ME F217
Applied thermodynamics
Dr. M. Srinivas, ME F217 Applied Thermodynamics
1
Contact Information
Prof. M. Srinivas
Mechanical Engineering Department
E-mail: morasrini@hyderabad.bits-pilani.ac.in
Chamber consultation: Tuesdays (4 -5PM)
Dr. M. Srinivas, ME F217 Applied Thermodynamics
2
Gas power cycles
Dr. M. Srinivas, ME F217 Applied Thermodynamics
3
Introductory comments
 Two important applications of TD: Power generation
and Refrigeration
 Power generation is accomplished by heat engines
which run on power cycles
 Cycles




Gas cycles: the working fluid remains in gaseous phase as it
undergoes the TD cycle
Vapour cycles: working fluid exists in the vapor phase during one
part of the cycle and in the liquid phase during another part
Closed cycles: the working fluid is returned to the initial state at
the end of the cycle and is recirculated
Open Cycles: the working fluid is renewed at the end of each cycle
instead of being recirculated
Dr. M. Srinivas, ME F217 Applied Thermodynamics
4
Introductory comments
 Two types of heat engines
 External combustion engines (such as
steam power plants), heat is supplied
to the working fluid from an external
source such as a furnace, a
geothermal well, a nuclear reactor, or
even the sun
 In internal combustion engines (such
as automobile engines), this is done
by burning the fuel within the system
boundaries
Dr. M. Srinivas, ME F217 Applied Thermodynamics
5
Introductory comments
 The cycles encountered in actual
devices are difficult to analyze
because
 of the presence of complicating
effects, such as friction
 absence of sufficient time for
establishment of the equilibrium
conditions during the cycle.
 Actual cycle when stripped of all the
internal
irreversibilities
and
complexities, Ideal cycles
 In this course: we analyze Ideal cycles
( and to some extent, the real ones,
as well)
Dr. M. Srinivas, ME F217 Applied Thermodynamics
6
Introductory comments
 Reversible cycles such as Carnot
cycle have the highest thermal
efficiency of all heat engines
operating between the same
temperature levels.
 Unlike ideal cycles, they are
totally reversible, and unsuitable
as a realistic model.
 Thermal efficiency of heat engines
Dr. M. Srinivas, ME F217 Applied Thermodynamics
7
Idealization and
simplification of cycles
 The cycle does not involve any
friction. Therefore, the working fluid
does not experience any pressure drop
as it flows in pipes or devices such as
heat exchangers.
 All
expansion
and
compression
processes take place in a quasiequilibrium manner.
 The pipes connecting the various
components of a system are well
insulated, and heat transfer through
them is negligible.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
8
Idealization and
simplification of cycles
 On both P-V and T-s diagrams, the
area enclosed by the process curves
represents network of the cycle
 On T-s diagram, the ratio of the area
enclosed by the cyclic curve to the
area under the heat-addition process
curve
represents
the
thermal
efficiency of the cycle.
 Any modification that increases the
ratio of these two areas will also
increase the thermal efficiency of
the cycle.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
9
The Carnot cycle and its
importance
 The Carnot cycle is composed of four
totally reversible processes:
 1-2 isothermal heat addition
 2-3 isentropic expansion
 3-4 isothermal heat rejection
 4-1 isentropic compression
Dr. M. Srinivas, ME F217 Applied Thermodynamics
10
The Carnot cycle and its
importance
 Efficiency
derivation
of
Carnot
cycle,
 For both ideal and actual cycles:
 Thermal efficiency increases with an increase in the
average temperature at which heat is supplied to the
system or with a decrease in the average temperature
at which heat is rejected from the system.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
11
The Carnot cycle : Numerical
problem
 An air-standard Carnot cycle is executed in a closed system
between the temperature limits of 350 and 1200 K. The
pressures before and after the isothermal compression are
150 and 300 kPa, respectively. If the net work output per
cycle is 0.5 kJ, determine (a) the maximum pressure in the
cycle, (b) the heat transfer to air, and (c) the mass of air.
Assume variable specific heats for air.
 The variation in specific heats can be taken care of by using
relative properties concept, according to which, when air is
undergoing isentropic process
 Where (Pr1 / Pr4)is the ratio of relative specific pressures at
two different temperatures
Dr. M. Srinivas, ME F217 Applied Thermodynamics
12
The Carnot cycle : Numerical
problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
13
The Carnot cycle : Numerical
problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
14
Air standard assumptions
 IC engines (Example: SI and diesel
engines, GT): energy is provided by
burning a fuel within the system
boundaries.
 The fuel burnt produces gases and
these gases are thrown out of cylinder
at one point in the cycle.
 This implies: Even though IC engines
operate on a mechanical cycle (the
piston returns to its starting position
at the end of each revolution), the
working fluid does not undergo a
complete thermodynamic cycle
 IC engines are modelled to undergo TD
cycle, by considering the gas to be air
and the burning is replaced by heat
addition.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
15
Air standard assumptions
 Important assumptions
 The working fluid is air, which
continuously circulates in a
closed loop and 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.
 The exhaust process is replaced
by a heat-rejection process
that restores the working fluid
to its initial state.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
16
Air standard assumptions
 Additional assumptions(may
not be applicable all the
time)
 Specific
heats
are
constant
 Cold-air-standard
assumptions: When the
working fluid is considered
to be air with constant
specific heats at room
temperature (25°C)
Dr. M. Srinivas, ME F217 Applied Thermodynamics
17
Air standard assumptions
 Air-standard cycle: A cycle
for which the air-standard
assumptions are applicable
 Otto cycle
 Diesel cycle
 Stirling and Ericson cycles
 Brayton cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
18
Reciprocating engines:
Nomenclature
 Top dead center (TDC)
 the position of the piston
when it forms the smallest
volume in the cylinder
 Bottom dead center (BDC)
 the position of the piston
when it forms the largest
volume in the cylinder
 Stroke of the engine
 The distance between the
TDC and the BDC which is
the largest distance that the
piston can travel in one
direction
Dr. M. Srinivas, ME F217 Applied Thermodynamics
19
Reciprocating engines:
Nomenclature
 Bore
 The diameter of the piston
is called the bore
 Intake valve
 Valve through which the
air or air–fuel mixture is
drawn into the cylinder
 Exhaust valve
 Valve through which The
combustion products are
expelled from the cylinder
through.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
20
Reciprocating engines:
Nomenclature
 Clearance volume
 The
minimum
volume
formed in the cylinder
when the piston is at TDC
 Displacement volume
 The volume displaced by
the piston as it moves
between TDC and BDC
Dr. M. Srinivas, ME F217 Applied Thermodynamics
21
Reciprocating engines:
Nomenclature
 Compression ratio
 The ratio of the maximum
volume formed in the
cylinder to the minimum
(clearance) volume
Dr. M. Srinivas, ME F217 Applied Thermodynamics
22
Reciprocating engines:
Nomenclature
 Mean effective pressure
 is a fictitious pressure that, if
it acted on the piston during
the entire power stroke,
would produce the same
amount of net work as that
produced during the actual
cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
23
Reciprocating engines:
Nomenclature
 Mean effective pressure
 can be used as a parameter
to
compare
the
performances
of
reciprocating engines of
equal size
 The engine with a larger
value of MEP delivers more
net work per cycle and thus
performs better
Dr. M. Srinivas, ME F217 Applied Thermodynamics
24
Reciprocating engines: SI
and CI engines
 Differentiated based on how combustion takes
place with in the cylinder
 SI engines
 the combustion of the air–fuel mixture is
initiated by a spark plug
 Ideal cycle: Otto cycle
 CI engines
 the air–fuel mixture is self-ignited as a result of
compressing the mixture above its self-ignition
temperature.
 Ideal cycle: Diesel cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
25
Otto cycle: The ideal cycle for
SI engines
 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
 Actual 4-stroke SI engines : working
Dr. M. Srinivas, ME F217 Applied Thermodynamics
26
Otto cycle: The ideal cycle for
SI engines
 Actual 2-stroke SI engines
 all four functions are executed in
just two strokes
 Two strokes are: the power stroke
and the compression stroke
 Hardware changes
 the crankcase is sealed, and the
outward motion of the piston is
used to slightly pressurize the air–
fuel mixture in the crankcase
 the intake and exhaust valves are
replaced by openings (ports) in
the lower portion of the cylinder
wall
Dr. M. Srinivas, ME F217 Applied Thermodynamics
27
Otto cycle: The ideal cycle for
SI engines
 Sequence of events
 During the latter part of the power
stroke, the piston uncovers first the
exhaust port
 the exhaust gases are partially
expelled
 Then the intake port is uncovered
 Fresh air–fuel mixture will be rushed
in and drive most of the remaining
exhaust gases out of the cylinder.
 Mixture is then compressed as the
piston moves upward during the
compression
stroke
and
is
subsequently ignited by a sparkplug
Dr. M. Srinivas, ME F217 Applied Thermodynamics
28
Otto cycle: The ideal cycle for
SI engines
 Four-stroke cycle
 1 cycle = 4 stroke = 2 revolution
 Two-stroke cycle
 1 cycle = 2 stroke = 1 revolution
 Two-stroke engines special features
 generally less efficient than fourstroke engines
 they are relatively simple and
inexpensive
 have high power-to-weight and
power-to-volume ratios.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
29
Otto cycle: The ideal cycle for
SI engines
 TD analysis of actual 4-stroke or 2-stroke cycle is
complex
 Simplified by using air-standard assumptions
 Resulting cycle is: Otto cycle
 Ideal 4-stroke SI engines - working
Dr. M. Srinivas, ME F217 Applied Thermodynamics
30
Otto cycle: The ideal cycle for
SI engines
 1-2 Isentropic compression
 2-3 Constant-volume heat addition
 3-4 Isentropic expansion
 4-1 Constant-volume heat rejection
Dr. M. Srinivas, ME F217 Applied Thermodynamics
31
Otto cycle: The ideal cycle for
SI engines
 Above ideal cycle is further
modified to include intake and
exhaust strokes
 Process 0-1: Air enters the cylinder
through the open intake valve at
atmospheric pressure P0 as the
piston moves from TDC to BDC.
 Process 1-2: The intake valve is
closed at state 1 and air is
compressed isentropically to state
2. Piston moves from BDC to TDC.
 Process 2-3: Heat is transferred at
constant volume.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
32
Otto cycle: The ideal cycle for
SI engines
 Process 3-4: Air is expanded
isentropically
 Process 4-1: Heat is rejected at
constant volume.
 Process 1-0: Air is expelled through
the open exhaust valve.
 Work interactions during intake and
exhaust cancel each other, and thus
inclusion of the intake and exhaust
processes has no effect on the net
work output from the cycle.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
33
Otto cycle: Analysis
Dr. M. Srinivas, ME F217 Applied Thermodynamics
34
Otto cycle: Analysis
 Some
important
conclusions
 The
thermal
efficiency of the
ideal Otto cycle
increases
with
both
the
compression ratio
and the specific
heat ratio.
 This is also true
for actual sparkignition
internal
combustion
engines.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
35
Otto cycle: Analysis
 Some
important
conclusions
 For
a
given
compression ratio,
the
thermal
efficiency of an
actual
sparkignition engine is
less than that of an
ideal Otto cycle
because of the
irreversibilities,
such as friction,
and other factors
such as incomplete
combustion.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
36
Otto cycle: Analysis
 Some
important
conclusions
 thermal efficiency
curve is rather
steep
at
low
compression ratios
but flattens out
starting with a
compression ratio
value of about 8.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
37
Otto cycle: Analysis
 Some
important
conclusions
 Therefore,
the
increase in thermal
efficiency with the
compression ratio
is
not
as
pronounced at high
compression ratios.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
38
Otto cycle: Analysis
 Auto ignition and engine knock
 puts a limit on going for higher
compression ratios
 With higher CRs, temperatures may
reach auto ignition temperatures of
fuels
 This results in early and rapid burn of
the fuel at some point or points ahead
of the flame front
 This results in almost instantaneous
inflammation of the end gas.
 Produces lot audible noise called as
engine knock
 Can not be tolerated because engine
life comes down
Dr. M. Srinivas, ME F217 Applied Thermodynamics
39
Otto cycle: Numerical
problem
 An ideal Otto cycle has a compression ratio of 8. At the beginning of
the compression process, air is at 95 kPa and 27 C, and 750 kJ/kg of
heat is transferred to air during the constant-volume heat-addition
process. Taking into account the variation of specific heats with
temperature, determine (a) the pressure and temperature at the
end of the heat addition process, (b) the net work output, (c) the
thermal efficiency, and (d) the mean effective pressure for the
cycle.
 The variation in specific heats can be taken care of by using relative
properties concept, according to which, when air is undergoing
isentropic process
 Where (vr2 / vr1)is the ratio of relative specific volumes at two
different temperatures. Applicable only for ideal gases undergoing
isentropic processes
Dr. M. Srinivas, ME F217 Applied Thermodynamics
40
Otto cycle: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
41
Otto cycle: Numerical
problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
42
Diesel cycle: The ideal cycle
for CI engines


Proposed by Rudolph Diesel in the 1890
Salient points on CI engines
 Also called as Diesel engines
 Working is almost same as that of SI
engines
 Instead of fuel-air mixture, only air is
compressed to a temperature that is above
the auto ignition temperature of the fuel
 fuel injection process in diesel engines
starts when the piston approaches TDC and
continues during the first part of the
power stroke.
 combustion starts on contact as the fuel is
injected into this hot air
 Therefore, the combustion process takes
place over a longer interval.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
43
Diesel cycle: The ideal cycle
for CI engines
 Salient points on CI engines
 Because of this longer duration,
the combustion process could be
approximated as a constantpressure heat-addition process
 Since there is no problem of auto
ignition
 Engines can be designed to operate
at much higher compression ratios
than SI engines, typically between
12 and 24
 fuels that are less refined (thus
less expensive) can be used in
diesel engines.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
44
Diesel cycle: The ideal cycle
for CI engines
 Processes sequence
 1-2 isentropic compression
 2-3
constant-volume
heat
addition
 3-4 isentropic expansion
 4-1
constant-volume
heat
rejection.
 Otto and Diesel cycles comparison
Dr. M. Srinivas, ME F217 Applied Thermodynamics
45
Diesel cycle: Analysis
 Noting that the Diesel cycle is
executed in a piston–cylinder device,
which forms a closed system, the
amount of heat transferred to the
working fluid at constant pressure and
rejected from it at constant volume
can be expressed as
Dr. M. Srinivas, ME F217 Applied Thermodynamics
46
Diesel cycle: Analysis
 a new quantity, the cutoff ratio rc
 the ratio of the cylinder volumes
after and before the combustion
process
Dr. M. Srinivas, ME F217 Applied Thermodynamics
47
Diesel cycle: Analysis
 Using the cutoff ratio rc, and the
isentropic ideal-gas relations for
processes 1-2 and 3-4,
Dr. M. Srinivas, ME F217 Applied Thermodynamics
48
Diesel cycle: Analysis
 Observations from
 under the cold-air-standard
assumptions, the efficiency of a
Diesel cycle differs from the
efficiency of an Otto cycle by
the quantity in the brackets.
 This quantity is always greater
than 1
 For the same compression ratio
Dr. M. Srinivas, ME F217 Applied Thermodynamics
49
Diesel cycle: Analysis
 Some
more
observations
on
comparison of Gasoline and Diesel
engines
 as the cutoff ratio decreases, the
efficiency of the Diesel cycle
increases
 For the limiting case of rc = 1, the
quantity in the brackets becomes
unity, and the efficiencies of the
Otto and Diesel cycles become
identical.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
50
Diesel cycle: Analysis
 Some
more
observations
on
comparison of Gasoline and Diesel
engines; Otto/Diesel cycles from
 Diesel engines operate at much
higher compression ratios and
thus are usually more efficient
than the spark ignition (gasoline)
engines.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
51
Diesel cycle: Analysis
 Some
more
observations
on
comparison of Gasoline and Diesel
engines; Otto/Diesel cycles from
 The diesel engines also burn the
fuel more completely since they
usually
operate
at
lower
revolutions per minute and the
air–fuel mass ratio is much higher
than spark-ignition engines.
 Thermal efficiencies of large
diesel engines 35 to 40 percent.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
52
Dual cycle
 A more realistic ideal cycle model for
modern, high-speed compression
ignition engine
 In modern high-speed compression
ignition engines, fuel is injected into
the combustion chamber much sooner
compared to the early diesel engines.
 Fuel starts to ignite late in the
compression stroke, and consequently
part of the combustion occurs almost
at constant volume.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
53
Dual cycle
 Fuel injection continues until the
piston reaches the top dead center,
and combustion of the fuel keeps the
pressure high well into the expansion
stroke.
 Thus, the entire combustion process
can better be modeled as the
combination of constant-volume and
constant-pressure processes.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
54
Diesel cycle: Numerical
problem
 An air-standard Diesel cycle has a compression ratio of 16
and a cutoff ratio of 2. At the beginning of the
compression process, air is at 95 kPa and 27 C. Accounting
for the variation of specific heats with temperature,
determine (a) the temperature after the heat-addition
process, (b) the thermal efficiency, and (c) the mean
effective pressure.
 The variation in specific heats can be taken care of by
using relative properties concept, according to which,
when air is undergoing isentropic process
 Where (vr2 / vr1)is the ratio of relative specific volumes at
two different temperatures. Applicable only for ideal gases
undergoing isentropic processes
Dr. M. Srinivas, ME F217 Applied Thermodynamics
55
Diesel cycle: Numerical
problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
56
Diesel cycle: Numerical
problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
57
Diesel cycle: Numerical
problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
58
Some characteristic features
of Otto and Diesel cycles
 Both are internally reversible, because all the processes are
reversible
 But not externally reversible since there is a finite
temperature difference that is responsible for heat
addition/heat rejection processes
 Hence
 total cycle is irreversible
 Thermal efficiency of an Otto or Diesel engine will be less than
that of a Carnot engine operating between the same
temperature limits
 One way to make it close to Carnot cycle is by making the
heat addition / rejection at constant temperature
 Could be achieved by regeneration
Dr. M. Srinivas, ME F217 Applied Thermodynamics
59
What is regeneration
 A process during which heat
is transferred to a thermal
energy storage device during
one part of the cycle and is
transferred back to the
working fluid during another
part of the cycle
 The
device
is
called
regenerator
 Use of regeneration gives two
cycles
 Stirling cycle
 Erickson cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
60
Stirling cycle: Basic
processes

Processes





1-2 T = constant expansion
(heat addition from the
external source)
2-3 v = constant regeneration
(internal heat transfer from
the working fluid to the
regenerator)
3-4 T = constant compression
(heat rejection to the external
sink)
4-1 v = constant regeneration
(internal heat transfer from
the regenerator back to the
working fluid)
Usually difficult to achieve
Dr. M. Srinivas, ME F217 Applied Thermodynamics
61
Stirling cycle: Execution
 Requires special hardware


a cylinder with two pistons
on each side
Regenerator:
 Positioned in the middle
 is used for the temporary
storage of thermal energy.
 can be a wire or a ceramic
mesh or any kind of porous
plug with a high thermal
mass (mass times specific
heat)

Mass of working fluid with
in the regenerator at any
instant is negligible.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
62
Stirling cycle: Execution
 Working sequence
 Initially, the left chamber
houses the entire working
fluid (a gas), which is at a
high temperature and
pressure.
 During process 1-2, heat is
transferred to the gas at
TH from a source at TH.
 As the gas expands
isothermally,
the
left
piston moves outward,
doing work, and the gas
pressure drops.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
63
Stirling cycle: Execution
 Working sequence
 During process 2-3, both
pistons are moved to the
right at the same rate (to
keep
the
volume
constant) until the entire
gas is forced into the right
chamber.
 As the gas passes through
the regenerator, heat is
transferred
to
the
regenerator and the gas
temperature drops from
TH to TL.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
64
Stirling cycle: Execution
 Working sequence


For this heat transfer
process to be reversible,
the temperature difference
between the gas and the
regenerator should not
exceed
a
differential
amount dT at any point.
Thus, the temperature of
the regenerator will be TH
at the left end and TL at
the right end of the
regenerator when state 3 is
reached.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
65
Stirling cycle: Execution
 Working sequence
 During process 3-4, the
right piston is moved
inward, compressing the
gas.
 Heat is transferred from
the gas to a sink at
temperature TL so that
the
gas
temperature
remains constant at TL
while the pressure rises.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
66
Stirling cycle: Execution
 Working sequence



Finally, during process 4-1,
both pistons are moved to
the left at the same rate
(to keep the volume
constant),
forcing
the
entire gas into the left
chamber.
The gas temperature rises
from TL to TH as it passes
through the regenerator
and picks up the thermal
energy stored there during
process 2-3.
This completes the cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
67
Stirling cycle: Execution
 Important notes
 the net heat transfer to
the regenerator during a
cycle is zero.
 That is, the amount of
energy stored in the
regenerator
during
process 2-3 is equal to the
amount picked up by the
gas during process 4-1
Dr. M. Srinivas, ME F217 Applied Thermodynamics
68
Ericson cycle: Basic
processes and execution





Is same as Stirling cycle, except
 that the two constantvolume
processes
are
replaced by two constantpressure processes
Could be achieved in a steady
flow
Isothermal
expansion
and
compression: In a turbine and a
compression, respectively
Regenerator: a counter-flow
heat exchanger
Hot and cold fluid streams
enter the heat exchanger from
opposite ends, and heat
transfer takes place between
the two streams.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
69
Ericson cycle: Basic
processes and execution
 In the ideal case,
 the
temperature
difference between the
two fluid streams does
not
exceed
a
differential amount at
any point
 cold fluid stream leaves
the heat exchanger at
the inlet temperature
of the hot stream.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
70
Stirling and Ericson cycles:
Some important points






Both the Stirling and Ericsson cycles are totally reversible, as is the Carnot
cycle
All three cycles will have the same efficiency
The Stirling and Ericsson cycles give a message: Regeneration can increase
efficiency
Difficult to achieve both the cycles because of finite temperature
difference required to HT take place
Both are external combustion engines. That is, the fuel in these engines is
burned outside the cylinder, as opposed to gasoline or diesel engines
Stirling engines suitable for trucks, buses etc. are developed by

The Ford Motor Company

General Motors Corporation

The Phillips Research Laboratories, Netherlands
Dr. M. Srinivas, ME F217 Applied Thermodynamics
71
Ericson cycle: Numerical problem
 Consider an Ericson cycle working
between 300K and 950K in a steady flow
device. Air is the working substance.
Rejected heat is 150kJ/kg. The lowest
pressure in the cycle is 120kPa.
Determine maximum pressure in the
cycle, network output and thermal
efficiency of the cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
72
Ericson cycle: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
73
Ericson cycle: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
74
Brayton cycle for Gas
Turbines




Proposed by George Brayton in 1970
Used in Gas turbine
Open cycle GT: Working
Open cycle GT is modelled as closed cycle GT using air standard
assumptions
Dr. M. Srinivas, ME F217 Applied Thermodynamics
75
Brayton cycle for Gas
Turbines: Process diagrams
Pressure
ratio
Dr. M. Srinivas, ME F217 Applied Thermodynamics
76
Brayton cycle for Gas
Turbines: Analysis
Pressure
ratio
Dr. M. Srinivas, ME F217 Applied Thermodynamics
77
Brayton cycle for Gas Turbines:
interesting points out of Analysis
 The thermal efficiency increases
with pressure ratio and k, which is
also the case for actual gas turbines
 The highest temperature in the cycle
occurs at the end of the combustion
process (state 3), and it is limited by
the maximum temperature that the
turbine blades can withstand.
 This also limits the pressure ratios
that can be used in the cycle.
Pressure
ratio
Dr. M. Srinivas, ME F217 Applied Thermodynamics
78
Brayton cycle for Gas Turbines:
interesting points out of Analysis




For a fixed turbine inlet temperature T3,
the net work output per cycle increases
with the pressure ratio, reaches a
maximum, and then starts to decrease
Therefore, there should be a compromise
between the pressure ratio (thus the
thermal efficiency) and the net work
output.
With less work output per cycle, a larger
mass flow rate (thus a larger system) is
needed to maintain the same power
output, which may not be economical.
In most common designs, the pressure
ratio of gas turbines ranges from about 11
to 16.
Pressure
ratio
Dr. M. Srinivas, ME F217 Applied Thermodynamics
79
Brayton cycle for Gas Turbines:
interesting points about air used
 The air in gas turbines supplies the necessary oxidant for
the combustion of the fuel
 It serves as a coolant to keep the temperature of various
components within safe limits.
 An air–fuel ratio of 50 or above is not uncommon.
 Therefore, in a cycle analysis, treating the combustion
gases as air does not cause any appreciable error
Dr. M. Srinivas, ME F217 Applied Thermodynamics
80
Brayton cycle for Gas Turbines:
Backwork ratio
 the ratio of the compressor work to
the turbine work
 Usually very high in GT , up to 50%
 Steam turbines very less. Why?
 A power plant with a high back
work ratio requires a larger turbine
to provide the additional power
requirements of the compressor.
 Therefore, the turbines used in gasturbine power plants are larger
than those used in steam power
plants of the same net power
output.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
81
Gas Turbines: Deviation of actual
GT cycles from Ideal
 Reasons for deviations



pressure drop during the heataddition
and
heat-rejection
processes
actual
work
input
to
the
compressor is more, and the actual
work output from the turbine is
less
Essentially all these are due to
irreversibilities in the actual GT
cycle
Dr. M. Srinivas, ME F217 Applied Thermodynamics
82
Gas Turbines: Deviation of actual
GT cycles from Ideal
 The
deviation
of
actual
compressor and turbine behavior
from the idealized isentropic
behavior can be accurately
accounted for by utilizing the
isentropic efficiencies of the
turbine and compressor
Dr. M. Srinivas, ME F217 Applied Thermodynamics
83
Gas Turbines: Numerical problem
 Consider a GT working between the temperature and
pressure limits as given. Isentropic efficiencies of
compressor and turbine are 85% and 87% respectively. At
the entry to compressor 850 m3 of air enters per minute.
Determine the net power output, back work ratio and
thermal efficiency
Dr. M. Srinivas, ME F217 Applied Thermodynamics
84
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
85
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
86
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
87
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
88
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
89
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
90
Brayton cycle for Gas Turbines:
With regeneration
 In gas-turbine engines, the temperature
of the exhaust gas leaving the turbine is
often considerably higher than the
temperature of the air leaving the
compressor.
 The high-pressure air leaving the
compressor can be heated by the hot
exhaust gases in a counter-flow heat
exchanger (a regenerator).
 Working
Dr. M. Srinivas, ME F217 Applied Thermodynamics
91
Brayton cycle for Gas Turbines:
With regeneration
 T-S diagram
 The highest temperature occurring
within the regenerator is T4, the
temperature of the exhaust gases
leaving the turbine and entering the
regenerator.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
92
Brayton cycle for Gas Turbines:
With regeneration
 Under no conditions can the air be
preheated in the regenerator to a
temperature above this value.
 Air normally leaves the regenerator at a
lower temperature, T5.
 In the limiting (ideal) case, the air exits
the regenerator at the inlet temperature
of the exhaust gases T4.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
93
Brayton cycle for Gas Turbines:
With regeneration

The extent to which a regenerator
approaches an ideal regenerator is called
the effectiveness ε and is defined as

Under cold air assumptions

The thermal efficiency of the Brayton
cycle increases as a result of regeneration
since less fuel is used for the same work
output.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
94
Brayton cycle for Gas Turbines:
With regeneration
 Under
the
cold-air-standard
assumptions, the thermal efficiency of
an ideal Brayton cycle with regeneration
is
 The thermal efficiency depends on the
ratio of the minimum to maximum
temperatures as well as the pressure
ratio.
 Regeneration is most effective at lower
pressure ratios and low minimum-tomaximum temperature ratios.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
95
Brayton cycle for Gas Turbines:
With intercooling, reheating and regeneration


The three principles:
Principle 1: Multistage compression with
intercooling: The work required to
compress a gas between two specified
pressures can be decreased by carrying
out the compression process in stages
and cooling the gas in between. This
keeps the specific volume as low as
possible.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
96
Brayton cycle for Gas Turbines:
With intercooling, reheating and regeneration
 The three principles
 Principle 2: Multistage expansion
with reheating keeps the specific
volume of the working fluid as high
as possible during an expansion
process, thus maximizing work
output.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
97
Brayton cycle for Gas Turbines:
With intercooling, reheating and regeneration
 The three principles:
 Principle 3: Intercooling and reheating
always
decreases
the
thermal
efficiency unless they are accompanied
by regeneration.
 These three principles are used here
Dr. M. Srinivas, ME F217 Applied Thermodynamics
98
Brayton cycle for Gas Turbines:
With intercooling, reheating and regeneration
 Working
 T- S diagram
 As the number of compression and
expansion stages increases, the gasturbine
cycle
with
intercooling,
reheating,
and
regeneration
approaches the Ericsson cycle.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
99
Brayton cycle for Gas Turbines:
With intercooling, reheating and regeneration
 For
minimizing
work
input
to
compressor and maximizing work
output from turbine:
 For a two stage compressor/turbine
this ratio is equal to square root of
overall pressure ratio, rp
Dr. M. Srinivas, ME F217 Applied Thermodynamics
100
Gas Turbines: Numerical problem
 Consider a regenerative gasturbine power plant with two
stages of compression and two
stages of expansion. The overall
pressure ratio of the cycle is 9.
The air enters each stage of the
compressor at 300 K and each
stage of the turbine at 1200 K.
Accounting for the variation of
specific heats with temperature,
determine the minimum mass
flow rate of air needed to
develop a net power output of
110 MW.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
101
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
102
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
103
Gas Turbines: Numerical problem
 Consider an ideal gas-turbine cycle
with two stages of compression
and two stages of expansion with
T-S diagram as shown. The
pressure ratio across each stage of
the compressor and turbine is 3.
The two temperature limits are
300 K and 1200 K, as shown. The
work inputs for both stages of
compressor are identical and so
also the work outputs for the two
stages of turbine. Determine the
back work ratio and the thermal
efficiency of the cycle, assuming
(a) no regenerator is used and (b) a
regenerator with 75 percent
effectiveness is used. Use variable
specific heats.
Dr. M. Srinivas, ME F217 Applied Thermodynamics
104
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
105
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
106
Gas Turbines: Numerical problem
Dr. M. Srinivas, ME F217 Applied Thermodynamics
107
THANK YOU
Dr. M. Srinivas, ME F217 Applied Thermodynamics
108