This document provides an overview of thermodynamic analysis and modeling of internal combustion engines. It discusses ideal thermodynamic cycles that are used to model different types of engines, including the Otto cycle for spark ignition engines, the Diesel cycle for early compression ignition engines, and the Dual cycle to model modern compression ignition engines. The key cycles and processes are defined and the calculations for thermal efficiency are shown. Factors that influence work output and efficiency, such as compression ratio, specific heat ratio, and fuel-air ratio, are also examined.

1. Thermodynamic Analysis of
Internal Combustion Engines
P M V SUBBARAO
Professor
Mechanical Engineering Department
IIT Delhi
Work on A Blue Print Before You Ride on an Actual Engine….
It is a Sign of Civilized Engineering….

2. SI Engine Cycle
A
I
R
Combustion
Products
Ignition
Intake
Stroke
FUEL
Fuel/Air
Mixture
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Actual
Cycle

3. Actual SI Engine cycle
Ignition
Total Time Available: 10 msec

4. Early CI Engine Cycle
A
I
R
Combustion
Products
Fuel injected
at TC
Intake
Stroke
Air
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Actual
Cycle

5. Modern CI Engine Cycle
Combustion
Products
Fuel injected
at 15o bTC
Intake
Stroke
A
I
R
Air
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Actual
Cycle

6. Thermodynamic Cycles for CI engines
• In early CI engines the fuel was injected when the piston reached TC
and thus combustion lasted well into the expansion stroke.
• In modern engines the fuel is injected before TC (about 15o)
• The combustion process in the early CI engines is best approximated by
a constant pressure heat addition process  Diesel Cycle
• The combustion process in the modern CI engines is best approximated
by a combination of constant volume and constant pressure  Dual Cycle
Fuel injection starts
Fuel injection starts
Early CI engine Modern CI engine

7. Thermodynamic Modeling
• The thermal operation of an IC engine is a transient cyclic process.
• Even at constant load and speed, the value of thermodynamic
parameters at any location vary with time.
• Each event may get repeated again and again.
• So, an IC engine operation is a transient process which gets
completed in a known or required Cycle time.
• Higher the speed of the engine, lower will be the Cycle time.
• Modeling of IC engine process can be carried out in many ways.
• Multidimensional, Transient Flow and heat transfer Model.
• Thermodynamic Transient Model USUF.
• Fuel-air Thermodynamic Mode.
• Air standard Thermodynamic Model.

8. Ideal Thermodynamic Cycles
• Air-standard analysis is used to perform elementary analyses
of IC engine cycles.
• Simplifications to the real cycle include:
1) Fixed amount of air (ideal gas) for working fluid
2) Combustion process not considered
3) Intake and exhaust processes not considered
4) Engine friction and heat losses not considered
5) Specific heats independent of temperature
• The two types of reciprocating engine cycles analyzed are:
1) Spark ignition – Otto cycle
2) Compression ignition – Diesel cycle

9. Air
TC
BC
Qin Qout
Compression
Process
Const volume
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
Otto
Cycle
Otto Cycle
A
I
R
Combustion
Products
Ignition
Intake
Stroke
FUEL
Fuel/Air
Mixture
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Actual
Cycle

10. Process 1 2 Isentropic compression
Process 2  3 Constant volume heat addition
Process 3  4 Isentropic expansion
Process 4  1 Constant volume heat rejection
v2
TC
TC
v1
BC BC
Qout
Qin
Air-Standard Otto cycle
3
4
2
1
v
v
v
v
r 

Compression ratio:

11. First Law Analysis of Otto Cycle
12 Isentropic Compression
)
(
)
( 1
2
m
W
m
Q
u
u in




2
1
1
2
1
2
v
v
T
T
P
P


AIR
)
(
)
( 1
2
1
2 T
T
c
u
u
m
W
v
in




23 Constant Volume Heat Addition
m
W
m
Q
u
u in



 )
(
)
( 2
3
)
(
)
( 2
3
2
3 T
T
c
u
u
m
Q
v
in




2
3
2
3
T
T
P
P

AIR Qin
TC
1
1
2
1
1
2 










 k
k
r
v
v
T
T

12. 3  4 Isentropic Expansion
AIR
)
(
)
( 3
4
m
W
m
Q
u
u out




)
(
)
( 4
3
4
3 T
T
c
u
u
m
W
v
out




4
3
3
4
3
4
v
v
T
T
P
P


4  1 Constant Volume Heat Removal
AIR Qout
m
W
m
Q
u
u out



 )
(
)
( 4
1
)
(
)
( 1
4
1
4 T
T
c
u
u
m
Q
v
out




1
1
4
4
T
P
T
P

BC
1
1
4
3
3
4 1











 k
k
r
v
v
T
T

13.    
 
2
3
1
2
4
3
u
u
u
u
u
u
Q
W
in
cycle
th







   
2
3
1
4
2
3
1
4
2
3
1
u
u
u
u
u
u
u
u
u
u









Cycle thermal efficiency:
th
in
th
in
cycle
r
r
u
m
Q
k
r
r
V
P
Q
P
imep
V
V
W
imep 
 



























1
/
1
1
1 1
1
1
1
2
1
Indicated mean effective pressure is:
Net cycle work:
   
1
2
4
3 u
u
m
u
u
m
W
W
W in
out
cycle 





First Law Analysis Parameters
1
2
1
2
3
1
4 1
1
1
)
(
)
(
1 







 k
v
v
r
T
T
T
T
c
T
T
c

14. Effect of Compression Ratio on Thermal Efficiency
• Spark ignition engine compression ratio limited by T3 (autoignition)
and P3 (material strength), both ~rk
• For r = 8 the efficiency is 56% which is twice the actual indicated value
Typical SI
engines
9 < r < 11
k = 1.4
1
1
1 

 k
const c
th
r
V


15. Effect of Specific Heat Ratio on Thermal Efficiency
1
1
1 

 k
const c
th
r
V

Specific heat
ratio (k)
Cylinder temperatures vary between 20K and 2000K so 1.2 < k < 1.4
k = 1.3 most representative

16. The net cycle work of an engine can be increased by either:
i) Increasing the r (1’2)
ii) Increase Qin (23”)
P
V2 V1
Qin
Wcycle
1
2
3
(i)
4
(ii)
Factors Affecting Work per Cycle
1’
4’
4’’
3’’
th
in
cycle
r
r
V
Q
V
V
W
imep 










1
1
2
1

17. Effect of Compression Ratio on Thermal Efficiency and MEP














 k
in
r
r
r
V
P
Q
P
imep 1
1
1
1
1
1
k = 1.3

18. Ideal Diesel Cycle
Air
BC
Qin Qout
Compression
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process

19. Process 1 2 Isentropic compression
Process 2  3 Constant pressure heat addition
Process 3  4 Isentropic expansion
Process 4  1 Constant volume heat rejection
Air-Standard Diesel cycle
Qin
Qout
2
3
v
v
rc 
Cut-off ratio:
v2
TC
v1
BC TC BC

20. 2
3
1
4
1
1
h
h
u
u
m
Q
m
Q
in
out
cycle
Diesel







 
 









 
1
1
1
1
1 1
c
k
c
k
const c
Diesel
r
r
k
r
V

For cold air-standard the above reduces to:
Thermal Efficiency
1
1
1 

 k
Otto
r

recall,
Note the term in the square bracket is always larger than one so for the
same compression ratio, r, the Diesel cycle has a lower thermal efficiency
than the Otto cycle
Note: CI needs higher r compared to SI to ignite fuel

21. Typical CI Engines
15 < r < 20
When rc (= v3/v2)1 the Diesel cycle efficiency approaches the
efficiency of the Otto cycle
Thermal Efficiency
Higher efficiency is obtained by adding less heat per cycle, Qin,
 run engine at higher speed to get the same power.

22. Air
TC
BC
Qin Qout
Compression
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
Dual
Cycle
Qin
Const volume
heat addition
Process
Thermodynamic Dual Cycle

23. Process 1  2 Isentropic compression
Process 2  2.5 Constant volume heat addition
Process 2.5  3 Constant pressure heat addition
Process 3  4 Isentropic expansion
Process 4  1 Constant volume heat rejection
Dual Cycle
Qin
Qin
Qout
1
1
2
2
2.5
2.5
3
3
4
4
)
(
)
(
)
(
)
( 5
.
2
3
2
5
.
2
5
.
2
3
2
5
.
2 T
T
c
T
T
c
h
h
u
u
m
Q
p
v
in









24. Thermal Efficiency
)
(
)
(
1
1
5
.
2
3
2
5
.
2
1
4
h
h
u
u
u
u
m
Q
m
Q
in
out
cycle
Dual









 










 
1
)
1
(
1
1
1 1
c
k
c
k
c
const
Dual
r
k
r
r
v 



1
1
1 

 k
Otto
r

 
 









 
1
1
1
1
1 1
c
k
c
k
const c
Diesel
r
r
k
r
V

Note, the Otto cycle (rc=1) and the Diesel cycle (=1) are special cases:
2
3
5
.
2
3 and
where
P
P
v
v
rc 
 

25. The use of the Dual cycle requires information about either:
i) the fractions of constant volume and constant pressure heat addition
(common assumption is to equally split the heat addition), or
ii) maximum pressure P3.
Transformation of rc and  into more natural variables yields



















  1
1
1
1
1 1
1
1 k
r
V
P
Q
k
k
r k
in
c

 1
3
1
P
P
rk


For the same inlet conditions P1, V1 and the same compression ratio:
Diesel
Dual
Otto 

 

For the same inlet conditions P1, V1 and the same peak pressure P3
(actual design limitation in engines):
otto
Dual
Diesel 

 


26. For the same inlet conditions P1, V1
and the same compression ratio P2/P1:
For the same inlet conditions P1, V1
and the same peak pressure P3:






3
2
1
4
1
1
Tds
Tds
Q
Q
in
out
th

“x” →“2.5”
Pmax
Tmax
Po
Po
Pressure,
P
Pressure,
P
Temperature,
T
Temperature,
T
Specific Volume
Specific Volume
Entropy Entropy