Can I use a Stirling generator to make electricity from our wood fired stove?

[Moochingaround]

TL;DR Summary

I'm trying to come up with an efficient way to make electricity from our wood fired stove. I've come up with an idea evolved from a stirling engine and I need some help with the physics of it.

For the last few weeks I've been breaking my head over an efficient way to make electricity from our wood fired stove. We don't need huge amounts, but about 500 watts would be nice.
I'm a retired engineer and I'm taking this on as a hobby really.
I've gone through various ideas and iterations in my quest to make it more efficient. But now my head is too full with all kinds of parameters to be able to tell if my latest idea is viable haha.
The math and physics has never been my strong point. The numbers just start dancing around in my head.

On to the idea:
Imagine two spaces with equal volume. One is in my fire, the other is water cooled. In between I would have two vane motors. One with double the displacement of the other.
Both the motors are connected with a gear or belt.
When I start my fire I hope to heat up one space at least 400 degrees, so doubling the pressure in there.
Now that pressure drives the bigger vane motor which transports that hot air to the cold space.
While doing that it powers the smaller vane motor, which transports half the amount of air from the cold space to the hot. Where it will get heated up and continue the process.

Am I correct in thinking that in an ideal world this would keep going as long as I have a hot enough fire going?
Am I missing something?

Thank you for your time.

 

[Baluncore]

400 degrees should be sufficient to run a Stirling engine, even better if they are Celsius degrees, not the cheap Fahrenheit ones available in the USA.

In your system, one vane pump is pumping cold dense air into the hot high-pressure chamber, the other is a motor, driven by hot air returning for cooling, driving the pump, and an electric generator in the process.

The power needed to pump an incompressible fluid is the volume in metres cubed, multiplied by the pressure difference in pascals. The pressure difference is the same for both sides, and the gas is changing pressure due to temperature, not compression, so I think it might work. If you are lucky, the cold side will be heated at about the same rate that the generator produces electricity.

If you could employ a compressed gas in the pump-motor loop, you might improve the power output with smaller pumps and motors. The main problem will be finding a high temperature vane motor with graphite vanes that will survive the pressure difference.

Your system would be more efficient if you could adjust the ratio of the two vane motor/pumps. You could do that by using a variable gear ratio between the motor and pump, so the volume being pumped is correct for the chamber gas densities. The mass transfer rate of air will then be equal, so the system will be in a steady state.

Flue gas can heat the hot side, while air, being inducted into the furnace, can cool the cold side. Better to economise by pre-heating the air, at the cold side, on its way to the furnace. If you use water for cooling, you must use it or lose it.

I don't think it is a perpetual motion machine.
This will need some thinking about.

 

[Baluncore]

By employing a closed system, with positive displacement motors and pumps, I think what we are considering here is the Stirling gas turbine equivalent, of a Stirling piston engine.
Search Stirling cycle turbine.
https://en.wikipedia.org/wiki/Closed-cycle_gas_turbine

 

[jack action]

I don't think you will achieve a Stirling cycle with this setup. You will most likely get the cycle in green in the following figure. It is compared to the equivalent Stirling cycle having the same low & high temperatures, at the same pressure low and high pressures. (Points 3 & 4.)

Starting at 1, you will most likely experience an isentropic expansion, not an isothermal expansion as required by a Stirling cycle. You would have to carefully add heat to your vane motor as it decompresses the gas. It cannot be done "easy", certainly not "fast".

Like most vane motors/pumps, the compression lasts for so long and at one point the partially decompressed gas is presented suddenly to a much lower pressure, giving the isochoric step seen on the graph. In your cooling tank, you have an isentropic cooling period, bringing the gas to your expected lower pressure and temperature at point 3.

Going from point 3 to 1, you have the reverse process: Partial compression in your vane pump followed by a sudden compression when the gas is exposed to the hot, high-pressure, tank, and finally an isentropic heat addition to your expected high pressure and temperature at point 1.

Whatever isentropic heat addition you input in your hot tank, you get the same energy output in the isentropic expansion in your motor. Similarly, whatever heat you remove isentropically in your cold tank, you will put it back during the initial compression phase. And if the isochoric events of your motor and pump coincide, you basically get no work output. If they would pass that point, your system would actually require a work input.

But all of this is assuming that your tanks have different inlet and outlet pressures. That may be difficult to achieve with a [slow] Stirling engine. So your heating and cooling processes would most likely be isobaric as presented below. (Although, with a well-designed system, there wouldn't be an isobaric cooling process; the isochoric process during the discharge of the motor into the cooling tank would be sufficient.)

As you can see, your motor inlet pressure may not be as high as you expected.

 

[Moochingaround]

Thank you for the answers! This is really insightful.
It seems my idea has indeed evolved from a Stirling cycle to a Brayton cycle.
The variable gear solution is worth looking into mechanically. It can optimize the ratio between the two motors. Am I right in assuming that in stead of the compressor pumping half the displacement of the motor, it can also pump the same volume, but at half speed?

Jack action's answer taught me a lot, I had to read it a few times to make sure I understood it correctly haha.
I had a different idea about the vane motor though. In my initial design I thought about the compressing and decompressing stages. And in stead of suddenly releasing it into a lower pressure volume I would design the inlet and outlet in a way that would allow the gas to expand inside the vane chamber to the pressure it is going into.
So for example I take in 10 bar and 5cc in the hot space, I let the vane motor turn until that expands to 10cc at 5 bar (or as close to that as I can) and then release it into the cold chamber.
The opposite for the compressor side.
That way I catch all the work the gas can do. I would also make sure that the work is done in a hot vane motor, so not to lose too much to the gas cooling down. And on the other side the compressor would be kept cool as long as possible.
I think this would prevent some of the issues you mentioned. But then again, it's just my theory.

 

[Baluncore]

Am I right in assuming that in stead of the compressor pumping half the displacement of the motor, it can also pump the same volume, but at half speed?

In effect, yes, but that does not mean you must use identical devices, they must each be selected on merit.
You are thinking volume and density, but in the closed cycle, it is the mass of air being moved that must be the same through both the turbine and the compressor, to give them their proper names. Otherwise, the hot and cold chamber pressures, would not remain stable during continuous operation.

 

[Moochingaround]

That makes sense. Thank you!

 

[Flyboy]

Yeah, Brayton cycle would probably be better. And to be honest, might be worth doing a steam engine at that point. More moving parts and a bit fiddly to adjust to proper performance, but it's very simple to manufacture and maintain yourself. At that point it boils down to, well, your boiler system. (Pun very much intended) I'm no engineer by profession, but I can think of a couple ways to efficiently boil a steady flow of water to feed a steam engine, starting with a simple copper pipe wrapped around the exhaust flue and going all the way up to custom made boiler that sits in the flue. It really does depend on what you'd be comfortable with.

That said, there are some other uses you can use that heat for, too, if you want to get real fancy about it. Use the HVAC ducting and the fan to blow air across a heat exchanger to cool the water back down after being used for mechanical work is the biggest one that comes to mind. It'd be less efficient at heating that air than using an air-to-air heat exchanger, or a closed loop heat exchanger system dedicated to the purpose, but hey, it's still helping to move that heat from the flue to the rest of the house, it's cooling down the water to be run through the system again, and it's capturing that waste energy that's literally going up in smoke up the flue. Complicated? Oh, definitely. But it might be worth it if you're looking to extract that heat energy and turn it into electrical energy.

 

[sophiecentaur]

it's still helping to move that heat from the flue to the rest of the house

This is a difficult design problem. Wood burner flues need to run hot to reduce the build up of creosote. Cooling the exhaust gases could make this worse.

 

[Nik_2213]

Given you have a fair temperature at source, would thermo-electric array, either primary or secondary position, help ? Upside, no moving parts, and array may be modular plus part of flue / chimney....

 

[sophiecentaur]

This thread is interesting as a chat topic but it would need some serious engineering calculations to assess the workability of such a project. It's a chain with several potentially weak links, I think.

The only experience I have of Seebeck effect generators is in two stove top fans with about 40mm square cells. It seems that they are thermally a bit fragile and the maximum temperature they can survive is not much more than 100C at the hot end (in my versions). The efficiency is not good; enough output power to spin a small fan with a model DC motor (not a cheap eBay motor). Not very impressive performance but a good conversation piece.
This link gives a summary of work on Tegs and they are potentially better than what you can buy for a 'fun fan' and they are cheaper than the equivalent Stirling Engine versions. I see that they are investigated for energy recovery in IC vehicles but they are probably expensive. The technology for modern TEGs seems to produce up to about 500W but the experiments seem to be aimed at vehicle exhaust systems and not suitable for home development ('yet').

The temperatures in vehicle exhaust gases are a fair bit higher than in a log burner and that could affect the suitability of any external combustion cycle.

 

[Nik_2213]

Well said !!
I would agree that modern 'semiconductor' thermo-electrics are probably unsuitable, despite their much higher efficiency than traditional bi-metallics. My experience of 'semi' thermo-electrics is limited to HPLC column heaters: elegant, nimble and devourer of many Watts. However, I've vague memories of 'bi-metallics' being built into base of kettles, used for 'camp generation' of enough power for map-reading by 'torch-light' plus field-radios...

Added: Ha !! Knew I'd seen a recent reference...
https://solar.lowtechmagazine.com/2020/05/thermoelectric-stoves-ditch-the-solar-panels/