How does a Stirling engine work?

In summary

Like a steam engine or an internal combustion car engine, a Stirling engine converts heat energy ,to mechanical energy (work) by repeating a series of basic operations, known as its cycle. Let’s consider a simplified displacer-type Stirling engine. It’s actually quite confusing and hard to figure out until you realize that what’s happening is that the gas inside is alternately expanding and contracting and, in between, moving from the hot side of the cylinder to the cool side and back again. The dark blue work piston’s job is to use energy from the expansion of the gas to drive the machine the engine is powering, then compress the gas so the cycle can repeat. The green displacer piston’s job is to shuttle the gas from the hot side of the cylinder (on the left) to the cold side (on the right) and back. Working as a team, the two pistons ensure that heat energy is repeatedly being moved from the source to the sink and converted into useful mechanical work.

1. 
   Cooling and compression: Most of the gas (shown by the blue squares) is over on the right at the cooler end of the cylinder. As it cools and contracts, giving up some of its heat, which is removed by the heat sink, both pistons move inward (toward the center).
2. Transfer and regeneration: The displacer piston moves to the right and the cooled gas moves around it to the hotter part of the cylinder on the left. The volume of the gas remains constant as it passes back through the regenerator (heat exchanger) to pick up some of the heat it previously deposited.
3. Heating and expansion: Most of the gas (shown by the red squares) is now on the left in the hot end of the cylinder. It’s heated by the fire (or other heat source) so its pressure rises and it expands, absorbing energy. As the gas expands, it pushes the work piston to the right, which drives the flywheel and whatever the engine is powering. In this part of the cycle, the engine converts heat energy into mechanical energy (and does work).
4. Transfer and cooling: The displacer piston moves to the left and the hot gas moves around it to the cooler part of the cylinder on the right. The volume of the gas remains constant as it passes through the regenerator (heat exchanger), giving up some of its energy on the way. The cycle is now complete and ready to repeat itself.

Although the engine goes through a cycle, ending up back where it started, it’s not a symmetrical process: energy is constantly removed from the source and deposited at the sink. That happens because the hot gas does a certain amount of work on the work piston when it expands, but the piston does less work compressing the cooled gas and returning it to the start.

In theory

Now you might be thinking: “This is all very elaborate! Why mess around with two pistons when a simple steam engine can get by with just one? Why all these separate stages? Why not make the whole thing simpler?” To answer those questions properly, you need to understand the theory of engines: that an efficient engine moves a gas through a cycle of processes according to the gas laws (the basic laws of classical physics that describe how a gas’s pressure, volume, and temperature are related). The best known, idealized cycle is called the Carnot cycle and involves repeating a cycle of isothermal (constant temperature) and adiabatic (heat-conserved) expansion, followed by isothermal and adiabatic compression.

1. Isothermal (constant temperature) compression: Our stage (1) above, where the volume of the gas decreases and the pressure increases as it gives up heat to the sink.
2. Isovolumetric (constant volume) heating: Our stage (2) above, in which the volume of the gas remains constant as it passes back through the regenerator and regains some of its previous heat.
3. Isothermal (constant temperature) expansion: Our stage (3) above, in which the gas absorbs energy from the source, its volume increases and its pressure decreases, while the temperature remains constant.
4. Isovolumetric (constant volume) cooling: Our stage (4) above, in which the volume of the gas remains constant as it transfers through the regenerator and cools.

A real Stirling engine operates through a more complex, less ideal version of this cycle, which is beyond the scope of this article. It’s enough simply to note that the four stages aren’t rigidly separated but do blend into one another. If you’re interested, there’s much more about this in Wikipedia’s article on the Stirling cycle.