Brayton Cycle

The Brayton cycle models the ideal continuous-flow processes of a gas-turbine engine. It consists of four processes: isentropic compression (1→2), constant-pressure heat addition (2→3), isentropic expansion (3→4), and constant-pressure heat rejection (4→1). In the air-standard idealization the working fluid is treated as air with constant specific heats, compression and expansion are reversible and adiabatic, and the pressure ratio rp = p2/p1 is the principal design parameter. Thermal efficiency of the ideal cycle depends only on pressure ratio: η_th = 1 − rp^−(k−1)/k. Net specific work, however, reaches a maximum at an intermediate pressure ratio that balances compressor work against turbine work for given turbine-inlet and ambient temperatures. Real engines deviate from the ideal cycle through component irreversibilities, pressure losses, and variable specific heats; regeneration, intercooling, and reheating are common modifications used to raise efficiency or specific work.

Governing FormulaAir-standard ideal Brayton (constant cp, cv; k = cp/cv): rp = p2/p1 T2 = T1 · rp^{(k−1)/k} (isentropic compressor) T4 = T3 / rp^{(k−1)/k} (isentropic turbine) η_th = 1 − rp^{−(k−1)/k} w_c = cp (T2 − T1) w_t = cp (T3 − T4) w_net = w_t − w_c = cp [(T3 − T4) − (T2 − T1)] Ẇ = ṁ · w_net rp,opt (max w_net) = (T3/T1)^{k/[2(k−1)]} Temperatures in kelvin; specific work in J/kg.

Knowledge Check

10 Questions

1.Which Brayton-cycle component performs the primary task of increasing the working-fluid pressure prior to heat addition?

2.For an ideal Brayton cycle with air (k = 1.4), inlet temperature T1 = 300 K and pressure ratio rp = 10, what is the isentropic compressor exit temperature T2?

3.Using the same conditions (k = 1.4, rp = 10), what is the ideal Brayton thermal efficiency?

4.An ideal Brayton cycle operates with rp = 10, k = 1.4, cp = 1005 J/kg·K, T1 = 300 K and T3 = 1400 K. What is the net specific work?

5.For fixed T1 and T3, how does increasing the compressor pressure ratio affect ideal Brayton efficiency and net specific work?

6.Calculate the pressure ratio that maximises net specific work for an ideal Brayton cycle with T1 = 300 K, T3 = 1200 K and k = 1.4.

7.If turbine isentropic efficiency drops below 100 % while the compressor remains ideal, what happens to net specific work and cycle thermal efficiency relative to the fully ideal cycle?

8.An ideal Brayton cycle has cp = 1005 J/kg·K, k = 1.4, ṁ = 2.0 kg/s, T1 = 300 K, rp = 8 and T3 = 1300 K. What is the approximate shaft power output?

9.A regenerator is placed between the turbine exhaust and the compressor exit. Under what temperature condition does it reduce the external heat addition required?

10.For an ideal Brayton cycle with T1 = 288 K, rp = 5, T3 = 1400 K, k = 1.4 and cp = 1005 J/kg·K, compute the specific compressor work and specific turbine work.