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Thermodynamics
Brayton cycle efficiency
Ideal efficiency of a gas turbine, set by the overall pressure ratio.
- Ref
- THE-14
- Rev
- v1
- Field
- Thermodynamics
- Result
- η
r_p is the overall pressure ratio of the compressor (outlet pressure over inlet) and γ the ratio of specific heats (1.4 for air). η is the ideal air-standard Brayton cycle efficiency: compression, constant-pressure heat addition, expansion, constant-pressure heat rejection. In this ideal cycle it depends on the pressure ratio alone.
Ideal efficiency of a gas turbine, set by the overall pressure ratio.
Calculator
- Temperature ratio across the compressor rp(γ−1)/γ1.931
- Efficiency at twice the pressure ratio0.5751
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A pressure ratio of 10 gives an ideal efficiency of 48 %; doubling it to 20 gives 57.5 %. This is why modern turbofans have overall ratios of 40 and above.
- Real engines reach about 30 to 40 %, because compressor and turbine losses, cooling air and the temperature limit of the blades all reduce it.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| rp Pressure ratio | 1.5 to 60 | 0.1094 | 0.6896 | 0.5802 | +10% | +2.89 % |
| γ Ratio of specific heats | 1.1 to 1.67 | 0.1889 | 0.603 | 0.4141 | +10% | +14.9 % |
Sweep of Pressure ratio
| Pressure ratio | Ideal efficiency |
|---|---|
| 1.5 | 0.1094 |
| 8.813 | 0.463 |
| 16.13 | 0.5481 |
| 23.44 | 0.5939 |
| 30.75 | 0.6242 |
| 38.06 | 0.6465 |
| 45.38 | 0.6638 |
| 52.69 | 0.6778 |
| 60 | 0.6896 |
Sweep one variable
Variables and how each one contributes
Ideal efficiency
What the equation gives you. Everything else feeds it.
Pressure ratio
The compressor pressure ratio. Rises with diminishing returns: at rp = 10 a 10 % rise in rp raises η by about 2.9 %.
Ratio of specific heats
The ratio of specific heats of the working gas. Raises η: more of the compression work is recovered at higher γ. Real cycles use lower values in the hot section, which lowers η.
Worked example with the values above
- Exponent: (γ − 1)/γ = 0.4/1.4 = 0.28571.
- Temperature ratio: rpexp = 100.28571 = 1.9307.
- η = 1 − 1/1.9307 = 0.4821, or 48.21 %.
Assumptions and limits
- Air-standard cycle with constant γ and no losses.
- Constant-pressure heat addition and rejection, with isentropic compression and expansion.
Common mistakes
- Using the formula for the Otto cycle, which has a different exponent and uses the volume ratio.
- Expecting the ideal value in a real engine without applying component efficiencies.
Statistics and uncertainty
Efficiency is weakly sensitive to the pressure ratio at the default (a 5 % error in rp shifts η by about 1.4 %), but real engine efficiency also depends on turbine inlet temperature, which this formula ignores entirely. Component efficiencies of 85 to 90 % cut the real value far more than any input error here.
Where it is used
- Comparing gas turbine designs.
- Understanding why modern engines use high pressure ratios.
Maths you need
- Isentropic relations: T ∝ p(γ−1)/γ
- Pressure ratio: outlet over inlet