NACA 0012 at 10 degrees: lift extrapolated from three grids sits +2.14 % above a reference code and +3.4 to +3.8 % above experiment

3Case parameters

4Experiment

Three references, all from the NASA Turbulence Modeling Resource files on disk. Lift: Ladson, NASA TM 4074 (1988), Re 6 million, transition tripped, Mach 0.15; interpolated to 10° it gives 1.0628. Surface pressure: Gregory and O'Reilly, NASA R&M 3726 (1970), at Re 2.88 million, digitised from a photocopy, approximate, upper surface only.

The reference computation is CFL3D with the SST model on a 897 × 257 grid. It is not an experiment: it is compressible at Mach 0.15 where I solve incompressible, and the reference codes on that page scatter by about a percent in lift themselves.

5Set-up

A 2-D O-grid around a NACA 0012 with a near-sharp trailing edge (base thickness 0.0003 c), far field at 2000 chords. The three grids share the geometry and only scale the cell counts; refinement ratios between neighbours are 1.334 and 1.502. The free-stream turbulence follows the NASA specification (turbulence intensity 0.052 %, nut/nu 0.009).

The pressure plots on this page come from a separate, longer run of the coarse grid recipe (48,120 cells, 20,000 iterations, final lift 1.0805); the grid ladder uses 6000 iterations per grid.

Numerics and convergence

Steady simpleFoam, SIMPLEC (consistent), 2 non-orthogonal correctors. Convection: bounded Gauss linearUpwindV grad(U) for velocity, bounded Gauss limitedLinear 1 for k and omega.

Convergence is judged from the force history, not residuals: the gate is a tail-mean drift below 1e-5. The two finer grids miss it (drift 3.9e-5 and 1.8e-5, lane audit).

6Mesh

The finest grid was solved despite its failed check, and the failure is not explained in any case note. Its lift enters the order and the GCI below, so both carry that caveat.

7Results

Lift converges monotonically, 1.08028, 1.08840, 1.09212, to an extrapolated 1.10083: +2.14 % above CFL3D (1.07781). Corrected for the grid, the lift over the angle range sits +3.41 to +3.77 % above the Ladson experiment, flat with angle.

The surface pressure follows CFL3D closely: the suction peak is −5.5924 against −5.60. Drag is not grid-converged (124.23, 122.45 and 123.38 drag counts on the three grids, down then up), so I give no drag result.

A NACA 4412 at high lift was also run with the same recipe. That run was made after the experimental value was known and with a changed set-up, so it is not a blind test; the one genuinely blind run used a recipe later found defective and is invalid. It is a single grid, its aft upper-surface pressure is wrong, and the experimental lift it was scored against is not stored on this machine, so it is not compared on this page.

8Numerical accuracy

Method: three-grid Richardson extrapolation with the unequal-ratio form (Celik et al.), run with the project's shared gci.py. On the five-digit lift values it gives an observed order of 1.241, an extrapolated 1.100768, a GCI of 0.990 % and an asymptotic check of 1.003. The freeze document's 1.10083 and 1.00 % come from the same data; the differences are input rounding.

Three grids give one value of the order and no way to check it, and the fine-grid force noise moves it noticeably, so the honest figures are p ≈ 1.2 ± 0.1 and GCI ≈ 1.0 ± 0.15 %. The order is well below the formal 2. An earlier GCI from a defective formula was retracted; the retraction is kept in the freeze document and in the ledger note below.

The grid correction for the polar uses a multiplier of 1.0190 from this ladder. Drag has no grid-convergence result.

GCI      N=(48120,108540,193200)  r21=1.3342 r32=1.5019  (unequal-ratio form: YES)
         f: coarse=1.080280 medium=1.088400 fine=1.092120
         observed order p = 1.241   (formal 2.0)
         Richardson f(h->0) = 1.100768
         GCI_fine = 0.990 %   (Fs=1.25 auto; approx. rel. err fine-vs-medium = 0.341 %)
         asymptotic check = 1.003  (want ~1.0)
         WARNING: 3-grid family: p has NO redundancy and is unverifiable. Quote p ~ 1.2 (+-0.1 under force-tail noise), not to 3 s.f. Use >=4 grids (gci_multi.py) for a checkable order.

9Why they differ, and what I distrust

• The finest grid fails checkMesh on aspect ratio (12 cells) and the location of those cells was never documented; the order and GCI depend on that grid.
• Both finer grids drift more than my own convergence gate (3.9e-5 and 1.8e-5 against 1e-5).
• CFL3D is a compressible code at Mach 0.15 using a variant of SST; I solve incompressible with OpenFOAM's SST, so the +2.14 % is a code and model difference I have quantified but not explained.
• The pressure plots come from the coarse grid, not a grid-converged solution, and the Gregory and O'Reilly data are approximate and at a different Reynolds number.
• Drag is not grid-converged.
• The NACA 4412 run is not blind, is single-grid and fails the aft pressure plateau; its experimental lift has no source on disk.

10References

1. NASA Turbulence Modeling Resource, 2-D NACA 0012 validation case: CFL3D SST results (n0012clcd_cfl3d_sst.dat, n0012cp_cfl3d_sst.dat), as stored locally.
2. Ladson, NASA TM 4074, 1988: lift and drag at Re 6 million, transition tripped, M 0.15 (TMR file CLCD_Ladson_expdata.dat).
3. Gregory & O'Reilly, NASA R&M 3726, Jan 1970: upper-surface pressure at Re 2.88 million, digitised (TMR file CP_Gregory_expdata.dat).
4. Celik et al.: the unequal-ratio Richardson / GCI procedure, as implemented in the project's gci.py.

Source files

• D:/CFD/airfoil/RUNG1-FREEZE.md (read with its ERRATUM)
• D:/CFD/airfoil/naca0012-fs2-r10/, fs2-r15/, fs2-r20/ (log.checkMesh, postProcessing/yPlus1)
• D:/CFD/airfoil/naca0012-final-a10/ (0/, constant/, system/, log.checkMesh, postProcessing/)
• D:/CFD/data/airfoil/tmr_naca0012/ (n0012cp_cfl3d_sst.dat, n0012clcd_cfl3d_sst.dat, CLCD_Ladson_expdata.dat, CP_Gregory_expdata.dat)
• investigation/lane-B-verification.md (evidence audit, drift recompute)
• site/public/data/naca-0012/ (surface_cp.csv, README.txt, chart JSON and gci.json from pipeline/case_data/naca-0012.py)

Last updated 2026-11-14. One-page summary (prints to one A4 page), also as a PDF. Every number on this page is checked against its source file by pipeline/check_numbers.py.