Overview🔗

• Based on https://turbmodels.larc.nasa.gov/naca0012_val.html [53]
• References: Gregory-O’Reilly (1970) [21], McCroskey (1987) [47], Ladson (1988) [32], Spalart-Allmaras (1994) [69], and Krist et al. (1997) [29]
• See the resources section for additional data files

Flow physics:

• External flow
• Steady
• High Reynolds number
• Low Mach number, subsonic
• Newtonian, single-phase, incompressible, non-reacting

Solver:

• simpleFoam

Tutorial case:

• $FOAM_TUTORIALS/incompressible/simpleFoam/airFoil2D

Physics and Numerics🔗

Physical domain:

• The case is a two-dimensional airfoil located around the centre of a computational domain whose dimensions are considerably larger than the chord-length of the airfoil.
  • \(x\): Longitudinal direction (mean flow direction)
  • \(y\): Spanwise direction (statistically homogeneous direction)
  • \(z\): Vertical direction (wall-normal direction)
  • \(O\): Origin at the leading edge of the airfoil

Physical modelling:

• Reynolds number based on local chord length: \(\text{Re}_c = U_x \, c \, \nu^{-1} \approx 6\times10^6\)
  • Streamwise far-field flow speed: \(U_x = 51.4815\) [m⋅s^-1]
  • Characteristic length (Local chord length of the airfoil): \(c = 1.0\) [m]
  • Kinematic viscosity of fluid: \(\nu_\text{fluid} = 8.58 \times 10^{-6}\) [m²⋅s^-1]
• Mach number: \(\text{Ma} = U_x / U_s \approx 0.15\)
  • Speed of sound: \(U_s = 343.21\) [m⋅s^-1]
• Turbulence model: Spalart Allmaras

Numerical domain modelling:

• Shape: extruded C-grid
• Dimensions: \((x, y, z) \approx (985.5, 1.0, 1015.6)\) [m]
• Sketch (View direction to \(y\)-positive):

Spatial domain discretisation:

• Mesh type: hexahedral cells in plot3d format
• Mesh converter: plot3dToFoam
• Number of cells, \(N\) : \((N_x, N_y, N_z) = (257, 1, 897)\)
• First wall-normal cell centre height: \(\Delta_y^+ < 1\)
• Mesh detail (View direction to \(y\)-positive):

Equation discretisation:

Spatial derivatives and variables:

• Gradient: Gauss linear
• Divergence:
  • default: Gauss linear
  • div(phi,U): bounded Gauss linearUpwind grad(U)
  • div(phi,nuTilda): bounded Gauss linearUpwind grad(nuTilda)
• Laplacian: Gaussian linear corrected
• Surface-normal gradient: corrected

Temporal derivatives and variables:

• ddtSchemes: steadyState

Numerical boundary conditions:

• Velocity, \(\mathbf{U}\)

• Kinematic pressure, p

• Turbulent kinematic viscosity, nut (i.e. \(\nu_t\))

• Spalart-Allmaras model modified viscosity, nuTilda (i.e. \(\tilde{\nu}\))

Solution algorithms and solvers:

• Pressure-velocity: SIMPLE
• Parallel decomposition of spatial domain and fields: Not applicable
• Linear solvers:

Results🔗

List of metrics:

• Lift coefficient \(\mathrm{C}_\mathrm{L}\) vs. Angle of attack \(\alpha\)
• Drag coefficient \(\mathrm{C}_\mathrm{D}\) vs. Angle of attack \(\alpha\)
• Drag coefficient \(\mathrm{C}_\mathrm{D}\) vs. Lift coefficient \(\mathrm{C}_\mathrm{L}\)
• Surface pressure coefficient \(\mathrm{C}_p\) vs. Normalised chord length \(x/c\)
• Surface skin friction coefficient \(\mathrm{C}_f\) vs. Normalised chord length \(x/c\)
• \(\{\overline{\cdot}\}\) is the time-averaging operator

Resources🔗

Note: Links will take you to the NASA website

Mesh🔗

• Mesh description
• Mesh: (3-D) 2 x 897 x 257 with 2 x 513 points on airfoil surface (gzipped, 5.1 MB)

Datasets for verifications (plain text)🔗

Lift and drag coefficients vs angle of attack

• Experiment [32]
• Numerical (CFL3D software) [29]

Pressure distribution vs local chord length

• Experiment [32]
• Numerical (CFL3D software) [29]

Lift coefficient vs angle of attack

• Theoretical [47]

Skin friction coefficient vs local chord length

• Numerical (CFL3D software) [29]