Page 221 - Advanced Gas Turbine Cycles

Appendix A

DERIVATION OF REQUIRED COOLING FLOWS

A.1. Introduction

The stagnation temperature and pressure change in the cooling mixing process have
been shown to be dependent on the cooling air flow (w,) as a fraction of the entering gas
flow (w,), i.e. on JI = wc/wg. In this Appendix, an analysis by Holland and Thake [l],
which allows external film cooling (flow through the blade surface) as well as internal
convective cooling (flow through the internal passages), is summarised (see also Horlock
et al. [2] for a full discussion). It is based mainly on the assumption that the external
Stanton number (Sr,), which is generally a weak function of the Reynolds number, remains
constant as engine design parameters (Tco, and r) are changed.

A.2. Convective cooling only

A simple heat balance for a typical convectively cooled blade (as illustrated in
Fig. A. 1 a, 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. Tc, < Thus, the concept of a cooling efficiency is
introduced

so that

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

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