Page 62 - Advanced Gas Turbine Cycles

38 Advanced gas turbine cycles

T

1

S
Fig. 3.10. T,s diagram for irreversible closed recuperative cycle [CHTII.

and the thermal efficiency is

7 = (a[l - (l/x)] - (x - l)}/{Ecr[l - (l/x)] + (1 - E)(B - x)], (3.23)

Optimum conditions and graphical plot
The isentropic temperature ratio for maximum efficiency (x,) is again obtained by
writing a~/ax = 0; after some algebra this yields

A'(x,)~ + B'x, + d = 0, (3.24)
where

A' = (1 - &)(a - p + 11, B' = -2Nl - E), c' = ~.[p E@ + l)].
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For the [CHTXII plant, with the cycle parameters quoted above for the [CHTII plant:
(i) with E = 0.5, the values of x for maximum efficiency and maximum work become
identical, x, = x, = allz = 1.697 and 7 = 0.337;
(ii) with E = 0.75, x, = 1.506, x, = 1.697, and 7 = 0.385.
For their graphical interpretation, Hawthorne and Davis wrote

NDHT = q/[cp(T3 - Ti )I = E(NDNW) + [AI, (3.25)
where [A] = [(2~ - 1)NDCW + (1 - E)], and the efficiency as
7 = NDNW/NDHT = {E + ([A]/NDNW))-'. (3.26)

The graphical representation is not as simple as that for the [CHTII cycle, but still
informative. It is also shown in Fig. 3.8, which gives a plot of the [CHTXII efficiency
against x for the parameters specified earlier, and for E = 0.75. The term in the square