Stirling Engine

Why is it difficult to scale-up the size of a model LTD Stirling engine?

Most large Stirling engines require a fire or other similar temperature heat source applied to one side of the engine. An LTD Stirling engine only requires a small difference in temperature to operate. I haven’t seen a large LTD engine that could be use for practical power generation. I have read that it is difficult to scale up an LTD SE but the article doesn’t specify what the difficulty is.

well with most engines, the larger they are, the greater the frictional losses are. a LTD (low-temperature-differential) stirling can operate on such a small temperature difference because they are so small and light, and because there is very little losses (air drag around the wheel, and friction in the bearings/moving parts).

in general, the heavier something is, the greater the sliding or rolling friction is. the frictional force of a mass sliding on a surface is proportional to the mass of the object (actually, proportional to the force with which it presses down on the surface).

on the other hand as you increase the size of the stirling engine, you find a case of diminishing returns in terms of the work you can extract. have a look at the very first diagram on this page:

http://www.cse.iitk.ac.in/~amit/courses/371/abhishe/main2.html

that is a closed curve that represents the stirling cycle. the work that can be extracted from one cycle is the area inside the box. notice that the top and bottom parts of the box are curved. these are isotherms or lines of constant temperature, and those temperatures are the two temperatures in the differential that drives the stirling engine. notice that as you increase volume, they get closer and closer together.

so think about what happens if you scale up the size of your engine. the box that defines the stirling cycle grows towards the right, but because those isotherms are getting closer and closer together, the larger you make it the less additional work you get. at some point you will stop gaining any measurable amount of work at all!

so there is a trade-off at work here – on the one hand, a larger engine means more work can be extracted – but more frictional losses, too.

since the amount of friction grows linearly with the size of the engine, and the amount of extra work grows less-than-linearly with the size of the engine, then the best ones are clearly the small ones! if the amount of energy extracted grew at the same rate as the amount of energy lost through friction, then all sizes would be equivalent.

ps – this relationship also holds true in 4-stroke otto cycle internal combustion engines, and pretty much any thermodynamic engine – and it’s why big engines typically have several cylinders rather than one humongous one. bigger cylinders gain you less and less.

Stirling engine example