When you place the Stirling engine on a beaker of hot water, after a minute or two it begins to operate. (You will most likely have to give the propeller a push to get the engine to start. The sticker on the front of the engine shows in which direction the propeller rotates.) When you set the engine on a cold pack (not shown), after a minute or two it begins to rotate in the opposite direction. (Again, you will probably have to give the propeller a nudge to get the engine to start.) To avoid early failure of the membrane that acts as the drive piston, please do not leave the engine running for long periods.
As its name would indicate, the operation of the engine shown above is based on the Stirling cycle, named for the Reverend Robert Stirling, who invented the engine that is based on it. The four steps in this cycle are the heating of a gas at constant volume, the isothermal expansion of the gas (with addition of heat), cooling of the gas at constant volume, and then isothermal compression of the gas (with rejection of heat). The engine (a PASCO SE-8575/American Stirling Company MM-1) consists of a short, clear acrylic cylinder, which is sealed on the bottom to an aluminum disc, and sealed on the top to the flat bottom of an aluminum plate whose ends are bent to support the drive shaft of the engine. Within the cylinder is a foam regenerative displacer, which is moved up and down by a rod that runs through the aluminum plate and a guide to a crank arm on the drive shaft. Covering a hole near one end of the plate is a thin silicone membrane, connected by a rod to a second crank arm on the drive shaft. This membrane acts as a piston. At the front end of the drive shaft is a model airplane propeller, which provides a load and acts as a flywheel to keep the crank turning during those parts of the cycle when no work is being done on the drive shaft. The crank arms for the displacer and the piston are 90 degrees out of phase, so that as you face the front of the engine, relative to the crank arm for the displacer, the crank arm for the piston is 90 degrees in the clockwise direction. The plates at the top and the bottom of the cylinder provide interfaces to the hot and cold reservoirs between which the engine operates.
To examine how the engine operates, let us say that we have set it on the beaker of hot water, and the displacer is at the top of the cylinder (the piston is in the middle of its stroke). The air inside the cylinder (most of which is below the displacer) is heated by the beaker of hot water. The heated air then expands, driving the piston up to the top of its stroke, which rotates the shaft in the counterclockwise direction and moves the displacer down. The crank turns until the displacer is at the bottom of the cylinder and the piston is again in the middle of its stroke. The air is now in contact with the top plate, and it cools. The external pressure on the piston forces it down, compressing the air, and the displacer now moves upward. When the displacer reaches the top of its stroke (and the piston is again in the middle of its stroke), the cycle begins again. As noted, the engine operated in this way (hot reservoir on the bottom and cold reservoir on top) rotates counterclockwise when you set it with the propeller facing you.
Now we consider the engine sitting on the cold pack. The hot reservoir is now the room air, at the top plate, and the cold reservoir is the cold pack, on which the bottom plate sits. We start with the displacer at the bottom of the cylinder and the piston in the middle of its stroke. The air in the cylinder (which is mostly above the displacer) is heated by the room air. The heated air then expands, driving the piston up to the top of its stroke, which rotates the shaft in the clockwise direction and moves the displacer up. The crank turns until the displacer is at the top of the cylinder and the piston is again in the middle of its stroke. The air is now in contact with the bottom plate, and it cools. The external pressure on the piston forces it down, compressing the air, and the displacer now moves downward. When the displacer reaches the bottom of its stroke (and the piston is again in the middle of its stroke), the cycle begins again. As noted, the engine operated in this way (hot reservoir on top and cold reservoir on the bottom) rotates clockwise when you set it with the propeller facing you.
The displacer in this engine actually performs two functions. If the displacer were solid, the air in the cylinder would flow around it as it moved up and down, and being so displaced would undergo alternating cycles of cooling (followed by compression) and heating (followed by expansion) as it alternately came into contact with the surface at each end of the cylinder. With such a displacer, however, the engine would not be as efficient as possible, because the heat rejected during the cooling cycle (the third step in the cycle) would be lost. If we could recover this heat during the heating cycle (the first step in the cycle), we could improve the efficiency of the engine. To this end, the displacer in this engine is made of a porous material, a type of foam, which allows the air in the cylinder to flow through it as well as around it. As the displacer moves to displace the air from the hot end of the cylinder to the cold end, some of the air passes through the displacer and deposits heat in it. When the displacer then moves in the opposite direction to displace the air from the cold end of the cylinder to the hot end, it releases this heat to the air that passes through it. If this heat recovery is done reversibly, then all of the heat exchange from the hot reservoir to the engine occurs at the temperature of the hot reservoir, T2, and all the heat loss from the engine to the cold reservoir occurs at the temperature of the cold reservoir, T1. If the compression and expansion processes are reversible, then the efficiency of the Stirling engine matches that of the Carnot cycle for reservoirs at the same two temperatures, or E = (T2 - T1)/T2. A device that performs this heat recovery is called a regenerator. (Stirling called it an economizer.) Since the displacer in this Stirling engine performs both this function and that of displacing the air from one end of the cylinder to the other, it is called a regenerative displacer.
The Stirling engine is interesting in that, as noted above, with the use of a regenerator its theoretical efficiency matches that of the Carnot cycle. Also, Stirling engines tend to run very quietly. A disadvantage they have is that they require some time to start. Though it is possible to design them so that they can start in under a minute, it is impossible to design them to start immediately. Also, since changing the temperature of either the hot or cold reservoir invariably takes some time, one cannot change the operating speed of a Stirling engine quickly. Because of these properties, Stirling engines find practical use in applications where immediate startup is not important, the load is fairly stable and the engine can operate at a steady speed, and quiet operation and high efficiency are particularly desirable. Early in their history, Stirling engines were perhaps most commonly used as water pumps. One also provided power for all the machinery in a Dundee iron foundry. Today, because of their quiet, efficient operation, Stirling engines are often used in submarines.
Another interesting thing about the Stirling engine is that when one drives it with an external motor, it acts as a heat pump, transferring heat from one side of the engine to the other. The Stirling engine therefore also finds use as a refrigerator, particularly for cryocoolers of various sizes, which typically can get to temperatures of several tens of kelvins. For examples, see https://www.sunpowerinc.com/products/stirling-cryocoolers/cryotel-cryocoolers, https://advancedtech.airliquide.com/markets-solutions/space/pulse-tubes and https://www.stirlingcryogenics.com/products/cryogenerators.
References:
1) Lee, John F. and Sears, Francis Weston. Thermodynamics - An Introductory Text for Engineering Students (Reading, Massachusetts: Addison-Wesley Publishing Company, Inc., 1963) pp. 459-60.
2) http://www.stirlingengine.com/ and links therein.
3) PASCO SE-8575 manual (©1995 PASCO Scientific).