Page 32 - Advanced Gas Turbine Cycles

where T = (T&T-). 5 is then an overall measure of the failure of the real cycle to
achieve the maximum and minimum temperatures and is always less than unity (except for
the Carnot cycle, where 5 becomes unity).
Caput0 then introduced a parameter (a) which is a measure of the irreversibilities
within the real cycle. He first defined

(1.14)

which, from the definitions of T, can be seen to be the entropy changes in heat supply and
heat rejection, respectively. The parameter u is then defined as
ffB
ff= - (1.15)
CA
the ratio of entropy change in heat supply to entropy change in heat rejection. For the
Carnot cycle u is unity, but for other (irreversible) cycles, a value of u less than unity
indicates a ‘widening’ of the cycle on the T,s diagram due to irreversibilities (e.g. in
compression and/or expansion in the gas turbine cycle) and a resulting loss in thermal
efficiency.
The overall effect of these failures to achieve Carnot efficiency is then encompassed in
a new parameter, p, where
p = tu. (1.16)
The efficiency of the real cycle may then be expressed in terms of T (the ratio of
minimum to maximum temperature) and p. For

For the Carnot cycle u = 1, 8 = 1 and p = 1, so that qcAR = 1 - T.
For the JB cycle of Fig. 1.4, there is no ‘widening’ of the cycle due to irreversibilities,
so that ffA = ffB and u = 1. The efficiency then is given by
7
q= 1 - - < qcm = 1 - 7, (1.18)
5
and the failure to reach Carnot cycle efficiency is entirely due to non-achievement of T,,
and/or T~,,. pis less than unity, so q < qCm.
For an irreversible gas turbine cycle (the irreversible Joule-Brayton (LTB) cycle of
is
Fig. 1.9), ffA > ffB (a less than unity) and 5 < 1 so that the thermal efficiency is
T
q= 1 - 7 = 1 - G. (1.19)

1.5. Modifications of gas turbine cycles to achieve higher thermal efficiency

There are several modifications to the basic gas turbine cycle that may be introduced to
raise thermal efficiency.