Enter the compressor pressure ratio and specific heat ratio into the calculator to determine the ideal Brayton cycle efficiency. The Brayton cycle is an ideal cycle for gas turbines and describes the workings of a constant-pressure heat-addition engine.
Brayton Cycle Efficiency Formula
The following formula is used to calculate the ideal (air-standard) Brayton cycle thermal efficiency (as a decimal):
\eta = 1 - \frac{1}{r_p^{(k - 1)/k}}Variables:
- η is the Brayton cycle thermal efficiency (decimal; multiply by 100 for %)
- rp is the compressor pressure ratio (P2/P1)
- k is the specific heat ratio (Cp/Cv)
To calculate the Brayton cycle efficiency, compute rp(k−1)/k, divide 1 by that value, subtract the result from 1, and then multiply by 100 to get the percentage.
What is Brayton Cycle Efficiency?
Brayton cycle efficiency is a measure of the thermodynamic efficiency of a Brayton cycle, which is the idealized cycle for a gas turbine engine. It represents the fraction of heat energy converted into useful work and is influenced by the compressor pressure ratio and the specific heat ratio of the gas. Higher efficiencies indicate a more effective engine that can do more work with the same amount of heat energy.
How to Calculate Brayton Cycle Efficiency?
The following steps outline how to calculate the Brayton Cycle Efficiency.
- First, determine the compressor pressure ratio (rp) of the gas turbine engine.
- Next, determine the specific heat ratio (k) of the gas being used in the engine.
- Use the formula above to calculate the Brayton cycle efficiency (η) as a decimal.
- Finally, convert the efficiency to a percentage by multiplying by 100.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Compressor Pressure Ratio (rp) = 10
Specific Heat Ratio (k) = 1.4
Efficiency: η = 1 − 1/10(1.4−1)/1.4 ≈ 0.4829 → 48.29%
