Cabin Outflow Valve Sizing

Cabin Outflow Valve Sizing (vehicle-design/sizing/cabin-outflow-valve-sizing)

Use when the task is sizing the cabin outflow and pressure-relief valve effective area of a pressurized transport at the conceptual level: the valve must pass the governing pack inflow through a choked orifice at the cabin pressure, so the effective area follows from the choked-flow mass-flux relation G = p sqrt(gamma/(R T)) (2/(gamma+1))^((gamma+1)/ (2(gamma-1))) as A = m_dot / G. This leaf implements the choked-flow valve sizing step in pure Python, stdlib only. It consumes the pack mass flow and cruise cabin pressure from vehicle-design/sizing/environmental- control-sizing, which owns the pressurization schedule; this leaf covers only the valve discharge sizing step for the outflow and relief cases.

Domain quick reference

• Choked-flow mass flux: G = p * sqrt(gamma/(R T)) * (2/(gamma+1))^ ((gamma+1)/(2(gamma-1))), with gamma 1.4, R 287.0 J/(kg K). The flux factor (2/(gamma+1))^((gamma+1)/(2(gamma-1))) equals 0.578704 for air, so G = 0.578704 * p * sqrt(gamma/(R T)).
• Critical pressure ratio: (2/(gamma+1))^(gamma/(gamma-1)) = 0.528282. The flow chokes only while p_amb/p_cab stays below this threshold; at the threshold itself the flow is not choked (strict). The rounded 0.528 lies just below the exact threshold, so a cabin ratio of 0.528 is still choked; the module applies the strict comparison against the exact constant.
• Effective area and diameter: A = m_dot / G, D = sqrt(4*A/pi). The area is an effective flow area, not a geometric orifice area.
• Outflow valve at cruise: sized with p_cab at the cruise cabin pressure (75262 Pa for the 8000 ft cabin at 39,000 ft) and the cruise pack inflow m_pack from the ECS sizing as the governing flow.
• Pressure-relief valve at the clamp: upstream pressure p_cab = p_amb + dp_clamp (11597 + 61363 = 72960 Pa at 50,000 ft with the 8.9 psi clamp); the same pack flow then needs a larger effective area because the relief upstream pressure is lower than the cruise cabin pressure.
• Fit verdict: PASS when the equivalent diameter stays at or below the nominal valve diameter limit, FAIL otherwise.
• Units are SI throughout: Pa, K, kg/s, m2, m.
• FAR 25.841 frames the cabin pressurization context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Take the governing inputs from the ECS sizing leaf: pack mass flow m_pack, cruise cabin pressure p_cab, and the ISA ambient pressure at the sizing altitude (19677 Pa at 39,000 ft).
2. Confirm the cruise flow is choked with is_choked (pressure ratio 19677/75262 = 0.2614 is well below the 0.528 threshold); the sizing functions raise ValueError on an unchoked condition.
3. Compute the cruise mass flux with choked_mass_flux at the cabin temperature (default 288 K).
4. Size the outflow valve: outflow_valve_sizing(m_pack, p_cab, p_amb, max_valve_diameter_m) returns the choked flag, mass flux, effective area, equivalent diameter and the PASS/FAIL fit verdict against the nominal diameter limit.
5. For the pressure-relief case, take the ISA ambient at the relief altitude (11597 Pa at 50,000 ft) and the differential pressure clamp (default 61363 Pa, 8.9 psi).
6. Size the relief valve: relief_valve_sizing(m_pack, p_amb, dp_clamp_pa, max_valve_diameter_m) with upstream pressure p_amb + dp_clamp and its own choked check at the clamp ceiling.
7. Compare both diameters with the nominal valve diameter limit and report the fit verdicts with the effective areas.
8. Confirm the deterministic checks with the contract test scripts/test_cabin_outflow_valve_sizing.py.

Worked example

Reference installation: cruise at 39,000 ft with p_cab = 75262 Pa (8000 ft cabin), pack inflow 3.156617 kg/s; relief case at 50,000 ft with the 8.9 psi (61363 Pa) differential clamp; nominal valve diameter limit 0.16 m.

• Cruise pressure ratio: 19677/75262 = 0.2614, below 0.528, so the outflow is choked.
• Cruise mass flux: choked_mass_flux(75262) = 179.2499 kg/(m2 s).
• Outflow valve: outflow_valve_sizing(3.156617, 75262, 19677, 0.16) gives area 0.017610 m2, diameter 0.14974 m (149.7 mm), fit verdict PASS against the 0.16 m limit.
• Relief upstream pressure: 11597 + 61363 = 72960 Pa; ratio 11597/72960 = 0.1590, choked.
• Relief mass flux: 173.7672 kg/(m2 s); relief_valve_sizing(3.156617, 11597, 61363, 0.16) gives area 0.018166 m2, diameter 0.15208 m (152.1 mm), fit verdict PASS.
• The relief valve is 3.2% larger in effective area than the outflow valve because its upstream pressure at the clamp ceiling is lower.

Verification

• Confirm choked_mass_flux(75262) returns 179.2499 kg/(m2 s) and that G/(p*sqrt(gamma/(R T))) equals the closed-form flux factor 0.578704 within 1e-6.
• Confirm outflow_valve_sizing(3.156617, 75262, 19677, 0.16) returns area 0.017610 m2 within 1e-5 and diameter 0.1497 m within 1e-3, with fit verdict PASS; against a 0.14 m limit the verdict is FAIL.
• Confirm relief_valve_sizing(3.156617, 11597, 61363, 0.16) returns area 0.018166 m2 within 1e-5 and diameter 0.1521 m within 1e-3.
• Confirm the is_choked truth table: ratio 0.2614 -> True; 0.7 -> False; at the critical ratio itself -> False (strict threshold).
• Confirm the area round trip: pi*(D/2)^2 recovers the effective area.
• Confirm ValueError rejection of non-positive mass flow, pressure, temperature, differential clamp and diameter limit, and of unchoked outflow and relief conditions (e.g. pressure ratio 0.7).
• Run the contract test offline: python3 scripts/test_cabin_outflow_valve_sizing.py (34 tests, deterministic).

Related leaves

• vehicle-design/sizing/environmental-control-sizing: computes the governing pack inflow m_pack, the cabin pressure at cruise and the pressurization schedule that are the inputs to this sizing step.
• vehicle-design/sizing/avionics-bay-cooling-sizing: equipment cooling flow sizing, a separate ECS discipline that does not touch the cabin outflow path.
• vehicle-design/sizing/aircraft-oxygen-system-sizing: the emergency oxygen side of cabin altitude protection, complementary to the pressure-relief path.

Pitfalls

• Sizing the outflow valve from the pressurization schedule alone: the valve area follows from the choked-flow relation at the cruise cabin pressure, A = m_dot / G; the schedule regimes belong to the ECS sizing leaf and only set the operating point used here.
• Applying the relation when the flow is not choked: the mass-flux formula is valid only below the critical pressure ratio 0.528; an unchoked case (ratio 0.7) must raise, not silently return an area.
• Mixing the cruise and relief upstream pressures: the outflow valve sees the cruise cabin pressure 75262 Pa, while the relief valve sees the clamp ceiling p_amb + dp_clamp = 72960 Pa at 50,000 ft, a lower upstream pressure that yields a 3.2% larger effective area for the same pack flow.
• Treating the pack inflow as a valve output: m_pack is the governing flow computed by the ECS sizing leaf from the occupant and thermal requirements; this leaf only sizes the discharge path for it.
• Reporting effective area as geometric orifice area: A = m_dot / G is an effective flow area; a real valve adds discharge coefficient and trim effects that belong to a later detailed design step.
• Using sea-level ambient pressure: the cruise anchor is 19677 Pa at 39,000 ft and the relief anchor 11597 Pa at 50,000 ft; ambient at the wrong altitude shifts the choked ratio and the area.

Behavior contract (gate 3)

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

python3 scripts/test_cabin_outflow_valve_sizing.py

The test covers the choked-flow mass flux at the cruise and relief worked conditions (179.2499 and 173.7672 kg/(m2 s)), the closed-form flux identity G/(p*sqrt(gamma/(R T))) = 0.578704 within 1e-6, the is_choked truth table with the strict critical-ratio threshold, the outflow valve effective area 0.017610 m2 within 1e-5 and diameter 0.1497 m within 1e-3 with PASS/FAIL fit verdicts against 0.16 m and 0.14 m limits, the relief valve area 0.018166 m2 within 1e-5 and diameter 0.1521 m within 1e-3, the area round trip through the equivalent diameter, the relief upstream pressure as p_amb plus the clamp, determinism, exact dict keys, and ValueError rejection of every non-physical input and of unchoked outflow and relief conditions.

Compliance

• Standards referenced, not reproduced: FAR 25.841 is the pressurization cabin context (cabin pressure altitude limits and the differential pressure clamp); the choked-flow relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.