Apu Fuel Burn Sizing

APU Fuel Burn Sizing (vehicle-design/sizing/apu-fuel-burn-sizing)

Use when you must compute the fuel burn of the auxiliary power unit (APU) at a fixed electrical and bleed load point on a conceptual aircraft or rotorcraft. The APU is a small shaft and bleed powerplant that produces no propulsive force: it drives a generator and a load compressor, so its fuel flow follows from the electrical output converted back through the generator efficiency plus the bleed mass flow priced as adiabatic compression work, all divided by the APU thermal efficiency and the fuel lower heating value. This leaf implements that model in pure Python, stdlib only. It pairs with vehicle-design/sizing/aircraft-electrical-load-analysis, which owns the electrical load rollup and supplies the generator electrical output as the input here; the main-engine fuel flow analog lives in vehicle-design/sizing/engine-sizing.

Domain quick reference

• Generator shaft power: P_gen = P_elec / eta_gen, with the default generator efficiency eta_gen = 0.85. The electrical output is the AFTER generator efficiency, so the shaft side always carries more.
• Adiabatic compression work per kg of bleed: w = cp * T_in * (PR^((gamma-1)/gamma) - 1), with cp = 1005 J/kg K and gamma = 1.4. PR is the absolute total-pressure ratio across the APU load compressor and T_in the compressor inlet temperature (288 K default).
• Bleed pumping-power equivalent: P_bleed = m_dot_bleed * w / eta_comp, with the default load compressor efficiency eta_comp = 0.75. Bleed is priced in kg/s, never in kW.
• Total equivalent shaft load: P_total = P_gen + P_bleed. The APU must deliver this shaft power to hold the fixed load point.
• Fuel flow: m_dot_fuel = P_total / (eta_th * LHV), with the default thermal efficiency eta_th = 0.18 and jet fuel LHV = 43.2 MJ/kg; the hourly rate is exactly 3600 times the kg/s rate.
• Valid inputs: pressure ratio must exceed 1, every efficiency lies in (0, 1], bleed flow and inlet temperature and LHV are positive, and the electrical load is non-negative. All other values raise ValueError.
• FAR 25.903 frames the powerplant installation context for the APU and its controls; the relations above are standard engineering methodology, summary-only.

Workflow

1. Take the generator electrical output P_elec (W) from the electrical load analysis and the bleed demand m_dot_bleed (kg/s) at the load compressor pressure ratio PR from the bleed system context.
2. Convert the electrical output to the required generator shaft power with generator_shaft_power(p_elec_w, eta_gen).
3. Convert the bleed flow to its pumping-power equivalent with bleed_pumping_power(m_bleed_kg_s, pressure_ratio, t_inlet_k, eta_comp).
4. Sum both loads into one record with total_shaft_load(p_elec_w, m_bleed_kg_s, pressure_ratio): the dict carries generator_shaft_w, bleed_pumping_w and total_shaft_w.
5. Convert the total equivalent shaft load to the fuel flow with apu_fuel_burn(total_shaft_w, eta_th, lhv_j_kg): the dict carries fuel_kg_s and fuel_kg_h.
6. For a one-call result at the default 288 K inlet, run apu_summary(p_elec_w, m_bleed_kg_s, pressure_ratio), which returns all five outputs.
7. Confirm the deterministic checks with the contract test scripts/test_apu_fuel_burn_sizing.py.

Worked example

Reference APU load point: 30 kW electrical output at 0.85 generator efficiency, 0.40 kg/s bleed at pressure ratio 3.5 from a 288 K inlet with 0.75 compressor efficiency, thermal efficiency 0.18 and LHV 43.2 MJ/kg. Module outputs:

• Generator shaft power: 30000 / 0.85 = 35294.1 W (35.3 kW).
• Ratio term: 3.5^((1.4-1)/1.4) - 1 = 0.4304; bleed pumping power: 0.40 * 1005 * 288 * 0.4304 / 0.75 = 66435.2 W (66.4 kW).
• Total equivalent shaft load: 35294.1 + 66435.2 = 101729.3 W (101.7 kW).
• Fuel flow: 101729.3 / (0.18 * 43.2e6) = 0.013082 kg/s, which is 47.10 kg/h; the module reports 47.0969 kg/h and the kg/h rate is 3600 * 0.013082 to float precision.
• The bleed side dominates: the 66.4 kW pumping burden is nearly twice the 35.3 kW generator shaft load at this point.

Verification

• Confirm generator_shaft_power(30000) returns 35294.1 W, within 0.1 of 30000 / 0.85.
• Confirm bleed_pumping_power(0.40, 3.5) returns 66435.2 W, within 0.1 of the adiabatic-work hand value, and that the pressure ratio term vanishes as PR approaches 1 (the continuous zero-work limit; PR of exactly 1 is rejected).
• Confirm total_shaft_load(30000, 0.40, 3.5) totals 101729.3 W, the exact sum of its two parts.
• Confirm apu_fuel_burn gives 0.013082 kg/s within 1e-6 and 47.10 kg/h within 1e-2, with fuel_kg_h equal to 3600 * fuel_kg_s within 1e-9.
• Confirm doubling the total shaft load doubles the fuel flow, and that the dict keys are exactly generator_shaft_w, bleed_pumping_w, total_shaft_w, fuel_kg_s, fuel_kg_h in the documented order.
• Confirm ValueError rejection of a negative electrical load, bleed flow at or below zero, pressure ratio at or below 1, inlet temperature at or below zero, shaft load at or below zero, LHV at or below zero, and any efficiency outside (0, 1].
• Run the contract test offline: python3 scripts/test_apu_fuel_burn_sizing.py (35 tests, deterministic).

Related leaves

• vehicle-design/sizing/aircraft-electrical-load-analysis: the load rollup and generator sizing that produce the electrical output used as the input here.
• vehicle-design/sizing/engine-sizing: the main-engine fuel flow and sizing analog for the propulsion powerplant.
• vehicle-design/sizing/fire-protection-sizing: the APU compartment fire protection that is specified there, not here.

Pitfalls

• Treating the generator electrical output as shaft power: the shaft side is P_elec / eta_gen (35294 W for a 30 kW output at 0.85), so sizing the fuel burn on 30 kW alone understates the load by about 18%.
• Pricing the bleed in kg/s as if it were power: the pumping burden only appears after the adiabatic work relation at the stated pressure ratio (66.4 kW for 0.40 kg/s at PR 3.5), so a bare bleed flow number has no fuel-flow meaning.
• Accepting a pressure ratio of 1 or below: a load compressor must raise the total pressure, so the guard rejects PR <= 1 and the zero-work point only exists as the continuous limit from above.
• Reporting the kg/s fuel rate when the hourly rate is wanted: the two differ by a factor of 3600 (0.013 kg/s versus 47.1 kg/h).
• Recomputing the electrical load rollup here: the generator kW is the output of the electrical-load-analysis leaf and an input to this one, so duplicating the rollup would drift the two leaves apart.
• Borrowing the main-engine fuel flow relation: the APU is a shaft and bleed powerplant with no propulsive output, so engine-sizing owns the main-engine relation and this leaf prices only the shaft and bleed burden.

Behavior contract (gate 3)

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

python3 scripts/test_apu_fuel_burn_sizing.py

The test covers the reference load point (30 kW electrical, 0.40 kg/s bleed at pressure ratio 3.5) against the spec magnitude bounds, the generator identity P_elec / eta_gen, the zero-work continuous limit of the pressure ratio term, linear scaling of the pumping power with mass flow, the kg/h = 3600 * kg/s identity, the doubling-load doubling-fuel identity, exact dict key contracts for the three dict functions, determinism, and ValueError rejection of every non-physical input in the validation list.

Compliance

• Standards referenced, not reproduced: FAR 25.903 is the powerplant installation and APU context for this sizing (25.903 powerplant/APU per standards-map.yaml); the thermodynamic relations above are standard engineering methodology, summary-only.
• compliance: STANDARDS-REF, gated: false.