[aicha]

Hi,

Please, I want to know is this true?

In laminar regime, to find the distribution of the velocity of a fluid flowing in a porous medium, the fluent solves the following equation of Darcy:


v= [-(k/a)(∂P/∂x)]

v: velocity, k: permeability; a is the dynamic viscosity of the fluid and ∂P/∂x is the pressure gradient in the flow direction.
Thank you very mutch
Aicha

[LuckyTran]

Fluent uses the Darcy-Forchheimer Law, which has both viscous (v) and inertial resistance coefficients (v^2). You can achieve classical Darcy's law by setting the Forchheimer term to zero (by setting inertial resistance to zero).

[aicha]

Thank you LuckyTran

[macfly]

Originally Posted by LuckyTran

Fluent uses the Darcy-Forchheimer Law, which has both viscous (v) and inertial resistance coefficients (v^2). You can achieve classical Darcy's law by setting the Forchheimer term to zero (by setting inertial resistance to zero).

It's confusing because when we read section 6.2.3.2 in User's Guide 15.0, it sounds like Fluent still uses the momentum equation added with source terms:

Porous media are modeled by the addition of a momentum source term to the standard fluid flow equations. The source term is composed of two parts: a viscous loss term (Darcy, the first term on the right-hand side of Equation 6.1 (p. 225), and an inertial loss term (the second term on the right-hand side of Equation 6.1 (p. 225))

Then in section 6.2.3.2.1. it sounds like the momentum equation is not used, Darcy's Law is used instead (if inertial resistance is set to 0):

Ignoring convective acceleration and diffusion, the porous media model then reduces to Darcy’s Law:

Just to make sure, when a fluid zone is defined as porous and inertial resistance factor is set to 0, Fluent only uses the above Darcy's Law? Darcy's law becomes the momentum equation?

[LuckyTran]

Originally Posted by macfly

It's confusing because when we read section 6.2.3.2 in User's Guide 15.0, it sounds like Fluent still uses the momentum equation added with source terms:

Then in section 6.2.3.2.1. it sounds like the momentum equation is not used, Darcy's Law is used instead (if inertial resistance is set to 0):

Just to make sure, when a fluid zone is defined as porous and inertial resistance factor is set to 0, Fluent only uses the above Darcy's Law? Darcy's law becomes the momentum equation?

The momentum equation is always used. The momentum equation is modified with an additional source/sink term to model the pressure drop across the porous media. A question is then how to model the pressure drop?

Fluent uses the Darcy-Forchheimer Law to model the pressure drop. If inertial resistance is set to 0, you get classical Darcy law for the momentum sink term.

Think of the momentum source/sink as you would any other model. Example: The generalized momentum equation can choose to represent the fluid shear stresses and model them as a Newtonian fluid.

In other words, momentum equation still exists whether or not you choose to model specific effects using Newtonian/Non-newtonian or Darcy/other models.

[macfly]

We often see momentum transfer reduced to Darcy's law in litterature, e.g., when Brinkman and Forchheimer corrections are ignored in eq. (6.153) of chapter 6 of this book (Conservation Equations): http://link.springer.com/book/10.1007/1-4020-3962-X

Whitaker (author of the chapter mentioned above) writes that in general, the transient and convective terms are negligible.

Same in Comsol's theory guide, many papers, etc. where continuity equation + Darcy's law + ideal gas law make a defined model. I understand that a model can be as complicated as the level of details wanted, but Fluent chose a complex porous model instead of the general one?

[LuckyTran]

Originally Posted by macfly

Whitaker (author of the chapter mentioned above) writes that in general, the transient and convective terms are negligible.

If one also neglects the transient + convective terms (in addition to the Forchheimer) then the momentum equation reduces to a simple evaluation whatever is left (the diffusion & sources/sinks). Note that if one neglects momentum transport due to convection + transient effects, the momentum equation itself becomes trivial. One can then consider then the Darcy's law to be the entire momentum equation, because all other terms (transient, convective) terms are being neglected.

Originally Posted by macfly

I understand that a model can be as complicated as the level of details wanted, but Fluent chose a complex porous model instead of the general one?

Fluent chooses a well-complicated model for modelling the porous media. However, the general equation, the momentum equation is still present. It is very important to distinguish between the momentum transport equation and modelling the influence of the porous media onto the fluid flow problem through a momentum sink via Darcy's Law. Only the sink term in the momentum equation composes Darcy's Law (or any of the more complicated variations).

One can always make reasonable arguments that specific terms are negligible (transient terms, convective terms, etc) and show that the momentum equation reduces to Darcy's Law. But Fluent is not neglecting the momentum equation and using Darcy's law in place of the momentum equation.