Jack, I would expect the output power to be greater for your first case(1) due to the tendency of the core activity to 'stick' longer at the highest temperature. This effect is mainly due to the time constant being lengthened by the positive feedback acting like a negative resistance. When you are operating at the lower temperature, the thermal time constant is shorter and temperature changes occur at a more rapid pace.
It appears to be the tendency to 'stick' that leads to the highest COP. If your control system is capable of maintaining the temperature at very nearly the level where the input power required becomes zero watts, the COP will be enormous. I have simulated a system using negative feedback of a traditional linear nature and it appears to work fairly well. And, of course a PWM drive signal will also work. To answer your question, I would expect it to require less total input power in the case of the PWM drive signal(1) operating between two moderately separated core temperature levels than with input drive producing a fixed temperature level at the average between them(2). This effect will become much more pronounced as the highest power output level approaches the point where the core generated power becomes close to the power that is radiated and convected from the device. When those powers are equal, the time constant approaches infinity and the temperature 'sticks' at that level for a significant time while requiring very little drive power. And, at that high level, when the PWM drive is zeroed the temperature begins to move downwards with a time constant that is quite long. As you might imagine, the effective time constant falls off rapidly as you move away from the above mentioned balance point. It should be significantly shorter by the time you reach the temperature level between the two PWM turning points unless these temperatures are very close together. The actual rate at which the time constant reduction falls off with temperature depends upon the curves defining the core generation power function and the output power escape function. Jack, I am assuming that you will have a type 3 system that is capable of thermal run away. I make this assumption because it is difficult to adjust the parameters of the defining equations necessary to achieve a type 2 design. A 10% error is enough to completely miss type 2 behavior and I find that I generally have to use Excel in order to obtain coefficients that work well. It takes too much time to run simulations alone to obtain that desired result. Excel however can be used to obtain the characteristic curve quickly. Of course, a type 1 system is relatively easy to test but the COP is limited to less than 3 which is not super interesting. Dave -----Original Message----- From: Jack Cole <jcol...@gmail.com> To: vortex-l <vortex-l@eskimo.com> Sent: Thu, Nov 19, 2015 1:16 pm Subject: [Vo]:Questions about self-sustaining reactions I have been working on an algorithm to detect excess heat in a slightly different way, but wanted to see if others could perhaps provide some insight. Here are my thoughts: 1) utilize an on/off heating and cooling cycle within a specified range (e.g., 1000-1200C) - input power turns off at 1200C and back on at 1000C and repeats 2) compare this to a steady state run at the average temperature from the cycling range (let's say 1100C) If you have a theoretical excess heat running continuously at 20W in both conditions would you expect the average input power in #1 to be greater than #2. I suspect the answer may be no, unless the excess heat is truly capable of self-sustaining the reaction for a period of time. I would welcome any thoughts on this process. I suspect Dave could speak well to this from the perspective of his simulations. Thanks, Jack
