Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

If the number of compression and expansion stages is increased, the ideal
gas-turbine cycle with intercooling, reheating, and regeneration approaches
the Ericsson cycle, as illustrated in Fig. 9–45, and the thermal efficiency
approaches the theoretical limit (the Carnot efficiency). However, the contri-
bution of each additional stage to the thermal efficiency is less and less, and
the use of more than two or three stages cannot be justified economically.

Chapter 9 | 519

s

T

TH,avg

TL,avg

P

= const.

P = const.

FIGURE 9–45

As the number of compression and

expansion stages increases, the gas-

turbine cycle with intercooling,

reheating, and regeneration

approaches the Ericsson cycle.

EXAMPLE 9–8 A Gas Turbine with Reheating and Intercooling

An ideal gas-turbine cycle with two stages of compression and two stages of

expansion has an overall pressure ratio of 8. Air enters each stage of the

compressor at 300 K and each stage of the turbine at 1300 K. Determine

the back work ratio and the thermal efficiency of this gas-turbine cycle,

assuming (a) no regenerators and (b) an ideal regenerator with 100 percent

effectiveness. Compare the results with those obtained in Example 9–5.

Solution An ideal gas-turbine cycle with two stages of compression and two

stages of expansion is considered. The back work ratio and the thermal effi-

ciency of the cycle are to be determined for the cases of no regeneration and

maximum regeneration.

Assumptions 1 Steady operating conditions exist. 2 The air-standard assump-

tions are applicable. 3 Kinetic and potential energy changes are negligible.

Analysis The T-sdiagram of the ideal gas-turbine cycle described is shown

in Fig. 9–46. We note that the cycle involves two stages of expansion, two

stages of compression, and regeneration.

For two-stage compression and expansion, the work input is minimized

and the work output is maximized when both stages of the compressor and

the turbine have the same pressure ratio. Thus,

Air enters each stage of the compressor at the same temperature, and each

stage has the same isentropic efficiency (100 percent in this case). There-

fore, the temperature (and enthalpy) of the air at the exit of each compres-

sion stage will be the same. A similar argument can be given for the turbine.

Thus,

At inlets:

At exits:

Under these conditions, the work input to each stage of the compressor will

be the same, and so will the work output from each stage of the turbine.

(a) In the absence of any regeneration, the back work ratio and the thermal

efficiency are determined by using data from Table A–17 as follows:

h 2 
404.31 kJ>kg

Pr 2 

P 2

P 1

Pr 1 
 281 1.386 2 
3.92ST 2 
403.3 K

Pr 1 
1.386

T 1 
300 KSh 1 
300.19 kJ>kg

T 2
T 4 ,¬h 2
h 4 ¬and¬T 7
T 9 ,¬h 7
h 9

T 1
T 3 ,¬h 1
h 3 ¬and¬T 6
T 8 ,¬h 6
h 8

P 2

P 1

P 4

P 3

28
2.83¬and¬

P 6

P 7

P 8

P 9

 28 
2.83

s

T, K

qprimary

qout

6

1

10

8

9

7

5

4

3

2

qreheat

1300

300

FIGURE 9–46

T-sdiagram of the gas-turbine cycle

discussed in Example 9–8.