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Eulerian multiphase tracer transport - value of scalar?

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Old   January 14, 2015, 10:44
Default Eulerian multiphase tracer transport - value of scalar?
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Dominik Schmidt
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Dear Foamers,

I believe the answer to my question is quite simple, but I couldn't find a clear definition for it:

I'm adding a scalar transport equation to an incompressible multiphase solver, where the scalar should only be transported by/in the liquid phase,
representing e.g. a solution of salt in water.

\frac{\partial {\alpha_L Tr}}{\partial {t}} + \nabla \cdot (\alpha_L U_L Tr) = \nabla \cdot (\alpha_L \Gamma) \nabla Tr)

Code:
fvm::ddt(alpha1, Tracer)    
+ fvm::div(fvc::interpolate(alpha1)*phi1, Tracer)
- fvm::laplacian(fvc::interpolate(alpha1)*DT, Tracer)
Assuming this part is correct (please correct me, if it isn't),
my questions is about the "value" of the transported scalar:


1.) "Tracer" = mass(Tracer) per cell-volume (= concentration in each cell)?

... so to get the concentration in the liquid phase in each cell one has to divide "Tracer"-value by alpha1 (volumetric phase fraction of liquid phase)?

or

2.) the value for "Tracer" already represents the concentration in the liquid phase?

or

3.) anything else?


In short: Does the Tracer-value represent a concentration based on the cell volume or based on the liquid volume in each cell?
Or is a completely different approach necessary to get the concentration of e.g. a salt in the water phase for the evaluation of homogeneity inside the domain.


Thanks for your help!

Dominik


EDIT:
Reading http://www.sciencedirect.com/science...85894714015587 helped me to understand that the second option should be correct.

Last edited by dschmidt; January 19, 2015 at 04:10.
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Old   February 2, 2015, 00:21
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Alberto Passalacqua
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Yes, your equation is correct and refers to a tracer into the liquid phase (note that alpha_L is in all the terms).
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