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But not because they're small.

I finally got my hands on a high temperature Gamma model engine to play around with. Quite an impressive show these things put on. Light the alcohol lamp and stand back in awe as it rips away at high rpm while lighting the leds with a belt driven generator. But maybe a deeper look will help to better understand these "toys".

First some specs.

Power piston displacement: 1.5cc

Displacer cylinder total volume: 2.6cc

Actual swept displacer volume: 1.14cc

Estimated extra dead volume(transfer port): .25cc

Geometric compression ratio: 1.52:1

Theoretical compression gain: 7.35psi

Observed cold compression gain with my test gauge: ~4psi (reduced amount likely due to blow by past piston and added volume of test rig)

Cold end temperature as measured by IR: 120 degrees F (322k)

Hot end source temperature from alcohol flame: ~1800 degrees F (1255k)

Now, with a starting volume of 2.6cc at 320k we have .0001 moles.

The total volumes after heating are as follows:

400k: 3.2cc
500k: 4.1cc
600k: 4.9cc
800k: 6.5cc
1200k: 9.8cc


The actual observed total volume while at operating temperature is 3.1cc for a total gain of .5cc!!!!!

This corresponds to a delta T of less than 80k!! And that's what makes these things toys. Not for being small, but for being shadows of their potential.

This is a pathetic DTU(delta temperature utilization), but an illustration of how much untapped potential these engines have. This volume ratio to actual thermal ratio would leave most scholars scratching their heads and traditional Stirling guys in a fit.

It's basically just beyond a self sustaining adiabatic bounce at this point. But it still runs at high rpm and makes pretty impressive power and noise.

What's the difference between no compression and 2 psi pressure gain and 1.5 to 1 compression with the same 2 psi pressure gain?

The latter is leaving TDC with 7 extra psi of force, allowing a much higher rpm and therefore much higher power output from the same input(per cycle). These toys are operating at ratios similar to(or beyond) what I was suggesting in the second page of this thread viewtopic.php?t=5572&start=15

Now, imagine a scale HTD engine with the same volume to thermal ratios but with an actual delta T of over 300. We don't just have to imagine, it can be built.

If I understand you, you are saying that with a hot side at 1,200°K (∆T 880°k) there should be an expansion from 2.6cc to 9.8cc but the actual expansion is only to 3.1cc

Which is what might be expected if the ∆T were only 80°K rather than 880°K

Is that right?

I think this relates to what I have been trying to explain about the Pressure and Volume (or PV diagram) not revealing or actually indicating the work output or conversion of heat into work.

As the gas expands and heat is converted to mechanical action the rate of pressure, temperature and expansion increase is reduced accordingly in proportion to the mechanical work output.

So, the apparent discrepancy.

The "missing" 800°K represents the joules of heat being converted to joules of work. That is the ripping "away at high rpm while lighting the leds with a belt driven generator".

All that mechanical and electrical activity and output has to come from somewhere.

If I understand you, you are saying that with a hot side at 1,200°K (∆T 880°k) there should be an expansion from 2.6cc to 9.8cc but the actual expansion is only to 3.1cc

Which is what might be expected if the ∆T were only 80°K rather than 880°K

Is that right?

Exactly

The "missing" 800°K represents the joules of heat being converted to joules of work. That is the ripping "away at high rpm while lighting the leds with a belt driven generator".

I do not agree with this, though I may be wrong. I think the engine is just running on the 80 degree delta and that's it. There may be a bit more magic to it at speed but likely just due to the piston acting as a 2 way check valve, letting in and out air as the engine reaches max and min internal pressure.

If you work out Horse power with PLAN/33,000, the output seems much closer to an 80k pressure gain than 800k.

Good if you ask me, if this model was the peak of performance, I would give up the chase right now and focus on other things.

Most likely the engine is operating at a much higher end of the temperature scale, say 500k-580k, as the displacer inside the engine gets extremely hot and along with the glass hot cap, has much more surface area than the "cold side". That said, the aluminum cold end stays under 120 degrees F when the flame is on. The glass hot cap has incredibly low thermal conductivity, such that the silicone o-ring, only an inch away from the flame, is never in danger of melting.

Tom, this is surely why your wooden displacer offered much better performance in your high temperature model. Displacer surface temperature and thermal conductivity plays a critical role in these engines.

I'll make a new displacer to test the theory. Also looking forward to getting this engine for testing, having a glass tube displacer as well and offering very good performance. Combined with a much better transfer port arrangement and bigger cooling side, it should have much better DTU.

https://www.youtube.com/watch?v=dtuvNYMS84I&t=418s

2 psi(mean effective pressure) x .041(length) x .785(area) x 3000(power strokes per minute at 1500rpm)= 193

96.5/33,000= .005848 horse power = 4.35 watts......

Now with a true delta T of 800 from 300-1100k, we would have a peak pressure of over 50 psi, and perhaps an MEP of 20? Maybe. Either way, that's ten times more power, 40 watts! Definitely not happening on my end! Though I aim to get there.

In reality peak power is likely at a lower rpm, so we don't see even 4 watts.

So, VincentG, are you suggesting that the temperature constraints, Th and Tc, aren't the only limits and that the temperatures of the gas inside the engine are significantly closer together? Lower and higher than the reservoirs. I agree.

That seems to explain a lot in why most engines get less than half the Carnot value.

It takes a temperature difference to produce heat flow. Each surface adding up it's difference.

Yes but I'm not suggesting this is breaking news. Just surprising to me how mechanically inefficient they are. And I already knew they would be inefficient.

What's missing in your calculations is heat transfer rate. Air has a poor heat transfer rate and the faster the engine RPM, the less time for transfer.
Theoretically, the slower the RPM, the higher the power and efficiency should be as the time for heat/energy to be transferred would be.

Not overlooked, just ignored for the purpose of this exercise.

There is the efficiency as defined by the heat taken in by the gas and converted to work, and as defined by thermal leakage between both ends of the displacer chamber itself.

At this point my version of efficiency is as defined by the Tmin and Tmax of the gas itself, in relation to the external Tmin and Tmax of the source. And these tests are performed at essentially static conditions with ample time for heat transfer.

For the above mentioned engine, seen here https://www.touchofmodern.com/sales/dst ... ine?open=1 ,
if the displacer is moved through its full travel by hand, the performance of the displacer chamber can be roughly doubled. Still nothing close to the full available temperature delta.

Vincent, as to the drop from expected 7psi to measured 4psi in your opening post, did you add around the displacer to dead-space? I'm sure it doesn't bottom or top out, and it's probably an annular gap type regenerator? As to that, without a proper regenerator, much more of the working gas temperature difference has to come from the hot and cool end exchanges, which accounts for the gas temperature difference in the running engine being way lower than the external source/sink. Anyway, as to using full expansion of whatever available pressure the engine does produce, of course it might need either more power piston or less displacer, but then it wouldn't run at lower temps. Perhaps a variable displacement scheme to best use varying temp ranges? Even at that, remember the last half of a stroke that achieves full expansion will only add a fraction of the power to the first half stroke, so diminishing returns as you get closer. Anyway, there are probably a lot of budget compromises and a lot of room for improvement in those little models.

Bumpkin

Yup Bumpkin that was all measured. Considering the compression ratio, it's amazing how low a flame this will run on. I'd like to know who is designing these little engines, and what knowledge base they have at hand.

VincentG, I have a book by Andy Ross that on page 95, compares a Ford 351 CID engine from 1975: to a 52.5 CID Stirling "4-215" (Siemens/Rinia) engine made in collaboration with Ford and Phillips. They show a photo of one installed in a 1975 Ford Torino on page 97.

V8: 150 HP, 244 ft-lb torque

Stirling: 170 Hp, 300 ft-lb torque

That pretty much blows away anything currently discussed here. The theory they used was the standard 200 year old theory I speak of here. It was about a 150 year old theory when Phillips used it. If they abandoned it, they are talking as if not.

It was pressurized using hydrogen, not helium, so would be very cheap and easy to replenish, as needed.

My guess is they were unable to come up with a competitive cost of manufacturing plan. The same as for the Chrysler turbine cars.

Exotic materials are cheaper now, so I don't know if it would now be possible, or not?

My hope is that we could improve on that success.

Wow, I don't think I've heard power claims that high. Incredible. Would love to get my hands on that book.

I've looked into those Philips engines, or as much as I can find online. While astounding in their performance, I believe they went down a dead end road that leads to high cost of manufacture, high complexity, and require a high level of machining skill/equipment.

Stirling Cycle Engines, by Andy Ross.

Yes an excellent book. Might be in the library.

https://www.amazon.com/Stirling-Cycle-E ... B004I3YSBW