Rocket Nozzle Flow Separation

Rocket Nozzle Flow Separation (propulsion/rocket/rocket-nozzle-flow-separation)

Use when you must predict wall flow separation inside an overexpanded rocket nozzle operating below its design altitude. This leaf applies the separation-pressure-ratio criterion (Summerfield class) to decide whether the nozzle wall flow separates, locates the separation station on the divergent section through the isentropic area-Mach relation, finds the altitude at which the nozzle un-separates as the ambient pressure falls, and reports the separated-thrust correction and the side-load regime flag that gate off-design nozzle operation. Pure Python, stdlib only. It pairs with propulsion/rocket/nozzle-design, which owns the ideal attached-flow sizing envelope from the chamber conditions, and with propulsion/rocket/combustion-chamber-design for the chamber-side performance that feeds the nozzle.

Domain quick reference

• Separation criterion: wall separation occurs when the local wall static pressure falls to p_sep = K_SEP * pa with K_SEP = 0.4 (sea-level anchor, documented model constant), pa the ambient pressure in Pa.
• Separation Mach number: M_sep = sqrt(((pc/p_sep)**((gamma-1)/gamma) - 1)
  • 2/(gamma-1)), from the chamber pressure pc and the separation pressure.
• Separation station: A_sep/At from the isentropic area-Mach relation at M_sep; the flow separates when the exit area ratio Ae_At exceeds A_sep/At, and stays attached when Ae_At <= A_sep/At.
• Area-Mach relation: A/A* = (1/M) * ((2/(gamma+1)) * (1 + (gamma-1)/2 * M2))((gamma+1)/(2*(gamma-1))); at M = 1 the ratio is exactly 1 (the throat), and the supersonic branch is monotonic.
• Separation altitude: the altitude where the ISA ambient pressure equals the design exit pressure pe_design (bisection over 0 to 20000 m, 100 iterations), the un-separation altitude for a nozzle designed for pe_design; results clamp to the bracket ends.
• ISA pressure: p(h) = 101325 * (1 - 0.0065*h/288.15)**5.2561 below 11000 m and the isothermal form above, with module data R = 287.0 and G0 = 9.80665; the troposphere base is 101325 Pa at 0 m.
• Side-load regime: separated flow with the nozzle overexpanded (design exit pressure pe_design below the ambient pressure pa) is where asymmetric separation side loads occur.
• Model notes: the corrected thrust in separated_thrust_loss evaluates the momentum and the pressure term at the separation station and neglects the pressure term beyond it, so the loss is measured against the design-point reference m_dot * v_exit at perfect expansion (exit pressure matched to ambient); when pe_design is omitted the side-load flag follows the separation verdict because reaching p_sep below the ambient pressure already means the nozzle runs overexpanded.
• Units are SI throughout: pressures in Pa, temperature in K, areas in m^2, flow rate in kg/s, thrust in N, altitude in m.
• ECSS frames the launch-vehicle propulsion context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the operating point: chamber pressure pc, ambient pressure pa, specific heat ratio gamma, exit-to-throat area ratio Ae_At, and the design exit pressure pe_design. Use GAMMA_DEFAULT 1.2 for hot combustion products when gamma is unknown.
2. Get the separation pressure with separation_pressure_ratio(pa): the wall static pressure that triggers separation at this ambient pressure.
3. Compute the separation Mach number with separation_mach(pc, p_sep, gamma) and the station area ratio with separation_station_area_ratio(pc, pa, gamma).
4. Judge the nozzle with separated_verdict(Ae_At, A_sep_At): True means the exit lies downstream of the separation station and the flow separates at this ambient pressure.
5. Find the un-separation altitude with separation_altitude(pe_design), where the ISA ambient pressure equals the design exit pressure, and read the ambient pressure at any flight altitude with isa_pressure.
6. Size the thrust impact with separated_thrust_loss(pc, Tc, At, pa, gamma, Ae_At): chamber temperature Tc and throat area At scale the choked flow; the dict carries the design-point thrust, the corrected thrust, the loss and the relative loss.
7. Flag the side-load regime with side_load_flag(separated, pc, pa, pe_design): True only when the flow separates while the nozzle runs overexpanded at that ambient pressure.
8. Confirm the deterministic checks with the contract test scripts/test_rocket_nozzle_flow_separation.py.

Worked example

pc = 10 MPa, pa = 101325 Pa (sea level), gamma = 1.2, Ae_At = 40, pe_design = 40 kPa; the thrust-loss scale uses Tc = 3500 K and At = 0.1 m^2:

• Separation pressure: p_sep = 0.4 * 101325 = 40530 Pa.
• Separation Mach number: M_sep = 3.8787 (3.8787 within 1e-3 of the spec anchor at pc/p_sep = 246.7).
• Separation station area ratio: A_sep/At = 23.797 (module output 23.79742), so the sea-level station sits well upstream of the Ae_At = 40 exit.
• Verdict: separated_verdict(40, 23.797) is True, the nozzle wall flow separates at sea level; a nozzle with Ae_At = 20 stays attached.
• Separation altitude: separation_altitude(40000) = 7185 m (module 7185.16 m, within 1 percent of 7185 m); isa_pressure(9000) = 30741 Pa and isa_pressure(10000) = 26435 Pa bracket the flight corridor.
• Un-separation: at 7185 m the ambient pressure has fallen to the 40 kPa design exit pressure and the verdict flips to attached flow.
• Side-load flag: side_load_flag(True, 1e7, 101325, 40000) is True at sea level, the separated and overexpanded regime; an un-separated nozzle never flags.
• Thrust impact: the design-point thrust is 1.8008 MN and the corrected (separation-capped) thrust is 1.5965 MN, a loss of 204.2 kN, 11.34 percent of the design point. A mild nozzle with Ae_At = 10 stays attached and shows zero loss.

Verification

• Confirm separation_station_area_ratio(1e7, 101325, 1.2) returns 23.79742, within the spec bound of 23.797, and that the station area ratio grows as the ambient pressure falls (higher altitude, less separation).
• Confirm separated_verdict(40, 23.797) is True and that a nozzle whose Ae_At stays at or below the separation station area ratio is attached.
• Confirm area_ratio_from_mach(1.0, gamma) equals 1.0 for gamma 1.2 and 1.4, and that separation_altitude(40000) lands within 1 percent of 7185 m with an ISA pressure round trip back to 40000 Pa.
• Confirm the separated case reports a design-point thrust above the corrected thrust with a positive loss, and the attached case reports equal thrusts with zero loss.
• Confirm every non-physical input raises ValueError: pc <= 0, pa <= 0, gamma <= 1, Ae_At <= 1, pe_design <= 0, negative altitude, negative Mach, and a separation pressure at or above the chamber pressure.
• Run the contract test offline: python3 scripts/test_rocket_nozzle_flow_separation.py (35 tests, deterministic, under a second).

Related leaves

• propulsion/rocket/nozzle-design: the ideal attached-flow nozzle sizing envelope from the chamber conditions; this leaf adds the off-design separation correction that nozzle-design does not model.
• propulsion/rocket/combustion-chamber-design: chamber-side performance that supplies the chamber pressure and temperature inputs used here.
• propulsion/rocket/thrust-vector-control: actuated thrust deflection, whose side loads interact with the separated flow regime flagged here.

Pitfalls

• Reading the separation pressure as an exit pressure: p_sep = K_SEP * pa (40530 Pa at sea level) locates a station inside the divergent section; the wall flow separates there, so A_sep/At (23.8) is well below the Ae_At = 40 exit in the separated case.
• Inverting the verdict: separated means Ae_At exceeds A_sep/At, the exit farther downstream than the separation station; an equal or smaller exit area ratio keeps the flow attached, and the exact-equal boundary is attached.
• Treating the separation altitude as a direct root of the A_sep_At = Ae_At crossing: separation_altitude returns the altitude where the ISA pressure equals the design exit pressure (bisection over 0 to 20000 m, clamped at the ends), the design-point un-separation marker; the verdict flips somewhere at or below it on the ascent.
• Confusing the side-load regime with plain separation: side loads need separation AND an overexpanded state (pe_design < pa); a separated nozzle running at or above its design point does not flag.
• Comparing the corrected thrust against the attached-flow estimate: dropping the exit-side pressure deficit of an overexpanded nozzle would raise the estimate above the corrected value, which inverts the loss; the correction is measured against the design-point reference m_dot * v_exit, where the pressure term vanishes.
• Forgetting the flow scale: separated_thrust_loss needs the chamber temperature Tc and the throat area At to size the choked flow; without them only the area-ratio statements of the criterion are available.

Behavior contract (gate 3)

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

python3 scripts/test_rocket_nozzle_flow_separation.py

The test must pass with exit 0 and covers the worked-example anchors (p_sep = 40530 Pa, M_sep = 3.8787 within 1e-3, A_sep/At = 23.797, separation_altitude(40000) near 7185 m within 1 percent, ISA pressures at 9000, 10000 and 11000 m), the area-Mach identity at M = 1 for gamma 1.2 and 1.4, the verdict truth table including the exact-equal boundary, the growth of the separation station as the ambient pressure falls, the verdict flip at the separation altitude, the side-load flag across separated, un-separated and design-above-ambient states, the separated thrust correction (design point above corrected with a positive loss) and the attached zero-loss case, the ISA round trip, bracket clamping, determinism, and ValueError rejection of every non-physical input listed in the spec.

Contract test

Run the contract test from the repo root:

python3 skills/propulsion/rocket/rocket-nozzle-flow-separation/scripts/test_rocket_nozzle_flow_separation.py

Stdlib unittest only, deterministic, offline, 35 test methods, exit 0 in about a second. The test imports the sibling logic module rocket_nozzle_flow_separation_logic from its own scripts directory, so no install or path configuration is needed.

Compliance

• Standards referenced, not reproduced: ECSS frames the launch-vehicle propulsion context; the Summerfield-class separation criterion, the isentropic relations and the ISA standard atmosphere above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.