ME # 804466-4
Power Plants
Dr. Kamel Mohamed Guedri
Mechanical Engineering Department, The College of Engineering and Islamic Architecture,
Umm Al-Qura University, Room 1091
1
Gas-turbine Power Cycles
Chapter 3
2
3
Brayton Cycle: Ideal Cycle for Gas-Turbine Engines
Gas turbines usually operate on an open cycle (Fig. 6-1).
Air at ambient conditions is drawn into the compressor, where its
temperature and pressure are raised. The high pressure air proceeds into the
combustion chamber, where the fuel is burned at constant pressure.
The high-temperature gases then
enter the turbine where they
expand to atmospheric pressure
while producing power output.
Some of the output power is used
to drive the compressor.
The exhaust gases leaving the
turbine are thrown out (not re-
circulated), causing the cycle to be classified as an open cycle.
(Fig. 6-1
4
The open gas-turbine cycle can
be modelled as a closed cycle,
using the air-standard
assumptions (Fig. 6-2).
The compression and expansion
processes remain the same, but
the combustion process is
replaced by a constant-pressure
heat addition process from an
external source.
The exhaust process is replaced
by a constant-pressure heat
rejection process to the ambient
air.
Closed Cycle Model
(Fig. 6-2
5
The ideal cycle that the working fluid
undergoes in the closed loop is the
Brayton cycle. It is made up of four
internally reversible processes:
1-2 Isentropic compression;
2-3 Constant-pressure heat addition;
3-4 Isentropic expansion;
4-1 Constant-pressure heat rejection.
The T-s and P-v diagrams of an ideal
Brayton cycle are shown in Fig. 6-3.
Note: All four processes of the Brayton
cycle are executed in steady-flow devices
thus, they should be analyzed as steady-
flow processes.
The Brayton Cycle
(Fig. 6-3
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Both Rankine and Brayton Cycles
(Two isobaric processes)
+ (Two isentropic processes)
Two phase : Rankine cycle Steam Power Plant
Single phase : Brayton cycle Gas Turbine
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Thermal Efficiency
The energy balance for a steady-flow process
can be expressed, on a unitmass basis, as
The heat transfers to and from the working fluid
are:
The thermal efficiency of the ideal Brayton cycle,
is the pressure ratio. where
Constant specific heats
Example 6.1
In an air-standard Brayton cycle the air enters the compressor
at 0.1 MPa, 15C. The pressure leaving the compressor is 1.0
MPa, and the maximum temperature in the cycle is 1000C.
Determine
1. The pressure and temperature at each point in the cycle\
2. The compressor work, turbine work, and cycle efficiency
Solution of Example 6.1
For each of the control volumes analyzed, the model is ideal gas
with constant specific heat, value at 300 K, and each process is
SSSF with no kinetic or potential energy changes.
Control volume: Compressor
Inlet state: P1, T1 known; state fixed.
Exit state: P2 known.
2 1
2 1
1
2 2
1 1
c
k
k
w h h
s s
T P
T P
Control volume: Turbine
Inlet state: P3, T3 known; state fixed.
Exit state: P4 known.
1
2
1
2
2 1 2 1
1.932
556.8
269.5 /
k
k
c p
P
P
T K
w h h C T T kJ kg
3 4
3 4
1
3 3
4 4
t
k
k
w h h
s s
T P
T P
Control volume: High-temperature heat exchange
Inlet state: state 2 fixed.
Exit state: State 3 fixed.
1
3
4
4
3 4 3 4
1.932
710.8
664.7 /
395.2 /
k
k
t p
net t c
P
P
T K
w h h C T T kJ kg
w w w kJ kg
3 2 3 2 819.3 /H pq h h C T T kJ kg
Control volume: Low-temperature heat exchange.
Inlet state: state 4 fixed.
Exit state: State 1 fixed.
4 1 4 1 424.1 /
48.2%
L p
netth
H
q h h C T T kJ kg
w
q
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Problem
A stationary gas-turbine power plant operates on a simple
ideal Brayton cycle with air as the working fluid. The air enters
the compressor at 95 kPa and 290 K and the turbine at 760
kPa and 1100 K. Heat is transferred to air at a rate of 35,000
kJ/s.
Determine the power delivered by this plant:
(a) assuming constant specific heats at room temperature,
and
(b) accounting for the variation of specific heats with
temperature.
Ideal and Actual Gas-Turbine (Brayton) Cycles
14
The thermal efficiency of an ideal
Brayton cycle depends on the pressure
ratio, rp of the gas turbine and the
specific heat ratio, k of the working
fluid.
The thermal efficiency increases with
both of these parameters, which is also
the case for actual gas turbines.
A plot of thermal efficiency versus the
pressure ratio is shown in Fig. 6-4, for
the case of k =1.4.
Parameters Affecting Thermal
Efficiency
(Fig. 6-4
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The early gas turbines (1940s to 1959s) found only limited use despite their
versatility and their ability to burn a variety of fuels, because its thermal
efficiency was only about 17%. Efforts to improve the cycle efficiency are
concentrated in three areas:
1. Increasing the turbine inlet (or firing) temperatures.
The turbine inlet temperatures have increased steadily from about 540C
(1000F) in the 1940s to 1425C (2600F) and even higher today.
2. Increasing the efficiencies of turbo-machinery components (turbines,
compressors).
The advent of computers and advanced techniques for computer-aided
design made it possible to design these components aerodynamically
with minimal losses.
3. Adding modifications to the basic cycle (intercooling, regeneration or
recuperation, and reheating).
The simple-cycle efficiencies of early gas turbines were practically
doubled by incorporating intercooling, regeneration (or recuperation), and
reheating.
Improvements of Gas Turbines Performance
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Actual Gas-Turbine Cycles
Some pressure drop occurs during the heat-
addition and heat rejection processes.
The actual work input to the compressor is
more, and the actual work output from the
turbine is less, because of irreversibilities.
Deviation of actual compressor and
turbine behavior from the idealized
isentropic behavior can be accounted
for by utilizing isentropic efficiencies
of the turbine and compressor.
Turbine:
Compressor:
(Fig. 6-5
Example 6.2
Solution of Example 6.2
Solution of Example 6.2
Example 6.3
Solution of Example 6.3
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Problem
A simple Brayton cycle using air as the working fluid has a pressure
ratio of 8. The minimum and maximum temperatures in the cycle are
310 K and 1160 K, respectively. Assuming an isentropic efficiency of 75
percent for the compressor and 82 percent for the turbine, determine:
(a) the air temperature at the turbine exit,
(b) the net work output, and
(c) the thermal efficiency.
Assume variable specific heats conditions.
Ideal and Actual Gas-Turbine (Brayton) Cycles
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Problem
Air enters the compressor of a gas-turbine engine at 300 K and 100
kPa, where it is compressed to 700 kPa and 580 K. Heat is transferred
to air in the amount of 950 kJ/kg before it enters the turbine.
For a turbine efficiency of 86 percent, determine:
(a) the fraction of turbine work output used to drive the
compressor,
(b) the thermal efficiency.
Assume:
(a) variable specific heats for air.
(b) constant specific heats at 300 K.
Ideal and Actual Gas-Turbine (Brayton) Cycles
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Brayton Cycle With Regeneration Temperature of the exhaust gas leaving the turbine
is higher than the temperature of the air leaving the
compressor.
The air leaving the compressor can be heated by
the hot exhaust gases in a counter-flow heat
exchanger (a regenerator or recuperator) a process called regeneration (Fig. 6-6 & Fig. 6-4).
The thermal efficiency of the Brayton cycle
increases due to regeneration since less fuel is
used for the same work output.
Note:
The use of a regenerator is
recommended only when the
turbine exhaust temperature is
higher than the compressor
exit temperature.
(Fig. 6-6
(Fig. 6-7
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Effectiveness of the regenerator,
Effectiveness under cold-air standard assumptions,
Thermal efficiency under cold-air standard assumptions,
Effectiveness of the Regenerator
Assuming the regenerator is well insulated and changes in kinetic and
potential energies are negligible, the actual and maximum heat transfers
from the exhaust gases to the air can be expressed as
(Fig. 6-7
Example 6.4
Solution of Example 6.4
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Problem
Air enters the compressor of a regenerative gas-turbine engine
at 300 K and 100 kPa, where it is compressed to 800 kPa and
580 K. The regenerator has an effectiveness of 72 percent, and
the air enters the turbine at 1200 K.
For a turbine efficiency of 86 percent, determine:
(a) the amount of heat transfer in the regenerator, and
(b) the thermal efficiency.
Assume variable specific heats for air.
Answers: (a) 152.5 kJ/kg, (b) 36.0 percent
Brayton Cycles with Regeneration
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Problem
The 7FA gas turbine manufactured by General Electric is reported
to have an efficiency of 35.9 percent in the simple-cycle mode and
to produce 159 MW of net power. The pressure ratio is 14.7 and
the turbine inlet temperature is 1288C. The mass flow rate
through the turbine is 1,536,000 kg/h.
Taking the ambient conditions to be 20C and 100 kPa, determine:
(a) the isentropic efficiency of the turbine and the compressor,
(b) the thermal efficiency of this gas turbine if a regenerator
with an effectiveness of 80 percent is added.
Assume constant specific heats at 300 K.
Brayton Cycles with Regeneration
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Problem
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 respectively.
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.
Answers: (a) 783 K, (b) 108.1 kJ/kg, (c) 22.5 percent
Brayton Cycles with Regeneration
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Thermal efficiency of Brayton cycle with regeneration depends on:
a) ratio of the minimum to maximum temperatures, and
b) the pressure ratio.
Regeneration is most effective at lower pressure ratios and small minimum-to-maximum temperature ratios.
Factors Affecting Thermal Efficiency
(Fig. 6-8
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Brayton Cycle With Intercooling, Reheating, & Regeneration
The net work output of a gas-turbine cycle can be
increased by either:
a) decreasing the compressor work, or
b) increasing the turbine work, or
c) both.
The compressor work input can be decreased by
carrying out the compression process in stages
and cooling the gas in between (Fig. 9-9), using
multistage compression with intercooling.
The work output of a turbine can be
increased by expanding the gas in stages and
reheating it in between, utilizing a multistage
expansion with reheating.
(Fig. 6-9
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Physical arrangement of an ideal two-stage
gas-turbine cycle with intercooling, reheating,
and regeneration is shown in Fig. 9-10.
(Fig. 6-10
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The work input to a two-stage compressor is minimized when equal
pressure ratios are maintained across each stage. This procedure also
maximizes the turbine work output.
Thus, for best performance we have,
Conditions for Best Performance
Intercooling and reheating always
decreases thermal efficiency unless
are accompanied by regeneration.
Therefore, in gas turbine power
plants, intercooling and reheating are
always used in conjunction with
regeneration.
(Fig. 6-11
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Example 6.5 Brayton Cycle with Intercooling, Reheating, and Regeneration
A regenerative gas turbine with intercooling and reheat operates at steady state.
Air enters the compressor at 100 kPa, 300 K with a mass flow rate of
5.807kg/s. The pressure ratio across the two-stage compressor is 10.
The pressure ratio across the two-stage turbine is also 10. The
intercooler and reheater each operate at 300 kPa. At the inlets to the
turbine stages, the temperature is 1400 K. The temperature at the
inlet to the second compressor stage is 300 K. The isentropic
efficiency of each compressor and turbine stage is 80%. The
regenerator effectiveness is 80%.
Determine
a) The thermal efficiency
b) The net power developed (kW)
c) The back work ratio
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Solution of Example 6.5 Step 1: Draw a diagram to represent the system
To better visualize what is happening during
the cycle we can draw a T-s process diagram.
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Solution of Example 6.5 Step 2: Prepare a property table Step 3: State your assumptions
Assumptions:
1) ke, pe 0
2) air-standard assumptions are applicable
3) air is an ideal gas with constant specific
heats at room temperature
4) SSSF
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
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Solution of Example 6.5 Step 4: Calculation
Step 5: Concluding remarks and Discussion
49
Example 6.6
Consider an ideal gas-turbine cycle with two stages of
compression and two stages of expansion. The pressure ratio
across each stage of the compressor and turbine is 3. The air
enters each stage of the compressor at 300 K and each stage
of the turbine at 1200 K. Determine:
(a) the back work ratio, and
(b) the thermal efficiency of the cycle
assuming:
(I) no regenerator is used, and
(II) a regenerator with 75 percent effectiveness is used.
Use a variable specific heats assumption.
Brayton Cycle with Intercooling, Reheating, and Regeneration
50
Solution of Example 6.6
51
Solution of Example 6.6
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Solution of Example 6.6
53
Problem
Consider a regenerative gas-turbine 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
net power output of 110 MW.
Answer: 250 kg/s.
Brayton Cycle with Intercooling, Reheating, and Regeneration
Second-law Analysis of Gas Power Cycles
The exergy destruction for a closed system can be expressed as
A similar relation for steady-flow systems can be expressed, in rate form, as
On a unitmass basis, for a one-inlet, one-exit steady-flow device,
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The ideal Otto, Diesel, and Brayton cycles may involve irreversibilities
external to the system. A second-law analysis of these cycles will reveal
where the largest irreversibilities occur and where to start the improvements.
Exergy
Destruction!
The exergy destruction of a cycle
is the sum of the exergy
destructions of the processes that
compose that cycle.
It depends on the magnitude of the
heat transfer with the high- and
low-temperature reservoirs
involved and on their
temperatures.
For a cycle that involves heat transfer
only with a source at TH and a sink at TL,
the exergy destruction becomes
Closed system,
Flow stream, 55
Exergy of
56
Problem
A gas-turbine power plant operates on the simple Brayton cycle
between the pressure limits of 100 and 700 kPa. Air enters the
compressor at 30C at a rate of 12.6 kg/s and leaves at 260C. A
diesel fuel with a heating value of 42,000 kJ/kg is burned in the
combustion chamber with an airfuel ratio of 60 and a combustion efficiency of 97 percent. Combustion gases leave the combustion
chamber and enter the turbine whose isentropic efficiency is 85
percent.
Treating the combustion gases as air and using constant specific
heats at 500C, determine:
(a) the isentropic efficiency of the compressor,
(b) the net power output and the back work ratio,
(c) the thermal efficiency, and
(d) the second-law efficiency.
Second-Law Analysis of Gas Power Cycles
The End
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