Page 47 - Advanced Gas Turbine Cycles

24 Advanced gas turbine cycles

where ho and so are the specific enthalpy and specific entropy at the ambient pressure po
and the temperature To, respectively. For a semi-perfect gas withp = pRT and cp = cp(T),

(2.44)

s - so = 4 - R ln@/po), (2.45)
T
b - bo = [ - cpdT - To+ + RTo ln(plpo), (2.46)

2.6. The work output and ratiom- rfficiency of an open c-dt gas turbine

The statements on work output made for a real process (Eq. (2.23)) and for the ideal
chemical reaction or combustion process at @o. To) (Eq. (2.37)) can be compared as

(2.47)

The first equation may be applied to a control volume CV surrounding a gas turbine
power plant, receiving reactants at state R, Ro and discharging products at state Py =
P4. As for the combustion process, we may subtract the steady flow availability function
for the equilibrium product state (GPO) from each side of Eq. (2.47) to give

This equation, as illustrated in the (T, s) chart of Fig. 2.8 for an open circuit gas turbine,
shows how the maximum possible work output from the ideal combustion process splits
into the various terms on the right-hand side:
0 the actual work output from the open circuit gas turbine plant;
0 the work potential of any heat transferred out from various components, which
if transferred to the atmosphere at To, becomes the work lost due to external irrever-
sibility, gW = ZEm;
0 the work lost due to internal irreversibility, ZcR (which may occur in various
components);
0 the work potential of the discharged exhaust gases, (Bp4 - GPO).
Note that in Eq. (2.49) the term (BRX - GRO) does not appear as it has been assumed
here that all reactants enter at the ambient temperature TO, for which [-AGO] is known. For
a compressed gaseous fuel, (BM - GRO) will be small but not entirely negligible.