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 fpingqian January 7, 2008 08:38

Viscous resistance coefficients in porous medium

Fluent manual tell us that, for laminar flow through a fibrous mat, we can calculate the viscous resistance coefficients using Blake-Kozeny equation, and ignore the inertial resistance. In my question, the dimension of the geometry is micro scale, so the viscous resistance coefficient is up to e-10. In this condition, I can't obtain the good result compared with the experimental one. However, when I change the the viscous resistance coefficient to a higher value, for example, e10, the results can be well agreement with the experimental one. Hope someone can tell me what leads to this, and how to calculate the viscous resistance coefficient in porous medium. Thanks in advance.

 srjp August 12, 2009 06:19

Viscous and Inertial Resistances

The viscous and inertial resistances to flow in a porous medium can be calculated from the Ergun equation, which gives the total pressure drop through a porous medium.
Check any book on fluid mechanics for the Ergun equation
Total pressure drop = Viscous loss + inertial loss

dp/dl = [150*mu*(1-e)^2/phi^2*D^2*e^3]*v + [1.75*rho*(1-e)/phi*D*e^3]*v^2

The first term is the viscous loss (proportional to velocity) and the second term is the inertial loss (proportional to velocity squared).

Compare this to the Fluent's expression for momentum sink:

dp/dl = Rv*mu*v + (Ri/2)*rho*v^2

This gives the values for Rv and Ri,

Rv = [150*(1-e)^2/phi^2*D^2*e^3]

Ri = [2*1.75*(1-e)/phi*D*e^3]

Nomenclature:
Rv: Viscous resistance
Ri: Inertial resistance
mu: Viscosity
rho: Density
e: Porosity of the medium
phi: Sphericity of the particles making the medium (can assume 0.75)
D: Diameter of particles making the medium
v: Average velocity

 coglione August 12, 2009 07:12

Hello,

always keep in mind, that Fluent requires the input of 1/a, where a is the permeability you get from your Blake-Kozeny equation. In other words, you have to insert the inverse of a for each direction in your porous zone. In your case a=1e-6 --> 1/a = 1e+6 what is exactly the correct value as you found out at least.

cheers

 srjp August 12, 2009 07:21

Hi,
You are right.
Resistance is the inverse of permeability. It is normally in the range of 1e+6 to 1e+10 m2.

 mehr bano October 26, 2009 08:43

Dear SRJP

could you please explain from where I can find diffrent values for phi ,Sphericity ? while i compared with some eurgen equation but i didn`t find this term , I am modelling prouse media in kiln and i need to clculate it, thank you in advance ,

maryam

 srjp October 26, 2009 08:57

Hi,
The Ergun equation assumes that the bed is filled with uniform sized and shaped particles. The sphericity parameter is used as a conversion factor for non-spherical particles (comparing the surface-volume ratio of those particles to an equivalent spherical particle).

Of course, for fully spherical particle, the sphericity = 1.

Sphericity = (6/Dp)/(Sp/Vp)

Dp = Diameter of the particle
Sp = Surface area of the particle
Vp = Volume of the particle

For 'not so crazy' shapes, like sand particles, you can use sphericity around 0.8 - 0.9.

Complete list of sphericity values can be found in "Perry's Chemical Engineers Handbook", or "Unit Operations of Chemical Engineering by McCage, Smith and Harriot" or similar books.

 arashoil June 1, 2011 23:50

ceramic membrane

Hi,

i am working in modeling of ceramic membrane with 19 channel.i want to know what mesh i must use for best result.then i must export that geometry to fluent and solve it by porous zone and multiphase flow.

thank you so much

 srjp June 2, 2011 05:41

It should be noted that the porous domain calculation in Fluent is an approximate one: It just adds a momentum sink in 3 directions due to the inertial and viscous resistance.
The mesh type will depend on the accuracy, convergence and speed of the simulation. If not difficult, better to go with high quality hex meshes.

 zhhjll June 14, 2011 15:08

hi.
I'm trying to model a micro filtration membrane(MF), are these parameters useful for a filter or a membrane?! and, in porous media approuch via fluent, we should set this two parameters for X,Y direction!!! can we set Ri and Rv from this equations for X,Y direction??
best regards

zohreh

 zhhjll June 21, 2011 03:09

hi.
I'm trying to model a micro filtration membrane(MF), are these parameters useful for a filter or a membrane?! and, in porous media approuch via fluent, we should set this two parameters for X,Y direction!!! can we set Ri and Rv from this equations for X,Y direction??
best regards

zohreh

 srjp June 21, 2011 05:27

Yes,
You can still use the porous zone model for the membrane, since the membrane is porous anyway.
If the membrane is homegeneous and symmetric, you can use the same resistance values in all directions (x,y and z). If not, you may have to calculate the porosity and permeabilities separately in the three directions. This would be the case on the regular asymmetric ultrafiltration and reverse osmosis membranes.

 zhhjll June 21, 2011 17:59

dear srjp
thanks a lot for your answer, I want to model a micro filter, This filter (membrane) is rectangular (10×5 cm) with the thickness 12e-5. so,I calculate this parameters from Ergun equation which D=1e-6, because of the Micro filter type. is this assumption true??
i think this is very thin filter so there in not flow through in the membrane, in this situation is inertial coefficieant higher in Y direction? or not?when i set y-direction inertial coefficient higher than x-direction got better answer! is this resonable?

I am looking forward to hearing from you.
Sincerely yours.

 arashoil November 26, 2011 18:10

asphaltene precipitation

hi,

can i modelling asphaltene precipitation that exist in crude oil by uusing ceramic filter monolit by defult formolation in fluent?

i want to modelling separation of asphaltene from crude oil by 19-channel ceramic filter,but i think it is not define in FLUENT that precipitate asphaltene on surface of ceramic channel base on diffrences between pore size.

i must write UDF for this porpuse or not?

most of oil flow must pass through the membrane wall and most of asphaltene must form a gel-layer and precipitation on inner surface od channel.

thank you so much

 arashoil November 26, 2011 18:46

asphalteene

Quote:
 Originally Posted by srjp (Post 312868) Yes, You can still use the porous zone model for the membrane, since the membrane is porous anyway. If the membrane is homegeneous and symmetric, you can use the same resistance values in all directions (x,y and z). If not, you may have to calculate the porosity and permeabilities separately in the three directions. This would be the case on the regular asymmetric ultrafiltration and reverse osmosis membranes.
hi,

can i modelling asphaltene precipitation that exist in crude oil by uusing ceramic filter monolit by defult formolation in fluent?

i want to modelling separation of asphaltene from crude oil by 19-channel ceramic filter,but i think it is not define in FLUENT that precipitate asphaltene on surface of ceramic channel base on diffrences between pore size.

i must write UDF for this porpuse or not?

most of oil flow must pass through the membrane wall and most of asphaltene must form a gel-layer and precipitation on inner surface od channel.

thank you so much

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 reynolds039 August 9, 2012 11:54

hello, thank's for this explanation of the viscous resistance equation,
but i have a question : we know that: viscous resistance=1/absolute permeability, but in the multiphase flow: viscous resistance= 1/effective permeabiliy , or viscous resistance=1/absolute permeability, i need an answer please.

 chime April 25, 2013 11:03

Simulating Flow over Porous Medium

Hi, I have the data from the flow over a bundle of tubes (in the context of a bundle of tubes at the bed of the channel). I was thinking of using the Ergun equation as in the ANSYS manual to calculate the viscous and inertial resistance, where the the tube diameter = diameter of particle, to create a macroscopic simulation of the flow in FLUENT, however, I haven't been able to obtain a similar velocity profile.

 srjp April 26, 2013 08:39

Is the flow across the pipes or along the pipes? This will change the diameter to be used. Also, ergun equation is only for spherical particles, for cylinders, you may have to use the appropriate sphericity.

 Tanjina July 18, 2013 11:32

Hydraulic conductivity of porous zone

Hi,

I am trying to model a 2D porous zone filled with sand lied above a perforated pipe and water will pass through it. I have some queries, hope someone can help me out.

1) Porous zone should have a definite hydraulic conductivity(K). But in fluent, I didn't find any input button for this. Does inertial and viscous resistance represent the inverse of K in fluent? If yes, should I calculate the resistance value by the formula provided above for X and Y direction both or only for y direction since flow is in Y direction?

2)If not, then how can I assign K value?

 A CFD free user July 28, 2013 13:21

@Tanjina
Viscous resistance is actually the inverse of permeability value and it's regarding to resistance exerted to flow by porous media. As far as I know, there's nothing about hydraulic conductivity in modeling porous zone, but, if you mean the heat conductivity of the porous material, it should be defined by a UDF,due to anisotropic behavior of porous solid.

 Tanjina July 29, 2013 11:33

two-phase porous zone

Quote:
 Originally Posted by A CFD free user (Post 442444) @Tanjina Viscous resistance is actually the inverse of permeability value and it's regarding to resistance exerted to flow by porous media. As far as I know, there's nothing about hydraulic conductivity in modeling porous zone, but, if you mean the heat conductivity of the porous material, it should be defined by a UDF,due to anisotropic behavior of porous solid.

Thank you very much for your reply. Yup, I also come to know that in fluent, we use permeability . And permeability is related to Hydraulic conductivity.

Do you have any experience about modeling of two phase flow in porous zone? Please let me know.

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