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I am designing my first Stirling engine and I am wondering how much clearance the displacer should have inside of the chamber. I'm guessing that the bigger the chamber the bigger the gap, but I guess it also has to do with the amount of air above and below the displacer. If the inside of my chamber is about 1.25 inches, what diameter should my displacer be? And what is a reccomended material to make the displacer out of?

Ivspiano,A gap of 1 mm to 1.5 mm is a good starting place, 2 mm will work. With a displacer of 1.25" the displacer should be about 3.75" long,make the cylinder 3 or 4 mm longer than the displacer plus the stroke. If you can make both parts out of stainless steel, the hot end of the cylinder (1.5" to 2")make as thin as you can if you are carving it out of solid bar, otherwise get very thin tube (some vacuum cleaners have a tube about 35 mm dia), get an end TIGwelded on it, same goes for the displacer, the ones like that, that I have used are about .010" thick. For the displacer you can get away with mild steel, but if you intend to use a good amount of heat, and want a bit of efficiency, don't use aluminium, it will collapse, OK if your just using a candle.
The ratio of capacity between the displacer, and the power cylinder should be near enough to 1.5: 1 for a high temp motor. Ian S C

Ian S C thanks so much for the help! After doing more research I am sort of leaning more towards the LTD type, with a wide and short displacer cylinder. I'm going to try to get some 100mm clear tube and use that, and make it about an inch tall. So should my displacer be around 3/4" tall? And what diameter/length should my power piston be? By the way I don't have access to any lathes or mills or welders, so I'm going to have to get creative. I'm very handy with a bench grinder and dremel though, so I don't think I am going to have any trouble fabricating parts.

Ivespiano, because the displacer is a loose fit, its cylinder does not need to be particularly round. So don't go to the cost and hassle of getting large clear tube. I now use foil wrapped, lapped and zapped round a handy former. Foils for baking or microwave bags will take quite a high temperature. For tiny models I've used the very thin foils from microwave meals.

The foil will still have to seal to the hot and cold ends. I've used small rubber tube (from tackle shops), slit along its length and pushed over the ends of the cylinder as a sort of U-seal. To eliminate leakage from one end, I now permanently bond the foil to one plate.

You ask about the proportions of the displacer. The radial clearance is not at all critical. The larger the less the flow resistance and the faster the engine, but remember the displacement is displacer diameter (not the cylinder's) x stroke. You can also try perforating the displacer so that jets through it impinge on the end plates to improve heat transfer (perhaps).

In theory, having a thicker displacer allows some regeneration as the air flows along the gap. I've tried lots of displacer shapes and sizes in the same engine but couldn't tell much difference. Indeed, for a see-through engine I used a thin Mylar disc for a dispolacer quite successfully. A thicker displacer will require a longer cylinder, and that will reduce the conduction to the cold end (which can cause the engine to peter out).

The displaceent ratio depends on the temperature difference. Broadly, air expands about 1% for each 3*C rise, but you have to allow for leakage and friction losses. Senft's LTD engine uses a ratio of 150.

Ivspiano, I'm not much into LTD motors, but I'v built one, it's 6" in dia, with a 1" dia power piston, it runs on a bowl of hot water, or ice packs. The aluminium for the top and bottom plates were frying pans, and the displacer cylinder is a 1 1/4" length of 6" plastic water pipe. The displacer is made from foam packing from some electronic gear cut to shape with a simple hot wire cutter to a disc 5 3/4" dia by 1/2" thick. Ian S C

Jester, thanks for the great info! Can you explain the regeneration concept? I've heard the term before but I don't know what it means.

Ian, cool idea, I think if I make an LTD, I'll use pickle jar lids for the top and bottom of the displacer cylinder. They are redily availible and not too hard to work with (I hope )

If I can get into the speech:
The origin of the Stirling engine patent is precisely the regeneration.
(The hot air engines were already present before Stirling).

The displacement obtained from the gas displacer transferred via the cold spot to hot spot, how is greater the difference in temperature between the hot spot and cold, and greater is the energy, pull-out. In the cold point, however, escapes the thermal energy on a massive scale.

To limit heat loss in the path of the gas between hot spot and cold spot, is the regenerator.
In very few time the regenerator trapping the gas heat that is passing from the hot spot to the cold that has gone to act on the cylinder engine, coming back the gas pass again to the regenerator, where it recovers the heat that had caved in and returns to step preheated hot already.

To do this, the regenerator must be a good conductor, having little mass (to easily vary the temperature), and have a large surface of contact with gas.
As you were saying even the side wall of the displacer in the clearance 1-2 mm, can act as a regenerator.
In cases with greater technology, the regenerator is contained in a special compartment, and consists of thin metal sheets, metal sponges, or very thin metal wires.

Eh... thats all beyond me For a first engine, I just want to do it basic. Is Italian your first language, Ferraccio?

Yes, that helps. Have you got any good examples?

With a small high temperature motor, with a long, narrow displacer (L=3x the dia), a certain amount of regeneration occurs along the length of the displacer. On LTD motors i'm not sure if any measurable effect can be gained with regeneration, but I did see plans for one motor using a thin disc of foam, with 6 quite large hole through the disc, these were packed with steel wool. Ian S C

Thanks, all.

For vlspiano,
yes it is, I'm Italian; excuse me for my poor english.
For theropod2, anf for vlspiano, yes: copper (very thin foil or wire) are good for low temperature, but for upper temperatures (also if not so good for thermal characteristics) is commonly used stainless steel, (to temperature near 350-400°C copper loose its mechanical characteristics and collapse).
For very high performances ade used nickel in very thin foils.
Ferraccio

Ha, ivspiano, everyone else has done the explanation of regeneration for me!

A good design of regenerator consists of a stack of gauze discs. They break the airstream up into minute threads with plenty of impacts for good heat transfer. Also, the longitudinal conduction is quite low so little heat leaks to the cold end. The wire needs to be very thin so all the metal is reached. Copper is the best cheap conductor but corrodes at high temperature. Stainless gauze is better if you can find it. Cutting all those discs is a chore, though.

Wire wool is widely used in models. There is a slight advantage if you can preserve the “grain” of the wool and arrange that the wire is predominantly across the airflow, again to reduce longitudinal conduction. Some people use pan scrubbers successfully, although the wire is not so fine. Some claim to have found copper pan scrubbers, but watch that it isn’t just plated steel. Stainless wool is the best for hotter engines, if you can find it.

I use plastic foam. (Metal would be much better but is expensive.) It is light (so the engine is easily balanced) and easily cut – and cheap enough to throw away and start again, but it is not brilliant thermally. I’ve tried plastic pan scrubbers, but I doubt if they exchange much heat at all because the strands are thick and plastic is such a poor conductor. There are various filters for air conditioners and fish tanks that are readily available for trying.

The regenerator acts as a temporary heat store during the cycle. Note that its temperature is essentially constant (because the thermal capacity of the matrix is chosen to be high compared with that of the air shuttling through it), so heat is exchanged without much change of temperature. However, there is a temperature gradient along it. Air entering it from the hot end heats that end most. By half way it has lost half its heat and it emerges almost cold, leaving little heat there. Without the regenerator, all that heat would be lost – as before Stirling. With the regenerator the return flow can pick up the heat it left behind. On entry from the cold end the temperature is not raised much but by half way along it’s been heated half way back up and it emerges at high temperature, leaving the heater to do little more than make up some incidental losses and replace the heat rejected at the cooler. By mutual cooperation, the regenerator saves and returns the heat to the air while the shuttling air maintains the temperature gradient along the regenerator. Magic.

Cooling is usually a problem. It would be much worse if the regenerator hadn’t already done most of it. The heat exchanged with the regenerator in an efficient engine can be four or five times the heat supplied by the heater. Thus the regenerator is a vital component of a powerful engine – though it is not essential for LTD’s.

Jester.

Ah, such a wealth of knowledge on this forum. You guys are great!