Page 83 - Advanced Gas Turbine Cycles

Chapter 4. Cycle eficiency with turbine cooling (cooling pow rates specified) 59

4.2.2.4. Cycle with multi-step cooling [CHTII~~
The two step cooling example given above can in theory be extended to multi-step
cooling of the turbine. It is more convenient to treat the turbine expansion as a
modification of normal polytropic expansion; the analysis is essentially an adaptation of
that given in Section 4.2.1.3 for the multi-step cooled turbine cycle.
If the polytropic efficiency in the absence of cooling is qp, then it may be shown [5] that
T/p' = C/( 1 + (4.33)

where u = (y - I)qp/y and 6 = 1 - (de). At the exit state E,

TEITI = O/ra(l + &)'. (4.34)

Alternatively,
~/p~' constant, (4.35)
=
where u' = (y - l)q,/Hl - A), and A is obtained from heat transfer analysis as indicated
earlier. A 'modified' polytropic efficiency is dp = qp/(l - A), so that u/ = dP(y - l)/y.
The turbine temperature at exit is then given by

TE/Tl = O/F'. (4.36)
Clearly, if A is zero (no heat transfer), then the normal polytropic relation holds. A point of
interest is that if qp = (1 - A) then dP = 1 and the expansion becomes isentropic (but not
reversible adiabatic).

4.2.2.5. Comment
For the various reversible cycles described in Section 4.2.1, the thermal efficiency was
the same, independent of the number of cooling steps. This is not the case for the
irreversible cycles described in this section. Both the thermal efficiency and the turbine
exit temperature depend on the number and nature of cooling steps (whether the cooling
air is throttled or not).

43. Open cooling of turbine blade rowdetailed fluid mechanics
and thermodynamics

4.3. I. Introduction

The preliminary a/s analyses of turbine cooling described above contained two
assumptions:
(i) open cooling with the cooling fraction known;
(ii) adiabatic mixing at constant pressure (low velocities were assumed, stagnation and
static conditions being the same).
In Chapter 5 (and Appendix A), the detailed fluid mechanics and thermodynamics
involved in cooling an individual turbine blade row are discussed, enabling JI to be