CFD Solution Verification · Lift Generation · interactive
NACA0012 Airfoil: Lift-Curve Slope vs Thin-Airfoil Theory
OpenFOAM simpleFoam (v2312) · steady incompressible RANS, Spalart-Allmaras ·
angle-of-attack polar · digitalmodel CFD capability (issue #1174, epic #1161)
VERIFIED — lift-curve slope within 2.2% of experiment
1 Objective
Verify the digitalmodel CFD pipeline for a lift-generating body — a new physics regime beyond the drag/friction and vortex-shedding cases in the suite. The benchmark is the classic NACA0012 airfoil, whose lift-curve slope in the linear (pre-stall) regime is set by thin-airfoil theory and well documented experimentally.
thin-airfoil theory: dCl/dα = 2π per radian = 0.1097 per degree
Real airfoils fall slightly below 2π because of finite thickness and the viscous displacement effect; the measured NACA0012 slope is ≈0.106/deg (Abbott & von Doenhoff).
What this gates in real work
Lift generation is the physics of every control and lifting surface offshore. A verified lift-curve slope qualifies:
- Rudders and stabilizer fins — the rudder-manoeuvring capability's lift coefficients (Clarke/OCIMF screens) assume section data of exactly this kind; RANS closes the loop for non-catalogue sections (see the rudder explorer under /hydro/).
- Hydrofoils, thruster nozzles and propeller blade sections — section polars feed BEM and lifting-line design tools.
- Wind turbine blades — the floating-wind sizing workflows consume airfoil polars; the same solver + wall treatment produces them for arbitrary sections.
2 The lift mechanism
3 Result — the lift curve
Lift-curve slope = 0.1037 per degree — within 2.2% of the
experimental NACA0012 value (0.106/deg) and 5.4% below the ideal thin-airfoil 2π/rad
(0.1097/deg). Falling slightly below 2π is the physically correct thickness/viscous behaviour, not
an error — the slope, not the absolute Cl, is the incidence-independent quantity that verifies
the lift physics.
| α (deg) | Cl | Cd |
|---|---|---|
| 0 | 0.142 | 0.0102 |
| 1 | 0.249 | 0.0110 |
| 2 | 0.356 | 0.0122 |
| 3 | 0.461 | 0.0139 |
| 4 | 0.564 | 0.0161 |
| 5 | 0.666 | 0.0187 |
| 6 | 0.763 | 0.0220 |
| 7 | 0.853 | 0.0260 |
| 8 | 0.923 | 0.0315 |
4 Drag polar
5 A note on the reference frame
Zero-lift angle recovered as a check. The mesh (the OpenFOAM
airFoil2D
NACA0012 C-grid) carries a small built-in geometric incidence; the fit recovers it as a zero-lift angle of
-1.4°. Because a rigid incidence offset shifts the curve's intercept but not its slope, the lift-curve
slope — the verification target — is unaffected. Forces are resolved in wind axes (drag along the
free stream, lift normal to it), and the reference area uses the measured chord (≈35, from the walls
patch) times the span, so the coefficients are correctly normalised.6 Numerical model
| Item | Specification |
|---|---|
| Solver / model | simpleFoam + SpalartAllmaras (RANS), steady |
| Mesh | OpenFOAM airFoil2D C-grid, 10,720 cells; far field ≈7 chords |
| Flow | |U∞|=26 m/s, ν=10⁻⁵ → Re ≈ 9×10⁷ (chord ≈35) |
| Polar | α = 0–8° swept by rotating the free stream; Cl/Cd from forceCoeffs in wind axes |
| Verification | lift-curve slope vs 2π/rad and experiment; each α converged (residuals <10⁻⁶) |
7 Conclusion
Verified. The digitalmodel CFD pipeline reproduces the NACA0012 lift curve with a
slope of 0.1037/deg, within 2.2% of experiment and 5.4% of thin-airfoil
theory, with a physical drag polar. This extends the verified capability to lift generation, alongside
the boundary-layer (laminar & turbulent) and bluff-body cases.
References
- Abbott, I. H. & von Doenhoff, A. E. (1959). Theory of Wing Sections. Dover.
- Anderson, J. D. (2017). Fundamentals of Aerodynamics, 6th ed., McGraw-Hill (thin-airfoil theory).
- Ladson, C. L. (1988). "Effects of independent variation of Mach and Reynolds numbers on the low-speed aerodynamic characteristics of the NACA0012." NASA TM-4074.
- OpenFOAM v2312 tutorials —
incompressible/simpleFoam/airFoil2D.