### Air-Standard Cycles and Their Analysis

```KARADENİZ TECHNICAL UNIVERSITY
İsmail ALTIN, PhD
Assistant Professor
Faculty of Marine Sciences
Department of Naval Architecture and Marine Engineering
TURKEY
Research interest
• Internal combustion engines
• Thermodynamic modeling of ICEs
• Fuels and combustion
For details:
www.ismailaltin.info
Air-Standard Cycles and Their Analysis
Contents
1.
2.
3.
4.
5.
6.
7.
Introduction
Air-standart cycle
Analysis of Dual cycle
Analysis of Otto cycle
Analysis of Diesel cycle
Comparison of the cycles
Comprehensive examples
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.
1.Introduction…
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
performance.
that
influence
engine
1.Introduction…
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.
2. Air-standart cycle
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.
2. Air-standart cycle…
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.
2. Air-standart cycle…
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.
3. Analysis of Dual cycle
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 or limited 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.
3. Analysis of Dual cycle…
pV   const.
dQ  0
Figure 3.1. Dual cycle
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.
3. Analysis of Dual cycle…
Heat supplied during the process 2-3  mcv (T3  T2 )
Heat supplied during the process 3-4  mc p (T4  T3 )
Total heat supplied,
Q1  mcv (T3  T2 )  mc p (T4  T3 )
Total rejected during process 5-1, Q2  mcv (T5  T1 )
(3.1)
(3.2)
Thermal efficiency:
(3.3)
3. Analysis of Dual cycle…
Three ratios are used to analysis the Dual cycle:
Q1
(3.4)
Q2
(3.5)
(3.6)
Three ratios are always greater than 1.
3. Analysis of Dual cycle…
(3.7)
(3.8)
(3.9)
3. Analysis of Dual cycle…
(3.10)
3. Analysis of Dual cycle…
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)
3. Analysis of Dual cycle…
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 of α and β depend on what part of the heat is added at constant
volume and what part at constant pressure. An increase in the value of α and the
corresponding reduction in β results in a higher thermal efficiency.
3. Analysis of Dual cycle…
Working done during cycle,
(3.12)
3. Analysis of Dual cycle…
Swept volume,
(3.13)
Mean effective pressure,
(3.14)
(3.15)
4. Analysis of Otto cycle
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-V and T-s diagrams in Figure
4.1(a) and Figure 4.1(b) respectively.
4. Analysis of Otto cycle…
pV   const.
dQ  0
Q1
Q2
Figure 4.1. Otto cycle
Here:
Process 1-2 is isentropic compression.
Process 2-3 is reversible constant volume process.
Process 3-4 is isentropic expansion.
Process 4-1 is reversible constant volume process.
4. Analysis of Otto cycle…
For dual cycle, thermal efficiency has been defined as
   1
  1   1
r   1      1

V3
 1 is used for thermal efficiency of Otto cycle. We get
V2
  1
1
r  1
(3.16)
4. Analysis of Otto cycle…
Figure 4.2. Thermal efficiency vs. compression ratio for
different values of the adiabatic exponent 
4. Analysis of Otto cycle…
Mean effective pressure,
p1r 
pm 
   1      1
 1 r 1
 1
p1   1 r 
pm 
  1 r  1
(3.17)
Figure 4.3 Mean effective pressure vs. pressure
ratio for different values of compression ratio r.
5. Analysis of Diesel cycle
Q1
pV   const.
dQ  0
Q2
Figure 5.1. Diesel cycle
Here:
Process 1-2 is isentropic compression.
Process 2-3 is reversible constant pressure process.
Process 3-4 is isentropic expansion.
Process 4-1 is reversible constant volume process.
5. Analysis of Diesel cycle…
For dual cycle, thermal efficiency has been defined as
   1
  1   1
r   1      1

p3
 1 is used for thermal efficiency of Diesel cycle. We get
p2
1    1 
  1   1 

r      1 
(3.18)
5. Analysis of Diesel cycle…
Figure 5.2 Thermal efficiency vs. cut-off ratio at different
5. Analysis of Diesel cycle…
Mean effective pressure,
p1r 
pm 
   1      1
 1 r 1
 1
p1r 
pm 
    1
 1 r 1
(3.19)
6. Comparison of the cycles
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.
6. Comparison of the cycles…
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
Otto   Dual   Diesel
6. Comparison of the cycles…
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
6. Comparison of the cycles…
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
6. Comparison of the cycles…
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, Q1 )
6. Comparison of the cycles…
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 the
three cycles.
 Diesel   Dual  Otto
7. Comprehensive examples
Examples of thermodynamic cycles can be found in handout.
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
FACULTY OF MARINE SCIENCES