Hong Life CalculatorsUnderstanding the Brayton cycle efficiency calculator — concept and principle
The Brayton cycle is the idealised model of a gas turbine, the machine used in jet engines and gas-fired power stations. Air is compressed, heated by burning fuel at constant pressure, expanded through a turbine and exhausted. This calculator returns the ideal thermal efficiency from just two inputs: the compressor pressure ratio and the heat-capacity ratio γ.
How it is calculated
η = 1 − r_p^(−(γ−1)/γ) = 1 − 1 / r_p^((γ−1)/γ)
- r_p: pressure ratio, compressor outlet pressure ÷ inlet pressure (dimensionless).
- γ = c_p/c_v: about 1.4 for air at moderate temperatures.
The result is the fraction of fuel heat that becomes net work in the ideal cycle, shown in percent.
The principle
The ideal Brayton cycle has four steps: reversible adiabatic compression, heat addition at constant pressure, reversible adiabatic expansion and heat rejection at constant pressure. During adiabatic compression the temperature rises by the factor r_p^((γ−1)/γ). Because both heat exchanges happen at constant pressure and the same temperature factor applies to compression and expansion, the efficiency reduces to 1 − T₁/T₂, where T₁ and T₂ are the compressor inlet and outlet temperatures. A higher pressure ratio raises the compressor outlet temperature, so heat is added at a higher average temperature, and efficiency increases, the same logic as for the Carnot cycle.
Worked example
- Inputs: r_p = 15, γ = 1.4.
- Exponent: (γ − 1) / γ = 0.4 / 1.4 = 0.285714.
- Temperature factor: 15^0.285714 = 2.16783.
- 1 / 2.16783 = 0.461290.
- η = 1 − 0.461290 = 53.87%.
| γ | Ideal efficiency |
|---|---|
| 0.35 | -15,181.62% |
| 0.7 | -219.18% |
| 1.05 | 12.1% |
| 1.4 | 53.87% |
| 1.75 | 68.67% |
| 2.1 | 75.79% |
| 2.8 | 82.46% |
How to read the result
The ideal efficiency depends only on the pressure ratio; it does not depend on the turbine inlet temperature. In real machines it does, because compressor and turbine losses mean that net work and efficiency peak at an optimum pressure ratio that rises with turbine inlet temperature. Real simple-cycle gas turbines achieve noticeably less. When the hot exhaust is used to raise steam for a second turbine (combined cycle), modern power plants exceed 60% overall.
Common mistakes
- Entering pressures in gauge rather than absolute values when computing r_p yourself.
- Using the pressure ratio directly as a temperature ratio; the exponent (γ−1)/γ is essential.
- Expecting efficiency to keep rising with pressure ratio in a real engine; component losses set an optimum.
Frequently asked questions
How do regenerators improve gas turbine efficiency?
A regenerator uses hot turbine exhaust to preheat compressed air before the combustor, so less fuel is needed. It helps most at low pressure ratios, where exhaust is hotter than compressor outlet air.
Is a jet engine a Brayton cycle?
Yes. The difference is that part of the expansion energy accelerates the exhaust to produce thrust instead of driving a generator shaft.
Sources: Y. A. Çengel and M. A. Boles, Thermodynamics: An Engineering Approach, McGraw-Hill · H. I. H. Saravanamuttoo, G. F. C. Rogers and H. Cohen, Gas Turbine Theory, Pearson