Page 63 - Advanced Gas Turbine Cycles

Chapter 3. Basic gas turbine cycles 39
brackets [A] in Eq. (3.25) is linear with x, passing through the x, y points [l, 01; [ 1, (1 - E)];
[(p + 1)/2,1/2], where l = 1 - [(p - 1)(1 - E)/(~E - l)] = -0.2.
The effect of varying E can also be interpreted from this type of diagram. For E = 1.0,
i.e. for a cycle [CHTIIXR, the maximum efficiency occurs when r = 1.0 (the 'square
bracket' line becomes tangent to the NDNW curve at x = 1.0). For high values of E
(greater than 0.5), the tangent meets the curve to the left of the maximum in NDNW,
whereas for low E the tangent point is to the right. For E = 0.5 the point [l, 01 is located at
[ - 001 and the 'square bracket' line becomes horizontal, touching the NDNW curve at its
maximum at r = r,; so that for E = 0.5, re = r,.

3.2.3. Discussion

The Hawthorne and Davis approach thus aids considerably our understanding of a/s
plant performance. The main point brought out by their graphical construction is that the
maximum efficiency for the simple [CHT], cycle occurs at high pressure ratio (above that
for maximum specific work); whereas the maximum efficiency for the recuperative cycle
[CHTX], occurs at low pressure ratio (below that for maximum specific work). This is a
fundamental point in gas turbine design.
Fuller analyses of a/s cycles embracing intercooling and reheating were given in a
comprehensive paper by Frost et al. [3], but the analysis is complex and is not reproduced
here.

3.3. The [CBTII open circuit plant-a general approach

In practical open circuit gas turbine plants with combustion, real gas effects are present
(in particular the changes in specific heats, and their ratio, with temperature), together with
combustion and duct pressure losses. We now develop some modifications of the a/s
analyses and their graphical presentations for such open gas turbine plants, with and
without heat exchangers, as an introduction to more complex computational approaches.
The Hawthorne and Davis analysis is first generalised for the [CBTII open circuit plant,
with fuel addition for combustion, f per unit air flow, changing the working fluid from air
in the compressor to gas products in the turbine, as indicated in Fig. 3.1 1. Real gas effects
are present in this open gas turbine plant; specific heats and their ratio are functions off
and T, and allowance is also made for pressure losses.
The flow of air through the compressor may be regarded as the compression of a gas
with properties (c~~)~~ and (ya)12 (the double subscript indicates that a mean is taken over
the relevant temperature range). The work required to compress the unit mass of air in the
compressor is then represented as

where x is now given by x = r('") and z = (ya)12/[(ya)12 - 11.
The pressure loss through the combustion chamber is allowed for by a pressure loss
factor Ap23 = (p2 - p3)/~2, so that (p3/p2) = 1 - (Ap/p)23. Similarly, the pressure loss