Page 53 - Handbook of Electrical Engineering

32 HANDBOOK OF ELECTRICAL ENGINEERING

The energy equations for the compressor and turbine become,

1
U cea = C pc (T 2 − T 1 ) kJ/kg (2.28)
η c
and

1
U tea = C pt (T 3 − T 4 ) kJ/kg (2.29)
η t
Also assume that the specific heat C pf of the fuel–air mixture is the value corresponding to
the average value of T 2 and T 3 , see Reference 4, sub-section 4.7.1, (2.23).

Hence the fuel energy equation becomes, from (2.23),

U fea = C pf (T 3 − T 2ea ) kJ/kg (2.30)

Where
β c − 1 + η c )
T 1 (r p
T 2ea = (2.31)
η c
Where r c and r t apply to the compressor and turbine and are found from C pc , C pt and C v .
The work done on the generator is now,

C pc T 1
δ t β t
U outea = C pt T 3 (1 − r p )η t − (r p − 1) (2.32)
η c
and
T 4ea = T 3 (η t r p + 1 − η t )
δ c
From U fea and U outea the thermal efficiency η pa can be found as,

U outea
η pa = (2.33)
U fea

2.2.4 Effect of Ducting Pressure Drop and Combustion Chamber Pressure Drop

Practical gas turbines are fitted with inlet and exhaust silencing and ducting systems to enable the
incoming air to be taken from a convenient source and the outgoing gas to be discharged to a second
convenient location. These systems can be long enough to create significant pressure drops at the
inlet and outlet of the gas turbine itself. The inlet system reduces the pressure at the entry to the
compressor, by an amount P 1. The exhaust system increases the pressure at the exit of the power
turbine, by an amount P 4 .
Between the outlet of the compressor and the inlet to the turbine there is a small pressure
drop caused by the presence of the combustion chamber and the throttling effect of its casing. Let
this pressure drop be P 23 .