Page 84 - Advanced Gas Turbine Cycles

60 Advanced gas turbine cycles

determined so that computer calculations for ‘real’ plants can be made. Here we continue
to assume that the cooling fraction is known, but use a computer code based on real gas
data to undertake parametric estimates of plant performance (the code developed by
Young [ 111 was employed, as in Chapter 3 for uncooled cycles).
We concentrate here on open loop cooling in which compressor air mixes with the
mainstream after cooling the blade row, the system most widely used in gas turbine plants
(but note that a brief reference to closed loop steam cooling in combined cycles is made
later, in Chapter 7). For a gas turbine blade row, such as the stationary entry nozzle guide
vane row where most of the cooling is required, the approach first described here (called
the ‘simple’ approach) involves the following:
(a) assuming a value of +, use of the steady flow energy equation to determine the
overall change in the mainstream flow temperature from combustion temperature to
rotor inlet temperature;
(b) determining the magnitude of the stagnation pressure drop involved in the process
(which is also dependent on the magnitude of +).
From (a) and (b), the stagnation pressure and temperature can thus be calculated at exit
from the cooled row; they can then be used to study the flow through the next (rotor) row.
From there on a similar procedure may be followed (for a rotating row the relative (To),,
and (po),, replace the absolute stagnation properties). In this way, the work output from
the complete cooled turbine can be obtained for use within the cycle calculation, given the
cooling quantities +.

Young and Wilcock [7] have recently provided an alternative to this simple approach.
They also follow step (a), but rather than obtaining po as in (b) they determine the
constituent entropy increases (due to the various irreversible thermal and mixing effects).
Essentially, they determine the downstream state from the properties To and the entropy s,
rather than To and po. This approach is particularly convenient if the rational efficiency of
the plant is sought. The lost work or the irreversibility (11 = TOEAS) may be subtracted
from the ideal work [ - AGO] to obtain the actual work output and hence the rational
efficiency,

(4.37)

These two approaches may be shown to be thermodynamically equivalent and, given the
same assumptions, will lead to identical results for the state downstream of a cooled row
(if the input conditions are the same-see the published discussion of Ref. 171). But the
Young and Wilcock method gives a fuller understanding of the details of the cooling
process.
Here we first describe the ‘simple’ approach, assuming that I,/J is known, and describe
how po and To downstream of the cooled row are obtained (steps (a) and (b) above). We
then briefly describe the Young/Wilcock approach which leads to the determination and
summation of the component entropy increases, again for a given +.
We defer to Chapter 5 (and Appendix A) a description of how the required cooling
fraction + (and the heat transferred) can be obtained from heat transfer analysis, following
the work of Holland and Thake [ 121.