Brayton Cycle | Sahithyan's Notes

Ideal cycle for gas turbines. Open cycle. Named after George Brayton.

The cycle is converted to a closed cycle using a heat exchanger (aka. heat recovery steam generator) in combined cycle plants.

Processes

1 → 2: isentropic compression (compressor) 2 → 3: constant-pressure heat addition (combustor) 3 → 4: isentropic expansion (turbine) 4 → 1: constant-pressure heat rejection

Pressure Ratio

r_p = \frac{P_2}{P_1}

Efficiency

\eta = 1 - \frac{1}{r_p^{(k-1)/k}}

Here:

$r_p$ : pressure ratio
$k$ : specific heat ratio ( $c_p / c_v$ ), approximately 1.4 for air

Efficiency increases with higher $r_p$ . Practical limits exist due to material temperature constraints at the turbine inlet.

Back-Work Ratio

BWR = \frac{W_\text{comp}}{W_\text{turb}} = \frac{W_\text{in}}{W_\text{out}}

Gas turbine BWR is high (40–80%), meaning the compressor consumes a large fraction of turbine output. Much higher than steam turbine pump work ratio.

Regeneration

Exhaust gases (state 4) are hot. A regenerator preheats the compressed air (state 2) using exhaust heat before the combustor. Reduces fuel input and increases efficiency.

\eta_\text{regen} > \eta_\text{basic}

Only effective when turbine exhaust temperature exceeds compressor exit temperature.