Page 86 - Advanced Gas Turbine Cycles

62 Advanced gas turbine cycles

is given by

and hence

Cpg[(TO).?g - (T0)SgI = J/cpc[(T0)5c - (T0)2cl? (4.40)
where the specific heats are now mean values over the relevant temperature range.
These equations enable the exit temperature Tosm to be determined. Alternatively, the
exit enthalpy can be obtained directly from

(h0)3g - (h0)5g = fl(h0)Sc - (hO)2cl* (4.41)
if tables of gas properties are used instead of specific heat data.

4.3.2.2. Change of total pressure through an open cooled blade row
It has already been shown that (stagnation) pressure losses have an appreciable effect
on cycle efficiency (see Section 3.3), so as well as obtaining the enthalpy change, it is
important to determine the stagnation pressure change in the whole cooling process.
To determine the overall change in total pressure we must now consider the three
control surfaces A, B and C of Fig. 4.8 separately.
For the fluid streams flowing through control surface A and B we may regard each as
undergoing a Rayleigh process-a compressible fluid flow with friction and heat transfer.
According to Shapiro [ 131, in such a process the change in total pressure Apo over a length
du is related to the change in stagnation temperature ATo and to the skin friction as

APO~PO -(YM*/N(ATO/TO) - (4fdr/d,)l, (4.42)
=
where M is the Mach number, f the skin friction coefficient and dh the hydraulic mean
diameter of the duct. For the mainstream gas flow in control surface A, (AT0& = -Q/c,;
and for the cooling air flow in B, (ATo)c = +e/@,, where Q is the heat transferred,
which is determined from heat transfer analysis as described in Chapter 5 and Appendix A.
In the simple approach, the change pO due to Q (the first term in Eq. (4.42)) is usually
ignored for both streams. The change of po due to frictional effects in the mainstream flow
is usually included in the basic polytropic efficiency (qp) of the uncooled flow, so that

[@0)3g - @0)xgl/(P0)3g = YM:,[l - TpV2 (4.43)
is already known. The change of po due to friction in the coolant flow through the complex
internal geometry is usually obtained using an empirical friction factor k so that

[(PO)ZC - (Po)xcI/(Po)2c = wf2c>2/2. (4.44)
Thus, po and To at exit from the control surfaces A and B are given by
A (mainstream gas)

==
(To)x~ (T0)3g - Q/cpg, (Po)x~ (P0)3g{ 1 - YM&[~ - ~pl/2}, (4.45)
=