Page 120 - Advanced Gas Turbine Cycles

92 Advanced gas turbine cycles

T

I
S
Fig. 6.6. Temperature-entropy diagram for dry [CHTIIXR plant.
cycle they then concluded the turbine work (WT) to be equal to the heat supplied (eB)
so
the efficiency becomes
7 = w/& = (w~ wc)/w~ = 1 - (wc/w~). (6.17)
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Note also that the heat rejected is equal to the compressor work in this case. For this air
standard cycle with constant specific heats, Eq. (6.17) reduces simply to
q = 1 - (x/a), (6.18a)
where a = qc%(T3/Tl), x = r(y-lyy and qc and are isentropic efficiencies.
Consider next a similar recuperative cycle, but one in which the compression process
approximates to isothermal rather than isentropic, with the work input equal to the heat
rejected (this may be achieved in a series of small compressions of polytropic efficiency
qp, followed by a series of constant pressure heat rejections). It may then be shown that the
thermal efficiency of this cycle is given by
77 = 1 - (In #,qe(i - 4-lR>]), (6.18b)
where 6 = T3/TI, 4 = r" and (+= (y - 1)/-yqP. This cycle is more efficient than the
[CBT]& cycle, and this will be important when we consider its evaporative version later
(the TOPHAT or van Liere cycle).
For the (CICBT)IXR, (CBCBT)rXR and (CICBTBT)IXR cycles, with equal pressure
ratios across the 'split' compressors and turbines, it may be shown that the corresponding
expressions for efficiency are
q = 1 - &/a(x'" + 1), (6.18~)
q = 1 - (x'n + x)/2a, (6.18d)
I"
q= 1 -x /a, (6.18e)
respectively, indicating that the efficiency increases with a in each of these cycles.
The thermal efficiencies (q) of these five cycles, all with perfect recuperation, are
plotted in Fig. 6.7 against the isentropic temperature ratio x, for %qc = 0.8 and T3/T1 = 5