Thermodynamics I
Gas Power Cycles
Dr.-Eng. Zayed
Al-Hamamre
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Content
Internal Combustion Engines
o Otto Cycle
o Diesel Cycle
o Dual Cycle
Gas Turbine Cycles
o Brayton Cycle
o Regenerative Gas Turbines
o Regenerative Gas Turbines with Reheat and Intercooling
o Gas Turbines for Aircraft Propulsion
o Ericsson and Stirling Cycles
Compressible flow through Nozzles and Diffusers
Combined Gas-Vapor Cycles
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Introduction
 Many work-producing devices (engines) utilize a working fluid that is always a gas.
 The spark-ignition automotive engine is a familiar example, as are the diesel engine and the
conventional gas turbine.
 In all these engines there is a change in the composition of the working fluid, because during
combustion it changes from air and fuel to combustion products.
 These engines are called internal combustion engines
 Because the working fluid does not go through a complete thermodynamic cycle in the engine
(even though the engine operates in a mechanical cycle), the internal combustion engine
operates on the so-called open cycle.
 For analyzing internal-combustion engines, the air-standard cycle approach is assumed.
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Air Standard Assumption
1. A fixed mass of air is the working fluid throughout
the entire cycle, and the air is always an ideal gas.
The combustion process is replaced by a process
transferring heat (heat-addition process) from an
external source.
2. All the processes that make up the cycle are
internally reversible.
3. The exhaust process is replaced by a heat-rejection
process that restores the working fluid to its initial
state, i.e. the cycle is completed by heat transfer to
the surroundings (in contrast to the exhaust and
intake process of an actual engine).
4. An additional assumption is often made that air has a
constant specific heat, recognizing that this is not the
most accurate model.
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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.
Intake valve
Exhaust valve
 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 is drawn into the cylinder
through the intake valve, and the combustion products
are expelled from the cylinder through the exhaust
valve.
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Reciprocating Engines
 The minimum volume formed in the cylinder when the piston is
at TDC is called the clearance volume.
 The volume displaced by the piston as it moves between TDC
and BDC is called the displacement volume
 The ratio of the maximum volume formed in the cylinder to the
minimum (clearance) volume is called the compression ratio r
of the engine
 Another term frequently used in conjunction with reciprocating engines is the mean effective
pressure (MEP).
 It 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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Reciprocating Engines
 Reciprocating engines are classified , depending on how the
combustion process in the cylinder is initiated, as
i.
Spark-ignition (SI) engines: the combustion of the
air–fuel mixture is initiated by a spark plug
 The air–fuel mixture is compressed to a temperature that is
below the autoignition temperature of the fuel, and the
combustion process is initiated by firing a spark plug
 The Otto cycle is the ideal cycle for spark-ignition
reciprocating engines.
ii.
Compression-ignition (CI) engines: the air–fuel
mixture is self-ignited as a result of compressing the
mixture above its self ignition temperature.
 The air is compressed to a temperature that is above the
autoignition temperature of the fuel, and combustion starts
on contact as the fuel is injected into this hot air
 The Diesel
cycle is the ideal cycle for CI reciprocating
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7 Reciprocating Engines
 With the intake valve open, the piston makes an intake
stroke to draw a fresh charge into the cylinder.
 With both valves closed, the piston undergoes a
compression stroke, raising the temperature and pressure
of the charge. A combustion process is then initiated,
resulting in a high-pressure, high-temperature gas
mixture.
Intake valve
Exhaust valve
 In compression-ignition engines, combustion is initiated
by injecting fuel into the hot compressed air, beginning
near the end of the compression stroke and continuing
through the first part of the expansion.
 A power stroke follows the compression stroke, during
which the gas mixture expands and work is done on the
piston as it returns to bottom dead center.
 The piston then executes an exhaust stroke in which the
burned gases
are purged
fromDepartment
the cylinder
through
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8 Otto Engine
1. Initially, both the intake and the exhaust valves are closed,
and the piston is at its lowest position (BDC).
2. During the compression stroke, the piston moves upward,
compressing the air–fuel mixture. Shortly before the piston
reaches its highest position (TDC), the spark plug fires and
the mixture ignites, increasing the pressure and temperature
of the system.
3. The high-pressure gases force the piston down, which in turn
forces the crankshaft to rotate, producing a useful work
output during the expansion or power stroke.
 At the end of this stroke, the piston is at its lowest position (the
completion of the first mechanical cycle), and the cylinder is
filled with combustion products.
 Now the piston moves upward one more time, purging the
exhaust gases through the exhaust valve (the exhaust stroke), and
down a second
time, drawing in fresh air–fuel mixture through
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intake
the intake valve
(the6 535
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9 Otto Engine
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Otto Engine
i.
Process 1–2 is an isentropic compression of the air as the piston moves from bottom dead
center to top dead center.
ii.
Process 2–3 is a constant-volume heat transfer to the air from an external source while the
piston is at top dead center. This process is intended to represent the ignition of the fuel–air
mixture and the subsequent rapid burning.
iii. Process 3–4 is an isentropic expansion (power stroke).
iv. Process 4–1 completes the cycle by a constant-volume process in which heat is rejected
from the air while the piston is at bottom dead center.
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Otto Engine
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Otto Engine
Substituting these equations into the thermal efficiency
relation and simplifying,
where
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Otto Engine
 Remember that for an adiabatic process
 For a given compression ratio, an ideal Otto cycle using a monatomic gas (such as argon or
helium, k 1.667) as the working fluid will have the highest thermal efficiency.
 The specific heat ratio k, and thus the thermal efficiency of the ideal Otto cycle, decreases as
the molecules of the working fluid get larger
 In gasoline engines, a mixture of air and fuel is
compressed during the compression stroke, and
the compression ratios are limited by the onset
of autoignition or engine knock
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Example
An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air
is at 100 kPa and 17°C, and 800 kJ/kg of heat is transferred to air during the constant-volume
heat-addition process. Accounting for the variation of specific heats of air with temperature,
determine (a) the maximum temperature and pressure that occur during the cycle, (b) the net
work output, (c) the thermal efficiency, and (d ) the mean effective pressure for the cycle.
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Example Cont.
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Example Cont.
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Example Cont.
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Diesel Cycle
 In diesel engines, only air is compressed during the compression stroke, eliminating the
possibility of autoignition.
 Therefore, diesel engines can be designed to operate at much higher compression ratios,
typically between 12 and 24.
 The fuel injection process in diesel engines starts
when the piston approaches TDC and continues
during the first part of the power stroke.
 Therefore, the combustion process in these engines
takes place over a longer interval.
 Because of this longer duration, the combustion
process in the ideal Diesel cycle is approximated as a
constant-pressure heat-addition process.
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Diesel Cycle
2-3 constant-pressure heat-addition
(includes work and heat)
 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
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Diesel Cycle
2-3 constant-pressure heat-addition (involves work and heat)
And
 Where cutoff ratio rc, is the ratio of the cylinder volumes after and before the combustion21 process: Chemical Engineering Department | University of Jordan | Amman 11942, Jordan
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Diesel Cycle
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Diesel Cycle
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Diesel Cycle
 Utilizing this definition and the isentropic ideal-gas relations
 Comparing with Otto engine,
As rc is the ratio approaching 1
=
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Diesel and Otto Cycle
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Example
An ideal Diesel cycle with air as the working fluid has a compression ratio of 18 and a cutoff
ratio of 2. At the beginning of the compression process, the working fluid is at 14.7 psia, 80°F,
and 117 in3. Utilizing the cold-airstandard assumptions, determine (a) the temperature and
pressure of air at the end of each process, (b) the net work output and the thermal efficiency, and
(c) the mean effective pressure
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Example Cont.
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Example Cont.
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Example Cont.
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Example Cont.
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Dual Cycle
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Dual Cycle
During the isentropic compression process 1–2 there is no heat
transfer, and the work is
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Dual Cycle
the constant-volume heat rejection process 5–1 that completes the cycle involves heat transfer but
no work
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Striling and Ericsson Cycles
 Stirling cycle
•
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)
 Both cycles are totally reversible,
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Striling and Ericsson Cycles
 The Stirling and Ericsson cycles give a
message: Regeneration can increase efficiency.
 The Ericsson cycle is very much like the
Stirling cycle, except that the two
constant-volume processes are replaced
by two constant-pressure processes.
A steady-flow Ericsson engine.
The execution of the Stirling cycle.
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35
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Example
Using an ideal gas as the working fluid, show that the thermal efficiency of an Ericsson cycle is
identical to the efficiency of a Carnot cycle operating between the same temperature limits.
For a reversible isothermal
process, heat transfer is
The entropy change of an ideal gas during
an isothermal process
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Brayton Cycle for Modeling Gas Turbine Power Plants
 Brayton Cycle is the ideal cycle for modeling gas turbine power plants.
 It is used for gas turbines only where both the compression and expansion processes take
place in rotating machinery
Constant-pressure
heat-addition
Constant-pressure
heat-removal
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Brayton Cycle for Modeling Gas Turbine Power Plants
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Brayton Cycle for Modeling Gas Turbine Power Plants
Assuming the turbine operates adiabatically and with negligible effects of kinetic and potential
energy, the work developed per unit of mass is
compressor work per unit of mass is
The heat added to the cycle per unit of mass is
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Brayton Cycle for Modeling Gas Turbine Power Plants
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Brayton Cycle for Modeling Gas Turbine Power Plants
 For the same pressure rise, a gas turbine compressor would require a much greater work input
per unit of mass flow than the pump of a vapor power plant because the average specific
volume of the gas flowing through the compressor would be many times greater than that of
the liquid passing through the pump
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Brayton Cycle for Modeling Gas Turbine Power Plants
 For fixed values of Tmin and Tmax, the net
work of the Brayton cycle first increases
with the pressure ratio, then reaches a
maximum at rp = (Tmax/Tmin)k/[2(k - 1)], and
finally decreases.
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Brayton Cycle for Modeling Gas Turbine Power Plants
 The highest temperature in the cycle 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.
 The air in gas turbines supplies the necessary oxidant for the combustion of the fuel, and 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.
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Example
Gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas
temperature is 300 K at the compressor inlet and 1300 K at the turbine inlet. Utilizing the airstandard assumptions, determine (a) the gas temperature at the exits of the compressor and the
turbine, (b) the back work ratio, and (c) the thermal efficiency.
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Example Cont.
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Example Cont.
OR
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Example Cont.
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Development of Gas Turbines
 Increasing the turbine inlet (or firing) temperatures
 Increasing the efficiencies of turbomachinery components (turbines, compressors):
 Adding modifications to the basic cycle (intercooling, regeneration or recuperation, and
reheating).
Deviation of Actual Gas-Turbine
Cycles from Idealized Ones
 Reasons: Irreversibilities in turbine and
compressors, pressure drops, heat losses
 Isentropic efficiencies of the compressor
and turbine
The deviation of an actual gasturbine cycle from the ideal
Brayton cycle as a result of
irreversibilities.
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48 THE BRAYTON CYCLE 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.
 Therefore, the high-pressure air leaving the compressor can
be heated by the hot exhaust gases in a counter-flow heat
exchanger (a regenerator or a recuperator).
 The thermal efficiency of the Brayton cycle increases as a
result of regeneration since less fuel is used for the same work
output.
A gas-turbine engine with regenerator.
T-s diagram of a Brayton
cycle with regeneration.
 In the limiting (ideal)
case, the air exits the
regenerator at the
inlet temperature of
the exhaust gases
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THE BRAYTON CYCLE WITH REGENERATION
Effectiveness of
regenerator
Effectiveness under cold-air
standard assumptions
Under cold-air standard
assumptions
T-s diagram of a Brayton
cycle with regeneration.
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.
Thermal efficiency of
the ideal Brayton
cycle with and without
regeneration.
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50 THE BRAYTON CYCLE WITH INTERCOOLING, REHEATING, AND
REGENERATION
For minimizing work input to
compressor and maximizing
work output from turbine:
A gas-turbine engine with two-stage compression with
intercooling, two-stage expansion with reheating, and
regeneration and its T-s diagram.
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THE BRAYTON CYCLE WITH INTERCOOLING, REHEATING, AND
REGENERATION
 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.
 Multistage expansion with reheating keeps the specific volume of the working fluid as high as
possible during an expansion process, thus maximizing work output.
 Intercooling and reheating always decreases the thermal efficiency unless they are
accompanied by regeneration. Why?
Comparison of work
inputs to a single-stage
compressor (1AC) and a
two-stage compressor
with intercooling
(1ABD).
As the number of compression and expansion
stages increases, the gas-turbine cycle with
52 intercooling, reheating, and regeneration
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Jordanthe Ericsson cycle.
approaches
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IDEAL JET-PROPULSION CYCLES
 Gas-turbine engines are widely used to power aircraft because they are light and compact and
have a high power-to-weight ratio.
 Aircraft gas turbines operate on an open cycle called a jet-propulsion cycle.
 The ideal jet-propulsion cycle differs from the simple ideal Brayton cycle in that the gases are
not expanded to the ambient pressure in the turbine. Instead, they are expanded to a pressure
such that the power produced by the turbine is just sufficient to drive the compressor and the
auxiliary equipment.
 The net work output of a jet-propulsion cycle is zero. The gases that exit the turbine at a
relatively high pressure are subsequently accelerated in a nozzle to provide the thrust to propel
the aircraft.
 Aircraft are propelled by accelerating a fluid in the opposite direction to motion. This is
accomplished by either slightly accelerating a large mass of fluid (propeller-driven engine)
or greatly accelerating a small mass of fluid (jet or turbojet engine) or both (turboprop
engine).
In jet engines, the high-temperature and highpressure gases leaving the turbine are
accelerated in a nozzle to provide thrust.
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IDEAL JET-PROPULSION CYCLES
Thrust (propulsive force)
Propulsive power
Propulsive efficiency
Propulsive power is the thrust acting on the
aircraft through a distance per unit time.
Basic components of a turbojet engine and the T-s diagram for the ideal turbojet cycle.
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54 Combined Gas-Vapor Cycles
 A gas power cycle topping a vapor power cycle, which is called the combined gas–vapor
cycle, or just the combined cycle
 The combined cycle of greatest interest is the gas-turbine (Brayton) cycle topping a steam
turbine (Rankine) cycle.
 The modified cycle has a higher thermal efficiency than either of the cycles executed
individually
 Gas-turbine cycles typically operate at considerably higher temperatures than steam cycles.
 The maximum fluid temperature at the turbine inlet is about 620°C for modern steam power
plants, but over 1425°C for gas-turbine power plants.
 Gas-turbine cycles have a greater potential for higher thermal efficiencies.
 However, the gas-turbine cycles have one inherent disadvantage: The gas leaves the gas
turbine at very high temperatures (usually above 500°C), which erases any potential gains in
the thermal efficiency.
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Combined Gas-Vapor Cycles
 The efficiency can be modified by using the high temperature exhaust gases as the energy
source for the bottoming cycle such as a steam power cycle.
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Example
Consider the combined gas–steam power cycle
shown. The topping cycle is a gas-turbine cycle
that has a pressure ratio of 8. Air enters the
compressor at 300 K and the turbine at 1300 K.
The isentropic efficiency of the compressor is 80
percent, and that of the gas turbine is 85 percent.
The bottoming cycle is a simple ideal Rankine
cycle operating between the pressure limits of 7
MPa and 5 kPa. Steam is heated in a heat
exchanger by the exhaust gases to a temperature of
500°C. The exhaust gases leave the heat exchanger
at 450 K. Determine (a) the ratio of the mass flow
rates of the steam and the combustion gases and (b)
the thermal efficiency of the combined cycle.
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Example Cont.
Energy balance on the heat exchanger:
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Example Cont.
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