← All work — 2026

Nosecone CFD

Codename ARIA V&V

Density-based OpenFOAM simulation of the ARIA sounding-rocket nosecone at Mach 1.8, validated against NACA wind-tunnel data to within the tunnel's own uncertainty.

RoleSole author: CFD, V&V campaign, paper

ARIA (Bristol SRS) →

Split-field plot of the ARIA nosecone solution at Mach 1.8: numerical schlieren above the axis, Mach number below, with the exact Taylor-Maccoll conical shock at 34.43 degrees drawn as a red dashed line lying on the computed shock — Schlieren (upper) and Mach number (lower) with the exact Taylor-Maccoll conical shock, β = 34.43°, overlaid. M = 1.8, ISA 9 km.

Mean |ΔCp| vs wind tunnel

0.0040

Apex p/p∞ vs exact theory

+0.2 %

LTS speed-up

12.7×

The inherited target was wrong

I inherited a handoff comparing OpenFOAM to STAR-CCM+ with a 23.3 % tip-pressure discrepancy and a tip target of p/p∞ = 1.860. The first job was an audit. The ARIA nose is not a tangent ogive: all 21 design coordinates fit the parabolic-series profile r = 0.156x − 0.14625x² (K′ = 3/4) to a residual of about 1e-17 m, tip half-angle 8.87°.

Exact Taylor-Maccoll for that tip at M = 1.8 gives p/p∞ = 1.206, not 1.860; the target had been transcribed from the NACA body at M = 1.98. The fine-grid apex lands within +0.2 % of exact. The discrepancy was a near-wall sampling artifact plus STAR-CCM+'s faceted geometry over-predicting the tip region by 2.8×. STAR-CCM+ was the outlier.

Wall pressure coefficient along the ARIA body: three OpenFOAM curves straddle the tangent-cone and shock-expansion theory lines and hit the exact tip value, while orange STAR-CCM+ points sit two to three times higher over the whole nose — OpenFOAM (cell-centred, wall-extrapolated, tip-refined) against exact theory; STAR-CCM+'s faceted geometry over-predicts the nose by about 2.8×.

Three body profiles stacked on a common x/d axis: the short blunt NACA fineness-3 ogive, the ARIA parabolic-series nose, and the long slender NACA fineness-5.75 ogive — The three bodies: NACA A54H23 (fineness 3), ARIA (parabolic series, K′ = 3/4), NACA A53E01 (fineness 5.75). A53E01 is the geometrically closest validation case.

Validated against wind-tunnel data

Agreement with another code proves nothing, so I validated against published experiment. Two NACA wind-tunnel datasets at M = 1.98, run with identical numerics. RM A53E01, a fineness-5.75 body and the closest geometry to ARIA: mean |ΔCp| = 0.0040, at or below the quoted ±0.004 tunnel uncertainty. RM A54H23, a fineness-3 body and a harder shock-capture test: mean |ΔCp| = 0.0138.

The captured shock angle on the NACA body was 36.88° against an exact 37.17°. In the three-panel summary the CFD sits inside the experimental error band while the legacy STAR-CCM+ benchmark sits far above both experiment and theory.

Three-panel pressure-coefficient validation: NACA fineness-3 and fineness-5.75 bodies with red experimental points and their error band tracked by the blue OpenFOAM line, and the ARIA body where orange STAR-CCM+ points sit far above both CFD and theory — (a) NACA A54H23, mean |ΔCp| 0.0138. (b) NACA A53E01, mean |ΔCp| 0.0040, inside the ±0.004 tunnel band. (c) ARIA with the exact tip anchor; the legacy STAR-CCM+ benchmark is the outlier.

Greyscale numerical schlieren of the NACA fineness-3 body at Mach 1.98 with the exact Taylor-Maccoll shock line dashed along the captured shock and the freestream Mach angle dotted from the shoulder — Shock capture on the NACA body: measured shock angle 36.88° against exact 37.17°.

Wide numerical schlieren of the full ARIA body showing the attached tip shock, the expansion fan off the shoulder and the base shock at the aft end, with the freestream Mach angle drawn as a blue dashed line — Full body: attached tip shock, shoulder expansion, base shock. Mach-angle overlay μ = 33.75°.

Grid and scheme

Verification before validation. A refinement-ratio-2 GCI triplet of 2,950, 11,800 and 47,200 cells on a structured axisymmetric mesh bounds the inviscid nose wave drag at C_d,nose = 0.0364 ± 8 %. Doubling the farfield moved mean |ΔCp| by 1.2e-4. Swapping scheme, limiter, flux and energy formulation moved nose drag by ±2 %. Steadiness drift was at most 0.008 %. Framework: the AIAA V&V guide and ASME V&V 20.

Structured quadrilateral mesh bending to follow the red nose contour from the tip to the shoulder at 0.4 m and along the cylinder — The structured axisymmetric mesh hugging the nose contour.

Drag

The viscous phase ran k-ω SST at the flight Reynolds number, Re_D ≈ 1.33e6. ARIA total drag came out at C_d = 0.197 referenced to frontal area, of which 85 % is skin friction: pressure 0.030, friction 0.167. That is what a slender L/d ≈ 21 body looks like; the nose wave drag is the small part. Wall temperature recovers toward T₀ = 378.5 K.

A 3-D case at α = 5° on the NACA body gave a viscous normal force of 0.300 against the experimental 0.272, about 10 %. Three-grid Richardson extrapolation showed the gap is mostly grid and converges to a few percent.

Bar chart of drag coefficient referenced to frontal area: pressure 0.0296, skin friction 0.1672, total 0.1968 — Viscous drag split at flight Re: pressure 0.030, skin friction 0.167, total 0.197. A slender body is 85 % skin friction.

Mach number contours around the full ARIA body at freestream Mach 1.8, with a dark boundary layer along the wall, a yellow expansion at the base and the Mach angle drawn as a dashed line — Mach contours around the full body, freestream M = 1.8.

Static temperature field around the body next to a line plot of static and total temperature along the wall, with total temperature holding near 378.5 kelvin and static temperature near 230 kelvin — Thermal loading: static-T field and wall recovery toward T₀ = 378.5 K.

Three-dimensional rendering of the NACA fineness-3 body at 5 degrees angle of attack coloured by surface pressure coefficient, yellow compression on the windward nose and blue suction on the leeward side — 3-D case: surface Cp on the NACA body at α = 5°, M = 1.98. Windward compression, leeward suction.

Faster

OpenFOAM's localEuler local time-stepping converges the same steady case 12.7× faster than global time-stepping. I treated it as one more thing to verify rather than a free lunch: the Cp distributions and nose drag from the LTS run match the global-step run, so the acceleration is accuracy-neutral.

Paper

The full write-up is a research-paper-style V&V report, Experimentally Anchored Verification and Validation of Density-Based CFD for Supersonic Slender Bodies, v6, June 2026. It follows the AIAA V&V guide and ASME V&V 20 and records every number above with its uncertainty. The repo is public under MIT with the cases, data and figure scripts archived.

Experimentally Anchored Verification and Validation of Density-Based CFD for Supersonic Slender BodiesExperimentally Anchored Verification and Validation of Density-Based CFD for Supersonic Slender Bodies. v6, June 2026.53 pp