Ch2 - Gas Turbines

GAS TURBINES
Brayton Cycle: Ideal Cycle for Gas-Turbine Engines

Chapter Objective
To carry out first law analysis on a gas turbine plant in which the working fluid is
assumed as a perfect gas.
How a Gas Turbine Works?
• Fresh 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 resulting high-temperature gases
then enter the turbine, where they
expand to the atmospheric pressure
while producing power.
• The exhaust gases leaving the turbine
are thrown out (not re-circulated),
causing the cycle to be classified as an
open cycle.
Application
Aircraft propulsion system
Electric power generation

Introduction
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.
The fraction of the turbine work used to drive

4
the compressor is called the back work ratio.
Brayton Cycle
A closed-cycle gas-turbine engine. An open-cycle gas-turbine engine.
5
Closed Cycle Model
The open gas-turbine cycle can be
modelled as a closed cycle, using
the air-standard assumptions (Fig.
9–30).
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.
6
Brayton Cycle Closed
Therefore, the energy balance for each process of the Brayton cycle
can be expressed, on a unit mass basis, as:
7
The first-law of thermodynamic states that, for a closed system
undergoing a cycle, the net work output is equal to net heat input i.e.,
8
9
10
11
The Brayton Cycle
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 (in a
compressor);
2-3 Constant-pressure heat addition;
3-4 Isentropic expansion;
4-1 Constant-pressure heat rejection (in a
turbine).
The T-s and P-v diagrams of an ideal Brayton cycle are shown in
Figure.
Note: All four processes of the Brayton cycle are executed
in steady-flow devices thus, they should be analyzed as
steady-flow processes.
Thermal Efficiency
The energy balance for a steady-flow process can be
expressed, on a unit–mass basis, as
The heat transfers to and from the working fluid

are:
The thermal efficiency of the ideal Brayton cycle,
Constant specific heats
where is the pressure ratio.

Problem-Ideal and Actual Gas-Turbine (Brayton) Cycles
9-81 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 290 K and 1100 K,
respectively. Determine:
(a) the air temperature at the compressor exit,
(b) the back work ratio, and
(c) the thermal efficiency.
Assume variable specific heats conditions.
14
The properties of air are given in Table A-17.
15
16
9–91 An aircraft engine operates on a simple ideal Brayton

cycle with a pressure ratio of 10. Heat is added to the cycle
at a rate of 500 kW; air passes through the engine at a rate
of 1 kg/s; and the air at the beginning of the compression is
at 70 kPa and 0 °C. Determine the power produced by this
engine and its thermal efficiency. Use constant specific
heats at room temperature.
17
18
19
20
Parameters Affecting Thermal Efficiency
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 Figure,
for the case of k =1.4.
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:
9–89 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.
23
24
Improvements of Gas Turbine’s Performance
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 540°C
(1000°F) in the 1940s to 1425°C (2600°F) 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.
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. 9-38 & Fig. 9-39).
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
26 exit
temperature.
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
Effectiveness of the regenerator,
Effectiveness under cold-air standard

assumptions,
Thermal efficiency under cold-air

standard assumptions,
Problem-Brayton Cycle Regeneration
9–106 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 1288°C. The mass flow
rate through the turbine is 1,536,000 kg/h.
Taking the ambient conditions to be 30°C 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 65 percent is added.
28
29
30
Factors Affecting Thermal Efficiency
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.
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. 9-42), 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.
Regeneration
Physical arrangement of an ideal two-stage gas-turbine cycle with intercooling,
reheating, and regeneration is shown in Fig. 9-43.
33
Regeneration
Conditions for Best Performance
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,
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
34
conjunction with regeneration.
Problem-Brayton Cycle with Intercooling, Reheating, and Regeneration
9–121 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.
35
36
37

Ch2 - Gas Turbines

Uploaded by

Copyright:

Available Formats

Ch2 - Gas Turbines

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Ch2 - Gas Turbines

Uploaded by

Copyright:

Available Formats

GAS TURBINES

Brayton Cycle: Ideal Cycle for Gas-Turbine Engines

Aircraft propulsion system

Electric power generation

The fraction of the turbine work used to drive

A closed-cycle gas-turbine engine. An open-cycle gas-turbine engine.

The heat transfers to and from the working fluid

The thermal efficiency of the ideal Brayton cycle,

Constant specific heats

where is the pressure ratio.

9-81 A simple Brayton cycle using air as the working fluid

Assume variable specific heats conditions.

9–91 An aircraft engine operates on a simple ideal Brayton

The thermal efficiency of an ideal

Deviation of actual compressor and turbine

9–89 Air enters the compressor of a gas-turbine engine at

Effectiveness of the regenerator,

Effectiveness under cold-air standard

Thermal efficiency under cold-air

The compressor work input can be

The work output of a turbine can be increased by

Intercooling and reheating always decreases

9–121 Consider an ideal gas-turbine cycle with two stages of

You might also like