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Regenerative Brayton cycle at a pressure ratio of 10 with 85 % / 90 % compressor and turbine efficiencies: air with variable specific heats against the cold-air standard

Tool	Power and Refrigeration Cycles
Source	McBride, B. J., Zehe, M. J., and Gordon, S. (2002). NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species. NASA/TP-2002-211556, NASA Glenn Research Center, Cleveland, OH (equations 1–3, appendix D "Air" record); Cengel, Y. A., and Boles, M. A. (2015). Thermodynamics: An Engineering Approach, 8th ed. McGraw-Hill Education, New York. Chapter 9 (Brayton cycle with regeneration, eqs 9-17 and 9-22).
Level	Undergraduate

Problem

Air enters the compressor of a gas-turbine plant at 300 K and 100 kPa and is compressed through a pressure ratio of 10 with an isentropic efficiency of 85 %; a regenerator of effectiveness 0.80 preheats it with the exhaust before the combustor raises it to 1,400 K, and the turbine (isentropic efficiency 90 %) expands it back to 100 kPa. Find every state, the compressor and turbine work, the heat added, the net work, the thermal efficiency and back-work ratio, the Carnot bound and the air flow for 1 MW, with variable specific heats, and compare with the cold-air-standard (k = 1.4) values.

Inputs to Enter

Cycle Brayton, working gas air (NASA Glenn record), cold-air k 1.4, net power 1,000 kW
T_1 26.85 °C (300 K), p_1 100 kPa, r_p 10, T_3 1,126.85 °C (1,400 K), η_c 0.85, η_t 0.90, regenerator ε 0.80, no intercooling or reheat

Open the Power and Refrigeration Cycles tool (loaded with this example)

Answers

Compressor: T_2s = 574.02 K from s°(T_2s) = s°(T_1) + R ln 10; T_2 = 621.01 K, w_c = h_2 − h_1 = 329.07 kJ/kg
Turbine: T_4s = 787.80 K, T_4 = 851.86 K, w_t = h_3 − h_4 = 636.14 kJ/kg; regenerator exit T_5 = 806.61 K
q_in = h_3 − h_5 = 686.17 kJ/kg, q_out = 379.09 kJ/kg, w_net = 307.08 kJ/kg, η_th = 44.75 %, back-work ratio 0.517, Carnot 78.6 %
Air flow for 1 MW: 3.257 kg/s (heat input 2.235 MW)
Cold-air standard (k = 1.4) with the same efficiencies and regenerator: η = 43.56 %, w_net = 280.21 kJ/kg; ideal closed form 1 − 10^(−0.4/1.4) = 48.21 %; maximum-work pressure ratio (1400/300)^1.75 = 14.82
USCS switch (80.33 °F / 2,060.33 °F, 14.504 psia): the same 44.75 %, w_net 132.02 Btu/lb, 7.179 lb/s

Notes

The tool's default inputs are this cycle; press Submit. The case is the brief's regenerative Brayton cycle computed with the NASA Glenn air properties and checked against an independent numpy/scipy solution of the same cycle (References/Thermodynamic-Cycles/checks/cycles_check.py) in test_thermodynamic_cycles.php, which also reproduces the NASA Table B1 values at 298.15 K and the NIST-JANAF rows at 1,000 and 2,000 K for the six gases, the cold-air closed forms of the Otto, Diesel and Brayton cycles through the same code, and the Rankine and R-134a refrigeration defaults against the NIST Chemistry WebBook tables; it is not a worked example printed in a textbook.