I'm planning to build a Stirling generator to work off heat from our kitchen stove.

[VincentG]

Agreed that while the regenerator may increase "efficiency" it in almost every other way, at least without near 100% optimization, hurts outright performance.

I don't think that there's NO place for a regenerator, just that the base engine should be designed to maximize output without one. Only after that, maybe it should be introduced to gain efficiency, hopefully not in trade of power density.

[matt brown]

Ideally the displacer should change positions at top and bottom dead center of the power piston position. That way the gas reaches full hot temperature at the beginning of the expansion stroke. The opposite for the cold compression stroke. Lost motion links, dwell, have been used to improve that over the more common harmonic motion, sinusoidal crank and slider motion.

Going to lost link, basically a Bang-Bang motion, is a compromise on beneficial vs detrimental effects. The energy of moving the displacer is lost, not saved by the crank-flywheel speed, and there will be more, noise and pounding. Meaning it will only work for small low mass engines and displacers. Great for proving a small toy model engine will run at extremely low temperature differentials and extremely slow speeds, rpms. However, it will provide very very low power, I.E., microwatts, with an incessant clicking.

The energy loss from many 'clever' schemes is often overlooked, since the output per rpm is quite low unless mega atm charge pressure. Even then, mechanical efficiency usually sinks such schemes.

Having harmonic motion for the crankshaft and piston means that timing is a compromise. At some advanced adjustment point, the heat will be added before top dead center enticing the engine to move backward. In the extreme, it may run excellent but be very difficult to start. Momentum of the crankshaft will have to push it through exactly the same as for an ICE. So timing other than 90° may very well be beneficial. Variable timing may also be an option. How to do that???

This classic phasing issue is the hallmark of typical two chamber SE with an unregulated gas flow. If one is willing to add some complexity to design (more chambers, regulation, whatever) then this inherent limitation disappears.

The regenerator is a heat suppler and saver, as you've said, preheater. A bit more complicated, okay for now. It's timing will be slaved to the displacer motions. It is plain and simply an efficiency enhancer, a very very important one.

Matt Brown pointed out that the regenerator saves multiple times the heat entering the engine per cycle. Imagine, at extreme, an engine getting 25% efficiency with regeneration, getting 5% without. Or 5% with and 1% without. With "free heat", efficiency doesn't seem important, but imagine getting five times more electricity from the same engine? 20 Watts without vs 100 Watts with. Build one with and without to see which has more kick.

The basic efficiency is the Carnot function, but this relates only to external heat input and output. A glance at a common Stirling PV may confirm Carnot, but gives no indication of total cycle heats. The main omission is the heat of regeneration which is the heat required between the high and low isotherms, and this is more than the input heat for most SE cycles. A typical 300-600k SE cycle has max Carnot=.5 eff and raising cycle values to 300-1200k will increase max Carnot=.75 eff. Assuming the same SE could use both of these cycles, simply raising the input temperature raises Carnot eff. as if by magic. However, the heat between the 300-1200k isotherms also increases, so the ratio of regen heat to input heat remains constant (this ratio is known as regen load or simply 'load' in the trade).

If we consider Tr=thermal ratio and Vr=volume ratio, most comm'l SE have Tr>Vr as if Carnot gain will save their design. Unfortunately, as Vr shortens relative any Tr, each rpm produces less output per rpm since regen is required every rpm. It should be obvious, but rarely seen anywhere, is that Vr>Tr should be the focus where the aim is to produce as much work per rpm as possible between each regen cycle. The problem is that typical SE tap out around Vr=2 for various reasons. The only common SE with Vr>Tr is typical LTD (with 'long' banner-like PV plot).

The lack of regeneration is probably the main reason rotary displacers have not replaced their sliding counterparts.

I think Bumpkin nailed this rotary issue suggesting regen favors pistons, but his oscillating rotary idea proves there are other possibilities. I favor piston schemes for positive displacement where the rings are both side and end seals. Rotary schemes may appear to solve some old issues, but they always have seal issues.

[Tom Booth]

...

Heat goes, in during expansion, out during compression. Work comes out.

Opposite for a refrigerator. Work goes in.

I know everyone here knows that. Sorry. I get off onto a tangent. I find this fascinating and helpful. Thanks.

Not everyone. As I would assume you already know, I have challenged those assumptions on theoretical, experimental and mathematical grounds, as well as, I think, direct measurement.

Most notably in a "free piston" Stirling, yes, you have heating and expansion driving out the piston and doing work. Then what happens to effect the return of the piston to TDC seems like a bit of thermal slight of hand.

How this might influence the design of a rotary displacer engine is something I haven't thought about.

But the THEORY being that the added heat gets entirely converted to work which leaves the working fluid cold so that it NATURALLY or AUTOMATICALLY contracts and returns the piston to its starting position without any requirement for any heat "rejection" at all.

A merry-go-round comes to mind.

In pushing a merry-go-round, if we were to think of each PUSH as heat input and expansion being converted to work, where do we have any, or any need or requirement for push-rejection.

For each push we "put in" we have to take a push out, right?

I mean, that is the logic behind the Carnot heat engine theory. Not only do we need heat input we also need to take heat away to "complete the cycle".

IMHO, wrong!

Maybe a rotary displacer doesn't need a cold side any more than a merry-go-round needs some kind of ANTI-push or push taking away mechanism to remove the push that was put in so the merry-go-round can complete a revolution.

https://youtu.be/70NH2F7RBjs?si=HvDFTJAgvwMCyAgf

[Tom Booth]

Looking at your rotary vane air motor:

Resize_20231124_004948_8853.jpg (168.78 KiB) Viewed 30119 times

Instead of compressed air injection, I think bumpkin mentioned earlier he thought you could just heat the cylinder, instead of air injection, just have heat injection at the same, or approximately the same points. (Red dots)

There would, of course, though, be no need for any air inlet or outlet ports. And I don't think you need any heat outlet.

As the hot gas drives the motor around it just naturally cools and contracts as a consequence of imparting energy to the rotor. Heat is converted rather than "removed" to a sink.

[Jack]

That would be ideal I guess, but can that happen fast enough for it to move an engine?

I've been looking at the limitations of all my previous ideas and other engines and it's almost always heatsink. Delta T. There's only limited time to heat up and cool down the air. We try to solve that by adding surface area.

With this rotary vane engine it dawned on me that I could basically pause the heating and cooling phase of the cycle. Because there's the possibility of having 10-12 cycles at a time around one rotor, the work is separated. And if that's separated I can collect the fluid at it's two extremes and give it ample time to heat up or cool down, thus increasing the delta T considerably.

So I'd have a hot space and a cold space. One heated by the fire, the other water cooled. Basically two heat exchangers, or radiators with large surface area and volume.
I've switched my idea to two rotors in between the spaces, connected with gears or something similar.
Let's say the two spaces are the same volume at room temperature. 5 bar each. When I start my fire one side heats up to above 400C and thus doubles the pressure in there to 10 bar.
One rotor gets pushed by 10cc of this hot air every cycle, moving it into the cold space. This is powering the other rotor which moves 5cc into the hot space. While that heats up it will again increase to 10cc.
It seems to me that in a lossless world I can keep this going as long as the fire is going.
I'm guessing it needs some tinkering to get the balance right on that, because I do assume there will be some losses.

[Jack]

As the hot gas drives the motor around it just naturally cools and contracts as a consequence of imparting energy to the rotor. Heat is converted rather than "removed" to a sink.

Gas naturally cooling is it exchanging temperature with something else, right?
The faster you do this, the more sudden the difference in pressure is and easier to harvest the energy in that.

For what you're proposing I think we would need something like a snail house shape somehow.
Am I understanding you right?

[Jack]

Ah no, I see I misunderstood.

I was working on a design with exactly the idea you're proposing. But it seemed very difficult to transfer enough heat. It would end up with a very thin layer of fluid around the rotor. I'll post a picture of my design tomorrow.

[Tom Booth]

As the hot gas drives the motor around it just naturally cools and contracts as a consequence of imparting energy to the rotor. Heat is converted rather than "removed" to a sink.

Gas naturally cooling is it exchanging temperature with something else, right?
The faster you do this, the more sudden the difference in pressure is and easier to harvest the energy in that.

For what you're proposing I think we would need something like a snail house shape somehow.
Am I understanding you right?

Not sure, but I don't think so: "is it exchanging temperature with something else,"

No. Not "exchanging temperature". I don't think.

There is an energy exchange between the hot gas (working fluid) and the engine so that the heat of the gas (molecular motion) s converted to the mechanical motion of the engine.

As the gas loses energy its temperature decreases, but the energy transfer is not "thermal". The energy transfer is in the form of "work" rather than "heat".

Anyway, I had another idea, though I haven't quite decided if it is a good one or not.


Assuming, as I said, the gas cools and contracts due to work rather than heat transfer, there is no need for water or other cooling.

I was thinking the vanes could shift between two hot sides.

This drawing appears to be linear, but it could be considered an edge view of a rotor.

duel-vane-engine.jpg (558.43 KiB) Viewed 30089 times

[Tom Booth]

If you take a look at the four sections between each set of red dots on each side, as the vanes pass between the dots (areas of heat input) you basically have the four stages of the "ideal Carnot cycle". 1) isothermal expansion, 2) adiabatic expansion, 3)isothermal compression, and 4) adiabatic compression.

Though that was accidental.

[VincentG]

It seems that a standard vane motor has both too little heat transfer area, and far too much compression ratio.

These could, I think, both be solved by machining or drilling annular cavities into the rotor housing (and reducing the diameter of the rotor itself). Of course positioned so as not to ever interupt the full contact of the vane seal, so similar to the piston ports in a two stroke ICE. The number of vanes would likely have to be reduced to 4 so as not to have too much crossflow between rotary chambers and give ample time for heat transfer.

[Jack]

It seems that a standard vane motor has both too little heat transfer area, and far too much compression ratio.

Yeah that was my conclusion as well. I ran some rudimentary calculations and the transfer area compared to displacement is just too small. That's why I'm working on the two pools idea.

[Tom Booth]

Ah no, I see I misunderstood.

I was working on a design with exactly the idea you're proposing. But it seemed very difficult to transfer enough heat. It would end up with a very thin layer of fluid around the rotor. I'll post a picture of my design tomorrow.

Looking forward to seeing this design as I really have no idea what you might mean by "It would end up with a very thin layer of fluid around the rotor"

If you have the means to make your own rotor I'm not sure what relevance the issues with a "standard " vane motor have, as you can design in whatever surface areas, compression ratios, etc. you might want.

[Jack]

What I mean by that is that I figured the fluid needs a certain amount of heating and cooling surface area for it to transfer heat fast enough for it to generate enough difference in air pressure to be useable.
In a vane motor this is a ratio between outer cylinder wall, displacement and working "piston".

If I look at known engines and their power output, and somewhat guesstimate their heating surface area to fluid displacement ratio then I end up with the following sizes in a rotary motor.
https://www.dropbox.com/scl/fi/vmihqzwj ... enshot.jpg
The center circle is the rotor, the second circle is the "displacer" and the outside circle is the cylinder.

The bigger I make the rotor, the smaller (percentage wise) the "ring" around the rotor will get.
The same equations were used for these sizes:
https://www.dropbox.com/scl/fi/a9zg49e7 ... u7ei8&dl=0

This is the design I was working on, since abandoned haha:
https://www.dropbox.com/scl/fi/cq9ef4n1 ... vsn0r&dl=0

[Tom Booth]

...
https://www.dropbox.com/scl/fi/vmihqzwj ... enshot.jpg
The center circle is the rotor, the second circle is the "displacer" and the outside circle is the cylinder.

The bigger I make the rotor, the smaller (percentage wise) the "ring" around the rotor will get.
...

I don't understand what you mean by "displacer'.

You have the rotor, cylinder and presumably vanes dividing the space in between into sections. What is the function of this "displacer".

I don't really see how or why a displacer of some sort fits in with a rotary engine of the kind you've previously illustrated.

4de06e32e06725676551683bc1e9d1e8.jpg (26.16 KiB) Viewed 30035 times

Can you explain this in more detail?

Not all hot air engines have a displacer. Laminar Flow for example. I'm not able to grasp how or why there would be a displacer or how it would work.

I am, of course, very familiar with the general purpose and function of the displacer in hot air engines generally, just don't see how it would work in a rotary engine of this kind.

[Jack]

If we're working with expanding and contracting air, and I want a closed cylinder, I can't use the one like in the picture you mentioned above. Because it goes back to nothing or very little airspace at some point in the cycle.
The displacer in my rotary design is just a minimum of volume of air being moved around. The lobe created by the off centre rotor is the working area or "piston" if you will.

So to compare it with the picture above, I would need to move the rotor further back to the centre. And the minimum circle it makes then is my displacer. Or all the working fluid I have to work with.