Page 77 - Advanced Gas Turbine Cycles

Chapter 4. Cycle eflciency with turbine cooling (cooling pow rates specified) 53

But another approach to multi-step cooling [8, 91 involves dealing with the turbine
expansion in a manner similar to that of analysing a polytropic expansion. Fig. 4.4 shows
gas flow (1 + JI) at (p, T) entering an elementary process made up of a mixing process at
constant pressure p, in which the specific temperature drops from temperature T to
temperature T’, followed by an isentropic expansion in which the pressure changes to
(p + dp) and the temperature changes from T’ to (T + dT).
In the first mixing process, the entry mainstream flow (1 + $) mixes with cooling flow
dJI drawn from the compressor at temperature Tcomp. Thus, if cp is constant, then

(1 + JI+ dJIkp7J = (1 + JIkpT + d@pTcomp,
and

In the second process of isentropic expansion

cJ(T + dT) - 7‘1 = vdp, (4.12)

where v is the specific volume.
Subtracting Eq. (4.11) from Eq. (4.12), it then follows that in the overall elementary
process, (p, T, 1 + $1 to (p + dp, T + dT, 1 + $ + d$),
cpdT + cp(p - TmmP)dJI/(l + JI) = vdp, (4.13)

(4.14)

3

1

I
S
Fig. 4.4. Temperature-entropy diagram for multi-step cooling-reversible cycle [CHTIRW (after Ref. [5]).