Using built-in background turbulence generator

Physics

The OpenFOAM (seems to) uses a Passot-Pouquet spectrum. $E(k) = E_a (\frac{k}{k0})^4 e^{-2(\frac{k}{k0})^2}$ Two parameters need to be set, in constant/boxTurbDict, which are $E_a$ and $k_0$

• $E_a$ will influence the scale of velocity, but not the distribution.
• $k_0$ is the characteristic wave number. Adjust $k_0$ will change the scale of the turbulence.
• The Reynolds number $Re = \frac{ul}{\nu}$. Adjust $E_a$ will allow you to adjust the velocity. Adjusting $k_0$ will affect the integral length scale. The dynamic viscosity is a property of the fluid itself.

Integral length calculation

The integral length $l$ is calculated by $\int_{0}^{+\infty}k^{-1}E(k)dk /\int_{0}^{+\infty}E(k)dk$, suggested by https://en.wikipedia.org/wiki/Integral_length_scale.

It is evident that $E_a$ will not influence the $l$.

To make the calculation of $l$ easier, a Python script is offered here (An installation of Python 3 is required). Run

python integralLength.py <k0value>

Please note that an integral to positive infinity might not be numerically stable, to specify a upper limit, try

python integralLength.py <k0value> <upperLimit>

Generation Strategy

Generate a initial turbulent velocity field with in a domain larger than your target domain. And map the velocity back to your target domain!

2D generator

OpenFOAM does not provide a 2D initial turbulence generator. But we can easily implement one. I offered one, modified from "boxTurb". The velocity in the $z$ direction is set to 0.

To compile it, go to the boxTurb2D folder and run

wmake

Run

boxTurb2D

to generate the 2D background turbulence.

A 2D geometry is required.

Configure $E_a$ and $k_0$ in constant/boxTurbDict

See the box2d case for more information.

3D generator

OpenFOAM provides a built-in 3D initial turbulence generator. See the test case. Run

boxTurb

to generate the 3D background turbulence.

Configure $E_a$ and $k_0$ in constant/boxTurbDict

See the box3d case for more infomation.

Something to note

• The domain to generate the turbulence should be a box.
• The number of cells in each direction should be $2^n$, for $n \in \mathbb{N}$.

Relevant functions in OpenFOAM

The spectrum is implemented in https://cpp.openfoam.org/v10/Ek_8H_source.html.

The generator is implemented in https://cpp.openfoam.org/v10/turbGen_8C_source.html.

Please note that K is a mesh with wave number information.