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Porous Medium: Obtaining D/F coefficients from Pressure-Drop Experiment |
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August 3, 2017, 13:15 |
Porous Medium: Obtaining D/F coefficients from Pressure-Drop Experiment
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#1 |
New Member
Alwin
Join Date: Jun 2017
Posts: 11
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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) 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 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 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); } } } } } 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 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? |
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August 3, 2017, 14:22 |
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#2 |
Senior Member
alberto
Join Date: Apr 2016
Location: Mexico
Posts: 119
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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. |
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August 3, 2017, 15:10 |
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#3 |
New Member
Alwin
Join Date: Jun 2017
Posts: 11
Rep Power: 9 |
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. |
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August 3, 2017, 15:31 |
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#4 |
Senior Member
alberto
Join Date: Apr 2016
Location: Mexico
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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 |
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August 6, 2017, 11:38 |
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#5 |
New Member
Alwin
Join Date: Jun 2017
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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. |
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August 7, 2017, 10:15 |
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#6 |
Senior Member
alberto
Join Date: Apr 2016
Location: Mexico
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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. |
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August 7, 2017, 11:25 |
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#7 |
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Sebastian
Join Date: Feb 2017
Posts: 22
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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). |
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September 13, 2017, 11:14 |
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#8 |
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Sebastian Tück
Join Date: Aug 2016
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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 Code:
dp/dx = mu * d * v + 1/2 * f * rho * v² Coefficient comparisson leads to following expressions for d and f: Code:
f = (2 * a) / (rho * dx) d = b / (mu * dx) I hope this helps with your Problem. If you need the test case let me know and I'll send it to you. |
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February 11, 2018, 02:28 |
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#9 | |
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Ramana
Join Date: Jul 2017
Location: India
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Quote:
Reagrds, S.V.Ramana |
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March 10, 2018, 10:30 |
porous media
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#10 |
New Member
DEEPTI
Join Date: Sep 2017
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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?? |
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July 4, 2019, 05:40 |
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#11 |
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ombretta bistoni
Join Date: Dec 2018
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How did you find this relationship between porosity and permeability?
Thank you. |
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November 22, 2023, 18:33 |
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#12 | |
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West barkley
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Quote:
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