Afterburner Cycle

Afterburner (Reheat) Cycle (propulsion/gas-turbine-cycle/afterburner-cycle)

Use when the task is the afterburning (reheat) topping block of a gas turbine: reheat fuel is burned in the duct between the turbine exit and the nozzle to raise the gas temperature, which lifts the nozzle exit velocity and thrust at the cost of specific fuel consumption. This leaf implements the standard model in pure Python, stdlib only: the reheat fuel-air ratio from the duct energy balance, the reheat fuel flow, the dry and reheat nozzle exit velocities from a fully expanded ideal isentropic nozzle, the dry and reheat gross thrust, the thrust augmentation ratio, and the specific fuel consumption with and without reheat. It pairs with the gas-turbine-cycle and real-cycle-effects leaves, which supply the core upstream (the turbine exit state t04, p04 comes from the core analysis), and with combustor-design for the main combustor context. The fully expanded ideal nozzle is a documented simplification: real nozzles add a thrust coefficient below one.

Domain quick reference

• Reheat fuel-air ratio from the duct energy balance: f_ab = (1 + f_core) * CP * (t05 - t04) / (ETA_AB * LHV). The heat to raise the turbine exit products (air plus core fuel, 1 + f_core kg per kg of air) from t04 to t05 is divided by the useful heat released per kg of reheat fuel, ETA_AB * LHV.
• Reheat fuel flow: mdot_f_ab = f_ab * mdot_core.
• Nozzle static temperature after isentropic expansion: Te = Tt * (p_amb / p_total)^((GAMMA - 1) / GAMMA), GAMMA = 1.33.
• Fully expanded ideal nozzle exit velocity: v = sqrt(2 * CP * (Tt - Te)), CP = 1150 J/(kg K). Fully expanded means the exit pressure equals ambient, so the pressure thrust term is zero and the CP form carries the velocity; R = 287 J/(kg K) is documented but not used.
• Dry gross thrust: F_dry = mdot_core * (1 + f_core) * v_dry, with the nozzle entry at the turbine exit temperature t04.
• Reheat gross thrust: F_reheat = mdot_core * (1 + f_core + f_ab) * v_reheat, with the nozzle entry at the afterburner exit temperature t05.
• Thrust augmentation ratio: F_reheat / F_dry, about 1.4 for a typical augmented turbofan at full reheat.
• Specific fuel consumption: sfc = mdot_fuel / F in kg/(N s); multiply by 1e6 for mg/(N s).
• Module constants: CP = 1150.0 J/(kg K), LHV = 43.0e6 J/kg kerosene, ETA_AB = 0.97, GAMMA = 1.33, R = 287.0 J/(kg K). Units are SI throughout: K, Pa, kg/s, m/s, N, kg/(N s).
• FAR-33 frames the engine certification context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the operating point: the turbine exit total temperature t04_k and total pressure p04_pa (take them from the gas-turbine-cycle or real-cycle-effects core analysis), the core fuel-air ratio f_core, the core air mass flow mdot_core_kg_s, the chosen afterburner exit total temperature t05_k, and the ambient pressure p_amb_pa.
2. Compute the reheat fuel-air ratio with afterburner_far; the function rejects t05 <= t04 because an afterburner must add temperature.
3. Convert it to a reheat fuel flow with afterburner_fuel_flow.
4. Get the dry and reheat nozzle exit velocities with nozzle_exit_velocity, evaluated at t04 and at t05 with the same pressure ratio; the function requires p_total > p_amb for the fully expanded model.
5. Compute the dry gross thrust with thrust_dry and the reheat gross thrust with thrust_reheat (pass the f_ab from step 2).
6. Form the thrust augmentation ratio with augmentation_ratio.
7. Compute the specific fuel consumption with sfc for each mode: the core fuel flow f_core * mdot_core over the dry thrust, and the total fuel flow (f_core + f_ab) * mdot_core over the reheat thrust.
8. Run the whole operating point with analyze for the complete summary dict with all nine SI values.
9. Confirm the deterministic checks with the contract test scripts/test_afterburner_cycle.py.

Worked example

Augmented turbofan at full reheat: turbine exit 900 K, f_core 0.02, core flow 100 kg/s, afterburner exit 1700 K (an 800 K reheat temperature rise), p04 3.0e5 Pa, ambient 1.01325e5 Pa.

• f_ab = 1.02 * 1150 * 800 / (0.97 * 43e6) = 0.022498.
• mdot_f_ab = 0.022498 * 100 = 2.2498 kg/s.
• Dry nozzle: Te = 900 * (1.01325 / 3)^(0.33 / 1.33) = 687.6 K; v_dry = sqrt(2 * 1150 * (900 - 687.6)) = 699.1 m/s.
• Reheat nozzle: Te = 1298.7 K; v_reheat = 960.8 m/s.
• F_dry = 102 * 699.1 = 71,308 N (spec anchor 71,307 N, within 50 N).
• F_reheat = 104.2498 * 960.8 = 100,165 N (spec anchor 100,162 N, within 50 N).
• Augmentation ratio = 100,165 / 71,308 = 1.405.
• sfc_dry = 2.0 / 71,308 = 2.805e-5 kg/(N s) = 28.05 mg/(N s); sfc_reheat = 4.2498 / 100,165 = 4.243e-5 kg/(N s) = 42.43 mg/(N s), spec anchor 42.42 mg/(N s) within 2%. Reheat adds about 40% thrust but roughly doubles the specific fuel consumption, which is why military augmented engines use reheat only for dash and takeoff.

Verification

• Confirm afterburner_far(900, 1700, 0.02) returns 0.022498 within 1e-6, and that afterburner_fuel_flow gives 2.2498 kg/s within 1e-3.
• Confirm nozzle_exit_velocity returns 699.1 m/s at 900 K and 960.8 m/s at 1700 K, each within 1.0 m/s.
• Confirm thrust_dry returns 71,308 N within 50 N of the 71,307 N anchor and thrust_reheat returns 100,165 N within 50 N of the 100,162 N anchor.
• Confirm augmentation_ratio 1.405 within 0.005 and the identity F_reheat / F_dry from analyze equals the standalone ratio.
• Confirm sfc values are within 2% of the 28.05 and 42.42 mg/(N s) anchors, and that reheat SFC exceeds dry SFC.
• Confirm every invalid input raises ValueError: t05 <= t04, t04 <= 0, f_core < 0, non-positive mass flow, p04 <= p_amb, p_amb <= 0, zero fuel flow or negative fuel flow in sfc, non-positive dry thrust in augmentation_ratio.
• Run the contract test offline: python3 scripts/test_afterburner_cycle.py (35 tests, deterministic).

Related leaves

• propulsion/gas-turbine-cycle/gas-turbine-cycle: the ideal Brayton core upstream of the reheat duct; supplies t04 for the dry nozzle.
• propulsion/gas-turbine-cycle/real-cycle-effects: the non-ideal core with component efficiencies, the realistic source of t04 and p04.
• propulsion/gas-turbine-cycle/regenerative-cycle: the recuperated cycle alternative, which trades exhaust heat instead of burning reheat fuel.
• propulsion/gas-turbine-cycle/combustor-design: the main combustor fuel-air chemistry, distinct from the reheat duct topping block.
• propulsion/ramjet/ramjet-cycle: the continuous supersonic combustion cycle, the alternative high-speed propulsion path.
• propulsion/turbofan/turbofan-cycle: the turbofan core context of the augmented military engine.

Pitfalls

• Feeding an afterburner exit temperature at or below the turbine exit: t05 must exceed t04 or the duct energy balance is unphysical - the function rejects t05 <= t04 with ValueError, so the 800 K reheat rise in the worked example is the intended input shape.
• Ignoring the core fuel in the duct mass balance: the energy balance heats (1 + f_core) kg of gas per kg of air, and the reheat thrust carries (1 + f_core + f_ab) mdot_core, so dropping f_core (0.02 in the example) shifts both the fuel-air ratio and the thrust.
• Using the ideal-nozzle velocity for a real nozzle: the fully expanded ideal isentropic nozzle is a documented simplification with no pressure thrust term; real nozzles add a thrust coefficient below one, so the model overstates v and F.
• Evaluating the nozzle below the choked condition: nozzle_exit_velocity requires p_total > p_amb for the fully expanded model; feeding an unchoked or inverted pressure ratio raises ValueError rather than returning a partial-expansion velocity.
• Selling reheat as an efficiency measure: the worked example adds about 40% thrust (augmentation 1.405) but roughly doubles the specific fuel consumption (28.05 to 42.43 mg/(N s)) - the augmentation ratio alone hides the SFC cost.
• Reading the wrong SFC mode: sfc_dry divides only the core fuel flow f_core * mdot_core by the dry thrust while sfc_reheat divides the total fuel flow (f_core + f_ab) * mdot_core by the reheat thrust; swapping the denominators inverts the comparison.

Behavior contract (gate 3)

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

python3 scripts/test_afterburner_cycle.py

The test covers the worked-example anchors (reheat fuel-air ratio, reheat fuel flow, dry and reheat nozzle exit velocities, dry and reheat gross thrust, augmentation ratio, both SFC values), scaling trends with temperature rise, mass flow and pressure ratio, the augmentation identity at equal thrusts, the v = F / mdot_gas round trip inside analyze, and ValueError rejection of every non-physical input in the validation list.

Compliance

• Standards referenced, not reproduced: FAR-33 (Airworthiness Standards: Aircraft Engines) frames the engine certification context of the afterburner cycle assessment; the relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.