Every time I think that I have finished with this short project a new idea comes up that begs a test. The accuracy of my simulation is quite reasonable with the typical temperature error reading much less that .1 degree C over the entire time frame of the measurement period. But, I was curious about where the errors might lay, so I came up with a new concept to use to simulate the Mizuno calorimeter system.
This time, I directly calculated the expected time domain response by looking at each main contributing factor. Then, I used super position of the various signals to arrive at the final result. This procedure eliminated the need to integrate most of the waveforms since they can be calculated by means of interactions with a single time constant, but one noise signal still required that older process since it could not be well defined mathematically. So, I first calculated the average of the ambient temperature over the time frame of interest. This was very simple to do. I just added up all of the temperature measurements and divided by the number of them. Next, I obtained the ambient noise function by subtracting the average temperature determined above from each point measurement. Another important factor that must be obtained is the initial temperature reading of the coolant water. Since this measurement contains a significant amount of peak to peak noise I averaged the first few points to get an accurate number. Finally, the leakage power entering the water from the pump has to be determined since it has a significant effect upon the total calculation. Even though it is on continuously, it is impossible to achieve an accurate calculation without its influence being considered. The main time constant for the system was carefully measured and is .67 thermal resistance x 41000 joules per degree C of thermal capacitance. This yields 27470 seconds which is 7.631 hours. Using this time constant and the exponential relationship that most of us are familiar with V(t) = V(0) * exp(-t/RC) for a decaying initial value, I was able to directly calculate the temperature remaining from the initial charge on the thermal capacitance as a function of time. Next, a step in temperature feeding the RC model is calculated for any point in time by a similar functional relationship of V(t) = Vmax * (1- exp(-t/RC)) that takes the average ambient calculated above with the contribution of the pump leakage power included. Here the contribution of the pump power is seen by taking that leakage power magnitude and multiplying it by the thermal resistance. Add the ambient average temperature plus the pump delta temperature determined above to get Vmax and then send it as a step into the single RC network. The messy factor is due to the noisy ambient signal left over after the average is subtracted. I was unable to model that signal directly, but it is easy to integrate its effect upon the system coolant thermal capacitance to obtain its time domain behavior. The time steps I used are the actual ones published along with the thermal data in the report. This then gave me the time domain temperature response due to ambient noise fluctuations to combine with the other factors. The beauty of this technique is that the total overall response of the system to the ambient noise input is the sum of these three factors. I added the exponential decay waveform derived from the initial condition of the coolant water to the rising step response due to the constant average ambient thermal input with the constant pump power addition. To this sum was added the contribution of the ambient noise variation obtained by integration point by point. After these additions I obtained a time domain waveform that described in detail exactly how the ambient temperature variations and other factors impacted the measured desired coolant temperature. It was then possible to subtract this curve from the measured coolant temperature response to have a clear view of the true signal that is generated by the power pulse entering the system and any excess power it originates. I added a three pole digital filter following the subtraction to eliminate most of the nasty noise remaining. Each of the three input power pulses contained within this particular data file (October 21, 2014 ) was easy to measure when subjected to my process. I could determine that about 25% extra energy was generated by the Mizuno device for each pulse. That is about 2500 joules for each one of the three. An explanation as to why this number is less than that reported is revealed by my latest technique of separating out the individual contributions. The fact that the pump is on all of the time does in fact tend to hide its contributions to the final coolant measurements as has been assumed. The biggest problem is that during the night time hours when the ambient drops heat is extracted from the system through the thermal resistance as the device cools. This continues for several hours and since the time constant is 7.631 hours, a significant number of joules is lost for that extended period. In the early morning hours the heating system begins to operate and the ambient rises several degrees C at a rapid rate. If you recall the step response portion of my model above you will understand why this is so important. The final temperature that the average ambient step wants to drive the coolant toward becomes greater than the coolants initial value. The coolant is not able to keep up with the rapidly rising morning ambient due to the time constant so it lags behind. This can clearly be seen in figure 13(Oct 21) of Jed's report. The ambient rises more than 2 degrees in less than 2 hours which is much too fast to allow the coolant to reflect that change. So, when the input power pulses occur the coolant is already heating up rapidly which can be seen in that same figure, especially the reactor wall temperature curve. This major rate of rise must continue until the ambient plus pump power contribution step is handled. The total number of joules added during this transient will eventually balance out with the number than drained off during the preceding long night period. If any doubt remains, new energy measurements will drop back toward the 25% extra figure my system determines once the ambient is kept constant night and day as planned. The good news is that the calorimeter can be used as is with my calibration system obtaining an accuracy of approximately 1000 joules per pulse. It would be impossible to miss an excess energy pulse that equaled the energy contained within a 20 watt drive pulse which would double the height of the pulses presently viewed. I would nevertheless ensure that the ambient is not allowed to change significantly during night or day to stabilize the waveforms and improve the system accuracy. I have advanced my technique further by subtracting off the signal pulse as well for some displays in order to get a flat line. It adds complexity to an otherwise simple system since that requires me to include a two time constant integrating system in addition to the one described above to handle the signal shapes accurately. If anyone wishes more details about what I have written here or a better explanation of how my simulation operates just ask. Dave
