Brayton Cycle: The Thermodynamics Inside Every Jet Engine

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Thrust = 38,400 N — Brayton cycle, π_c=15, T₀₄=1400K at M 0.8

A turbojet with compression ratio 15, turbine inlet 1400K, at Mach 0.8 produces about 38.4 kN of net thrust with 48% ideal thermal efficiency.

Formula

Ideal thermal efficiency: η_th = 1 − 1/π_c^((γ−1)/γ)
Net thrust: F = ṁ(V_e − V_∞)
TSFC = ṁ_fuel / F

Compressing Air: The Foundation of Thrust

A turbojet ingests ambient air and compresses it through multiple axial compressor stages, raising pressure by a factor of 15 to 45. This compression requires enormous power — in a large engine the compressor absorbs up to 50 MW, all extracted from the turbine downstream. The simulation models ideal compression with an isentropic relationship, showing how pressure ratio directly determines the cycle's theoretical efficiency ceiling.

Combustion and the Temperature Limit

Fuel is sprayed into the compressed air and burned at nearly constant pressure, raising gas temperature to 1400-1900K. This is the hottest point in the engine and the primary design constraint. Higher turbine inlet temperature means more energy available for thrust, but the turbine blades must survive thousands of hours in this environment. Modern blades are single-crystal castings with labyrinthine internal cooling channels.

Turbine and Nozzle Expansion

The high-pressure, high-temperature gas first passes through the turbine, which extracts just enough energy to drive the compressor. The remaining enthalpy accelerates through a convergent (or convergent-divergent) nozzle to produce a high-velocity exhaust jet. Thrust equals the mass flow rate multiplied by the velocity increase from inlet to exit.

Flight Speed and Ram Effect

At flight Mach numbers above 0.3, the inlet acts as a diffuser, slowing incoming air and converting kinetic energy into additional pressure — ram compression. At Mach 2, ram compression alone provides a pressure ratio of about 7.8, significantly supplementing the mechanical compressor. The simulation shows how thrust and efficiency change across the subsonic and supersonic flight envelope.

FAQ

What is the Brayton cycle?

The Brayton cycle is the thermodynamic cycle used by all gas turbine engines. Air is compressed (rising temperature and pressure), fuel is added and burned at constant pressure, hot gas expands through a turbine (powering the compressor), and remaining energy accelerates exhaust through a nozzle to produce thrust.

How does compression ratio affect jet engine efficiency?

Higher compression ratios increase the ideal thermal efficiency as η = 1 − 1/π_c^((γ−1)/γ). Modern engines use compression ratios of 30-45. However, higher compression raises compressor exit temperature, limiting how much fuel can be added before exceeding turbine material limits.

What limits turbine inlet temperature?

Nickel superalloy blades melt around 1300°C but operate at gas temperatures up to 1700°C using film cooling, thermal barrier coatings, and internal convective cooling passages. Each 50K increase in TIT yields roughly 1-2% improvement in specific fuel consumption.

How is turbojet thrust calculated?

Net thrust equals mass flow rate times the difference between exhaust and inlet velocity, plus any pressure thrust: F = ṁ(Ve − V∞) + (Pe − P∞)Ae. At design conditions the nozzle is typically fully expanded, so the pressure term vanishes.

Sources

Embed

<iframe src="https://homo-deus.com/lab/propulsion/turbojet-cycle/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub