Calculating volume ratios using PV=nRT

[VincentG]

Our goals are different it seems.

Yes and no. I applaud your effort/hands on testing and I understand your view point on the consumption of heat. It does seem to me that the heat can be mostly, if not completely, used up in driving the piston towards BDC. This would seemingly be the most efficient way to complete an engine cycle.

To me though, the primary issue with ECE engines is power density, and this is not strictly linked with efficiency, in fact it's often the opposite. So attempting to keep gas temperature constant all the way to BDC will maximize power output, even if this comes at the expense of "waste heat". Waste heat in quotes because it can easily be recycled in a closed cycle heating system(to preheat the working medium before the main heater) and then used for other purposes, so none of the heat is wasted in my view.

I believe the adiabatic process will come back into play once we can make an engine with a low enough volume ratio that is past this zero point. Then there will be an efficiency boost along with a power boost. I think that these displacerless free piston engines are already past this point, but bring along a whole new set of challenges that I for one am not ready to tackle.

[VincentG]

I may have found an effective way to analyze what's happening inside my LTD engine while running. The engine in the following videos is running on a weak tea candle flame, and so the temperature delta is pretty low. It has far less power output than over a full boil. The engine is fitted with a magnetic load cell that will increase resistance with rpm. Its just a neo magnet running past a chunk of aluminum, like a magnetic brake system.

If you look at the connecting rod, I have made a sharpie mark to reference the piston to the rod. So you can see where it is within the slot that the wrist pin rides in. You can see the point where cylinder pressure changes from positive to negative and vice versa. In the second video, I have just added ice to the water to increase the delta. You can clearly see that the transitional point gets closer to TDC and BDC , back towards the zero point and therefore less actual compression and expansion work.

My thought is that at this low temperature, the long stroke engine is actually past the zero point, and is doing work on the gas. Using the position of the transition point, maybe we can calculate the actual temperatures that the internal gas is reaching based on the swept volume of the piston and the known expansion rate of the working gas, assuming my theory on the neutral state mass of the gas is accurate.

No ice. https://www.youtube.com/shorts/DQHZuIlLSwM

With ice. https://www.youtube.com/shorts/CI3rsA_ZJxs

[Tom Booth]

There are, I think, some problems with "recycling" heat, if heat really is a form of energy that is converted to mechanical work output.

1) If the heat goes out as "work" it no longer exists as heat to be recycled in any way whatsoever. It's already gone.

2) If there is some heat remaining it would be "rejected" at a much lower degraded temperature.

This IMO is the fallacy of the Carnot Theorem "proof" about the impossibility of a heat engine heat pump combination. That so-called "proof" always depicts the heat pump moving heat up from out of the "cold reservoir".

Why try to "recycle" heat that isn't there?

A heat pump is capable of moving heat within the hot reservoir to elevate the temperature more. Whatever "waste heat" ends up in the cold "reservoir" is either not even there at all as it has already been converted or not worth retrieving.

Why bother trying to "recycle" what may, or may not be going into the "cold reservoir", when there is an inexhaustible supply of higher grade heat available from the hot reservoir? Which only needs to be moved to a location where it can be used by the engine.

What I've come to realize, I think, is that the idea that a heat engine runs on a "temperature difference" is a myth.

The engine runs on heat from a heat source to expand the air, and then heat from the atmosphere, in the form of atmospheric pressure to "contract" or compress it back. The "cold side" of the engine, literally does nothing.

You do need a lack of heat (or "cold") as a starting point so the initially cold air can be expanded, do work as it expands and end up cold again, but that seems to be about it. Once the engine is up and running it just needs more heat to replace what's been converted.

Once heat has gone out as work it's no longer available to be recycled.

It is like a tennis match.

One player is the heat source, the other player is a second heat source. Between the two you have the ball in motion. Velocity.

If you extract some "work" from the velocity of the ball it slows down. If it slows down you don't need some means of taking away the excess heat/energy. You need to have one player or the other put in MORE energy to hit the ball harder to compensate for the work output.

Let's say the tennis ball is magnetic and the net the ball passes across is a coil generating electricity each time the ball passes over the net.

The electric power output slows the ball down.

If the players are hitting too hard and there is no electrical load, well, relax the "heat" input, it isn't needed.

When the electrical load increases, BOTH players will have to hit harder to compensate.

Neither player is a "cold sink".

The only energy sink is the electrical load.

To my mind, the whole idea that a heat engine runs on a temperature difference is a 200 year old fallacy.

Heat engines run on heat. We've just been thoroughly indoctrinated to imagine heat flowing through the engine from the hot to the cold side. No such thing takes place. If it does, it's just wasted heat, the wasted heat does not serve some cosmic purpose or "LAW".

Of course, in a tennis match, you only have one player hitting the ball at any one time.

You could say the active player is "Hot" and, at least, for the serve, to start the game, the passive player is "Cold". but this is only a transitory condition. Both players are a heat/energy source. They BOTH hit the ball.

Likewise heat "hits" the piston and atmosphere "hits" it back again in a heat engine. Both are "hot" energy sources. Neither is a "cold" heat "sink".

And you could not have both players at the fence trying to get the ball across simultaneously as the ball would just be suspended between the two rackets and have no velocity to cross the net.

So, in a way, you always need one "hot" side inputting energy and one "cold" side NOT inputting energy, but it is not a flow from hot to cold. It's an alternation or oscillation.

P.S. I missed your last post which snuck in as I was writing. I still need to read and watch the videos.

[Tom Booth]

I may have found an effective way to analyze what's happening inside my LTD engine while running. The engine in the following videos is running on a weak tea candle flame, and so the temperature delta is pretty low. It has far less power output than over a full boil. The engine is fitted with a magnetic load cell that will increase resistance with rpm. Its just a neo magnet running past a chunk of aluminum, like a magnetic brake system.

If you look at the connecting rod, I have made a sharpie mark to reference the piston to the rod. So you can see where it is within the slot that the wrist pin rides in. You can see the point where cylinder pressure changes from positive to negative and vice versa. In the second video, I have just added ice to the water to increase the delta. You can clearly see that the transitional point gets closer to TDC and BDC , back towards the zero point and therefore less actual compression and expansion work.

My thought is that at this low temperature, the long stroke engine is actually past the zero point, and is doing work on the gas. Using the position of the transition point, maybe we can calculate the actual temperatures that the internal gas is reaching based on the swept volume of the piston and the known expansion rate of the working gas, assuming my theory on the neutral state mass of the gas is accurate.

No ice. https://www.youtube.com/shorts/DQHZuIlLSwM

With ice. https://www.youtube.com/shorts/CI3rsA_ZJxs

It looks like a potentially promising means of doing some analysis, and I think I can see what you mean about the change with the addition of the ice, but it is hard to be certain as the camera position changes between one video and the other. Also that green tape or whatever it is on the power cylinder obscures things a bit.

Another potential problem could be that "claw" that holds the piston to the connecting rod. I know I've had problems with that not holding securely. It could slip. I think I ended up putting some super glue on mine for that reason.

Anyway, very interesting!

If you could extend the slow motion beyond just one revolution that would make observation a little easier.

Aside from those issues, it could be a valuable means of analysis.

It would also be interesting to see a comparison with and without the magnetic break, or with a variable load. Maybe additional magnets.

I just thought of another factor, which could throw things off.

The break, is it continuous? It looks like the magnet moves away from or to the side of the aluminum plate. If the breaking is variable or not continuous, the breaking resistance might be mistaken for compression or expansion resistance.

Actually, that might be possible even if continuous. How to distinguish break resistance from pressure? I'd have to think about that.

[VincentG]

Thats a good point, I'll redo this with a bigger plate and a smaller piece of tape(covers a hole in the cylinder). I don't think it's effecting the results much, as I can hear the rod knock with even a steady state load from my finger. Unfortunately, that is the longest super-slow motion video my phone will capture. The claw has been glued already as I've had the same exact problem with any additional power from stock.

I'll also do the same test at full temperature, where theoretically(if the plate exchangers are good enough) the cycle should move to the other side of the zero point. At that point the piston should be pushing and pulling the whole way through the stroke.

[Tom Booth]

I'm not entirely sure what you mean by "the zero point".

I've gone back to review your previous post where you also use that term a couple times but I'm still trying to guess what you mean by that exactly.

[VincentG]

To start, let me know if you understand(not agree) with my thoughts on the ideal mass of gas inside of the engine for a balanced cycle. With that in mind, the "zero point" is an ideal ratio between swept volume ratio and the target temperature delta. If you play around with an ideal gas calculator, its the point where internal pressure of the engine is 1atm at TDC full cold, and 1atm at BDC full hot. In a perfectly ideal engine, this would be the starting point for any Wneg. (edit: I have a more detailed explanation in the opening post)

So for an ideal 300k to 600k cycle, that point is a swept volume ratio of 1(displacer) to 1(PP). That's half the standard recommended volume ratio for that cycle.

I ran a quick test of the engine at full steam over boiling water. I couldn't take a video, but the sound of the rod clacking was completely gone, indicating to me that cylinder pressure was not transitioning mid stroke as with lower temperatures. I can only predict that once I increase the power piston volume roughly 3x to 15cc, it will be back around this zero point, or ideally just beyond it. At that point, the clacking noise may return at full temperature.

[Tom Booth]

Your "zero point" then, is the same as what Senft wrote about in "Mechanical Efficiency of Heat Engines". He called it "constant mechanical effectiveness" meaning internal pressure above atmosphere through the entire expansion stroke and below atmosphere through "compression".

In the book he describes this as something he considered possible but that he was not quite able to fully realize in practice. He certainly tried and came very close.

He had a lot of theory, charts, graphs, PV diagrams and so forth in his attempts to convey the idea.

His book, from the begining avoids the whole Carnot efficiency issue by making clear from the start he is not talking about thermal efficiency but mechanical efficiency.

I thought it a most interesting read. I've argued the point in here before that I really think that a free piston type thermal lag type engine is very nearly exhibiting Senft's "constant mechanical effectiveness", more or less as a natural consequence of being "free" to do so, not being constrained to follow the revolution of the crankshaft.

[Tom Booth]

Senft has several example pV diagrams of cycles that have "no forced work" on pg.11

Resize_20230918_015410_0329.jpg (331.87 KiB) Viewed 9090 times

[VincentG]

That's it exactly Tom, thanks for posting that excerpt. The only thing I would change about his ideal cycle (d) is to make equal the area under and above the buffer line. I really need to get a PV chart of my engine because I think it's very close to figure (a) but with equal area above and below, if not skewed towards the cold side due to the more ideal kinematics of a slider crank at BDC v. TDC.

[VincentG]

Finally got around to working out how increasing the volume ratio would play out and the results are promising. As always this is an ideal isothermal model. I believe, as seen above with the slotted connecting rod test, that I have been able to realize this zero point of constant mechanical effectiveness. I strongly believe that my next test bed LTD based engine will be capable of approaching isothermal compression and expansion past the zero point.

I think the key is how late in the stroke this compression and expansion work actually starts. 4 to 1 may be pushing the limits but I'd like to set the goal high and work backwards from there. The reason is that in this case reality may be better than theoretical. Theoretically if we can keep this compression and expansion isothermal(think low RPM), the available pressure gains from 4 to 1 seem incredible for a 1atm closed cycle engine.

In reality, the hot expansion stroke has reached 1atm at 55 degrees before bottom dead center. Past that point the air is being expanded even at 600k, so when the displacer shifts to cover the heat source, there should be a significant expansive cooling effect that may go below the cold sink temperature, and even more net pressure "loss".

Similarly, the cold return stroke has reached 1atm at the same 55 degrees before top dead center. Past this point the air is being compressed even at 300k. If the (likely partial)adiabatic compression and the displacer exposing the hot plate can align at just the right time, there could also be a max temperature that exceeds the hot sink temperature, and even more net pressure gain.

Because of how late in the stroke this compression is occurring, the flywheel has a lot of mechanical advantage over the piston, so getting past this "gas spring" may be rather easy. The volume ratio can be lowered to find the sweet spot here.

The real magic here is using half the amount of gas and heat to get twice the pressure gain, while bringing the meat of the cylinder pressure closer to the first 90 degrees of crank rotation, and speeding up the heating and cooling process close to TDC and BDC, similar to internal combustion engines.


1 to 1 power piston to displacer volume
Displacer = 100cc
Power piston= 100cc
Buffer charge= .004 moles(150cc @14.7psi @450k)
Internal pressure TDC @300k= 14.7psi(zero point) No compression work.
Internal pressure TDC @600k= 30psi
Net hot stroke pressure= 15psi

Internal pressure BDC @600k= 14.4psi(zero point) No expansion work.
Internal pressure BDC @300k= 7.2psi
Net cold stroke pressure= -7.2psi

4 to 1 power piston to displacer volume
Displacer = 25cc
Power piston= 100cc
Buffer charge= .002 moles(75cc @14.7psi @450k)
Internal pressure 55 degrees BTDC @300k= 14.7psi(zero point) Compression starts here.
Internal pressure TDC @300k= 29psi
Internal pressure TDC @600k= 58psi
Net hot stroke pressure= 29psi!!

Internal pressure 55 degrees BBDC @600k= 14.7psi(zero point) Expansion starts here.
Internal pressure BDC @600k= 11.4psi
Internal pressure BDC @300k= 5.7psi
Net cold stroke pressure= -5.7psi

[VincentG]

This video shows well how the resistance of the spring close to TDC has a good return on energy.

https://youtu.be/UjwnwwZ84RU?si=23OMNZS6LZOvSNCY

[matt brown]

Hey Vincent, check out fig. 7 in this article...

http://www.epi-eng.com/piston_engine_te ... basics.htm

piston vs volume_2.png (23.21 KiB) Viewed 7892 times

[VincentG]

Good find Matt, for reference my calcs were based on a Honda XR100 engine having a bore and stroke of 2.1" and 1.8" and a 2.2 to 1 rod to stroke ratio(I increased r/s ratio to game a smaller crank angle). As it turns out that graph matches the piston position and crank angle BTDC almost exactly. 55 degrees BTDC corresponds to 25 percent of power piston volume remaining.

[matt brown]

This article has a lot of interesting tidbits for 'piston scrapers' (lol). The text next to Fig. 6 is golden. I often use this chart since I often scheme with 4" bore, and 6" stroke is about minimum possible (chart is 4.00 bore with 6.10 stroke, so I love it).