Bump (2D)

Overview

• Solver: simpleFoam
• 2D flow over a bump at a Reynolds number of $3 \times 10^6$ (L=1m)
• Based on the description provided by the NASA Turbulence Modelling Resource
• bump2D

Mesh

• 2D structured mesh created using blockMesh

• bump described

  $$y(x) = \begin{cases} 0.05 [\sin(\pi \frac{x}{0.9}-\frac{\pi}{3})]^4, & 0.3 \le x \le 1.2, \\ 0 , & 0 \le x \lt 0.3 \, \text{and} \, 1.2 \lt x \le 1.5. \end{cases}$$

• this has been set in the blockMeshDict using a codeStream

Boundary conditions

• $U$ based on a Mach number of 0.2. Mach number, $Ma$, is defined as:

  $$Ma = \sqrt{\gamma R T}$$

  where $\gamma$ is the ratio of specific heats, $R$ the gas constant and $T$ the temperature. Using values for air at 300K, the inflow velocity is given as:

  $$U = 0.2 Ma = 0.2 \sqrt{1.4 \times 287 \times 300} = 69.44 m/s$$

• The laminar viscosity is derived from the Reynolds number, i.e.

  $$\nu_\infty = \frac{|\u| L}{Re} = \frac{69.44 \times 1}{3 \times 10^6} = 2.31 \times 10^{-5} m^2/s$$

Common fields

Velocity: U

Patch	Condition	Value
Inlet	fixedValue	69.44 m/s in x
Outlet	zeroGradient
Bump	noSlip
Walls	symmetryPlane

Pressure: p

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

Turbulence fields

• turbulence model: Spalart Allmaras

Turbulence viscosity: nut

Patch	Condition	Value
Inlet	calculated
Outlet	calculated
Bump	nutUSpaldingWallFunction
Walls	symmetryPlane

Spalart-Allmaras

Modified turbulence viscosity: nuTilda

Patch	Condition	Value
Inlet	fixedValue	based on $3 \nu_\infty$
Outlet	zeroGradient
Bump	fixedValue	0
Walls	symmetryPlane

Results

The NASA Turbulence Modelling Resource employs a code comparison to show that the FUN3D and CFL3D codes produce equivalent results for this case. OpenFOAM and CFL3D results are presented in the following series of images, showing that OpenFOAM results compare very favourably.