Injector Design

Rocket Engine Injector Design (propulsion/rocket/injector-design)

Use when you must design rocket engine injection elements and their atomization basis: sizing the orifices that meter propellant into the chamber, checking the impinging doublet momentum balance, and laying out the element count for a chamber mass flow and mixture ratio. This leaf implements the standard injector hydraulics model in pure Python, stdlib only: orifice discharge with a discharge coefficient, injection velocity from the Bernoulli head, momentum flux ratio, per-propellant orifice counts and the per-element flow balance. It pairs with propulsion/rocket/combustion-chamber-design for the chamber geometry upstream of the face and propulsion/rocket/rocket-engine-cycle for the feed pressure context.

Domain quick reference

• Orifice area: A = pi * d^2 / 4 for a round orifice of diameter d.
• Injection velocity: v = Cd * sqrt(2 * dP / rho), the discharge coefficient applied to the Bernoulli head of the pressure drop dP across the orifice.
• Orifice discharge: m_dot = rho * A * v = Cd * A * sqrt(2 * rho * dP), the standard discharge law written through the jet velocity.
• Momentum flux ratio: J = (rho_o * v_o^2) / (rho_f * v_f^2) per impinging unlike-doublet pair. For equal fuel and oxidizer pressure drops the Cd, dP and density factors cancel and J = 1 exactly, a known design consequence of equal-dP doublets; near-unity J gives a well-mixed atomized sheet, large excursions leave one jet dominant.
• Mass split at mixture ratio O/F: m_dot_f = m_dot_c / (1 + O/F) and m_dot_ox = m_dot_c - m_dot_f for the chamber mass flow m_dot_c.
• Orifice count: N = ceil(m_dot / m_dot_per_orifice) per propellant, rounded up to whole orifices.
• Element flow: the element layout fixes fuel and oxidizer orifices per element; the element carries fuel_orifices * m_dot_f_orifice plus oxidizer_orifices * m_dot_ox_orifice.
• ECSS E-ST-35-03 frames the liquid propulsion context; the relations above are standard engineering methodology, summary-only.
• Units are SI throughout: m, Pa, kg/m^3, m/s, kg/s, dimensionless ratios. Typical liquid engine values: Cd 0.6-0.9, injection dP 1-3 MPa, orifice diameters 1-3 mm.

Workflow

1. Fix the operating point: chamber mass flow and mixture ratio (injector_layout_summary arguments) and the propellant densities.
2. Choose the discharge coefficient Cd and the fuel and oxidizer pressure drops; equal drops are the usual unlike-doublet baseline because they give J = 1.
3. Pick the orifice diameters, then size one orifice of each propellant with orifice_mass_flow (area, jet velocity, per-orifice mass flow) or read the same values from the summary.
4. Check the momentum balance with momentum_flux_ratio; recompute J for unequal drops and confirm the dP ratio scaling.
5. Get the per-propellant orifice counts with orifice_count and the element count with the summary (binding side over orifices per element).
6. Balance one element with element_mass_flow and confirm the element count times the per-element flow covers the chamber flow.
7. Report the face layout: per-orifice flows, velocities, momentum flux ratio, orifice counts, element count and element balance from injector_layout_summary.
8. Confirm the deterministic checks with the contract test scripts/test_injector_design.py.

Worked example

RP-1/LOX injector: chamber flow 70.686 kg/s at O/F 2.56, Cd 0.8, dP 2.0 MPa on both sides, 2.5 mm orifices, RP-1 density 820 kg/m3, LOX density 1140 kg/m3, element layout one fuel plus two oxidizer orifices. Real module outputs:

• Orifice area: A = 4.9087e-6 m2 (anchor 4.909e-6 m2).
• Fuel injection velocity: 55.874 m/s, fuel per-orifice flow 0.22490 kg/s (anchors 55.87 m/s, 0.2249 kg/s).
• LOX injection velocity: 47.388 m/s, LOX per-orifice flow 0.26518 kg/s (anchors 47.39 m/s, 0.2652 kg/s).
• Momentum flux ratio: J = 1.000000 exactly on the equal-dP case.
• Mass split: fuel 19.856 kg/s, LOX 50.830 kg/s (anchors 19.86, 50.83); oxidizer over fuel is 2.56 exactly.
• Fuel orifices: ceil(19.856 / 0.22490) = ceil(88.28) = 89; LOX orifices: ceil(50.830 / 0.26518) = ceil(191.68) = 192.
• Element: 1 fuel + 2 LOX carries 0.22490 + 2 * 0.26518 = 0.75527 kg/s (anchor 0.7553 kg/s); the binding element count is 96 (LOX 192 orifices at two per element), and 96 * 0.75527 = 72.51 kg/s covers the 70.686 kg/s chamber flow.

Verification

• Confirm orifice_mass_flow returns mass_flow_kgs equal to density times area times velocity to 1e-12 and matching Cd * A * sqrt(2 rho dP) to 1e-9.
• Confirm momentum_flux_ratio on the equal-dP worked case returns 1.0 to 1e-9 and that an unequal case (2.5 MPa oxidizer against 2.0 MPa fuel) returns J = 1.25, the dP ratio.
• Confirm orifice_count ceil behavior: 88.28 to 89, 191.68 to 192, and no bump for exactly integral requirements.
• Confirm element_mass_flow(1, 2, 0.2249, 0.2652) totals 0.7553 kg/s to 1e-4 and the summary element count times the element flow covers the chamber flow.
• Confirm every non-positive Cd, pressure drop, density, diameter, orifice count, chamber flow and mixture ratio raises ValueError.
• Run the contract test offline: python3 scripts/test_injector_design.py (30 tests, deterministic).

Related leaves

• propulsion/rocket/combustion-chamber-design: the chamber this injector faces; boundary is chamber geometry and combustion performance upstream of the injection face.
• propulsion/rocket/rocket-engine-cycle: the feed system pressure context that sets the injection pressure drops.
• propulsion/rocket/propellant-selection: propellant property context for the density terms.

Pitfalls

• Truncating the orifice count: orifice_count rounds up with ceil, so 88.28 becomes 89 fuel orifices and 191.68 becomes 192 LOX orifices - rounding down under-feeds the chamber, and the element count must cover the chamber flow on the binding side (96 elements x 0.75527 kg/s covers the 70.686 kg/s chamber flow).
• Forgetting that equal pressure drops force J = 1: with matching fuel and oxidizer dP the Cd, dP and density factors cancel and the momentum flux ratio is exactly 1.0; a design that needs a different J must run unequal drops, where J scales as the dP ratio (1.25 in the verification case).
• Reading an element balance that does not cover the chamber flow: the per-element flow times the element count must exceed the chamber mass flow; the worked example's 96-element layout covers 72.51 kg/s against 70.686 kg/s - a layout below that under-injects.
• Mixing propellant densities in the mass split: the split at O/F 2.56 gives fuel 19.856 kg/s and LOX 50.830 kg/s from the mass ratio alone; density enters only the orifice sizing and momentum ratio, not the split.
• Feeding non-physical hydraulics: any non-positive Cd, pressure drop, density, diameter, orifice count, chamber flow or mixture ratio raises ValueError - and the 0.6-0.9 Cd and 1-3 MPa dP ranges are typical liquid-engine values to sanity-check the inputs against.

Behavior contract (gate 3)

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

python3 scripts/test_injector_design.py

The test covers the worked-example anchors (orifice area 4.909e-6 m2, fuel velocity 55.87 m/s and 0.2249 kg/s per orifice, LOX velocity 47.39 m/s and 0.2652 kg/s per orifice, mass split 19.86/50.83 kg/s, orifice counts 89/192, element balance 0.7553 kg/s), the discharge identity mass flow equals density times area times velocity, the equal-dP momentum flux ratio identity J = 1.0 and the unequal-dP 1.25 scaling, ceil behavior of orifice counts, layout summary dict keys, determinism, chamber-flow coverage by the element count, and ValueError rejection of non-positive Cd, pressure drop, density, diameter, counts and mixture ratio.

Compliance

• Standards referenced, not reproduced: ECSS E-ST-35-03 is a free ESA download (ecss.nl/standards); the injector hydraulics relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.