Carnot Cycle, Ideal Gas Law, Thermodynamics Processes, Properties of Air, Air-Standard Assumptions, Terminology for Reciprocating Devices, Otto Cycle The Ideal Cycle for Spark-Ignition Engines, Diesel Cycle, Dual Cycle, Criteria of Performance, Indicated Power, Brake Power, Friction Power, Mechanical Efficiency, Brake Mean Effective Pressure, Brake Thermal Efficiency, Specific Fuel Consumption, Volumetric Efficiency

1. th
net
in
W
Q

th Carnot
L
H
T
T
,  
1
Upon derivation the performance of the real cycle is often measured in
terms of its thermal efficiency
The Carnot cycle was introduced as the most efficient heat engine that
operate between two fixed temperatures TH and TL. The thermal
efficiency of Carnot cycle is given by
Review – Carnot Cycle
1

2. The ideal gas equation is defined as
mRT
PV
or
RT
Pv 

where P = pressure in kPa
v = specific volume in m3/kg (or V = volume in m3)
R = ideal gas constant in kJ/kg.K
m = mass in kg
T = temperature in K
Review – Ideal Gas Law
2
The Δu and Δh of ideal gases can be expressed as
)
( 1
2
1
2 T
T
C
u
u
u v 




)
( 1
2
1
2 T
T
C
h
h
h P 




Δu - constant volume process
Δh - constant pressure process

3. Process Description Result of Ideal Gas Law
isochoric constant volume (V1 = V2)
isobaric constant pressure (P1 = P2)
isothermal constant temperature (T1 = T2)
polytropic -none-
isentropic constant entropy (S1 = S2)
 According to a law of constant

n
V
P
2
2
1
1
T
P
T
P

2
2
1
1
T
V
T
V

2
2
1
1 V
P
V
P 
1
2
1
1
2
2
1



















n
n
n
T
T
V
V
P
P
Review – Thermodynamics Processes
3
A polytropic process is a thermodynamic process that obeys the relation pVn=C: where p is the
pressure, V is volume, n is the polytropic index, and C is a constant. The polytropic process
equation describes expansion and compression processes which include heat transfer.
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both
adiabatic and reversible. The work transfers of the system are frictionless, and there is no net
transfer of heat or matter.
In thermodynamics, an adiabatic process is a type of thermodynamic process that occurs
without transferring heat or mass between the thermodynamic system and its environment.
Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as
work.

4. Ideal gas constant, R= 0.2871 kJ/kg.K
specific heat at constant pressure, Cp = 1.005 kJ/kg.K
specific heat at constant volume, Cv = 0.718 kJ/kg.K
specific heat ratio, k = 1.4
Review – Properties of Air
4

5.  Air continuously circulates in a closed loop.
 Always behaves as an ideal gas.
 All the processes that make up the cycle are internally reversible.
 The combustion process is replaced by a heat-addition process
from an external source.
Air-Standard Assumptions
6

6.  A heat rejection process that restores the working fluid to its initial
state replaces the exhaust process.
 The cold-air-standard assumptions apply when the working fluid is
air and has constant specific heat evaluated at room temperature
(25o
C or 77o
F).
 No chemical reaction takes place in the engine.
Air-Standard Assumptions
7

7.  Top dead center (TDC), bottom dead center (BDC), stroke, bore,
intake valve, exhaust valve, clearance volume, displacement
volume, compression ratio, and mean effective pressure
Terminology for Reciprocating Devices
8

8.  The compression ratio r of an engine
is defined as
r
V
V
V
V
BDC
TDC
 
max
min
 The mean effective pressure (MEP)
is a fictitious pressure that, if it
operated on the piston during the
entire power stroke, would produce
the same amount of net work as that
produced during the actual cycle.
MEP
W
V V
w
v v
net net




max min max min9

9. Otto Cycle
The Ideal Cycle for Spark-Ignition Engines
10

10.  The processes in the Otto cycle are as per following:
Process Description
1-2 Isentropic compression
2-3 Constant volume heat addition
3-4 Isentropic expansion
4-1 Constant volume heat rejection
1
2
3
4
Qout
Qin
Pvg
Constant
v1
v2 v
P
s
T
Qout
Qin
1
2
3
4
(a) P-v diagram (b) T-s diagram 11

11.  Related formula based on basic thermodynamics:
Process Description Related formula
1-2 Isentropic compression
2-3 Constant volume heat addition
3-4 Isentropic expansion
4-1 Constant volume heat rejection
1
2
1
1
2
2
1



















n
n
n
T
T
V
V
P
P
1
2
1
1
2
2
1



















n
n
n
T
T
V
V
P
P
 
3 2
in v
Q mC T T
 
 
4 1
out v
Q mC T T
 
12

12.  Thermal efficiency of the Otto cycle:
th
net
in
net
in
in out
in
out
in
W
Q
Q
Q
Q Q
Q
Q
Q
  

 
1
 Apply first law closed system to process 2-3, V = constant.
 Thus, for constant specific heats
Q U
Q Q mC T T
net
net in v
,
, ( )
23 23
23 3 2

  

,23 ,23 23
3
,23 ,23 ,23
2
0 0
net net
net other b
Q W U
W W W PdV
  
    

13

13.  Apply first law closed system to process 4-1, V = constant.
 Thus, for constant specific heats,
Q U
Q Q mC T T
Q mC T T mC T T
net
net out v
out v v
,
, ( )
( ) ( )
41 41
41 1 4
1 4 4 1

   
    

 The thermal efficiency becomes
th Otto
out
in
v
v
Q
Q
mC T T
mC T T
,
( )
( )
 
 


1
1 4 1
3 2
,41 ,41 41
1
,41 ,41 ,41
4
0 0
net net
net other b
Q W U
W W W PdV
  
    

14

14. th Otto
T T
T T
T T T
T T T
,
( )
( )
( / )
( / )
 


 


1
1
1
1
4 1
3 2
1 4 1
2 3 2
 Recall processes 1-2 and 3-4 are isentropic, so
 Since V3 = V2 and V4 = V1,
3 3
2 4
1 4 1 2
T T
T T
or
T T T T
 
1
1
3
2 1 4
1 2 4 3
k
k
T
T V V
and
T V T V


 
 
   
 
   
15

15.  The Otto cycle efficiency becomes
th Otto
T
T
,  
1 1
2
 Since process 1-2 is isentropic,
 where the compression ratio is
r = V1/V2 and
th Otto k
r
,   
1
1
1
1
2 1
1 2
1 1
1 2
2 1
1
k
k k
T V
T V
T V
T V r

 
 
  
 
   
 
   
 
 
16

16.  The processes in the Diesel cycle are as per following:
Process Description
1-2 Isentropic compression
2-3
Constant pressure heat addition
3-4 Isentropic expansion
4-1
Constant volume heat rejection
Diesel Cycle
17

17. c
v r
ratio
off
Cut
v
v
and
r
ratio
n
Compressio
v
v
,
,
2
3
2
1



Diesel Cycle
18

18.  Related formula based on basic thermodynamics:
Process Description Related formula
1-2 Isentropic compression
2-3 Constant pressure heat addition
3-4 Isentropic expansion
4-1 Constant volume heat rejection
1
2
1
1
2
2
1



















n
n
n
T
T
V
V
P
P
1
2
1
1
2
2
1



















n
n
n
T
T
V
V
P
P
 
3 2
in P
Q mC T T
 
 
4 1
out v
Q mC T T
 
19

19.  Thermal efficiency of the Diesel cycle
th Diesel
net
in
out
in
W
Q
Q
Q
,   
1
 Apply the first law closed system to process 2-3, P = constant.
 Thus, for constant specific heats
Q U P V V
Q Q mC T T mR T T
Q mC T T
net
net in v
in p
,
,
( )
( ) ( )
( )
23 23 2 3 2
23 3 2 3 2
3 2
  
    
 

 
,23 ,23 23
3
,23 ,23 ,23
2
2 3 2
0 0
net net
net other b
Q W U
W W W PdV
P V V
  
    
 

20

20.  Apply the first law closed system to process 4-1, V = constant
Q U
Q Q mC T T
Q mC T T mC T T
net
net out v
out v v
,
, ( )
( ) ( )
41 41
41 1 4
1 4 4 1

   
    

 Thus, for constant specific heats
 The thermal efficiency becomes
th Diesel
out
in
v
p
Q
Q
mC T T
mC T T
,
( )
( )
 
 


1
1 4 1
3 2
,41 ,41 41
1
,41 ,41 ,41
4
0 0
net net
net other b
Q W U
W W W PdV
  
    

21

21. PV
T
PV
T
V V
T
T
P
P
4 4
4
1 1
1
4 1
4
1
4
1
 

where
 Recall processes 1-2 and 3-4 are isentropic, so
PV PV PV PV
k k k k
1 1 2 2 4 4 3 3
 
and
 Since V4 = V1 and P3 = P2, we divide the second equation by
the first equation and obtain
 Therefore,
3
4
4 2
k
k
c
V
P
r
T V
 
 
 
 
 
, 1
1
1
1
1
k
c
th Diesel k
c
r
r k r
 

 

22

22.  Dual cycle gives a better approximation to a real engine. The heat addition
process is partly done at a constant volume and partly at constant pressure.
From the P-v diagram, it looks like the heat addition process is a
combination of both Otto and Diesel cycles.
Dual Cycle
23

23. Process Description
1-2 Isentropic compression
2-3 Constant volume heat addition
3-4 Constant pressure heat addition
4-5 Isentropic expansion
5-1 Constant volume heat rejection
 The same procedure as to Otto and Diesel cycles can be applied to Dual
cycle. Upon substitutions, the thermal efficiency of Dual cycle becomes
   
  1
1
1
1
1 





 k
v
c
p
p
k
c
p
th
r
r
c
k
r
r
r

Dual Cycle
24

24.  Indicated power (IP)
 Brake power (bp)
 Friction power (fp) and mechanical efficiency, m
 Brake mean effective pressure (bmep), thermal efficiency
and fuel consumption
 Volumetric efficiency, v
Criteria of Performance
25

25.  Defined as the rate of work done by the gas on the piston as
evaluated from an indicator diagram obtained from the engine using
the electronic engine indicator.
2
LANn
p
IP i

 For four-stroke engine,
 And for two-stroke engine,
LANn
p
IP i

Indicated Power
26
ip = work done per cycle × cycle per minute
n is the number of cylinders.

26. Indicated Power
27
constant
diagram
of
length
diagram
of
area
net


i
p
 Indicated mean effective pressure, pi given by:,
 For one engine cylinder
Work done per cycle = pi  A  L
Where A = area of piston
L = length of stroke
time
unit
per
cycle
AL
P
ip i 

 Power output = (work done per cycle) x (cycle per minute)
 For four-stoke engines, the number of cycles per unit time is N/2
and for two-stroke engines the number of cycles per unit time is N,
where N is the engine speed.
volume
nt
displaceme
cycle
per
done
work

i
p

27.  Brake power is a way to measure the engine power output.
 The engine is connected to a brake (or dynamometer) which can be
loaded so that the torque exerted by the engine can be measured.
 The torque is obtained by reading off a net load, w at known radius, r.
Wr


Brake Power
28

28.  Therefore

N
bp 2

2
2
LANn
P
LANn
p
IP
bp b
i
m
m 




 Brake power is also can be expressed as
 Then the brake mean effective pressure (Pb) is
i
m
b P
P 

29

29. Friction Power
30
The difference between the Ip and bp is the friction power (fp). It
is the power that overcome the frictional resistance of the engine
parts.
bp
IP
fp 


30.  Power input to the shaft is usually bigger than the indicated
power due to frictional losses or the mechanical efficiency.
power
indicated
power
brake
mech 

Mechanical Efficiency
31

31. Brake Mean Effective Pressure
32
 From the definition of Brake power IP
BP m


 Since
2
LANn
p
IP i
 for 4 stroke engine and
2
2
LANn
P
LANn
p
bp b
i
m



 Since and Pi are difficult to obtain, they may be combined and replaced by a
brake mean effective pressure, Pb
m

 Equating this equation to another definition of bp: NT
LANn
Pb

2
2

T
LAn
Pb

4

 So:
 Its observed that bmep is proportional to torque.

32. Brake Thermal Efficiency
33
 The power output of the engine is obtained from the chemical energy of the fuel
supplied. The overall engine efficiency is given by the brake thermal efficiency,
v
net
f
p
fe
p
bp
Q
m
b
P
b
,
power
equivalent
fuel
power
brake
given
power
power
brake





 mf = mass flow fuel , Qnet,v = net calarofic value of the fuel.

33.  sfc is the mass flow rate of fuel consumed per unit power output and is
a criterion of economical power production.
bp
m
sfc
f


Specific Fuel Consumption
34

34.  Volumetric efficiency is only used with four-stroke cycle engine,
which have a distinct induction process.
 The parameter used to measure the effectiveness of an engine’s
induction process is the volumetric efficiency.
s
V
V
V


Volumetric Efficiency
35