Brayton Cycle.pdf

Brayton Cycle

Ab Hashemi

2/20/2008 Ab Hashemi 2

Brayton CycleOpen-cycle gas-turbine

Isen

trop

icco

mpr

essi

on

Constant pressure heat addition

Isentropic expansion

Constant pressure heat rejection


Brayton Cycleclosed-cycle gas turbineIs

entr

opic

com

pres

sion

Constant pressure heat addition

Isentropic expansion

Constant pressure heat rejection


T-s and P-v Diagrams


Brayton Cycle Thermal Efficiency

( ) ( ) inletexitoutinoutin hhwwqq −=−+−

( )23p23in TTchhq −=−=

( )14p14out TTchhq −=−=( )( )( )( )1TTT

1TTT1

TTcTTc

1qq1

qw

232

141

23p

14p

in

out

in

netBrayton,th

−−

−=

−−

−=−==η

( ) ( )

4

3k1k

4

3k1k

1

2

1

2

TT

PP

PP

TT

=⎟⎠

⎞⎜⎝

⎛=⎟

⎠

⎞⎜⎝

⎛=

−−

( ) k11−k

pBrayton,th r

1−=η

1

2p p

pr =

Process 1-2 and 3-4 are isentropic and P2=P3 and P4=P1, thus:

From conservation of energy (First Law):


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.A cycle for which the air-standard assumptions are applicable is frequently referred to as an air-standard cycle.


Cold-air Assumption

• 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 (25°C, or 77°F).

• When this assumption is utilized, the air-standard assumptions are called the cold-air-standard assumptions.

• A cycle for which the cold-air assumptions are applicable is frequently referred to as a cold-air cycle.


ExampleA 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 air-standard 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.


SolutionA power plant operating on the ideal Brayton cycle is considered. The compressor and turbine exit temperatures, back work ratio, and the thermal efficiency are to be determined. Assumptions:

Steady operating conditions existThe air-standard assumptions are applicableKinetic and potential energy changes are negligibleThe variation of specific heats with temperature is to be considered.

Analysis: The T-s diagram of the ideal Brayton cycle described is shown. We note that the components involved in the Brayton cycle are steady-flow devices.

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Solution (a)

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Solution (b)

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Solution (c)

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Deviations from Ideal Cycle

1a2

1s2

a

sc hh

hhww

−−

==η

s43

a43

s

at hh

hhww

−−

==η

Compressor Efficiency:

Turbine Efficiency:

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ExampleActual Gas-turbine Cycle

Assuming a compressor efficiency of 80 percent and a turbine efficiency of 85 percent for the previous example, determine (a) the back work ratio, (b) the thermal efficiency, and (c) the turbine exit temperature of the gas-turbine cycle discussed in the previous example

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Solution (a)(a) The T-s diagram of the cycle is shown in the figure. The actual

compressor work and turbine work are determined by using the definitions of compressor and turbine efficiencies:

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Solution (b)

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Solution (c)

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Gas-turbine engine with regeneratorIn 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 transferring heat to it from the hot exhaust gases in a counter-flow heat exchanger, which is also known as a regeneratoror a recuperator.

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Why Regeneration?

The thermal efficiency of the Brayton cycle increases as a result of regeneration since the portion of energy of the exhaust gasesthat is normally rejected to the surroundings is now used to preheat the air entering the combustion chamber.

This, in turn, decreases the heat input (thus fuel) requirementsfor the same net work output.

Note, however, that the use of a regenerator is recommended only when the turbine exhaust temperature is higher than the compressor exit temperature. Otherwise, heat will flow in the reverse direction (tothe exhaust gases), decreasing the efficiency. This situation is encountered ingas-turbine engines operating at very high pressure ratios.

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Gas-turbine engine with regenerator 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.

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.

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Regenerator Effectiveness

Assuming the regenerator to be well insulated and any changes in kinetic and potential energies to be negligible, the actual and maximum heat transfers from the exhaust gases to the air can be expressed as

The extent to which a regenerator approaches an ideal regenerator is called the effectiveness, ε, and is defined as

25act,regen hhq −=

242'5max,regen hhhhq −=−=

24

25

max,regen

act,regen

hhhh

qq

−−

==ε

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Cold-air Assumptions

When the cold-air-standard assumptions are utilized, it reduces to

24

25

TTTT

−−

≅ε

Under the cold-air-standard assumptions, the thermal efficiency of an ideal Braytoncycle with regeneration is:

( )( ) k1kp

3

1regen,th r

TT1 −⎟⎟⎠

⎞⎜⎜⎝

⎛−=η

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