Thanks for the compliment. I used data from the US cell since I wanted to improve the model with information that was likely to be quiet. Now that I have this tool working well, it is time to use it to our advantage. The beauty of this analysis is that it operates throughout the entire transition period as the temperature is increasing within the cell. It will work very well to demonstrate whether or not there are any special temperatures of interest that may arise as the temperature is effectively swept.
I have not applied it to the EU case yet since I am not sure that a good calibration has been obtained thus far without any excess heating and due to the fact that I just perfected the model. I guess I am getting a bit slow these days. The data I used is shown in the last posting for reference. Now may be the time to begin to analyze the EU data and that will be my next endeavor. The model requires accurately calibrated values for the a, b, and c coefficients of the second order fit for power input versus temperature of the cell. This has been a near perfect second order function for all of the data thus far and I have my fingers crossed that it will continue to be true. If the cells are modified in some manner that changes this behavior drastically then a more difficult differential equation might result. I also need to have at least one curve generated by a change in input power drive such as from 10 watts steady state to 48 watts steady state. This transition information is used to calculate the effective thermal capacity of the cell. With accurate measurements of these parameters I can plot the temperature versus time behavior to a high degree of accuracy. Dave -----Original Message----- From: Arnaud Kodeck <[email protected]> To: vortex-l <[email protected]> Sent: Tue, Dec 25, 2012 2:21 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave, You have made a very interestinganalysis. What your model say when a +8W apparent excess heat was reported withEU cell? Can your model able to calculate the apparent excess power anytime? Notwhen equilibrium has been reached. For the data, did youtake the UScell or EU cell? US cell is currently less interesting has the celani’s wireseems to be fried. Merry Christmas, Arnaud From:David Roberson [mailto:[email protected]] Sent: mardi 25 décembre2012 20:08 To: [email protected] Subject: Re: [Vo]:Non Linear Modelof Celani Device Mark, I can give you a hint as to howwell the model matches the actual real life data. I have plotted a curveof the difference between the actual data and my model prediction. Thedifference looks like random noise that is more or less evenly distributedabout 0 volts throughout the entire power input to temperature outputtransition. This includes the case I analyzed beginning at 48.2 watts andending with 82.7 watts. I see no evidence of any curvature associatedwith the error between my simulation and the real data. There is a small,almost sinusoidal, signal hidden deeply within the noise that continuesthroughout the entire time frame which in this case is 9541 seconds long. The total noise peaks tend to be in thevicinity of .5 degrees C while the average of the flat noise is more in linewith .2 degrees C. Perhaps I should make a plot of the output and send itfor you to review. It is pretty impressive to see consistent noise whenthe large time domain transition signal is balanced out. My mention of the possible excess poweris based upon my having to include an additional 1 watt of input power for mymodel to achieve the perfect match. It is quite obvious that the extrapower is required for the curve to fit so perfectly. The data I used was from 11/30/2012 at2200 hours according to my download from the MFMP replication site. Iused the history points for my curve fitting and analysis. I fitted thetransition between the two power levels shown above. I just took a lookat the small noisy sinusoidal signal hidden within the noise and it appears tobe in the ballpark of 2000 seconds in period. Maybe this corresponds tothe cycle time for the heating system. I guess I can attempt an RMS noisemeasurement which will be next on my list. The small sinusoidalinterference will color that result a bit. I will report the results ofthe test when completed. Dave -----OriginalMessage----- From: MarkI-ZeroPoint <[email protected]> To: vortex-l <[email protected]> Sent: Tue, Dec 25, 2012 12:18 pm Subject: RE: [Vo]:Non Linear Model of Celani Device Dave: Can you perform some stats on the modelvs reality and give us the std deviation? -Mark From: David Roberson [mailto:[email protected]] Sent: Tuesday, December 25, 20129:15 AM To: [email protected] Subject: Re: [Vo]:Non Linear Modelof Celani Device During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differentialequation I have been forced to modify the constant of integration slightly awayfrom the ideal value as determined by steady state measurements. Thisseemed strange, but now I realize that it is required to compensate for thedisplacement of the rising edge due to the above delay. It is necessary to add back the initialplug of energy lost when the best differential equation solution is followed. This ideal solution for the best overall data match must start at a valuethat is below the actual temperature of the cell at t=0 in order to accommodatethe delayed behavior. The addition of this missing energy is exactly theamount required! So now I can say with confidence thatthere exists a delay mechanism which retards the reading of the temperature atthe outer glass surface. This delay is in addition to the ideal nonlinear differential equation solution time domain response which is discussedbelow. So, another way to envision the effect is to realize that it takes30 to 40 seconds before the addition of heat applied to the cell isregistered at that test point. An exponential smoothing (filtering)factor is applied. My suspicion is that the extra pulse ofheat must be distributed within the gas and then result in a temperaturereading at the outer glass monitor after heating the envelop. The heatingof the other structure elements may also be involved in the overall action. A careful review of the waveform hintsthat the test might be demonstrating an excess power of about 1 watt during theexperiment that supplied the data. This is a small amount of excess powerand only additional, careful analysis would enable me to be sure. Atleast it is in the right direction! My virtually perfect curve fit to thedata tends to support this conclusion. Merry Christmas! Dave -----Original Message----- From: David Roberson <[email protected]> To: vortex-l <[email protected]> Sent: Tue, Dec 25, 2012 2:13 am Subject: [Vo]:Non Linear Model of Celani Device The data has been flooding in from theMFMP and I have been seeking a time domain model of the system behavior whenpower to the Celani replication device is modified. Most of myeffort has been exerted by analyzing the rising edge of the time domainwaveform when the drive power is stepped up by a significant amount. Thetemperature follows a certain path as it ramps up to the value required tobalance the input and output power of the cell. We have been fortunate in this particularcase to find that the relationship between temperature and input power is wellbehaved and follows a second order curve to a remarkable degree. It isnot uncommon to see a curve fit with R^2=.9999 or better in many independenttest runs. I initially was expecting to see a power series that includeda forth order term of significance due to the S-B radiation equation. This has not ever been dominate in any test and I still am trying tounderstand why this is true. For the time being I will accept this gifthappily. A quick glance at the shape of the risingedge of the temperature curve suggests that it follows an exponential. Ithus began my model by making that assumption and got fairly reasonableresults. It was always evident that my curve fit contained holes, but acouple of degrees of error did not seem too excessive at that time. Beinga perfectionist, I decided to improve the situation and to determine how well amodel could match the real life test. I very soon added a second exponential tothe mix and noticed that the fit improved remarkably. Also, I noticedthat the second real frequency was close to the second harmonic of the firstone determined by my earlier work. A light went off inside my head and Irealized that this would be expected since the non linearity is mainly ofsecond order in the relationship between variables. Now, I saw that theaccuracy of my model was becoming very acceptable. There remained a shortperiod of time at the initial power increase where the fit was not as good as Ihoped. To fix this problem I added another exponential with an associatedtime constant of about 40 seconds. With this model, I could obtain anexcellent match between my simulation and the real world data. I could have left it in this state, butit is hard to accept imperfection. To pursue the matter further I used aLTSpice model of the system. I guessed correctly in my first try withthe model and was rewarded with a well behaved simulation that included thesecond order distortion effects. This model was used for a significanttime as it matched the real world waveforms everywhere except for the initialshort period that required another time constant to fix. Looking at my spice model gave me aninteresting idea. I used a capacitor to represent storage of the incomingenergy and the node it is connected to reads expected time domain temperaturefor the outside glass sensor. In parallel with the storage capacitor is apair of current sources, one representing power applied to the cell, the otherpower being taken away by the various paths. The draining current sourceappears as a parallel conductance who's value depends upon the voltage at thetemperature node. I, of course, was seeking verification of the timeconstant associated with the exponential rise waveforms and attempted to usethe effective conductance value in parallel with my storage capacitor for aquick check. This lead to the non linear differential equation definitionthat works so well. It occurred to me that my model could beexpressed in the form of a non linear differential equation with a littlemanipulation of the shape. Basically you have a parallel capacitor beingdriven by a current source that is paralleled by a non linear conductance. The non linear conductance is neatly defined by the second order equationderived from the calibration runs for the Celani cell. Now, all I had todo was to solve the non linear differential equation that I constructed andinsert the initial conditions to define the temperature and power over any timeframe. My first thought was yipes! I consulted our favorite source wikipediato find the solution to unusual integrals. The one I needed to solve wasin the form of: Integral dx/(a*x^2+b*x+c) with initial condition of thetemperature of the steady state value just prior to the application of anincrease in power. I transformed the time scale so that time = 0 was withthis application of extra power. It turns out that there is an exact solutionto such an equation which you can look up at your convenience to save time andspace here. I had to perform some interesting series adjustments to getthe curve within the desired temperature band, and I was a bit rusty at first. Finally, a perfect curve was being generated that matched the time domaindata extremely well except for that nagging time region at the very start. I continue to have to include anadditional exponentially rising pulse function with a time constant around 40seconds at the application of the extra drive to get virtually perfect trackingto the real world data. Next, I included another drive current waveformof this nature to my spice model and it tweaks the start of the rising edge atiny amount much like a delay. I am still seeking a good explanation forthe necessity of this extra pulse source and I wonder if it can be traced tothe IR effects or some other relatively large time constant such as the glassheating. The nature of the extra leading edgedrive pulse can be described as a signal that begins at a certain level anddecays exponentially to zero with a time constant of 40 seconds. Theeffective DC component of the waveform is taken out by the action of the nonlinear conductance. One interesting observation is that thecalibration determined a,b, and c that constitute coefficients of the secondorder equation defining Power versus Outside Glass Temperature along with theinput power uniquely determine the steady state temperature of the device. These four variables define operation over the entire range of inputpowers. My model also includes a capacitor that acts as the energystorage stand in. One good temperature rising transition allows me tochoose the correct capacitor to enter into the model. The additionalshort time exponential must be determined by curve fitting within a shortinitial period typically 100 seconds. I have found this exercise interestingand educational. If a good explanation for that initial power pulse isobtained I can relax and fool with the incoming data. I am hoping that mycontributions will enable us to discover any excess power that may occur by itssignature outside of the normal that I now model and observe. Dave
