Fuel Feed System Sizing

Fuel Feed System Sizing (vehicle-design/sizing/fuel-feed-system-sizing)

Use when the task is sizing the aircraft fuel feed system between the tank outlet and the engine at the conceptual level: converting the per-engine engine fuel flow demand into the feed line velocity and Reynolds number, computing the line pressure loss from the Darcy friction factor with the major loss over the line length and the minor losses from the fitting loss coefficient, adding the static head gain from the tank to the engine-driven pump, and checking the net positive suction head available at the pump inlet against the required NPSH with the boost pump pressure rise added at cruise altitude. This leaf implements the model in pure Python, stdlib only, in scripts/fuel_feed_system_sizing_logic.py. It pairs with vehicle-design/sizing/fuel-tank-sizing as the storage side (fuel mass to tank volume, ullage and capacity fit, which this leaf's feed starts from) and vehicle-design/sizing/engine-sizing as the demand side (the engine fuel flow this leaf's line must carry).

Domain quick reference

• Feed flow: the per-engine feed mass flow m_dot follows the engine fuel flow demand at takeoff; the volumetric feed flow is Q = m_dot / rho.
• Line velocity: V = m_dot / (rho * A) with A = pi D^2 / 4 for the representative feed line of diameter D from the tank outlet to the engine-driven pump inlet.
• Reynolds number: Re = V D rho / mu, with mu the fuel dynamic viscosity; Re below 2300 is laminar, above it turbulent.
• Darcy friction factor: f = 64/Re for Re < 2300, else the Blasius correlation f = 0.3164 Re^-0.25.
• Major line loss: dP_major = f (L/D) rho V^2 / 2 over the line length L; it scales linearly with length and with the square of velocity.
• Minor loss: dP_minor = K rho V^2 / 2 from the fitting loss coefficient sum K (elbows, valves, couplings, filter and flow meter); K = 0 gives no minor loss.
• Static head: dP_static = rho g h, the tank outlet height h above the pump inlet; a pump above the tank makes h negative and reduces the available head.
• NPSH available: NPSHa = (p_source + dP_static - dP_line - p_vapor) / (rho g) in metres of fuel column, with p_source the tank vent pressure at the operating altitude and dP_line the total major plus minor loss. The signed value is returned; negative NPSHa means the pump inlet cannot be fed.
• Feed verdict: PASS when NPSHa >= NPSHr (the pump required NPSH), else FAIL; the margin is NPSHa - NPSHr. With a boost pump the rise dp_boost adds to the source pressure before the NPSH check.
• Boost pump power: P = Q dp_boost / eta from the volumetric feed flow, the pressure rise (15 psi class for Jet A at cruise) and the pump efficiency.
• Units are SI throughout (kg/s, m, Pa, kg/m3, Pa s); PSI_TO_PA = 6894.757 converts a boost pump rating.
• FAR 25.955 (fuel flow) and 25.975 (fuel feed context) frame the transport category fuel system requirement; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the feed operating point: per-engine feed mass flow m_dot from the engine fuel flow demand, fuel density rho, line diameter D and length L, viscosity mu and the fitting loss coefficient K.
2. Get the line velocity and area with line_velocity; doubling the flow doubles the velocity at fixed diameter.
3. Compute the Reynolds number with reynolds_number and pick the friction branch with friction_factor (64/Re laminar, Blasius turbulent).
4. Compute the major loss with major_loss_pa and the minor loss with minor_loss_pa; the total line loss is their sum.
5. Convert the tank height above the pump with static_head_pa and evaluate the NPSH available with npsh_available from the vent pressure, static head, line loss and vapor pressure.
6. Check the feed with feed_verdict against the pump required NPSH: PASS or FAIL with the margin in metres.
7. For a boost pump at cruise altitude, convert the pressure rise to Pa with PSI_TO_PA and get the hydraulic power with boost_pump_power from the volumetric feed flow over the efficiency.
8. Run the whole chain in one call with feed_system_summary for the complete sizing dict (15 keys: velocity_m_s, area_m2, reynolds, friction_factor, major_loss_pa, minor_loss_pa, total_line_loss_pa, static_head_pa, npsh_available_m, npsh_required_m, margin_m, verdict, npsh_with_boost_m, boost_pressure_rise_pa, boost_power_w), then confirm the deterministic checks with the contract test scripts/test_fuel_feed_system_sizing.py.

Worked example

Reference feed line: per-engine flow 0.45 kg/s, Jet A density 800 kg/m3, line diameter 0.05 m, length 12 m, viscosity 2.4e-3 Pa s, minor loss coefficient 3.0, tank 1.5 m above the pump inlet, tank vent pressure 24.3 kPa at 40,000 ft, fuel vapor pressure 1.0 kPa, required NPSH 3.0 m, boost pump rise 15 psi at 0.60 efficiency. Real module outputs:

• line_velocity(0.45, 800.0, 0.05): velocity_m_s = 0.28648 (spec anchor 0.2865 m/s), area_m2 = 0.0019635.
• reynolds_number: 4774.65 (turbulent, anchor 4775).
• friction_factor(4774.65): 0.038063 (Blasius, anchor 0.0381).
• major_loss_pa: 299.89 Pa (anchor 299.9); minor_loss_pa(3.0, ...): 98.48 Pa (anchor 98.5); total_line_loss_pa = 398.37 (anchor 398.4).
• static_head_pa(800.0, 1.5): 11767.98 Pa (anchor 11768.0).
• npsh_available: (24300 + 11767.98 - 398.37 - 1000) / 7845.32 = 4.4191 m (anchor 4.42 m) against 3.0 m required -> feed_verdict PASS, margin 1.4191 m (anchor 1.42 m).
• With the 15 psi boost rise (103421.36 Pa): npsh_available = 17.6017 m (anchor 17.60 m), margin 14.60 m.
• boost_pump_power(5.625e-4, 103421.36, 0.60): power_w = 96.96 W (anchor 97 W); the volumetric feed flow is 0.45/800 = 5.625e-4 m3/s.
• feed_system_summary(...) returns all 15 keys in one dict with verdict PASS.

Pitfalls

• Confusing the friction branches: Re below 2300 is laminar (f = 64/Re exactly) while turbulent flow uses the Blasius correlation f = 0.3164 Re^-0.25, with the Blasius branch applying at Re = 2300 exactly; the wrong branch changes the loss by several times.
• Signing the static head backwards: dP_static = rho g h uses the tank height ABOVE the pump inlet, so a pump above the tank makes h negative and REDUCES the available head (a pump 1.0 m above the tank costs 2.5 m of NPSH against the 1.5 m tank case).
• Quoting NPSH without the boost pump context: the boost pump rise adds to the source pressure at cruise altitude (4.42 m plain versus 17.60 m with the 15 psi rise in the worked example); the verdict must name which configuration it applies to.
• Treating a negative NPSH available as a rounding artifact: the signed value is returned on purpose - negative NPSHa means the pump inlet cannot be fed at all.
• Ignoring the velocity-squared losses: both major and minor losses scale with V^2 (doubling the velocity quadruples them), so a feed line sized at cruise flow can starve the pump at the takeoff flow.
• Forgetting the losses live between the tank and the pump: the NPSH check subtracts the line losses from the source pressure at the engine-driven pump inlet; feed system losses downstream of the pump do not belong in NPSHa.

Verification

• Confirm line_velocity(0.45, 800.0, 0.05) returns velocity 0.28648 m/s and that doubling the mass flow doubles the velocity.
• Confirm friction_factor(1000.0) equals 64/1000 exactly (laminar) and friction_factor(4775.0) equals the Blasius value 0.0381 within 1e-4; at Re = 2300 exactly the Blasius branch applies.
• Confirm the loss scaling identities: doubling the line length doubles the major loss at fixed velocity, and doubling the velocity quadruples both the major and the minor loss; minor_loss_pa with K = 0 returns 0.0 Pa.
• Confirm npsh_available on the worked case returns 4.4191 m (within 1e-2 of 4.42 m), that required 5.0 m gives FAIL with margin -0.58 m, that the boost case returns 17.60 m within 1e-2, and that a zero boost rise leaves the NPSH unchanged.
• Confirm the static head sign: a pump 1.0 m above the tank (height -1.0 m) reduces the available NPSH by 2.5 m against the 1.5 m tank case.
• Confirm boost_pump_power(5.625e-4, 103421.36, 0.60) returns 96.96 W within 1e-1, that efficiency 1.0 gives the Q dp product exactly and efficiency 0.5 doubles the power.
• Confirm feed_system_summary returns exactly the 15 documented keys and that identical inputs give identical dicts (determinism).
• Confirm every non-positive mass flow, density, diameter, length, viscosity and friction factor, K below 0, negative source or vapor pressure, negative required NPSH, a flow or pressure rise of zero in boost_pump_power, efficiency outside (0, 1] and a negative boost rise all raise ValueError.
• Run the contract test offline: python3 scripts/test_fuel_feed_system_sizing.py (35 tests, deterministic).

Related leaves

• vehicle-design/sizing/fuel-tank-sizing: the storage side, fuel mass to tank volume with ullage and capacity fit ahead of the feed line.
• vehicle-design/sizing/engine-sizing: thrust and engine fuel flow demand that set the per-engine feed flow.
• vehicle-design/sizing/hydraulic-system-sizing: hydraulic, not fuel, pump mechanics for the aircraft systems.
• space-systems/subsystems/propellant-tank-sizing: spacecraft propellant tank and pressurant sizing, the space analogue.
• propulsion/turbomachinery/rocket-turbopump: rocket LOX and kerosene turbopump design, not aircraft feed pumps.

Behavior contract (gate 3)

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

python3 scripts/test_fuel_feed_system_sizing.py

The test covers the reference feed line contract (velocity 0.2865 m/s, Reynolds 4775, friction 0.0381, major loss 299.9 Pa, minor loss 98.5 Pa, static head 11768.0 Pa, NPSH available 4.42 m PASS with margin 1.42 m, boost case 17.60 m and boost power 96.96 W), the exact laminar friction branch and the Blasius bound at Re 4775, the length-linear and velocity-squared loss identities, the static head sign, the zero boost rise and zero K minor loss cases, the exact 15 key summary dict, determinism, and ValueError rejection of every non-physical input.

Compliance

• Standards referenced, not reproduced: FAR 25.955 and 25.975 are regulatory text; the sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.