imperfect insulation, etc.

OUTPUT

What we get for output is the amount of idealized SOLAR FLUX GAIN on the oven cavity over what the cavity would have gotten directly from the sun without any concentration. This is not a temperature; it is a ratio. The minimum value will always be 1.0 unless the cavity is in shadow or blocked from direct rays, where the value could fall to zero. The maximum value depends on all the inputs.

Because of the large quantity of possible combinations of input variables, I must find a way to lock some of them down so they can be temporarily ignored. That will simplify the problem and help us make sense of where we are in our journey to the “perfect” design. I do not know if there can ever be a proof that a particular design is the best possible one. There might always be a combination of inputs hitherto unconsidered that will yield a greater flux gain than what we thought was the best. If there is such a proof, a bigger brain than my own will need to find it.

That is why I am willing to share my program listing with anyone who is interested and who agrees to keep my program or any derived from it in the public domain, not for profit.

I am also willing to do runs for others who would like to see particular results of inputs meaningful to them. Perhaps they have built an oven or two and want to see what the simulation says about comparative performance. If you are interested, just leave your request in the comments section and I may publish my response or run results in a future post.

Next, some multi-mirror runs:

For the time being I will keep R1-R2 angle at 60.0 degrees. The decision is arbitrarily based on the fact that an oven I built uses that angle. In the long run, there may be a better angle.

Also, for now I keep the width of R1 at 4.0 cavity diameters. I do that because prior runs with R3-only seemed to result in 4.0 as the optimum size for the side of R3, given the R1-R2 angle = 60.0 degrees. The length of a side of R3 is the same as the width of R1 (and R2). Lastly, to start, I make the height of R1 equal to its width.

nov1029a.jpg

Chart “nov1029a” shows the effect of cavity extension on flux gain where only R1 and R2 are in play. For these inputs, the best value seems to be 1.4, but it depends on the angle of the sun. By this chart, for sun angles higher than about 40.0 degrees we might want to make the cavity extension less than 1.4 cavity diameters.

Next, keeping cavity extension at 1.4 and everything else the same, we do four runs, one for each of four different heights of R1-R2. That results in chart “nov1030” where
red (1) = 4.0
green (2) = 6.0
blue (3) = 8.0
black (4) = 10.0
cavity diameters.

nov1030a.jpg

We see gains increasing at higher sun angles as the height of R1-R2 increases. The gain increment decreases so returns are diminishing. At this point I will make the compromise of R1-R2 height = 6.0 and keep that for the next set of runs.

I cannot resist the temptation to add more mirrors at this point. Chart “nov1032” run (1) is a repeat of “nov1030” run (2), for reference. It looks different because the vertical axis of the chart is re-calibrated to cover higher gains.

nov1032a.jpg

Note the gain still peaks at about 6.0. That gain makes sense when you consider that two mirrors at a 60.0 degree angle would allow the sun to see six images of the cavity. Run (1) is only with R1 and R2 in play.

For run (2) I merely add reflector R3 to the play, and the results show a significant increase in gain. If we consider that R3 would double 6 images to 12, the gain seen of about 9.0 makes sense, considering some of the images will be partially obscured.

Now we take a lesson from a prior post when we were testing with only R3 and learned that it is best to elevate the cavity somewhat over R3. We do just that in run (3) and see that the gain is even closer to 12.0. Supposedly, the reason is that the images are less obscured when the cavity is elevated.

In run (4) I put R4 in play and made R4 the same size and shape of R1 and R2. It is a handy size if the oven is collapsible and you stack the reflectors for storage. The solar flux gain reached 14.0. One might worry that the simulation is malfunctioning because the flux gain is below 1.0 for very low angles of the sun. More thought reveals that at these low solar angles the cavity and lower part of the oven are in the shadow of R4, so one’s confidence in the program rebounds.

Is this the best design? I doubt it. Only more testing can tell, I guess. At least, it is a benchmark for measuring more attempts.

In a future post I can make the input variables conform to the oven I have actually constructed and see what the simulation says. I will be able to compare a real oven with this benchmark and tell what changes might make it better or worse without getting my hands dirty (not meaning to disparage getting one’s hands dirty).

Advertisements

The URI to TrackBack this entry is: https://curlydock.wordpress.com/2007/11/27/first-multi-mirror-solar-oven-simulations/trackback/

RSS feed for comments on this post.

25 CommentsLeave a comment

  1. Curlydock here;
    If you would like me to run my simulation with your own inputs or would like some clarification, feel free to leave a comment.

  2. It’s interesting to see just how pervasive digital memory has become in our every day lives. It’s like everywhere I turn, I see something with a card slot or USB jack, lol. I guess it makes sense though, considering how cheap memory has become as of late…Ahhh… I shouldn’t be complaining. I can’t get through a single day without my R4 / R4i!(Submitted using Ting2 for R4i Nintendo DS.)

  3. sat receiver test
    Great work! This is the type of information that are meant to be
    shared around the internet. Shame on the seek engines
    for now not positioning this submit higher! Come on over and consult with my website .
    Thanks =) sat receiver test

  4. I am sure this paragraph has touched all the internet people,
    its really really good article on building up new weblog.

  5. Since the announcement of the alleged Iphone 5 release date, which is scheduled for Sept.
    twelfth 2012, the Apple iphone 5 and iPad Mini from Apple continue
    to have the internet in a frenzy. As usual, the Cupertino company is extremely
    stingy with info, therefore providing totally free rein to
    the wildest rumors. As we have seen with the release of the Apple iphone 4S and its previous rumors,
    most had been false.

    Fortunately, your phone manufacturer might not understand that you’ve hacked it.
    Thus, they will not have any rationality to terminate
    your warranty. One possible way in which they would find out would happen if you
    introduced the gadget to a shop to insist a
    support person look at it, and he recognized that the device was unlocked.

    So consider a nearer look at the iPhone Dev Secrets and techniques video program.
    Apple iphone Dev Secrets and techniques is a revolutionary web video sequence that coaches you
    how to make money from Iphone and iPad software improvement.
    The creator of Apple iphone Dev Secrets states that you are guaranteed to make cash with your initial Iphone application by subsequent
    the course outlined in his series.

    I concur that Apple offers you a range of apps
    but most of them are not helpful and Apple has reportedly
    banned 3rd-celebration applications. Individuals have this incredible device in
    their hands but they can’t personalize it the way they want.
    Jailbreaking is authorized in the country but it nullifies the guarantee arrangement the consumer shares with Apple Inc.

    Use the Apple iphone in horizontal mode for Safari.
    Sounds apparent, but it is shocking how simple it is to neglect and discover yourself squinting at
    the display. If you simply rotate your Iphone into landscape mode, utilizing Safari, each studying and getting into info with the keyboard widget will be a lot much
    more simple.

    Unlike iMovie, Garageband is also available for the first-generation iPad, and takes full benefit of the large multitouch
    display to provide a collection of digital instruments including a keyboard, guitar,
    bass, and drums, that are all playable on your device. The application is packed complete of incredible features that make music creating
    for each newbies and professionals an incredibly fulfilling encounter, this kind
    of as the ability to hook up your electrical guitar and record your jam straight into Garageband.

    When you restart your device, you’ll see a new icon on your homescreen, known as Cydia.
    Open it up. This is your new App Store. Don’t be concerned,
    the regular Application Store still functions. Now you’ve just got an additional
    one.

    Angel From the Coastline is about of all things a professional hit lady.

    The lyrics are purposely vague; Lynott felt it was important that the listener depend on his or her own creativeness.
    The subsequent monitor, Running Back again veers somewhat from the typical Thin Lizzy hard
    rock. A catchy tune influenced by Van Morrisons musical style, Lynotts Operating Back again deals with a attempted and true subject: misplaced adore.
    When they say it’s more than / It’s not all more than, there’s
    still the discomfort / I’d arrive operating / I’d come operating back to you once more.
    The tunes Romeo and the Lonely Woman and Warriors spherical out the initial side of jailbreak.

    Some jailbreaking resources have bugs. For example, the jailbreakme tool disables FaceTime and MMS, but this problem has recently been fixed.
    Nonetheless, issues like that do arise, and it takes time for options to arrive.

    So these were some pros and disadvantages of the iPad.
    Searching at the subsequent points, it is hard to
    decide whether the iPad is a intelligent buy or not.
    Individuals who are intrigued in buying this product are advised to have a personal appear at the components and software attributes and
    then make an uniformed decision.

  6. Having rough patches of skin on some oof your body parts could be an unpleasant experience.
    Yet another method to possess a evewn more
    youthful skin is to phsically erase the several years of the face by even more advnce processes.
    Before, numbing creams can only be administered by licensed dermatologists,
    tattoo artists, and dentists.

  7. Doesn’t make a difference if the genuine Apple iphone 5G turns out
    to be some thing else at its launch. No specific knowledge or skills are needed.

    This Apple iphone situation is priced at $29.95.

  8. When a new iPhone is sold Since 2008 there has been a vacation blackout for AT&T
    workers. You merely need to Push the 8 key, and the quantity is likely
    to be marked as junk for several future calls.

  9. You would like to learn how to cure diabetes. Figure Out How
    To read beyond that advertising tag to separate your lives the harmful hype in the lean fact.
    Imagine avoiding Type 2 diabetes and treating Type 1 diabetes.

  10. The casting group will be helped by this to be in contact
    with you in the event of anything. The humor is classic, which can be
    difficult for humor todo. The focus is gradually shifting to the on-line press.

  11. You will certainly find it quite attractive to once more eat food that you like.
    Oz is sounding the alarm on America’s national diabetes crisis.
    I have an issue with this specific as do thousands of people.

  12. The very first will be the Samsung Universe Notice 2. So, you must certanly be in a position to recognize today, they possess no cause to scam you.
    Your phone could be a number of unfamiliar programs and
    commercials.

  13. Yes, that’s correct – theyare getting 5M by giving the world
    free online games. City dollars to the other
    hand are particular. Nevertheless, I prefer to
    right click around the photography and start a fresh tab.

  14. Increase 3 table spoon of cinnamon in 1 liter of boiling water.
    Millions of people need to know the answer to the question but only hundreds
    look for the answer. They’re primarily divided into simple and complex sugars.

  15. Itis crucial to grow crops that work-around your reallife plan. All those activities provides you with experience.
    The game starts by participants placing wagers for the
    main box.

  16. Exercising: Stringent and laborious exercising is over blown by many diet programs today.

    This method of losing weight has been the overriding consideration in the Fat Burning Furnace product.
    Not only did he achieve his fat loss goals, the steps he took also served as a
    foundation for his system which he shares with you in his guide.

  17. Thank you for the auspicious writeup. It if truth be told used to
    be a leisure account it. Look complicated to far added agreeable from you!
    By the way, how could we keep up a correspondence?

  18. What’s up, for all time i used to check webpage posts here early in the daylight, because i enjoy to gain knowledge of more and more.

  19. Hurrah, that’s what I was exploring for, what a information! existing here at this webpage, thanks admin of this web
    page.

  20. I am sure this piece of writing has touched all the internet visitors,
    its really really fastidious post on building up new webpage.

  21. It’s nearly impossible to find knowledgeable people on this topic, but you
    sound like you know what you’re talking about!
    Thanks

  22. Eu percep prin urmare distanțat la fel de punct de vedere fizic ( el internat nedefinit ) și emoțional .
    Pentru a intra in starea de spirit înființat o pătură și o multime de perne
    suficient de confortabile pentru salon pe . Chiar a merge la plaja ar
    putea fi o bătălie .

  23. Good post. I learn something totally new and challenging
    on blogs I stumbleupon on a daily basis. It’s always helpful to read articles from
    other writers and use something from other web sites.

  24. I was excited to discover this page. I want to to thank you for your time due to this wonderful
    read!! I definitely loved every part of it and
    i also have you book marked to see new information on your website.

  25. What the heck i just read? Testimonials and Research Since the development that Teeth Whitening Products herb can end up being utilized to reduction fat, a great deal
    of study, research, and personal opinions have got been widespread
    in the marketplace. The sights indicated by customers, industry commentators,
    as nicely as study companies possess been optimistic and
    motivating. Statistics have got demonstrated that the get from the Teeth Whitening Products vegetable is certainly efficient for dropping weight.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: