Page 224 - Advanced Gas Turbine Cycles

186 Advanced gas turbine cycles

A.4. The cooling efficiency
The cooling efficiency can be determined from the internal heat transfer. If Tbl is taken
to be more or less constant, then it may be shown that

where 6 = (h,A,/w,c,) = (St,A,/A,,), St, is now the internal Stanton number, and A,
and A,, refer to surface and cross-sectional areas of the coolant flow.
Experience gives values of 8 for various geometries, but Sr, is also a weak function of
Reynolds number and so, in practice, there is relatively little variation in cooling efficiency
(0.6 < cool < 0.8). In the cycle calculations described in Chapter 5, cool was taken as
0.7, and assumed to be constant over the range of cooling flows considered.

AS. Summary

Since ‘open’ film cooling is now used in most gas turbines, the form of Eq. (AI 3) was
adopted for the cycle calculations of Chapter 5, i.e.

Taking (cpg/cF)(As,/Ag) = 20 as representative of modern engine practice, and
Sr, = 1.5 X a value of C = 0.03 is obtained. The ratio (cpg/cF) should then increase
with Tg (but only by about 8% over the range 1500-2200K). This variation was,
therefore, neglected in the cycle calculations described in Chapter 5.
However, it was found that the cooling flows calculated from these equations were less
than those used in recent and current practices in which film cooling is employed. This is
for two main reasons:
(i) designers are conservative, and choose to increase the cooling flows
(a) to cope with entry temperature profiles (the maximum temperature being well
above the mean) and local hot spots on the blade and
(b) locally, where cooling can be achieved with relatively small penalty on mixing
loss (and hence on polytropic efficiency), so regions remote from these injection
points are cooled with this low loss air;
(ii) in practice, some surfaces in a turbine blade row will be convectively cooled with no
film cooling. The use of Eq. (A15) with Eq. (AI 1) for the whole blade row assembly
therefore leads to the total cooling flow being underestimated. Film cooling leads to
more efficient cooling, which is reflected in W+ being much less than w+; for the
NGVs of a modem gas turbine W+ may take a value of about 2 but w + about 4.
In the calculations described in the main text, allowance was made for such practical
issues by increasing the value of the constants C by a ‘safety factor’ of 1.5. Thus, cooling
flows were determined from