Handbook of Electrical Engineering

GAS TURBINE DRIVEN GENERATORS 33

The effects ofP 1 ,P 23 andP 4 can be found by modifying their corresponding pressure
ratios,rpcfor the compressor andrptfor the turbine, and using the binomial theorem to simplify the
results.P 23 andP 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,

y+y=

(

x+x

w+w

)n

( 2. 34 )

and,

y=

(x

w

)n

( 2. 35 )

which upon expanding becomes,

ywn+ny wn−^1 w+wny=xn+nxn−^1 x ( 2. 36 )

Where the second and higher orders ofare neglected. If the initial values are deducted then
the expression relating the small changes becomes,

ny wn−^1 w+wny=nxn−^1 x ( 2. 37 )

Hence the change inybecomes,

y=

nxn−^1

wn

x−

ny

w

w ( 2. 38 )

For the compressor it is assumed that the inlet pressure is increased byP 1. The pressure
ratio remains unchanged and so the change in output pressure is,

P 2 =rpP 1

Since the pressure ratio is unchanged the output temperature will be unchanged atT 2.

The heat from the fuel is a function ofT 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 chamberP 23 and one for the turbine
exhaust pressure due to ductingP 4. The two pressure drops at the inlet to the turbine can be
combined as,
P 223 =P 2 +P 23 ( 2. 39 )

In (2.34)x isP 223 andw isP 4. Hence their effect on the turbine pressure ratio is
rptnt,

rptnt=

ntP 3 nt−^1

P 4 nt

P 223 −

ntrptnt

P 4

P 4 ( 2. 40 )