Gas Turbine Brayton Cycle Calculator
Compute the net power output of a Brayton-cycle gas turbine given pressure ratio, temperatures, mass flow rate, and component efficiencies. Essential for preliminary gas turbine and jet engine performance analysis.
About this calculator
The Brayton cycle describes the thermodynamic process of a gas turbine: isentropic compression, constant-pressure heat addition, and isentropic expansion. Net specific work (kJ/kg) combines turbine work minus compressor work. For air (cp ≈ 1.005 kJ/kg·K, γ = 1.4), the isentropic temperature ratio exponent is (γ−1)/γ = 0.286. The calculator uses: W_net = ṁ × cp × [T_4 × (1 − r_p^(−0.286)) × (η_t/100) − T_1 × (r_p^(0.286) − 1) / (η_c/100)] / 1000, where T_4 is turbine inlet temperature (K), T_1 is ambient temperature (K), r_p is the pressure ratio, η_t is turbine isentropic efficiency (%), and η_c is compressor isentropic efficiency (%). Dividing by 1000 converts W to kW. Higher pressure ratios increase ideal efficiency but also raise compressor outlet temperature, so an optimum ratio exists for maximum net work.
How to use
Consider a gas turbine with pressure ratio r_p = 10, turbine inlet T_4 = 1200 K, ambient T_1 = 300 K, mass flow ṁ = 50 kg/s, η_c = 85%, η_t = 88%. Turbine work term: 1200 × (1 − 10^(−0.286)) × 0.88 = 1200 × (1 − 0.5179) × 0.88 = 1200 × 0.4821 × 0.88 = 509.1 kJ/kg. Compressor work term: 300 × (10^(0.286) − 1) / 0.85 = 300 × (1.9307 − 1) / 0.85 = 300 × 1.0949 = 328.5 kJ/kg. Net specific work = 509.1 − 328.5 = 180.6 kJ/kg. Net power = 50 × 180.6 = 9030 kW ≈ 9.0 MW.
Frequently asked questions
How does pressure ratio affect gas turbine efficiency and net power output?
Increasing the pressure ratio raises the ideal Brayton cycle thermal efficiency, since more compression means more work can be extracted from the same fuel input. However, higher pressure ratios also raise the compressor outlet temperature (T2), which reduces the temperature rise possible in the combustor for a fixed turbine inlet temperature limit. As a result, net specific work peaks at an intermediate pressure ratio. For modern gas turbines with turbine inlet temperatures around 1400–1600 K, optimal pressure ratios for maximum power typically fall between 15 and 25, while optimal efficiency ratios are somewhat higher.
What is the role of isentropic efficiency in a real Brayton cycle calculation?
Isentropic efficiency accounts for irreversibilities in the compressor and turbine. A compressor isentropic efficiency below 100% means more work is required than the ideal isentropic case; a turbine isentropic efficiency below 100% means less work is extracted. These two penalties compound: the compressor consumes more power while the turbine delivers less, significantly reducing net output. For example, dropping both efficiencies from 100% to 85% can reduce net power by 30–40%. This is why advances in blade aerodynamics and cooling technology — which raise η_c and η_t — have driven dramatic improvements in gas turbine performance over recent decades.
Why is air modelled with a specific heat of 1.005 kJ/kg·K and γ = 1.4 in gas turbine calculations?
Dry air at moderate temperatures behaves approximately as a diatomic ideal gas with five active degrees of freedom, giving a ratio of specific heats γ = cp/cv = 1.4 and cp ≈ 1.005 kJ/kg·K. These values are used in the simple air-standard analysis of the Brayton cycle. In reality, cp and γ vary with temperature — air entering the turbine at 1200 K has cp closer to 1.15 kJ/kg·K. More accurate analyses use variable-property (real-gas or polynomial-fit) models. The constant-property assumption is standard for introductory calculations and gives results within about 5–10% of more rigorous analyses.