Page 95 - Advanced Gas Turbine Cycles

Chapter 5

FULL CALCULATIONS OF PLANT EFFICIENCY

5.1. Introduction

In Chapter 4 calculations were made on the overall efficiency of CBT plants with
turbine cooling, the fraction of cooling air ($) being assumed arbitrarily. In this chapter,
we outline more realistic calculations, with the cooling air fraction +being estimated from
heat transfer analysis and experiments.
There are several papers in the literature which give details of cycle calculations, and
include details of how the cooling flow quantity may be estimated and used. Here we
describe one such approach used by the author and his colleagues. Initially, we summarise
how +can be obtained (fuller details are given in Appendix A). We then illustrate how this
information is used in calculations, once again using a computer code in which real gas
effects are included.
Subsequently, we refer briefly to other comparable studies, including the calculations
of exergy losses and rational efficiency. Finally, we show the ‘real gas’ exergy calculations
for two practical plant~-[CBT]~ and [CBTXII.

5.2. Cooling flow requirements
The method devised by Holland and Thake [I] for estimating the cooling air (w,), as a
fraction of mainstream entry flow to a blade row (w& i.e. + = w,/wg, was described by
Horlock et al. [2] and is reproduced in Appendix A; Fig. A.l shows diagrammatically the
notation employed there and the same symbols are defined and used below.
5.2.1. Convective cooling

Consider first a convectively cooled blade row (Fig. A. la). It is shown in Appendix A
that the mass flow of cooling air (w,) required for a mass flow of mainstream gas (wg),
entering at temperature Tgi, is given by
+= WJW, = cw+, (5.1)

where w+ is a ‘temperature difference ratio’ defined as

(5.2)
with Tbl, the allowable blade temperature and Tci, the cooling air entry temperature.

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