Page 156 - Advanced Gas Turbine Cycles

126 Advanced gas turbine cycles

As
It can be seen from Fig. 7.10 that the curve for dcp lies above that for dH. for the gas
turbine cycle the pressure ratio for maximum efficiency in the combined plant may
be obtained by drawing a tangent to the work output curve from a point on the x-axis where
x = 1 + qc(O - I), i.e. x = 4.6 in the example. The optimum pressure ratio for the
combined plant (r = 18) is less than that for the gas turbine alone (r = 30) although it is
still greater than the pressure ratio which gives maximum specific work in the higher plant
(r = 1 I). However, the efficiency qcP varies little with r about the optimum point.
It may also be noted that by differentiating Eq. (7.9) with respect to r (or x), and putting
the differential equal to zero for the maximum efficiency, it follows that

(7.34)

and

(7.35)

since (qo)H and (qo)L are little different in most cases. Hence, the maximum combined
cycle efficiency (7,1~)~~ occurs when the efficiency of the higher cycle increases with r at
about the same rate as the lower cycle decreases. Clearly, this will be at a pressure ratio
less than that at which the higher cycle reaches peak efficiency, and when the lower cycle
efficiency is decreasing because of the dropping gas turbine exit temperature.
This approach was well illustrated by Briesch et al. [14], who showed separate plots of
(T~)~, (qo)L and (qo)cp against pressure ratio for a given T,,, and Tmin (Fig. 7.1 I),
illustrating the validity of Eq. (7.35). But note that the limiting allowable steam turbine
entry temperature also influences the choice of pressure ratio in the gas turbine cycle.

7.7. Reheating in the upper gas turbine cycle

The case for supplementary heating at the gas turbine exhaust has already been
considered; Cem [IO] showed that it leads to lower overall combined plant efficiency,
except at low maximum temperature. Although there is a case for supplementary heating
giving higher specific work, the modem CCGT plant with its higher gas turbine inlet
temperature does not in general use supplementary heating. However, there is an argument
for reheating in the gas turbine itself (Le. between HP and LP turbines), which should lead
to higher mean temperatures of supply and high overall efficiency.
Rice [ 151 made a comprehensive study of the reheated gas turbine combined plant. He
first analysed the higher (gas turbine) plant with reheat, obtaining ( qo)H, turbine exit
temperature, and power turbine expansion ratio, all as functions of plant overall pressure
ratio and firing temperatures in the main and reheat burners. (The optimum power turbine
expansion ratio is little different from the square root of the overall pressure ratio.) He then
pre-selected the steam cycle conditions rather than undertaking a full optimisation.
Rice argued that a high temperature at entry to the HRSG (resulting from reheat in the
gas turbine plant) leads via the pinch point restriction to a lower exhaust stack temperature
and ‘heat loss’, in comparison with an HRSG receiving gas at a lower temperature from