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difference between Navier–Stokes and Darcy's law
Posted Mar 18, 2011, 12:51 p.m. EDT Computational Fluid Dynamics (CFD), Porous Media Flow 3 Replies
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Hi,
In the poroelastic theory, the fluid phase is governed by Darcy's law.
The value of permeability in Darcy's law describes how fast the fluid can diffuse. If use an extreme high value of permeability, can this be used to describe the flow for a purely fluid which is usually modeled with Navier-Stockes equation?
I want to simulate a system with poroelasticity interact with purely fluid.
And planning to use Darcy's law with very high permeability for the fluid phase, in this case, it will simplify the problem when comes to the interaction with the poroelastic media (since they share the same fluid equation).
Then the question is, how good is this simplification? What is the difference by using Navier-stokes equation and use a very high permeability value for Darcy's law in this case?
Thanks a lot.
XLi
In the poroelastic theory, the fluid phase is governed by Darcy's law.
The value of permeability in Darcy's law describes how fast the fluid can diffuse. If use an extreme high value of permeability, can this be used to describe the flow for a purely fluid which is usually modeled with Navier-Stockes equation?
I want to simulate a system with poroelasticity interact with purely fluid.
And planning to use Darcy's law with very high permeability for the fluid phase, in this case, it will simplify the problem when comes to the interaction with the poroelastic media (since they share the same fluid equation).
Then the question is, how good is this simplification? What is the difference by using Navier-stokes equation and use a very high permeability value for Darcy's law in this case?
Thanks a lot.
XLi
3 Replies Last Post May 20, 2011, 6:23 p.m. EDT
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Posted:
1 decade ago
Hi,
Sorry to say, but this is a very bad idea.
in darcy law, the velocity field (darcy's velocity) is somehow proportional to the gradient of pressure, so you solve for "just" one dependent variable: the pressure.
In Navier-stokes, you have two equations, one for the mass conservation, and one momentum equation, so you solve for 4 dependent variables in 3D (2D the velocity field contains only 2 dependent variables).
also, navier stokes are non-linear eq. due to the convective terms, you need stabilization...
I have no idea how your poro-elastic material is built, but for sure Darcy will never recover NAvier-Stokes behavior.
... you might want to try with brikman....
Sorry to say, but this is a very bad idea.
in darcy law, the velocity field (darcy's velocity) is somehow proportional to the gradient of pressure, so you solve for "just" one dependent variable: the pressure.
In Navier-stokes, you have two equations, one for the mass conservation, and one momentum equation, so you solve for 4 dependent variables in 3D (2D the velocity field contains only 2 dependent variables).
also, navier stokes are non-linear eq. due to the convective terms, you need stabilization...
I have no idea how your poro-elastic material is built, but for sure Darcy will never recover NAvier-Stokes behavior.
... you might want to try with brikman....
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Posted:
1 decade ago
Hi John,
Thanks a lot for your response. I am aware that it might be a bad idea to use Darcy's law in for purely fluid, but I don't know how bad it could be. Thanks a lot for your explanation.
But if I am only concerning about the pressure (pressure is not important factor for my problem), do you think they will give similar result given that permeability for Darcy's law is high enough?
Thanks again.
XLi
Thanks a lot for your response. I am aware that it might be a bad idea to use Darcy's law in for purely fluid, but I don't know how bad it could be. Thanks a lot for your explanation.
But if I am only concerning about the pressure (pressure is not important factor for my problem), do you think they will give similar result given that permeability for Darcy's law is high enough?
Thanks again.
XLi
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Posted:
1 decade ago
i am working on studying deformation and motion in porous media ... i tried using solid mechanics, but it considers the porous structure as impenetrable solid. And if i use proroelasticity, it uses Darcy's law, but the flow inside the porous structure is governed by Brinkman eqaution. Is there a way around this problem?
- JD
- JD