Page 72 - Advanced Gas Turbine Cycles

48 Advanced gas turbine cycles
temperature in cycle analyses, and Tfit as Ts, the temperature after cooling of the first
NGV row.
In this chapter, cycle calculations are made with assumed but realistic estimates of the
probable turbine cooling air requirements which include some changes from the uncooled
thermal efficiencies. Indeed it is suggested that for modem gas turbines there may be a
limit on the combustion temperature for maximum thermal efficiency [2,3].
As discussed in Chapter 3, analysis of uncooled gas turbine cycles was developed in
three stages:
(a) for air-standard (ds) reversible cycles;
(b) for ds irreversible cycles;
(c) for real gas irreversible cycles.
By introducing the effects of turbine cooling a similar development is followed in this
chapter. Here, we look initially at the effect of turbine cooling in
(a) in reversible ds cycles; and
(b) in irreversible a/s cycles.
For the purpose of the cycle analyses (a) and (b), the following assumptions are made:
(i) cooling is of the open type, with a known air flow fraction ($) first cooling a blade
row and then mixing with the mainstream; and (ii) complete mixing takes place, under
adiabatic conditions, at constant static pressure and low Mach number (and therefore
constant stagnation pressure). Before moving on to more realistic cycle calculations (but
with the cooling air quantity ($) assumed to be known), we consider the irreversibilities
in the turbine cooling process, showing how changes in stagnation pressure and
temperature (and entropy) are related to $. These changes are then used in cycle
calculations for which $ is again specified, but real gas effects and stagnation pressure
losses are included.
Subsequently, in Chapter 5, we shall show how the cooling quantities may be
determined; we give even more practical cycle calculations, with these cooling quantities
($) being determined practically rather than specified ab initio. But for the discussions in
this chapter, in which we assess how important cooling is in modifying the overall
thermodynamics of gas turbine cycle analysis, it is assumed that $ is known.
The nomenclature introduced by Hawthorne and Davis [4] is adopted and; gas turbine
cycles are referred to as follows: CHT, CBT, CHTX, CBTX, where C denotes compressor;
H, air heater; B, burner (combustion); T, turbine; X, heat exchanger. R and I indicate
reversible and irreversible. The subscripts U and C refer to uncooled and cooled turbines in
a cycle, and subscripts 1,2, M indicate the number of cooling steps (one, two or multi-step
cooling). Thus, for example, [CI-TJI,-2 indicates an irreversible cooled simple cycle with
two steps of turbine cooling. The subscript Tis also used to indicate that the cooling air has
been throttled from the compressor delivery pressure.

4.2. Air-standard cooled cycles

The initial analysis [5] is presented by reference to closed ds cycles using a perfect gas
as a working fluid in an externally heated plant. As for the uncooled cycles studied in
Chapter 3, it is argued subsequently that many of the conclusions reached in this way