APPLIED
THERMODYNAMICS
(ME F217)
BITS Pilani
Pilani Campus
Dr. Suvanjan Bhattacharyya
Department of Mechanical Engineering.
suvanjan.bhattacharyya@pilani.bits-pilani.ac.in
Friday, December 1, 2023
Engine
What is Heat Engine?
• A device for producing motive power from heat called heat
engine.
• There are two types of heat engine available:
Internal Combustion Engine (IC Engine)
External Combustion Engine (EC Engine)
• An internal combustion engine (IC Engine) is heat engine
where the combustion of a fuel occurs with an air in a
combustion chamber that is an integral part of the working
fluid flow circuit.
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What is / is not an IC Engine?
IS
• Gasoline-fueled
reciprocating piston engine
• Diesel-fueled reciprocating
piston engine
• Gas turbine
• Rocket
IS NOT
• Steam power plant
• Solar power plant
• Nuclear power plant
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Engine
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Engine
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Engine
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Engine
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Engine
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Engine
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Engine
The actual gas power cycles are rather complex.
To reduce the analysis to a manageable level, we utilize the following approximations,
commonly known as the air-standard 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.
• Another assumption that is often utilized to simplify the analysis even more is that
air has constant specific heats whose values are determined at room temperature
(25oC). When this assumption is utilized, the air-standard assumptions are called the
cold-air-standard assumptions. A cycle for which the air-standard assumptions are
applicable is frequently referred to as an air-standard cycle.
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Four – Stroke Cycle
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Four – Stroke Cycle
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Numerical
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Otto Cycle
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Otto Cycle
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Otto Cycle
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Diesel Cycle
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Diesel Cycle
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Diesel Cycle
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Diesel Cycle
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Otto Cycle: Numerical
A gas engine working on the Otto cycle has a cylinder of diameter 200 mm and
stroke 250 mm. The clearance volume is 1570cc. Find the air-standard efficiency.
Assume Cp=1.004 kJ/kg K and Cv=0.717 kJ/kg K for air.
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Otto Cycle: Numerical
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Otto Cycle
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Otto Cycle: Numerical
In an Otto cycle air at 17◦C and 1bar is compressed adiabatically until the pressure is
15bar. Heat is added at constant volume until the pressure rises to 40bar.
Calculate the air-standard efficiency, the compression ratio for the cycle.
Assume Cv = 0.717 kJ/kg K and R = 8.314 kJ/kmol K.
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Dual Cycle
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Dual Cycle: Thermal Efficiency
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Dual Cycle: Thermal Efficiency
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Dual Cycle: Thermal Efficiency
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Mean Effective Pressure
Mean effective pressure (MEP) 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.
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Otto Cycle: Numerical
In an air standard Otto cycle the compression ratio is 7 and compression begins at
35oC and 100 kPa. The maximum temperature of the cycle is 1100oC.
Find: (a) the temperature and pressure at the cardinal points of the cycle,
(b) The heat supplied per kg of air,
(c) The work done per kg of air, and
(d) The cycle efficiency.
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Otto Cycle: Numerical
In a S.I. engine working on the ideal Otto cycle, the compression ratio is 5.5. The
pressure and temperature at the beginning of compression are 1 bar and 27◦C
respectively. The peak pressure is 30 bar. Determine the pressure and temperatures at
the salient points, and the air-standard efficiency. Assume ratio of specific heats to be
1.4 for air.
TRY
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Otto Cycle: Numerical
An engine working on the Otto cycle has an air-standard efficiency of 56% and rejects
544 kJ/s of heat. The pressure and temperature of the air at the beginning of
compression are 0.1 MPa and 60oC respectively. Compute (a) the compression ratio of
the engine, (b) the work done per kg of air, (c) the pressure and temperature at the end
of compression and (d) the maximum pressure in the cycle. Take Cv = 0.718 kJ/kg K.
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Diesel Cycle: Numerical
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STIRLING AND ERICSSON CYCLES
• Consider a heat engine operating between a heat source at TH and a heat sink at TL.
• For the heat-engine cycle to be totally reversible, the temperature difference
between the working fluid and the heat source (or sink) should never exceed a
differential amount dT during any heat-transfer process.
• That is, both the heat-addition and heat-rejection processes during the cycle must
take place isothermally, one at a temperature of TH and the other at a temperature
of TL.
• This is precisely what happens in a Carnot cycle.
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STIRLING AND ERICSSON CYCLES
• Now, there are two other cycles that involve an isothermal heat-addition process at
TH and an isothermal heat-rejection process at TL: the Stirling cycle and the
Ericsson cycle.
• They differ from the Carnot cycle in that the two isentropic processes are replaced
by two constant-volume regeneration processes in the Stirling cycle and by two
constant-pressure regeneration processes in the Ericsson cycle.
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STIRLING CYCLE
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STIRLING CYCLE
In the isothermal compression of a gas there is
work done on the system to decrease the volume
and increase the pressure. Doing work on the gas
increases the internal energy and will tend to
increase the temperature. To maintain the constant
temperature energy must leave the system as heat
and enter the environment.
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STIRLING CYCLE
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STIRLING CYCLE
PLEASE CHECK THE CLASS NOTE FOR DETAIL
CALCULATION THAT I SOLVED IN THE CLASS
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Ericsson cycle
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Ericsson cycle
PLEASE CHECK THE CLASS NOTE FOR DETAIL
CALCULATION THAT I SOLVED IN THE CLASS
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STIRLING AND ERICSSON CYCLES
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STIRLING AND ERICSSON CYCLES
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Diesel Cycle: Numerical
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 27oC.
Accounting for the variation of specific heats with temperature, determine (a) the
temperature after the heat-addition process, and (b) the thermal efficiency.
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Diesel Cycle: Numerical
In an air-standard Diesel cycle, the pressure and temperature at the intake are 1.03 bar
and 27oC respectively. The maximum pressure in the cycle is 47 bar and heat supplied
during the cycle is 545 kJ/kg. Determine the:
(i) Compression ratio
(ii) Temperature at the end of the compression
(iii) Temperature at the end of the combustion
(iv) Air-standard efficiency
Assume: Cp = 1.005 kJ/kg K for air.
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Diesel Cycle: Numerical
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
•
The Brayton cycle was first proposed by George Brayton for use in the reciprocating oilburning engine that he developed around 1870.
•
Today, 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 and as well as a closed cycle by utilizing the
air-standard assumptions.
•
The two major application areas of gas-turbine engines are aircraft propulsion and electric
power generation.
•
When it is used for aircraft propulsion, the gas turbine produces just enough power to drive
the compressor and a small generator to power the auxiliary equipment.
•
The majority of the Western world’s naval system already use gas-turbine engines for
propulsion and electric power generation. The General Electric LM2500 gas turbines used to
power ships have a simple-cycle thermal efficiency of 37 percent.
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GAS-TURBINE ENGINES
Commercial Aircraft Propulsion
LM2500 Gas Turbines
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
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BRAYTON CYCLE:
THE IDEAL CYCLE FOR GAS-TURBINE ENGINES
In gas-turbine power plants, the ratio of
the compressor work to the turbine
work, called the back work ratio
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BRAYTON CYCLE:
THE ACTUAL CYCLE FOR GAS-TURBINE ENGINES
• The actual gas-turbine cycle differs from
the ideal Brayton cycle on several
accounts.
• More importantly, the actual work input
to the compressor is more, and the
actual work output from the turbine is
less because of irreversibilities.
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THE BRAYTON CYCLE WITH
REGENERATION
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BRAYTON CYCLE:
THE ACTUAL CYCLE FOR GAS-TURBINE ENGINES
The effectiveness of most regenerators used in practice is below 0.85.
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BRAYTON CYCLE:
THE ACTUAL CYCLE FOR GAS-TURBINE ENGINES
The effectiveness of most regenerators used in practice is below 0.85.
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BRAYTON CYCLE: Numerical
A gas-turbine power plant operates on the simple Brayton cycle with air as the working
fluid and delivers 32 MW of power. The minimum and maximum temperatures in the
cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the
value at the compressor inlet. The isentropic efficiency of 80 percent for the
compressor and 86 percent for the turbine, determine the mass flow rate of air
through the cycle. Account for the variation of specific heats with temperature.
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BRAYTON CYCLE: Numerical
A gas-turbine power plant operates on the simple Brayton cycle with air as the working
fluid and delivers 32 MW of power. The minimum and maximum temperatures in the
cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the
value at the compressor inlet. The isentropic efficiency of 80 percent for the
compressor and 86 percent for the turbine, determine the mass flow rate of air
through the cycle. Account for the variation of specific heats with temperature.
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BRAYTON CYCLE: Numerical
A simple Brayton cycle using air as the working fluid has a
pressure ratio of 10. The minimum and maximum
temperatures in the cycle are 295 and 1240 K. Assuming an
isentropic efficiency of 83 percent for the compressor and 87
percent for the turbine, determine (a) the air temperature at
the turbine exit, (b) the net work output, and (c) the thermal
efficiency.
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BRAYTON CYCLE: Numerical
A simple Brayton cycle using air as the working fluid has a pressure ratio of 10. The
minimum and maximum temperatures in the cycle are 295 K and 1240 K. Assuming an
isentropic efficiency of 83 percent for the compressor and 87 percent for the turbine,
determine (a) the air temperature at the turbine exit, (b) the net work output, and (c)
the thermal efficiency.
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
For
two-stage
compression
and
expansion, the work input is minimized
and the work output is maximized when
both stages of the compressor and the
turbine have the same pressure ratio.
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
A Brayton cycle with regeneration using air as the working fluid has a pressure ratio
of 7. The minimum and maximum temperatures in the cycle are 310 and 1150 K.
Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent
for the turbine and an effectiveness of 65 percent for the regenerator, determine (a)
the air temperature at the turbine exit, (b) the net work output, and (c) the thermal
efficiency.
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
A gas turbine for an automobile is designed with a regenerator. Air enters the
compressor of this engine at 100 kPa and 30oC. The compressor pressure ratio is
10; the maximum cycle temperature is 800oC; and the cold air stream leaves the
regenerator 10oC cooler than the hot air stream at the inlet of the regenerator.
Assuming both the compressor and the turbine to be isentropic, determine the rates
of heat addition and rejection for this cycle when it produces 115 kW. Use constant
specific heats at room temperature.
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
A gas-turbine power plant operates on a modified Brayton cycle shown in the figure with an
overall pressure ratio of 8. Air enters the compressor at 0oC and 100 kPa. The maximum cycle
temperature is 1500 K. The compressor and the turbines are isentropic. The high pressure
turbine develops just enough power to run the compressor. The pressure at the exit of high
pressure turbine is 457 kPa.
Assume constant properties for air at 300 K with cv = 0.718 kJ/kgK, cp = 1.005 kJ/kgK, R =
0.287 kJ/kgK, k = 1.4.
(a) Sketch the T-s diagram for the cycle. Label the data states.
(b) If the net power output is 200 MW, determine mass flow rate of the air, in kg/s.
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
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THE BRAYTON CYCLE WITH
INTERCOOLING, REHEATING, AND
REGENERATION
Air enters the compressor of a regenerative gas turbine engine at 310 K and 100 kPa, where it
is compressed to 900 kPa and 650 K. The amount of heat transfer in the regenerator is 193
kJ/kg, and the air enters the turbine at 1400 K. For a turbine efficiency of 90 percent,
determine the thermal efficiency. Assume variable specific heats for air.
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IDEAL JET-PROPULSION CYCLES
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Turbojet Engines
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Turbojet Engines
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Thank you!
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