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 Mehdi BEN ELHADJ May 20, 2001 06:11

The viscosity field

The density field can be calculated in SEM or in HOL as follows:

RHO = RHOG * (1-VFOL) + RHOL * VFOL (it's logical)

but

why ? the viscosity field is calculated as follows:

ENUL = ENULG * (1-VFOL) + ENULL * VFOL

 Kike May 21, 2001 08:30

Re: The viscosity field

Hi, Medhi

In my oppinion it is a simple, but a very nice and strong question? You maybe are "touching" a delicate point inside those methods.

Could you be more specific about why you think it is improper to calculate the viscosity by this expression? In principle, you are averaging the fluids properties.

Kike

 Mehdi BEN ELHADJ May 21, 2001 16:11

Re: The viscosity field

Hi, Enrique

If you take a cell and you want to calculate the density, you can write

Mt = Ml+Mg

where

Mt: total mass, Ml: mass of liquid and Mg: mass of gas.

so,

Mt/Vt = Ml/Vt+Mg/Vt

Vt: total volume of the cell.

and finally

Mt/Vt= (Ml/Vl)*(Vl/Vt) + (Mg/Vg)*(Vg/Vl)

Where

Vl: volume of liquid and Vg: volume of gaz

and we have:

RHO = RHOG * (1-VFOL) + RHOL * VFOL

but I don't know why we can calculate the viscosity in this form:

ENUL = ENULG * (1-VFOL) + ENULL * VFOL

 Kike June 12, 2001 06:21

Re: The viscosity field

Dear Medhi

I am sorry to ansuwer you so late. Effectively there is no physical explanation for this "special average". It is a gross approximation to obtain a transport coefficient for momentum according to the presence of the two phases inside the cell.

In those cells you have the stress balance expresions (normal and tangential to the interface) and you can extract a different relation for the viscosity coefficients ENULG, ENULL and a total viscosity coefficient ENUL from the tangential relation. It is more consistent with the stress continuity at interfaces considering piecewise linear velocity profile in each phase. After some algebraic calculations you will have:

1/ENUL=VFOL*(1/ENULL)+((1-VFOL)*(1/ENULG))

This has been proposed for a professor of CALTEC but I don't remember his name. It was a friend of mine who gave me the hint.

Nevertheless, every body uses the relation you find into PHOENICS and it works for most cases (I mean with respect to experimental results). Try to implement the new relation and see what the differences are. Please tell me what you find after the change in your problem.

Regards

Kike

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