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Results (TOC)
Verification
of Operation
(TOC)
A calculation verified
that the blackbody size and material type, as well as the type of heat pump,
would adequately change the temperature of the plate in the required amount
of time. The time required to change the temperature of the copper plate is
given by:
(4.1)
Where:
T is the time interval in hours
m is the weight of the copper plate in pounds
D T is the temperature change of the material in °F
Q is the heat added or removed in BTU/hr.
The value of Q can be determined from the heat pump specification sheet in Appendix A. This corresponds to a value of 21 BTU/hr for each heat pump. Since there are nine heat pumps, this would be 189 BTU/hr for the 3.9V @ 7.8A condition. The weight of the copper plate, m is around 2 pounds. The specific heat of copper is 0.0923 BTU/lb. °F and the maximum temperature change of the material would be around 122°F or 50°C. Hence the time required to change the temperature of the copper plate would be around 7 minutes. This is more than reasonable since the actual time frame to prep the blackbody for scanning by the MISI is around 15 minutes.
General Response of the Blackbody (TOC)
Thermistors were place on the front and rear surfaces of the blackbody in order to evaluate the general response of the copper plate, heat pump, heat sink configuration. This set up was described in section 3.4. Two modes of operation were then employed to assess the response; heating the copper plate (heating mode) and, by reverse biasing, cooling the copper plate (cooling mode). The voltage controlled power supply was set to +4v and -4v, respectively to obtain the results. Figure 4.1 shows the thermistor activity on the blackbody as a function of time for the two modes of operation.
An equation was then found (Figure 4.2), that related thermistor resistance to temperature values. Through the use of the thermistor LUT (See Appendix H) the resistance values were converted to temperature values (See Figure 4.2).
Further more, a plot of the temperature differential between the front (copper plate) and back (heat sink) of the blackbody was constructed (See Figure 4.4) using the data from Figure 4.3.
It is seen in Figure 4.3 that the peak temperature for the copper plate in heating mode was about 45°C or 113°F. Similarly, the peak (cold) temperature in cooling mode was about 10°C or 50°F, for the given ambient. This shows that the blackbody range, for a ±4v input, is around 45°C - 10°C for an ambient of 20°C. Clearly there is not an even response in temperature about the ambient point for the given input voltage. That is because the heat sink is a much more effective heat exchanger than the copper plate. This effect can also be seen in Figure 4.4 where the temperature delta from front to back is much greater in heating mode than it is in cooling mode.
It is desired to have the blackbody reach temperatures on the order of ±15°C of ambient, where ambient varies from -10°C to 25°C. This would correspond to a full range of -25 to 40°C. It is seen from Figure 4.3 that the radiation source in its current state cannot achieve the low end temperatures with an input voltage of 4.0v.
Another consideration of the blackbody is time response. It is desired that the blackbody be able to reach and stabilize itself at some temperature set point in less than 15 minutes. From Figure 4.3, it is seen that, in heating mode, the blackbody is able to reach a temperature of +8°C above ambient in less than 2 minutes. This time response is also seen in Figure 4.4 where the temperature delta in 2 minutes time is about 10°C. This says that the blackbody, in heating mode, can reach any temperature in the defined range with in the allotted 15 minutes. This type of response was not seen in cooling mode.
Another variable that was monitored during the two modes of operation was current. It is seen in Figure 4.5 that, for a fixed voltage of 4v, the current decreased from 8.5A to 6.5A in heating mode and 8.5A to 7.5A in cooling mode. This supports the theory that the heat sink is a much more effective heat exchanger than the copper plate. Because of this fact, the power supply does not have to work as hard in heating mode as it does in cooling mode.
Time Response (TOC)
The time response of the blackbody was also determined. This time response or time constant t was found by setting the supply to a given voltage and letting the blackbody come to a steady condition over a long period of time. On average, this took anywhere from 15 to 20 minutes. The results of this experiment can be seen in Figure 4.6.
In order to determine the time constant of the exponential curves in Figure 4.6, the data was entered into a T1 Algorithm7. This was a program that calculated time constants for a given set of time varying data. The resulting time constants from this program can be found in Table 4.1.
|
Blackbody Time Constant |
|
|
Voltage |
Time constant t (sec) |
|
4 |
335 |
|
3.5 |
306 |
|
3 |
290 |
|
2 |
295 |
|
1 |
370 |
Table .1 Blackbody time constant.
On average it is seen that the time constant for the plate was about 5 minutes. This was expected since the copper plate posses a rather large thermal inertia. Further more it is seen from Figure 4.6 that the blackbody has a first order type response. In this light, the blackbody’s response can be modeled an exponential. That is:
(4.2)
Where DC is an offset term and k is a temperature constant. For example an equation to model the 4 volt response might look like:
(4.3)
where t ranges from 0 to 3000 seconds. This information proves to be useful when modeling the control system. This modeling can play a significant role when trying to implement a PID type control system. It is for that reason that this information is presented.
Blackbody Uniformity (TOC)
The uniformity of the blackbody was assessed using an IR camera as mentioned in section 3.3. The surface profile of the radiation source was looked at during three different conditions; 1) as the temperature of the radiation source was increasing rapidly, 2) when it was at a steady state condition, and 3) when it was at a steady state condition with the plate fully insulated. These profiles were then compared to a laboratory standard. All of the data obtained for examining uniformity issues were taken with the blackbody in heating mode only.
Profile during
temperature increase
With construction complete, it
was desired to look at the heat pumps immediate response during an initial
startup from ambient. For this an image of the surface was captured while
the temperature was in a state of rapid increase. The image was taken 1
minute after startup. At that time, the plate reached a temperature of 26°C.
This region of rapid increase can be seen in Figure 4.3. Figure 4.7 shows
the captured image of the copper plate where black is cold and white is
hot. This image shows that the temperature at the cross hair position was
26.0°C. It also displays a step wedge calibration strip. The two temperature
values at the ends of the step wedge correspond to grey values at the extremes
of the wedge. With this information DC values can be converted into temperature
values via a LUT. To further enhance the discrete temperature pattern generated
by heat pumps, a thresholding was employed. This result can be seen in Figure
4.8.
Figure .7 Grey scale image of blackbody during rapid temperature increase.
Figure .8 Rapid temperature increase image after thresholding.
It was found that the average temperature in quadrant one of Figure 4.8 was 25.8°C. Similarly for quadrants two, three, and four the average temperatures were 25.6°C, 25.9°C, and 26.2°C, respectively. This shows that without any corrections or adjustments the variation across the surface was less than 1.0°C.
Profile during
steady state condition
In order to
examine the uniformity more accurately, the copper plate was brought to
an equilibrium with the surrounding ambient. To do this a constant voltage
of 3.5v was used, over a period of 1 hour, to bring the blackbody to a
steady state temperature of approximately 45°C. The temperature disturbances
in the lab were minimized so as to not effect the copper plate. This result
can be seen in Figure 4.9. The same thresholding technique used for Figure
4.8 was also employed for Figure 4.9. The result of thresholding is shown
in Figure 4.10.
Figure .9 Grey scale image of blackbody during steady state condition.
Figure .10 Steady state image after thresholding.
Here it is seen that the discrete temperature variations of the heat pumps has vanished. The average temperature for each quadrant was again calculated using the calibration step wedge. From this it was found that the variation across the surface was less than 0.5°C. A quantitative analysis is found in section 4.3.6.
Profile of
laboratory standard
In order to
get a better feel for uniformity, a laboratory standard blackbody was
used as a means of reference. This laboratory blackbody was described
in section 3.5. The techniques used to capture the previous images were
also employed for imaging the laboratory source. Figures 4.11 and 4.12
show the imaged laboratory source.
Figure .11 Grey scale image of lab blackbody during steady state condition
Figure .12 Lab steady state image after thresholding
The laboratory images are very similar to the images acquired for the blackbody constructed in this research. A similarity in the grey scale pattern can been seen between the lab blackbody and the constructed blackbody (Figures 4.9 and 4.11). This pattern similarity is also scene in the two images after a thresholding has been applied (Figures 4.10 and 4.12). In the case of the laboratory blackbody, it was found that the variation across the surface was less than 0.5°C.
Steady state
with insulation
The blackbody
constructed in this research exhibited some heat loss at the edges of
the copper plate, as seen in Figure 4.10. To prevent some of this heat
loss, the copper plate was fully insulated around the edges with styrofoam.
This makes the constructed blackbody similar in design to the lab blackbody.
The results of this insulation are best seen when 1D slices of the images
are taken and 3D plots are generated. These result are further explained
in sections 4.3.5 and 4.3.6.
3D representation
Three-dimensional
plotting was also employed as another tool to graphically evaluate the
surface uniformity. Figure 4.13 shows a 3D representation of the surface
for the steady state non-insulated, steady state insulated, and laboratory
standard images. It is noticed in the non-insulated case that there is
a slight fall off in temperature at the corners of the copper plate. This
fall off is reduced slightly at one of the corners in the insulated case
though still apparent in the other corners. The "roughness"
of the surface in the insulated case may be due to oils, grease, or glue
left on the copper plate surface. These materials were used during the
insulation process of the blackbody. The laboratory standard shows decent
uniformity overall with a slight temperature loss at the edges.
Quantitative
profile analysis
To further
investigate the uniformity of the blackbody, 1D slices were taken across
the images in the x direction only. The location of the slices are referred
to as lo, mid, and hi. Figure 4.14 graphically illustrates the location
of these slices. This slice analysis was used on the steady state non-insulated,
steady state insulated, and laboratory standard images. The elevation
data from these images was combined with x-axis data to generate 2D plots
representing uniformity along the x-axis. Figure 4.15 represents the lo
slice while Figures 4.16 and 4.17 represent the mid and hi slices, respectively.
Figure .13 3D plots of uniformity
Figure .14 Diagram showing location of 1D slices.
Figure .15 2D "lo slice" profile of blackbody.
Figure .16 2D "mid slice" profile of blackbody.
Figure .17 2D "hi slice" profile of blackbody.
The variation in temperature, for a given slice, can be used as a means of comparing each blackbody image. Since there are three slices for each image, and three images, the data can be represented in a 3x3 matrix. The first matrix constructed evaluates the temperature variation across the entire surface of the blackbody (See Table 4.2). The second matrix evaluates the temperature variation across a 2 in2 region located at the center of the blackbody (See Table 4.3).
|
Temperature Variation Across Full Surface (x-direction) °C |
|||
|
Slice |
Non-Insulated |
Insulated |
Lab Standard |
|
Hi |
.702 |
.670 |
.725 |
|
Mid |
.727 |
.549 |
.769 |
|
Lo |
.845 |
.618 |
.575 |
Table .2 Variation in temperature along various x-axis slices for full surface.
|
Temperature Variation Across 2in2 region (x-direction) °C |
|||
|
Slice |
Non-Insulated |
Insulated |
Lab Standard |
|
Hi |
.374 |
.447 |
.369 |
|
Mid |
.396 |
.391 |
.380 |
|
Lo |
.311 |
.451 |
.224 |
Table .3 Variation in temperature along various x-axis slices for 2in2 region.
Full surface
analysis
When comparing
the non-insulated and insulated images, it is noticed that the variation
in temperature was reduced when the blackbody was insulated. This reduction
in variation is seen in all three slices of the images. This shows that
insulating the blackbody can reduce the overall temperature variation
across the surface of the plate (if noise is neglected). When looking
at the laboratory standard, however, it is noticed that some of the slices
actually had a larger variation in temperature, as compared to the insulated
case. This is apparent in the Hi and Mid slices (with the Lo slice having
a smaller variation). It may be that for two of the slices the insulated
blackbody was more uniform than the laboratory standard. Upon closer analysis
however, the data may be subject to noise so it is difficult to say with
absolute certainty how the insulated blackbody compared to the laboratory
standard.
Center region
analysis
For this analysis a small 2in2
region in the center of the blackbody was examined. It is first noticed
that the temperature variations for the non-insulated and insulated cases
are very similar. This shows that the insulation on the blackbody does
not effect the center temperatures. It is also noticed that the laboratory
standard had the lowest variation of all. This was expected since the
manufactures of the laboratory blackbody are concerned with maintaining
high uniformity in the central region of the source.
Temperature Control and Regulation (TOC)
Control Algorithm
Because of the availability of BASIC routines and commands via the RTI interface board, the blackbody was software controlled. As mentioned in section 3.2.3 the controlling algorithm was coded in BASIC using the GW-BASIC interpreter available in the computer (See Appendix L). The general flow of the algorithm used for control can be seen in Figure 4.18.
In operation, the algorithm prompts the user to enter a desired temperature set point (Tset) and time interval between samples. It then converts the temperature to a digital count based on a LUT. This digital set point is compared to a temperature sample of the blackbody as a function of time. A direct comparison of the two DC values is then performed. If the sampled DC is greater than the set point DC (i.e. overshoot) the power supply turns off and the room temperature is used to drive the temperature down below the set point. On the other hand, if the sampled DC is less than the set point DC, the routine keeps the supply at a nominal 4v, which will induce an eventual overshoot. This cycle continues resulting in an on/off controlling scheme and produces an oscillation around a given temperature set point. This type of algorithm is very similar to the thermostat operation found in many households.
Algorithm results
The results of the controlling algorithm can be seen in Figure 4.19. This plot shows the temperature increase and regulation as a function of time. In this plot it is seen that the blackbody can reach the desired temperature set point of 35.0°C in less than 3 minutes. The regulation aspect of the algorithm is also clearly apparent by the numerous oscillations around the set point.
Figure .19 Results of controlling algorithm using the AD-590 temperature sensor.
To closely examine the oscillations around the set point, a zoom of Figure 4.19 was constructed as shown in Figure 4.20. The oscillation pattern becomes more apparent with the zoomed plot thus revealing more information about the controlling scheme. The solid lines located at T=35.1°C and T=34.9°C are to show the ±0.1°C tolerance. This means that the blackbody could be regulated to 0.2°C if kept with in this range. Similarly, the dotted lines located at T=35.05°C and T=34.95°C are to show the ±0.05°C tolerance and if kept with in this range, the blackbody could be regulated to 0.1°C. It was found that the current algorithm could regulate the blackbody to about ±0.15°C. This is equivalent to having control with in 0.3°C. Furthermore, it is seen that the control resolution of 0.027°C/DC was well with in the smallest tolerance thus making it possible to control down to that level. This could be possible if a steady-state type algorithm is implemented.
Figure .20 Zoom of controlling algorithm.
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