Page 100 - Advanced Gas Turbine Cycles

Chapter 5. Full calculations of plant eficiency 75

the arbitrary assumptions made in Chapter 4 for the calculations to illustrate the changes in
thermal efficiency for gas turbine plants in which single-step cooling is introduced.
The cooling fraction obviously increases with combustion temperature, but the
compressor pressure ratio (and hence the cooling air temperature T2) is also critically
important. It is seen that the arbitrary assumptions made for I/, in Chapter 4 (linearly
increasing with the combustion temperature T,,, = T3) would be approximately valid for a
cycle with a pressure ratio just below 30.

5.4. Single step cooling
The results of a set of computer calculations for a CBT plant with single-step cooling
(i.e. of the first stage nozzle guide vanes) are illustrated in Fig. 5.2, in the form of
(arbitrary) overall thermal efficiency (70) against pressure ratio (r) with the combustion
temperature T,,, as a parameter, and in Fig. 5.3 as 70 against T,, with r as a parameter.
Young's computer code [4] was used for these efficiency calculations. It involves an
assumption that the mainstream gas is expanded through a nominal (small) pressure ratio,
mixed with cooling air at compressor delivery conditions and this mixed gas then
expanded through the full turbine pressure ratio. Within the calculations, the values of I/,
given in Fig. 5.1 were also used to derive the extra stagnation pressure loss associated with
mixing (as described in Section 4.3.2.2 leading to Eq. (4.47), with the empirical constant K
taken as 0.07). This extra stagnation pressure loss was added to the assumed stagnation
pressure loss in combustion, (Apo/po)cc = 0.03.
Fig. 5.2 shows that for the single-step cooled CBT plant at a given combustion
temperature, the overall efficiency of the cooled gas turbine efficiency increases with
pressure ratio initially but, compared with an uncooled cycle, reaches a maximum at a
lower optimum pressure ratio. Fig. 5.3 shows that for a given pressure ratio the efficiency
generally increases with the combustion temperature T,,, even though the required cooling
fraction increases.
Fig. 5.4 shows a carpet plot of overall efficiency against specific work for the cooled
[CBTIIcl plant (single step) with pressure ratio and combustion temperature as
parameters. As shown earlier, by the preliminary air standard analysis and the subsequent
calculations in Chapter 4, there are relatively minor changes of thermal efficiency
compared with the uncooled plant [CBTIIUc, but there is a major effect in the reduction of
specific work.

5.5. Multi-stage cooling

At very high combustion temperatures, it is not sufficient that the first blade row alone
needs to be cooled. In practice, up to half a dozen rows may be cooled in an industrial gas
turbine, if the combustion temperature is high and the allowable blade metal temperature is
low. The cooling fractions for each of the cooled rows must be estimated and used in the
cycle calculations, which now become complex.
Illustrations of such calculations, for an open cycle [CBTIIC3 plant, were given by
Horlock et al. [2], in which it was assumed that three blade rows were film cooled, the two