Thermodynamics chapter:7 Some Power and Refrigerator Cycle

[R Gnyawali / P Timilsina] Page 1
Chapter-7
Some Power and Refrigeration Cycles
1. Classification of Cycles
1. Based upon work producing or absorbing
a. Power Cycle: A cycle which continuously converts the heat into work is called power
cycle. This cycle is called work producing. Example: Heat Engine
b. Refrigeration Cycle: A cycle which continuously transfers heat from a lower temperature to
higher temperature region is called refrigeration cycle. This cycle is called work absorbing
because it needs work input. Example: Heat Pump, Refrigerator
2. Based upon working fluid
a. Gas Cycle: The cycle in which the phase of working fluid doesn’t change during entire
process is called gas cycle. Example: Diesel Cycle, Otto Cycle
b. Vapor Cycle: If the working fluid is alternatively vaporized and condensed, then the cycle
is called vapor cycle. Example: Rankine Cycle, Refrigeration Cycle.
3. Based upon heat supplied
a. Internal Combustion Cycle (burning of fossil fuel within engine itself).
b. External Combustion Cycle (burning of fossil fuels in a boiler).
2. Components of Power/Refrigeration Cycles
1. Source: It is a thermal reservoir which is at high temperature and can supply heat energy to the
system. Example: Furnace, Combustion Chamber.
2. Sink: It is a thermal reservoir which is at low temperature and can absorb heat energy rejected by
the system. Example: Atmospheric Air, Ocean.
3. Working Fluid: The fluid within the system which absorbs heat and rejects heat while undergoing
a cycle is called working fluid. Example: Air, Water, Ammonia.
3. External Heat Transfer Cycles
3.1 Brayton Cycle
The Brayton Cycle, also called the Joule Cycle, was developed originally for use in a piston engine with
fuel injection. This cycle is the ideal cycle for the simple gas turbine. The air standard Brayton cycle is
composed of constant pressure heat transfer processes separated by isentropic expansion and compression
processes.
The closed-cycle Brayton engine is shown in figure below. The working fluid air enters the compressor in
state 1, where it is compressed isentropically until state 2 is reached and enters high temperature heat
exchanger. In this heat exchanger heat will be added to the fluid at constant pressure until state 3 is
reached. Now high temperature air enters the turbine, where an isentropic expansion occurs, producing
mechanical work. The working fluid (air) leaves the turbine at state 4 and enters low temperature heat
exchanger, where heat will be rejected from the fluid until state 1 is reached. After completing a cycle
previous processes will be repeated in same order.
Compression in compressor and expansion in turbine are assumed to be isentropic processes in the ideal
closed cycle air standard Brayton cycle. It is easier to construct compressor and turbine which operates
nearly adiabatic. However, it is difficult to approach reversibility.

Closed Brayton Cycle Open Brayton Cycle
The efficiency of Brayton cycle is given by,
)(
)(
1
1
23
14
TTmC
TTmC
Q
Q
P
P
H
L
B
−
−
−=
−=η
)1(
)1(
1
2
3
2
1
4
1
−
−
−=
T
T
T
T
T
T
Bη
Here, process 2-3 and 4-1 are constant pressure process so P2 = P3 and P1 = P4
For isentropic process 1-2,
γ
γ 1
1
2
1
2
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
P
P
T
T
For isentropic process 3-4,
1
2
1
1
2
1
4
3
4
3
T
T
P
P
P
P
T
T
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
−−
γ
γ
γ
γ
So,
2
3
1
4
T
T
T
T
=
………….eq(1)
Now, using eq(1) above efficiency equation becomes as;

( ) γ
γ
γ
γ
η
1
1
1
2
3
4
2
1
1
1
1
111
−
−
−=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=−=−=
p
B
r
P
P
T
T
T
T
Where,
4
3
1
2
P
P
P
P
rp == is the pressure ratio.
* The efficiency of Brayton cycle depends upon the isentropic pressure ratio.
4. Internal Combustion Cycles
In many power producing devices, such as the automotive gasoline engine, the diesel engine, and the gas
turbine, the working fluid is a gas. Broadly speaking, these devices take in either mixture of fuel and air or
fuel and air separately, compress this charge to a high pressure and cause the fuel to burn. A part of the
energy liberated as heat as a result of combustion is converted into useful work by causing the high
pressure and temperature products of combustion to expand in the engine or turbine while the remainder is
carried away with the exhaust gas living the device.
In general, the properties of the fuel air mixture before combustion approximates closely to those of air.
The properties of the products of combustion also do not differ much from those of pure air. For this
reason, it is convenient to analyze the performance of these devices by devising the idealized cycles
known as air standard cycles.
The air-standard cycles are based on the following hypothetical assumptions:
1. The working substance consists of a fixed mass of air. This closed system undergoes a cycle of
processes so that the system is restored to its initial state at the end of each cycle.
2. The combustion process is replaced by an equivalent heat addition process from an external
source. Thus there is no change in the chemical composition of the working fluid.
3. The exhaust process is replaced by an equivalent heat rejection process.

4. Compression and expansion processes in the cycle are reversible adiabatic processes.
5. The specific heats CP and CV of air do not vary with temperature.
4.1 Air-standard Otto Cycle
The Otto Cycle is an ideal cycle for SI (Spark Ignition) engines. In most SI engines (Petrol engine) the
piston executes the four complete strokes within the cylinder and completes a thermodynamic cycle. The
working fluid for an Otto cycle is air. Before the combustion, the working fluid is mixture of fuel and air
and after the combustion the working fluid is combustion gases. However, for approximation, property of
air is considered. An Otto cycle is completed by four processes.
Process 1-2: Isentropic Compression: Fuel-air mixture is taken into the cylinder through suction
and the mixture inside the cylinder is compressed until the piston reaches the Top Dead Center (TDC).
This process is reversible and adiabatic. The pressure and temperature of the air increase.
Process 2-3: Constant Volume Heat Addition: The compressed air-fuel mixture is burned with a
spark which makes the pressure and temperature of the combustion gases to rise. This process is assumed
to occur at constant volume.
Process 3-4: Isentropic Expansion: The piston begins to move until it reaches Bottom Dead Center
(BDC) so the expansion of gas occurs adiabatically and reversibly. This process generates work output
and the pressure and temperature of air decreases consequently.
Process 4-1: Constant Volume Heat Rejection: The exhaust valve opens and the pressure and
temperature of gas decreases at constant volume. Then the gas is removed from the cylinder by movement
of piston and the cycle is completed.
The thermal efficiency of this cycle is given as:
H
L
H
LH
Q
Q
Q
QQ
−=
−
=
1
η
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−=
−
−
−=
1
1
1
)(
)(
1
2
3
2
1
4
1
23
14
T
T
T
T
T
T
TTmC
TTmC
V
V

Since process 1-2 and 3-4 are isentropic, we can write,
( ) 1
1
2
1
1
2 −
−
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
γ
γ
cr
V
V
T
T
Where, ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
2
1
V
V
rc is called compression ratio
And,
1
2
1
2
1
1
3
4
4
3
T
T
V
V
V
V
T
T
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
−− γγ
So,
( ) 1
2
1 1
11 −
−=−= γ
η
crT
T
This shows that the efficiency of the otto cycle depends on the compression ratio. Efficiency of the otto
cycle increases with increase in compression ratio.
Mean Effective Pressure (MEP) is defined as the pressure that, if it acted on the piston during the entire
power stroke, would do an amount of work equal to that actually done on the piston.
21minmax vv
q
VV
W
eSweptvolum
Workdone
MEP HNET
−
=
−
==
η
1
2
3
4
Suction Exhaust
P
V
QH
QL
W
1
2
3
4
T
S
Q
H
QL
W
TDC BDC
Stroke

4.2 Air-Standard Diesel Cycle
The diesel cycle is the ideal cycle for Compression Ignition (CI) engines. In diesel cycle, air is compressed
to a higher temperature which ignites the fuel. The diesel cycle differs from Otto Cycle, in that heat is
supplied at constant pressure instead of at constant volume. The working fluid for a Diesel cycle is air.
Before the combustion, the working fluid is atmospheric air and after the combustion the working fluid is
combustion gases. However, for approximation, properties of air are considered. A diesel cycle is
completed by four processes.
Process 1-2: Isentropic Compression: Air is taken into the cylinder through suction and air inside
the cylinder is compressed until the piston reaches the Top Dead Center (TDC). This process is reversible
and adiabatic. The pressure and temperature of the air increase.
Process 2-3: Constant Pressure Heat Addition: Fuel is injected in the cylinder so that compressed
air and fuel is burned spontaneously which makes the pressure and temperature of the combustion gases to
rise. Simultaneously, the piston moves maintaining the pressure inside the cylinder. This process is
assumed to occur at constant pressure.
Process 3-4: Isentropic Expansion: The piston begins to move until it reaches Bottom Dead Center
(BDC) so the expansion of gas occurs adiabatically and reversibly. This process generates work output
and the pressure and temperature of air decreases consequently.
Process 4-1: Constant Volume Heat Rejection: The exhaust valve opens and the pressure and
temperature of gas decreases at constant volume. Then the gas is removed from the cylinder by movement
of piston and the cycle is completed.
The thermal efficiency of diesel cycle is given by,
QL

⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−=
−
−
−=
−=
−
=
=
1
1
1
)(
)(
1
1
2
3
2
1
4
1
23
14
T
T
T
T
T
T
TTmC
TTmC
Q
Q
Q
QQ
Q
W
P
V
H
L
H
LH
H
γ
η
Here
Compression Ratio, ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
2
1
V
V
rc
Cut-off Ratio, ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
2
3
V
V
ρ
So,
3
4
3
1
2
3
2
1
V
V
V
V
V
V
V
V
rc
==
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
ρ
Process 1-2 is adiabatic compression, so, ( ) 1
1
2
1
1
2 −
−
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
γ
γ
cr
V
V
T
T
Process 3-4 is adiabatic expansion, so,
11
3
4
4
3
−−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
γγ
ρ
cr
V
V
T
T
Or,
11
4
3 −−
= γγ
ρ cr
T
T
Therefore,
1
21
4
3
T
T
T
T
=−γ
ρ
So, 1
2
3
1
4 −
= γ
ρ
T
T
T
T
Now,

( )
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
−
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−=
−
−
1
1
1
1
1
1
1
2
3
1
2
3
1
2
3
2
1
4
1
T
T
T
T
r
T
T
T
T
T
T
c
γ
γ
ρ
γ
γ
η
For constant pressure process 2-3, ρ==
2
3
2
3
V
V
T
T
So,
( )
( ) ⎥
⎦
⎤
⎢
⎣
⎡
−
−
−=
⎥
⎦
⎤
⎢
⎣
⎡
−
−
−=
−
−
−
1
11
1
1
11
1
1
1
1
ρ
ρ
γ
ρ
ρρ
γ
η
γ
γ
γ
γ
c
c
r
r
The compression ratio of the diesel cycle is always greater than the expansion ratio. So for a given
compression ratio rC, the diesel engine always has lower efficiency than an Otto engine operating at the
same compression ratio.
5. Rankine Cycle
Rankine Cycle is the theoretical cycle on which steam power plants work. In Rankine cycle has water as
working fluid which is used to handle the phase change between liquid and vapor. The processes involved in
a Rankine cycle are:
Process 1-2: Reversible adiabatic compression in pump
Process 2-3: Constant pressure transfer of heat in the boiler
Process 3-4: Reversible adiabatic expansion in the turbine
Process 4-1: Constant pressure transfer of heat in the condenser
In an ideal Rankine Cycle as shown in figure below, the process 1-2, a pump is used to increase the
pressure of the working fluid. The working fluid enters the pump as a saturated liquid (State 1, x1 = 0) and
exits the pump as a sub-cooled liquid (state 2). The fluid entered into boiler has relatively low temperature
is heated at constant pressure and leaves the boiler as a saturated vapor (state 3, x3 = 1). This saturated
vapor is expanded isentropically through turbine to produce the work and leave as state 4. The low
pressure saturated mixture is again condensed at constant pressure in the condenser leaving as low
pressure low temperature saturated liquid (state 1). Following condensation, the liquid enters the pump.
The working fluid is returned to the high pressure for heat addition at the higher boiler temperature, and
the cycle is repeated.
For Boiler: Heat addition qin = h3 – h2
For Pump: Work Absorbed WP = h2 – h1

For Turbine: work produced WT = h3 – h4
For Condenser: Heat loss qout = h4 – h1
So, efficiency of Rankine Cycle is:
)(
)()(
23
1243
hh
hhhh
−
−−−
=η
As compared to WT, WP is very small so in many cases we can write,
)(
)(
23
43
hh
hh
−
−
=η

Effect of Pressure and Temperature on Rankine Cycle
1. Decreasing Condenser Pressure:
Let the exhaust pressure drop from P4 to P4’, with the corresponding decrease in temperature at which the
heat is rejected. The heat transfer to the steam is increased and the net work is also increased. The net
result is an increase in efficiency.
2. Increasing Boiler Pressure:
By increasing boiler pressure, the heat rejected decreases by keeping the maximum temperature constant.
The net work tends to remain same. Hence the efficiency increases.
3. Superheating Steam in Boiler:
The work increases and the heat transfer in boiler also increase. Since the ratio
HQ
W
′
′
is greater than
HQ
W
,
the efficiency of the cycle increases.
6. Vapor Compression Refrigeration Cycle
The most common method of providing air-conditioning and chilling as well as heat pumping is the vapor
compression cycle. In this cycle, the working substance changes phase during the cycle, in a manner
equivalent to that of Rankine cycle. The basic operation involved in vapor compression refrigeration cycle
is shown in figure below. It consists of four processes.

1. Compression: At state 1, the fluid is a saturated or superheated vapor. This fluid is compressed
reversibly and adiabatically in process 1-2 by the compressor. As a result, the pressure and
temperature of vapor increases.
2. Condensation: The vapor is then condensed in process 2-3 through the condenser. In this process,
the vapor rejects heat to the surroundings at constant pressure and is converted into saturated
liquid.
3. Expansion: The saturated liquid is allowed to expand adiabatically in the throttling valve in
process 3-4. In this process, the pressure and temperature of the fluid decreases but enthalpy
remains constant. At state 4, the fluid is in two-phase mixture.
4. Evaporation: The two-phase mixture, then, absorbs heat from the surroundings and is converted
to saturated vapor in the evaporator. This process 4-1 occurs at constant pressure. This saturated
vapor is passed to compressor and the cycle completes.
The performance of a refrigeration system is defined as
12
41
hh
hh
W
Q
COP
in
L
R
−
−
==
Similarly, for the heat pump
12
32
hh
hh
W
Q
COP
in
H
HP
−
−
==

Thermodynamics chapter:7 Some Power and Refrigerator Cycle

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Thermodynamics chapter:7 Some Power and Refrigerator Cycle