Porous media - Permeability vs Darcy/Forchhiemer coefficients implementation?
In HW CFD/AcuSolve, I'm looking for clarification on how are the porous media permeability coefficients (K1, K2, K3) brought into the pressure drop prediction, in contrast to the Darcy and Forchheimer coefficients?
If the Darcy (D) value is related to velocity and the Forchheimer (F) value is related to velocity^2, are K1,2,3 multiplied to both D and F? D only? F only? Linearly, inversely? The math isn't clear in the user guide.
I'm speaking in reference to: https://en.wikipedia.org/wiki/Darcy's_law#Quadratic_law
So in Wikipedia, D = 1/k and F = 1/k_1
Thanks in advance.
Best Answer
-
The permeability coefficients are used to distinguish the directionality of the porous media or filter material. In the porosity_model command, you can specify the coordinate directions for each of the three permeability coefficients with respect to the global coordinate system. Generally, the permeability directions correspond to the direction of flow through the porous media volume and the two directions which are orthogonal. For example, if the flow is through a duct along the x direction then the permeability directions will be the x, y, and z axis.
Once the three directions are determined, you would define the permeability coefficients such that the direction of flow through the porous media volume is preserved while transverse cross flow would be limited. Using the above example, the permeability in the x direction k_1 = 1.0 while the permeability coefficients in the y and z direction are very small (ie k_2 = k_3 = 1e-3). If we were to compute the Darcy and Forchheimer coefficients using these definitions, we would see that the resisting force in the x direction follows the pressure drop data but the resisting force in the y and z direction is nine orders of magnitude higher. This essentially blocks the flow in the transverse directions.
1
Answers
-
The permeability coefficients are used to distinguish the directionality of the porous media or filter material. In the porosity_model command, you can specify the coordinate directions for each of the three permeability coefficients with respect to the global coordinate system. Generally, the permeability directions correspond to the direction of flow through the porous media volume and the two directions which are orthogonal. For example, if the flow is through a duct along the x direction then the permeability directions will be the x, y, and z axis.
Once the three directions are determined, you would define the permeability coefficients such that the direction of flow through the porous media volume is preserved while transverse cross flow would be limited. Using the above example, the permeability in the x direction k_1 = 1.0 while the permeability coefficients in the y and z direction are very small (ie k_2 = k_3 = 1e-3). If we were to compute the Darcy and Forchheimer coefficients using these definitions, we would see that the resisting force in the x direction follows the pressure drop data but the resisting force in the y and z direction is nine orders of magnitude higher. This essentially blocks the flow in the transverse directions.
1 -
Stuart Walker_22458 said:
The permeability coefficients are used to distinguish the directionality of the porous media or filter material. In the porosity_model command, you can specify the coordinate directions for each of the three permeability coefficients with respect to the global coordinate system. Generally, the permeability directions correspond to the direction of flow through the porous media volume and the two directions which are orthogonal. For example, if the flow is through a duct along the x direction then the permeability directions will be the x, y, and z axis.
Once the three directions are determined, you would define the permeability coefficients such that the direction of flow through the porous media volume is preserved while transverse cross flow would be limited. Using the above example, the permeability in the x direction k_1 = 1.0 while the permeability coefficients in the y and z direction are very small (ie k_2 = k_3 = 1e-3). If we were to compute the Darcy and Forchheimer coefficients using these definitions, we would see that the resisting force in the x direction follows the pressure drop data but the resisting force in the y and z direction is nine orders of magnitude higher. This essentially blocks the flow in the transverse directions.
Stuart, thank you for the explanation. All clear now.
Did I miss this in the documentation somewhere?
0