AIR STANDARD

8/12/2019 AIR STANDARD

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AIR STANDARD CYCLES

Theoretical Analysis

The accurate analysis of the various processes taking place in an internal combustion engine is avery complex problem. If these processes were to be analyzed experimentally, the analysis

would be very realistic no doubt. It would also be quite accurate if the tests are carried out

correctly and systematically, but it would be time consuming. If a detailed analysis has to be

carried out involving changes in operating parameters, the cost of such an analysis would bequite high, even prohibitive. An obvious solution would be to look for a quicker and less

expensive way of studying the engine performance characteristics. A theoretical analysis is the

obvious answer.

A theoretical analysis, as the name suggests, involves analyzing the engine performance

without actually building and physically testing an engine. It involves simulating an engine

operation with the help of thermodynamics so as to formulate mathematical expressions, whichcan then be solved in order to obtain the relevant information. 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 theeasier the calculations, but the lesser will be the accuracy of the final results.

The simplest theoretical analysis involves the use of the air standard cycle, which has thelargest number of simplifying assumptions.

A Thermodynamic Cycle

In some practical applications, notably steam power and refrigeration, a thermodynamic cycle

can be identified.

A thermodynamic cycle occurs when the working fluid of a system experiences a numberof processes that eventually return the fluid to its initial state.


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In steam power plants, water is pumped (for which work WP is required) into a boilerand evaporated into steam while heat QA is supplied at a high temperature. The steam flows

through a turbine doing work WTand then passes into a condenser where it is condensed into

water with consequent rejection of heat QRto the atmosphere. Since the water is returned to itsinitial state, the net change in energy is zero, assuming no loss of water through leakage or

evaporation.

An energy equation pertaining only to the system can be derived. Considering a system

with one entering and one leaving flow stream for the time period t1to t2

Q is the heat transfer across the boundary, +ve for heat added tothe system and

ve for heat taken fromthe system.

W is the work transfer across the boundary, +ve for work done bythe system and

-ve for work added tothe system

is the energy of all forms carriedby the fluid across the boundary intothe system

is the energy of all forms carriedby the fluid across the boundary outof system

Esystemis the energy of all formsstoredwithin the system, +ve for energy increase

-ve for energy decrease


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In the case of the steam power system described above

All thermodynamic cycles have a heat rejection process as an invariable characteristic

and the net work done is always less than the heat supplied, although, as shown in Eq. 2, it is

equal to the sum of heat added and the heat rejected (QRis a negative number).

The thermal efficiency of a cycle, th, is defined as the fraction of heat supplied to a

thermodynamic cycle that is converted to work, that is

This efficiency is sometimes confused with the enthalpy efficiency, e, or the fuel

conversion efficiency, f

This definition applies to combustion engines which have as a source of energy the

chemical energy residing in a fuel used in the engine.


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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 surroundingsis called a heat engine.

A heat engine is, thus, a device that produces work. In order to achieve this purpose, the

heat engine uses a certain working medium which undergoes the following processes:

1. A compression process where the working medium absorbs energy as work.

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. The air standard cycles, usingair 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

The air standard cycle is a cycle followed by a heat engine which uses air as the working

medium. Since the air standard analysis is the simplest and most idealistic, such cycles are alsocalled ideal cyclesand 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 combustionengine 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.


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Assumptions

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 (cycle).

In 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 easymathematical 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 usefulness.

Equivalent Air Cycle

A particular air cycle is usually taken to represent an approximation of some real set of processeswhich 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 tominimum pressure for gas turbine engines.


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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. Figures 1 and 2 show the P-V and T-s diagrams of the cycle.

Fig. 1 Fig. 2

Assuming that the charge is introduced into the engine at point 1, it undergoes isentropic

compression from 1 to 2. The temperature of the charge rises from Tminto Tmax. At point 2, heat

is added isothermally. This causes the air to expand, forcing the piston forward, thus doing work

on the piston. At point 3, the source of heat is removed and the air now expands isentropically topoint 4, reducing the temperature to Tminin the process. At point 4, a cold body is applied to the

end of the cylinder and the piston reverses, thus compressing the air isothermally; heat is rejected

to the cold body. At point 1, the cold body is removed and the charge is compressed

isentropically till it reaches a temperature Tmaxonce again. Thus, the heat addition and rejectionprocesses are isothermal while the compression and expansion processes are isentropic.

From thermodynamics, per unit mass of charge


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Heat supplied from point 2 to 3

Heat rejected from point 4 to 1

Now p2v2= RTmax (7)

And p4v4= RTmin (8)

Since Work done, per unit mass of charge, W = heat suppliedheat rejected

We have assumed that the compression and expansion ratios are equal, that is

Heat supplied Qs= R Tmaxln (r) (10)


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Hence, the thermal efficiency of the cycle is given by

From Eq. 11 it is seen that 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 1 if the minimum temperature is zero,which happens to be the absolute zero temperature in the thermodynamic scale.

This equation also indicates that for optimum (Carnot) efficiency, the cycle (and hencethe 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 highestpossible 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 orderto obtain the maximum amount of work. These conditions are the aims of all designers ofmodern heat engines. The conditions of heat rejection are governed, in practice, by the

temperature of the atmosphere.

It is impossible to construct an engine which will work on the Carnot cycle. In such an

engine, 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 strokewould produce only a small amount of work most of which would be absorbed by the friction of

the moving parts of the engine.


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Since the efficiency of the cycle, as given by Eq. 11, 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 working medium.

Piston Engine Air Standard Cycles

The cycles described here are air standard cycles applicable to piston engines. Engines bases onthese cycles have been built and many of the engines are still in use.

The Lenoir Cycle

The Lenoir cycle is of interest because combustion (or heat addition) occurs without

compression of the charge. Figures 3 and 4 show the P-V and T-s diagrams.

Fig. 3 Fig. 4

According to the cycle, the piston is at the top dead center, point 1, when the charge is

ignited (or heat is added). The process is at constant volume so the pressure rises to point 2.From 2 to 3, expansion takes place and from 3 to 1 heat is rejected at constant pressure.

Heat supplied, Qs= cv(T2T1) (12)


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Heat rejected, Qr= cp(T3T1) (13)

Since W = Qs- Qr (14)

W = cv(T2T1)cp(T2T1) (15)

Thus (16)

(17)

Since and


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Here, re= V3/V1, the volumetric expansion ratio. Equation 18 indicates that the thermal

efficiency of the Lenoir cycle depends primarily on the expansion ratio and the ratio of specific

heats.

The intermittent-flow engine which powered the German V-1 buzz-bomb in 1942 during

World War II operated on a modified Lenoir cycle. A few engines running on the Lenoir cycle

were built in the late 19th

century till the early 20th

century.

The Otto Cycle

The Otto cycle, which was first proposed by a Frenchman, Beau de Rochas in 1862, was firstused on an engine built by a German, Nicholas A. Otto, in 1876. The cycle is also called a

constant volume or explosion cycle. This is the equivalent air cycle for reciprocating piston

engines using spark ignition. Figures 5 and 6 show the P-V and T-s diagrams respectively.

Fig. 5 Fig. 6

At the start of the cycle, the cylinder contains a mass M of air at the pressure and volume

indicated at point 1. The piston is at its lowest position. It moves upward and the gas iscompressed isentropically to point 2. At this point, heat is added at constant volume which raises

the pressure to point 3. The high pressure charge now expands isentropically, pushing the piston

down on its expansion stroke to point 4 where the charge rejects heat at constant volume to the

initial state, point 1.


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The isothermal heat addition and rejection of the Carnot cycle are replaced by the

constant volume processes which are, theoretically more plausible, although in practice, even

these processes are not practicable.

The heat supplied, Qs, per unit mass of charge, is given by

cv(T3T2)

the heat rejected, Qrper unit mass of charge is given by

cv(T4T1)

and the thermal efficiency is given by

Now


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And since

Hence, substituting in Eq. 19, we get, assuming that r is the compression ratio V1/V2

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 ratiois preferred sometimes.

Equation 20 shows that the thermal efficiency of the theoretical Otto cycle increases with

increase in compression ratio and specific heat ratio but is independent of the heat added

(independent of load) and initial conditions of pressure, volume and temperature.

Figure 7 shows a plot of thermal efficiency versus compression ratio for an Otto cycle for

3 different values of . It is seen that the increase in efficiency is significant at lower

compression ratios.

r


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Figure 7

This is also seen in Table 1 given below, with = 1.4.

Table 1

r

1 02 0.242

3 0.356

4 0.426

5 0.475

6 0.512

7 0.541

8 0.565


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From the table 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%

Mean effective pressure:

9 0.585

10 0.602

16 0.67

20 0.698

50 0.791


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It is seen that the air standard efficiency of the Otto cycle depends only on the compression ratio.

However, the pressures and temperatures at the various points in the cycle and the net work

done, all depend upon the initial pressure and temperature and the heat input from point 2 topoint 3, besides the compression ratio.

A quantity of special interest in reciprocating engine analysis is the mean effective

pressure. Mathematically, it is the net work done on the piston, W, divided by the pistondisplacement volume, V1 V2. This quantity has the units of pressure. Physically, it is that

constant pressure which, if exerted on the piston for the whole outward stroke, would yield work

equal to the work of the cycle. It is given by

where Q2-3is the heat added from points 2 to 3.

Now

Here r is the compression ratio, V1/V2

From the equation of state:


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R0is the universal gas constant

Substituting for V1from Eq. 3 in Eq. 2 and then substituting for V1V2in Eq. 1 we get

The quantity Q2-3/M is the heat added between points 2 and 3 per unit mass of air(M is

the mass of air and m is the molecular weight of air); and is denoted by Q, thus

We can non-dimensionalize the mep by dividing it by p 1 so that we can obtain thefollowing equation


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Since , we can substitute it in Eq. 25 to get

The dimensionless quantity mep/p1 is a function of the heat added, initial temperature,compression ratio and the properties of air, namely, cvand . We see that the mean effective

pressure is directly proportional to the heat added and inversely proportional to the initial (or

ambient) temperature.

We can substitute the value of from Eq. 20 in Eq. 26 and obtain the value of mep/p 1for the

Otto cycle in terms of the compression ratio and heat added.

Figure 8

Figure 8 shows plots of mep/p1 versus compression ratio for different values of heatadded function.

In terms of the pressure ratio, p3/p2 denoted by rpwe could obtain the value of mep/p1as follows:


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We can obtain a value of rpin terms of Q as follows:

Another parameter, which is of importance, is the quantity mep/p3. This can be obtained from the

following expression:

Figure 9


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Figure 9 shows plots of the quantity mep/p3versus r. This shows a decrease in the

value of mep/p3when r increases.

Choice of Q

We have said that

M is the mass of charge (air) per cycle, kg.

Now, in an actual engine

Mfis the mass of fuel supplied per cycle, kg

Qcis the heating value of the fuel, kJ/kg

Mais the mass of air taken in per cycle

F is the fuel air ratio = Mf/Ma


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Substituting for Eq. (B) in Eq. (A) we get

So, substituting for Ma/M from Eq. (33) in Eq. (32) we get

For isooctane, FQcat stoichiometric conditions is equal to 2975 kJ/kg, thus

Q = 2975(r 1)/r (35)

At an ambient temperature, T1of 300K and cvfor air is assumed to be 0.718 kJ/kgK, we get a

value of Q/cvT1= 13.8(r1)/r.

Under fuel rich conditions, = 1.2, Q/ cvT1= 16.6(r1)/r.

Under fuel lean conditions, = 0.8, Q/ cvT1= 11.1(r1)/r


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The Diesel Cycle

This cycle, proposed by a German engineer, Dr. Rudolph Diesel to describe the processes of his

engine, is also called the constant pressure cycle. This is believed to be the equivalent air cyclefor the reciprocating slow speed compression ignition engine. The P-V and T-s diagrams are

shown in Figs 10 and 11 respectively.

Figures 10 and 11

The cycle has processes which are the same as that of the Otto cycle except that the heat

is added at constant pressure.

The heat supplied, Qsis given by

cp(T3T2)

whereas the heat rejected, Qris given by

cv(T4T1)



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From the T-s diagram, Fig. 11, the difference in enthalpy between points 2 and 3 is the

same as that between 4 and 1, thus

and

Substituting in eq. 36, we get


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Now

When Eq. 38 is compared with Eq. 20, it is seen that the expressions are similar except

for the term in the parentheses for the Diesel cycle. It can be shown that this term is always

greater than unity.

Now where r is the compression ratio and reis the expansion ratio

Thus, the thermal efficiency of the Diesel cycle can be written as

Let re= r since r is greater than re. Here, is a small quantity. We therefore have


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We can expand the last term binomially so that

Also

We can expand the last term binomially so that

Substituting in Eq. 39, we get


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Since the coefficients of , etc are greater than unity, the quantity in the

brackets in Eq. 40 will be greater than unity. Hence, for the Diesel cycle, we subtract timesa quantity greater than unity from one, hence for the same r, the Otto cycle efficiency is greater

than that for a Diesel cycle.

If is small, the square, cube, etc of this quantity becomes progressively smaller, so thethermal efficiency of the Diesel cycle will tend towards that of the Otto cycle.

From the foregoing we can see the importance of cutting off the fuel supply early in the

forward stroke, a condition which, because of the short time available and the high pressures

involved, introduces practical difficulties with high speed engines and necessitates very rigid fuelinjection gear.

In practice, the diesel engine shows a better efficiency than the Otto cycle engine because

the compression of air alone 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 temperaturedeveloped 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.

Thus 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.

We can obtain a value of rcfor a Diesel cycle in terms of Q as follows:


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We can substitute the value of from Eq. 38 in Eq. 26,reproduced below and obtain the value ofmep/p1for the Diesel cycle.

In terms of the cut-off ratio, we can obtain another expression for mep/p1as follows:

For the Diesel cycle, the expression for mep/p3is as follows:

Modern high speed diesel engines do not follow the Diesel cycle. The process of heataddition is partly at constant volume and partly at constant pressure. This brings us to the dual

cycle.

The Dual Cycle


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An important characteristic 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 affectsthe strength required of the engine structure. In the constant-volume cycle, shown in Fig. 10, it is

seen that the quantity mep/p3falls off rapidly as the compression ratio increases, which means

that for a given mean effective pressure the maximum pressure rises rapidly as the compressionratio increases. For example, for a mean effective pressure of 7 bar and Q/cvT1 of 12, themaximum pressure at a compression ratio of 5 is 28 bar whereas at a compression ratio of 10, it

rises to about 52 bar. Real cycles follow the same trend and it becomes a practical necessity to

limit the maximum pressure when high compression ratios are used, as in diesel engines. Thisalso indicates that diesel engines will have to be stronger (and hence heavier) because it has to

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 atconstant 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 cutoff early in the expansion stroke, both to give sufficient time for the fuel to burn and thereby

increase combustion efficiency and reduce after burning but also 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 modernhigh 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 combustion is nearly at constant volume(like in a spark ignition engine). But the peak pressure is limited because of strength

considerations so the rest of the heat addition is believed to take place at constant pressure in a

cycle. This has led to the formulation of the dual combustion cycle. In this cycle, for high

compression ratios, the peak pressure is not allowed to increase beyond a certain limit and toaccount for the total addition, the rest of the heat is assumed to be added at constant pressure.

Hence the name limited pressure cycle.

The cycle is the equivalent air cycle for reciprocating high speed compression ignition

engines. The P-V and T-s diagrams are shown in Figs.12 and 13. In the cycle, compression and

expansion processes are isentropic; heat addition is partly at constant volume and partly at

constant pressure while heat rejection is at constant volume as in the case of the Otto and Dieselcycles.


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Figure 12 Figure 13

The heat supplied, Qsper unit mass of charge is given by

cv(T3T2) + cp(T3T2)

whereas the heat rejected, Qrper unit mass of charge is given by

cv(T4T1)



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From thermodynamics

the explosion or pressure ratio and

the cut-off ratio.

Now,

Also


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And

Thus

Also

Therefore, the thermal efficiency of the dual cycle is

We can substitute the value of from Eq. 46 in Eq. 26 and obtain the value of mep/p1forthe dual cycle.

In terms of the cut-off ratio and pressure ratio, we can obtain another expression formep/p1as follows:

For the dual cycle, the expression for mep/p3is as follows:


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Since the dual cycle is also called the limited pressure cycle, the peak pressure, p 3, isusually specified. Since the initial pressure, p1, is known, the ratio p3/p1 is known. We can

correlate rpwith this ratio as follows:

We can obtain an expression for rcin terms of Q and rpand other known quantities as

follows:

We can also obtain an expression for rpin terms of Q and rcand other known quantities

as follows:

Figure 14 shows a constant volume and a constant pressure cycle, compared with a

limited pressure cycle. In a series of air cycles with varying pressure ratio at a given compression

ratio and the same Q, the constant volume cycle has the highest efficiency and the constantpressure cycle the lowest efficiency.


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Figure 15 compares the efficiencies of the three cycles for the same value of

for the same initial conditions and three values of p3/p1 for the dual cycle. It isinteresting to note that the air standard efficiency is little affected by compression ratio above a

compression ratio of 8 for the limited pressure cycle.

The curves of mep/p3versus compression ratio for the same three cycles as above are

given in Fig. 10. It is seen that a considerable increase in this ratio is obtained for a limited

pressure cycle as compared to the constant volume or constant pressure cycles.

Figure 14


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Figure 15

The Atkinson Cycle

This cycle is also referred to as the complete expansion cycle.Inspection of the P-V diagrams of

the Otto, Diesel and Dual cycles shows that the expansion process to point 4 does not reach 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 withconsequent dissipation of available energy. This is necessary so as to allow the gases to flow out


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due to pressure difference and hence reduce the piston work in driving out the gases. The air

standard cycle shows a loss of net work because of the reduction in area of the P-V diagram.

In the Otto cycle, if the expansion is allowed to completion to point 4 (Fig. 16) and heatrejection occurs at constant pressure, the cycle is called the Atkinson cycle.

The heat supplied, Qsper unit mass of charge is given by

cv(T3T2)

Figure 16

whereas the heat rejected, Qrper unit mass of charge is given by

cp(

T4T

1)



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Now

As before,

And

The efficiency is therefore given by

If we denote the expansion ratio as V4/V3, we can rewrite the thermal efficiency as


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Since the Atkinson cycle area under the P-V diagram is larger than the correspondingOtto cycle, the efficiency, for the same compression ratio and heat input, will be higher.

An engine can be built to make use of complete expansion, but the stroke length of such

an engine will be extremely long and will not be economically feasible to offset the improvementin power and efficiency. Also, there are some operational problems with such a cycle.

The Miller Cycle

This cycle, proposed by Ralph Miller, (Fig. 17), is applicable for engines with very early or late

closing of the inlet valve. If the valve closes before the piston reaches bottom center, at point 1,

the charge inside will first expand to point 7. Compression will be from point 7 through 1 topoint 2. Work done in expansion from 1 to 7 is the same as the compression work from point 7 to

1. The actual compression work will be from 1 to 2.

If the valve closes after the piston crosses the bottom center, it will do so again at point 1.

Compression will begin after the valve closes. For this case, process 1 to 7 and 7 to 1 will not

exist.

The parameter, , is defined as the ratio of the expansion ratio reto the compression ratio,rc, thus:

Fig. 17


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Fig. 17

(Equations 58-61)

The thermal efficiency of the Miller cycle is a function of the compression ratio, the

specific heat ratio, the expansion ratio and the heat added. The ratio of the Miller cycle thermal

efficiency and the equivalent Otto cycle thermal efficiency is plotted against in Fig. 18 (Taken

from Ferguson and Kirkpatrick[1]). For high values of , the Miller cycle is more efficient. A

plot of the ratio of indicated mean effective pressures of the two cycles against (Fig.19, alsotaken from the same reference) shows that the Miller cycle is at a significant disadvantage. This

is because, as increases, the fraction of the displacement volume that is filled with the inletfuel-air mixture decreases, thereby decreasing the IMEP. The decrease in the IMEP for the

Miller cycle can be compensated by supercharging the inlet mixture.
http://iqsoft.co.in/bme/asc.htm#_ftn1http://iqsoft.co.in/bme/asc.htm#_ftn1http://iqsoft.co.in/bme/asc.htm#_ftn1


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Figure 18

Figure 19

The Brayton Cycle


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The Brayton cycle is also referred to as the Joule cycle or the gas turbine air cycle because allmodern gas turbines work on this cycle. However, if the Brayton cycle is to be used for

reciprocating piston engines, it requires two cylinders, one for compression and the other for

expansion. Heat addition may be carried out separately in a heat exchanger or within theexpander itself.

The pressure-volume and the corresponding temperature-entropy diagrams are shown inFigs 20 and 21 respectively.

Fig. 20


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Fig. 21

The cycle consists of an isentropic compression process, a constant pressure heat addition

process, an isentropic expansion process and a constant pressure heat rejection process.

Expansion is carried out till the pressure drops to the initial (atmospheric) value.

Heat supplied in the cycle, Qs, is given by

Cp(T3T2)

Heat rejected in the cycle, Qs, is given by

Cp(T4T1)

Hence the thermal efficiency of the cycle is given by


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Now

And since

Hence, substituting in Eq. 62, we get, assuming that rpis the pressure ratio p2/p1

This is numerically equal to the efficiency of the Otto cycle if we put


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so that

where r is the volumetric compression ratio.

For gas turbines it is convenient to speak of pressure ratio p2/p1 rather than the

compression ratio V2/V1unless we are talking of a reciprocating type of Brayton cycle engine.

Reciprocating engines that operate on this cycle would require a very long stroke so that theworking medium can expand to atmospheric pressure. This will increase the friction power and

hence reduce the brake power.

The heat addition at constant pressure of the Brayton cycle makes it more efficient than

the diesel cycle although the latter also has a constant pressure heat addition. This is because

expansion in the former cycle proceeds to atmospheric pressure rather than to a higher pressurein the former cycle.

The spark ignition and compression ignition engines are more efficient than the gasturbine. This is because the SI and the CI engines operate at higher peak cycle temperatures.

Moreover, the compression and expansion processes are more efficient in the piston-cylinder

system due to lower fluid friction and turbulence. On the other hand, the mass flow rate througha gas turbine is much greater than that through a CI or SI engine; hence the gas turbine is ideallysuited for higher power than the CI engine. The gas turbine may be provided with intercooling

during compression, reheating during expansion, and regeneration prior to heat addition. These

are techniques used to increase the power and efficiency of a simple gas turbine.

Gas turbines generally run at maximum fuel-air ratios that are about a quarter of the

chemically correct ratio. Hence, such cycles analysis may be carried out with Q = 2980/4 = 745

kJ/kg air. There is no concept of a clearance volume in a gas turbine so the value of M a/M in eq.

32 is taken as unity.

For a gas turbine, the ratio of work per unit time (or power) to the volume of air at inletconditions (per unit time) or W/V1 has units of pressure. Its significance is similar to that of

mean effective pressure in reciprocating engines.


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A gas turbine cycle of the type described above, at the most, gives an idea of the upper

limit of possible cycle efficiency. It does not, however, predict the trends of real gas turbine

performance very well, even when the compressor, combustion chamber and turbine efficienciesare assumed to be constant.

Comparison of Air Cycles

Fig 22

The Lenoir, Otto, Diesel, dual, Atkinson and Brayton cycles may be compared for similar

parametric conditions. In all these comparisons it is assumed that initial conditions of pressureand temperature are identical. One of the parameters that may be kept the same for all the cycles

is the heat input. Another factor that may be kept the same is the compression ratio, maximum

pressure or maximum temperature. Another set of factors that can be kept the same are the


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temperature and pressure. In the case of the dual cycle, another comparison is on the basis of

different proportions of heat added at constant pressure relative to heat added at constant volume.

Same Compression Ratio and Heat Input

It is already seen that adding heat at constant volume results in the highest maximum pressure

and temperature for the Otto and Atkinson cycles. Adding heat at constant pressure results in thelowest maximum temperature and pressure for the constant pressure Diesel cycle. The

corresponding values for the dual cycle lie in between those for the Otto and Diesel cycles.

This is seen Fig. 22, which gives the pressure-volume diagrams for all cycles except theLenoir cycle which has no compression therefore no compression ratio. The Lenoir cycle (with

the same heat input) has a peak temperature between the Otto and Diesel cycles but a

displacement volume of about 6.6 times that of the other cycles.

Fig. 23


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In the temperature-entropy diagram shown in Fig. 23, the area under a curve represents

the heat (added or rejected as the case may be). For the Otto, dual and Diesel cycles, the areaunder the lower constant volume line represents the heat rejected, between the entropy limits of

any given cycle. From Fig. 23, it is seen that the area under the heat rejected curve is the least for

the Otto cycle and the highest for the Diesel cycle, while for the limited pressure (dual) cycle, itlies in between. Since the heat rejected by the Otto cycle is the lowest, and


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,

it the most efficient while the Diesel is the least efficient because in this cycle, the heat rejected

is the highest. The efficiency of the dual cycle lies in between. This explains why a petrol engine

will be more efficient than a diesel engine if the compression ratio is the same. Unfortunately, adiesel engine cannot have the same compression ratio as that of a petrol engine because the

diesel fuel would not be able to auto-ignite. However, it is clear from the foregoing in any

engine, the addition of heat should be such that maximum possible expansion of the working

fluid should occur in order to obtain the maximum thermal efficiency.

When comparing the constant-pressure heat rejection curves of the Brayton, Atkinson

and Lenoir cycles, the heat rejection is the highest for the Lenoir and hence its efficiency is thelowest. Thus, the relative values of the heat rejection (in ascending order) and the corresponding

thermal efficiency (in descending order) are as follows: Atkinson, Otto, Brayton (numerically

equal to that of the Otto), dual, Diesel, and Lenoir cycles. The main reason why the diesel cycle

is at a disadvantage is its lower isentropic expansion ratio.

Fig. 24


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Same Maximum Pressure and Heat Input

A comparison of all the cycles except the Lenoir air cycle with the same maximum pressure andheat input, as seen in Fig. 24, indicates that the heat rejected is the lowest for the Brayton cycle

and the highest for the Otto cycle. The relative order of efficiencies (in ascending order is as

follows: Otto, Atkinson, dual, diesel, and Brayton cycles. The Lenoir cycle would not be feasible

because the temperatures reached at the end of combustion would be extremely high. A much


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lower compression ratio must be used with the Otto and Atkinson cycles than with the Brayton

and diesel cycles in order to attain the same maximum pressure. The compression ratio for the

dual cycle will lie in between.

This explains why the diesel engine (which follows the dual cycle more closely) is more

efficient than a petrol engine. In a real engine, the maximum pressures would be comparable and

so also the heat inputs because the heating values of the two fuels are more or less similar.

Same Maximum Temperature and Heat Input

The same conclusion as in the previous case can be obtained in this case, that is, the Otto cycle isthe least efficient and the Brayton is the most efficient. Here also the compression ratio of the

Otto and Atkinson cycles will have to be kept much lower than that of the Brayton and Diesel

cycles. The dual cycle case falls in between.

Same Maximum Pressure and Maximum Temperature

For this case, the heat rejected for those cycles where the heat is rejected at constant volume isthe same. However, the heat added in the diesel cycle is the highest, making it the most efficient

cycle, followed by the dual and Otto cycles. The heat rejected for those cycles where the heat is

rejected at constant pressure will be lower, and since the heat added in the Brayton cycle ishigher than that for the Atkinson cycle, the Brayton cycle is the most efficient of them all,

followed by the Atkinson, Diesel, dual and Otto cycles. The compression ratio in the Diesel

cycle will be higher than that of the Otto.

Same Maximum Pressure and Output

While the temperature-entropy plots are best suited for comparing cycles on the basis of heat

input and temperatures, the pressure-volume diagram is best suited for comparing cycles on thebasis of pressure and work output. The temperature-entropy diagram would nevertheless be still

required in order to determine the efficiency. The temperature-entropy curves will be similar to


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the case of same maximum pressure and same heat input. Hence the order of efficiency will be

the same, that is Otto, Atkinson, dual, Diesel, and Brayton cycles.

Additional Information on the Miller Cycle

Taken from Everything2.com:-

The Miller Cycle, developed by AmericanengineerRalph Millerin the 1940's, is a modified

Otto Cyclethat improves fuel efficiency by 10%-20%. It relies on asupercharger/turbocharger,

and takes advantage of the superchargers greater efficiency at low compression levels. As withotherforced inductionengines more power can be had from a smaller engine, but without the

efficiency penalties usually associated with forced induction (e.g. a Miller Cycle v6 can get the

power of a v8 yet still retain the fuel efficiency of a v6).

During theintake strokethe supercharger overcharges the cylinder with fuel and air, and during

the first bit of thecompression strokethe intake valves are left open and some of the overchargeis pushed out. While the overcharge is being forced out and until the intake valves close the

piston isn't pushing against anything and in effect the compression stroke is shortened compared

to the 'normal'power stroke.While the supercharger normally employed does use some of theengines power, it's much less than the power saved from the shortened compression stroke. The

lowerfrictionassociated with the smaller engine also improvesefficiency

Taken from Wikipedia:-

A traditionalOtto cycleengine uses four "strokes", of which two can be considered "high power"the compression stroke (high power consumption) and power stroke (high power production).

Much of the internal power loss of an engine is due to the energy needed to compress the charge

during the compression stroke, so systems that reduce this power consumption can lead to

greater efficiency.

In the Miller cycle, the intake valve is left open longer than it would be in anOtto cycleengine.In effect, the compression stroke is two discrete cycles: the initial portion when the intake valve

is open and final portion when the intake valve is closed. This two-stage intake stroke creates the

so called "fifth" cycle that the Miller cycle introduces. As the piston initially moves upwards in

what is traditionally the compression stroke, the charge is partially expelled back out the still-open intake valve. Typically this loss of charge air would result in a loss of power. However, in

the Miller cycle, this is compensated for by the use of asupercharger.The supercharger typically

will need to be of the positive displacement type due its ability to produce boost at relatively lowengine speeds. Otherwise, low-rpm torque will suffer.

A key aspect of the Miller cycle is that the compression stroke actually starts only after thepiston has pushed out this "extra" charge and the intake valve closes. This happens at around
http://everything2.com/index.pl?node=engineerhttp://everything2.com/index.pl?node=engineerhttp://everything2.com/index.pl?node=Ralph%20Millerhttp://everything2.com/index.pl?node=Ralph%20Millerhttp://everything2.com/index.pl?node=Ralph%20Millerhttp://everything2.com/index.pl?node=Otto%20Cyclehttp://everything2.com/index.pl?node=Otto%20Cyclehttp://everything2.com/index.pl?node=superchargerhttp://everything2.com/index.pl?node=superchargerhttp://everything2.com/index.pl?node=turbochargerhttp://everything2.com/index.pl?node=turbochargerhttp://everything2.com/index.pl?node=turbochargerhttp://everything2.com/index.pl?node=forced%20inductionhttp://everything2.com/index.pl?node=forced%20inductionhttp://everything2.com/index.pl?node=forced%20inductionhttp://everything2.com/index.pl?node=intake%20strokehttp://everything2.com/index.pl?node=intake%20strokehttp://everything2.com/index.pl?node=intake%20strokehttp://everything2.com/index.pl?node=compression%20strokehttp://everything2.com/index.pl?node=compression%20strokehttp://everything2.com/index.pl?node=compression%20strokehttp://everything2.com/index.pl?node=power%20strokehttp://everything2.com/index.pl?node=power%20strokehttp://everything2.com/index.pl?node=power%20strokehttp://everything2.com/index.pl?node=frictionhttp://everything2.com/index.pl?node=frictionhttp://everything2.com/index.pl?node=frictionhttp://everything2.com/index.pl?node=efficiencyhttp://everything2.com/index.pl?node=efficiencyhttp://everything2.com/index.pl?node=efficiencyhttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Superchargerhttp://en.wikipedia.org/wiki/Superchargerhttp://en.wikipedia.org/wiki/Superchargerhttp://en.wikipedia.org/wiki/Superchargerhttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://en.wikipedia.org/wiki/Four-stroke_cyclehttp://everything2.com/index.pl?node=efficiencyhttp://everything2.com/index.pl?node=frictionhttp://everything2.com/index.pl?node=power%20strokehttp://everything2.com/index.pl?node=compression%20strokehttp://everything2.com/index.pl?node=intake%20strokehttp://everything2.com/index.pl?node=forced%20inductionhttp://everything2.com/index.pl?node=turbochargerhttp://everything2.com/index.pl?node=superchargerhttp://everything2.com/index.pl?node=Otto%20Cyclehttp://everything2.com/index.pl?node=Ralph%20Millerhttp://everything2.com/index.pl?node=engineer


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20% to 30% into the compression stroke. In other words, the actual compression occurs in the

latter 70% to 80% of the compression stroke. The piston gets the same resulting compression as

it would in a standard Otto cycle engine for less work.

To understand the reason for the delay in closing the intake valve, consider the action of the

crankshaft, piston and connecting rod in creating a mechanical advantage. At bottom dead center("BDC") or top dead center ("TDC"), the rotational axis of the crank comes into alignment with

the wrist pin, and the big end of the crank. When these three points (rotational axis of the crank,

wrist pin center, and big end center) are in alignment, there is no lever arm to create or userotational energy. But as the crank rotates a bit, the big end of the crank moves away from

alignment with the other two points, creating the mechanical leverage needed to do the work of

compression. By delaying the closing of the inlet port, compression of the air in the cylinder is

delayed to a point where the crankshaft is once again very effective. In the meantime, the aircharge has been easily pushed out of the cylinder and back upstream in the inlet tract where it

meets the pressurized charge from the supercharger head-on, causing the inlet pressure to

increase just as the inlet port closes. In the inlet tract, the supercharger continues to add pressure

until the inlet valve opens again. The net gain comes from moving the work of compressionaway from the most inefficient region of the crank rotation, namely the rotation near BDC, and

letting the work of compression be done during the near-BDC period by the more efficientSupercharger. This trick of inlet timing and compression allows the crank to turn freely aroundBDC and makes Miller Cycle engines free revving and fuel efficient.

The Miller cycle results in an advantage as long as the supercharger can compress the chargeusing less energy than the piston would use to do the same work. Over the entire compression

range required by an engine, the supercharger is used to generate low levels of compression,

where it is most efficient. Then, the piston is used to generate the remaining higher levels ofcompression, operating in the range where it is more efficient than a supercharger. Thus the

Miller cycle uses the supercharger for the portion of the compression where it is best, and the

piston for the portion where it is best. In total, this reduces the power needed to run the engine by

10% to 15%. To this end, successful production engines using this cycle have typically usedvariable valve timingto effectively switch off the Miller cycle in regions of operation where it

does not offer an advantage.

In a typical spark ignition engine, the Miller cycle yields an additional benefit. The intake air is

first compressed by the supercharger and then cooled by anintercooler.This lower intake charge

temperature, combined with the lower compression of the intake stroke, yields a lower finalcharge temperature than would be obtained by simply increasing the compression of the piston.

This allows ignition timing to be advanced beyond what is normally allowed before the onset of

detonation, thus increasing the overall efficiency still further.

An additonal advantage of the lower final charge temperature is that the emission of NOx in

diesel engines is decreased, which is an important design parameter in large diesel engines on

board ships and power plants.

Efficiency is increased by raising thecompression ratio.In a typical gasoline engine, thecompression ratio is limited due to self-ignition (detonation) of the compressed, and therefore
http://en.wikipedia.org/wiki/Variable_valve_timinghttp://en.wikipedia.org/wiki/Variable_valve_timinghttp://en.wikipedia.org/wiki/Intercoolerhttp://en.wikipedia.org/wiki/Intercoolerhttp://en.wikipedia.org/wiki/Intercoolerhttp://en.wikipedia.org/wiki/Compression_ratiohttp://en.wikipedia.org/wiki/Compression_ratiohttp://en.wikipedia.org/wiki/Compression_ratiohttp://en.wikipedia.org/wiki/Compression_ratiohttp://en.wikipedia.org/wiki/Intercoolerhttp://en.wikipedia.org/wiki/Variable_valve_timing


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hot, air/fuel mixture. Due to the reduced compression stroke of a Miller cycle engine, a higher

overall cylinder pressure (supercharger pressure plus mechanical compression) is possible, and

therefore a Miller cycle engine has better efficiency.

The benefits of utilizing positive displacement superchargers come with a cost. 15% to 20% of

the power generated by a supercharged engine is usually required to do the work of driving thesupercharger, which compresses the intake charge (also known as boost).

[1]Ferguson and Kirkpatrick, Internal Combustion Engines, 2

nd

Ed., John Wiley & Sons NewYork, 2001
http://iqsoft.co.in/bme/asc.htm#_ftnref1http://iqsoft.co.in/bme/asc.htm#_ftnref1

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