Page 565 - Handbook of Electrical Engineering

WORKED EXAMPLE FOR CALCULATING THE PERFORMANCE OF A GAS TURBINE 557

Let
δt
T 4a = T 3 (1 − r pt )η c η t
βt
T 1a = T 1 (r pt − 1)
T 3a = T 3 η c
and
βt
T 2a = T 1 (r pc − 1 + η c )
then
T 4a − T 1a
η pa =
T 3a − T 2a
therefore,
◦
T 4a = 1223.0 × (1.0 − 10.3743 −0.24423 ) × 0.85 × 0.87 = 393.627 K
γ c − 1 1.394917 − 1.0
β c = = =+0.28311
γ c 1.394917
◦
T 1a = 293.0 × (11.0 +0.28311 − 1.0) = 284.694 K
◦
T 3a = 1223.0 × 0.85 = 1039.55 K
◦
T 1a = 293.0 × (1.971652 − 1.0 + 0.85) = 533.744 K
393.627 − 284.694
η pa = = 0.2154 per unit
1039.55 − 533.744
Step 19. Find the overall thermal efficiency η pao .
From (2.33) and allowing for the losses in the gearbox and generator, the overall thermal
efficiency η pao can be found as follows.
U oute
η pao = η gb η gen
U fea
The value of C pf can be taken as the average value of T 3 and T 2e ,callthis T 23 ,
1223.0 + 627.934 ◦
T 23 = = 925.467 K
2
Substitute T 23 in the cubic expression for a fuel–air ratio of 0.01 in Table 2.1 to find the appropriate
value of C pf ,

C pf = 1.0011 − 1.4117 × 10 −4 × 925.467
3
2
+ 5.4973 × 10 −7 × 925.467 − 2.4691 × 10 −10 × 925.467 = 1.14558
U fea = 1.14558 × (1223.0 − 627.934) = 681.695 kJ/kg
197.530
U outea
η pa = = = 0.28976 per unit
U fea 681.695
η pao = 0.28976 η gb η gen
= 0.28976 × 0.985 × 0.985 = 0.28114 per unit