Page 76 - Advanced Gas Turbine Cycles

52 Advanced gas turbine cycles

T 3 T 3
TB

1 TA 1

compression of & from I to 7). An equivalent cycle of mass flow (1 + &) through the
states [ 1,2,5,6] is thus produced, with the state 5 formed after mixing of (unit) heated gas at
temperature T3 with cooling air (CIH at temperature T2. But the efficiency of that cycle
[ 1,2,5,6] is the same as that of the original uncooled cycle [ 1,2,3,4], with a unit mass flow.
Thus, the original conclusion that single step cooling does not change the efficiency of a
reversible simple cycle [cHT]R", is extended; two step cooling, with air abstracted from
the compressor at the appropriate pressure, also does not change the thermal efficiency,

(r))RC? = [1 - (l/x)l = (r))RU- (4.9)
However, it is important to note that this conclusion becomes invalid if the air for cooling
the LP turbine is taken from compressor delivery (as in Fig. 4.3b) and then throttled at
constant temperature (T2 = T7t) to the lower pressure before being mixed with the gas
leaving the HP turbine. The thermal efficiency drops as another internal irreversibility is
introduced; it can be shown [5] that
($RC?T = (TJ)~)RU - [~(xH - l)l48 - 4. (4.10)
The drop in thermal efficiency due to throttling the LP air is very small. For example, a
cycle [cHT]Rcz with a pressure ratio of r = 36.27 (x = 2.79) has a thermal efficiency of
(7))~~2 (r))~" = 0.642. For the cycle [CHT]RC~T with I+~L 0.05 and XH = 1.22, 8 = 6,
=
=
the second term in Eq. (4.10) is only 0.003, i.e. the thermal efficiency drops from 0.642 to
(T)RCZT = 0.639.
4.2.1.3. Cycle [CHTIRcM with multi-step cooling
The argument developed in Section 4.2.1.2 can be extended for three or more steps of
cooling, to give the same efficiency as the uncooled cycle. Indeed the efficiency will be the
same for multi-step cooling, with infinitesimal amounts of air abstracted at an
infinite number of points along the compressor to cool each infinitesimal turbine stage
at the required pressures.