Eulerian multiphase tracer transport - value of scalar?

dschmidt · January 14, 2015, 09:44

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.

alberto · February 1, 2015, 23:21

Yes, your equation is correct and refers to a tracer into the liquid phase (note that alpha_L is in all the terms).

Z.Q. Niu · November 18, 2018, 23:26

Hi Dominik,
I have also write a same equation in the interFoam solver to add tracker into one phase of interFoam. But I found if alpha1 equals zero, the solver will crash, unlesss you set a small value for alpha1, e.g. 1e-6 or smaller one. Did you have this situation? It will be great if you cold you share your code! The following is my code:
fvm::ddt(alpha1, CFai)
+ fvm::div(fvc::interpolate(alpha1)*phi, CFai)
- fvm::laplacian(fvc::interpolate(alpha1)*DT_L, CFai)

January 14, 2015, 09:44	Eulerian multiphase tracer transport - value of scalar?	#1
dschmidt New Member Dominik Schmidt Join Date: Mar 2014 Posts: 11 Rep Power: 12	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 03:10.

February 1, 2015, 23:21		#2
alberto Senior Member Alberto Passalacqua Join Date: Mar 2009 Location: Ames, Iowa, United States Posts: 1,912 Rep Power: 36	Yes, your equation is correct and refers to a tracer into the liquid phase (note that alpha_L is in all the terms). __________________ Alberto Passalacqua GeekoCFD - A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as in both physical and virtual formats (current status: http://albertopassalacqua.com/?p=1541) OpenQBMM - An open-source implementation of quadrature-based moment methods. To obtain more accurate answers, please specify the version of OpenFOAM you are using.

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November 18, 2018, 23:26		#3
Z.Q. Niu Member Niu Join Date: Apr 2014 Posts: 55 Rep Power: 12	Hi Dominik, I have also write a same equation in the interFoam solver to add tracker into one phase of interFoam. But I found if alpha1 equals zero, the solver will crash, unlesss you set a small value for alpha1, e.g. 1e-6 or smaller one. Did you have this situation? It will be great if you cold you share your code! The following is my code: fvm::ddt(alpha1, CFai) + fvm::div(fvc::interpolate(alpha1)phi, CFai) - fvm::laplacian(fvc::interpolate(alpha1)DT_L, CFai)