firctional viscosity

Arne87 · March 24, 2017, 06:04

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

mohit68 · May 22, 2018, 09:56

can you tell me how did you decided the value of internal frictional angle?

March 24, 2017, 06:04	firctional viscosity	#1
Arne87 New Member Arne Join Date: Oct 2013 Posts: 16 Rep Power: 12	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: $\mu_{s,fric} =\frac{p_ssin \phi}{2\sqrt{I_{2D}}}$ 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

May 22, 2018, 09:56	internal frictional angle	#2
mohit68 New Member mohit dhoriya Join Date: Mar 2018 Posts: 9 Rep Power: 8	can you tell me how did you decided the value of internal frictional angle?

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