Brayton Cycle

The four processes

Step	Process	Component	What changes	Heat / Work
1 → 2	Adiabatic compression	Compressor	P, T rise; volume falls	W_c absorbed by air, Q = 0
2 → 3	Isobaric heat addition	Combustor	T rises at constant P	Q_in = c_p (T₃ − T₂)
3 → 4	Adiabatic expansion	Turbine	P, T fall; volume rises	W_t done by gas, Q = 0
4 → 1	Isobaric heat rejection	Atmosphere / heat exchanger	T falls at constant P (= P₁)	Q_out = c_p (T₄ − T₁)

The cycle is open-flow: fresh air enters at 1, exhaust leaves at 4, never closing the same mass back through the engine. The air-standard idealization treats steps 4 → 1 as a fictitious heat exchanger that returns the gas to state 1, allowing closed-cycle analysis.

Efficiency vs pressure ratio

From the two adiabats sharing the same temperature ratio T₂/T₁ = T₃/T₄ = r_p^((γ−1)/γ):

η_Brayton = 1 − Q_out / Q_in
          = 1 − (T₄ − T₁) / (T₃ − T₂)
          = 1 − T₁/T₂
          = 1 − r_p^((1−γ)/γ)

Efficiency depends only on the pressure ratio and γ — not on the turbine inlet temperature T₃, which sets the work output but not the efficiency.

Pressure ratio r_p	η for γ = 1.4	Example engine
4	32.6%	1940s industrial gas turbines
10	48.2%	Pratt & Whitney JT3 (early 707)
15	53.9%	GE J79 (F-4 Phantom)
20	57.5%	GE LM2500 industrial
30	62.1%	CFM56 (737, A320)
40	64.6%	GE GEnx (787 / 747-8)
50	66.7%	Pratt PW1100G (A320neo)
60	68.4%	GE9X (777X)

Real engines fall well below these ideal numbers (35 to 50% for aero turbofans) because of compressor and turbine inefficiencies (88 to 92% each), pressure losses, cooling-air bleeds, and combustor pressure drops.

Worked example — typical airliner cruise

State	Location	P (kPa)	T (K)
1 — inlet (sea level)	Compressor entry	101	288
2 — compressor exit	Combustor entry	3030 (r_p = 30)	772
3 — combustor exit	Turbine entry	3030	1700 (limit)
4 — turbine exit	Nozzle entry	101	634

Ideal η = 1 − 288/772 = 62.7%. Net specific work: c_p (T₃ − T₄) − c_p (T₂ − T₁) = 1.005 (1700 − 634 − 772 + 288) = 585 kJ/kg. For a CFM56-class engine flowing 200 kg/s of air, that is 117 MW (≈ 157,000 hp) — about half of which is reabsorbed by the compressor, so net shaft power at the turbine is around 60 MW. In a turbojet that net power is converted to thrust by accelerating the exhaust; in a turbofan, most of it spins a large bypass fan instead.

Variants

• Regenerative Brayton. Recuperator passes hot turbine exhaust over compressed air before the combustor. Boosts efficiency at low pressure ratios where T₄ > T₂; useful for microturbines (Capstone, Bladon Jets). Stops helping once r_p reaches the cross-over r_p,max = (T₃/T₁)^(γ/(2(γ−1))).
• Intercooled Brayton. Cool the air between two compressor stages with a heat exchanger; reduces compressor work for the same overall r_p. Common in large industrial gas turbines (GE LMS100 uses intercooling + recuperation, reaching 46% simple-cycle efficiency).
• Reheat Brayton. Burn additional fuel between two turbine stages, raising the mean heat-addition temperature; boosts work output but slightly hurts efficiency unless combined with regeneration. Mitsubishi M501J and Siemens HL-class heavy-frame turbines use reheat.
• Combined cycle (Brayton + Rankine). The gas-turbine Brayton exhaust drives a heat-recovery steam generator feeding a Rankine bottoming cycle. Net plant efficiency 60 to 64%. Workhorse of modern natural-gas baseload electricity.
• Closed-cycle Brayton. Working fluid (helium, CO₂, nitrogen) is sealed and recirculated, with external heat sources (nuclear, solar) and external cooling. Used in supercritical CO₂ power cycles and high-temperature gas-cooled nuclear concepts.
• Turbojet, turbofan, turboprop, turboshaft. Same Brayton thermodynamics; differ in how the turbine's net power is routed — through a nozzle (jet), a fan (fan), a propeller (prop), or a shaft (shaft). High-bypass turbofans dominate modern airliners because they convert thrust per fuel-pound much more efficiently at subsonic speeds.

JavaScript — Brayton thermodynamics

function braytonEfficiency(rP, gamma = 1.4) {
  return 1 - Math.pow(rP, (1 - gamma) / gamma);
}

console.log(`r_p=10: η = ${(braytonEfficiency(10) * 100).toFixed(1)}%`); // 48.2
console.log(`r_p=30: η = ${(braytonEfficiency(30) * 100).toFixed(1)}%`); // 62.1
console.log(`r_p=60: η = ${(braytonEfficiency(60) * 100).toFixed(1)}%`); // 68.4

// Ideal cycle states (air-standard)
function braytonStates({ P1, T1, rP, T3, gamma = 1.4, cp = 1005 }) {
  const exp = (gamma - 1) / gamma;
  const P2 = P1 * rP;
  const T2 = T1 * Math.pow(rP, exp);
  const T4 = T3 / Math.pow(rP, exp);
  const w_compressor = cp * (T2 - T1);   // J/kg absorbed by air
  const w_turbine    = cp * (T3 - T4);   // J/kg delivered by air
  const w_net        = w_turbine - w_compressor;
  const q_in         = cp * (T3 - T2);
  const eta          = w_net / q_in;
  return {
    1: { P: P1,    T: T1 },
    2: { P: P2,    T: T2 },
    3: { P: P2,    T: T3 },
    4: { P: P1,    T: T4 },
    w_compressor, w_turbine, w_net, q_in, eta,
  };
}

const cfm56 = braytonStates({ P1: 101e3, T1: 288, rP: 30, T3: 1700 });
console.log(cfm56);
// eta ≈ 0.627, w_net ≈ 585 kJ/kg

// With component inefficiencies (more realistic)
function braytonRealistic({ P1, T1, rP, T3, gamma = 1.4, cp = 1005, eta_c = 0.90, eta_t = 0.92 }) {
  const exp = (gamma - 1) / gamma;
  const T2s = T1 * Math.pow(rP, exp);
  const T4s = T3 / Math.pow(rP, exp);
  const T2 = T1 + (T2s - T1) / eta_c;
  const T4 = T3 - eta_t * (T3 - T4s);
  const w_c = cp * (T2 - T1);
  const w_t = cp * (T3 - T4);
  const w_net = w_t - w_c;
  const q_in = cp * (T3 - T2);
  return { T2, T4, w_c, w_t, w_net, q_in, eta: w_net / q_in };
}

const real = braytonRealistic({ P1: 101e3, T1: 288, rP: 30, T3: 1700 });
console.log(`Realistic CFM56-like: η = ${(real.eta * 100).toFixed(1)}%`);  // ~45%

Where the Brayton cycle matters

• Commercial aviation. Every jet airliner in service runs a Brayton-cycle turbofan. The CFM LEAP, Pratt PW1000G, RR Trent XWB, and GE GEnx between them power the entire fleet.
• Military jets. Low-bypass turbofans (F119 in F-22, F135 in F-35) and afterburning turbojets all follow the Brayton cycle with afterburner reheat for short bursts of high thrust.
• Helicopters and turboprops. Turboshafts in helicopters (T700 in Black Hawks, RTM322 in NH90) and turboprops in regional aircraft (PW150 in Q400, PT6 in countless small planes) use the same cycle with a free-turbine drive.
• Natural-gas electricity. Combined-cycle gas-turbine plants generate roughly 25% of global electricity, with single-shaft units up to 500 MW per train.
• Pipeline compressors. Gas pipelines use Brayton-cycle prime movers driving the compressors that push gas hundreds of miles between cities.
• Microturbines and APUs. Aircraft auxiliary power units (Honeywell 131-9, Hamilton-Sundstrand) and microturbines (Capstone) run the same cycle at scales of 30 to 1000 kW.
• Spacecraft and nuclear. Closed-cycle Brayton with helium or supercritical CO₂ is the leading candidate for next-generation high-temperature nuclear reactors and lunar-base power.

Common mistakes

• Confusing pressure ratio with compression ratio. Brayton uses r_p = P₂/P₁ (pressures), Otto uses r = V₁/V₂ (volumes). Related by r_p = r^γ in air-standard, but they are different quantities and listed differently in spec sheets.
• Forgetting compressor work eats turbine output. In a typical jet, the turbine extracts roughly twice the power the compressor needs; only the remaining half is available for thrust or shaft work. Back-of-envelope estimates that omit compressor work overstate available power.
• Mixing up efficiency limit and work output. Efficiency depends only on r_p; net specific work depends additionally on T₃/T₁. Pushing r_p further raises η but reduces work-per-kilogram once T₂ approaches T₃.
• Treating regeneration as always beneficial. Above the cross-over pressure ratio r_p,max ≈ (T₃/T₁)^(γ/(2(γ−1))), the recuperator would heat-load backwards — useless or worse than nothing. Modern high-r_p turbines have no regenerator.
• Confusing T₃ limit with cycle ceiling. Turbine inlet temperature T₃ is set by metallurgy (cooled superalloys, 1700 to 2000 K). Higher T₃ increases work, but does not increase ideal Brayton efficiency.
• Forgetting open-cycle is not the same as Carnot. Brayton with heat rejection to a fixed-temperature atmosphere has η < η_Carnot computed between T₃ and T₁. The pressure-ratio formula gives the upper bound for Brayton specifically.

Performance — push for more efficiency

Three engineering frontiers continue to raise Brayton efficiency. (1) Higher pressure ratios: Rolls-Royce UltraFan targets r_p = 70, the GE9X already runs 60 in service. (2) Higher turbine inlet temperatures: single-crystal superalloy blades with internal film cooling now survive 2000 K gas at sustained operation — up from 1500 K in the 1980s. Each 100 K increase yields ~2 to 3% more cycle efficiency. (3) Combined cycles: bottoming with a steam Rankine cycle recaptures ~10 percentage points of efficiency from exhaust waste heat, taking plant efficiency from ~45% (simple cycle) to ~64% (combined cycle). The all-time record for any prime mover is held by Siemens's HL-class combined-cycle plant in Lausward, Germany: 61.5% net thermal efficiency. The IEA projects the next decade will see commercial combined-cycle units crack 65%.