Learning Forum

[Dino]

Hello,

For flow in a porous medium, the momentum equation is different in two different versions of Fluent, which one is correct?

In one version the sink term is not multiplied by the porosity at all while in the other version it is multiplied by porosity^2 and porosity^3?

Is there a clear source for what equations Fluent uses in Superficial formulations vs Physical formulations?

[Surya Deb]

Hello,
Can you let me know which are these two different versions of Fluent you are looking at?
I will cross check at my end then.
Regards SD

[Dino]

Thank you for the help. The second one is from the ANSYS Fluent User Guide version 2021 R1 while the first is from ANSYS Fluent User Guide version 12.0. Both versions are discussing the physical velocity formulation. I am just trying to figure out what shape of equations Fluent uses for both superficial and physical velocity. If version 2021 R1, why the source term in the momentum equation has porosity^2 and porosity^3 for the first two terms instead of porosity and porosity^2; for physical velocity?
Best

[Dino]

Here is the issue and I hope I get an answer or ANSYS Fluent correct it or make it clear in the upcoming versions:
The formulation from the latest version of Fluent is the correct one but here is the problem:
Eq 7-19 Fluent User Guide 2021 R1 is in terms of the physical velocity. superficial velocity = porosity x physical velocity. Substituting this into Eq 7-19, we get the following in terms of the superficial velocity:
Here "u" is the superficial velocity and epsilon is the porosity. ANSYS Fluent User Guide is saying that "Porous media are modeled by the addition of a momentum source term to the standard fluid flow equations". Basically, it is the last term on the right-hand side without the porosity. Most papers just use the standard governing equations with the additional sink term and state that this is how Fluent considers for porous medium. Please clarify and help with this.
Thanks

[Surya Deb]

Hello,
Please check Equations (7-2) [Source Term implementation for superficial velocity], (7-16)[Relation between superficial and physical velocities] and (7-17) [the last term of this equation where the source term gets multiplied by porosity].
I have not derived it from scratch but substituting for superificial velocity along with source term implementation should get you the documented momentum equation in the latest version.
Regards SD

[Dino]

Hello Thank you. Yes, I agree with you that Eqs. (7.17-7.19) in the latest version are correct. The issue is still with the latest version. In section 7.2.3.2., "Porous media are modeled by the addition of a momentum source term to the standard fluid flow equations." and this source is Eq. (7.2). So, ANSYS Fluent for porous medium uses the standard momentum equation with the addition of Eq. (7.2) to account for the porous medium.
Now, let's focus on Eq. (7.19) which we agreed is the correct one and it is in terms of the physical velocity. If we substitute Eq. (7.16), you will get a momentum equation in terms of the superficial velocity. This equation is NOT the standard momentum equation with the additional source term of Eq. (7.2) as Section 7.2.3.2 stated. The resulted momentum equation takes the form:
My question is, for the superficial velocity, Does ANSYS Fluent uses the standard governing equations with the additional source term in the momentum (Eq.7.2), if this is the case that contradicts with Eqs. (7.17-7.19), OR the momentum equation I mentioned above is what Fluent really uses?
Please check this and thank you very much for your help.