Page 97 - Advanced Gas Turbine Cycles

Chapter 5. Full calculations of plant e$ciency 73

A new ‘temperature difference ratio’ W+ is written as

w+ = [Taw - Tbll/[Tco - Tcil

(5.10)
= [&O - (l - %~ol)&F - EOEF~cooll/r)cool(l - EO),
and it is shown in Appendix A that the cooling fraction is now given by

(5.1 1)

where
P = hf,/[h,( 1 + B)1, (5.12)

in which (hfg/hg) is the ratio of the heat transfer coefficient under film cooling conditions
(hf,) to the convectively cooled heat transfer coefficient (hg), and B = hf@ is the Biot
number, which takes account of a thermal barrier coating (TBC) of thickness t and
conductivity k. In practice, hf, increases above hg, and (1 + B) is increased as TBC is
added. For the purposes of the cycle calculations described below, p is taken as unity so
that
+=cw+, (5.13)

where C is the same constant as the one for convective cooling only.

5.2.3. Assumptions for cycle calculations

In the cycle calculations described below [2], film cooling was assumed. Further, as
described in Appendix A, various assumptions were made for the critical constants, as
follows. The constant C in Eq. (5.13) was taken as 0.045, and within W+, the cooling
efficiency cool as 0.7 and the film cooling effectiveness eF as 0.4. All were assumed to be
constant over the range of cooling flows considered.
In a particular blade row, for a given gas entry temperature Tgi, a cooling air entry
temperature Tci, and an assumed allowable blade metal temperature Tbl, the blade cooling
effectiveness EO is obtained. With EF = 0.4 and cool = 0.7, W+ then follows from
Eq. (5.10). With C = 0.045 the cooling air flow fraction + is obtained from Eq. (5.13).

53. Estimates of cooling flow fraction

The results of calculations for the cooling air flow fractions in the first (nozzle guide
vane) row of the turbine, based on the assumptions outlined in Section 5.2 for film cooled
blading, are illustrated in Fig. 5.1. The entry gas temperature Tgi was taken as the
combustion temperature Tc, = T3 and the cooling air temperature as the compressor
delivery temperature T2. The cooling air required is shown here as a fraction of the exhaust
gas flow, i.e. as +/(l + +), plotted against compressor pressure ratio and combustion
temperature for an allowable blade metal temperature, Tbl = 800°C. Also shown are