Why in Hrvoje Jasak's thesis diffusion term has "rho"?
 

Hello Foamers. I hope all is well with you.

I ran into the scalar transport equation in Hrvoje Jasak's thesis (page 77).
He used div(rho*gamma*grad(phi)) as the diffusion term!

Why do you think he used "rho" in the diffusion term. I can't understand that!
In standard form of the transport equation there is not rho in the diffusion term.

This is not correct, if you look here:

https://en.wikipedia.org/wiki/Convec...usion_equation

The density here is hidden in the gradient.

This means you have a discretization in mass parts. In CFD you want a discretization in volume, since you have a volumetric mesh (fixed volumetric cells in the Euclidian space). This leads to the formulation in Jasak's thesis.

Regards,

Daniel

Thanks for your response dear Daniel
BTW, I totally can't understand what you mean by hidden in gradient!
Just take a look at Henrik Rusche thesis in "Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions" in page 79.
How can we justify this one?
Now which one is correct? In Jasaks thesis or Rusches thesis?

Hi everyone !

I encoutered the same interrogation today... And tried to figure it out where does this "rho" come from.
I can find this formulation of the generic transport of equation with a "rho" written in the diffusion term in :

• Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows from Dr. H. Jasak (page 69)
• Combustion Engines Development from G. P. Merker, C. Schwarz and R. Teichmann (page 450)

It looks like this "rho" comes from the mixture fraction... Could someone enlighten us about this particular formulation ?


Thanks in advance and have a nice week-end!

Hi,

As far as I know, a diffusion term with 'rho' is more general.

I would recommend you to read this article:

Novaresio, V., García-Camprubí, M., Izquierdo, S., Asinari, P., & Fueyo, N. (2012). An open-source library for the numerical modeling of mass-transfer in solid oxide fuel cells. Computer Physics Communications, 183(1), 125-146.

Pay attention to Eqs. (8), (9) and (10).

Regards,

Yan

Hello,

I looked this up again, though it has been a while. In short: Rusche is wrong and Jasak is correct. Diffusivity has m^2/s as unit, so Rusche's formulation has a unit missmatch.

I think the error steams from the often used formulation to use rho phi as single variable. In chemical engineering this is done quite often. In this case, you get gradient rho phi in the diffusion term instead of of rho gradient phi. This is what I mean with "hidden in the gradient".

Regards,

Daniel

Thank you for your answers and explanations. I will try to get my hands on this article!

Thanks again!