Subsonic Inlet Recovery

Subsonic Inlet Recovery (propulsion/gas-turbine-cycle/subsonic-inlet-recovery)

Use when you must compute the total-pressure recovery and the compressor-face condition for a subsonic turbofan or turboprop intake at a flight condition: the ram recovery ratio from the free-stream Mach number, the free-stream stagnation pressure ratio from the isentropic relation, the total pressure delivered at the engine face after the duct total-pressure efficiency, the required capture area for the engine mass flow at the flight speed and density, and the capture verdict against the intake highlight area. This leaf implements the standard subsonic intake model in pure Python, stdlib only. It pairs with propulsion/gas-turbine-cycle/gas-turbine-cycle and propulsion/turbofan/turbofan-cycle, whose cycle decks take the face total pressure this leaf produces as an input at the fan face station; the shock-dominated intake regimes of the ramjet family belong to propulsion/ramjet/ramjet-inlet, and the exhaust side is handled by propulsion/gas-turbine-cycle/propelling-nozzle.

Domain quick reference

• Ram recovery ratio: the fraction of the free-stream total pressure that survives the intake at the engine face, before the duct loss. It is unity at and below Mach 1, and rolls off above Mach 1 with a MIL-E-5008B style curve, rr = 1 - 0.075 * (M - 1)^1.35 for 1 < M < 5. Beyond Mach 5 the subsonic model no longer applies.
• Free-stream stagnation pressure ratio: p0_ratio = (1 + 0.2 * M^2)^3.5 from the isentropic relation at gamma = 1.4 (standard atmosphere still air total-to-static ratio at the flight Mach).
• Engine face total pressure: pt_face = p0 * p0_ratio * rr * duct_efficiency. The duct total-pressure efficiency carries all duct losses between the intake highlight and the fan face, so at subsonic Mach with a perfect duct the face total pressure is simply p0 * p0_ratio, the free-stream stagnation value.
• Capture area: the streamtube area that passes the engine mass flow at the free-stream condition, A_cap = m_dot / (rho * V), with the free-stream density rho = p0 / (R * T0) and speed V = M * sqrt(gamma * R * T0), R = 287.0 J/(kg K), gamma = 1.4.
• Capture verdict: full-capture when A_cap <= A_highlight, the capture streamtube fits inside the intake highlight area; spillage when A_cap > A_highlight, the intake spills the excess flow around the lip and the engine is starved of its demanded streamtube.
• Units are SI throughout: Pa, K, kg/s, m2, m/s, Mach dimensionless.
• FAR Part 25 frames the installation context (the intake is part of the engine installation); the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the flight condition: free-stream static pressure p0, static temperature T0 and Mach number M (free-stream values, not total).
2. Get the ram recovery ratio with ram_recovery(M): unity at subsonic Mach, rolled off above Mach 1 by the MIL-E-5008B style curve.
3. Promote the free stream to stagnation with stagnation_pressure_ratio(M).
4. Apply the duct total-pressure efficiency and form the engine face total pressure with face_total_pressure(p0, M, duct_efficiency); this value is the inlet station input for the cycle deck.
5. Size the intake for the engine mass flow with capture_area(mass_flow, p0, T0, M), which builds the free-stream density and speed and divides the mass flow by their product.
6. Judge the intake against its highlight area with capture_verdict(capture_area, highlight_area): full-capture or spillage.
7. Confirm the deterministic checks with the contract test scripts/test_subsonic-inlet-recovery.py.

Worked example

Flight condition (11 km standard day): Mach 0.82, p0 = 101325 Pa, T0 = 216.65 K, duct_efficiency 0.98, engine mass flow 200 kg/s.

• Ram recovery: ram_recovery(0.82) = 1.0, full recovery at subsonic Mach. At Mach 1.5 the roll-off gives ram_recovery(1.5) = 0.9705781, and ram_recovery(2.0) = 0.925 exactly.
• Stagnation ratio: stagnation_pressure_ratio(0.82) = 1.5552097, so the free-stream stagnation pressure is 101325 * 1.5552097 = 157581.5 Pa.
• Face total pressure: face_total_pressure(101325, 0.82, 0.98) = 154429.99 Pa, the stagnation pressure cut by the 0.98 duct efficiency (spec anchor 154430 Pa, matched within 1 Pa).
• Capture area: rho = 101325 / (287.0 * 216.65) = 1.62958 kg/m3, V = 0.82 * sqrt(1.4 * 287.0 * 216.65) = 241.935 m/s, and capture_area(200, 101325, 216.65, 0.82) = 200 / (1.62958 * 241.935) = 0.507289 m2 (spec bound 0.5075 m2, matched within 1e-3).
• Capture verdict: against a 0.60 m2 highlight the intake is in full-capture; against a 0.45 m2 highlight the same flow demands a larger streamtube than the lip admits, so the verdict is spillage.

Verification

• Confirm ram_recovery(0.82) returns 1.0 and ram_recovery(2.0) returns 0.925 exactly.
• Confirm face_total_pressure(101325, 0.82, 0.98) returns 154429.99 Pa, within 1 Pa of the 154430 Pa spec anchor.
• Confirm capture_area(200, 101325, 216.65, 0.82) returns 0.507289 m2, within 1e-3 of the 0.5075 m2 spec bound, and that doubling the free-stream density halves the required area (inverse density scaling identity).
• Confirm capture_verdict(0.507289, 0.60) is "full-capture" and capture_verdict(0.507289, 0.45) is "spillage".
• Confirm negative Mach, Mach at or above 5, non-positive pressure, temperature or mass flow, zero or negative duct efficiency, duct efficiency above 1 and non-positive capture or highlight areas all raise ValueError.
• Run the contract test offline: python3 scripts/test_subsonic-inlet-recovery.py (31 tests, deterministic).

Related leaves

• propulsion/gas-turbine-cycle/gas-turbine-cycle: consumes the face total pressure this leaf produces as the cycle inlet condition.
• propulsion/turbofan/turbofan-cycle: fan-face station input from the intake recovery at the turbofan design point.
• propulsion/ramjet/ramjet-inlet: the shock-dominated ramjet intake model for the regimes this leaf does not cover.
• propulsion/gas-turbine-cycle/propelling-nozzle: the exhaust side counterpart that turns the cycle exit state into thrust.
• propulsion/gas-turbine-cycle/real-cycle-effects: component loss bookkeeping that complements the single duct efficiency here.

Pitfalls

• Feeding total conditions as the free-stream static state: the model takes free-stream static p0 and T0, not stagnation values; the stagnation ratio and ram recovery are applied on top of p0 to reach the face total pressure.
• Expecting the ram recovery to fall below unity at subsonic Mach: rr = 1.0 for all M <= 1.0, the roll-off only begins above Mach 1, so a Mach 0.82 intake with duct efficiency 0.98 loses all of its 1.5% pressure loss in the duct, not in the external stream.
• Reading the face total pressure as the free-stream total pressure: the duct total-pressure efficiency is a separate multiplier, 0.98 in the worked example, that the free-stream stagnation value does not include (157581.5 Pa against 154429.99 Pa at the face).
• Judging capture without the highlight area: a small capture area is not by itself good or bad; the verdict compares it with the intake highlight area, and the same 0.5073 m2 streamtube is full-capture at a 0.60 m2 highlight and spillage at 0.45 m2.
• Extending the recovery curve to high Mach: the MIL-E-5008B style roll-off is only valid below Mach 5, and the whole model is subsonic in intent, so Mach 5 and above raises ValueError by design.

Behavior contract (gate 3)

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

python3 scripts/test_subsonic-inlet-recovery.py

The test covers the worked-example contract (face total pressure 154430 Pa within 1 Pa, capture area 0.5075 m2 within 1e-3), the ram recovery truth table at Mach 1.2 and 2.0 and the 0.970578 bound at Mach 1.5, unity recovery across the subsonic range, the stagnation pressure ratio formula and its Mach 0.82 anchor, the subsonic full-recovery identity pt_face = p0 * p0_ratio at duct efficiency 1.0, the inverse-density capture area identity, the full-capture and spillage verdicts against both highlight areas, determinism of every function, and ValueError rejection of negative Mach, Mach at or above 5, non-positive pressure, temperature and mass flow, duct efficiency outside (0, 1] and non-positive capture or highlight areas.

Compliance

• Standards referenced, not reproduced: far-33 (family spine, the engine installation context in which the intake lives, FAR Part 25 installation text named only); the recovery curve follows MIL-E-5008B style practice, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.