Project 01 · October 2026 · YJSP Propulsion

Vespula LOx Manifold CFD

A steady RANS study in STAR-CCM+ of how evenly one LOx manifold feeds its 17 swirl elements.

Velocity magnitude on a plane through the plenum, with the inlet stem at the centre and 17 swirl elements around it — Velocity magnitude through the plenum

Swirl elements fed: 17
σ of element flow: 0.92%
Manifold pressure drop: 132psi
Polyhedral cells: 1.72M

STAR-CCM+Steady RANSSST k-ωPolyhedral meshingHand calcs

Question: If one element draws more LOx than the others, it runs off the design mixture ratio and burns at a different flame temperature than its neighbors.
Result: All 17 elements flow within 2% of the average of 0.2082 kg/s. The largest deviations are +1.88% at inj-1 and −1.36% at inj-12, and the standard deviation across all 17 is 0.92%.
Why: The distribution is tight because each element has a 132 psi pressure drop.
Next: To reduce the inner-ring bias, I would add a perforated splash plate under the stem to break up the inlet jet.

Stem, plenum and two rings of elements

Liquid oxygen enters through a single stem at the top of the manifold. A cone on the plenum floor sits directly under the stem and turns the downward jet outward across the floor.

Numbered layout of the 17 elements, six on the inner ring and eleven on the outer ring, coloured by angle — Inj-1 through 6 make up the inner ring, inj-7 through 17 the outer ring

Meshed injector face seen from the chamber side, showing the 17 swirl element outlets — The injector face from the chamber side

Assumptions and values

With the total flow fixed at the inlet and the pressure fixed at the outlets, the solver determines how that flow divides among the elements.

Steady flow	Steady solver
Incompressible liquid	ρ = 1141 kg/m³, μ = 1.8e-4 Pa·s
Turbulence	RANS, SST k-ω
Wall treatment	All y+
Inlet	Mass flow, 3.54 kg/s
Outlets (17)	Static pressure, 240 psig each
Walls	No-slip, smooth

1.72 million polyhedral cells

The elements and their tangential slots have much finer cells than the plenum.

Section through the mesh showing the stem, the centre cone, the plenum and two elements — Section through the stem, cone and plenum

Close-up of the mesh around one element showing prism layers along the walls — Each wall has 4 prism layers with a total thickness of 0.37 mm

Convergence and sanity checks

The residuals dropped 3 to 6 orders of magnitude and leveled off by about 300 iterations. To confirm the answer is also physical, I checked four quantities.

Continuity error: 0.013%
Manifold ΔP: 132.2 psi
Outlet pressure: 239.8 psi
Wall y+: 0.4–205

Residual plot for continuity, momentum, turbulent kinetic energy and specific dissipation rate over 468 iterations — Residuals over 468 iterations

Wall y+ contour on the plenum floor, with a yellow ring around the centre where the inlet jet lands — Wall y+ on the plenum floor

Mass flow monitors showing inlet at minus 3.54, outlets at plus 3.54 and the net settling to zero — Mass flow. Inlet −3.54, outlets +3.54, net → 0 kg/s

Pressure monitors in pascal showing the inlet settling near 2.57e6 Pa and the outlets near 1.65e6 Pa — Pressure in Pa. Inlet ≈ 372 psi, outlets ≈ 240 psi

Hand calcs agree with the CFD

Each element acts as an orifice, so its mass flow scales with the square root of its pressure drop.

Quantity	Hand calc	CFD
Avg element flow	3.54 ÷ 17 = 0.2082 kg/s	0.2082 kg/s (Σ = 3.5396)
Stem velocity	ṁ ÷ (ρ·A_stem) ≈ 16.6 m/s *	≈ 15 m/s in the velocity scene
Stem Reynolds no.	ρVD ÷ μ ≈ 1.6 × 10⁶, turbulent	Supports the RANS model
Plenum dynamic head	½ρv² at 3 m/s ≈ 0.7 psi	Tiny next to the 132 psi ΔP
Element CdA	ṁ_el ÷ √(2ρΔP) ≈ 4.6 mm²	Uses the CFD ΔP of 132.2 psi
Flow sensitivity	δṁ/ṁ ≈ ½ · δP/ΔP (orifice)	+1.88% at inj-1 ⇒ ≈ 5 psi extra

* Stem diameter ≈ 15.4 mm, inferred from the tutorial's 16.6 m/s inlet velocity and still to be confirmed against CAD.

Every element within ±2% of the average

The inner ring averages 0.6% above the mean and the outer ring 0.3% below it. Plotting flow against angle shows no trend around the manifold.

LOx mass flow for each of the 17 elements, with the average and a one standard deviation band — Mass flow per element, with a ±1σ band

Bar chart of each element's deviation from the average mass flow, from plus 1.88 percent at inj-1 to minus 1.36 percent at inj-12 — Deviation from average. Blue is above, orange is below

LOx mass flow plotted against angular position for the inner and outer rings, with the empty slot marked near 315 degrees — Mass flow by angular position, inner ring against outer ring

What the flow field shows

When the LOx leaves the stem, the flow area increases sharply. Continuity requires the velocity to drop to a few m/s, and the pressure in the plenum stays high and close to uniform. Most of the 132 psi pressure drop occurs across the swirl slots.

Velocity vectors on a section through the stem and two elements, showing the jet turning along the cone and running outward along the plenum floor — Velocity vectors on a slice through the stem and two elements

Pressure contour through the plenum, nearly uniform away from the stem, with low pressure at each element outlet — Pressure in psi through the plenum and elements

What would tighten these results

The modified geometry has not been run yet.
LOx density and viscosity were held constant, temperature was never an input, and the walls were modeled as smooth.
Each outlet also has 41 to 48 faces of backflow, caused by the low-pressure swirl core sitting on the outlet plane.
Some of the ±2% spread may also come from mesh error.