Page 562 - Handbook of Electrical Engineering

554 HANDBOOK OF ELECTRICAL ENGINEERING

Step 9. The relationship between ‘γ ’ over the range of 1.33 to 1.4 and ‘C p ’ over the range of
1.005 and 1.147 respectively, is approximately a straight-line law of the form ‘y = a + bx’. Hence
by using these pairs of points, a = 1.895425 and b =−0.49296.
Therefore,
γ = 1.895425 − 0.49296 C p

Step 10. The pressure ratio is not affected by the change in inlet pressure to the compressor. The
◦
◦
outlet temperature will remain constant at T 2 = T 2e = 632.18 K or 359.18 C.
Step 11. The outlet pressure of the compressor will be,

P 2 + P 2 = r p (P 1 + P 1 ) = 11.0 × (1.0 − 0.01226)
= 10.8651 bar

The inlet pressure to the turbine will be,

P 3 = P 2 + P 2 − P 23 = 10.8651 − 0.44 = 10.4251 bar

The outlet pressure of the turbine will be,

P 4 = P 4 + P 4 = 1.0 + 0.0049 = 1.0049 bar
Hence the pressure ratio of the turbine is,

P 3 10.4251
r pt = = = 10.3743

P 4 1.0049
The specific heats C pc and C pt are functions of the temperature within the compressor and
turbine respectively. A reasonable approximation is to use the average of T 1 and T 2e for the com-
pressor, call this T 12e , and the average of T 3 and T 4e for the turbine, call this T 34e . The variation of
C p with temperature is given in Table 2.1 as a cubic equation for three fuel-to-air ratios, zero, 0.01
and 0.02 per unit by mass. The value of 0.01 is appropriate for this example. At the same time the
ratio of specific heats γ c and γ t are functions of the specific heat at constant pressure. Simple linear
functions can be used to estimate the appropriate value of γ for a given C p , as follows,

γ c = a c + b c C pc and γ t = a t + b t C pt ,
where
a c = a t = 1.895425 and b c = b t =−0.49296

An iterative procedure is necessary in order to stabilise the values of C pc , γ c and T 2e for
the compressor and C pt , γ t and T 4e for the turbine. The conditions for the compressor need to be
calculated before those of the turbine.