Gas Turbine Brayton Cycle Calculator
Analyze the thermal efficiency of a gas turbine engine using the Brayton cycle, accounting for real compressor and turbine isentropic efficiencies. Used by aerospace and power generation engineers evaluating gas turbine designs.
About this calculator
The ideal Brayton cycle efficiency depends only on the pressure ratio: η_ideal = 1 − 1 / r_p^((γ−1)/γ), where r_p is the compressor pressure ratio and γ = 1.4 for air. In reality, compressor and turbine irreversibilities reduce performance. The actual cycle efficiency incorporates isentropic efficiencies η_c (compressor) and η_t (turbine): η = (1 − 1/(r_p^(0.4/1.4) × η_t)) × (1 − 1/(r_p^(0.4/1.4) / η_c)) expressed as a percentage. Higher pressure ratios increase efficiency up to an optimum point beyond which compressor work penalties dominate. Turbine inlet temperature (TIT) governs specific work output: higher TIT allows more fuel energy to be converted. Modern industrial gas turbines achieve pressure ratios of 15–30 and TITs above 1400 °C for efficiencies exceeding 40%.
How to use
Let pressure ratio = 10, compressor isentropic efficiency = 85% (0.85), turbine isentropic efficiency = 88% (0.88). Step 1 — Compute r_p^(0.4/1.4): 10^(0.2857) ≈ 1.9307. Step 2 — Turbine term: 1 − 1/(1.9307 × 0.88) = 1 − 1/1.699 = 1 − 0.5886 = 0.4114. Step 3 — Compressor term: 1 − 1/(1.9307/0.85) = 1 − 0.85/1.9307 = 1 − 0.4403 = 0.5597. Step 4 — Multiply and convert: 0.4114 × 0.5597 × 100 ≈ 23.0%. The estimated Brayton cycle efficiency under these real conditions is approximately 23%.
Frequently asked questions
How does pressure ratio affect Brayton cycle thermal efficiency?
Increasing the pressure ratio raises the temperature of air leaving the compressor and allows more heat to be added at higher pressure, improving cycle efficiency similar to the Carnot principle. For an ideal cycle with γ = 1.4, doubling the pressure ratio from 10 to 20 raises ideal efficiency from about 48% to 57%. However, real cycles hit diminishing returns because a higher pressure ratio also demands more compressor work, and compressor inefficiencies grow. There is therefore an optimal pressure ratio that maximizes specific net work output, which designers balance against the efficiency peak.
What is the difference between isentropic efficiency and thermal efficiency in a gas turbine?
Isentropic efficiency describes how closely an individual component — the compressor or turbine — approaches the ideal reversible process. A compressor with 85% isentropic efficiency uses 1/0.85 times more work than the ideal. Thermal efficiency is an overall cycle metric: net work output divided by the heat input from fuel. These two quantities are related but distinct — you can have high component isentropic efficiencies yet still have modest thermal efficiency if the pressure ratio or turbine inlet temperature is low. Both must be optimized together to maximize plant performance.
Why is turbine inlet temperature so important in gas turbine performance?
Turbine inlet temperature (TIT) sets the upper temperature of the Brayton cycle and directly controls the specific work output: higher TIT means more enthalpy available for expansion and greater net work per kilogram of air. Increasing TIT while keeping pressure ratio constant raises both power output and thermal efficiency. The main constraint is material strength — turbine blades must withstand enormous centrifugal stresses at temperatures exceeding the melting point of conventional alloys, requiring internal cooling channels, thermal barrier coatings, and single-crystal superalloys. Advances in blade cooling are one of the primary drivers of gas turbine efficiency improvements over recent decades.