Turbulent flat plate

Overview

• Solver: simpleFoam
• 2D flat plate test case based on the reference https://turbmodels.larc.nasa.gov/flatplate.html
• Zero pressure gradient
• Reynolds number based on the plate length of $Re_L = 5 \times 10^6$
• Turbulence is modelled using the kOmegaSST
• turbulentFlatPlate

The domain comprises a 2D rectangular slab as shown below:

Mesh

Several meshes are employed to highlight the sensitivity of the computed skin friction coefficient to the near wall $y^+$ over the range $0.05 < y^+ < 100$. All meshes are generated using blockMesh and employ the same number of cells whereby the first cell height is varied by changing the expansion ratio from the wall patch.

Boundary conditions

Common fields

Velocity: U

Patch	Condition	Value
Inlet	fixedValue	69.4 m/s in x
Outlet	zeroGradient
Walls	noSlip

Pressure: p

Patch	Condition	Value
Inlet	zeroGradient
Outlet	fixedValue	0 Pa (static)
Walls	zeroGradient

Turbulence viscosity: nut

Patch	Condition	Value
Inlet	calculated
Outlet	calculated
Walls	nutUSpaldingWallFunction

Turbulence fields

Inlet conditions are based on an inlet turbulence intensity of 0.0039%, and turbulence viscosity ratio of 0.009.

Turbulence kinetic energy: k

Patch	Condition	Value
Inlet	fixedValue	based on 0.039% intensity
Outlet	zeroGradient
Walls	kqRWallFunction

Turbulence specific dissipation rate: omega

Patch	Condition	Value
Inlet	fixedValue	based on nut/nu = 0.009
Outlet	zeroGradient
Walls	omegaWallFunction

Results

The following figures show the predicted skin friction coefficient as a function of Reynolds number, compared against the experimental data from Weighardt 88