Adapted from “Introduction
to Thermodynamics and Heat Engines” by David Mooney, “Thermodynamics”
by Edward F. Obert and “Engineering Thermodynamics”
by James B. Jones and George A Hawkins
When internal combustion engine operation is examined, it is
seen to differ in the process of heat supply for a typical heat
engine cycle because there is a permanent change in the working
fluid during combustion. Therefore the fluid does not pass through
a cycle so the internal combustion engine is often referred to
as an "open cycle" device, not a cyclic thermodynamic
The term "open cycle", while meaningless from a thermodynamic
perspective, refers to the fact that energy is supplied to the
engine from outside in the form of petroleum fuel and the unconverted
portion of energy remaining in the spent combustion mixture is
exhausted to the environment. “Closing the cycle”,
i.e., returning the rejected products to the starting point where
they can be reused, is left for nature to accomplish – hence
the term “open cycle”.
An internal combustion engine is therefore a device for releasing
mechanical energy from petroleum fuel using air as the working
medium rather than a heat engine for processing air in a thermodynamic
cycle. Heat, as such, is not supplied to the internal combustion
engine, so it cannot be a heat engine in the sense described in
most thermodynamic references.
A simulated heat engine cycle can be constructed to correspond
approximately to the operation of an internal combustion engine
by substitution of analogous heat transfer processes for some
of the actual engine processes. The specific mechanism of such
heat transfer is neglected because the simulation is only a theoretical
model of the engine, not an actual device. Such cycles, called
air standard cycles, are useful in the elementary study
of internal combustion engines.
It is important to note that air standard cycles apply to the
performance of an internal combustion engine because once the
fuel ignites, it releases its energy as heat. If the process of
combustion is ignored and the heat released is considered as heat
applied during the appropriate portion of an air standard cycle,
the heat conversion process in the internal combustion engine
can be examined with standard thermodynamic methods.
It is equally important to remember, however, that the air standard
cycle is not an internal combustion engine, so one must be careful
not to carry the anology too far. Some individuals attempt to
apply limitations and requirements for closed cycles to processes
that are not closed. This can easily lead to an incorrect analysis
of the open process because an open process by definition can
gain or lose heat in the system by means that a closed cycle cannot.
Air Cycle Analysis
Studying internal combustion engine performance characteristics
through use of air standard cycles involves making a number of
simplifying assumptions. It involves simulating engine operation
with the help of thermodynamics so as to formulate mathematical
expressions which can then be solved in order to obtain the relevant
The method of solution will depend upon the complexity of the
formulation of the mathematical expressions which in turn will
depend upon the assumptions that have been introduced in order
to analyze the processes in the engine. The more the assumptions,
the simpler will be the mathematical expressions and the easier
the calculations, but the lesser will be the accuracy of the final
Any device that operated in a thermodynamic cycle, absorbs thermal
energy from a source, rejects a part of it to a sink and presents
the difference between the energy absorbed and energy rejected
as work to the surroundings is called a heat engine.
A heat engine is, thus, a device that produces work. In order
to achieve this purpose, the air cycle heat engine working medium
undergoes the following processes:
1. A compression process where the working medium absorbs energy
2. A heat addition process where the working medium absorbs
energy as heat from a source.
3 An expansion process where the working medium transfers energy
as work to the surroundings.
4. A heat rejection process where the working medium rejects
energy as heat to a sink.
If the working medium does not undergo any change of phase during
its passage through the cycle, the heat engine is said to operate
in a non-phase change cycle. A phase change cycle is one in which
the working medium undergoes changes of phase. Air standard cycles,
using air as the working medium are examples of non-phase change
cycles while the steam and vapor compression refrigeration cycles
are examples of phase change cycles.
Air Standard Cycles
Since the air standard analysis is the simplest and most idealistic
way of modeling an internal combustion engine, such cycles are
also called ideal cycles and the engine running on such cycles
are called ideal engines.
In order that the analysis is made as simple as possible, certain
assumptions have to be made. These assumptions result in an analysis
that is far from correct for most actual combustion engine processes,
but the analysis is of considerable value for indicating the upper
limit of performance. The analysis is also a simple means for
indicating the relative effects of principal variables of the
cycle and the relative size of the apparatus.
1. The working medium is a perfect gas with constant specific
heats and molecular weight corresponding to values at room temperature.
2. No chemical reactions occur during the cycle. The heat addition
and heat rejection processes are merely heat transfer processes.
3. The processes are reversible.
4. Losses by heat transfer from the apparatus to the atmosphere
are assumed to be zero in this analysis.
5. The working medium at the end of the process (cycle) is unchanged
and is at the same condition as at the beginning of the process
When selecting an idealized process one is always faced with
the fact that the simpler the assumptions, the easier the analysis,
but the farther the result from reality. The air cycle has the
advantage of being based on a few simple assumptions and of lending
itself to rapid and easy mathematical handling without recourse
to thermodynamic charts or tables or complicated calculations.
On the other hand, there is always the danger of losing sight
of its limitations and of trying to employ it beyond its real
Equivalent Air Cycle
A particular air cycle is usually taken to represent an approximation
of some real set of processes which the user has in mind. Generally
speaking, the air cycle representing a given real cycle is called
an equivalent air cycle. The equivalent cycle has, in
general, the following characteristics in common with the real
cycle which it approximates:
1. A similar sequence of processes.
2. Same ratio of maximum to minimum volume for reciprocating
engines or maximum to minimum pressure for gas turbine engines.
3. The same pressure and temperature at a given reference point.
4. An appropriate value of heat addition per unit mass of air.
The Carnot Cycle
This cycle was proposed by Sadi Carnot in 1824 and has the highest
possible efficiency for any cycle. The Carnot cycle, which is
the basis for thermodynamic analysis of heat engines, only applies
to cyclic engines that process heat in a closed cycle operating
with a working fluid that is a perfect (ideal) gas. An ideal gas
or perfect gas is a hypothetical gas consisting of particles of
zero volume, no intermolecular forces, where the constituent particles
undergo perfectly elastic collisions and are in constant random
motion. Real gases do not behave this way, although the approximation
is often good enough to describe real gases far from their critical
The thermal efficiency of the Carnot cycle is only a function
of the maximum and minimum temperatures of the cycle. The efficiency
will increase if the minimum temperature (or the temperature at
which the heat is rejected) is as low as possible. According to
this equation, the efficiency will be equal to 100% if the minimum
temperature is zero, which happens to be the absolute zero temperature
in the thermodynamic scale.
For optimum efficiency, the Carnot cycle (and hence the heat
engine) must operate between the limits of the highest and lowest
possible temperatures. In other words, the engine should take
in all the heat at as high a temperature as possible and should
reject the heat at as low a temperature as possible.
For the first condition to be achieved, combustion (as applicable
for a real engine using fuel to provide heat) should begin at
the highest possible temperature, for then the irreversibility
of the chemical reaction would be reduced. Moreover, in the cycle,
the expansion should proceed to the lowest possible temperature
in order to obtain the maximum amount of work. These conditions
are the aims of all designers of modern heat engines. The conditions
of heat rejection are governed, in practice, by the temperature
of the atmosphere.
It is impossible to construct a real engine which will work
on the Carnot cycle. In that sense, like the air standard cycle,
the Carnot cycle is but a theoretical construct useful only for
analytical purposes in thermodynamics.
If such an engine were built, it would be necessary for the piston
to move very slowly during the first part of the forward stroke
so that it can follow an isothermal process. During the remainder
of the forward stroke, the piston would need to move very quickly
as it has to follow an isentropic process. This variation in the
speed of the piston cannot be achieved in practice. Also, a very
long piston stroke would produce only a small amount of work most
of which would be absorbed by the friction of the moving parts
of the engine.
Since the efficiency of the Carnot cycle is dependent only on
the maximum and minimum temperatures, it does not depend on the
working medium. It is thus independent of the properties of the
The Otto Cycle
The Otto cycle, which was first proposed by a Frenchman, Beau
de Rochas in 1862, was first used on an engine built by a German,
Nicholas A. Otto, in 1876. The cycle is also called a constant
volume or explosion cycle.
An equivalent air cycle for reciprocating piston engines using
spark ignition operates as folows:
At the start of the cycle, the cylinder contains a mass of air
at a given pressure and volume when the piston is at its lowest
position. The piston moves upward and the gas is compressed isentropically
to point near the top of the stroke. At this point, heat is added
at constant volume which raises the pressure to its maximum. The
high pressure charge now expands isentropically, pushing the piston
down, expanding to the bottom of the stroke, where the charge
rejects heat at constant volume, returning to the initial state.
The isothermal heat addition and rejection processes of the
Carnot cycle are replaced by constant volume processes which are
theoretically more plausible, although in reality, even these
processes are not practical.
In a true thermodynamic cycle, the term expansion ratio and
compression ratio are synonymous. However, in a real engine, these
two ratios need not be equal because of the valve timing and therefore
the term expansion ratio is preferred.
The thermal efficiency of a theoretical air standard cycle simulation
of an Otto cycle increases with the increase in compression ratio
and specific heat ratio but is independent of the heat added and
initial conditions of pressure, volume and temperature.
A plot of thermal efficiency versus compression ratio for an
Otto cycle shows that the increase in efficiency is significant
at lower compression ratios.
From the table below, it is seen that if:
CR is increased from 2 to 4, efficiency increase is 76%
CR is increased from 4 to 8, efficiency increase is only 32.6%
CR is increased from 8 to 16, efficiency increase is only 18.6%
vs Compression Ratio
|Compression Ratio (CR)
The Diesel Cycle
This cycle, proposed by a German engineer, Dr. Rudolph Diesel
to describe the processes of his engine, is also called a constant
pressure cycle In practice, the diesel engine shows a better efficiency
than the Otto cycle engine because the compression of air without
fuel in the former allows a greater compression ratio to be employed.
With a mixture of fuel and air, as in practical Otto cycle engines,
the maximum temperature developed by compression must not exceed
the self ignition temperature of the mixture; hence a definite
limit is imposed on the maximum value of the compression ratio.
Otto cycle engines have compression ratios in the range of 7 to
12 while diesel cycle engines have compression ratios in the range
of 16 to 22.
Modern high speed diesel engines do not follow the Diesel cycle.
The process of heat addition is partly at constant volume and
partly at constant pressure. Such engines operate on a dual cycle.
The Dual Cycle
One of the important characteristics of real cycles is the ratio
of the mean effective pressure to the maximum pressure, since
the mean effective pressure represents the useful (average) pressure
acting on the piston while the maximum pressure represents the
pressure which chiefly affects the strength required of the engine
It becomes a practical necessity to limit the maximum pressure
when high compression ratios are used, as in diesel engines. This
also indicates that diesel engines will have to be stronger (and
hence heavier) because they must withstand higher peak pressures.
Constant pressure heat addition achieves rather low peak pressures
unless the compression ratio is quite high. In a real diesel engine,
in order that combustion takes place at constant pressure, fuel
has to be injected very late in the compression stroke (practically
at the top dead center). But in order to increase the efficiency
of the cycle, the fuel supply must be cut off early in the expansion
stroke, both to give sufficient time for the fuel to burn and
thereby increase combustion efficiency as well as reducing after-burning
and also to reduce emissions.
Such situations can be achieved if the engine was a slow speed
type so that the piston would move sufficiently slowly for combustion
to take place despite the late injection of the fuel. For modern
high speed compression ignition engines it is not possible to
achieve constant pressure combustion. Fuel is injected somewhat
earlier in the compression stroke and has to go through the various
stages of combustion.
Thus it is seen that early combustion is nearly at constant
volume (like in a spark ignition engine). But the peak pressure
is limited due to strength considerations. The rest of the heat
addition after the onset of combustion is believed to take place
at (or close to) constant pressure. This has led to the formulation
of the dual combustion air standard cycle.
In this cycle, for high compression ratios, the peak pressure
is not allowed to increase beyond a certain limit and to account
for the total heat addition. The balance of the heat added is
assumed to be added at constant pressure. Hence the name limited
The Otto, Diesel and Dual cycle expansion process do not proceed
to the lowest possible pressure, namely, atmospheric pressure.
This is true of all real engines; when the exhaust valve opens,
the high pressure gases undergo a violent blow-down process with
consequent dissipation of available energy. This is necessary
so as to allow the gases to flow out due to the pressure difference
and hence reduce the piston work in driving out the gases.
The equivalent air cycle does not have these losses and therefore
does not accurately reflect real engine operation. Again, one
is reminded that care must be taken when modeling real engines
with equivalent air cycles so as not to stray too far from the