Page 563 - Handbook of Electrical Engineering

WORKED EXAMPLE FOR CALCULATING THE PERFORMANCE OF A GAS TURBINE 555

Step 12. Find the compressor conditions

The starting conditions for iterating the compressor variables are,
C pc = 1.005

γ c = 1.895425 − 0.49296 × 1.005 = 1.4
◦
T 1 = 293.0 K
◦
T 2e = 632.18 K, found from Step 4 [step 12.1]
◦
The average value of T 1 and T 2e is 462.59 K. From the cubic expression in Table 2.1 for a fuel-to-air
ratio of zero, the revised value of C pc is,

C pcn = 0.99653 − 1.6117 × 10 −4 × 462.59
2
+ 5.4984 × 10 −7 × 462.59 − 2.4164 × 10 −10 × 462.59 3
= 0.99653 − 0.074557 + 0.117662 − 0.023921 = 1.015718
The new value of γ c is 1.895425 − 0.49296 × 1.015718 = 1.3947. Now recalculate T 2e ,

293.0 × (11.0 − 1.0 + 0.85)
◦
T 2e = = 627.78 K
0.85
◦
The new average value of T 1 and T 2e is 460.39 K.
Step 13. Recycle.
Repeat this iterative process from [step 12.1] until the variables settle at their stable values.
These eventually become,
C pc = C pcn = 1.01531

γ c = γ cn = 1.394917
◦
◦
T 2e = 627.934 K or 354.934 C
Step 14. Find the turbine conditions.
The starting conditions for iterating the turbine variables are,

C pt = 1.005

γ t = 1.895425 − 0.49296 × 1.147 = 1.33
◦
T 1 = 293.0 K
0.2481 0.2481 ◦
T 4 = r pt = 10.3743 = 684.46 K [step 14.1]
◦
T 4e = 684.46 × η t + (1 − η t ) × 1223.0 = 754.47 K