Methods

Experimental Setup

Particle Image Velocimetry was performed on the 1-D scale-up Solar Oven at three discrete water temperatures (30^o C, 50^o C, and 70^o C) in order to characterize how the role of convection currents changes over the heating of the oven.  One way to predict and describe velocity distribution in convection cells is the dimensionless Grashof number:

Where:
B = distance between hot and cold bodies
ρ = density of fluid at mean temperature
∆T = temperature difference
β = inverse of mean temperature
g = gravitational acceleration
µ = viscosity of fluid at mean temperature

This ratio of buoyant to viscous forces describes a fluid's natural ability to form convection currents.  Using PIV, we are able to directly measure convection cell mean strength and location over varying heating conditions. 

Due to time constraints, we were unable to alter pot quantity or placement and instead measured change of convection over varying temperature.  During the experiment, we had a thermal sink of a black pot with 5 lbs. of water in the center of the oven.  The field of view covered the right side of the oven from the bottom black plate to the pot on the left side.  In order for the camera to be able to view inside the oven from the front, the plywood door had to be removed and a piece of glass was duct taped into place. Additionally, the back of the oven is covered with reflective sheet metal.  This had to be covered with a piece of cardboard duct taped into place.  We assume these changes had a negligible effect on oven performance.

Figure 1 - PIV schematic

 

Figure 2 - Picture of PIV setup in DeFrees lab.

An Aragon Ion laser was used at a wavelength of 488 nm.  This wavelength was chosen because it provided the highest emission from the particular laser and also was imaged brighter on our particular camera than the other principal emission wavelengths.  In order to spread the beam into a laser sheet, a cylindrical lens was placed above the oven and the sheet was dispersed through the top glass sheets.

Thermocouples were placed in the pot of water, on the black plate at the bottom of the oven, and on the inside of the glass at the top of the oven.  The thermocouples were sampled at a rate of .1 Hz with a DaqPro Data Logger. 

The oven was heated with 15 halogen lamps located 24" from the top of the oven in an array of:

 

Figure 3 - Lighting arrangement of halogen lamps above PIV setup. 

The oven started at room temperature and the 5 lb. pot of water started at roughly 20^o C before heating with the lamps began. 

PIV Details

The oven was seeded with fly ash and compressed air after it was determined that the particles created ideal images under the condition of an Argon Ion laser sheet and no halogen lamp illumination.  While it was tested to see if good images could be captured under the condition of a laser sheet and halogen lamps, which would ensure that no cooling was occurring during the image capture, there was not enough of a contrast between the illuminated particles and lit background.  We therefore used a fairly short sampling time of about 1 min. and collected 1758 images per temperature to ensure that cooling didn't take place. 

An image size of 600 x 800 pixels was used as that was the default output of the camera.  An image capture rate of 30 Hz was used because it non-redundantly captured particle movements on the order of 1-3 pixels between image pairs.

Figure 4 - Front view of PIV experiment being run. 

 

Figure 5 - Top view of PIV experiment being run. 

Data Processing

Once the images were obtained, some data processing had to be performed in order to get the desired results and filter out erroneous data.  Image pairs were processed with a subwindow size of 16pix x 16pix.  This size was somewhat arbitrary, but was hoped to capture high image correlation between pairs.  This choice of subwindow size resulted in a map of mean displacements in each subwindow. Using an image of a ruler to calibrate distance as well as knowing that the camera image rate was 30 Hz, these displacements were then converted to velocities by the equation:

The U and V displacement matrices were also run through a simple band pass filter that set a tolerance for upper and lower bounds of displacement and cut out background noise.  Histograms of U and V data for each temperature data set were examined and upper and lower bounds were chosen based on visual inspection.  If a data point appeared outside of these bounds, the data point was set to the mean value at that data point. 

 

Figure 6 - Band Pass Filter schematic and generic Matlab code used to process the data.

Results

PIV was run at three temperatures and vector maps were created displaying mean velocity at each subwindow.  Additionally, video was captured from both the scientific camera and a handheld camera showing convection behavior dynamically.  The handheld video is accompanied on the CD of this report.  We assumed in doing PIV that convection movement was relatively two-dimensional, so convection cell strength can be characterized by looking at the maximum U and V mean velocities (Table 1). Averaging the two values, we found that convection cell strength increases by 12% from 30^oC to 50^oC and by 27% from 50^oC to 70^oC. 

Table 1 - Maximum mean velocities in the U and V direction at each discrete temperature.

Convection cell strength increases markedly between temperature points.  As is seen from the Grashof number (eq. 1), increasing mean temperature and increasing dynamic viscosity have the effect of lowering the natural convective forces, but the increase in difference between the pot of water and ambient air increase enough to still cause an increase in convection strength.  This leads us to believe that a smaller thermal mass (less water) would equilibrate to the ambient oven air faster and that convective forces may not play as strong a role in its heating.  On a cooking scale, the 5 lb. pot of water may actually be a small amount of thermal mass to put in such a large oven, but it also leaves a large open area for the convection cell to set up (a large B³term in the Grashof equation).  It is difficult to know without more tests whether the larger thermal mass of food in a real oven (helps convection) and the smaller volume for convection cells to set up in (hurts convection) would increase or decrease the role of convection heating. 

From the PIV and heating mechanism isolation tests, we conclude that weather stripping the oven should have a positive effect on convection heating in the oven.  With convection playing such a large role, air escape across a large temperature gradient (the leak) should have a very negative effect on oven performance.   

We also note that these PIV results generally agree with the heating mechanism isolation tests.  Of the three mechanisms, we can only expect that energy gained from radiation will remain constant from the beginning of heating through all temperatures.  As the black plate gets hotter relative to the pot, we expect that conduction's role in heating would increase.  And finally, as convection cell strength increases (as is seen in PIV) we expect the role of convection to also increase.  While the contribution of the three mechanisms was more uniform across temperatures than we might think, there was a definite decrease in radiation's contribution at high temperatures.

Figure 7 - Vector map of mean displacements at 30°C. 

Figure 8 - Vector map of mean displacements at 50°C. 

Figure 9 - Vector map of mean displacements at 70°C. 

Critical Theory Issues and Challenges

The investigation of the heating mechanisms behind food cooking is an interesting project for the solar oven team to delve into.  It adds knowledge that will potentially affect the way in which future ovens are constructed and/or used.  The effectiveness of these changes is largely unknown without testing, so care must be taken to give advice without first knowing all of the performance implications.  We believe that showing the handheld video of the PIV experiment being run would help users of the oven visualize and understand how heating takes place in the oven. 

We have found that convection plays the largest role of the three heating mechanisms during our experiment.  We therefore stress the importance of sealing cracks in the oven.  We have also found that preheating the oven has a large effect on cooking time, but comes at the cost of requiring greater preparation and planning.  It could also potentially affect the glass strength if very high temperatures are reached before food is placed in the oven.  We also discuss black plate thickness, which would reduce cooking time if increased.  This additional thermal mass would require even longer heating up and would again require greater planning and preparation on the part of the user.  It also increases the material cost of the oven, which could deter users for a potentially small gain in performance.   

As there is an existing methodology and good deal of knowledge concerning the way in which the current oven design is built and used, it would be difficult to convince the users of the oven to change the design or use based on new information gained from these experiments. While it would be easy to recommend that Las Mujeres Solares change a design parameter that would boost the efficacy of convection currents or that black plate thickness changes in a way that better promotes conduction, both of these undervalue the societal implications these changes would have.  Making a major change to the design process would possibly slow the production rate and could lower the income stream that the Solar Ovens bring to Las Mujeres Solares. Similarly, a change in cooking procedure could have the positive impact of cooking faster at higher temperatures, but could come at the cost of negatively impacting the users' interaction with the technology; if they are told to change the procedure they are used to and are unable to notice the difference (a few percent faster or hotter cooking will go unnoticed) for a reason they are unable to understand (energy transfer mechanisms), they will be less likely to heed future advice.