3-internal compustion engine

10.0] Heat Engines & Refrigeration Systems
v3.1.6 / chapter 10 of 14 / 01 jan 08 / greg goebel / public domain
* This chapter follows up the discussion of the basic laws of thermal physics by considering heat engines, both theoretical and practical, and refrigeration systems. [10.1] HEAT ENGINES & THE SECOND LAW
[10.2] PRACTICAL ENGINES
[10.3] REFRIGERATION SYSTEMS
[10.4] FOOTNOTE: MAXWELL'S DEMON & THE SECOND LAW

[10.1] HEAT ENGINES & THE SECOND LAW


* All mechanical engines are "heat engines", in which heat is converted to work. Automotive engines burn fuel to set the vehicle rolling, while jet engines burn fuel to generate thrust to keep the aircraft flying. Such engines obtain heat from a high-temperature reservoir, derive work from it, and then pass the waste heat on to a low-temperature reservoir. The Second Law of Thermodynamics has particular application in the analysis of the operation of heat engines.
In an "ideal" heat engine, all the heat is converted to work. However, the French engineer Nicolas Leonard Sadi Carnot (1796:1832) demonstrated that there is no way to build a 100% efficient heat engine. In a work published in 1824, Carnot showed that the efficiency of an engine is proportional to the temperature difference between the input and output, and to obtain 100% efficiency the difference would have to be infinite.

For example, a power turbine uses steam obtained from a boiler heated by coal or oil to drive the turbine, with the exhaust of the turbine consisting of steam that has cooled in the process. Ideally, the heat flowing out of the process is equivalent to the heat flowing into the process minus the work done: heat_out = heat_in - work
Stated another way: work = heat_in - heat_out
The efficiency of the engine is given by the proportion of the heat input that is actually converted to work, or: _________________________________________________________________________

work heat_in - heat_out heat_out
efficiency = --------- = ---------------------- = 1 - ----------
heat_in heat_in heat_in
_________________________________________________________________________

Obviously, the efficiency is maximum when the heat output is zero -- meaning the heat input is completely used up -- but this never happens in practice, and this circumstance can be theoretically shown to be impossible. This is a consequence of the Second Law, though the analysis is too complicated to be presented in this document.
* Carnot established these basic rules by performing a theoretical analysis of a simple "ideal" heat engine that provides a basis for the discussion of all heat engines. The "Carnot engine", as it is now known, is a simple cylinder plugged by a piston and containing a quantity of gas, or "working fluid".
Heat engines operate on "thermodynamic cycles", or steps of thermodynamic processes that operate in a circular fashion. The Carnot engine cycles through four phases of operation, as shown at the left side of the illustration below. The changes in pressure and volume for each phase are shown in the "PV (pressure-volume) chart", also known as an "indicator diagram", at the right side of the illustration.

In more detail, the cycle works as follows:

• [1] Input of heat "Qh" at high temperature "Th" results in constant-temperature (isothermal) expansion, raising the piston.
  
• [2] Heat input is removed, and gas continues to expand, raising the piston further. Heat does not escape from the system during this phase of the cycle, or in other words this phase is an "adiabatic" process.
  
• [3] Loss of heat "Ql" at a low temperature "Tl" causes the gas to compress in an isothermal fashion.
  
• [4] Heat no longer flows out of the cylinder but the gas continues to compress as an adiabatic process. The engine then starts over at phase 1.
  

The amount of work W performed by the Carnot engine is given by the area enclosed by the PV curve. This work is equivalent to the input heat Qh less the output heat Ql. As above, this means the efficiency of the Carnot engine is: efficiency = 1 - ( Ql / Qh )
Carnot's mathematical analysis of his engine showed that the ratio of input and output heat of his engine was the same as the ratio of input and output temperatures, and so: _________________________________________________________________________

efficiency = 1 - ( Tl / Th )
_________________________________________________________________________

What this means is that the Carnot engine becomes more efficient as the difference between the input and output temperatures increases. It also shows that an engine can never be 100% efficient, since that would imply a Tl of zero degrees Kelvin, which can never be actually reached. Another implication of the Carnot engine is that it requires that heat be drained out of the cylinder for it to work. If the heat were not drained, pushing the piston back in would require as much work as was produced when it was pushed out, and the net work delivered by the engine would be zero.
* The Carnot engine is a theoretical construct, devised simply to provide a starting point for thermodynamic analysis and the understanding of practical engines. The details of operation of practical engines don't quite match this ideal due to factors such as friction, heat losses, the temperature limits of the materials used to build the engine, and so on. However, the basic revelations of the Carnot engine hold true: efficiency is roughly proportional to the temperature difference between engine inlet and outlet, and waste heat must be produced by the engine for it to work.
The fact that engine efficiency is directly proportional to the temperature difference gives an insight into the definition of entropy as heat transfer at a given absolute temperature. As the absolute temperature falls for a heat transfer process, the ability of the heat to do useful work, its "quality", falls or "degrades" as well, or in other words its entropy increases. A quantity of heat transferred at a high temperature has low entropy; the same quantity of heat transferred at a low temperature has high entropy.
This is the Second Law of Thermodynamics in action. Over time, in a closed system the transfers of heat occur at lower and lower temperatures, reducing the ability of the system to do work for both artificial engines and natural processes. This implies that the entire Universe is running down slowly, towards an ultimate "heat death" in the distant future.
BACK_TO_TOP
[10.2] PRACTICAL ENGINES


* A number of practical heat engines have been invented and are now in use. One of the most elegant, though one of the least-used, is the "Stirling cycle" engine. This is an "external combustion" engine, meaning that it is powered by an external source of heat. Any reasonably practical heat source can be used, such combustion of gasoline, kerosene, wood or manure, or sunlight focused by a mirror. All the Stirling cycle engine needs to run is a source of heat on one side and a cooling sink on the other.
The Stirling cycle engine's indifference to fuel source is its main advantage, and it is of some use in undeveloped countries where access to fuels is limited. Its disadvantage is that it has a poor "power to weight ratio (PWR)". All other engines in common use can provide the same power for much less weight.
The illustration below is an example of a simple (and idealized) implementation of a Stirling cycle engine. It consists of two cylinders, each with their own piston, linked through a gearbox. In this example, steam is fed around the first "hot" cylinder as a heat source, while cooling water is fed around the other "cold" cylinder as a heat sink. The "heads" of the two cylinders are linked by a heat-storage element known as a "regenerator".

The operation of the engine's gearbox is a bit difficult to follow, since it will bring one piston to a dead stop while moving the other piston, or allowing it to move.

The gearbox steps the engine through a four-part cycle as follows:

• [1] While the piston in the cold cylinder is stopped at the top of its travel, heat input into the hot cylinder causes the piston there to move downward. This is the power stroke, an isothermal expansion process.
  
• [2] The piston in the hot cylinder is then moved to the top of its travel while the piston in the cold cylinder is moved to the bottom of its travel. The volume of the working gas in the engine remains the same, while heat from the gas is stored in the regenerator. This is a constant-volume cooling process.
  
• [3] The piston in the hot cylinder is stopped at the top of its travel while the piston in the cold cylinder is moved up the cylinder to half its full travel. This compresses the working gas, but the temperature remains constant because heat is being drawn off by the cold water. This is an isothermal compression process.
  
• [4] Now the piston in the hot cylinder is moved downward to half its full travel, while the piston in the cold cylinder is moved to the top of its travel. This is a constant-volume process, in which heat from the regenerator is fed back into the gas flowing into the hot cylinder. The cycle is now ready to begin all over again.
  

This two-cylinder configuration is sometimes known as an "alpha" Stirling engine. In practice, Stirling engines are often built in a "beta" or "displacer" configuration, in which both pistons are in one cylinder, on top of one another and operated by concentric rods, and the regenerator runs up the sides of the cylinder, with ports between the two pistons and above the top piston. The top piston is called the "displacer", since its function is to "displace" the working fluid, while the bottom piston is called the "power piston", since it provides the drive power out of the engine.
The beta Stirling engine's operating principles are exactly the same as those of an alpha Stirling engine, though it is trickier to understand. There is also a "gamma" Stirling engine configuration, which is exactly the same as the beta configuration except that it is rearranged a bit to avoid the use of concentric rods. The illustration below shows a beta Stirling engine stepping through its cycles, with an idealized Stirling engine shown below to help clarify its operation, along with a gamma configuration engine.

In practice, the gearing system that drives a beta Stirling engine is designed so that a piston may slow down but won't ever actually stop, except for the instant between reversals of direction. This construction "rounds off" the edges of the PV diagram, but otherwise the operation is the same.
* The most popular heat engine in service is the automotive internal combustion engine, known formally as the "Otto cycle" engine and more popularly as the "four-stroke" engine.

Operation of the Otto cycle is conceptually simple:

• [1] In the first part of the cycle, the "intake stroke", the intake valve opens and the piston moves down to its lowest position. This draws in a gasoline-air mixture at (constant) atmospheric pressure.
  
• [2] In the "compression stroke", the intake valve is closed and the piston moves to its top position, compressing the fuel-air mixture. This is done quickly enough so that this part of the cycle is effectively adiabatic.
  
• [3] In the "power stroke", an electric spark plug ignites the compressed fuel-air mixture, driving the piston to its lowest position.
  
• [4] In the "exhaust stroke", the exhaust valve opens and the piston moves up, exhausting the combustion products of the fuel-air mixture at (constant) atmospheric pressure.