Concentrated Cooker- Prototype One
Description 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.
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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:
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6) Estimate whether the pan is approaching expected temperatures by placing a small quantity of water inside to boil
Matlab Modeling
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Figure 2
In 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.
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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.
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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.
Figure 3
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.
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