Solução Fundamento Da Termodinâmica Ed 8

12.1

Is a Brayton cycle the same as a Carnot cycle? Name the four processes.

No. The Brayton cycle approximates a gas turbine.

1-2:

2-3:

3-4:

4-1:

An isentropic compression (constant s)

An isobaric heating (constant P)

An isentropic expansion (constant s)

An isobaric cooling, heat rejection (constant P)

Compressor

Combustor

Turbine

Heat exchanger

Comment: This cycle is the same as the Rankine cycle 4 processes, but it takes

place in the ideal gas region of states. The last process does not exist

in the real gas turbine which is an open cycle.

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Borgnakke and Sonntag

12.2

Why is the back work ratio in the Brayton cycle much higher than in the Rankine

cycle?

Recall the expression for shaft work in a steady flow device

w = − ⌠ v dP

⌡

The specific volume in the compressor is not so much smaller than the

specific volume in the turbine of the Brayton cycle as it is in the pump

(liquid) compared to turbine (superheated vapor) in the Rankine cycle.

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Borgnakke and Sonntag

12.3

For a given Brayton cycle the cold air approximation gave a formula for the

efficiency. If we use the specific heats at the average temperature for each change

in enthalpy will that give a higher or lower efficiency?

The specific heats are increasing functions of temperature. As the expression for

the efficiency is from p.477

η=1−

h4 − h1

CP 4-1 T4 − T1

=1− C

h3 − h2

P 3-2 T3 − T2

The average T from 4 to 1 is lower than the average T from 2 to 3 and therefore

the ratio of the two specific heats is lower than one yielding a higher efficiency

than the cold air approximation gives.

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Borgnakke and Sonntag

12.4

Does the efficiency of a jet engine change with altitude since the density varies?

No, just like the standard Brayton cycle the simple model performance

depends only on the compression ratio.

12.5

Why are the two turbines in Figures 12.7-8 not connected to the same shaft?

Such a configuration gives a little more flexibility in the control of the

cycle under varying loads. The two turbines would then not have to run at the

same speed for various power output levels.

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adopted. Any other reproduction or translation of this work beyond that permitted by Sections 107 or 108

of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

Borgnakke and Sonntag

12.6

Why is an air refrigeration cycle not common for a household refrigerator?

The capacity of the air cycle per mass flowing through the system is very

small compared with the vapor