Page 96 - Advanced Gas Turbine Cycles

72 Advanced gas turbine cycles

If EO is the blade cooling effectiveness, defined as

(5.3)
and vcml is the cooling efficiency,

in which T,, is the cooling air outlet temperature before mixing, then it follows that

The ‘constant’ C is

in which St, is the external gas Stanton number, A,, and A, are the gas surface and cross-
sectional flow areas, and cpg, cF are the gas and cooling air specific heats, respectively.
The cooling efficiency can be determined from the internal heat transfer. If Tbl is
considered to be more or less constant, then it may be shown that

77,001 = 1 - exp(-O, (5.6)
where c= (h~A,,lw,c,) = (SfJc3/Acx), and Sr, is now the internal cooling air Stanton
number, A,, and A,, refemng to surface and cross-sectional areas of the internal cooling
air flow, respectively.
Experience gives values of 6 for various geometries, but St, is found to be a weak
function of Reynolds number, so in practice there is relatively little variation in cooling
efficiency (0.6 < vCwl < 0.8). Thus, both C and vcml do not vary greatly and if they are
amalgamated into a single constant, K = C/qcool, then

or

@ = K(Tgi - Tbl)/(Tbl - Tcil, (5.8)

a form used by El-Masri [3] for his cycle calculations, and also used in the last chapter to
relate T,,, and Tfit.

5.2.2. Film cooling
For a film cooled blade row, cooling air at outlet temperature T,, is discharged into the
mainstream through the holes in the blade surface to form a cooling film (Fig. A. 1 b).
A film cooling effectiveness is now defined as

where Taw is the adiabatic wall temperature.