Beta Stirling Project

[Akya2120]

Hello, I am new here but I came here because I needed to find a community of people who know about this stuff (somewhat unlike me.) I am building a beta as a class project and I am looking for a couple pointers. I am planning to use a combination of 3D printed parts, machined parts, and off the shelf items (like 608 ball bearings, and gaskets.) My design is currently a bore and stroke of 5cm, which means a swept volume of 98.17cc. I initially started just designing one from scratch but I quickly realized that there are many aspects that should be taken into consideration. I would greatly appreciate if someone could recommend a correct displacer length, stroke, and diameter, and dead volume (or if you could direct me towards the calculations I would need to do this right.) Do we define dead volume with the power piston in the top dead center position? There are certainly other questions that will come up that that is what I have now. Thanks for your time!

[Akya2120]

I was looking at a post IAN S C made talking about the beta engine from a post.

"Oilman, if you are going to make the displacer from the 40 mm aluminium tube, don't(I know, I tried[twice]). If you want to get any power out of the motor, you need more heat than the aluminium will stand.
The displace should be three time it's diameter long, and from what I see of your diagrams (B) is the one, you want say a mm or so clearance between the displacer and the piston, and the same at the other end.
You will be ok with a normal crankshaft and con rods. To get the correct ratio 1.5 : 1, you just have to make the displacer crank a bit longer, and remember that the cranks are at 90*. An example is my second motor the power stroke is 3/4", and the displacer stroke is 1 3/16". With a GAMMA motor you can keep tme both the same, and reduce the bore of the power cylinder. Ian S C"

If my throw on the power piston is 5 centimeters, then this means the throw on the displacer should be 7.5cm?

For the dead space volume (I am still not sure if that is volume with the piston at top dead center, but I would imagine so,) I was looking at a paper which was talking about the Beale number and how that could be used to calculate a desirable volume but it didn't seem clear on how the equation actually helps me.

It said (Volume enclosed)=(nominal power output)/(Beale number)(pressure)(operating frequency)

Now if that is true, that means you can have a relatively small motor which produces huge power by having large pressure and operating frequency. The paper doesn't explicitly state that it is pressure enclosed but I don't know why we would be dealing with atmospheric pressure inside a pressurized vessel. The other question about this is, would that be the change in pressure from uncompressed to compressed?

Since it seems like the operating frequency is somewhat determined by the design. That doesn't seem like something I should just pick arbitrarily and there isn't much discussion about finding good frequency in the paper.

Does the displacer volume really matter as long as the dead space is right? I read somewhere that the domed shape of the displacer is important, is the reason for this the so that the regenerator can see more airflow?

[Ian S C]

With a BETA motor the dead space is governed by the clearance you allow between the displacer and the power piston at one end, and the displacer and the end of the hot cap at the other.
The time you see a domed hot cap, and displacer is when they are made from test tubes. It's much easier to make a square end.
Ian S C

[Aviator168]

There is also a gap between the displacer and the cylinder

[Akya2120]

I don't want to assume that 7.5 cm is the displacer throw, am I correct to design for that?

I will modify my design so that I don't have a domed displacer and cylinder, that does make things easier. Thanks :)

I get that the displacer determines the amount of dead space, but I am curious how to select a good starting ratio? I could see where I could make a variable displacer that essentially has different caps which screw onto it (and have locking screws) making for more or less dead space. Something similar could also be done with the head of the cylinder, where we could essentially make risers for the head to adjust the dead space volume.

With those two ideas it seems like I should start with the minimum amount of dead space and then it would allow me to later adjust the volumes. Unfortunately I don't think I have time to take on a project with that much added complexity. Which is why I am trying to find a good calculation for the dead space. I was thinking I would have a displacer clearance of 1-2mm above the power piston and below the top of the cylinder. If the throw on the displacer is 7.5 cm, my displacer height seems like it should fall between 3-5cm and the total height from the bottom piston position to the top of the cylinder should be 12.7-12.9 cm. Those are just my guesses though, I was hoping to find a resource that has some sort of way of generalizing the enclosed volume.

Thanks for any input :)

[Aviator168]

I don't know how much is minimum amount of dead space to you. Dead space is a necessary devil. Minimum amount of dead space leads to minimum amount of heating and cooling space.

[Akya2120]

Minimum dead space also means minimum working fluid which is the important part of the engine. It would likely just be added complexity to make a somewhat modular unit for the purpose of testing. Though that might be a great way to empirically test the system and see what changes have a positive effect.

Has anyone tried putting the regenerator in the displacer of a beta? This to me means the displacer would need to have a tighter tolerance in the cylinder. I am thinking of trying this if it doesn't make my design too complex, even though this will be my first Stirling.

Also has anyone tried something like this for their regenerators? I know steel wool is common but copper is a better conductor, which to me means it will take and give heat more efficiently.

http://www.artistsupplysource.com/produ ... fgodKjQAJQ

[Ian S C]

I think you mean the stroke if 7.5 cm, the throw is the off set of the crank, and if the throw was 7.5 the stroke would be 15 cm. So stroke 5 cm power piston, 7.5 cm displacer.
My largest motor is an ALPHA, the bore is 5.7 cm, the power stroke is 3.2 cm, and the displacer has a stroke of 4.5 cm, you can see a photo of it I my gallery, it's the large one with cast iron legs, and two 15 cm flywheels.
Ian S C

[Akya2120]

Thanks! My mistake I should have remembered that. I read somewhere that have a square stroke is a good balance between rpms and power which is why I went that direction. My brother was under the impression that an over square stroke is better for producing power, is that true or should I keep the square stroke?

-Currently my cylinder is 241mm, is this going to be a hard cylinder to get correct?

-I have a displacer measuring 120mm, and a 1mm clearance between head and piston in their respective positions. My dead space is 149.22 cc not including the small volume around the displacer. Is this reasonable, or should I modify it? my intentions are to be machining in 2-3 weeks.

-I would really like to cast these parts, does anyone have experience with this? I am just looking for some casting tolerances so that I can print the correct size positive for my cast. I am planning to use 3D printed positives for the castings.

-I am also planning to use a 3D printed crank shaft, connecting rods, and 608 ball bearings to let it all spin. Is this a crazy notion? If I am able to cast with suitable proficiency I will likely cast the connecting rods, too.

-Should my cooling system extend from the bottom of the displacer to the top of the piston, or would that be over kill?

As always, thanks for any insight :)

[Ian S C]

Your displacer should be about 3 x it's diameter long, 150 mm +/-, clearance 1 mm to 1.5 mm is about right, it should be made of thin stainless*, or mild steel (* best). the hot cap should be stainless steel. The displacer should be as light as you can make it. The hot cap is best if it is less than 1 mm thick.
The power cylinder is best made of steel, or cast iron*(stainless is ok)(*best).
Don't get too obsessed with dead spaces, and Beale numbers. Build it.
Ian S C

[Akya2120]

It looks like I am going to be sand casting as much of this as I can. Hopefully I will be able to make it from iron but that depends on what will be available in the program I am working with. The professor I will be working with wants me to keep the cast parts small, so I am thinking about casting the cylinder in two pieces. The question I wound up asking myself is, how would I get the two halves of the cylinder to seal? RTV only goes up to 315 C, which would limit my operating temperature pretty significantly. I haven't found any O rings that would work either. How about something like this though? http://www.gasketsinc.com/product/g83-c ... 0degc/1809

[Ian S C]

I presume that it is the power cylinder, and piston, and supports for the crankshaft, and the flywheel that you intend to cast. I don't think it possible to cast such as the displacer or hot cap, it's not possible to make a casting thin enough, 0.25 mm stainless steel. My largest motor BETA 58 mm bore has 2 150 mm flywheels 24 mm wide, there is a photo in my gallery, a vertical motor with 4 cast legs (legs off an old stove).
Ian S C

[Akya2120]

Well I was thinking about casting the hot cap and then machining it to spec. Same deal with the displacer. I know I had mentioned it before but I was planning on putting the regenerator inside the displacer. After more research I have found plenty of gaskets that would handle operating temps. Also since my main goal for this device is sun powered energy I would think using aluminum would be acceptable, unless in the future I end up getting a rather large parabolic lens.

[Ian S C]

Your main problem with aluminium is heat conduction. With a good solar heating system you should on a good day get a stainless hot cap to near if not better than red heat. I ran the largest horizontal motor in my gallery with a large freznel lens(about 450 mm x 600 mm), the focal point etched a line across the stainless hot cap, but the motor had a greater power out put than when using the LPG burner.
For a moderate heat, aluminium aerosol cans serve quite well for short runs with reducing power as it heats up. Ian S C

[Akya2120]

Okay, in that case I will do what I can to use stainless or iron, but if my only option is aluminum that is what it will have to be. I doubt I will be able to have much influence since I am doing this as a project for credit through my school and the professors are doing what they can to facilitate it. I would figure that good thermal conductivity would be a plus, just not to the other parts of the cylinder.

Any input about putting the regenerator inside the displacer? Seems like it could be a good idea, except for the added rotating weight which if done right might be fairly negligible.

I am sizing down my cylinder to 4cm to make it a little more realistic of a project for my program. I am just going to write my logic here on the length measurements in the cylinder, please correct me if something sounds worng. That means to keep a square stroke I would want to have 4cm of piston stroke 6cm of displacer stroke. My displacer should be 12cm which is ~3X it's diameter. To keep a 1mm tolerance between the piston and displacer, and displacer and cylinder head I would want an OAL of the cylinder to be 12cm(displacer length) + 6.2cm(displacer stroke) + 2cm(half piston stroke) + (110% of the piston length [extra 10% just to keep the power piston in the cylinder at all times.]) Does that make sense (or am I missing anything?)

I read somewhere in these forums about someone using teflon for their power piston. For me this sounds like a good idea since I don't have a ton of machining experience, I will be attempting to produce this project over the next 2.5 months (plus a normal class load,) and machining teflon is probably much more forgiving than most metals. What would be a good operating tolerance for a teflon piston? On second thought, this is all very dependent of operating temperature and material choice (that whole, everything expands and contracts at different rates, thing.) I need to nail down what will be materials will be available to me before I can worry about operational tolerances.

Thanks again for all the help! :)