Thermodynamic Cycles
Air-standard analysis is a simplification of the real cycle
that includes the following assumptions:
1) Working fluid consists of fixed amount of air (ideal gas)
2) Combustion process represented by heat transfer into
and out of the cylinder from an external source
3) Differences between intake and exhaust processes not
considered (i.e. no pumping work)
4) Engine friction and heat losses not considered
SI Engine Cycle vs Air Standard Otto Cycle
FUEL
A
Ignition
I
R
Fuel/Air
Mixture
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Qin
Otto
Cycle
Air
Exhaust
Stroke
Qout
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:
v1 v4
r 
v2 v3
Qin
Qout
v2
TC
v1
BC
TC
BC
First Law Analysis of Otto Cycle
12 Isentropic Compression
AIR
Win
Q
(u 2  u1 )   ( )
m
m
Win
 (u 2  u1 )
m
vr2
v2 1
 
vr1 v1 r
P2 v2 P1v1 P2 T2 v1
R

  
T2
T1
P1 T1 v2
First Law Analysis of Otto Cycle
23 Constant Volume Heat Addition
Qin W
(u3  u 2 )  ( ) 
m m
Qin
 (u3  u 2 )
m
P3
P3 T3
P2
v

 
RT2 RT3 P2 T2
Qin
AIR
TC
First Law Analysis of Otto Cycle
3  4 Isentropic Expansion
Wout
Q
(u 4  u3 )   (
)
m
m
AIR
Wout
 (u3  u 4 )
m
vr4
v4
 r
vr3 v3
P4 v4 P3v3 P4 T4 v3

  
T4
T3
P3 T3 v4
First Law Analysis of Otto Cycle
4  1 Constant Volume Heat Removal
Qout W
(u1  u 4 )  (
)
m
m
Qout
 (u 4  u1 )
m
P4
P1
P4 P1
v

 
RT4 RT1 T4 T1
AIR
Qout
BC
First Law Analysis
Net cycle work:
Wcycle  Wout  Win  mu3  u4   mu2  u1 
Cycle thermal efficiency:
th 
th 
Wcycle
Qin

Wout  Win u3  u4   u2  u1 

u3  u2 
Qin
u3  u2   u4  u1 
u3  u2
 1
u4  u1
u3  u2
Cold Air-Standard Analysis
• For a cold air-standard analysis the specific heats are assumed to be
constant evaluated at ambient temperature values (k = cp/cv = 1.4).
• For the two isentropic processes in the cycle, assuming ideal gas with
constant specific heat using Pv k  const. Pv  RT yields:
12:
34:
T2  v1 
  
T1  v2 
T4  v3 
  
T3  v4 
th
const cV
k 1
k 1
 1
 r k 1
1
 
r
k 1
k 1
 k
T2  P2
  
T1  P1 
k 1
 k
T4  P4
  
T3  P3 
cv (T4  T1 )
T
1
 1  1  1  k 1
cv (T3  T2 )
T2
r
Effect of Specific Heat Ratio
th
const cV
 1
1
r k 1
Specific heat
ratio (k)
Cylinder temperatures vary between 20K and 2000K where 1.2 < k < 1.4