Page 48 - Handbook of Electrical Engineering

GAS TURBINE DRIVEN GENERATORS 27

From here onwards the following substitutions will be used in order to keep the presentation
of the equations in a simpler format.

γ − 1 γ c − 1 γ t − 1
β = ,β c = ,β t =
γ γ c γ t
1 − γ 1 − γ c 1 − γ t
δ = ,δ c = ,δ t =
γ γ c γ t

Where subscript ‘c’ refers to the compressor and ‘t’ to the turbine, the absence of a subscript
means a general case.
Divide (2.2) by (2.13) to obtain an expression for the compressor,
δ

P 2 T 1
= (2.14)
P 1 T 2
Similarly for the turbine,
δ
P 3 T 4
= (2.15)
P 4 T 3
It is of interest to determine the work done on the generator in terms of the ambient temperature
T 1 and the combustion temperature T 3 .

From (2.14),
β
T 2 = T 1 r p

And from (2.15),
δ
T 4 = T 3 r p
Therefore (2.11) becomes,

β
δ
U out = C p (T 3 − T 3 r p − T 1 r p + T 1 )
δ
β
= C p T 3 (1 − r p ) − C p T 1 (r p − 1) (2.16)
The ideal cycle efficiency η i can also be expressed in terms of T 1 and T 3 .
δ
T 3 r p − T 1
η i = 1 − (2.17)
β
T 3 − T 1 r p
The specific heat C p is assumed to be constant and equal for both compression and expansion.
In practice these assumptions are not valid because the specific heat C p is a function of temperature.
The average temperature in the turbine is about twice that in the compressor. Also the products
of combustion i.e. water vapour and carbon dioxide, slightly increase the specific heat of air–gas
mixture in the turbine. Figures 2.8 and 2.9 show the spread of values for the pressure ratio and
exhaust temperature for a range of gas turbines from 1 MW to approximately 75 MW.