CFD Online Discussion Forums - firctional viscosity

Dear Foamers,

I am trying to implement the grannular theory into the multiphaseEulerFoam solver of openFOAM. This implementation has been done often in a Euler-Euler Framework.

(See for example: Cornelissen(2007) CFD modelling of a liquid–solid fluidized bed or different works of Berend van Wachem)

The implementation is almost finished it produces reasonable results. However, I have some problems with the term for the frictional viscosity. In most cases the approach of Schaeffer is used:

$\mu_{s,fric} =\frac{p_s*sin \phi}{2*\sqrt{I_{2D}}}$

here

is the solid pressure, $\phi$ is the internal friction angle ( in my case 30 degree) and $I_{2D}$ is referred to as the "second invariant of the deviatoric stress tensor". Cornelissen et. al. state that the $I_{2D}$ is non dimensional. The dimension of

is

$\frac{kg }{s^2 \cdot m}$ .

As this isn't a viscosity this can't be right.

Following the description of the term "second invariant of the deviatoric stress tensor" $I_{2D}$ should have the dimension:

$\frac{kg^2 }{m^2 \cdot s^4}$ .

Anyways using this I again don't end up with the right dimension.

If anybody has experience with this term or can identify my mistake I would be glad to get some input.

Best

Arne