Department of Mechanical Engineering
ME 322 – Mechanical Engineering
Thermodynamics
Lecture 28
Internal Combustion Engine Models
The Otto Cycle
The Diesel Cycle
IC Engine Terminology
Finally … here is one of the reasons we spent so much
time analyzing piston-cylinder assemblies in the early part of
the course!
VTDC
Vdisp  VBDC  VTDC
CR 
VBDC
VTDC
VBDC
2
IC Engine Terminology
• Fuel-Air ignition
– Spark
• Gasoline engines
– Compression
• Diesel engines
• 4-Stroke Engine
– Four strokes (intake, compression, power stroke,
exhaust) are executed for every two revolutions of the
crankshaft, and one thermodynamic cycle
• 2-Stroke Engine
– Two strokes (intake, compression, power stroke, and
exhaust) are executed for every one revolution of the
crankshaft, and one thermodynamic cycle
3
IC Engine Performance
Thermal Efficiency
Wnet
th 
Qin
Mean Effective Pressure
net work for one cycle
mep 
displacement volume
The mep provides a way to compare two engines that
have the same displacement volume
4
Modeling the IC Engine
• Air Standard Analysis (ASC or hot ASC)
– The working fluid is a fixed mass of air treated as
an ideal gas
• No intake or exhaust
– The combustion process is replaced with a heat
transfer from a high-temperature source
– The exhaust process is replaced with a heat
transfer to a low-temperature sink
– All processes are internally reversible
• Cold Air Standard Analysis (cold ASC)
– All of the above
– Heat capacity of the air is assumed to be constant
at the ambient temperature
5
SI Engine - Otto Cycle
1
2
3
P
3
4
2
TDC
4
BDC
1
BDC
TDC
• 1-2 Isentropic compression from BDC to TDC
v
T
3
W12  m  u2  u1 
• 2-3 Isochoric heat input (combustion)
Q23  m  u3  u2 
4
2
1
s
6
SI Engine - Otto Cycle
1
2
3
P
3
4
2
TDC
4
BDC
1
BDC
TDC
• 3-4 Isentropic expansion (power stroke)
v
T
3
W34  m  u3  u4 
• 4-1 Isochoric heat rejection (exhaust)
Q41  m  u4  u1 
4
2
1
s
7
Otto Cycle Performance
P
3
Compression Ratio
2
CR 
v1 v4

v2 v3
4
1
BDC
TDC
Thermal Efficiency
v
T
th,ASC 
th ,cold ASC
Wnet W34  W12
u u

 1 4 1
Qin
Q23
u3  u2
3
T
 1  1  1  CR1 k
T2
4
2
1
s
8
Otto Cycle Performance
P
3
Mean Effective Pressure
2
W
W  W12  u3  u4    u2  u1 
mep  net  34

Vdisp
Vdisp
 v1  v2 
4
1
BDC
TDC
mepcold ASC 
cv T3  T4   T2  T1  
 v1  v2 
v
T
3
Cold ASC values (Table C.13a) ...
Btu
c p  0.24
lbm-R
k
9
Btu
cv  0.172
lbm-R
cp
cv
 1.4
4
2
1
s
CI Engine - Diesel Cycle
P
2
1
2
3
3
4
TDC
4
BDC
1
BDC
TDC
• 1-2 Isentropic compression from BDC to TDC
v
T
W12  m  u2  u1 
• 2-3 Isobaric heat input (combustion)
3
2
4
Q23  W23  m u3  u2 
1
s
10
CI Engine - Diesel Cycle
P
2
1
2
3
3
4
TDC
4
BDC
1
BDC
TDC
• 3-4 Isentropic expansion (power stroke)
v
T
W34  m  u3  u4 
• 4-1 Isochoric heat rejection (exhaust)
3
2
4
Q41  m  u4  u1 
1
s
11
Diesel Cycle Performance
P
2
Compression Ratio
CR 
v1
v2
3
Cutoff Ratio
CO 
v3
v2
4
1
BDC
TDC
Thermal Efficiency
v
T
th,ASC 
Wnet W23  W34  W12
u u

 1 4 1
Qin
Q23
h3  h 2
th ,cold ASC  1 
CR1 k  CO k  1
3
2
4
k  CO  1
1
s
12
Diesel Cycle Performance
P
2
3
Mean Effective Pressure
Wnet W23  W34  W12  h3  h 2    u4  u1 
mep 


Vdisp
Vdisp
 v1  v2 
4
1
BDC
TDC
mepcold ASC 
c p T3  T2   cv T4  T1 
 v1  v2 
v
T
3
Cold ASC values (Table C.13a) ...
Btu
c p  0.24
lbm-R
k
13
2
Btu
cv  0.172
lbm-R
cp
cv
 1.4
4
1
s
Cycle Evaluation
• Strategy
– Build the property table first, then do the
thermodynamic analysis
• Real fluid model
– EES (fluid name = ‘air_ha’)
• Air standard model
– Ideal gas with variable heat capacities
• Table C.16 (Air Tables)
• EES (fluid name = ‘air’)
• Cold air standard model
– Ideal gas with constant heat capacities evaluated
at the beginning of compression
• Atmospheric conditions
14
IC Engine Performance
• Known Parameters
– Number of cylinders in the engine
– Enough information to determine
the mass of the air trapped in the
cylinder
– Engine ratios (compression and cutoff)
– Rotational speed of the engine (rpm)
– Engine type
• All cylinders complete a thermodynamic cycle in either
two or four strokes
– P and T at the beginning of compression
– P or T at the end of combustion
15
IC Engine Performance
The power developed by the engine can be determined by
 
Wnet  NcylWnet 

N
 r
Crankshaft rotational speed
Number of cylinders
Wnet
 rev 
 Btu   min   hp-min 
  cyl 



 cyl-cycle   rev   Btu 
 cycle 


From the Otto or
Diesel Cycle analysis
Crankshaft revolutions per cycle
16
conversion factor