I’m currently working on a low-temperature engine for use in a solar-powered sculpture project. Fortunately it really doesn’t need to run anything other than itself. Ideally it will not use concentrated solar to keep the project simple although that limits the engine to a very low temperature ratio. A low temperature ratios mean low power. This engine is a test to if it is practical to run with a delta T between the hot and cold sources of around 20 to 30 degrees F.
Although this engine may look a little crude, I designed it to minimize friction sources as much as possible within reasonable limits. The levers are used to perform mass balancing of the displacer and power piston. The long rod lengths keep side loads to a minimum.
Operating between 99 deg F and 74 degF my simulation shows .004 watts at 60 rpm. That is equivalent to lifting 16 grams one inch every second, not much power to divide among all the friction sources, but apparently enough to run. The engine will run down to a differential of about 21 degF.
Major friction sources
The major sources of friction are the displacer rod shaft running through the seal and the power piston. The power piston caused me less difficulty. Turning an aluminum piston until it just slips in the brass cylinder is not difficult and the leakage is reasonably low. With the cylinder port closed the 12-gram piston settles under its own weight at a rate of about .75 inches in 16 seconds. This type of arrangement works well but I have yet to try it over an extended temperature range. A thermal expansion coefficient mismatch can cause lockup or allow too much leakage if the temperature varies over a wide range.
The displacer rod seal caused me more trouble. The displacer is an ABS tube sealed on both ends and is quite heavy, around 60 grams. The .047” rod slips through a brass guide hole that is about .048”. This small clearance adds very little leakage. When I test the displacer pressure variation with a manometer, the leakage rate is quite low. The downside is that the rod must be carefully aligned. Oil or any lubricant is a disaster for friction. I found that polishing the displacer rod and running it completely dry gave the best performance. I did try drilling the guide out to .052 (the next drill size I had on hand). That extra clearance made the friction very low but the leakage made the engine inoperable. I need to try a drill around .049.
Designing for higher temperature vs operating at higher temperature
One of the design considerations that is very apparent on low temperature engines but applies really to all Stirling engines is the operating temperature ratio used in the design. There is a big difference between operating a given engine design at a higher temperature and designing it to run at the higher temperature.
The engine I’m discussing here was designed for operation between 100F and 75F. Thermodynamically it should have a gross power of .004 watts at 60 rpm (1.0 hz) and my elevation (900 ft). If I increase the temperature ratio (1.047) to 1.094, the power should double to .008 watts at 60 rpm. If instead I design a new engine for this temperature ratio, the gross power will be about .016 Watts. In the first case the power doubles, in the second case, the power goes up four times. The difference is that when designing for the higher temperature, I increase the pressure ratio (a larger piston or longer stroke) to match the higher temperature ratio.
When you design a Stirling engine the power increases roughly with the square of the temperature (assuming the same displacer volume and adjusting the power piston displacement to match the pressure ratio). This is why it is a mistake for people to think they can make a 200 degree delta T engine perform half as well as a 400 degree delta T engine of the same size.
The case actually seems to be worse than I’ve painted here. As the temperature increases you can usually budget more power to pumping and heat transfer losses and thereby operate at higher RPM.
The other side of this argument is that if you lower the operating temperature on an engine designed for a higher temperature it just quits running.
Let me point out that I have been discussing the gross engine power. For small engines a significant proportion of the gross power goes into overcoming friction. For the engine I just made, if I operate it at the elevated temperature ratio, I should measure about .004 Watts power output at 60 RPM. Of the .008W of gross power the engine should use .004W in overcoming friction. I know this because it runs with no load at this RPM when the gross power is .004W. The other .004W will be excess power that I should be able to measure at the shaft.