NACA0012
Transonic airfoil validation.

A compressible transonic benchmark meshed with RobustMesh and exported directly to OpenFOAM 2406, run with rhoSimpleFoam for a steady k–ω SST RANS calculation.

TRANSONIC SHOCK · WALL-FUNCTION RANS · SHOCK–BOUNDARY-LAYER INTERACTION · STEADY COMPRESSIBLE AERODYNAMICS

Mesh

305,801 cells

Prismatic layer

30 layers

First prismatic cell height

1 × 10⁻³ m

Expansion ratio

1.05

Near-wall target

y⁺ > 30

Core mesh type

Triangle

01 / NACA0012 geometry

This study considers the symmetric NACA0012 profile at an angle of attack of 1.55°. Dimensions are normalised by the reference chord c_ref = 1 m.

NACA0012 airfoil geometry — Flow regimeTransonic · M = 0.699

Angle of attack1.55°

Reference chord1 m

02 / Mesh composition and spatial resolution

The final mesh combines three nested refinement zones with 30 prismatic layers around the NACA0012. The first layer is 1 × 10⁻³ m thick and the layers use an expansion ratio of 1.05, targeting the wall-function range y⁺ > 30. The rest of the circular far field is discretised with a graded triangular core.

Prismatic layers 15,720

Prismatic cells · 30 layers around the airfoil

Core region 290,081

Triangular cells · graded from the far field to the prismatic layer

Exported mesh 305,801

Total cells

Mesh images

Final NACA0012 mesh overview — **NACA0012 mesh overview**

Mesh detail around the NACA0012 leading edge — **Leading edge**Prismatic layers and triangular core

Mesh detail around the NACA0012 trailing edge — **Trailing edge**Layer closure and core transition

Close view of the NACA0012 prismatic layer — **Prismatic layer**30 wall-normal layers · ratio 1.05

03 / Mesh quality

The values and distributions below come directly from the OpenFOAM checkMesh fields for the final 305,801-cell mesh.

Angular quality

Non-orthogonality

Min0.0000°

Mean4.7963°

Max41.5070°

89.34%

0°–10° 416,442

10.24%

10°–20° 47,736

0.32%

20°–30° 1,469

0.10%

30°–40° 454

0.01%

40°–41.51° 56

Cell distortion

Skewness

Min0.0000

Mean0.0782

Max0.5760

68.08%

0.0000–0.1 317,337

26.90%

0.1–0.2 125,411

4.28%

0.2–0.3 19,929

0.68%

0.3–0.4 3,191

0.06%

0.4–0.576 289

Cell stretching

Aspect ratio

Min1.0000

Mean1.2372

Max3.9903

66.38%

1–1.25 202,999

23.80%

1.25–1.5 72,769

7.76%

1.5–2 23,737

1.79%

2–3 5,472

0.27%

3–3.99 824

Interpolation quality

Face weight

Min0.1983

Mean0.4985

Max0.8545

0.0002%

0.1983–0.2 1

0.05%

0.2–0.3 218

0.49%

0.3–0.4 2,265

49.88%

0.4–0.5 232,536

49.58%

0.5–0.8545 231,137

04 / Simulation results

The completed compressible steady k–ω SST RANS calculation was run with rhoSimpleFoam from OpenFOAM 2406 for 25,000 iterations at M = 0.699, Re = 1.185 × 10⁷ and α = 1.55°.

Simulation diagnostics

Convergence and wall resolution

Convergence

Normalised solver residuals over 25,000 iterations

Iterations Normalised residuals

Uₓ final · 1.59e-5

Uᵧ final · 5.62e-5

p final · 1.29e-5

ω final · 3.06e-6

k final · 1.09e-5

Wall resolution

y⁺ distribution at iteration 25,000

Min29.62

Mean186.83

Max303.15

0.193%

0–30 1

0.000%

30–50 0

0.965%

50–100 5

16.02%

100–150 83

46.91%

150–200 243

27.61%

200–250 143

8.30%

250–350 43

Flow solution

Mean pressure and velocity

Mean pressure-coefficient field around the NACA0012 from iterations 18001 to 25000 — Pressure coefficient **C_p field · mean over iterations 18,001–25,000**

Mean velocity-magnitude field around the NACA0012 from iterations 18001 to 25000 — Velocity magnitude **|U|/U_∞ field · mean over iterations 18,001–25,000**

Experimental validation

Aerodynamic validation and pressure coefficient at α = 1.55°

Coefficient	Experiment	RobustMesh + OpenFOAM 2406	Percent error
C_lLift coefficient	0.241¹	0.240²	-0.4%
C_dDrag coefficient	0.0079¹	0.0081²	+2.5%

x/c Mean Cₚ

Experimental upper surface¹

Experimental lower surface¹

RobustMesh + OpenFOAM2406 upper surface²

RobustMesh + OpenFOAM2406 lower surface²

Surface distribution C_p versus x/c

05 / Files

All RobustMesh configuration files, the complete OpenFOAM 2406 case, the generated mesh, and the final simulation results can be downloaded here.