Page 88 - Advanced Gas Turbine Cycles

64 Advanced gas turbine cycles
the area Ax,, required to pass the coolant flow, is also determined. Obviously a degree of
successive approximation should be involved in obtaining the full solution to the complete
cooling flow process.
An empirical development of the approach described above uses experimental cascade
data, obtained with and without coolant discharge, to obtain an overall relationship
between the total cooling flow through the blade row ($) and the extra stagnation pressure
loss arising from injection of the cooling air. In film cooling, the air flow leaves the blade
surface at various points round the blade profile causing variable loss (noting that injection
near the trailing edge causes little total pressure loss-it may even reduce the basic loss in
the wake). If there is an elementary amount of air d$ at a particular location where the
injection angle is 4, then an overall figure for the extra total pressure loss due to coolant
injection in a typical blade row can be obtained by ‘integrating’ the Hartsel equation (4.47)
round the blade profile [3]. An overall exchange factor for the extra blade row stagnation
pressure mixing loss in the row can thus be obtained in the form
APoJPo = - K$, (4.48)
to be used in the subsequent cycle calculations. Alternatively, Eq. (4.48) can be converted
into a modified small stage or polytropic efficiency, q,, = vstage

vmgelqstage = K’ rcI, (4.49)
using the relationship given in Ref. [3],

[(Y
K/d = [~~stage/~stage~~[ ~AP~JP~] - 1)l~~xstage - I), (4.50)
(v- IYY .
in which xStage = rstage

4.3.3. Breakdown of losses in the cooling process
The simple approach described before involves approximations, particularly to obtain
the stagnation pressure loss. The full determination of (p&, and (TO)5m from the various
equations given above can lead to an approximation for the downstream entropy (sjm),
using the Gibbs relation applied between stagnation states,
TOAS = Ah0 - ApoJp~. (4.5 1)

If the outlet specific entropy ~5, is determined in this way the gross entropy generation in
the whole process is also obtained,

AS = (1 + $)’)S5m - (Slg + $s2c). (4.52)
and hence the total irreversibility I = TOAS. However, this does not give details on how
the various irreversibilities arise in the cooling process.
Young and Wilcock [7] provided a much more rigorous approach which includes an
illuminating discussion of how the losses arise in the cooling process. They prefer to
address the problem by breaking the overall flow into flows through the ‘component’