Concentrated Cooker- Prototype One

 Description of the problem

The basic insulated box oven has been the primary foundation of Amanecer's work since inception; however, we have been interested in producing a simple and effective concentrating cooker capable of achieving high temperatures on a cooking surface. Such a cooker would allow for the solar cooking of tortillas, fried dishes, and grilled foods which are inherently incompatible with oven-based cooking. A subteam of the Fall 2009 group conceived a novel design concept that was intended to be powerful, user-friendly and simpler to construct than comparable existing designs. One of the primary goals of this semester was to complete the few remaining construction steps needed for the first prototype and conduct testing on the validity of the design concept and the performance of the prototype.

Details of the design process that produced the prototype can be found in the CEE 4920 final report of Fall 2009. In addition, Alice Yu prepared a three-session "crash course" early in the semester designed to ensure all members of the team had an expert understanding of the background and thought processes associated with the prototype. The handouts from these sessions can be found on the Amanacer Spring 2010 CD-ROM

Conventions were established for discussions of the geometry of the cooker and its reflectors:

• X-dimension: the "width" (left-right from the cook's perspective, i.e. east-west). Right is positive; left is negative
•  Y-dimension: the "length" (front-back from the cook's perspective, i.e. north-south). Forward is positive (closer to the sun); backward is negative (closer to the cook).
•  Z-dimension: the "height" (up-down from the cook's perspective). Up is positive; down is negative.
• The origin (0,0,0): defined to be the desired focal point upon which light should theoretically be converging; the center of the "target" we are trying to hit. Thus, the primary reflector is a section of parabolic trough whose focus is the x-axis.

* The secondary reflectors are sections of a parabolic trough whose focus is the y-axis.

BIG Idea competition

An additional sub-component of the concentrating cooker effort was the completion of deliverables for a contest called "The BIG Idea Competion." Sponsored by Entrepreneurship@Cornell, the competition is for Cornell undergraduates who have an idea for a business or social enterprise. Entrants compete for mentorship opportunities, exposure, and cash prizes. The concentrating cooker concept was entered under the name "The Solar Fire Project." This was done primarily to raise visibility for the project and for Engineers for a Sustainable World. Further details about the competition can be found at the BIG Idea website (http://entrepreneurship.cornell.edu/BigIdea/).

"The Solar Fire Project" ultimately made it to the Finalist round and received 2^nd place in the "Social Enterprise" track. In addition to the exposure gained via the Final Presentations - presented before an audience of entrepreneurs, faculty, and peers - our participation in the competition contributed to appearances in the Cornell Chronicle and photos in the Daily Sun. A portion of the $1000 prize will be donated to Grupo Fenix. The deliverables prepared for the competition are included on Amanecer Spring 2010 CD-ROM.

Methods

Construction

Before field testing could begin, several finishing steps needed to be completed in the construction of the Solar Fire prototype. These included:

 - Building a shutter system on a sliding track to control solar radiation through the cooking hole

 - Covering vulnerable surfaces with sheet metal cladding in order to reflect stray radiation and eliminate the danger of overheating and combustion of structural components

- Devising a pulley system to allow adjustment of the reflector array to accommodate varying solar elevations

 - Covering the primary and secondary reflectors with mylar to enhance reflectivity

 - Adding a reflective back panel in order to protect the cook from any stray radiation coming from the reflectors

 - Adding an indicator attachment to the reflector assembly that allows users to determine whether its angle is properly adjusted for solar elevation; this is done by ensuring that the wooden post casts no shadow upon its plywood base

Outdoor testing

Once the prototype was ready for field-testing, the team waited for an appropriately sunny day, placed the solar cooker on a cart, and took it outside into the south-facing parking lot behind Winter Lab. This was done on March 7, 2010 around solar noon. Given Ithaca's high latitude compared to Nicaragua, the solar elevation at this time was lower than the prototype had been designed to accommodate. However, we were able to lower the angle of the reflector assembly by positioning the front edge of the cooker to protrude past the edge of the cart, allowing us to lower the reflectors below the level of what would normally be the ground. The team decided to test performance qualitatively for the initial run, with the plan that more systematic quantitative tests could be devised if performance met expectations. The following protocol was employed for the qualitative testing run:

1)      Select one of several black pans and place it over the cooking hole

2)      Open the shutter to expose the pan to solar radiation

3)      Adjust for hour angle by turning the cooker in the XY plane such that the reflectors are facing the point on the horizon   directly below the sun

4)      Adjust for solar elevation by raising or lowering the reflector assembly until no shadow is cast by the indicator attachment

5)      Visually inspect the underside of the pan and tabletop to determine whether light appears to be converging as expected

6)      Estimate whether the pan is approaching expected temperatures by placing a small quantity of water inside to boil

Matlab Modeling

 In addition to field testing, we wanted o test the theoretical concepts underpinning the design - namely, whether the interaction of the two parabolic trough geometries would cause incoming light rays to converge on a point as the design assumed. We felt that the intuitive analysis from Fall 2009 was insufficient and that a more rigorous vector-based analysis was required in order to accurately understand how the light was reflecting from the prototype's reflectors. To this end, Scott Johnson developed a MATLAB script that would model the three-dimensional trajectories of the incoming light rays and determine how much of it would reach the target.  It also estimates the total incoming power reaching the target.
The model starts by expressing the positions and directions of the incoming light rays as vectors.  For each reflection it calculates where in space the light ray will strike the reflective surface and what its new direction will be. After going through all of the reflections, it calculates where the light will land on the cooking platform.  See "How the Reflection Model Works" in Appendix B for a basic discussion of the math in the model. 

The file LightRays.m (Appendix C) is a script that creates vectors that represent where the light hits the reflector.  The comments in the file explain how to use the script in more detail.  One can plot the vectors created by the script to see and understand how the light reflects and where it intercepts each of the reflectors and the cooking platform. 

The model can be used to test new designs.  By following the same basic method, one could add more reflectors or change the shape of the existing reflectors.  For instance, the prototype currently has a back reflector.  It may be interesting to add the back reflector to the model and see if it improves the power of the cooker.

The model used a different coordinate system than the one used in the design of the prototype, but in the end the script converts the coordinates back to the agreed upon coordinate conventions.

Results

 Outdoor testing

A single outdoor testing run was sufficient to determine that the prototype was performing but falling short of design specifications. The expectation was that the interaction of the primary and secondary reflectors would produce a line through the origin along the x-axis with a bright point at the origin itself. The line would be the result of light reflecting directly from the primary reflector, and the point would be the result of light that had reflected from both the primary and secondary reflectors. However, visual inspection did not support this expectation. Although the primary-reflector radiation did produce a line along the x-axis as expected, the secondary-reflector radiation did not converge on a single point; instead, it appeared divergent and scattered, and it was clear that the amount of radiation landing within the ten-inch cooking hole was less than assumed by the design.

Qualitative observations of the heating of the pan produced similar conclusions. The pan did grow appreciably hot to the point where it could not be touched with bare skin, and a small quantity of water placed inside could be made to bubble slightly after several minutes, indicating a surface temperature greater than 100 C (212 F). However, it was clear that the pan was not intercepting the 1000 W of solar radiation necessary for desired performance and that it was not reaching the desired temperatures of 450 F. Such temperatures would have produced much more rigorous boiling in the water, based on common experience.

The team decided not to pursue quantitative testing on this prototype, electing to instead focus attention on evaluating the premise of the design.

Video of the outdoor testing is included on the Amanacer Spring 2010 CD-ROM.

Matlab Model

The Matlab model calculates the efficiency of the cooker as: 

ε = (amount of light reflected onto the pan) / (amount of light intercepted by reflectors)

The Matlab model shows that the efficiency changes as a function of the zenith angle for small zenith angles, but for Ithaca (where the sun is always at a large zenith angle), the efficiency is always 15%.  This calculation is done without a back reflector.  With the back reflector, the efficiency probably increases, because some of the radiation that is reflected out by the secondary reflector could be reflected back onto the pan.  The following figure shows how the light rays fall onto the plane of the platform.  The green represents the area of the black pan.  The blue dots represents light ray elements.

The horizontal line represents the light that is reflected off of the primary reflector that does not reflect off of the secondary reflector.  The remaining blue dots represent the light that reflects off of both reflectors.  This model shows that the once reflected light behaves as originally expected, but the twice reflected light does not behave as originally expected.

Conclusions

Our field testing and MATLAB modeling indicates that the Solar Fireprototype devised by the Fall 2009 sub-team does not perform in the manner that had been assumed under the design, because the twice-reflected light does not converge on a single point. The thought process behind the original design concept can be summarized as such:

-  the primary reflector focuses light in the YZ plane only (toward a line at y = 0, z = 0)

-  the secondary reflector focuses light in the XZ plane only (toward a line at x = 0, z = 0)

-  the combined effect of reflection off both reflectors in sequence will result in XYZ focusing (toward a point at x = 0, y = 0, z = 0), allowing two 2D geometries to achieve 3D focusing.

The flaw is that both reflectors influence the z-component of the light's trajectory; thus, their focusing behaviors cannot be considered "independent" of each other in this fashion. The error was in believing this point to be irrelevant because each reflector operating on its own would direct parallel light onto a line in the plane z = 0 and that the secondary influence on the trajectory's z-component would thus be merely "redundant" with the first one. In truth, the secondary change in the z-component "stacks" with the primary change in z-component, and the reflected rays are no longer convergent.

Although the first prototype did not reflect light in the manner initially assumed, it was an illustrative endeavor that will benefit future design work for a concentrating cooker. The parametric vector-based approach used in the MATLAB model can be adapted to model future design ideas and allow them to be tested virtually before being constructed.

In addition, some design subcomponents developed for this prototype may remain relevant and be retained in future designs:

Shutter system: the shutter system serves both as a safety measure and a means of modulating the amount of radiation reaching the bottom of the pan, allowing the cook to adjust heat under the pan much like she would on a gas or electric range

Pulley system: the pulley system devised by Nick Chisholm allows the cook to raise or lower the reflector assembly without needing to move away from her position behind the table. This would be a convenient feature to include if future designs also incorporate swing-mounted reflectors. We recommend using rope or cord rather than the wire used for this year's prototype, in order to make the line more comfortable to manipulate.  

The experience of constructing the prototype also yielded a number of construction insights that future teams may wish to note:

- The reflective mylar should be handled with care and the following practices observed:

• The mylar should be cleaned using an air-gun or other non-abrasive method; using a towel can be abrasive and damage the reflectivity of the material
• Avoid touching the mylar surfaces excessively, as bare skin can leave interfering oils and fingerprints
• When using spray adhesives to affix mylar to flat surfaces, it is very easy for some of the adhesive to stray onto the "good" side and interfere with the reflectivity. Water, soap, and solvents cannot remove adhesive without reducing the mylar's reflectivity
• Mylar should be cut to fit the intended surface; any excess should be cut off rather than bent over an edge
• transporting large sheets of cut mylar should be done with two people if possible so that it is well-supported at all four corners; otherwise, it is easily wrinkled
  

- When cutting sheet metal reflector pieces to fit within a frame, it is better to err small than err large; if you err large, the sheet metal will fail to lie flat and will deform in a manner that can significantly alter its intended geometry

- If future designs use a secondary reflector, the cutting of the secondary reflector should also err on the small side to avoid shading the primary reflector more than necessary

Future work

Although we did not choose to conduct quantitative performance testing on the prototype, future teams may elect to do so in order to corroborate the observed "wattage" with that predicted by the MATLAB model.

Although the built Solar Fire prototype has limited utility from a design standpoint, it can still be used to seek insights related to construction practices. For example, if parabolic troughs will be used in future designs, this year's prototype could be used as a tool in measuring to what extent small errors in the shape of the trough will compromise its focusing performance, perhaps with the aid of parallel lasers to track the trajectories of incoming light rays (see laser section). This could be part of a sensitivity analysis to quantify the level of stringency needed in ensuring geometric fidelity when constructing a parabolic reflector.

The main priority resulting from this year's concentrating cooker work, however, would be to explore other design possibilities that meet the design criteria listed on page 18 of the Fall 2009 CEE 4920 report. The Spring 2010 team has begun brainstorming a number of approaches as described in the next section, which future teams may choose to build upon.