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The Brayton cycle, explained

In Hebrew: מחזור ברייטון

The Brayton cycle is the gas-turbine cycle: compress air, burn fuel at constant pressure, expand through a turbine. Its ideal efficiency, 1 − 1/r_p^((γ−1)/γ), depends only on the pressure ratio.

Brayton cycle calculator

Pre-filled with the worked example below. Change any value.

Ideal efficiency
48.21%
Net work
397.6kJ/kg
Back work ratio
41.37%

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The four processes

Air is compressed isentropically from state 1 to state 2, heated at constant pressure in the combustor to state 3, and expanded isentropically through the turbine to state 4. In an open cycle the exhaust leaves to the atmosphere; the ideal analysis closes the loop with a constant-pressure heat rejection back to state 1.

Unlike the Rankine cycle, the working fluid is a gas the whole way round, so the compressor is expensive. It typically absorbs 40 to 50 per cent of what the turbine produces. That fraction is the back work ratio, and it is why a gas turbine is so sensitive to compressor and turbine efficiency.

Pressure ratio and turbine inlet temperature

Raising the pressure ratio raises the ideal efficiency. But for fixed inlet and turbine temperatures, the net work per kilogram peaks at an intermediate pressure ratio and then falls. Designers balance the two, and the real limit on both is how hot the turbine blades can run.

Real plants add regeneration, intercooling and reheat. The biggest gain is the combined cycle: the turbine exhaust is still hot enough to raise steam for a Rankine cycle underneath, and the pair exceeds 60 per cent.

A worked number

Air enters at 300 K, the pressure ratio is 10, and the turbine inlet is 1400 K, with γ = 1.4 and c_p = 1.005 kJ/kg·K. The temperature ratio is 10^0.2857 ≈ 1.931, so T₂ ≈ 579 K and T₄ ≈ 725 K.

The compressor takes 1.005 × 279 ≈ 281 kJ/kg, the turbine gives 1.005 × 675 ≈ 678 kJ/kg, and the net work is about 398 kJ/kg. Heat in is 1.005 × 821 ≈ 825 kJ/kg, so the efficiency is 398 / 825 ≈ 48 per cent, matching the formula. The back work ratio is 281 / 678 ≈ 41 per cent.

Common mistakes

  • Using temperatures in Celsius in the temperature ratios.
  • Applying the pressure ratio directly to temperatures instead of raising it to (γ − 1)/γ.
  • Assuming a higher pressure ratio always gives more work. Efficiency keeps rising; net work does not.

Mechanical engineering, explained