The Brayton cycle models the basic operation of gas turbine engines used in aircraft propulsion and power generation. This reference helps students connect the pressure, temperature, work, and heat transfer changes that occur in compressors, combustors, turbines, and exhaust systems. It is useful because many engineering problems require tracking energy across each component and comparing ideal results with practical improvements.
The ideal Brayton cycle has four main processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant pressure heat rejection. The most important relationships use pressure ratio, specific heat, temperature ratios, and the steady-flow energy equation. Efficiency improves when the turbine extracts more useful work compared with the heat added, and real systems often use regeneration, intercooling, and reheating to improve performance.
Key Facts
- The ideal Brayton cycle consists of 1 to 2 isentropic compression, 2 to 3 constant pressure heat addition, 3 to 4 isentropic expansion, and 4 to 1 constant pressure heat rejection.
- The compressor pressure ratio is r_p = P2 / P1, and for an ideal cycle the turbine pressure ratio is also P3 / P4 = r_p.
- For an isentropic ideal gas process, T2 / T1 = (P2 / P1)^((k - 1) / k).
- Compressor work input per unit mass is w_c = c_p(T2 - T1).
- Turbine work output per unit mass is w_t = c_p(T3 - T4).
- Net work output per unit mass is w_net = w_t - w_c.
- Heat added in the combustor is q_in = c_p(T3 - T2), and heat rejected is q_out = c_p(T4 - T1).
- For an ideal Brayton cycle with constant specific heats, thermal efficiency is eta = 1 - 1 / r_p^((k - 1) / k).
Vocabulary
- Brayton cycle
- A thermodynamic cycle that models gas turbine engines using compression, heat addition, expansion, and heat rejection.
- Pressure ratio
- The ratio of compressor exit pressure to compressor inlet pressure, written as r_p = P2 / P1.
- Isentropic process
- An ideal process with no entropy change, often used to model reversible adiabatic compression or expansion.
- Specific heat at constant pressure
- The energy needed to raise the temperature of one kilogram of gas by one kelvin at constant pressure, written as c_p.
- Thermal efficiency
- The fraction of heat input converted into net work output, written as eta = w_net / q_in.
- Regeneration
- A gas turbine improvement that uses hot exhaust to preheat compressed air before combustion.
Common Mistakes to Avoid
- Using Celsius temperatures in Brayton formulas is wrong because temperature ratios must use absolute temperature in kelvins.
- Adding compressor work instead of subtracting it is wrong because the compressor requires work input, so w_net = w_t - w_c.
- Applying the isentropic temperature relation to the combustor is wrong because heat addition in the ideal Brayton cycle occurs at constant pressure, not isentropically.
- Assuming higher pressure ratio always improves every performance measure is incomplete because very high pressure ratios can reduce net work if turbine inlet temperature is limited.
- Confusing regeneration with reheating is wrong because regeneration transfers exhaust heat to compressed air, while reheating adds heat between turbine stages.
Practice Questions
- 1 An ideal Brayton cycle has T1 = 300 K, r_p = 8, k = 1.4, and c_p = 1.004 kJ/kg K. Find T2 using T2 / T1 = r_p^((k - 1) / k).
- 2 For a gas turbine, T1 = 300 K, T2 = 560 K, T3 = 1400 K, T4 = 760 K, and c_p = 1.004 kJ/kg K. Find w_c, w_t, and w_net.
- 3 Using T2 = 560 K, T3 = 1400 K, T4 = 760 K, T1 = 300 K, and c_p = 1.004 kJ/kg K, calculate q_in, q_out, and eta = 1 - q_out / q_in.
- 4 Explain why regeneration can improve Brayton cycle efficiency but may not help if the turbine exhaust temperature is lower than the compressor exit temperature.