Big Beta Stirling 1kw, 100degC to 400degC

[zhivko]

Hi everybody,

I'm putting effort and time to make this beta stirling to work.

Finnaly I made it all way to flywheel, that is pretty heavy (around 30kg).
Working piston is prety big (250mm).

Please feel free to check my gallery at: [album]BigBetaStirling gallery[/album] big beta stirling[/url] advice why and how to improve.

the main two questions I have:

1)Are the kinematics of working piston and displacer OK?
2)Will the area of fi 250mm be enough for transfering heat from gas burner to air that is used as working media (stirling should run with 250 rotations per minute) so that means that in 1 fourth of second all this air should be heated and cooled later.


Stirling still needs to be started.

Hope to get some constructive comments.

This is specification (technical data for that stirling) from SolarHeatEngines

Input Specification Value Units
Power cylinder diameter 250 mm
Power cylinder stroke 235,37 mm
Displacer diameter 250 mm
Displacer stroke 158 mm
Dead volume (Hot) 0 cm^3
Dead volume (Cold) 0 cm^3
Dead volume
(Regenerator) 0 cm^3
Engine cycles/sec 4 Hz
Hot gas temperature 400 degC
Cold gas Temperature 100 degC
Average Pressure 1 Atm
Gas Constant .2870kJ/kg-K
Results Value Units
Net Work (per cycle) 287.8 Joules
Work out 479.8 Joules
Work in -192.0 Joules
Power = net Work x cycle/sec 1151 watt
Max Pressure 1.753 Atm
Min Pressure 0.5696 Atm
Pressure ratio 3.078
Max volume 1.929e+4 cm^3
Min volume 7756 cm^3
Volume ratio 2.487
Mass of operating gas 9.596 g
Temperature ratio 1.804
Isentropic compression heating 54.70 %

[Geoff V]

zhivko

You certainly have done a lot of work on this engine project, unfortunately the proposed dimensions mean that it will not run at all!

The heater, I guess, has about 750 to 1000 sqcm, if the gap is about 1.5mm, the heat transfer will be about 1 to 2watts per sqcm or about 1 to 2Kw but only if you heat the sides of the cylinder where the heat transfer takes place. The displacer swept volume seems to be about 7750cc yet the displacer gap area is only 11.78 sqcm so the power required to pump the air through this small pass area will be enormous.

The compression piston (power piston) stroke of 235mm is about 1.5 times the displacer stroke, at the heat exchanger casing temperature difference of 300c this needs to be about 110mm stroke, or less, to give a displcement ratio (lambda) of nearer 0.7:1. The displacement ratio is impossible for me to calculate accurately as it varies on a beta depending on the crank geometry, but as proposed, the gas will not expand enough to create a pressure difference across the piston, the engine will not run. If you doubt me, construct the engine and with the compression piston disconnected, apply heat and turn the engine such that the displacer reciprocates and see how little distance the piston travels.

Finally, plain heat exchangers and no regenerator will realise an internal thermal efficiency of 5%, with luck, if you manage to impart the working gas with 2Kw, the power output will be about 100watts!

Sorry to be so depressing but I have been there several times over the last 30 years.

GeoffV

[Ian S C]

As Geoffv has said you have the displacer, power piston ratio back to front,ie., putting it in round figures, if the power piston had a stroke of 200 mm, the displacer would have a stroke of 300 mm 1 : 1.5. I would sugest that 2 mm to 3 mm gap would be a bit nearer. The length of the displacer should be about three the diameter. I imagine that you are using a water jacket for cooling the cold end, a good sized radiator will be needed, preferably with a pump to circulate the water, and a fan to cool it, with good cooling, I would run the motor vertically, easy way is displacer at the bottom, best way is displacer at the top, but it then needs some design work on burners. The vertical engine has less friction, and the displacer is easier to keep straight in its chamber. Ian S C

[zhivko]

Thanks guys for constructive comments, and as geoffv already guessed I hadn't have luck today witth running engine (I have put some more videos where I trained muscles starting beta stirling without success ).

It seems at the end of half an hour heating the front of inox cylinder didn't heat it enough (by the way heater is 12 to 38kW strong gas burner). The first two cooling fins could be easily touched by hand. It seems I would need to build heater guide as it is showed in bottom image (attached to this post).

Since the engine is already build I am thinking what would be the easiest (cheapest) way to modify it so it could run? I was thinking changing the displacer piston so it would have regenerator (steel wool) wounded around displacer piston.
@ Geoff V:
Do you think that adding regenerator at the sides of displacer (in current gap of 10mm betwween displacer and inox cylinder) would be enough? Of course I also plan to add heater guide that should increase heat transfer on the sides of inox cylinder. If I manage to bring temperature of planned 400 to arround 600 degreesC - do you think this crank that give displacement of 250mm would be ok? Current crank mechanism insures that working piston reaches top of aluminium cylinder.
So if I understand you correctly the pV diagram on the solarstirling engines with my specification is not correct??
Video of crank mechanism and displacement of working piston and displacer is here: video of crank mechanism in action

@Ian:
Cooler is designed as air cooler - for the moment would not like to over-complicate with water cooled system.

[Geoff V]

zhivko

The main reason it will not run is because the displcement ratio is way out, the displacer stroke must be greater than the piston stroke if the bores are the same. Disconnect the piston linkage, run the burner and turn the engine slowly, you will see that the piston moves much less than the stroke, therefore it cannot create a pressure difference across the piston so the engine will not run. There are many other things about your design which will require changing, the compression is far too high for example, but for now try the experiment I have suggested and you will be convinced that the crank geometry is the main fault.

GeoffV

[zhivko]

Geoffv,

thanks, ok I understand now. Is there any method beside the practical test, to calculate right displacer and piston displacement? If I assume right it depends on temperature ratio, medium, working pressure etc.
Is calculator at Stirling calculator worth of spending money?

But lets say for 100 to 400degC, atmosferic pressure, and 250mm cylinder bore.

That practical test is surely a thing I can do. Thanks again for suggestions.

Zhivko

[Geoff V]

zhivko

Save your money, I have a proffesional simulation program that doesn't even agree with a real engine when the data is input. I also have a good friend who has published five books on the Stirling engine and now agrees with me that the only data of value comes from the engine its self.

Regarding the best displacement ratio, there are many variables which will effect this, temperature ratio is the main one and the ability of the heat exchangers also have a big effect. By disconnecting the piston on your engine and cycling the displacer with the heater at temperature it will give you a very good indication of the displacement ratio your engine needs. If you consider a LTD model engine requires about 100:1 and a commercial hydrogen pressurised engine at 1000K works about 1:1 you will understand the benefits of measuring your engine.

Good luck.

GeoffV

[Ian S C]

zhivko, if you read my other posting you will find the correct ratio, and size of the displacer, this is the ratio used by Robert Stirling in his engines.
Have you built a working Stirling Engine? I would suggest that you build a small one, to the correct formula, and get it to work. Then study some fo the older, large engines, and then you might build an engine you can start without wearing your arm out, you don't need a sore arm, although you might get a sore wrist if you don't get the friction level right.
On your current engine the area heated should be about one third of its length, 250 mm, around its full circumference, and its end, and with gas firing, and a stainless steel hot cap, this should be at least a dull red. for cooling your air cooled motor of that size, a shroud around the fins, and an effective fan to push a large volume of air over the fins, its at least as important to get rid of the waist heat as it is to apply the heatat the hot end, just as the exhaust is most important in a IC engine if you want performance. Ian S C

[Ante]

zivko

today I made two excel sheets

first file(stirling pistons beta) you can see ratio of strokes(if piston stroke is same) in your beta engine to get volume ratios of 1.5 recomended for high temperature engine.
(calculator which you used is made for gama engine)

second file(zivko) I modified ross yoke to your drive linkage and try to reconstruct dimensions from picture. You can see that phase angle is about 58° that is maybe also one small brick in your story.

I hope that this will be useful to you

Salute!
Ante

[zhivko]

Thanks Ante,

I made a video of corrected crank geometry (as GeofV suggested), please see video at new crank (also includes displacements chart of touch points of displacer and working piston).
Now displacment ratio of both pistons is aprox 1:3 (see attached chart) - Ante is this the same like volume ratios (1.5) as you mention?

Ante if I understand correctly phase difference needs to be exactly 90degrees? I tried to understand second excel sheet you attached (named zivko), but its dificult for me to understand the point of attachment of of displacer and piston arms. Some additional sketching would be very nice to have...

Thank you all,

zhivko

[Ante]

i sending sketch

i made one eror blue line is piston movement and red line displacer in excel

Salute

[Ante]

i forget to tell you that my linkage is rotated for 90° (vertical engine)

[Ian S C]

If that drawing is to scale, the displacer should be much longer.
I don't understand what you mean,"my linkage is rotated 90* (vertical engine). Ian S C

[zhivko]

Ante, thanks for sketch - but it's still hard to understand - can you please mark with green circle static points and with yellow colour points of arm connections (displacer and working piston) - you could mark direction of arm movement with yellow arrow.

As Ian mentioned displacer movement should be bigger (still question for me how much bigger) - I corrected crank mechanism (please see picture from previous post and video).

@Ian & All:
1) Displacer and piston movements
Have you checked graph of moving pistons? Is it now OK? Do you think that strict sinusoidal movement is necessary?
2) Displacer
Is it OK to leave displacer long as it is, extend diameter of displacer to the inox wall, and fill outer half of displacer with inox steel wool? When I tried to rotate flywheel I experienced a lot of power was used to move displacer - it seems that if I replace outer half part of it with steel wool would ease the movement of displacer.

Thanks for answers,
zhivko

[zhivko]

OK - I carefully and slowly read all your posts (GeofV, Ian and Ante) under this topic - it seems that my first design is OK -BUT only with small change - I missed the orientation of one of crank arms (L shape) . The correct orientation would give right displacer and working piston movement ratio (1:1.5).

I checked first video (first crank geometry displacement ratio 1.5) and it seems its in 1.5 displacement ratio.

There is also the detail about displacer length(as Ian mentioned it should be 3 times the displacer diameter and Ante mentioned 2 times displacer diameter), but still I am unsure about the displacer to inox cylinder gap - Ian mentioned 3 mm.
That would be hard to achieve since displacer is welded design (it's not done on lathe), also the force to move displacer with 3mm gap would be enourmous (I think).

Filing outer half of displacer with steel wool (possibly copper wool instead stainless steel wool) seems better idea? What do you think guys?

zhivko00