Fundamentals of Gas Turbine Theory
Domain 1 - Fundamentals of Gas Turbine Theory
The exam tests the Brayton (constant-pressure) cycle, how pressure ratio and turbine entry temperature set efficiency and specific work, the thrust equation, and the station numbering used in later domains.
Core rules
- Ideal thermal efficiency is η = 1 − 1/PR^((γ−1)/γ). It rises with pressure ratio; turbine entry temperature does not change ideal efficiency but raises specific work until material limits intervene. Specific work peaks at a moderate pressure ratio, then falls as compressor work grows faster than turbine work.
- Thrust F = ṁ(Vj − V0) + (pj − p0)Aj. A turbojet gains thrust mainly from momentum change; a high-bypass turbofan gains it from large mass flow at modest jet velocity, which is quieter and more fuel-efficient at subsonic speed.
- Station numbers: 0 ambient, 1 inlet, 2 compressor face, 3 compressor discharge, 4 combustor exit (turbine inlet), 5 turbine exit, 7 exhaust nozzle exit. T4 limits material life; T5 (EGT) is the practical limit the crew sees.
- Compressor work = ṁ·cp·(T3 − T2)/ηmech. Turbine work must equal compressor work plus accessory and bleed loads.
Worked example
A compressor has PR 10, inlet total temperature 288 K and isentropic efficiency 0.85. Isentropic temperature ratio = 10^0.2857 = 1.931. Ideal rise = 288 × 0.931 = 268 K. Actual rise = 268/0.85 = 315 K, so T3 = 603 K. The 15% inefficiency becomes heat that must be paid for in fuel, which is why real fuel flow exceeds the ideal-cycle value.
Traps
- Confusing thermal efficiency with specific thrust.
- Assuming maximum thrust occurs at maximum pressure ratio.
- Balancing turbine and compressor work while forgetting bleed and accessory loads.