Page 54 - Handbook of Electrical Engineering

GAS TURBINE DRIVEN GENERATORS 33

The effects of P 1 , P 23 and P 4 can be found by modifying their corresponding pressure
ratios, r pc for the compressor and r pt for the turbine, and using the binomial theorem to simplify the
results. P 23 and P 4 apply to the turbine pressure ratio.
After a gas turbine has been operating for a long time the inlet filter pressure drop may become
high enough to indicate that the filter needs cleaning. The drop in pressure across silencers will remain
almost constant; the effect of ingress of particles or development of soot can be neglected.
The pressure ratio terms in (2.31) and (2.32) are of the general form,

n
x + x
y + y = (2.34)
w + w
and,
x
n
y = (2.35)
w
which upon expanding becomes,

n
n
n
yw + nyw n−1 w + w y = x + nx n−1 x (2.36)
Where the second and higher orders of are neglected. If the initial values are deducted then
the expression relating the small changes becomes,

n−1 n n−1
nyw w + w y = nx x (2.37)
Hence the change in y becomes,

nx n−1 ny
y = x − w (2.38)
w n w
For the compressor it is assumed that the inlet pressure is increased by P 1 . The pressure
ratio remains unchanged and so the change in output pressure is,

P 2 = r p P 1

Since the pressure ratio is unchanged the output temperature will be unchanged at T 2 .
The heat from the fuel is a function of T 2 and therefore it will also be unchanged.
For the turbine there are three pressure drops to consider. One for the compressor discharge
P 2 , one for the practical throttling effect in the combustion chamber P 23 and one for the turbine
exhaust pressure due to ducting P 4 . The two pressure drops at the inlet to the turbine can be
combined as,
(2.39)
P 223 = P 2 + P 23
In (2.34) x is P 223 and w is P 4 . Hence their effect on the turbine pressure ratio is
nt
r pt ,
nt−1 nt
nt n t P 3 n t r pt
r pt = P 223 − P 4 (2.40)
nt
P 4 P 4