Power Generation Thermodynamics, Microturbines & Recuperated Brayton Cycles
Recuperated Brayton Gas Turbine Effectiveness & Efficiency
Calculate Recuperated Gas Turbine / Microturbine Preheated Combustor-Inlet Temperature Tx (K), Combustor Fuel Heat Input Saved %, Simple Unrecuperated Brayton Efficiency, and Recuperated Thermal Efficiency.
Recover hot turbine exhaust into compressor discharge—only when T4 exceeds T2!
Moderate-pressure-ratio industrial gas turbines and microturbines discharge turbine exhaust at T4 (K) hotter than compressor exit air T2 (K)! Routing both streams through a counterflow Exhaust Recuperator of thermal effectiveness ε = (Tx - T2) / (T4 - T2) preheats air entering the combustor to Tx = T2 + ε * (T4 - T2)—slashing fuel consumption from Cp*(T3 - T2) down to Cp*(T3 - Tx) while leaving net shaft work Cp*((T3 - T4) - (T2 - T1)) unchanged (neglecting small recuperator pressure drops)! Beware the classic aero-derivative high-pressure-ratio trap: if high compression heats T2 ABOVE turbine exhaust T4, a recuperator would transfer heat backward out of compressor air and REDUCE cycle efficiency!
Verify on a 200 kW Recuperated Microturbine—Compressor_Exit_T2 = 500.0 K (B2), Turbine_Inlet_TIT_T3 = 1,300.0 K (B3), Turbine_Exhaust_T4 = 800.0 K (B4), Ambient_Inlet_T1 = 300.0 K (B5), and Recuperator_Effectiveness_ε = 0.80 (80.0%, B6): Preheated Combustor Inlet Tx reaches 500 + 0.80 * (800 - 500) = 740.00 K (E2), cutting Combustor Fuel Input by 240 / 800 = 0.3000 (30.00% in E3) and boosting Thermal Efficiency from 300 / 800 = 0.3750 (37.50% unrecuperated in E4) up to 300 / 560 = 0.5357 (53.57% in E5)!
| Recuperated Brayton Metric (T1=300 K, T2=500 K, T3=1300 K, T4=800 K, ε=0.80) | Formula | Verified Output |
|---|---|---|
| Preheated Combustor Inlet Tx (K) | T2 + ε * (T4 - T2) | 740.00 K (500.00 K @ ε=0) |
| Combustor Fuel Saved Ratio | (ε * (T4 - T2)) / (T3 - T2) | 0.3000 (30.00% Fuel Saved) |
| Simple Unrecuperated Efficiency | ((T3 - T4) - (T2 - T1)) / (T3 - T2) | 0.3750 (37.50%) |
| Recuperated Cycle Efficiency | ((T3 - T4) - (T2 - T1)) / (T3 - Tx) | 0.5357 (0.3750 @ ε=0) |
Recuperated Brayton Cycle Thermal Efficiency Formula
Enforce T1 > 0, T2 > T1, T4 > T2 (thermodynamic recuperability requirement!), T3 > T4, positive net shaft work (T3 - T4) > (T2 - T1), and ε in [0, 1)!
=LET(t_2, B2, t_3, B3, t_4, B4, t_1, B5, ep_r, B6, wn_t, (t_3 - t_4) - (t_2 - t_1), IF(OR(t_1 <= 0, t_2 <= t_1, t_4 <= t_2, t_3 <= t_4, wn_t <= 0, ep_r < 0, ep_r >= 1), "Invalid or Non-Recuperable Cycle (T2 >= T4)", LET(t_x, t_2 + ep_r * (t_4 - t_2), ROUND(wn_t / (t_3 - t_x), 4))))Bypassed Recuperator Baseline & High-Pressure-Ratio Crossover Guard Checks
Set Recuperator_Effectiveness B6 = 0 to confirm E5 collapses cleanly to Simple Unrecuperated Efficiency 0.3750! Then raise Compressor_Exit_T2 B2 to 850 K (> T4 = 800 K) to verify the crossover guard rejects reverse heat transfer!
=IF(ISTEXT(E5), E5, ROUND((B6 * (B4 - B2)) / (B3 - B2), 4))Try the example
Use the original values or change them to test your understanding.