Air-standard Cycles and Their Analysis

7/29/2019 Air-standard Cycles and Their Analysis

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smail ALTIN, PhDAssistant Professor

Karadeniz Technical University

Faculty of Marine Sciences

Department of Naval Architecture and Marine Engineering

TURKEY

KARADENZ TECHNICAL UNIVERSITY


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Research interest

Internal combustion engines

Thermodynamic modeling of ICEs

Fuels and combustion

For details:www.ismailaltin.info
http://www.ismailaltin.info/http://www.ismailaltin.info/http://www.ismailaltin.info/http://www.ismailaltin.info/http://www.ismailaltin.info/


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Air-Standard Cycles and Their Analysis


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1. Introduction

2. Air-standart cycle

3. Analysis of Dual cycle

4. Analysis of Otto cycle

5. Analysis of Diesel cycle

6. Comparison of the cycles

7. Comprehensive examples

Contents


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1.Introduction

In internal combustion engines (ICE), the

conversion of heat energy into mechanical work is a

complicated process. To examine all these changes

quantitatively and to account for all the variables,

creates a very complex problem.


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The two commonly employed approximations of an

actual engine in order of their increasing accuracy

are (a) the air-standard cycle and (b) the fuel-air

cycle. They give an insight into some of the

important parameters that influence engine

performance.

1.Introduction


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In the air-standard cycle the working fluid is

assumed to be air. The values of the specific heat of

air are assumed to be constant at all temperatures.

This ideal cycle represents the upper limit of the

performance, which an engine may theoretically

attain.

1.Introduction


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The analysis of the air-standard cycle is based on the following assumptions:


1. The working fluid in the engine is always an ideal gas, namely pure air with

constant specific heats.

2. A fixed mass of air is taken as the working fluid throughout the entire cycle. The

cycle is considered closed with the same air remaining in the cylinder to repeat the

cycle. The intake and exhaust processes are not considered.

3. The combustion process is replaced by a heat transfer process from an external

source.

4. The cycle is completed by heat rejection to the surrounding until the air temperature

and pressure correspond to initial conditions. This is in contrast to the exhaust and

intake processes in an actual engine.


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5. All the processes that constitute the cycle are reversible.

6. The compression and expansion processes are reversible adiabatic.

7. The working medium does not undergo any chemical change throughout the cycle.

8. The operation of the engine is frictionless.

Because of the above simplified assumptions, the peak temperature, the pressure, the

work output, and the thermal efficiency calculated by the analysis of an air-standard

cycle are higher than those found in an actual engine. However, the analysis shows the

relative effects of the principal variables, such as compression ratio, inlet pressure, inlet

temperature, etc. on the engine performance.


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In this lecture, the following air-standard cycles are described and their work output,

thermal efficiency, and mean effective pressure are evaluated:

1. Otto cycle

2. Diesel cycle

3. Dual cycle

Some shortcomings of these ideal cycles are obvious, but these cycles give a valuable

insight into real effects and possibilities.


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It is a theoretical cycle for modern high speed diesel engines. The heat supplied is

partly at constant volume and partly at constant pressure. This cycle is also called the

mixed cycle orlimited pressure cycle. The compression and expansion processes are

isentropic and heat is rejected at constant volume. The p-V and T-s diagrams are

shown in Figures 3.1 (a) and (b) respectively.


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Here:

Process 1-2 is isentropic compression.Process 2-3 is reversible constant volume process.

Process 3-4 is reversible constant pressure process.

Process 4-5 is isentropic expansion.

Process 5-1 is reversible constant volume process.

Figure 3.1. Dual cycle

.0

pV constdQ


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Heat supplied during the process 2-33 2( )vmc T T

Heat supplied during the process 3-4 4 3( )pmc T T

Total heat supplied, 1 3 2 4 3( ) ( )v pQ mc T T mc T T

Total rejected during process 5-1,2 5 1

( )v

Q mc T T

Thermal efficiency:

(3.1)

(3.2)

(3.3)


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Three ratios are used to analysis the Dual cycle:

Three ratios are always greater than 1.

(3.4)

(3.5)

(3.6)

1Q

2Q


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(3.8)

(3.9)

(3.7)


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(3.10)


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Substituting the values of T1, T2, T3 from Eqs. (3.7), (3.8), (3.9) and (3.10) respectively in

Eq. (3.3),

(3.11)


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Equation (3.11) shows that the increase in the compression ratio r, and the higher values of

the adiabatic exponent cause an increase in the thermal efficiency. With a constant amount

of heat added, the values ofand depend on what part of the heat is added at constantvolume and what part at constant pressure. An increase in the value of and thecorresponding reduction in results in a higher thermal efficiency.


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Working done during cycle,

(3.12)


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Swept volume, (3.13)

Mean effective pressure,

(3.14)

(3.15)


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A German scientist, A. Nicolaus Otto in 1876 proposed an ideal air-standard cycle with

constant volume heat addition, which formed the basis for the practical spark-ignition

engines (petrol and gas engines). The cycle is shown on p-Vand T-s diagrams in Figure

4.1(a) and Figure 4.1(b) respectively.


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Figure 4.1. Otto cycle

.0

pV constdQ

Here:

Process 1-2 is isentropic compression.




1Q

2Q


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11

11 1r

For dual cycle, thermal efficiency has been defined as

3

2

1V

V is used for thermal efficiency of Otto cycle. We get

1

11 r

(3.16)


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Figure 4.2. Thermal efficiency vs. compression ratio for

different values of the adiabatic exponent


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1 1 1

1 1m

p rp

r

1 1

1 1m p rp

r

1

Figure 4.3 Mean effective pressure vs. pressure

ratio for different values of compression ratio r.

(3.17)


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Figure 5.1. Diesel cycle

.

0

pV const

dQ

Here:

Process 1-2 is isentropic compression.

Process 2-3 is reversible constant pressure process.



1

Q

2Q


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11

1

1 1r

For dual cycle, thermal efficiency has been defined as

is used for thermal efficiency of Diesel cycle. We get

(3.18)

3

2

1p

p

11 11

1r


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Figure 5.2 Thermal efficiency vs. cut-off ratio at different

compression ratios and adiabatic exponents.


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1 1 1

1 1m

p rp

r

1

1 1

1 1m p rp

r

(3.19)


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The significant parameters in cycle analysis are compression ratio, peak pressure,

peak temperature, heat addition, heat rejection, and the net work. In order to compare

the performance of these cycles, some of the parameters are kept fixed.


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6.1. For the same compression ratio and heat addition

Figure 6.1. p-V and T-s diagrams having the same compression ratio and heat

addition for the three cycles.

Otto Dual Diesel


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6.2. For the same compression ratio and heat rejection

Figure 6.2. p-V and T-s diagrams having the same compression ratio and heat

rejection for the three cycles.

Otto Dual Diesel


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6.3. For the same same peak pressure, peak temperature and heat rejection

Figure 6.3. p-V and T-s diagrams having the same peak pressure, peak temperature

and heat rejection for the three cycles.

Diesel Dual Otto


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6.4. For the same maximum pressure and heat input

Figure 6.4. p-V and T-s diagrams having the same maximum pressure and heat input

for the three cycles.

Diesel Dual Otto (for the same, )

1

Q


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6.6. For the same maximum pressure and work output

Figure 6.7. T-s diagrams having the same maximum pressure and heat input for thethree cycles.

Diesel Dual Otto


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7. Comprehensive examples

Examples of thermodynamic cycles can be found in handout.


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Reference

1. H.N. Gupta, Fundamentals of Internal Combustion Engines, PHI Learning Private

Ltd., New Delhi, 2011.

2. W.W. Pulkrabek, Engineering Fundamentals of The Internal Combustion Engine,

Prentice Hall, New Jersey, 2003.

FACULTY OF MARINE SCIENCES


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FACULTY OF MARINE SCIENCES


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QUESTIONS

Thank you for your attention

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Air-standard Cycles and Their Analysis

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