A turbojet engine is a heat engine that turns the chemical energy of fuel into the kinetic energy of a fast exhaust jet. It matters because the thrust that moves an aircraft forward comes from changing the momentum of air passing through the engine. The turbojet follows the Brayton cycle, the same ideal thermodynamic cycle used to model gas turbines.
Understanding this cycle helps engineers predict thrust, fuel use, temperature limits, and engine efficiency.
Air enters the intake, is compressed to high pressure, receives heat from burning fuel in the combustor, expands through the turbine, and then accelerates through the nozzle. The compressor raises the air pressure and temperature, while the combustor adds energy mostly at nearly constant pressure. The turbine extracts enough work from the hot gas to drive the compressor, leaving the remaining energy to form a high-speed exhaust.
The nozzle converts thermal and pressure energy into jet velocity, producing thrust by Newton's third law and momentum conservation.
Key Facts
- Ideal Brayton cycle steps: isentropic compression, constant-pressure heat addition, isentropic expansion, constant-pressure heat rejection.
- Compressor pressure ratio: r_p = P2 / P1, where P2 is compressor exit pressure and P1 is inlet pressure.
- Ideal Brayton efficiency: η = 1 - 1 / r_p^((γ - 1)/γ), for an ideal gas with constant γ.
- Thrust from momentum change: F = ṁ(V_exit - V_inlet) + (P_exit - P_ambient)A_exit.
- Compressor work per unit mass is approximately w_c = c_p(T2 - T1).
- Turbine work per unit mass is approximately w_t = c_p(T3 - T4), and in a turbojet much of it powers the compressor.
Vocabulary
- Brayton cycle
- The ideal thermodynamic cycle for gas turbines, made of compression, heat addition, expansion, and heat rejection processes.
- Compressor
- The rotating engine section that raises the pressure and temperature of incoming air before combustion.
- Combustor
- The chamber where fuel mixes with compressed air and burns to add thermal energy to the flow.
- Turbine
- The rotating section that extracts energy from hot gas to drive the compressor through a shaft.
- Nozzle
- The duct at the engine exit that accelerates gas to high speed to create thrust.
Common Mistakes to Avoid
- Treating the turbine as the part that directly pushes the airplane forward is wrong because the turbine mainly powers the compressor, while thrust mostly comes from the exhaust jet leaving the nozzle.
- Assuming pressure stays high through the nozzle is wrong because the nozzle converts pressure and thermal energy into velocity, so static pressure usually drops as speed rises.
- Ignoring the inlet air speed is wrong because thrust depends on the change in momentum, so F is related to V_exit - V_inlet, not just exhaust speed alone.
- Using the ideal Brayton efficiency without checking assumptions is wrong because real engines have compressor losses, turbine losses, pressure drops, heat limits, and nonideal combustion.
Practice Questions
- 1 A turbojet ingests air at 250 m/s and exhausts it at 650 m/s. If the air mass flow rate is 40 kg/s and the pressure thrust term is zero, calculate the thrust.
- 2 For an ideal Brayton cycle with γ = 1.4 and compressor pressure ratio r_p = 9, calculate the ideal thermal efficiency using η = 1 - 1 / r_p^((γ - 1)/γ).
- 3 Explain why increasing turbine inlet temperature can increase turbojet performance, and also explain one engineering limit that prevents it from being increased without bound.