20  2D NACA0012 Airfoil — SA RANS Polar Validation

Lift, drag, and stall behavior against wind-tunnel data (Ladson/Abbott), with code-to-code agreement against NASA TMR CFL3D-SA in the attached-flow range

20.1 Run Provenance and Artifacts

Item	Value
Wake CFD baseline version	0.22.2
Solver	DBNS
Compute device	GPU (NVIDIA RTX A6000)
Parallel execution	1 MPI rank
Arithmetic precision	FP64
Run date	2026-09-09

Note

Results depend on the solver build that produced them. Read every figure in this report together with the version and date above — re-running the same input on a later build may give different numbers.

20.1.1 Downloadable Files

Not available: standalone input decks and solver result files have not yet been published for download.

20.2 Validation Objective

The NACA0012 airfoil is one of the most widely used cases for validating RANS turbulence models, in part because the NASA Turbulence Modeling Resource (TMR) publishes both curated wind-tunnel data (Ladson; Abbott & von Doenhoff) and matched-condition Spalart–Allmaras (SA) computations from the established CFL3D code. This case reproduces the NACA0012 lift/drag polar with Wake CFD’s SA implementation on a TMR-family mesh, and checks two different things at once:

• Code-to-code agreement with CFL3D-SA in the linear, attached-flow range, where two independent RANS codes solving the same equations on comparable meshes should agree closely if both are implemented correctly.
• Agreement with experiment (Ladson, Abbott & von Doenhoff) across the full angle-of-attack range, including lift-curve slope, maximum lift, and stall.

For users, this result supports confidence in Wake CFD’s SA implementation for conventional 2D lift/drag prediction in attached flow, and documents the size and direction of the expected error near and beyond stall.

20.3 Reference Solution and Data

Item	Setting
Reference (linear range)	CFL3D-SA, NASA TMR (code-to-code)
Reference (full range)	Ladson (NASA TM-4074, 80/120/180-grit trip) and Abbott & von Doenhoff (untripped), wind-tunnel experiment

20.4 Simulation Conditions

Item	Setting
Geometry	NACA0012 2D airfoil, chord c=1
Analysis	Steady, compressible DBNS, RANS
Freestream Mach	0.15
Reynolds number	Re_c=6.0×10^6
Angle of attack	-10° to 19°, 20 points

Constant viscosity is used in place of Sutherland’s law so that Re_c matches the target value exactly, following the same practice as other Wake CFD TMR verification cases.

20.5 Mesh

Item	Setting
Mesh	2D structured mesh, NASA TMR NACA0012 family (single-cell-thick 2D extraction of the 3D family used in TMR’s grid-convergence study); primary grid 897×257, spot-checked against 449×129 at AoA=0°, 10°, 15°

20.6 Boundary and Initial Conditions

N/A: Detailed boundary and initial conditions are not documented for this case.

20.7 Numerical Methods

Item	Setting
Turbulence model	Spalart–Allmaras, standard/ft2=true (“classic” SA, matching the CFL3D convention used by TMR)
Convective scheme	Roe (default entropy fix)
Spatial accuracy	Second order, no limiter
Gradient reconstruction	Green–Gauss
Nonlinear control / preconditioner	HANIM (adaptive nonlinear control) with a Jacobi linear-solver preconditioner
Convergence criterion	Cauchy-window monitor on CD (eps=1e-6 over a 1000-iteration window), max_iter=40000

20.8 Results

20.8.1 Linear Range (-10° to 10°)

Wake CFD’s lift-curve slope lies on top of both the CFL3D-SA point and the Ladson/Abbott experimental scatter over the full linear range.

NACA0012, Re_c=6×10^6, M=0.15: CL vs alpha, linear range

Drag is compared on an expanded axis (5-count ticks) to make small differences visible:

NACA0012, Re_c=6×10^6, M=0.15: CD vs alpha, linear range

NACA0012, Re_c=6×10^6, M=0.15: drag polar, linear range

A direct CFL3D-SA comparison for these angles is given together with 15° in the next section (Near and Beyond Stall), since the trend across all three points is easier to read as one table.

Left–right symmetry was also checked directly: CD at ±2°, ±4°, ±6°, ±8°, ±10° on the 897×257 mesh agrees to within 0.01 count between positive and negative angle of attack, confirming correct handling of the rotation and force-projection convention.

20.8.2 Near and Beyond Stall (11° to 19°)

NACA0012, Re_c=6×10^6, M=0.15: CL vs alpha, full range including stall

NACA0012, Re_c=6×10^6, M=0.15: CD vs alpha, full range including stall

NACA0012, Re_c=6×10^6, M=0.15: drag polar, full range including stall

Wake CFD reaches CL_max=1.669 at AoA=17°. The experimental references (Ladson 80-grit, Abbott & von Doenhoff untripped) peak about 1°–2° earlier, near 15°–16°, at CL_max≈1.5–1.6. Drag shows the same pattern: Wake CFD’s drag rise beyond stall is real but softer and later than the experimental rise. This is the well-documented tendency of steady RANS with a one-equation turbulence model (SA) to delay separation and over-predict CL_max — it is not specific to this solver.

The CFL3D-SA code-to-code comparison covers AoA=0°, 10° (linear range) and extends one point further, to AoA=15° — still attached, just before the stall break at 17°:

AoA	CFL3D-SA CD (counts)	Wake CFD 897×257 difference (counts)	Wake CFD 449×129 difference (counts)
0°	81.92	-0.94	-1.40
10°	123.11	+2.40	+11.98
15°	212.37	+6.13	+32.47

(1 count = 0.0001 in CD.) On the primary 897×257 mesh, Wake CFD matches CFL3D-SA to within about 2.5 counts in the linear range, and the gap keeps growing smoothly with angle of attack out to 15° (-0.94 → +2.40 → +6.13 counts) rather than jumping suddenly — consistent with gradually approaching, but not yet inside, separated flow. The coarser 449×129 mesh shows a larger and faster-growing gap (-1.40 → +11.98 → +32.47 counts), consistent with that mesh being under-resolved relative to the primary grid rather than with a modeling error — grid convergence itself has not been established for this configuration (see Applicable Scope).

Two angle-of-attack/mesh combinations did not reach the specified convergence tolerance within 40000 iterations:

• 449×129 at AoA=0° — isolated to this single coarse-mesh/angle combination; the finer 897×257 mesh at the same angle converges normally, and the root cause has not yet been identified.
• 897×257 at AoA=18°, 19° — the two most deeply stalled points. Over the final 1000 iterations, CD oscillates within a bounded range (about 3 and 30 counts respectively) rather than diverging, consistent with genuinely unsteady separated flow that a steady solver cannot bring to a single fixed point.

20.8.3 Convergence History

CFL is controlled by HANIM (adaptive nonlinear control), so its history is reported alongside the residual for four representative cases spanning the sweep: an attached case (AoA=-10°), the baseline (AoA=0°), a pre-stall case (AoA=15°), and the deepest unconverged stall case (AoA=19°).

NACA0012, 897×257 grid: residual history for four representative angles of attack

NACA0012, 897×257 grid: CFL history for four representative angles of attack

20.9 Conclusions and Applicable Scope

• Wake CFD with SA, the Roe scheme, no limiter, Green–Gauss gradients, and HANIM nonlinear control with a Jacobi preconditioner reproduces CFL3D-SA to within about 2.5 drag counts in attached flow (-10° to 10°) on the primary 897×257 mesh, and matches the Ladson/Abbott lift-curve slope closely.
• Near and beyond stall, expect Wake CFD/SA to predict a CL_max roughly 5–10% higher than experiment, 1°–2° later in angle of attack, with a correspondingly delayed and softened drag rise — consistent with the known behavior of steady RANS with one-equation turbulence models, not a Wake CFD-specific defect.
• This case establishes 2D, steady RANS/SA performance at one Mach number and one Reynolds number on one mesh family. It does not by itself establish grid-converged accuracy — only two mesh densities were compared, and only at three angles of attack — and it does not cover 3D/finite-span effects, transition, or other turbulence models (SST is not covered by this case).
• The two non-converged points (449×129/0° and 897×257/18°–19°) should be treated as open items rather than resolved behavior; see the run notes for follow-up.

20.10 References

• Rumsey, C.L., “2D NACA 0012 Airfoil Validation Case (Numerics),” NASA Turbulence Modeling Resource.
• Ladson, C.L., “Effects of Independent Variation of Mach and Reynolds Numbers on the Low-Speed Aerodynamic Characteristics of the NACA 0012 Airfoil Section,” NASA TM-4074, 1988.
• Abbott, I.H., and von Doenhoff, A.E., Theory of Wing Sections, Dover Publications, 1959.