In this exercise students will study diagrams of a Stirling heat engine. They will answer a set of questions and produce a report explaining how this Stirling engines works.
Heat engines use heat to do work. All heat engines absorb heat at a higher temperature, use some of the heat to do work, and expel the rest at a lower temperature. Most heat engines use a gas as their working fluid. The gas is confined in a cylinder with a movable piston. Heat is absorbed at the higher temperature, resulting in higher pressure in the cylinder. The hot gas expands, doing work equal to the average high pressure times the change in volume. Left over heat is expelled at a lower temperature, resulting in lower pressure in the cylinder. After the pressure has dropped, the gas is compressed. Work equal to the average low pressure times the change in volume must be done on the gas to compress it. The net work done per cycle is
W = (<Phigh> - <Plow>)DV = Qabsorbed - Qexpelled .
When steam engines and combustion engines expel heat at the lower temperature, they also expel the working fluid. There are, however, heat engines that use the same working fluid over and over again. A Carnot engine is such an engine. A Carnot engine is a frictionless, reversible engine. The engine contains a fixed quantity of gas in a sealed cylinder with a movable piston.
The particular type of Carnot engine described in the module works by letting the gas expand isothermally in contact with the high temperature reservoir. The isothermal expansion is followed by an adiabatic expansion, during which the gas cools. The gas is then compressed isothermally in contact with the low temperature reservoir, and finally it is adiabatically compressed back to its initial state. This cycle of isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression is called the Carnot cycle. The net work done during one cycle is the difference between the heat Qhigh absorbed from the high temperature reservoir and the heat Qlow dumped into the low temperature reservoir. For the Carnot cycle we have
Qhigh/Thigh = Qlow/Tlow.
The efficiency of the engine is
e = (Qhigh - Qlow)/Qhigh = (Thigh - Tlow)/Thigh.
No engine has a higher efficiency.
In this exercise students will examine a different cycle of heating, expansion, cooling, and compression, that is used in the Stirling engine. They will examine this cycle using the first law of thermodynamics, the kinetic theory, and the ideal gas law. Students will derive an expression for the efficiency of an ideal Stirling engine. They will then study diagrams of two different types of Stirling engines. Students will produce a report explaining how the two different types of Stirling engines work.
The ideal Stirling cycle is composed of four distinct thermodynamic processes. In reality, these processes are not completely isolated from each other, but they are usually identifiable parts of one cyclic process. The ideal engine is frictionless, and its moving parts have negligible mass. The work done by the expanding gas then is not done on the engine itself, and no external work is needed to move engine parts.
Students will use the following formulas to analyze each process.
An alpha configuration engine is one of three main configurations of Stirling engines, and it is probably the easiest to understand. It has two pistons in two separate cylinders. The pistons are connected by a crank. One cylinder is hot and one cylinder is cold. The cylinders are connected by a passage, whose opening may or may not be blocked by one of the pistons. The passage may contain a regenerator, a material through which gas must flow if it passes from one to the other cylinder. This material can absorb heat from and return it to the working gas to increase the efficiency of the engine.
 | (a) Let the Stirling cycle start with an isothermal
compression. The gas is in the cold cylinder. The temperature is T1
= Tc,
the volume is V1, and the pressure is P1. The passage between the
cylinders is blocked by the hot piston. The piston in the cold cylinder moves up and the
volume of the gas decreases to V2. The temperature is constant so the pressure
increases to P2.
Answer the following questions:
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| (b) Isothermal compression is followed by isometric heating.
The hot piston has moved down enough to unblock the passage between the two cylinders.
The
volume in the hot cylinder increases at the same rate as the volume in the cold cylinder
decreases. All the gas moves into the hot cylinder and is heated at constant volume from
temperature T1 to temperature T2 = Th. The gas pressure
increases to P3.
Answer the following questions:
|
| (c) The cold piston now blocks the passage and the gas absorbs more heat during an isothermal expansion.
It expands in the hot
cylinder at temperature T2 until the volume is again V1.
Answer the following questions?
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| (d) Isothermal expansion is followed by isometric cooling.
The hot piston moves up and the cold piston moves down. The passage between the cylinders
is open. The gas moves back at constant volume to the cold cylinder.
It is cooled at
constant volume from T2 to T1.
Answer the following questions?
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| The cycle now repeats. Answer the following question.
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Click here for a link to an animation of the ideal Stirling cycle.
Now study at the diagram of a real Stirling engine below. This is the diagram of a two-piston-type Stirling engine. Also look at the animation of the diagram.
Click here to animate the diagram.
| Formulate a theory and describe how this engine works. How does it differ from the ideal Stirling engine described above? |
The next diagram shows a displacer-type Stirling engine. The engine has a single cylinder. The displacer is not a piston. It is a regenerator that is used to move the gas from the lower part to the upper part of the cylinder. The gas does no work moving the displacer, it does work moving the piston against external forces. Study the diagram and formulate a theory, which explains how this engine works.
Click here to animate the diagram.
Inside the engine is a piece of yellow air filter foam. This is the displacer. It moves the gas from one side of the cylinder to the other. It also heats and cools very quickly as the gas flows around it. It can store heat as gas moves from the hot to the cold side, and re-supply this heat to the gas as it moves from the cold to the hot side. Less heat will be lost to the room this way. The piston assembly is made of about eight tiny parts that do not look like a piston at all. The piston looks more like a synthetic rubber diaphragm.
| Describe how a displacer-type Stirling engine works. How does it differ from the ideal Stirling engine? |
Here are some links to sites discussing Stirling engines.
| American Stirling Company |
| Stirling Technology |
| How the Stirling Engine works |
To earn extra credit prepare a Word document. In full sentences answer the questions posed in the Exercise. (The font color for the questions is blue.)
Save your Word document (your name_exm3.doc) and attach it to an e-mail message to mbreinig@utk.edu.
