• Introduce two areas of application Power
generation and Refrigeration.
• Engines: power cycles
• Refrigerators,
air
conditioners,
or
heat
pumps: refrigeration cycles
7.1.- BASIC CONSIDE RATIONS IN THE ANALYSIS
OF POWER CYCLES
Ideal cycle is a cycle with reversible processes.
P
Actual cycle
Ideal cycle
υ
Chapter 7
1
The idealizations and simplifications commonly
employed in the analysis of power cycles can be
summarized as follows:
1. The cycle does not involve any friction.
Therefore,
th e
working
fluid
does
not
experience any pressure drop as it flows in
pipes or devices such as heat exchangers.
2. All expansion and compression processes
take place in a quasi-equilibrium manner.
3. The
pipes
connecting
th e
various
components of a system are well insulated,
and heat transfer through them is negligible.
P
T
3
2
3
2
w net
1
w net
4
1
4
υ
Chapter 7
s
2
7.2.- THE CARNOT CYCLE AND ITS VALUE IN
ENGINEERING
The Carnot cycle, this was introduced and
discussed in Chap. 5, is composed of four totally
reversible processes: isothermal heat addition,
isentropic expansion, isothermal heat rejection,
and isentropic compression.
The P- υ and T-s diagrams of a Carnot cycle are
replotted
P
T
1
qin
TH
2
TH= const.
Isentropic
Wnet,
2
3
Isentropic
Isentropic
4
qin
TL
1
Isentropic
qout
4
TL= const.
qout 3
s
υ
The Carnot cycle can be executed in a closed
system (a piston cylinder device) or a steady-flow
system
(utilizing
tw o
turbines
and
two
compressor), and either a gas or vapor can be
Chapter 7
υ
3
utilized as the working fluid. The Carnot cycle is
the most efficient cycle that can be executed
between a thermal energy source at temperature
TH and a sink at temperature TL, and thermal
efficiency is expressed as
TL
η th = 1 −
TH
A steady-flow Carnot engine
Chapter 7
4
7.3.- AIR-STANDARD ASSUM PTIONS
In a gas power cycles, the working fluid remains a
gas throughout the entire cycle. Spark-ignition
automobile
engines,
diesel
engines,
and
convectional gas turbine are familiar examples of
devices that operate on gas cycle. That is, they
are INTERNAL COM BUSTION ENGINES.
The actual gas power cycl es are rather complex.
To reduce the analysis to a manageable level, we
utilize the following approximations, commonly
known as the AIR-STANDARD ASSUM PTIONS.
1. The working fluid is air that continuously
circulates in a closed loop and always
behaves as an ideal gas.
2. All the processes that make up the cycle are
internally reversible.
3. The combustion process is replaced by a heat
addition process from an external source.
Chapter 7
5
4. The exhaust process is replaced by a heat
rejection process that restores the working
fluid to its initial state.
AIR
Combustion
Chamber
COMBUSTION
PRODUCTS
FUEL
Actual
AIR
Heating
section
AIR
Ideal
Another assumption that is often utilized to
simplify the analysis even more is that the air has
constant
specific
heat
whose
values
are
determined at room temperature (25ºC, or 77ºF).
When this assumption is utilized, the air-standard
assumption are called the COLD-AIR-STANDARD
Chapter 7
6
ASSUM PTIONS. A cycle for which the air-standard
assumptions are applicable is frequently referred
to as an AIR-STANDARD CYCLE.
7.4.- BRIEF OVERVIEW OF RECIPROCATING
ENGINES
Despite its simplicity, the reciprocating engine
(basically a piston-cylinder device) is one of the
rare inventions that has proved to be very
versatile and to have a wide range of applications.
It
is the powerhouse
of
vast
majority
of
automobiles, trucks, light aircraft, ships, and
electric power generators, as well as many other
devices.
The basic components of a reciprocating engine
are show here:
Chapter 7
7
Nomenclatur e for reciprocating engines
The piston reciprocates in the cylinder between
two fixed positions called the TOP DEAD CENTER
(TDC)-the position of the piston when it forms the
smallest volume in the cylinder-and the BOTTOM
DEAD CENTER (BDC)-the position of the piston
when it forms the largest volume in the cylinder.
The distance between the TDC and the BDC is the
largest distance that the piston can travel in one
direction, and it is called the STROKE of the
engine. The diameter of the piston is called the
BORE. The air or air-fuel mixture drawn into the
cylinder through the INTAKE VALVE, and the
Chapter 7
8
combustion products are expelled from the
cylinder through the EXHAUST VALVE.
The minimum volume formed in the cylinder when
the piston is at TDC is called the CLEARANCE
VOLUM E. The volume displaced by the piston as
it moves between TDC and BDC is called the
DISPLACEM ENT
VOLUM E. The ratio of
th e
maximum volume formed in the cylinder to the
minimum
(clearance)
volume
is
called
th e
COM PRESSION RATIO “ r” of the engine:
r=
Vmax VBDC
=
Vmin
VTDC
Another term frequently used is conjunction with
reciprocating engines is the M EAN EFFECTIVE
PRESSURE (M EP). It is a fictitious pressure
which, if it acted on the piston during the entire
power stroke, would produce the same amount of
net work as that produced during that actual
cycle. That is,
Wnet = MEP X pistonarea x stroke = MEP x displacement volume
Chapter 7
9
MEP =
Wnet
w net
=
(kPa)
Vmax − Vmin υmax − υmin
The mean effective pressure can be used as a
paramet er to compare the performances of
reciprocating engines of equal size. The engine
that has a larger value of M EP will deliver more
net work per cycle and thus will perform better.
Reciprocating engines are classified as SPARKIGNITION
(SI)
ENGINES
or
COM PRESSION-
IGNITION (CI) ENGINES.
Chapter 7
10
7.5.- OTTO CYCLE-THE IDEAL CYCLE FOR
SPARK-IGNITION ENGINES
The Otto cycle is the ideal cycle for spark-ignition
reciprocating engines. It is named after Nikolaus
A. Otto, who built a successful four-stroke engine
in 1876 in Germany using the cycle proposed by
Frenchman Beau de Rochas in 1862. In most
spark-ignition engines, the piston executes four
complete strokes (two mechanical cycles) within
the cylinder, and the crankshaft completes 2
revolutions for each thermodynamic cycle. These
engines
are
called
FOUR-STROKE
internal
combustion engines.
Chapter 7
11
In TWO-STROKE engines, all four functions
described above are executed in just two strokes:
the power stroke and the compression stroke.
Chapter 7
12
The thermodynamic analysis of the actual fourstroke or two-stroke cycles described above is
not a simple task. However, the an alysis can be
simplified
significantly
if
the
air-standard
assumptions are utilized. The resulting cycle
which closely resembles the actual operations
conditions is the ideal Otto cycle. It consists of
four internally reversible processes:
1-2: Isentropic compression
2-3: v=constant heat addition
3-4: Isentropic expansion
4-1: v=constant heat rejection
Chapter 7
13
The Otto cycle is executed in a closed system,
and thus the first-law relation for any of the
processes is expressed, on a unit mass basis, as
q − w = ∆u (kJ / kg)
No work is involved during the two heat transfer
processes since both take place at constant
volume.
qin = q23 = u3 − u2 = Cv (T3 − T2 )
qout = − q41 = −(u4 − u1 ) = Cv (T4 − T1 )
Then the thermal efficiency of the ideal-airstandard Otto cycle becomes
η th,Otto =
w net
q
T − T1
T (T / T − 1)
= 1 − out = 1 − 4
=1− 1 4 1
qin
qin
T3 − T2
T2 ( T3 / T2 − 1)
Processes 1-2 and 3-4 are isentropic, and v2=v3
and v4=v1. Thus
υ 
T1
=  2 
T2
 υ1 
Chapter 7
k −1
υ 
=  3 
 υ4 
k −1
=
T4
T3
14
ηth,Otto = 1 −
r=
Vmax
Vmin
1
r k −1
V
υ
= 1 = 1
V2 υ2
k=Cp/Cv
7.6.- DIESEL CYCLE-THE IDEAL CYCLE FOR
COM PRESSION-IGNITION ENGINES
The Diesel cycle i s the ideal cycle for CI
reciprocating
engines.
The
CI
engine,
first
proposed by Rudolph Diesel in the 1980s, is very
similar to the SI engine discussed in the last
section,
differing
mainly in the method of
initiating combustion.
Gasoline engine
Chapter 7
Diesel engine
15
P- υ and T -s diagr ams for the ideal Diesel cycle
The Diesel style cycle, like the Otto cycle, is
executed in a piston-cylinder device, which forms
a closed system. Therefore, equations developed
for closed syst ems should be used in the analysis
of
individual
processes.
Under the cold-air
standard assumptions, the amount of heat added
to the working fluid at constant pressure and
Chapter 7
16
rejected from it at constant volume can expressed
as
qin = q23 = w 23 + (∆u)23 = P2 ( υ3 − υ2 ) + (u3 − u2 )
qin = q23 = h3 − h2 = Cp (T3 − T2 )
0
And
qout = −q41 = −w 41 − ( ∆u)41 = (u4 − u1 )
qout = − q41 = Cv (T4 − T1 )
Then the thermal efficiency of the ideal Diesel
cycle under the cold-air-standard assumptions
becomes
ηth,Diesel =
w net
q
T − T1
T (T / T − 1)
= 1 − out = 1 − 4
= 1− 1 4 1
qin
qin
k(T3 − T2 )
kT2 (T3 / T2 − 1)
We now define a new quantity, the CUTOFF RATIO
rc , as the ratio of the cylinder volumes after and
before the combustion process:
rc =
Chapter 7
V3 υ3
=
V2 υ2
17
Utilizing this definition and the isentropic idealgas relations for processes 1- 2 and 3-4, we see
that the thermal efficiency relation reduces to
k
1  rc − 1 
ηth,Diesel = 1 − k −1 

r k(rc − 1)
ηth,Otto > ηth,Diesel
7.7.- BRAYTON CYCLE-THE IDEAL CYCLE FOR
GAS-TURBINE ENGINES
The Brayton cycle was first proposed by George
Brayton for use in the reciprocating oil-burning
engine that he developed around 1870, it is used
for gas turbines only where both the compression
and expansion processes take place in rotating
machinery. Gas turbines usually operate on an
OPEN CYCLE ; but can be modeled as a CLOSED
CYCLE, by utilizing the air-standard assumptions
Chapter 7
18
An open-cycle gas-tur bine engine
A close-cycle gas-turbine engine
The ideal Brayon cycle, is made up off four
internally reversible processes:
Chapter 7
19
1-2: Isentropic compression
2-3: P= constant heat addition
3-4: Isentropic expansion (in a turbine)
4-1 P= constant heat rejection
Notice that all four process of the Brayton cycle
are executed in steady-flow devices; thus, they
should be analyzed as steady-flow processes.
Chapter 7
20
When the changes in kinetic and potential
energies are neglected, the conservation of
energy equation for a steady-flow process can be
expressed, on a unit mass basis, as
q − w = hexit − hinlet
Assuming
constant
specific heats
at
room
temperature (cold-air-standard assumption), heat
transfer to and from the working fluid becomes
qin = q23 = h3 − h2 = Cp (T3 − T2 )
0
qout = −q41 = h4 − h1 = Cp (T4 − T1 )
Then the thermal efficiency of the ideal Brayton
cycle becomes
ηth,Brayton =
C (T − T )
w net
q
T (T / T − 1)
= 1 − out = 1 − p 4 1 = 1 − 1 4 1
qin
qin
Cp (T3 − T2 )
T2 (T3 / T2 − 1)
Processes 1-2 and 3-4 are isentropic, and P2=P3
and P4=P1. Thus,
Chapter 7
21
P 
T2
=  2 
T1
 P1 
(k − 1 )
k
P 
=  3 
 P4 
(k − 1 )
k
=
T3
T4
Substituting these equations into the thermal
efficiency relation and simplifying give
ηth,Brayton = 1 −
rp =
1
( k −1) / k
rp
P2
P1 is the PRESSURE RATIO and k is the
specific heat ratio.
Chapter 7
22