Page 89 - Advanced Gas Turbine Cycles

Chapter 4. Cycle eficiency with turbine cooling (cooling flow rates spec8ed) 65

control surfaces of Fig. 4.8 and determining the various entropy changes directly. Their
breakdown of the gross entropy then involves writing
(4.53)

Here ASintemal is the entropy increase of the cooling fluid in control surface B due to
friction and the heat transfer (Q, in), ASmetal is the entropy created in the metal between the
mainstream and the coolant (or metal plus thermal barrier coating if present) due to
temperature difference across it, ASextemal is the entropy increase in the mainstream flow
within control surface A before mixing due to heat transfer (Q, out), plus the various
entropy increases due to the mixing process itself in control surface C.
The reader is referred to the original papers for detailed analysis, where the various
components of entropy generation and irreversibility are defined. The advantage of this
work is not only that it involves less approximation but also that it is revealing in terms of
the basic thermodynamics. It should also be used by designers who should be able to see
how design changes relate to increased or decreased local loss.

4.4. Cycle calculations with turbine cooling

In order to make a preliminary assessment of the importance of turbine cooling in cycle
analysis, the real gas calculations of a simple open uncooled cycle, carried out in Chapter 3
for various pressure ratios and combustion temperatures, are now repeated with single step
turbine cooling, i.e. including cooling of the first turbine row, the stationary nozzle guide
vanes.
Here the magnitudes of the cooling flow fractions are assumed, together with the extra
stagnation pressure loss due to mixing. Subsequently, in Chapter 5, the calculations are
repeated for cooling flow fractions accurately assessed from heat transfer analysis,
together with associated total pressure losses. But the present investigation concentrates
on whether the conclusion derived from the a/s analyses-that cooling makes relatively
little difference to plant thermal efficiency-remains valid when real gas effects are
included.
For the purpose of the current calculations the cooling flow fractions were assumed to
increase linearly with combustion temperature, from 0.05 at 1200°C. Thus, the following
values of cooling fraction were assumed: 0.05 at 1200°C; 0.075 at 1400°C; 0.10 at 1600°C;
0.125 at 1800°C; 0.15 at 2000°C.
The choice of these values is arbitrary. In practice, the cooling fraction will depend not
only on the combustion temperature but also on the compressor delivery temperature
(i.e. the pressure ratio), the allowable metal temperature and other factors, as described in
Chapter 5. But with +assumed for the first nozzle guide vane row, together with the extra
total pressure loss involved (K = 0.07 in Eq. (4.48)), the rotor inlet temperature may be
determined. These assumptions were used as input to the code developed by Young [ 1 13
for cycle calculations, which considers the real gas properties.
Fig. 4.9 shows the results of calculations based on these assumptions in comparison
with the uncooled calculations (the other assumptions were those listed for the earlier
uncooled calculations in Section 3.4.1). The (arbitrary) overall efficiency is shown plotted