Derivation of required cooling flows

A simple heat balance for a typical convectively cooled blade (as illustrated in Fig. A.la, which shows the notation) is 

It is assumed that the temperature of the coolant does not fully reach the temperature of the metal before it leaves the blade, i.e. Tp, 71,1. Thus, the concept of a cooling efficiency is introduced 

The exposed area for heat transfer (A g) is then replaced on the premise that, for a set of similar gas turbines, there is a reasonably constant ratio between A g and the cross-sectional area of the main hot gas flow A g. Thus, writing A g = AA g = XWg/pgVg in Eq. (A3) gives 

For a row in which the blade length is L, the blade chord is c, the spacing is s and the flow discharge angle is a, the ratio A is given approximately by 

With s/c = 0.8 and a = 75°, the value of A is then about 10. The total cooled surface area is found to be greater than the. surface area of the blade profiles alone because of the presence of cooled end-wall surfaces (adding another 30-40% of surface area), complex trailing edges and other cooled components. It would appear from an examination of practical engines that A(rpg/cp. ) could reasonably be given a value of about 20. Eq. (A4) then provides the basic form on which a cooling model can be based. 

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