Question

Air enters the compressor of a gas turbine at 100 Kpa and 25 o C. For a pressure ratio of 5

and a maximum temperature of 850°C. Determine the thermal efficiency using the Brayton

cycle​

Answer 1

Concept:

Joule (or Brayton) Cycle. Practically every gas turbine is based on the Brayton cycle, sometimes known as the Joule cycle.

Given:

Initial pressure = Kpa

Initial temperature, T1 = 25⁰C

Maximum temperature = 850⁰C

Pressure ratio = 5

Find:

We need to determine the thermal efficiency using the Brayton cycle

Solution:

At temperature, T1 = 25⁰C = 298K having pressure as p1

Therefore h1 = 295.17 + (298-295) / (300 - 295)× (300.9 - 295)

Therefore h1 = 298.608 kJ/kg

(pr)1 = 1.3068+(298−295)/(300−295) × (1.386−1.3068)

(pr)1 = 1.35432

Therefore, (pr)2 = (p2/p1) × (pr)1

(pr)2 = 5 × 1.35432

(pr)2 = 6.7716

By interpolating,

h2 becomes as h2 = 472.24+{(6.7716-6.742)/(7.268-6.742)} × (482.49-472.24)

h2 = 472.8168 kJ/kg

At temperature T3 =850⁰C = 1123 K

h3 = 1184.28+{(1123-1120)/(1140-1120)} × (1207.57-1184.28)

h3 = 1187.77 kJ/kg

(pr)3 = 179.7+{(1123-1120)/(1140-1120)}*(193.1-179.7)

(pr)3 =181.71

(pr)4 = (p4)/(p3) × (pr)3

(pr)4 = 1/5 × 181.71

(pr)4 = 36.342

Therefore, at (pr)4

By interpolation

h4 = 756.44+{(36.342-35.5)/(37.35-35.5)} × (767.29-756.44)

h4 = 767.38 kJ/kg

Therefore, the thermal efficiency cycle will becomes,

η = (h3 - h4) - (h2 - h1) / h3 - h2

η = (1187.77−767.38) − (472.8168−298.608) / 1187.77−472.8168

η = 0.344

η  = 34.4 %

Thus, the thermal efficiency using the Brayton cycle​ is 34.4%.

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