AIR STANDARD ENGINE
A cycle depicts the processes of compression, heat addition, expansion and heat rejection in an engine. However, it does not indicate how the working medium was taken into the engine and how it was removed. An air standard engine incorporates in it, along with the processes in an air standard cycle, the processes of intake and exhaust. Such an engine is also referred to as an ideal engine because it incorporates the ideal cycle. The intake and exhaust processes are also ideal.
The air standard engine uses air as the working medium. This air is assumed to be a perfect gas with constant specific heat. It does not undergo any dissociation. The engine has the same criteria as the air standard cycle for several of its processes.
Figure 1 shows the ideal P-V diagram of the Otto cycle. It consists of isentropic compression 1-2, and isentropic expansion 3-4 which are referred to as compression and expansion strokes of the piston. The constant volume heat addition process 2-3 is referred to as the constant volume combustion.
The constant volume heat rejection process 4-1 is replaced by a constant volumeblow downprocess 4-5 when the working medium is “blown down” into the atmosphere followed by a constant pressure and adiabatic exhaust stroke of the piston 5-6, which pushes the air remaining in the cylinderout. At the end of the exhaust stroke, the clearance space in the engine is filled with the exhaust gas which will dilute the incoming (fresh) charge.
This is now followed by a constant pressure adiabatic intake stroke of the piston 6-1.
According to this analysis, it does not matter whether the working medium is air alone, air plus fuel mixture or air, plus fuel plus residual gas. We assume air at present only to make the calculation easier.
The Exhaust Process
In the air standard engine, the exhaust process begins at the end of expansion; at point 4 when the exhaust valve opens. As far as the conditions inside the cylinder is concerned, the pressure drops instantaneously to atmospheric; that is, to point 1. This is seen in the P-V diagram. This process is referred to as Exhaust Blow down and is assumed to take place at constant volume. However, the pressure-specific volume diagram gives an idea of the state of the charge during this part of the cycle.
The ideal process is assumed to take place in two stages, namely, a release process and an exhaust process. During the ideal release process the piston is assumed to be stationary at the end of the expansion process.
The Release Process
During the release process, the charge in the cylinder at the end of the expansion stroke of the piston is assumed to be divided into 2 portions. One portion escapes from the cylinder while the other portion remains in the cylinder. The charge escaping from the cylinder undergoes a free expansion or a thermodynamically irreversible process, whereas the charge remaining in the cylinder is assumed to expand reversibly, in the ideal case, to atmospheric pressure before the piston begins the exhaust stroke.
The state of the charge that remains, is marked by the isentropic path 4-4’, which is the extension of the path 3-4, down to atmospheric. The expansion of the charge will force the second portion from the cylinder, which then escapes.
Consider the first element of the portion that escapes from the cylinder. This charge will expand into the exhaust pipe and will acquire a high velocity. It is assumed that the kinetic energy acquired by this first charge element in escaping from the cylinder is dissipated by the fluid friction and turbulence in the exhaust pipe into internal energy and flow work of the same charge element and, also, that no other heat transfer occurs. This will reheat the charge at constant pressure to the final state 4”. Succeeding elements of the charge will start to leave the cylinder at states between 4 and 4’, expand to atmospheric pressure 4’ and acquire a velocity which will be less than the first element; this will again be dissipated as friction. The end states of the successive elements will be along 4’-4” with the first element at 4” and the last element at 4’. The process 4-4” is an irreversible throttling process, as mentioned above, and is at a higher temperature than that of the charge remaining behind in the cylinder and, therefore, the specific volume at 4” will be greater than that at 4’. Thus,
By thermodynamics, the amount, or mass of fluid any point of the cycle is readily found when the volume of the fluid and the specific volume of the fluid are known, thus
The specific volume of the charge at 4’ is determined by assuming that the process 4-4’ is isentropic.
The mass of the exhaust gas remaining in the cylinder after blow down but before the start of the exhaust stroke is given by
At the end of the exhaust stroke, the mass of the exhaust gas, me, occupying the clearance space is given by
V6 is the clearance volume, which is the same as the volume at points 2, 3 or 6.
A quantity f, called the residual gas fraction, is defined as the ratio of the mass of clearance volume charge, me, which dilutes the fresh charge, to the mass of the total mixture, mm, that is, fresh charge plus residual charge. Thus
The quantity mm is constant throughout the entire cycle, which exists between points 1 to 4, and is given by
So, substituting for me and mm into the relation for f, we get
The concept is that point 4’ exists but point 5 does not exist. Point 5 is the actual case when exhaust process starts at 5 and ends at 6. Then 4-5 is the heat rejection, 5-6 is the exhaust process and 6-1 is the intake process.
Now
But
And
The residual gas fraction is a function of the specific volume of the charge at the start of compression and the specific volume of the charge at the start of the exhaust stroke.
We can obtain an expression for the residual gas fraction as derived by Heywood[1] based on inlet pressure, pi and exhaust pressure, pe and the other known quantities
The residual gas fraction increases as pi decreases below pe, decreases as r increases, and decreases as Q’/(cvT1) increases.
Through a similar analysis, the temperature of the residual gas, T6 can be determined
Energy in Exhaust
The complete expansion (Atkinson) cycle engine avoided the wasteful exhaust blow down process of the Otto cycle engine. The ideal work of such an engine can be found by multiplying the cycle efficiency obtained in Eq. 10 0r 11 by the head added, Qs. Thus, since the efficiency of the Atkinson cycle is given by either
or
It can also be obtained by determining the area under the P-V or P-v diagrams. Since the compression and expansion processes are isentropic, the work is given by a change in the internal energy. Thus, for the Atkinson cycle
whereas for the Otto cycle
The difference between Eq 13 and 14 gives the work dissipated in the exhaust blow down of the Otto cycle engine for any fluid. This is the maximum amount of work dissipated because it assumes that the process 4-4’ is isentropic. Thus, the blow down per unit mass of charge in the cylinder is given by
Consider Fig.3. The piston has reached the bottom dead center, that is, process 3-4 of the P-V diagram has been completed. The exhaust valve opens and the gas in the cylinder will expand isentropically (since ideal work is desired) to atmospheric pressure. The first element of gas to escape from a pressure at point 4 irreversibly to atmospheric pressure and in doing so will acquire a high velocity with a corresponding kinetic energy. Assume that this kinetic energy is converted into work by an ideal turbine, as shown in Fig. 3. It must be noted that all elements of releasing charge have the same history of pressure, that is, an initial pressure p4 and a final pressure p4’. However, each succeeding element of the charge leaving the engine has a progressively lower velocity and does progressively less work on the ideal turbine with the final element to escape doing so at nearly zero velocity.
Applying the energy equation to the exhaust charge, heat Q and Eflow in are zero while –W is a summation or integration of the variable kinetic energies, thus
-Wturbine = -Eflow out + ΔEsystem (16)
The summation of the energy flowing out of the system of Fig. 3 is readily accomplished since all elements pass from state 4 to 4’ and leave the turbine with essentially zero kinetic energy, so that
Eflow out = (m1 – m5)h4’ (17)
where m1 is the mass of charge in the cylinder before blow down and m5 is the mass of charge after blow down. Also
ΔEsystem = (mu)final - (mu)initial
= m5u4’ - m1u4 (18)
-Wturbine = (m1 – m5)h4’ + m5u4’ - m1u4 (19)
In a real engine, only a fraction (about 20%) of the blow down work indicated by the above equations can be realized because the real process is irreversible.
Pumping Work
In the four-stroke engine cycle, work is done on the piston during the intake and exhaust processes. The work done by the cylinder gases on the piston during exhaust is
We = pe(V2 - V1) (20)
The work done by the cylinder gases on the piston during intake is
Wi = pi(V1 - V2) (21)
The net work to the piston over the exhaust to intake strokes, the pumping work, is
Wp = (pi - pe)(V1 - V2) (23)
This is negative when pi is less than pe (part throttle SI) and positive when pi is greater than pe (supercharged CI or SI).
The pumping mean effective pressure (pmep) is usually defined as a positive quantity. Thus
For pi < pe: pmep = pe – pi (24A)
For pi > pe: pmep = pi – pe (24B)
The net and gross indicated mean effective pressures are related by
imepn = imepg - (pe – pi) (25)
The net fuel conversion efficiency (or thermal efficiency) is related to the gross value by
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