The following post was submitted by Esko Lyytinen
I think that the next kind of thinking and study is very essential to successful replication of the Rossi effect and further replications of the Parkhomov replication, with hoped-for good COP. I don’t think I have seen this discussed, but I’m not for sure — I am a long time follower of this site, but have not read everything.
(This kind of thinking is (for the most part) also quite new to me. I got to this thinking-chain when waking in the night and was kept awake for about 3 hours thinking this. This thinking of course continued when better awake.)
There are simplified assumptions in this, but even in a more complex situation, this kind of analysis is very important. We do not practically know some of the critical parameters, but some general level even conclusions can be reached. I have in this also some conclusions, but most of what follows may not be quite final. This is mainly to encourage further study and discussions.
Most of the existing discussions have been on the fuel composition, etc, but even if one has very good composition of the fuel, the discussed things may totally prevent a good COP with the setup and/or inevitably lead to the destruction of the tube/stick/bone.
The very recent results by Lenz team from Moscow (with DC energy input) may tell that to have the reaction is mainly dependent of the temperature with magnetic things of less or no importance. And even IF the magnetic things are of importance, the next type of analysis is still important.
I will now make simplified assumptions and try to avoid mathematical expressions with derivates etc. I try to explain some of the concepts by describing these, in order to give a god idea on these.
This does not deal with nuclear things, but only assumes that the reaction exists and is a function of the temperature (here dealt with the absolute temperature in Kelvin). The amount of heat is of course dependent of the amount of the fuel, (maybe can assume proportional to this). And there may be other things affecting things. Also the short and long term history are probably more or less affecting. But here we concentrate on the dependency by temperature.
Assume, that the dependency of energy by temperature in a given working point (temperature), can be described by a constant E. If the absolute temperature increases by 1% (or any small amount) and the power output also increases by 1% (the same proportional small amount), then E=1. If 1% temperature increase increases the power by 2% then E=2, etc. Here the power is the release of power form the reaction only.
Then we consider the thermal outflow from the reaction. IF all this were by the thermal radiation, then the outflow would be practically proportional to the fourth power of absolute temperature (assuming a not very warm ambient). We denote this coefficient of the reactor by R (not to mix to electric resistance ), which in the case would be 4. (In this we assume the outflow to be the same than energy generation at leas for a moment. Or we can in this consider the properties of the tube only independent of where the energy inside comes.)
On the other end, if the outflow would be completely by thermal conductivity to the ambient of 0 deg Kelvin (which of course is not reasonable). Then would be R=1. With some more reasonable ambient temperature, the R would be bigger than 1, much bigger if the reactor temperature were quite low, but would tend to get smaller towards 1 if the reactor temperature increases a lot above the ambient temperature.
IF there is no active regulation, then the condition for stability is: E R, then the increase of energy (from some temperature increase) would lead to even bigger further increase of temperature etc, leading to non-stabile run-away.
In the above we were thinking the R to be dependent only from the LENR energy. And the stability condition would then be even to complete ssm (self sustain mode). To have this, then also the amount of fuel should be just correct for the given working temperature.
Assume that there is some electric (or some other type) energy also in use in a non-ssm situation. IF we assume (for example) that the used energy is as big as the energy from the reaction, then a given increase of absolute temperature of say 1 % increases the total (reaction plus input) outflow of energy by 0.5*E*1%. We denote the (in this case) 0.5*E by Eef.
Now the COP=2 and more general thermal stability condition is Eef < R .
This situation now is of course more stable than in the assumed ssm condition. For each case the amount of fuel must also be suitable to this COP and working temperature. And in general it is easier to get the stability with smallish COP. If this condition is not fulfilled, it would appear that Eef is decreased by increasing the input energy, but this would of course increase the temperature and lead to an even more bad situation. The amount of fuel would need to be reduced to get it stable at all with any COP (near this temperature).
As to the suggested further study, the numeric dependency of the LENR energy by temperature would be most desirable. In principle (if having a working fuel etc) this could be measured with smallish amount of fuel and smallish COP, needing then of course good calibration and measurements.
I also do some further speculation on this by doing some assumptions of the value of E. The E is most probably ( a lot ) bigger than 1. IF this is somewhere between 3 and 4, then with these assumptions a thermally stable reactor in ssm would be possible. But for example some amount of the energy flows out by convection, for example making the R of the reactor smaller than 4, maybe around 3. (Some numbers could be retrieved from the Lugano test for example, I think, but did not try this.) Also the energy inside the tube first flows out by conduction trough the tube wall, this decreases the R of the tube and so also the.
IF The coefficient might indeed be this big, then all optimization in this would be very desirable to get a good COP. This includes also for example the wall thickness. As the coils tend to be around the tube and fuel, this also increases the wall thickness and decreases the R value. In this respect it would be desirable to have the coil inside the fuel. This would make the requirements of big temperature-durability of the coil even more important. (Might it be possible to have inside a gas-discharge tube to supply the electric input-energy.)
This kind of thinking makes is also quite clear, why it is so difficult to generate electricity with the Hot-Cat even with big enough temperature that can be reached. If one would have even a completely ssm-working reactor, to effectively couple this for example to a stirling-engine, would most probably result into a smallish COP or thermal instability of the reactor. All these things would need to reconsider very carefully. Also trying to use a flow calorimeter with a reactor that works well in the infrared thermal calibration, may not be quite simple for hopes of similarly good COP:
And considering for example attempts to further replicate the Parkhomov – replication, even if one has the very same fuel and (for example same amount) but has his own tube design, and tries to get it functioning at the same temperature than Parkhomov had in use, this would quite probably result to either smaller COP or thermal instability, this latest MAYBE even by necessity (independently of however carefully the temperature is increased). Only with some good luck would one get as good or better results in the COP.
Every known replication has needed several broken rector tubes. IF/WHEN getting to some more analysis of these stability issues is expected to be helpful in this.
With active input energy control the things may be somewhat easier. Then the control would need to be based on temperature measurements in (or very close) the fuel. But even then, if desired to get close to ssm, the stability considerations are very relevant.
And further, IF the above stability condition is true for the whole tube, any non-smoothness of the fuel (or warming coil) may locally get the situation as non-stable. So, it is of very big importance to have the fuel very evenly distributed.
In my opinion Rossi himself has made these kind of analysis quite thoroughly (with the hot-cat and also the (less hot) Ecat). And as to his recent new idea and version of his hot cat, I don’t know but I am expecting his new insight to have something to do with the stability issues.