HEAT ENGINES, WHICH CONVERT heat into useful mechanical work, are of two broad types: those in which combustion operates directly on a piston and those in which it operates indirectly by way of an intermediary known as the working fluid. The first type is an internal-combustion engine, of which the gasoline engine is the obvious example: when fuel is burned, the gaseous combustion products expand directly against a piston. The second type is an external-combustion engine. One example is the steam engine, in which water is the working fluid. First a fuel-coal, say- vaporizes the water; then the steam is introduced into a cylinder and expands against a piston.

Another example of an external-combustion engine is one that was introduced in Scotland in 1816 by the Reverend Robert Stirling. Originally its working fluid was air; later designs have used hydrogen or helium. The Stirling engine is interesting for several reasons. It recycles its working fluid continuously. Any source of heat will do, so that a fuel can be chosen for its low level of pollution. And at least in theory it should be highly efficient in converting heat into work. Nevertheless, for a variety of reasons Stirling's idea lost out-first to steam and then to internal combustion.

Recently the idea has made something of a comeback, in part because of the low-pollution possibility and the fact that the fuel need not be petroleum-derived. The engine has also caught the attention of some amateur scientists. One such tinkerer has been Peter L. Tailer of the Windfarm Museum on Martha's Vineyard, Mass., who modeled an engine after one developed in 1876 by A. K. Rider of Philadelphia. Tailer's apparatus is unlikely to compete with conventional engines because its output power is low. Still, it is easy to construct from common materials and allows one to study the associated thermodynamics.

One appealing feature of the apparatus is that it does not require finely machined cylinders and pistons, as other Stirling engines and all internal-combustion engines do. Instead it uses two cans (soda cans, say), which are partially submerged in water [left]. The water is contained in two tanks at the base of the apparatus. Each can is attached to the end of a rod; the other end of each rod is connected to a crank on a weighted flywheel at the top of the apparatus. An air-filled tube runs between the tanks and up into the can in each tank.

When the water in one of the tanks is heated by some source, such as a flame, the air in the interconnecting tube shuttles back and forth between the tanks, the cans rise and fall and the flywheel turns at several tens of revolutions per minute. These motions depend on two subtle features of the apparatus. One feature is the arrangement of the cranks at the flywheel: their outer arms are perpendicular to each other (as seen from the side). The other feature has to do with the way heat is transferred from the source to the air in one of the cans.

Before I explain the details of Tailer's apparatus, I shall examine the basic principles of a Stirling engine with a textbook version, which is illustrated in Figure 2. Two solid pistons fit snugly within a cylinder and can be moved to the left or right either by air pressure inside the cylinder or by machinery to which they are attached. At the center of the cylinder there is a porous material, such as a metal mesh, called the regenerator, which temporarily stores heat when the engine is running. Near the pistons there are two "thermal reservoirs," where the temperature is kept constant: on the left a "heat reservoir," maintained at a high temperature by a heat source, and on the right a "cold reservoir," whose temperature is kept low by some means of heat drainage.

During the engine's operation, the internal air undergoes cyclic variations of pressure, temperature and volume: the air is said to change in state. The piston arrangements for four of the states are shown in the illustration. The associated variations in the state of the air are best understood by following the graph of pressure versus volume in Figure 3. During its operation, the engine effectively cycles clockwise around a skewed and distorted rectangle on the graph.

First consider state 1, which corresponds to the first of the series of drawings and also to the upper left corner of the skewed

rectangle. Piston B on the right is adjacent to the regenerator; piston A on the left is somewhat farther from the regenerator. The air trapped between the pistons is at a high pressure. As the heat reservoir warms the air, the air expands, thereby pushing A to the left; the consequent increase in the volume of the space between the pistons diminishes the pressure. During the expansion, the temperature of the air is kept constant because of the proximity of the heat reservoir, and so the expansion is said to be isothermal. The expansion is represented by the upper curve on the graph's skewed rectangle. When A reaches its leftmost position, the air is in state 2.

Next both pistons are moved to the right-not by heating but by the machinery to which they are attached- until A reaches the regenerator and B is all the way to the right. The air is then in state 3. The movement of the pistons causes the air to flow through 9 the regenerator, which takes up some of the heat and thereby cools the air. Because the pistons move in synchrony, the volume of the air does not change during this transition, and so the transition is said to be one of constant volume.

Now the machinery attached to B pushes the piston toward the left. As the air is compressed, it gives up heat to the cold reservoir. Because the reservoir is fixed in temperature, the temperature of the air does not change and the transition is said to be an isothermal compression. At the end of the compression, the air is in state 4. To complete the cycle, the machinery moves both pistons together to the left until they are again in the arrangement for state 1. Again the transition takes place at constant volume. When the air flows through the regenerator, it regains the heat it lost in the previous constant-volume transition.

As the engine runs, it continues to cycle around the closed curve on the graph. In the transition from state 1 to state 2, one of the pistons is moved by expansion of the air. In the other three transitions, the pistons are moved by the machinery. Is the engine useful, that is, does the air do more work on the machinery than the machinery does on the air?

To answer the question, I must first explain what is meant by "work." Although commonly the term can mean almost any expenditure of energy, it has a narrower scientific definition: work is the transfer of energy that is needed to move something. On that restricted definition, if a force is applied to an object but the object does not move, no work is done. If there is movement, then the amount of work is the product of the force and the object's displacement. Whatever provides the force loses energy, and the energy shows up as motion.

Suppose that there is a closed container of air and that the air and the container are at the same temperature. The air molecules beat incessantly against the walls of the container, and the collective outward force on a wall from the collisions is the air pressure against that wall. If the wall does not move outward because of the pressure, the air performs no work on the wall. But if the wall yields, work is performed. For air to do work, then, it must somehow expand its container. In principle the work is the product of the force in each molecular collision and the displacement of the wall caused by that collision. The work is more easily expressed, however, as the product of the pressure (which is analogous to force) and the change in volume (which is analogous to displacement).

If an external force were to shrink the container, work would be done by that force rather than by the air. The agent responsible for the force (which might be you or some machinery) would then lose energy, which would be transferred first to the wall and then to the air molecules as the wall moved inward. In this case, work is done against the air. The amount of work is again the product of the pressure and the change in volume.

The idea behind an air-filled Stirling engine is to coax the air into doing work against a piston-pushing the piston outward and increasing the volume of the space between the pistons. The motion of the piston can then be transferred to machinery, where the acquired energy can be put to use. If there were only one such expansion, of course, the engine would hardly be helpful. The engine must instead somehow compress the air periodically so that the air can expand periodically and thereby continue to do work. In short, the volume of the air must be cycled repeatedly. But remember that for the air to be compressed, the machinery must do work on the air. If the machinery does as much work on the air in the course of a cycle as the air does on the machinery, the engine produces no net work and is useless.

The solution to the problem involves the temperature of the air. Suppose that whenever the air does work, it is hot. Then the collisions of the air molecules on the piston are vigorous, and the pressure is high. Because the work done on the piston depends directly on the pressure, the amount of work is large. Next suppose that whenever the machinery does work on the air, the temperature is low. Then the collisions are weaker, so too is the pressure, and the amount of work done on the air is small. If the temperature can be adjusted in this way, the air does more work on the machinery than the machinery does on the air.

Such a periodic variation in temperature and pressure lies behind the textbook Stirling engine (as well as other engines, in fact). Work is done by the air on piston A during the isothermal expansion, when the air temperature is high. Work is done by the machinery on the air during the isothermal compression, when the temperature is low. The engine has a net output of work.

The work involved in a cycle of the engine can be derived from the graph of pressure versus volume. During the isothermal expansion, the amount of work done by the air is represented by the area below the corresponding curve. The area is bounded by the curve, the volume axis of the graph and two vertical lines that extend from that axis up through the end points of the curve. During the isothermal compression, the amount of work done on the air is the area below the corresponding curve. No work is done during the constant-volume transitions because there is no change in volume, and so the area below those lines on the graph is zero. To find the net work done by the engine during a full cycle, you subtract the area beneath the compression curve from the area beneath the expansion curve. The result is the area within the skewed rectangle.

I now return to Tailer's apparatus. The heated tank is the heat reservoir. The other tank is the cold reservoir, whose temperature is maintained by thermal radiation and convection. The air-filled spaces, including the tube that connects the tanks, serve as the cylinder. Either the tube itself or some wire mesh that can be placed inside it functions as the regenerator. The machinery to which the cans are attached is the flywheel.

The series of drawings in Figure 8 indicates how the air trapped within the lower section of the apparatus responds to the heating and to the motion of the flywheel. The drawings show the elevation of the cans and the water, the direction of air flow and the orientations of the cranks for eight stages. The labels on the cranks indicate whether they are connected to the hot or the cold tank.

Tailer's engine is similar to the textbook engine but lacks any true isothermal or constant-volume transitions. Still, if you were to graph air pressure versus air temperature, the engine would cycle around on the graph somewhat as I described for the textbook engine. To follow the cycling, consider the engine as it goes through stage a, having just left stage h. During a the hot can rises faster than the cold one sinks. Next both cans rise until they reach c. Then the cold can rises faster than the hot one sinks, until they reach d. Notice that during the transition from h to d there is more air in the hot can than in the cold one. This means that more of the air is being heated than is being cooled, and so the air pressure increases. Notice too that during the transition from h to d the volume of the air increases. The expansion is driven by the additional pressure, which means that the air does work on the cans-and thus also on the flywheel.

When the engine moves between d and h, the variations in volume and pressure are just the reverse, and the flywheel does work on the air. The net motion of the cans compresses the air; the shift of air to the cold can diminishes the overall heating of the air and decreases the air pressure. During compression, the pressure is low, and so the work done by the flywheel on the air is less than the work that was done by the air on the flywheel during the earlier, h-to-d transition. The result is a net output of work by the air.

Tailer sent along specific plans for constructing his engine, but he points out that the details are easily varied according to the materials available. Fashion the crankshaft from stiff wire, such as sturdy clothes-hanger wire, so that it does not flex during the engine's operation. The crankshaft rests on aluminum strips 1/8 inch thick that serve as bearings. Drill holes through each strip, cut a notch at the top to support the crankshaft and then screw the strip to the interior of a wooden arm as shown in the illustration.

The flywheel is a pulley eight inches in diameter with a groove designed to accept a V-shaped belt. Its bore hole is fitted with a short length of wood through which a central hole is drilled for the crankshaft. Glue the wire to the wood insert with epoxy, and secure the insert to the pulley with the set screw on the pulley. Bring the crankshaft wire out past the bearings, and then bend and cut the ends so that about two inches of wire extends perpendicularly from the crankshaft axis. The end sections should also be perpendicular to each other as seen from the side.

Cut the tops off two soda cans with a hacksaw. Invert each can and glue a wooden dowel to the bottom of the can. These connecting rods should be about 3/16 inch in diameter and about 36 inches long. For the glue Tailer suggests the type of epoxy that requires slow curing; it withstands heat better than the fast-curing type. Later, during final assembly of the engine, the upper end of each connecting rod is glued or taped to a strip of aluminum 1/8 inch thick that is mounted on a long machine screw with nuts and washers. The screw also passes through two other aluminum strips that are fastened to the outer ends of the cranks with a shorter machine screw and a nut. The entire assembly is called a crank journal.

The tanks are one-pound coffee cans. The tube linking them is made of sections of copper tubing whose internal diameter is 3/4 inch. Before you connect them, you should attach a section 5 1/2 inches long to each can. Make radial cuts in the bottom surface of a can with a knife, and force the tube section inward through the flaps left by the cuts, leaving about an inch of tubing below the can.

You can seal the tubing to the can with slow-curing epoxy, but soldering works better. If you choose to solder, sand the surface of the tube to be soldered, smear soldering flux on the surface and on the adjacent region of the can, and direct a torch onto the solder so that it flows over the flux. Once both cans are prepared, lay them on their open ends. Then sand and coat with flux the interiors of the tubing elbows, and solder the elbows in place. Next add two short lengths of tubing and a central coupling that is equipped with a drain. Solder them together except for the piece that inserts into the elbow at the cold tank. Secure that last connection with a few tight turns of vinyl tape so that the assembly can later be disconnected if a regenerator is to be added or replaced. If you cannot locate a tubing section with a drain, simply drill a hole in a regular tube, smooth the sides of the hole and then close it with a wood or rubber plug. Construct a cradle that will support the tank assembly and that allows easy access to the drain.

Now run the dowels through screw eyes on the support column, and attach them to the outer metal strips of the crank journals as described above. To get a stroke length of 1.5 inches, set the screws on the journals so the long screw moves 3/4 inch below the shaft and 3/4 inch above it when the flywheel turns. Tape weights such as machine bolts to the flywheel to give it enough mass to complete a rotation when the engine is operated. Then oil the bearings and make sure that the flywheel and cans move easily.

To ready the engine, turn the crankshaft until both cranks are pointed up at 45 degrees to the vertical. Then, with the drain open, fill the cold tank with cold water until it overflows into the interconnecting tube and goes out through the central drain. Next pour hot water into the hot tank until it too overflows. Close the drain and begin to heat the hot tank with, say, a propane torch or Bunsen burner.

The speed at which the flywheel turns depends on the temperature difference between the two tanks. For example, one of Tailer's engines ran at 20 revolutions per minute when the water temperatures were 200 degrees and 60 degrees Fahrenheit but speeded up to 28 revolutions per minute when the hot water was brought closer to boiling. The operation of the engine can be enhanced if the interconnecting tube is partially filled with rolled strips of wire mesh to act as a regenerator. When Tailer added several such rolls to his engine, it rotated almost once per second.

In addition to varying the temperature, you might try adjusting several other parameters of Tailer's apparatus. If the stroke length is varied, does the flywheel turn faster? What happens if the angle between the cranks is varied somewhat from the 90 degrees I have described? (Indeed, why does the angle matter, and why should the hot crank lead the cold crank?) Can other types of regenerator material improve the engine? Does performance increase if you substitute another liquid for the water? (Do not use any liquid that might result in a fire or explosion!) What happens if you alter the length of the connecting rods to increase or decrease the average height of the column of air in the cans?

FURTHER READING

THE STIRLING ENGINE. Graham Walker in Scientific American, Vol. 229, No. 2, pages 80-87; August, 1973.

STIRLING ENGINES. Graham Walker. Oxford University Press, 1980.

LIQUID PISTON STIRLING ENGINES. C. D. West. Van Nostrand Reinhold Company, 1983.

OTHER EXTERNALLY REVERSIBLE CYCLES. J. B. Jones and G. A. Hawkins in Engineering Thermodynamics: An introductory Textbook. John Wiley & Sons, 1986.

PRINCIPLES AND APPLICATIONS OF STIRLING ENGINES. Colin D. West. Van Nostrand Reinhold Company, 1986.

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