Turbojet Cycle

Turbojet Cycle (propulsion/gas-turbine-cycle/turbojet-cycle)

Use when the task is the ideal single-stream turbojet core cycle at a flight Mach number: the inlet stagnation state, the compressor exit state, the combustor fuel-to-air ratio, the turbine exit state from the compressor-turbine work balance, the fully expanded nozzle state, and the net specific thrust, TSFC and propulsive efficiency that close the cycle. This leaf owns the compressor-turbine matching middle of the core-engine cycle assessment, which no other leaf computes. It pairs with the shaft-power cycle leaf (gas-turbine-cycle/gas-turbine-cycle) and the lossy cycle leaf (gas-turbine-cycle/real-cycle-effects) for the ideal-to-real follow-on, with gas-turbine-cycle/subsonic-inlet-recovery for the ram recovery that sets the inlet stagnation state, and with gas-turbine-cycle/combustor-design for the burner sizing side of the fuel-to-air ratio.

Domain quick reference

• Stations: 0 freestream, 3 compressor exit, 4 combustor exit (turbine inlet), 5 turbine exit, 9 nozzle exit. SI units throughout: K, kg fuel per kg air, N per (kg/s), kg/(N s), m/s.
• Freestream stagnation temperature: Tt0 = t0 * (1 + (gamma - 1)/2 * M^2). At mach 0.9 and 288.15 K this gives 334.8 K.
• Compressor exit temperature: T03 = Tt0 * pr^((gamma-1)/gamma). The compression traverse raises 334.8 K to 764.7 K at pressure ratio 18.
• Fuel-to-air ratio: f = cp_c * (t04 - t03) / (eta_b * lhv), the combustor energy balance at efficiency eta_b.
• Compressor-turbine work balance (the matching step): Tt5 = t04 - (cp_c/cp_g) * (t03 - Tt0). The turbine work equals the compressor work, so Tt5 falls when the compressor exit temperature rises at fixed turbine inlet temperature.
• Nozzle total pressure ratio chain: pt5/p0 = (1 + (gamma-1)/2 * M^2)^ (gamma/(gamma-1)) * pr * (Tt5/Tt4)^(gamma/(gamma-1)), the ram factor times the compressor ratio times the turbine expansion factor.
• Nozzle exit temperature: T9 = Tt5 * (p0/pt5)^((gamma-1)/gamma) for a fully expanded nozzle to ambient pressure.
• Exit velocity: v9 = sqrt(2 * cp_g * (Tt5 - T9)), the thermal expansion of the remaining enthalpy drop.
• Net specific thrust: F/mdot = v9 - v0 with v0 = M * sqrt(gamma * R * t0). The flight velocity term is the ram drag, so the specific thrust falls as the Mach number rises at fixed turbine inlet temperature.
• Turbojet TSFC: TSFC = f / (F/mdot) in kg/(N s); TSFC times the specific thrust equals the fuel-to-air ratio.
• Propulsive efficiency: eta_p = 2 * v0 / (v0 + v9), always below 1 and rising as v9 approaches v0.
• Module gas constants: gamma 1.4, cp_c 1005 J/(kg K), cp_g 1150 J/(kg K), R 287 J/(kg K), lhv 43 MJ/kg, eta_b 0.99; keyword overrides allowed. FAR 33 frames the engine context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the operating point: freestream static temperature t0, flight Mach number mach, compressor pressure ratio pr and turbine inlet temperature t04, all SI, the cycle_report input set.
2. Freestream stagnation temperature traverse: freestream_stagnation_ temperature(t0, mach) returns Tt0 from the Mach number.
3. Compression traverse: compressor_exit_temperature(t0, mach, pr) returns the compressor exit temperature T03.
4. Combustor energy balance: fuel_air_ratio(t03, t04) returns the fuel-to-air ratio f from the turbine inlet temperature, the combustor efficiency and the lower heating value.
5. Compressor-turbine matching step: turbine_exit_temperature(t03, t04, t0, mach) returns the turbine exit temperature Tt5 from the work balance; this is the canonical compressor-turbine matching of the core engine.
6. Nozzle expansion: nozzle_exit_temperature(t0, mach, pr, t04) returns the nozzle exit temperature T9 through the nozzle total pressure ratio chain, then exit_velocity(t05, t9) returns the exit velocity v9 from the thermal drop Tt5 - T9.
7. Thrust bookkeeping: net_specific_thrust(t0, mach, t05, t9) returns the net specific thrust F/mdot, turbojet_tsfc(f, F/mdot) returns the turbojet TSFC, and propulsive_efficiency(v0, v9) returns the propulsive efficiency.
8. Cycle report: cycle_report(t0, mach, pr, t04) returns the dict with keys tt0, t03, fuel_air, t05, t9, v9, specific_thrust, tsfc and propulsive_efficiency for the matching and trade study.
9. Verify: run python3 scripts/test_turbojet_cycle.py; the contract test asserts the worked-example anchors, the TSFC round-trip identity, the ram-drag trend, the zero-Mach degenerate thermal expansion identity and every ValueError guard.

Worked example

Sea level static day, t0 = 288.15 K, mach 0.9, pr 18, t04 = 1600 K. Module outputs (contract test anchors in parentheses):

• Tt0 = 334.83 K (334.8 within 0.2 K).
• T03 = 764.67 K (764.7 within 0.5 K).
• f = 0.01972 (0.0197 within 1e-4), about 19.7 g fuel per kg air.
• Tt5 = 1224.36 K (1224.4 within 0.5 K) from the compressor-turbine work balance.
• T9 = 602.93 K; v9 = 1195.53 m/s (1195.5 within 1 m/s).
• v0 = 306.24 m/s; F/mdot = 889.29 N/(kg/s) (889.3 within 1).
• TSFC = 2.218e-5 kg/(N s) (2.22e-5 within 1e-7), about 22.2 mg/(N s).
• Propulsive efficiency = 0.408 (0.408 within 0.002).
• Round trip: TSFC * F/mdot = 0.01972 = f exactly.
• The degenerate identity: at zero Mach the flight velocity vanishes and the net specific thrust equals the nozzle exit velocity, the thermal expansion of the added heat.

Verification

• Confirm freestream_stagnation_temperature(288.15, 0.9) returns 334.83 K and compressor_exit_temperature(288.15, 0.9, 18.0) returns 764.67 K.
• Confirm fuel_air_ratio(764.67, 1600.0) returns 0.01972 and turbine_exit_temperature(764.67, 1600.0, 288.15, 0.9) returns 1224.36 K.
• Confirm exit_velocity then net_specific_thrust reproduce v9 = 1195.53 m/s and F/mdot = 889.29 N/(kg/s); the TSFC round trip TSFC * F/mdot equals f.
• Confirm the net specific thrust decreases as the Mach number rises at fixed t04 (ram drag) and the propulsive efficiency stays below 1.
• Degenerate identity: the spec states it at zero Mach with a unity pressure ratio, but the model rejects pressure ratio 1 (no compression means no expandable pressure ratio, a ValueError guard in the validation list), so the identity is exercised at zero Mach with pressure ratio 18, where v0 = 0 and the net specific thrust equals the nozzle thermal expansion velocity, and in the near-unity limit at pressure ratio 1.001 where the cycle stays defined.
• Confirm every non-positive temperature or LHV, mach below 0, pressure ratio at or below 1, turbine inlet temperature at or below the compressor exit temperature, combustor efficiency outside (0, 1] and every non-finite input raises ValueError.
• Run the contract test offline: python3 scripts/test_turbojet_cycle.py (34 tests, deterministic, exits 0).

Related leaves

• propulsion/gas-turbine-cycle/gas-turbine-cycle: the shaft-power Brayton cycle leaf upstream of the propulsive stream.
• propulsion/gas-turbine-cycle/real-cycle-effects: component efficiencies and pressure loss that turn this ideal cycle real.
• propulsion/gas-turbine-cycle/subsonic-inlet-recovery: the ram recovery that sets the inlet stagnation state at flight Mach.
• propulsion/gas-turbine-cycle/combustor-design: burner geometry and efficiency on the fuel-to-air ratio computed in step 4.

Pitfalls

• Treating the ideal cycle as the real engine: this leaf assumes isentropic machines and no pressure loss; real-cycle-effects adds the component efficiencies that lower Tt5 and raise the TSFC.
• Balancing the shaft power on the wrong specific heats: the work balance Tt5 = t04 - (cp_c/cp_g) * (t03 - Tt0) mixes the cold-side compressor work (cp_c = 1005) with the hot-side turbine (cp_g = 1150); using one cp for both shifts Tt5 by tens of kelvin.
• Forgetting the ram drag: F/mdot is v9 minus v0, not v9; at mach 0.9 the 306 m/s flight velocity is a third of the exit velocity, so a gross-thrust number overstates the net specific thrust.
• Reading the degenerate identity at pressure ratio 1: the model rejects pressure ratio 1 by design, and the check runs at zero Mach where the ram term vanishes, not at a unity compression ratio.
• Quoting TSFC without the round trip: TSFC * F/mdot must equal the fuel-to-air ratio; if the product drifts from f, the fuel or thrust leg is inconsistent.
• Expanding states that cannot reach ambient: the nozzle model requires pt5/p0 above 1; states that do not expand to ambient raise ValueError instead of returning an imaginary exit velocity.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_turbojet_cycle.py

The test covers the worked-example anchors (Tt0 334.8 K, T03 764.7 K, f 0.0197, Tt5 1224.4 K, v9 1195.5 m/s, F/mdot 889.3 N/(kg/s), TSFC 2.22e-5 kg/(N s), propulsive efficiency 0.408), the closed forms of every traverse, the compressor-turbine work balance trend, the TSFC round-trip identity, the ram-drag trend, the zero-Mach degenerate thermal expansion identity, the exact cycle report keys, determinism, and ValueError rejection of pressure ratio at or below 1, turbine inlet temperature at or below the compressor exit temperature, negative Mach, non-positive temperatures and LHV, out-of-range combustor efficiency, non-finite inputs and nozzle states that do not expand.

Compliance

• Standards referenced, not reproduced: 14 CFR Part 33 (FAR 33) frames the engine type-certification context (ecfr.gov); the ideal cycle relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.