2D NACA 0012 Airfoil: Validation (SA)

Overview

The NACA 0012 is a symmetric airfoil section whose low-speed lift, drag, and surface pressure distribution have been documented across many wind-tunnel campaigns, making it a standard validation benchmark for turbulence models. At the incidence used here the flow stays attached over most of the chord, with a leading-edge suction peak on the upper surface.

This validation case compares Luminary's Spalart–Allmaras solution against experiment as well as against reference codes: the surface pressure of Gregory & O'Reilly and the lift and drag of Ladson, with the NASA CFL3D and FUN3D reference codes shown alongside. Conditions follow the NASA Turbulence Modeling Resource validation page, $M = 0.15$ , $R e = 6 \times 10^{6}$ , $α = 10^{\circ}$ , run on the same 897 × 257 C-grid CFL3D used, so the code-to-code comparison is grid-for-grid.

Problem Setup

The airfoil has unit chord and lies in the x–y plane at an angle of attack of $α = 10^{\circ}$ ; lift and drag are recovered by projecting the integrated surface force onto the wind axes. The free stream is air at $M = 0.15$ and a chord Reynolds number of $R e = 6 \times 10^{6}$ . Turbulence is modeled with Spalart–Allmaras, with the far-field point-vortex correction active. Discretization is second-order with no limiter, and every run is driven to a deep residual floor.

The boundary conditions are a no-slip adiabatic wall on the airfoil and a Riemann far field on the outer C-boundary. The mesh is NASA's published Family-I structured C-grid at 897 × 257 points, converted to a quasi-2D unit-span grid; using CFL3D's own grid removes mesh resolution as a variable in the comparison. The experimental data span two facilities and Reynolds numbers: Gregory's pressure data at $R e = 2.88 \times 10^{6}$ and Ladson's forces at $R e = 6 \times 10^{6}$ ; both are shown as reported.

Quantities of Interest

The validation quantities are the surface pressure coefficient $C_{p} (x / c)$ at $α = 10^{\circ}$ and the integrated lift and drag coefficients. The pressure distribution is compared to the CFL3D reference and to Gregory's upper-surface measurements; the lift and drag are tabulated beside CFL3D, FUN3D, and Ladson's tripped-boundary-layer measurement, each at $α = 10^{\circ}$ . The upper-surface skin-friction coefficient $C_{f} (x / c)$ is shown against CFL3D as a supporting boundary-layer check.

Sources

NASA Langley Turbulence Modeling Resource, "2D NACA 0012 Airfoil Validation Case" (SA model, with far-field point-vortex correction).: https://tmbwg.github.io/turbmodels/naca0012_val_sa.html
Reference

C_{p}

C_{f}

and

C_{L}

C_{D}

from the NASA CFL3D code on the 897 × 257 grid,

α = 10^{\circ}

N. Gregory and C. L. O'Reilly, "Low-Speed Aerodynamic Characteristics of NACA 0012 Aerofoil Section, including the Effects of Upper-Surface Roughness Simulating Hoar Frost," NASA R&M 3726, 1970.: https://tmbwg.github.io/turbmodels/naca0012_val_sa.html
Digitized upper-surface

C_{p}

α = 10^{\circ}

(

R e = 2.88 \times 10^{6}

C. L. Ladson, "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.: https://tmbwg.github.io/turbmodels/naca0012_val_sa.html
Measured

C_{L}

C_{D}

R e = 6 \times 10^{6}

M = 0.15

, boundary-layer tripped (80-grit).

Results

Lift and drag at

α = 10^{\circ}

vs CFL3D and experiment

Code	$C_{L}$	$C_{D}$
Luminary	1.0907	0.012453
CFL3D (SA)	1.0909	0.012311
FUN3D (SA)	1.0983	0.01242
Ladson (exp.)	1.0586	0.01191

Code

C_{L}

C_{D}

Luminary

1.0907

0.012453

CFL3D (SA)

1.0909

0.012311

FUN3D (SA)

1.0983

0.01242

Ladson (exp.)

1.0586

0.01191

Values on the finest grid (897 × 257, $ \alpha = 10^\circ $).

Wind-axis

C_{L}

and

C_{D}

α = 10^{\circ}

(897 × 257 grid). The Ladson measurement is the 80-grit-trip data interpolated to

α = 10^{\circ}

Surface pressure coefficient

C_{p} (x / c)

α = 10^{\circ}

$Surface pressure coefficient $ C_p(x/c) $ at $ \alpha = 10^\circ $$

Surface pressure coefficient at

α = 10^{\circ}

. The Gregory measurements (upper surface) are at

R e = 2.88 \times 10^{6}

Reference: NASA Langley Turbulence Modeling Resource, "2D NACA 0012 Airfoil Validation Case" (SA model, with far-field point-vortex correction). (CFL3D (SA), surface

C_{p}

α = 10^{\circ}

): https://tmbwg.github.io/turbmodels/naca0012_val_sa.html

Skin-friction coefficient

C_{f} (x / c)

α = 10^{\circ}

$Skin-friction coefficient $ C_f(x/c) $ at $ \alpha = 10^\circ $$

Reference: NASA Langley Turbulence Modeling Resource, "2D NACA 0012 Airfoil Validation Case" (SA model, with far-field point-vortex correction). (CFL3D (SA), upper-surface

C_{f}

α = 10^{\circ}

): https://tmbwg.github.io/turbmodels/naca0012_val_sa.html

2D NACA 0012 Airfoil: Validation (SA)

Overview

Problem Setup

Quantities of Interest

Sources

Results

Lift and drag at $α = 10^{\circ}$ vs CFL3D and experiment

Surface pressure coefficient $C_{p} (x / c)$ at $α = 10^{\circ}$

Skin-friction coefficient $C_{f} (x / c)$ at $α = 10^{\circ}$

Solver configuration

2D NACA 0012 Airfoil: Validation (SA)

Overview

Problem Setup

Quantities of Interest

Sources

Results

Lift and drag at α=10∘ vs CFL3D and experiment

Surface pressure coefficient Cp(x/c) at α=10∘

Skin-friction coefficient Cf(x/c) at α=10∘

Solver configuration

Lift and drag at $α = 10^{\circ}$ vs CFL3D and experiment

Surface pressure coefficient $C_{p} (x / c)$ at $α = 10^{\circ}$

Skin-friction coefficient $C_{f} (x / c)$ at $α = 10^{\circ}$