Power output- management of expectations

[brian hughes]

Is there an accepted formula for what power output to hope for given the engine RPM, displacer bore and stroke, and temperature difference? The engine under construction is working between an estimated 300 and 600 Kelvin, with a displacer 65mm diameter and 120mm stroke, running on air without pressurisation- what sort of power output can I expect? Watts? Milliwatts? Tens of watts? I do realise that more RPM means more power, and I would mention that I do have a degree in Physics, and I should know this, but my thermodynamics has got a bit rusty since 1979. Thanks for any help.

[Bumpkin]

Hi Brian, dunno no physics but here’s some basic thoughts. It sounds like rounding your numbers down to about 7 CID and at a 2/1 temp difference — (thank-you for understanding absolute temperature, though by the way, 300k is assuming some pretty good cooling,) and rounding up to 15 PSI atmospheric, (though an atmospheric engine of that temp difference with a “snifter” valve would run at more like 1.5 bar,) - and figuring two power strokes per revolution, you could theoretically get about 1.5 ft. Lb per revolution before considering dead space. Assuming no friction, that’s around .03 watts per rpm if I haven’t had too much to drink tonight. And that’s assuming a power stroke that exactly matches the 2/1 expansion/contraction, which of course, would make it difficult to run at lower temps. And obviously the faster the engine runs, less of the 2/1 temp difference will be transferred to the air for a 2/1 pressure/volume difference. How much less and the peak power rpm is dependent on the individual build, so I don’t see how there could be an “accepted formula,” but I have to appreciate you being worthy of giving me a headache thinking numbers tonight. Good luck, have fun.

[brian hughes]

Thanks for the reply- do I understand... that there's around 2 Joules per revolution given the swept displacer volume and temperature difference? How do you calculate that? I do realise that it's a theoretical upper limit, but I can see 10 Watts to charge a phone within reach. Could you bring me up to speed with snifter valves? Do I understand... that it would be a reed valve that keeps the average pressure above atmospheric, for a little bit more power density?

[Bumpkin]

Actually I just worked backwards from inch pounds and RPM to the standard 33,000 ft lb per minute =1 hp. I’m sure there are better/simpler formulas and I’m not even sure I did it right. Yes the snifter does just what you say. It needs to have a very light actuating pressure to get full advantage.
Bumpkin

[Tom Booth]

.... Could you bring me up to speed with snifter valves? Do I understand... that it would be a reed valve that keeps the average pressure above atmospheric, for a little bit more power density?

This is interesting. I haven't heard of that one before. Like a check valve?

So when the pressure in the engine drops, each time the gas is cooled, by being moved to the cold side, a little more air is taken in?

Is that by chance, what this little protrusion on this engine is ? I had assumed it was just to equalize pressure with atmosphere rather than increasing it.

fig169_01.jpg (54.18 KiB) Viewed 3489 times

[Bumpkin]

That’s probably what the picture is. It wouldn’t make much average pressure difference in a low temp low pressure engine but it’s also to replace blow-by. Not really necessary in a LTD, but helpful.
Bumpkin

[brian hughes]

https://www.sciencedirect.com/topics/en ... ling-cycle I think the answer that I'm looking for is the equation:

energy per cycle=(mass of air in play)*(gas constant for air)*(temperature difference)*ln(compression ratio)

so, putting in values of 0.0005 kilos of air, 319.3 for the gas constant, a 300K temperature difference, and a compression ratio of 1.1 yields a figure of 4.5 Joules per cycle. So, by my rusty maths, I can think about a ballpark of Watts of power. Not kilowatts, not milliwatts. What I will be doing is making the flywheel to a fixed moment of inertia, using an Arduino to measure the angular acceleration, and measuring the power with an inertial dyno.

[Alphax]

Brian,

One way of estimating power output is to disregard the engine altogether and think about the input power. You don't mention what your heat source is, but I assume it is a combustible fuel. The rate at which you burn it in order to reach your operating temperature range (300 to 600K) determines your power input. Your power output will (obviously) be less, so now you have an upper bound. Assuming you haven't discovered some earth shatteringly high efficiency, you will maybe get a tenth of your upper bound (power input) as output power. Until you get it running as sweet as a nut, you may struggle to do better than a twentieth of your input power.

If you have a physics background, then why not consider an electrically heated hot end? The calculations (input power) are vastly quicker and easier to do in real time and you'll have a much better control system than you could ever hope for with a combustion heat input. I realise you probably know a lot (if only you could remember those lectures....) about basic electric instrumentation, but one thing you may not know is how good and how cheap remote power monitoring sensors are. Radio controlled model aircraft sensors can give you millisecond data feeds (by radio - no need for messy wires) on current (as long as you don't want to go over 100 Amps) and Voltage (40V or less) with the radio TX giving you full digital control (fixed voltage of your choice and current on a throttle lever with instantaneous readout on the Tx screen). So - that would give you up to 4 kiloWatts to play with for input power and you can get your input power data (as three separate time files for voltage, current and power) continuously downloaded to a memory stick or micro-SD card. The Arduino - nice as they are - isn't really as good, though a Raspberry Pi 4 might be.

If you went electric, then once you'd got the engine to run as you want it you could switch to more conventional fuel burn. One other advantage of electric heating is that you can insulate the heating element and be sure most of the heat is going where you want it - the danger of heating beyond your working temperature (600 K) is eliminated if you have a cheap ceramics kiln sensor and monitor set to cut power at your predetermined maximum cap temperature.

[Alphax]

Brian,

If you wanted to make comparisons with other (Stirling) engines you could use an on-line solver such as:-

https://www.fxsolver.com/browse/formulas/Beale+number

That would allow you multiple "if this, then that" guesses at how sensitive your particular design parameters are to affecting power output and give you not only a "feel" for what to expect, but how it compares with published engine designs (which is what the Beale Number is for).

[Alphax]

Or... if you really wanted to do some rigorous estimates of output power for your specific engine design, then Allan Organ's excellent book has the essential equations and a few handy nomograms:-

Stirling Cycle Engines: Inner workings and Design, Allan J. Organ, Wiley press.

(Dr Organ spent 20 years as a lecturer in engineering at Cambridge University and is recognised as one of (quite probably the) most knowledgeable and competent engineers on how Stirling engines actually work - no mean feat given the wide variation and inherent complexity of design in these superficially "simple" machines).

eg:

[brian hughes]

Thanks for the reply- just to give a little bit more context, my heat source is going to be the -currently- wasted heat from my biochar making burners. I've currently got more heat than I know what to do with, by "heat", I mean hot flowing gas, and getting it transferred into the hot end is probably going to be the bottleneck. An electric test rig would be nice... but at present I don't have access to grid power- I could do some very good things if I had. The rough roadmap is: get the wheel going round, and build a dyno to measure the output. I'll add a generator- I presume a stepper motor could be pressed into service, and if I can get 10-20 Watts to take round the festivals this summer, I'll be very happy.

[Alphax]

Brian

Thats why I mentioned RC electric systems - you run them on Lipo batteries. You will have to charge them somewhere, of course, but they give a surprising amount of power for their weight and will easily run 4kWatt for an hour at a time. My model aircraft used less than that, it ran on 1.3 kWatt and the system variables were constantly displayed on my transmitter (Tx) via a link on the receiver (Rx) and instantly variable with finger tip control- absolutely ideal for taking round the festivals!



By the way.... if you succeed in a shaft output in the range of 10 - 20 Watts, then you will have achieved a very impressive result indeed.

You would be within touching distance of 50 Watts which is regarded by some as a commercially viable threshold. Fifty Watts would power a multitude of devices these days and could be really useful in lots of remote places.

I do think an experimental, non-optimised engine design might struggle in the early stages of development, though, and to get 10 watts usable power at the shaft, you may find you need a couple of kiloWatts at the hot end - but if you have that going to waste (as you say) then you are onto a winner!

Let us all know how you get on, and good luck!