That data is already quite old so not much meaning for us to model something we’ve already moved beyond. But anyway appreciate your work.
Does this mean that you think that the heat generation does not depend on temperature? Or that the dependence is qualitatively different from the Arrhenius-type of activation that Mizuno was assuming in the past?
I still prefer to work with actual data
Good! I used Mizuno's published data, and some of the data you posted here, to set the parameter values describing the dependence of heat generation on temperature.
It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia, also Tadahiko Mizuno-MTI)
It is just fine to use the sort of simple model I have made as an aid to understanding your results.
Once again, I have made few assumptions. I have assumed that the rate of LENR heat generation increases as temperature increases. This, after all, is what you yourself assume. Isn't it? And I have used Mizuno's empirically observed Arrheneius activation energy to characterize how the temperature dependence works. Finally, I treat your reactor as a lumped heat capacitance with Newtonian cooling. That is it.
It is highly simplistic. Intentionally so. And yet its qualitative behaviour agrees with some of the data you have posted on this thread. But it also shows some behaviours you have not so far seen. I think the model is saying that your own assumptions imply consequences you have not yet thought through.
Science is conjecture and refutation. The model I have proposed is part of this.
Pretty high temperature....what type of material are you using here. Thanks for clue.
This is from a mathematical model. The parameters of the model are set from experimental observations by Mizuno and Daniel_G. For those parameter values, it looks as though the system would like to operate at temperatures that would melt the components of current real systems. That is a challenge for actually engineering anything like this.
Perhaps my reasoning is wrong and yours is right. The data will tell us. I’m willing to be wrong. I believe I know what’s wrong with your model but no point to debate here until I get the data. Your models are well thought out indeed and that’s commendable.
Well thank you.
I am willing to be wrong too. In fact that is almost exactly the purpose of super simple models such as the one I have made. In model making you have to make your assumptions super clear. Thus, when the model results begin to depart from observations you have a good shot at understanding what makes the model wrong or (more likely) incomplete. And that is a step towards knowledge.
I remark, however, that so far your data agree with my model.
I prefer doing real experiments and then designing a model later that fits the data. Doing it your way, is a bit like the tail wagging the dog.
Well Mizuno has been doing real experiments for years. You have been doing experiments. I used these results in my model. And the overall nature of heat flow is well known, so I used that too. I haven't posited a particular mechanism for heat generation. Everything I have said would work for chemical heating or joule heating too if they delivered heat in a temperature-sensitive manner as you are claiming happens in your system. Really, all I am doing is thinking carefully about what happens when your claims for your LENR heating are taken seriously.
And you are model making too. In your head. Based on your experience and understanding you create chains of reasoning to guide your future actions. For instance the following ...
"No input power is required if your control system removes only the excess heat. Envision a system that reaches operating temperature of 600C and continues heating to 650C. A heat transfer medium leaving the reactor at 650C and returning at 600C would require input power? (hint: the answer is no) Just like we don't leave the starter motor running on a Diesel engine..."
Well I certainly understand where you are coming from, but as a general statement this turns out not to be true. In the model I created, I found that harvesting excess heat is not sustainable unless the system is already in a state that doesn't need any input at all to sustain the working temperature. And you haven't seen that yet. So I don't see that your reasoning works.
In 2018 I found that if you take the model I have been talking about here and add one more variable (in addition to temperature) you get bursting. At the time, I called that variable "inactivation". It would be something that opposes the generation of internal heat. Inactivation could be thought of, for instance, as local poisoning of the reaction by the end products or exhaustion of reactants. When inactivation builds up the temperature collapses back to ambient but then then slowly dissipates to allow a new burst to form.
Here is a diagram I made at the time. In the top 2 panels black shows the temperature response of a control reactor and red is the temperature of an lenr-active reactor. In the bottom the black trace is the temperature of an lenr-active reactor. Grey is inactivation. Input heating is continuous, not pulsatile. The bursting arises due to the internal dynamics of temperature and inactivation.
This is part III of my exploring the consequences of a temperature-sensitive source of internal heat generation in a thermal mass. My model is very simple. It really consists of nothing but standard thermodynamics and the sort of properties that Daniel_G and others believe characterize LENR heating.
I have already shown that if you heat the thermal mass in the model above a temperature threshold, the positive feedback of the temperature-sensitive internal heating causes the system to become unstable. The temperature rises either forever (if the temperature-dependence of activation is purely exponential) or up to a high stable state (if activation is sigmoidal with temperature). Once beyond the threshold and into the high-temperature state, you can turn off the external input and the system will stay at high temperatures. At this point the COP is infinity.
Now I ask will look at harvesting heat from the system while it is in the infinite COP state...
Result 7: Below is the temperature response to initial external heating to shove the system to the high-temperature state followed by the external heating being turned off at time t = 30. The behaviour is very much like Result 6 in my pervious post. The difference here is that not only is external heating turned off, but heat is additionally being harvested. The result is that temperature declines somewhat but still there is no external heating required to maintain the system in a high-temperature state. Energy that can be used to perform work is being siphoned off here (at just under twice the rate of the now extinguished external input). Mathematically this is a new stable state and could last indefinitely. Physically, the stable state would only last as long as raw materials for the reaction (deuterium?) last.
Result 8: Too much energy harvest can collapse the system out of the high-temperature state. Here (below) the rate of energy harvest has been increased by 25% beyond its setting in the figure above. A new threshold is now relevant. Once the temperature of the system goes below that threshold the positive feedback of the internal heating no longer beats out cooling and the systems collapses back to a stable state near room temperature. The temperature threshold for getting into the high-temperature state and that for collapsing out of it are not the same. The collapse threshold is at a higher temperature than the ignition threshold. Together these set an range of temperatures within which the system must operate in order to continuously withdraw energy at COP = infinity.
Result 9: It is hard to hold the system at temperatures where it doesn't want to be. The figure below shows an attempt to hold the model system below the 2000C operating temperature at which it would like to sit. In an attempt to hold the system near 1000C I I have turned off external input heating and turned on energy harvest early, at time t = 15. The system lingers near the desired 1000C for a while but then escapes up to near 2000C even though the energy harvest is unchanged. If I turn up the energy harvest rate marginally (by less than 0.5%) in an effort to keep the system near 1000C indefinitely, the systems collapses back to room temperature (not shown). I think, though, that with a sufficiently aggressive feedback control system that supplies a little bit of extra heating or cooling just when needed you might be able to regain stability. It is a bit like a fission reactor in that sense.
Remarks:
1) The red traces in the figures above always show the temperature response of a non-active system to the same input ... just for reference. Also, all figures were generated from systems in which internal heat activation is sigmoidally dependent on temperature (Arrhenius function). If the activation is purely exponential then there is no stable high-temperature state. Any energy harvest would have to be accomplished while using some sort of aggressive control system of the sort mentioned above to stop temperatures from either going up forever or collapsing down to room temperature.
2) All the temperature thresholds that shape the behaviours of the system can be calculated in closed form. Given sufficient knowledge of the parameters of the system you can predict how much energy you can get out of it and at what temperatures.
This is part II of my exploration of the consequences of harvesting heat in a simple model of a thermal mass with Newtonian cooling, a source of externally controllable heat delivery (the input), and an internal source of heat generation that is temperature dependent. The temperature dependence-of internal heating is described using an Arrhenius function with the activation energy measured empirically by Mizuno.
I am numbering my results and will continue the numbering from where I left off in my previous post except that I will first set the stage by reposting the first figure from last time
Result 1 (recap): Here is the time course of heating in response to turning on a moderate level of input power. "Moderate, here, is defined as an input that ends up activating only a small portion (~1%) of the maximal internal heat available.
Result 4 (new result, so continuing numbering from before): Increasing the input power by 25% results in a >25% larger temperature response (note the difference in temperature scale). Nonetheless, the overall behaviour is about the same as before and the steady-state excess heat activation is still only about 2% of maximum.
Result 5: Increasing the input power by only 10% more leads to a qualitatively different type of behaviour. Once the temperature goes past a threshold the system enters a regime of temperature instability. In this region, the internal heating establishes a positive feedback as the increased temperature provokes more activation which, in turn, provokes higher temperatures, etc. Below the threshold, increases in activation were more than balanced by increases in cooling, now they are not. This creates an inflection in the temperature time course. By the end of the segment shown below, the steady-state activation is more than 50% of maximum. The new, high-temperature steady state (note, once again, the revised temperature scale) is a reflection of the sigmoidal nature of the Arrhenius function. If activation was purely exponential, and not sigmoidal, there would be no high-temperature equilibrium at all and once temperature threshold sis passed the system would increase in temperature without limit.
Result 6: Once you have crossed the threshold and entered a high-temperature steady state, you can turn off the input power and the internal heating remains activated. It is like lighting a fire in your fireplace. You use a match to light it but once the fire catches you can blow out the match. In the figure below the input power is turned off at time t = 30
Remarks: All of this is implicit as soon as you add a source of temperature-activated heating to a thermal mass. The results are generic in the sense that, for such a system there should always be a threshold beyond which temperatures become unstable. The only question for particular situations is where the threshold is and how it relates to the actual physical properties of the system such as melting points of the components.
So much for Part II. Next time I will show what happens when you add heat harvesting to the mix.
Only when the heat captured by the air flow is less than input energy. When there is a lot of excess heat, the heat captured in the flow exceeds input energy, and you can ignore errors in other heat flow paths.
Yes. Good point!
One of the eccentricities of the Mizuno results with air-flow calorimetry was that the heat captured by the flowing air never rose above the input power. Even weirder, that it was often almost equal to input power. I recall that this worried you too.
I wonder what the situation with Daniel_G's oven setup is.
I’m saying if you like to ride unicycles on top of unicycles then have at it.
I am asking about your own empirical observations. Do you find that establishing temperature control is markedly more difficult in an oven with an active reactor compared to a nonactive reactor?
. It would be even harder than trying to steer a large ship with a compass that has a time constant on the order of 6 or 12 hours. At least for this ship the response would be linear. Now try to do it with a non linear rudder. Good luck!
Are you saying that it is harder to temperature-control your oven when it has an active reactor inside than when it has a nonactive reactor?
Any serious scientist would prefer steady state end points without any electronic intervention and integral calculations and PID controls.
As I read him, Paradigmnoia is suggesting steady-state endpoints with no electronic intervention, integral calculations, or PID controls.
I have been thinking about what happens when you harvest heat from a system equipped with a temperature-sensitive source of internal heating (which is how many people think LENR acts). The simplistic model I have mentioned before helps to think about these issues. To remind ... the model consists of an idealized thermal mass with Newtonian cooling, a source of controllable extrinsic heating, and internal (LENR-like) heating that is activated by an increase in temperature (and that activates quickly relative to the heating time constant of the mass). Recently, I have been using an Arrhenius function for the temperature dependence of the internal heating. This allows me to use some of Mizuno's own data in the model.
I now add to the model a term which corresponds to a harvest of heat from the thermal mass. For simplicity, I model this as withdrawing heat at a set rate (power) such that the rate doesn't depend on temperature. This is doable physically although it may not be the physically simplest way to withdraw heat. The reason I make this choice is that it is conceptually simple -- heat harvesting and heat input both then become temperature independent and, in fact, heat harvesting is really just the same as just turning down the power of the input.
Here is how the model behaves under particular circumstances. This is only part I. There will be more in subsequent posts.
Result 1 (below). Temperature (degrees C) of the system after the input is turned on. Red is control and blue is with a temperature-sensitive source of internal heating. The parameters of the model have been chosen to replicate the results described by Daniel_G earlier on this thread. Time is in dimensionless units that can be thought of as heating time-constants for the thermal mass (i.e., after 1 time constant the red trace is 1/e of its way to its settling temprature).
Result 2 below). Begin to harvest heat. Heat is withdrawn from the thermal mass at a rate that is 25% of the input power. The temperature declines accordingly and the internal heating becomes slightly less active.
Result 3 (below). Harvest heat at the same rate as it is input. The temperature declines right back to baseline. Excess heat is basically turned off.
Remarks: Although the temperature-sensitive internal heating is activated by the inputs shown here, with these inputs you can't get out of the system any more power than you put in. Thus, in the second panel above one might think 'Hey great, here I am constantly harvesting some of the excess heat being generated internally!' ... but the rate of harvest is less that the power being fed into the system to support the working temperature. Overall, no net power is being created. If you attempt to get around this by increasing the harvested power, as shown in the bottom panel, eventually the the temperature decreases so much that the excess heat turns off.
So ... no free lunch so far. To move beyond this you need to raise the system temperature enough that it becomes self heating. Then, theoretically, you can turn off the input altogether and harvest some of the heat that is still being released. It turns out that this is, indeed a capability of the model. That is next (maybe later today, maybe tomorrow).
Here is another example of remarkable primate behavior. They feel jealousy.
Interesting book. "Baboon Metaphysics" by Cheney and Seyrarth (2007).
Are baboons self aware? Do they lie? Do they realize that other baboons have minds like theirs and might also lie? Field experiments by a pair of biologists working in Botswana.
The title of the book paraphrases a quote from Darwin ... "He who understands baboon would do more towards metaphysics than Locke."
Sure, a lot of systematic errors (or better said, erroneous assumptions) can be made and have to be taken in account, but with a calibration reactor with identical mass but inert mesh, all these erroneous assumptions can be put to rest.
Paradigmnoia and I have already agreed with each other that there is nothing he found in his studies of Mizuno's air-flow calorimeter that would account for the differences he (Mizuno) sees between control and active mesh behaviours.
I thought it was solve for Q, ( = m•C•ΔT , the answer is in joules), then derive power.
How does one measure the oven output besides temperature that results in a power or energy output term? I think the oven method should probably work OK in its normal working, um, range, but the output really isn’t measured as such and so I’m on the fence if it it actually qualifies as a calorimeter in the true sense of the word.
I think that anything that tries to estimate the thermal energy of a system by a rise in temperature of one of its components is calorimetry. As far as I understand, you even really need to characterise all heat pathways for this to count as calorimetry. After all, if you know through calibration that the component you are measuring captures X% of the heat you can estimate what 100% is. Of course that is a risky process because if you don't have the right value for X, or if conditions in one of the other components changes, you might not be aware of it and your estimate could go badly awry.
It s these risks that you have been assessing for Mizuno's air-flow calorimeter.
Is this the same Bruce I have been arguing with? Aliens take over your body?
Yes Bruce you are correct. Perhaps my poor skills to explain were the problem…
My aliens and I thank you for your kind words.
My characterization of steady-state calorimetry above is exactly what I have been saying all along. No change. It is what is captured (in an extremely simplistic way) in the model I made.
Surely any calorimeter integrates over time.
Depends what you are doing with it. If you want to know how many calories in a 10 gram piece of cheese then food scientists put the cheese in a bomb calorimeter and heat it till it burns up and gives off its chemical heat. That sort of measurement has an end point. At that end point you turn off the heater and the total temperature rise in the calorimeter is an integration of all the heat put in and all the heat given off by the cheese.
I think that Daniel_G has in mind a different form of calorimeter that operates at a steady state. Thermal energy is always moving into the system, endogenous energy is always being released, and all these gains are just balanced by losses. There is no firm endpoint here to integrate to. So you just do all calculations using power.
I think that Paradigmnoia may have an answer to my question. He has lots of experimental experience with inert reactors.
