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….
SI Engine Cycle
FUEL
A
I
Ignition
R
Fuel/Air
Mixture
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Actual SI Engine cycle
Total Time Available: 10 msec
Ignition
Early CI Engine Cycle
Fuel injected
at TC
A
I
R
Combustion
Products
Air
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Exhaust
Stroke
Modern CI Engine Cycle
Fuel injected
at 15o bTC
A
I
R
Air
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Exhaust
Stroke
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)
Fuel injection starts
Early CI engine
Fuel injection starts
Modern CI engine
• 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
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.
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
FUEL
A
I
Otto Cycle
Ignition
R
Fuel/Air
Mixture
Combustion
Products
Actual
Cycle
Intake
Stroke
Otto
Cycle
Compression
Stroke
Qin
Power
Stroke
Exhaust
Stroke
Qout
Air
TC
BC
Compression
Process
Const volume
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
Air-Standard Otto cycle
Process 1 2
Process 2  3
Process 3  4
Process 4  1
Isentropic compression
Constant volume heat addition
Isentropic expansion
Constant volume heat rejection
Compression ratio:
r
Qin
Qout
v2
TC
v1
BC
TC
BC
v1 v4

v2 v3
First Law Analysis of Otto Cycle
12 Isentropic Compression
(u 2  u1 ) 
AIR
W
Q
 ( in )
m
m
Win
 (u2  u1 )  cv (T2  T1 )
m
T2  v1 
  
T1  v2 
k 1
r
k 1
P2 T2 v1
 
P1 T1 v2
23 Constant Volume Heat Addition
(u3  u 2 )  (
Qin W
)
m
m
Qin
 (u3  u2 )  cv (T3  T2 )
m
P3 T3

P2 T2
AIR
Qin
TC
3  4 Isentropic Expansion
(u 4  u3 ) 
W
Q
 ( out )
m
m
AIR
Wout
 (u3  u4 )  cv (T3  T4 )
m
T4  v3 
  
T3  v4 
k 1

1
r k 1
P4 T4 v3
 
P3 T3 v4
4  1 Constant Volume Heat Removal
(u1  u 4 )  (
Qout W
)
m
m
AIR
Qout
 (u4  u1 )  cv (T4  T1 )
m
Qout
BC
P4 P1

T4 T1
First Law Analysis Parameters
Net cycle work:
Wcycle  Wout  Win  mu3  u4   mu2  u1 
Cycle thermal efficiency:
th 
Wcycle
Qin
 1

u3  u4   u2  u1   u3  u2   u4  u1   1  u4  u1
u3  u2
u3  u2
u3  u2 
cv (T4  T1 )
T
1
 1  1  1  k 1
cv (T3  T2 )
T2
r
Indicated mean effective pressure is:
imep 
Wcycle
V1  V2

imep Qin  r 
1  Qin / m  r 






 th
th
P1
P1V1  r  1 
k  1  u1  r  1 
Effect of Compression Ratio on Thermal Efficiency
th
const cV
 1
1
r k 1
Typical SI
engines
9 < r < 11
k = 1.4
• 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
Effect of Specific Heat Ratio on Thermal Efficiency
th
const cV
 1
1
r k 1
Specific heat
ratio (k)
Cylinder temperatures vary between 20K and 2000K so 1.2 < k < 1.4
k = 1.3 most representative
Factors Affecting Work per Cycle
The net cycle work of an engine can be increased by either:
i) Increasing the r (1’2)
ii) Increase Qin (23”)
imep 
3’’
P
(ii)
3
4’’
Qin
Wcycle
4
4’
2
(i)
1
V2
V1
1’
Wcycle
V1  V2

Qin  r 

th
V1  r  1 
Effect of Compression Ratio on Thermal Efficiency and MEP
imep Qin  r 
1


1  k 
P1
P1V1  r  1  r 
k = 1.3
Ideal Diesel Cycle
Qin
Qout
Air
BC
Compression
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
Air-Standard Diesel cycle
Process 1 2
Process 2  3
Process 3  4
Process 4  1
Isentropic compression
Constant pressure heat addition
Isentropic expansion
Constant volume heat rejection
Cut-off ratio:
Qin
rc 
Qout
v2
TC
v1
BC
TC
BC
v3
v2
Thermal Efficiency
 Diesel
cycle
Qout m
u u
 1
 1 4 1
Qin m
h3  h2
For cold air-standard the above reduces to:
 Diesel
const cV




1  1 rck  1 
 1  k 1  

r  k rc  1 
recall,
Otto  1 
1
r k 1
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
Thermal Efficiency
Typical CI Engines
15 < r < 20
When rc (= v3/v2)1 the Diesel cycle efficiency approaches the
efficiency of the Otto cycle
Higher efficiency is obtained by adding less heat per cycle, Qin,
 run engine at higher speed to get the same power.
Thermodynamic Dual Cycle
Qin
Dual
Cycle
Qin
Qout
Air
TC
BC
Compression
Process
Const volume
heat addition
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
Dual Cycle
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
2.5
Qin
3
3
2
Qin
4
2.5
4
2
1
1
Qout
Qin
 (u2.5  u2 )  (h3  h2.5 )  cv (T2.5  T2 )  c p (T3  T2.5 )
m
Thermal Efficiency
 Dual  1 
cycle
Qout m
u4  u1
 1
Qin m
(u2.5  u2 )  (h3  h2.5 )
 Dual
const cv
where rc 

rck  1
1 
 1  k 1 
r  (  1)  k rc  1
v3
v2.5
and  
P3
P2
Note, the Otto cycle (rc=1) and the Diesel cycle (=1) are special cases:
Otto  1 
1
r k 1
 Diesel
const cV




1  1 rck  1 
 1  k 1  

r  k rc  1 
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
rc  1 
k  1  Qin  1
  1



k  P1V1  r k 1 k  1 

1 P3
r k P1
For the same inlet conditions P1, V1 and the same compression ratio:
Otto   Dual   Diesel
For the same inlet conditions P1, V1 and the same peak pressure P3
(actual design limitation in engines):
 Diesel   Dual  otto
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:
Pressure, P
Pmax
Pressure, P
“x” →“2.5”
th  1 
Po
 1
Po
Specific Volume
1
4 Tds
3
2 Tds
Tmax
Temperature, T
Temperature, T
Specific Volume
Qout
Qin
Entropy
Entropy