Page 114 - Advanced Gas Turbine Cycles

Chapter 6. ‘Wet’ gas turbine plants 87

In an experiment to determine the calorific value of the fuel at temperature To, and for
the same fuel flow the steady flow energy equation would yield
ha0 +.ho =f[cvlo + (1 +f)hg~. (6.2)
Subtracting Eq. (6.2) from Eq. (6.1) yields

ha2 - ha0 +f[cVl~ = (1 +f)(hg3 - hg~) + S(h,, - kh). (6.3)
If the compressor entry temperature TI is the same as the ambient temperature To then
Eq. (6.3) may be rewritten as
(h,2 - hall +f[CVI” =(I +f)[(hg3 - hg4) + (hg4 - hgs) + (hgs - hgoll
(6.3a)
+ S[(h,, - h,) + (44 - 4s) + (h,S - h\6)1.
But across the HRSG the heat balance is

(1 +f)[(hg4 - hgs) + S(h4 - h.1s)l = S(h,, - ~Ud, (6.4)
in which the pumping work for the water is ignored, and the water enters at ambient
temperature with enthalpy hWo.
Combining this equation with Eq. (6.3a) yields the final energy equation for the whole
plant as
f[cv]o = (WT - WC) + 1 +f)(hg5 - hg0) + S(h55 - hw0>17 (6.5)
in which the terms in brackets correspond to the three terms in Lloyd’s closed cycle
analysis, QB, W, QA, respectively, and
QB = W+ QA. (6.6)
The overall efficiency of the plant is

77 = (WT - wC)/f[cvlO
= { 1 +f][hg3 - hg41 + Ih.1, - hd - [hd2 - hail )lf[cvlo. (6.7)

so that

by analogy with the form given by Lloyd,

77 = W/QB = [I + (QA/~)]-’. (6.9)
Lloyd argues that for a plant with fixed pressure ratio and top temperature, the turbine
work output (and hence the net work output) is increased linearly with the steam quantity S
that is injected, but the QB and QA terms increase more slowly. Thus, the efficiency
similarly increases with S, but also more slowly.
Fig. 6.3, which gives illustrative plots of temperature against the fraction of heat
transferred, shows how the HRSG performs, first at low S (Fig. 6.3a), and then with higher
(optimum) S (Fig. 6.3b). Lloyd concludes that maximum efficiency is reached when