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 Simbelmynė November 6, 2012 05:53

Mass transfer in cfd

Hey,

I wonder if we usually ignore the mass convection caused by mass diffusion (i.g. by assuming dilute mixture and/or equimolar counter-diffusion) when writing codes?

My second question is if there is any dimensionless number that relates convection caused by pressure differences to the convection caused by diffusion of species?

 michujo November 6, 2012 06:36

Hi, as far as I know total mass transport must be accounted for in a multi-species formulation (by using for instance a correction velocity, to be added to the velocity vector). This is not needed when transporting a scalar (or a highly diluted mixture).

As for the second question the answer is the Peclet number, which quantifies the importance of advection to diffusion.

Did this help? Maybe some other people can give their opinion.

Cheers,
Michujo.

 Simbelmynė November 6, 2012 07:58

Quote:
 Originally Posted by michujo (Post 390532) Hi, as far as I know total mass transport must be accounted for in a multi-species formulation (by using for instance a correction velocity, to be added to the velocity vector). This is not needed when transporting a scalar (or a highly diluted mixture). As for the second question the answer is the Peclet number, which quantifies the importance of advection to diffusion. Did this help? Maybe some other people can give their opinion. Cheers, Michujo.
Thank you for your reply Michujo. Do you have any references to the correction velocity you speak of?

I am not certain that Pe number is the correct one to use here (it is certainly correct to use when we discuss heat or momentum transfer, but I have some doubts with regard to the mass transfer). I am probably wrong though and will understand soon (I hope ;) )

 michujo November 6, 2012 08:31

Hi, you are welcome. Off the top of my head I can think of the books by T.Poinsot and D. Veynante "Theoretical and numerical combustion" or the one by Bird "Transport phenomena" (I think the approximation is usually referred to as Hirschfelder-Curtiss approximation).

Cheers,
Michujo.

 michujo November 6, 2012 14:02

1) As stated before (as far as I know), in order to enforce mass conservation, either you apply the correction velocity or you store the error in the main species (usually nitrogen if you are working with a species diffusing in air).

2) You are right, I misunderstood your question. You refer to the relation between the convection due to pressure difference and the net velocity that appears as a result of two non-equimolar species diffusing in each other, right? I suggest you check out this link:

If this is not clear enough, it is most likely dealt with in the book by Bird et al. Probably you can work out a non-dimensional number relating the bulk velocity with the induced velocity (probably proportional to a diffusion coefficient, or the difference in molar weight of the species, since this is the driving force as far as I understand).

What do you think? I am also interested in knowing more about this stuff. Let me know if you come up with a conclusion.

Cheers,
Michujo.

 Simbelmynė November 6, 2012 15:18

Quote:
 Originally Posted by michujo (Post 390643) Hi, I have been thinking about your question. 1) As stated before (as far as I know), in order to enforce mass conservation, either you apply the correction velocity or you store the error in the main species (usually nitrogen if you are working with a species diffusing in air). 2) You are right, I misunderstood your question. You refer to the relation between the convection due to pressure difference and the net velocity that appears as a result of two non-equimolar species diffusing in each other, right? I suggest you check out this link: http://books.google.es/books?id=CjBT...fusion&f=false If this is not clear enough, it is most likely dealt with in the book by Bird et al. Probably you can work out a non-dimensional number relating the bulk velocity with the induced velocity (probably proportional to a diffusion coefficient, or the difference in molar weight of the species, since this is the driving force as far as I understand). What do you think? I am also interested in knowing more about this stuff. Let me know if you come up with a conclusion. Cheers, Michujo.
1) Ok, but I thought it was more a way to enforce that the sum of all mass fractions is one. This usually means that the largest species will vary due to numerical round off etc. of all species, but since it is large (hopefully) this variation is small.

2) I will check the link you provided, and I will try to dig a bit deeper in the book by B.S.L. If I come to a conclusion I will let you know ;)

Thanks!

 Simbelmynė November 9, 2012 08:39

After some more reading I found that in Cussler's "Diffusion - Mass transfer in fluid systems", they derive the continuity equation using mass averaged velocities and for the continuity equation of species they use volume averaged velocities.

In Themelis' "Transport and Chemical Rate Phenomena" they state that:

Velocities appearing in the species transport equation consists of two parts;
1. Velocity due to diffusion.
2. Velocity due to pressure differences.

In Bird et. Al I can not find any mention of how the diffusion velocity is coupled to the momentum equation although a comprehensive list of different frames of reference is given.

Any thoughts?

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