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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)

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In This Chapter We Cover the Following Topics

Art. Content Page

10.1 The Stirling Cycle 3

10.2 The Ericsson Cycle 4

10.3 Air Standard Otto Cycle 5

10.4 Air Standard Diesel Cycle 8

10.5 Air Standard Dual Cycle 11

10.6 Comparison of the Otto, Diesel and Dual Cycles 13

10.7 The Lenoir Cycle 14

10.8 The Atkinson Cycle 15

10.9 Air Standard Brayton Cycle 16

References:

1. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 6e,

John Wiley & Sons, Inc., New York, 2008.

2. G. J. Van Wylen, R. E. Sonntag, C. Borgnakke, Fundamentals of Thermodynamics,

John Wiley & Sons, Inc., New York, 1994.

3. J. P. Holman, Thermodynamics, 4e, McGraw-Hill, New York, 1988.

4. F. W. Sears, G. L. Salinger, Thermodynamics, Kinetic theory, and Statistical

Thermodynamics, 3e, Narosa Publishing House, New Delhi, 1998.

5. Y. A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach, 2e,

McGraw-Hill, New York, 1994.

6. E. Rathakrishnan, Fundamentals of Engineering Thermodynamics, 2e, PHI Learning

Private Limited, New Delhi, 2008.

7. P. K. Nag, Basic and Applied Thermodynamics, 1e, McGraw-Hill, New Delhi, 2010.

8. V Ganesan, Gas Turbine, 2e, Tata McGraw-Hill, New Delhi, 2003.

9. V Ganesan, I. C. Engine, 2e, Tata McGraw-Hill, New Delhi, 2003.




2 Chapter 10: Gas Power Cycles

10. Y. V. C. Rao, An Introduction to Thermodynamics, 1e, New Age International (P)

Limited, Publishers, New Delhi, 1998.

Please welcome for any correction or misprint in the entire manuscript and your

valuable suggestions kindly mail us [email protected].




3 Basic and Applied Thermodynamics By Brij Bhooshan

The operating cycle of an internal combustion engine can be broken down into a

sequence of separate processes viz., intake, compression, combustion, expansion and

exhaust. The internal combustion engine does not operate on a thermodynamic cycle as

it involves an open system i.e., the working fluid enters the system at one set of

conditions and leaves at another. However, it is often possible to analyze the open cycle

as though it were a closed one by imagining one or more processes that would bring the

working fluid at the exit conditions back to the condition of the starting point. The

accurate analysis of internal combustion engine processes is very complicated. In order

to understand them it is advantageous to analyze the performance of an idealized closed

cycle that closely approximates the real cycle. One such approach is the air-standard

cycle, which is based on the following assumptions:

(i) The working medium is assumed to be a perfect gas and follows the relation pV =

mRT or p = ρRT.

(ii) There is no change in the mass of the working medium.

(iii) All the processes that constitute the cycle are reversible.

(iv) Heat is assumed to be supplied from a constant high temperature source and not

from chemical reactions during the cycle.

(v) Some heat is assumed to be rejected to a constant low temperature sink during

the cycle.

(vi) It is assumed that there are no heat lasses from the system to the surroundings.

(vii) The working medium has constant specific heats throughout the cycle.

(viii) The physical constants viz., Cp, Cv, γ and M of working medium are the same as

those of air at standard atmospheric conditions.

Due to these assumptions, the analysis becomes over-simplified and the results do not

agree with those of the actual engine. Work output, peak pressure, peak temperature

and thermal efficiency based on air-standard cycles will be the maximum that can be

attained and will differ considerably from those of the actual engine. It is often used,

mainly because of the simplicity in getting approximate answers to the complicated

processes in internal combustion engines.

For the purpose of thermodynamic analysis of the internal combustion engines, the

following approximations are made:

a) The engine is assumed to operate on a closed cycle with a fixed mass of air which

does not undergo any chemical change.

b) The combustion process is replaced by an equivalent energy addition process from

an external source.

c) The exhaust process is replaced by an equivalent energy rejection process to

external surroundings by means of which the working fluid is restored to the

initial state.

d) The air is assumed to behave like an ideal gas with constant specific heat. These

cycles are usually referred to as air standard cycle.

10.1 THE STIRLING CYCLE

The Carnot cycle has a low mean effective pressure because of its very low work output.

Hence, one of the modified forms of the cycle to produce higher mean effective pressure

whilst theoretically achieving full Carnot cycle efficiency is the Stirling cycle. It consists

of two isothermal and two constant volume processes. The heat rejection and addition





take place at constant temperature. The p-V and T-s diagrams for the Stirling cycle are

shown in Diagrams 10.1(a) and 10.1(b) respectively. It is clear from Diagram 10.1(b)

that the amount of heat addition and rejection during constant volume processes is

same.

Diagram 10.1 The Stirling Cycle

Heat transfer in process 1-2 is




Now according to cycle Q2-3 = Q4-1.

Hence, the efficiency of the cycle is given as

10.2 THE ERICSSON CYCLE

The Ericsson cycle consists of two isothermal and two constant pressure processes. The

heat addition and rejection take place at constant pressure as well as isothermal

processes [Diagram 10.2]. Since the process 2-3 and 3-4 are parallel to each other on the

T-s diagram, the net effect is that the heat need be added only at constant temperature

T3 = T4 and rejected at the constant temperature T1 = T2.

The cycle is shown on p-V and T-s diagrams in Diagram 10.2(a) and 10.2(b) respectively.

The advantage of the Ericsson cycle over the Carnot and Stirling cycles is its smaller

pressure ratio for a given ratio of maximum to minimum specific volume with higher

mean effective pressure.

Diagram 10.2 The Ericsson Cycle

(a) P-V diagram (b) T-s diagram

2 1

4 3

3

T = C T = C

4

2

1

(a) p-V diagram (b) T-s diagram

4

1

2

3

Heat rejection to the sink

Heat added from/ heat added to the regenerator

Heat addition from the source

4 3

2 1





For 1 kg of ideal gas





Hence, the efficiency of the cycle is given as

The Ericsson cycle does not find practical application in piston engines but is

approached by a gas turbine employing a large number of stages with heat exchangers,

insulators and reheaters.

10.3 AIR STANDARD OTTO CYCLE

The main drawback of the Carnot cycle is its impracticability due to high pressure and

high volume ratios employed with comparatively low mean effective pressure. Nikolaus

A. Otto. (1876) proposed a constant-volume heat addition cycle which forms the basis for

the working of today's spark-ignition engines. One very common type of internal

combustion engines is the Spark Ignition (S.I.) engine used in automobiles.

Diagram 10.3 Air Standard Otto Cycle

Diagrams 10.3(a), and (b) illustrate the working principles of an Otto cycle. The Otto

cycle consists of the following processes.

0-1: Constant pressure suction during which a mixture of fuel vapour and air is drawn

into the cylinder as the piston executes an outward stroke.

1-2: The mixture is compressed isentropically due to the inward motion of the piston.

Because of the isentropic compression, the temperature of the gas increases.

2-3: The hot fuel vapour-air mixture is ignited by means of an electric spark. Since the

combustion is instantaneous, there is not enough time for the piston o move

outward. This process is approximated as a constant volume energy addition

process.

(a) Otto Cycle (b) P-V diagram

Combustion product

Inlet valve

Exhaust valve

Spark

Fuel air mixture

0

2

3

4

1





3-4: The hot combustion products undergo isentropic expansion and the piston executes

an outward motion.

4-1: The exhaust port opens and the combustion products are exhausted into the

atmosphere. The process is conveniently approximated as a constant-volume energy

rejection process.

1-0: The remaining combustion products are exhausted by an inward motion of the

piston at constant pressure.

Diagram 10.4 Air Standard Otto Cycle

Effectively there are four strokes in the cycle. These are suction, compression,

expression, and exhaust strokes, respectively. From the P-V diagram [Diagram 10.3] it

can be observed that the work done during the process 0-1 is exactly balanced by the

work done during 1-0. Hence for the purpose of thermodynamic analysis we need to

consider only the cycle 1-2-3-4, which is air-standard Otto Cycle [Diagram 10.4].

Suppose m be the fixed mass of air undergoing the cycle of operation as described above.

1-2: It is reversible adiabatic compression process. The air is compressed reversibly and

adiabatically from T1 to T2. In this process no heat addition or rejection by the air,

(–ve work, Wc).

2-3: Constant volume heating the air is now heated at constant volume from

temperature T2 to T3. Now heat absorb (+ve heat, Qg) is,

3-4: It is reversible adiabatically expansion process. The air is expended reversibly and

adiabatically from T3 to T4. In this process no heat addition or rejection by the air,

(+ve work, We).

4-1: It is constant volume cooling. The air is cooled at constant volume from temperature

T4 to T1. Heat rejection process (–ve heat, Qr).

Therefore, efficiency of the Otto cycle is

Now process 1-2 and 3-4 are isentropic processes for which T = Const.

Therefore,

where rk (=V1/V2) is the compression ratio.


2

3

4

1

2

3

4

1





and,

where re (=V3/V4) is the expansion ratio.

But, V1 = V4, and V2 = V3, then we have

So,

Now from equation (10.3), we get

Since rk > 1, the efficiency of the Otto cycle increases with increasing compression ratio.

However, in an actual engine, the compression ratio cannot be increased indefinitely

since higher compression ratios give higher values of T2 and this leads to spontaneous

and uncontrolled combustion of the gasoline-air mixture in the cylinder. Such a

condition is usually called knocking.

Diagram 10.5

Work Output

Performance of an engine is evaluated in terms of the efficiency (see Diagram 10.5).

However, sometime it is convenient to describe the performance in terms of mean

effective pressure, an imaginary pressure obtained by equating the cycle work to the

work evaluated by the following the relation

Now process 1-2 and 3-4 are isentropic processes for which p = Const.

Therefore,

where rp is the pressure ratio.

γ = 1.2

γ = 1.4

3 4 5 6 7 8 9 10

0.8

0.6 0.4

0.2





Mean Effective Pressure

The mean effective pressure is defined as the net work divided by the displacement

volume.

That is

Now swept volume is

Thus, it can be seen that the work output is directly proportional to pressure ratio, rp.

The mean effective pressure which is an indication of the internal work output increases

with a pressure ratio at a fixed value of compression ratio and ratio of specific heats. For

an Otto cycle, an increase in the compression ratio leads to an increase in the mean

effective pressure as well as the thermal efficiency.

10.4 AIR STANDARD DIESEL CYCLE

The Diesel cycle was developed by Rudolf Diesel in Germany. In actual spark-ignition

engines, the upper limit of compression ratio is limited by the self-ignition temperature

of the fuel. This limitation on the compression ratio can be circumvented if air and fuel

are compressed separately and brought together at the time of combustion. In such an

arrangement fuel can be injected into the cylinder which contains compressed air at a

higher temperature than the self-ignition temperature of the fuel. Hence the fuel ignites

on its own accord and requires no special device like an ignition system in a spark-

ignition engine. Such engines work on heavy liquid fuels. These engines are called

compression-ignition engines and they work on a ideal cycle known as Diesel cycle. The

difference between Otto and Diesel cycles is in the process of heat addition. In Otto cycle

the heat addition takes place at constant volume whereas in the Diesel cycle it is at

constant pressure. For this reason, the Diesel cycle is often referred to as the constant-

pressure cycle. It is better to avoid this term as it creates confusion with Joules cycle.

Diagram 10.6 Air Standard Diesel Cycle

(a) Diesel Cycle (b) P-V diagram

Combustion product

Inlet valve

Exhaust valve

Fuel

Air

0

2 3

4

1





Diagrams 10.6(a), and (b) explain the working principle of an Air Standard Diesel cycle.

The following are the processes.

0-1: Constant pressure suction during which fresh air is drawn into the cylinder as the

piston executes the outward motion.

1-2: The air is compressed isentropically. Usually the compression ratio in the Diesel

cycle is much higher them that of Otto cycle. Because of the high compression ratio,

the temperature of the gas at the end of isentropic compression is so high that when

fuel is injected, it gets ignited immediately.

2-3: The fuel (Diesel oil) is injected into the hot compressed air at state 2 and the fuel

undergoes a chemical reaction. The combustion of Diesel oil in air is not as

spontaneous as the combustion of gasoline and the combustion is relatively slow.

Hence the piston starts moving outward as combustion take place. The combustion

processes is conveniently approximated as a constant pressure energy addition

process.

3-4: The combustion products undergo isentropic expansion and the piston executes an

outward motion.

4-1: The combustion products are exhausted at constant volume when the discharge port

opens. This is replaced by a constant-volume energy rejection process.

1-0: The remaining combustion products are exhausted at constant pressure by the

inward motion of the piston.

From the P-V diagram it can be observed that the work done during the process 0-1 and

1-0 is zero. Hence, they can be ignored for the purpose of thermodynamic analysis we

need to consider only the cycle 1-2-3-4, which is air-standard Diesel Cycle. The cycle is

composed two reversible adiabatics and one reversible isobars, and one reversible

isochoric [Diagram 10.7].

Diagram 10.7 Air Standard Diesel Cycle

Suppose m be the fixed mass of air undergoing the cycle of operation as described above.

1-2: The air is compressed reversibly and adiabatically from T1 to T2. In this process no

heat addition or rejection by the air.

2-3: The air is now heated at constant volume from temperature T2 to T3. Now heat

absorb is,

3-4: The air is expended reversibly and adiabatically from T3 to T4. In this process no

heat addition or rejection by the air.

4-1: The air is cooled at constant volume from temperature T4 to T1. Heat rejection is

Therefore, efficiency of the Diesel cycle is


2

3

4

1

2 3

4

1





The efficiency of the cycle can be expressed in terms of the following ratios

Compression ratio, rk = V1/V2,

Expansion ratio, re = V4/V3,

Cut-off ratio, rc = V3/V2.

It is seen, as before that

The cut-off ratio is defined as the ratio of the volume at the end of constant-pressure

energy addition process to the volume at the beginning of the energy addition process.

Process 3-4 is Isentropic, then

Process 2-3 is Constant pressure, then

Process 1−2 is isentropic process, then

Substituting the values of T1, T2, and T4 in equations in (10.7), then

As rc > 1,

is also greater than unity. Therefore, the efficiency of the Diesel cycle

is less than that of the Otto cycle for the same compression ratio.

It may be noted that the efficiency of the Diesel cycle is different from that of the Otto

cycle only in the bracketed factor. This factor is always greater than unity. Hence for a

given compression ratio, the Otto cycle is more efficient. In diesel engines the fuel cut -off

ratio, rc, depends on output, being maximum for maximum output. Therefore, unlike the

Otto cycle the air-standard efficiency of the Diesel cycle depends on output. The higher

efficiency of the Otto cycle as compared to the Diesel cycle for the same compression

ratio is of no practical importance. In practice the operating compression ratios of diesel





engines are much higher compared to spark-ignition engines working on Otto cycle. The

normal range of compression ratio for diesel engine is 16 to 20 whereas for spark-

ignition engines it is 6 to 10. Due to the higher compression ratios used in diesel engines

the efficiency of a diesel engine is more than that of the gasoline engine.

Work Output

The net work output for a Diesel cycle is given by


The expression for mean effective pressure can be shown to be

10.5 AIR STANDARD DUAL CYCLE

The air standard Diesel cycle does not simulate exactly the pressure-volume variation in

an actual compression ignition engine, where the fuel injection is started before the end

of compression stroke. A closer approximation is the limited pressure cycle in which

some part of heat is added to air at constant volume, and the remainder at constant

pressure. Dual cycle is also termed as limited pressure cycle or Mixed cycle.

Diagram 10.8 Air Standard Dual Cycle


2

3 4

5

1

5

2

3

4

1





Diagrams 10.7(a) and (b) shows the working principles of a Dual cycle. In the dual cycle,

the energy addition is accomplished in two stages: Part of the energy is added at

constant volume and part of the energy is added at constant pressure. The remaining

processes are similar to those of the Otto cycle and the Diesel cycle. The efficiency of the

cycle can be estimated in the following way

Heat is added reversibly, partly at constant volume (2-3) and partly at constant pressure

(3-4).

Heat supplied

Heat rejected

Efficiency

Process 3-4

Process 2-3

Process 1−2

Process 4−5

Substituting the values of T1, T2, T3, and T5 in equations in (10.12), then

It can be seen from the above equation that a value of rp > 1 results in an increased

efficiency for a given value of rc and γ. Thus the efficiency of Dual cycle lies between that

of the Otto cycle and the Diesel cycle having same compression ratio. With rc = 1, it

becomes an Otto cycle, and with rp = 1, it becomes a Diesel cycle.





Work Output

The net work output for a Dual cycle is given by


The expression for mean effective pressure can be shown to be

10.6 COMPARISON OF THE OTTO, DIESEL AND DUAL CYCLES

The important variable factors which are used as the basis for comparison of the cycles

are compression ratio, peak pressure, heat addition, heat rejection and the net work. In

order to compare the performance of the Otto, Diesel and Dual combustion cycles some

of the variable factors must be fixed. In this section, a comparison of these three cycles is

made for the same compression ratio, same heat addition, constant maximum pressure

and temperature, same heat rejection and net work output. This analysis will show

which cycle is more efficient for a given set of operating conditions.

Diagrams 10.8

For same compression ratio and heat rejection (Diagrams 10.8(a) and (b))

1-6-4-5: Otto Cycle;

1-7-4-5: Diesel Cycle;

1-2-3-4-5: Duel Cycle

For the same Qr, the higher the Qg, the higher is the cycle efficiency


P

P = C

P = C

4

7

6

3

2

5

1

T

V = C

P = C

V = C 3

6

4

7

5

2

1





Diagrams 10.9

For the same maximum pressure and temperature (Diagrams 10.9(a) and (b))

1-6-4-5: Otto Cycle

1-7-4-5: Diesel Cycle

1-2-3-4-5: Duel Cycle

Qg is represented by:

area under 6-4 for Otto cycle

area under 7-4 for Diesel cycle and

area under 2-3-4 for Dual cycle and Qg is same for all the cycles

The actual cycles are modifications on the Air Standard cycles in the following manner:

10.7 THE LENOIR CYCLE

The Lenoir cycle consists of the following processes [see Diagram 10.10(a)]. Constant

volume heat addition (1-2); isentropic expansion (2-3); constant pressure heat rejection

(3-1). The Lenoir cycle is used for pulse jet engines.

Diagrams 10.10 The Lenoir Cycle

Heat given in process 1-2 is

Heat rejected in process 1-3 is

Efficiency


2

3 1

2

3

1

Air Standard cycle

Actual cycles

Actual properties of working medium and their variation with temperature

Time loss factor, Heat loss factor, Exhaust blow loss factor


P

6

2

7 3 4

5

1

T 3

7

2

6

1

5

4

5






Pressure ratio, rp = p2/p1,

Process 1−2

Process 3-2

Substituting the values of T1, and T3 in equations in (10.17), then

Thus the efficiency of the Lenoir cycle depends upon the pressure ratio as well as the

ratio of specific heats, viz., γ.

10.8 THE ATKINSON CYCLE

Atkinson cycle is an ideal cycle for Otto engine exhausting to a gas turbine. In this cycle

the isentropic expansion (3-4) of an Otto cycle (1234) is further allowed to proceed to the

lowest cycle pressure (3-5) so as to increase the work output. With this modification the

cycle is known as Atkinson cycle. The cycle is shown on p-V and T-s diagrams in

Diagrams 10.11(a) and (b) respectively.

Diagrams 10.11 The Atkinson Cycle

Heat given in process 2-3 is

Heat rejected in process 5-1 is


5

4

3

2

1

5

2

3

4

1





Efficiency


Compression ratio, rk = V1/V2,

Expansion ratio, re = V5/V3,

Process 1−2

Process 3-2

Now,

Process 5-3

Substituting the values of T2, T3, and T5 in equations in (10.19), then

10.9 AIR STANDARD BRAYTON CYCLE

Gas turbines function based on Brayton cycles. Air is first compressed adiabatically in

process 1-2, it then enters the combustion chamber where fuel is injected and burned

essentially at constant pressure in process 2-3, and then the products of combustion

expanded in the turbine to the ambient pressure in process 3-4, and are thrownout to

the surroundings. The cycle is open.

Diagram 10.12(a), (b) and (c) explain working of a Brayton cycle.

The air-standard Brayton cycle consists of





1-2: Isentropic compression of air

2-3: Constant pressure energy addition

3-4: Isentropic expansion

4-1: Constant Pressure energy rejection.

Diagram 10.12 Brayton cycles

Work input compression Wc

Heat supplied

Work output turbine WT

Heat rejection

Efficiency

Pressure ratio, rp = p2/p1,

and,

(a) Brayton cycle (b) P-V diagram (c) T-s diagram

T

P = C

P = C

2

1

5

3

4 P = C

P = C

P 2 3

1 4

B

C T

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