CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Software User Forums > OpenFOAM > OpenFOAM Running, Solving & CFD

Porous Medium: Obtaining D/F coefficients from Pressure-Drop Experiment

Register Blogs Community New Posts Updated Threads Search

Like Tree6Likes
  • 2 Post By sdfij6354
  • 2 Post By sdfij6354
  • 2 Post By SebT

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   August 3, 2017, 13:15
Default Porous Medium: Obtaining D/F coefficients from Pressure-Drop Experiment
  #1
New Member
 
Alwin
Join Date: Jun 2017
Posts: 11
Rep Power: 9
sdfij6354 is on a distinguished road
Hello,

I want to implement the pressure drop along a netting into my OpenFOAM case though the Porous Media and Darcy-Forchheimer-Equation.

OpenFOAM requires the coefficients D and F which I calculated according to
Darcy-Forchheimer law for specifying Porous Zones


Code:
F = 2 * a / (deltaP * dx)
D = b / (viscosity * dx)
With deltaP being the pressure drop and dx the length if the Porous Medium in x-Direction (0.5m). "viscosity" is the dynamic viscosity of air (1.789*10^-5 in my case, 20°C and sea level).


First, I measured the pressure drop along the real screen in a wind-tunnel experiment.
I obtained the variables a and b by fitting a second degree polynomial using R-Studio and the curve dp=f(v):

Code:
x <- c(7.4,4.3,3.1,0.0)  // inlet velocity
y <- c(67.4,33.2,21.4,0.0) // measured pressure drop
lm(formula = y ~ x + I(x^2))

Results were:
Coefficients:
(Intercept)            x       I(x^2)  
   -0.06875      5.57380      0.48012
Hence,
a = 0.48012
b = 5.57380


Then I calculated F and D

Code:
> velocity <- 4.2
> deltaP <- a*velocity^2+b*velocity
> print(deltaP)
[1] 31.87928

> dx <- 0.5
> viscosity <- 0.00001789
> F <- 2 * a / (deltaP * dx)
> D <- b / (viscosity * dx)
> print(F)
[1] 0.06024227
> print(D)
[1] 623119.1
and inserted it into fvOptions in /case/constant.


Code:
    explicitPorositySourceCoeffs
    {
        selectionMode   cellZone;
        cellZone        porousBlockage;

        type            DarcyForchheimer;

        DarcyForchheimerCoeffs
        {
            d   (623119.1 -1000 -1000);
            f   (0.06024227 650 650);

            coordinateSystem
            {
                type    cartesian;
                origin  (0 0 0);
                coordinateRotation
                {
                    type    axesRotation;
                    e1  (1 0 0);
                    e2  (0 1 0);
                }
            }
        }
    }
}
I've defined the cells for the Porous Medium using the command "topoSet" and defining the cellZone boundaries in the file "topoSetDict" in /case/system.



However, when running a test run with a simpleFoam case and measuring the pressure drop along the x-Axis in ParaView, I obtain just a deltaP of ~16, compared to the ~32 I should have according to the polynomial equation:

Code:
> a <- 0.48012
> b <- 5.57380
> v <- 4.2
> deltaP=a*v^2+b*v
> print(deltaP)
[1] 31.87928
I've also attached my complete case. Did I do anything wrong in calculating the D/F coefficients? Or is my case set up in the wrong way to verify the measured/simulated pressure drop across the screen? I appreciate any help

I've also read papers where the Porous-Medium / Darcy-Forchheimer-Equation was implemented using K (permeability) and Y (nonlinear momentum loss coefficient), but I don't know how to convert these values into D/F required by openFoam. Is there a way do to it and where could I find further information on how to do it?
Attached Files
File Type: zip porous_media_testcase.zip (185.1 KB, 66 views)
mayursathe and Takue like this.
sdfij6354 is offline   Reply With Quote

Old   August 3, 2017, 14:22
Default
  #2
Senior Member
 
alberto
Join Date: Apr 2016
Location: Mexico
Posts: 119
Rep Power: 10
dewey is on a distinguished road
Take a look to this file.

https://es.scribd.com/document/23868...orousInter-v11


The coefficient D specifies the viscous resistance , it is calculated as 1/K where k is the permeability, and Fij specifies inertial resistance, i dont know if you need the coeeficient F.
dewey is offline   Reply With Quote

Old   August 3, 2017, 15:10
Default
  #3
New Member
 
Alwin
Join Date: Jun 2017
Posts: 11
Rep Power: 9
sdfij6354 is on a distinguished road
Thank you for you answer, I will take a look at the document (need to sign up first though).
However, I'm wondering about D = 1/K. Doesn't depend D in some way also on the thickness of the porous media? Or is this irrelevant for OpenFOAM?

Since my K = (3.44*(10^-9)*(epsilon^1.6) with epsilon = screen porosity = 0.4 and hence K = 7.94062E-10, my D would be = 1259347462.
So I set
D = (1259347462 -1000 -1000) since the resistance is only in X-Direction and
F = (0 0 0).
This leads to a pressure drop of ~55 along the screen, which is still a bit off.
manuc and ombretta like this.
sdfij6354 is offline   Reply With Quote

Old   August 3, 2017, 15:31
Default
  #4
Senior Member
 
alberto
Join Date: Apr 2016
Location: Mexico
Posts: 119
Rep Power: 10
dewey is on a distinguished road
Take a look to this files, I hope this could help you.

It is irrelevant for OF. K is a resistance for the fluid.

I dont know if that is the way to do the resistance only in the X-direction, You could put the same value in the three directions, setting that it is a isotropic medium. Are you trying to do a 2D simulation? because if you want to do that, you only have to set the faces as empty.

I am working with porous media too, but I am not an expert, if I can help you in something, let me know.


https://www.dropbox.com/s/djktzs0umq...efano.pdf?dl=0

https://www.dropbox.com/s/ivb3igaj7o...r_v11.pdf?dl=0

https://www.dropbox.com/s/n127zo90so...eport.pdf?dl=0

https://www.dropbox.com/s/sxjj5hvu66j9gmd/leer.pdf?dl=0
dewey is offline   Reply With Quote

Old   August 6, 2017, 11:38
Default
  #5
New Member
 
Alwin
Join Date: Jun 2017
Posts: 11
Rep Power: 9
sdfij6354 is on a distinguished road
I have a question regarding to this paper:

https://www.dropbox.com/s/ivb3igaj7o...r_v11.pdf?dl=0

μ(kg·m−1·s−1) is defined as the "dynamic viscosity" - of air?
In my case, air is flowing through a tube with a netting in the middle. I want to implement this netting as my porous media.

I'm wondering, because I don't get feasible results using the equation for deltaPressure in the reference:

deltaPressure = (μ/k)*velocity

I have my permeability k calculated as 7.94062E-10. When assuming a dynamic viscosity of air at (μ) 20°C of 15.11*10^-6 m-2/s, I get unrealistic results for my pressure drop value. E.g. deltaPressure = 16897 with a velocity of 0.75 m/s, even though it should be around 4.5 according to my measurements.
sdfij6354 is offline   Reply With Quote

Old   August 7, 2017, 10:15
Default
  #6
Senior Member
 
alberto
Join Date: Apr 2016
Location: Mexico
Posts: 119
Rep Power: 10
dewey is on a distinguished road
Yes, it is the dynamic viscosity

You are trying to run your simulation with porousSimpleFoam right?

Do you know that this incompresible solver works with kinematic pressure ?

When I started, first of all I did the example of the page 73

https://www.dropbox.com/s/2ztsdtebjv...oleum.pdf?dl=0

and after i did an experiment for validate.

You should do that excercise and simulate to compare.
dewey is offline   Reply With Quote

Old   August 7, 2017, 11:25
Default
  #7
New Member
 
Sebastian
Join Date: Feb 2017
Posts: 22
Rep Power: 9
sepp.zell is on a distinguished road
Maybe you can also have a look at my comparison between Darcy's law and the OpenFOAM simulation.
porousSimpleFoam - comparison to Darcy's law

There it is shown that OpenFOAM might not work for flow through porous media. Maybe this is the same in your test case. I discussed this issue with the developers. In the moment there is no fix for it. One suggestion was to try different schemes.

You should also have a look at a plot for the velocity over the x-axis. There are some spurious oscillations over your porous netting. This seems to be the reason that the pressure drop is not computed correctly (see also here: https://bugs.openfoam.org/view.php?id=134).
sepp.zell is offline   Reply With Quote

Old   September 13, 2017, 11:14
Default
  #8
New Member
 
Sebastian Tück
Join Date: Aug 2016
Posts: 3
Rep Power: 10
SebT is on a distinguished road
Dear Alwin,

i looked a little bit into your problem and think i can solve some Problems. First of all you are calculating a regression curve with y-intercept. Since there is no pressure drop at 0 speed there should be none. Hence:

Code:
dp = a * v² + b * v
The Darcy-Forchheimer equation can be written as:

Code:
dp/dx = mu * d * v + 1/2 * f * rho * v²
with dx being the thickness of the porous medium.

Coefficient comparisson leads to following expressions for d and f:

Code:
f = (2 * a) / (rho * dx)
d = b / (mu * dx)
I attached a libre file to automatically calculate the coefficients from meassurments.I also set up a test case to check the values. When calculating the pressure drop with your settings I get a relative diviation regarding your measurments of 5.04 % for 7.4 m/s and 3.01 % for 4.3 m/s, which i consider completely ok. Maybe you forgot to multiply the pressure by the fluid density? Incompressible solvers in OpenFOAM use kinematic pressure pk which is defined as pk=p/rho. So to obtain static pressure you need to multiply with the fluid reference density.

I hope this helps with your Problem. If you need the test case let me know and I'll send it to you.


Attached Files
File Type: xls DarcyForchheimerCoefficients.xls (12.5 KB, 191 views)
manuc and keitaro7_14 like this.
SebT is offline   Reply With Quote

Old   February 11, 2018, 02:28
Default
  #9
Member
 
Ramana
Join Date: Jul 2017
Location: India
Posts: 58
Rep Power: 9
svramana is on a distinguished road
Quote:
Originally Posted by dewey View Post
Take a look to this files, I hope this could help you.

It is irrelevant for OF. K is a resistance for the fluid.

I dont know if that is the way to do the resistance only in the X-direction, You could put the same value in the three directions, setting that it is a isotropic medium. Are you trying to do a 2D simulation? because if you want to do that, you only have to set the faces as empty.

I am working with porous media too, but I am not an expert, if I can help you in something, let me know.


https://www.dropbox.com/s/djktzs0umq...efano.pdf?dl=0

https://www.dropbox.com/s/ivb3igaj7o...r_v11.pdf?dl=0

https://www.dropbox.com/s/n127zo90so...eport.pdf?dl=0

https://www.dropbox.com/s/sxjj5hvu66j9gmd/leer.pdf?dl=0
I am working on porous media on OpenFoam, i have a question about porosity and calculation of D and F coefficients. Can i have access to the above files ?

Reagrds,
S.V.Ramana
svramana is offline   Reply With Quote

Old   March 10, 2018, 10:30
Default porous media
  #10
New Member
 
DEEPTI
Join Date: Sep 2017
Posts: 2
Rep Power: 0
deeptiof is on a distinguished road
there are two coefficient D and F used in darcy forchhiemer equation for porous media modelling.
I have one doubt that why F value is set to zero for most of the cases??
deeptiof is offline   Reply With Quote

Old   July 4, 2019, 05:40
Default
  #11
New Member
 
ombretta bistoni
Join Date: Dec 2018
Posts: 2
Rep Power: 0
ombretta is on a distinguished road
How did you find this relationship between porosity and permeability?
Thank you.
ombretta is offline   Reply With Quote

Old   November 22, 2023, 18:33
Default
  #12
New Member
 
West barkley
Join Date: Nov 2023
Posts: 2
Rep Power: 0
west barkley is on a distinguished road
Quote:
Originally Posted by SebT View Post
Dear Alwin,

i looked a little bit into your problem and think i can solve some Problems. First of all you are calculating a regression curve with y-intercept. Since there is no pressure drop at 0 speed there should be none. Hence:

Code:
dp = a * v² + b * v
The Darcy-Forchheimer equation can be written as:

Code:
dp/dx = mu * d * v + 1/2 * f * rho * v²
with dx being the thickness of the porous medium.

Coefficient comparisson leads to following expressions for d and f:

Code:
f = (2 * a) / (rho * dx)
d = b / (mu * dx)
I attached a libre file to automatically calculate the coefficients from meassurments.I also set up a test case to check the values. When calculating the pressure drop with your settings I get a relative diviation regarding your measurments of 5.04 % for 7.4 m/s and 3.01 % for 4.3 m/s, which i consider completely ok. Maybe you forgot to multiply the pressure by the fluid density? Incompressible solvers in OpenFOAM use kinematic pressure pk which is defined as pk=p/rho. So to obtain static pressure you need to multiply with the fluid reference density.

I hope this helps with your Problem. If you need the test case let me know and I'll send it to you.


Hi, could you please help me with this question. where are the dp values? where can i find them to feed into the table?
west barkley is offline   Reply With Quote

Reply


Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Polydispersed phase pressure drop with drop size Laksh CFX 1 June 8, 2017 19:56
pressure porous medium acchavesg FLUENT 1 October 16, 2016 04:18
How to model pressure drop without modeling porous media Sanyo CFX 9 May 27, 2016 11:50
Calculate pressure drop coefficients in x,y,z, direction georgcfd FLUENT 0 April 16, 2010 08:09
Hydrostatic pressure in 2-phase flow modeling (long) DS & HB Main CFD Forum 0 January 8, 2000 16:00


All times are GMT -4. The time now is 13:07.