Page 47 - Handbook of Electrical Engineering

26 HANDBOOK OF ELECTRICAL ENGINEERING

Where, C p is the specific heat of the air at constant pressure, kcal/kg K 1.005
C v is the specific heat of the air at constant volume, kcal/kg K 0.718
R is the particular gas constant for air, kJ/kg K 0.287
γ is the ratio of specific heats 1.4

From (2.3) and (2.7),
γ C p
= (2.8)
γ − 1 R

Substitute (2.4, 2.5 and 2.8) into (2.1),

U c = C p (T 2 − T 1 ) kJ/kg (2.9)

The air leaving the compressor at pressure P 2 passes into the combustion chamber where its
temperature is raised to T 3 , at constant pressure.
The hot air–fuel mixture burns and the gaseous products of combustion pass into the turbine
where the pressure falls to the atmospheric pressure P 4 = P 1 (in practice slightly higher due to the
resistance or ‘back pressure’ of the exhaust silencer and ducting). The exhaust gas temperature is
T 4 and is lower than the combustion temperature T 3 . (The ducting systems should be arranged so
that the exhaust gas is discharged at a point far enough away from the inlet ducting entrance that no
interaction occurs i.e. T 4 does not influence T 1 .)
The turbine expansion process can be described by similar equations to (2.1) through (2.7),
with T 3 replacing T 2 and T 4 replacing T 1 . Hence the work done by the turbine (U t )is,

U t = C p (T 3 − T 4 ) kJ/kg (2.10)

The heat supplied by the fuel is C p (T 3 − T 2 ).
In a conventional gas turbine the turbine supplies power to drive its compressor and so the
power available to drive a generator is the net power available from the turbine. Neglecting ineffi-
ciencies in the compressor and the turbine, the work done on the generator at the coupling of the gas
turbine is U out ,
U out = U t − U c = C p (T 3 − T 4 − T 2 + T 1 ) kJ/kg (2.11)

The ideal cycle efficiency η i of the gas turbine is:

C p (T 3 − T 4 − T 2 + T 1 ) T 4 − T 1
η i = = 1 −
C p (T 3 − T 2 ) T 3 − T 2
Rejection temperature difference
= 1 − (2.12)
Combustion temperature difference

From (2.1), raise to the power γ ,
γ γ

P 2 V 2 P 1 V 1
= (2.13)
T 2 T 1