Formula & Calculator
Brayton Cycle Thermal Efficiency
Ideal thermal efficiency of the Brayton cycle used to model gas turbine and jet engine core performance.
Interpretation
Brayton cycle thermal efficiency: η_th = 1 − 1/(r_p^((γ−1)/γ)), where r_p is pressure ratio, γ is specific heat ratio. It is the ideal efficiency of a gas turbine. Example: r_p=20, γ=1.4 → η_th = 1 − 1/(20^(0.2857)) = 1 − 1/(2.37) ≈ 0.578.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| η_th | Thermal efficiency | |
| r_p | Pressure ratio | |
| γ | Ratio of specific heats |
What it means
The Brayton cycle is the thermodynamic cycle for gas turbine engines. Its thermal efficiency increases with pressure ratio. This ideal efficiency assumes isentropic compression and expansion. Real engines have lower efficiency due to component losses. The formula is used to assess the potential of a gas turbine design and to compare cycles. Understanding Brayton efficiency is essential for propulsion system design and for thermodynamic analysis of aircraft engines.
Worked example
Brayton Cycle Efficiency – Two Examples
Real‑World| Parameter | Value |
|---|---|
| r_p | 10 |
| γ | 1.4 |
| Parameter | Value |
|---|---|
| r_p | 20 |
Common mistakes
- Brayton cycle thermal efficiency: η_th = 1 − 1/(r_p^((γ−1)/γ)).
- r_p: Pressure ratio (p₂/p₁).
- γ: Specific heat ratio.
- Higher pressure ratio gives higher efficiency.
- Ideal cycle – actual has component losses.
Applications
Brayton cycle thermal efficiency, η_th = 1 − 1/(r_p^((γ−1)/γ)), is the ideal efficiency of a gas turbine engine based on pressure ratio. Higher pressure ratios yield higher thermal efficiency. Engineers use this to design compressors and turbines, to select optimum pressure ratios, and to assess the impact of improvements. By increasing pressure ratio through advanced materials and cooling, aerospace engineers can achieve higher thermal efficiency, reducing fuel consumption and emissions for gas turbine engines.
- Gas turbine engine thermodynamic design
- Compressor and turbine pressure ratio optimisation
- Cycle performance analysis for turbofans and turboprops
- Technology roadmaps for higher pressure ratios
- Environmental impact and fuel efficiency assessments
Frequently Asked Questions
It gives the ideal thermal efficiency of the Brayton cycle used to model gas turbine and jet engine core performance.
rp = pressure ratio (p2/p1)
γ = specific heat ratio of the working fluid (≈1.4 for air)
It measures how much of the heat added is converted into work. Higher pressure ratios give higher thermal efficiency.
Modern turbofans have pressure ratios of 40–50, giving ηth ≈ 0.45–0.50 (45–50%).
- Applying the ideal‑cycle result directly to a real engine without correcting for compressor/turbine polytropic efficiencies and losses.
- Using the wrong γ for the combustion gases (which are hotter and have γ ≈ 1.3).
- Confusing thermal efficiency with overall efficiency.
For rp = 30, γ = 1.4. ηth = 1 − 1/(30^(0.4/1.4)) = 1 − 1/(30^0.2857) = 1 − 1/(2.648) = 1 − 0.3777 = 0.6223 (62.2%).
Higher pressure ratio increases ηth, but the benefit diminishes at high ratios.
While the ideal efficiency depends only on pressure ratio, the actual efficiency also depends on turbine inlet temperature due to material limits.
The Brayton cycle adds heat at constant pressure (combustion), while the Otto cycle adds heat at constant volume.
Higher thermal efficiency reduces the fuel flow for a given power output, lowering TSFC.