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Simulation of a finescreen as porous media

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Old   August 10, 2017, 10:15
Default Simulation of a finescreen as porous media
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Stefan Schmidt
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I am using OpenFOAM (Version 5.0 since release) for two months now and it seems that I am stuck with a problem I can't solve on my own.

I'm doing a 2D-Simulation of the upstream area of a hydroelectric power plant. My simulation will be used for the design planning of a fish ladder for wich I need to determine the minimum distance between the intake structure of the bypass and the fish ladder.
In front of the bypass intake will sit a horizontal fine screen. Hence the model is in 2D there is no horizontal resolution (z-Direction) and I can't add it to my geometry.

I am trying to capture the pressure drop (due to the finescreen) with a porous zone.
The pressure drop and the velocity at the screen is known but I really don't know how to define a and b for DarcyForchheimer properly.

When I switch from Darcy-Forchheimer to power law I need Values for C0 and C1 wich I can't determine either.

The attachments are showing my geometry and the porous zone (red marker) that I defined.

case setup:
  • steady state - simpleFoam / porousSimpeFoam
  • 1 Inlet / 3 Outlets
  • no turbulence model yet
  • Inlet (on the right)
    • v - fixed value
    • p - zero Gradient
  • Main outlet (on the left)
    • v - zero Gradient
    • p - fixed value - uniform 0
  • fish ladder (first one in flow direction)
    • v - fixed value - nonuniform
    • p - zero Gradient
  • bypass (second one in flow direction)
    • v - fixed value - nonuniform
    • p - zero Gradient
Without the porous zone the model runs smoothly, converges and the solution is close to my expected pressure/velocity values but I need to set up the case with the finescreen to get a solution that fits my needs.
When I set up my model with a porous Zone with random values for d and f the simulation runs and converges, too but as you can imagine the solution doesn't make any sense.

Any suggestions how to work around this problem?
Maybe there is an easy fix and I don't even have to set up a porous Zone.

Thanks in Advance
Attached Images
File Type: png geometry.png (8.7 KB, 10 views)
File Type: png porous_zone.png (4.3 KB, 7 views)
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Old   August 11, 2017, 02:13
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Sebastian
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I don't know, if I got you completely but if you only want to determine the parameters for the Darcy-Forchheimer law, you can use a bunch of different formulas depending on the data of your screen.

As mentioned in many threads, the first coefficient d of the Darcy-Forchheimer law is nothing else than the inverse of the permeability of your porous medium. Depending on your kind of medium, you can for example use the Kozeny-Carman equation or if it is really only a screen, there are a bunch of articles dealing with permeability of periodic arrays of cylinders.

For the coefficient f you have to decide, if you really need it. If you have a slow flow, you can often neglected this part of Darcy-Forchheimer. In case not, you can for example have a look at the Ergun equation.
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Old   August 15, 2017, 11:04
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Stefan Schmidt
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Thank you for your reply and your suggestions in the first place.
It is really only a screen (clear span: 1 cm; bar width: 0,27 cm) but the velocity at the screen is in avg. 0.6 m/s and nonuniform (0.4 m/s up to 0.85 m/s). As a result Re > 10 and DarcyLaw (neglect f) on its own can't be applied in my case.

Thank you for the hint to look at the Kozeny-Carman equation. After a while I found a version of the Kozeny-Carman equation that I could use with the known characteristics of the screen (http://www.uwm.edu.pl/wnt/technicalsc/tech_17_3/b04.pdf). With the known pressure drop and alpha I could calculate beta and thereby d and f.

Everything works out fine know.

EDIT:
For the record: A and B are not equal d and f.

d = A
f = 2 * B

Last edited by Schmitzi; August 17, 2017 at 06:29. Reason: Adding Information
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Old   August 16, 2017, 01:43
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I am happy that my suggestions helped. If have to say thank you for the link to this interesting article. It must have been under my radar.
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finescreen, openfoam, porous medium, pressure drop, two dimensional

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