# permeability in porous media

 Register Blogs Members List Search Today's Posts Mark Forums Read

 January 23, 2012, 13:01 permeability in porous media #1 Member   albert Join Date: Jan 2012 Posts: 31 Rep Power: 6 Hi all, i´m trying to model a thin porous diffusor, about 1cm thick. I created a porous domain. The only problem is that i don´t know how some some coefficients are calculated in cfx. i´m talking about the permeability coefficient and the resistance loss coefficient. how are they calculated, and what is exactly their meaning? How do they affect de air oulet? Could someone help please? Thanks

 January 23, 2012, 15:51 #3 Member   albert Join Date: Jan 2012 Posts: 31 Rep Power: 6 i 've already read the manual, and everything related to these coefficients, but i don't find any information about how they are calculated in cfx!!! can anybody help me?

 January 26, 2012, 19:46 Hiii #4 Member   Arun raj.S Join Date: Jul 2011 Posts: 72 Rep Power: 7 Hi try to find in some journals ..that's the only way..I m solving for a screen ..I have found the formula from" Flow through the screens"..similarly find for your case

 January 26, 2012, 19:48 #5 Member   Arun raj.S Join Date: Jul 2011 Posts: 72 Rep Power: 7 If u r not able to find in journals use the formulaewhich has given in the manual n try to find the permeability

January 30, 2012, 11:29
#6
New Member

Join Date: Aug 2009
Posts: 15
Rep Power: 9
Quote:
 Originally Posted by pato Hi all, i´m trying to model a thin porous diffusor, about 1cm thick. I created a porous domain. The only problem is that i don´t know how some some coefficients are calculated in cfx. i´m talking about the permeability coefficient and the resistance loss coefficient. how are they calculated, and what is exactly their meaning? How do they affect de air oulet? Could someone help please? Thanks
Hi Pato,

I've used porous regions for various apps in the past from packed columns to pond reed, and nearly always re-confuse myself with the inputs. I'll scribble down a few notes I made, they might be of use, but I do advise hunting as many papers specific to your application as possible.

Apologies for the rather basic background, it's just easier for me to explain if I start simple. The aim is to solve the flow through a region which has a pressure drop. If we've no pressure drop profile, we have to utilise expressions which can calculate an estimate. A relatively multi-purpose (I think) approach is to use Ergun's Equation which I believe to be an advancement of Darcy's Law.

Darcy deduced that flow rate be proportional to a bed's x-sectional area and pressure drop, but inversely proportional to the thickness. However, it generated a constant term which was difficult to calculate, as it was a function of permeability, k (measurement of how well a porous material transmits fluid, and only found experimentally).

In order to get around this, you can use Kozeny's equation which calculates a permeability value using the following:

k = (epsilon^3)/((1-epsilon)^2)*K*(S^2)

where:
epsilon = porosity (void fraction)
K = Kozeny constant (2 for tubes, 3.1 for parallel fibres, 5 for random packing) (look up Coulson and Richardson to confirm values)
S = sphrecity (measure of how spherical) = ((pi^1/3)*(6Vp)^2/3)/Ap
Vp = volume of particle
Ap = area of particle

So how does this fit together in CFX?

You have to input a POROSITY, PERMEABILITY COEFFICIENT and RESISTANCE LOSS COEFFICIENT.

The porosity is simply the % VOID of the region.

The Permeability Coeff governs low speed viscous losses. If Erguns equation is to be adopted, this term can be calculated as:

Kperm = [(Dp^2)*(epsilon^3)*(S^2)]/[150*(1-epsilon)^2]

where:
Dp = equivalent spherical diameter of particle
= 6*(Volume of Particle/Surface Area of Particle)

The Resistance Loss term governs inertia effects and can be calculated as:

KLoss = 2[1.75*(1-epsilon)/(S*Dp*(epsilon^3)]

The above terms were found by rearranging the Ergun Equation in to the form of:

deltaP/L = -(viscosity/Kperm)Vs - KLoss(density/2)Vs^2

(as per Help Page // Theory Guide // 1. Basic Solver Capability Theory // 1.7. Sources // 1.7.1. Momentum Sources)

I know I commented above saying Ergun's Equation to be multi-purpose, and I have applied it myself to many scenarios, but I strongly recommend you read up and see if it is suitable for your diffuser.

All the best

Dimeflow

 January 30, 2012, 11:40 #7 Member   albert Join Date: Jan 2012 Posts: 31 Rep Power: 6 ooo it sounds good, thank you for all this information

 February 3, 2012, 06:53 #8 Member   albert Join Date: Jan 2012 Posts: 31 Rep Power: 6 Hi Dimeflow, a few days ago, you posted: In order to get around this, you can use Kozeny's equation which calculates a permeability value using the following: k = (epsilon^3)/((1-epsilon)^2)*K*(S^2) where: epsilon = porosity (void fraction) K = Kozeny constant (2 for tubes, 3.1 for parallel fibres, 5 for random packing) (look up Coulson and Richardson to confirm values) S = sphrecity (measure of how spherical) = ((pi^1/3)*(6Vp)^2/3)/Ap Vp = volume of particle Ap = area of particle So how does this fit together in CFX? You have to input a POROSITY, PERMEABILITY COEFFICIENT and RESISTANCE LOSS COEFFICIENT. The porosity is simply the % VOID of the region. The Permeability Coeff governs low speed viscous losses. If Erguns equation is to be adopted, this term can be calculated as: Kperm = [(Dp^2)*(epsilon^3)*(S^2)]/[150*(1-epsilon)^2] where: Dp = equivalent spherical diameter of particle = 6*(Volume of Particle/Surface Area of Particle) The Resistance Loss term governs inertia effects and can be calculated as: KLoss = 2[1.75*(1-epsilon)/(S*Dp*(epsilon^3)] my question is, is the "S" in Kperm is the same as in kozeny´s constant? If so, permeability of kozeny and permeability coefficient in CFX are different, aren´t they? For Kozeny the permeabiöity doesn´t depend directly on the diameter of the particle but on it´s form(spherecity). Therefore all porous media with spherical particles will have the same kozeny´s permeability On the other hand we have the CFX permeability coefficient which does not only depend on the sphericity, but also on the diameter. Is it right??

February 3, 2012, 08:04
#9
New Member

Join Date: Aug 2009
Posts: 15
Rep Power: 9
Quote:
 Originally Posted by pato Hi Dimeflow, a few days ago, you posted: In order to get around this, you can use Kozeny's equation which calculates a permeability value using the following: k = (epsilon^3)/((1-epsilon)^2)*K*(S^2) where: epsilon = porosity (void fraction) K = Kozeny constant (2 for tubes, 3.1 for parallel fibres, 5 for random packing) (look up Coulson and Richardson to confirm values) S = sphrecity (measure of how spherical) = ((pi^1/3)*(6Vp)^2/3)/Ap Vp = volume of particle Ap = area of particle So how does this fit together in CFX? You have to input a POROSITY, PERMEABILITY COEFFICIENT and RESISTANCE LOSS COEFFICIENT. The porosity is simply the % VOID of the region. The Permeability Coeff governs low speed viscous losses. If Erguns equation is to be adopted, this term can be calculated as: Kperm = [(Dp^2)*(epsilon^3)*(S^2)]/[150*(1-epsilon)^2] where: Dp = equivalent spherical diameter of particle = 6*(Volume of Particle/Surface Area of Particle) The Resistance Loss term governs inertia effects and can be calculated as: KLoss = 2[1.75*(1-epsilon)/(S*Dp*(epsilon^3)] my question is, is the "S" in Kperm is the same as in kozeny´s constant? If so, permeability of kozeny and permeability coefficient in CFX are different, aren´t they? For Kozeny the permeabiöity doesn´t depend directly on the diameter of the particle but on it´s form(spherecity). Therefore all porous media with spherical particles will have the same kozeny´s permeability On the other hand we have the CFX permeability coefficient which does not only depend on the sphericity, but also on the diameter. Is it right??

Hi Pato.

Well spotted, and apologies for the error.

In the Kozeney Equation, S actually refers to 'Specific Surface Area which is the 'volume of sphere'/'surface area sphere' which equals 6/diameter.

I'll log on later and double check the above.

D

 February 3, 2012, 08:15 #10 Member   albert Join Date: Jan 2012 Posts: 31 Rep Power: 6 and is there any difference between S in Kozeny equation and in Kperm for CFX?

November 25, 2014, 08:02
corrections...
#11
New Member

Join Date: Aug 2009
Posts: 15
Rep Power: 9
Quote:
 Originally Posted by Dimeflow Hi Pato, I've used porous regions for various apps in the past from packed columns to pond reed, and nearly always re-confuse myself with the inputs. I'll scribble down a few notes I made, they might be of use, but I do advise hunting as many papers specific to your application as possible. Apologies for the rather basic background, it's just easier for me to explain if I start simple. The aim is to solve the flow through a region which has a pressure drop. If we've no pressure drop profile, we have to utilise expressions which can calculate an estimate. A relatively multi-purpose (I think) approach is to use Ergun's Equation which I believe to be an advancement of Darcy's Law. Darcy deduced that flow rate be proportional to a bed's x-sectional area and pressure drop, but inversely proportional to the thickness. However, it generated a constant term which was difficult to calculate, as it was a function of permeability, k (measurement of how well a porous material transmits fluid, and only found experimentally). In order to get around this, you can use Kozeny's equation which calculates a permeability value using the following: k = (epsilon^3)/((1-epsilon)^2)*K*(S^2) where: epsilon = porosity (void fraction) K = Kozeny constant (2 for tubes, 3.1 for parallel fibres, 5 for random packing) (look up Coulson and Richardson to confirm values) S = sphrecity (measure of how spherical) = ((pi^1/3)*(6Vp)^2/3)/Ap Vp = volume of particle Ap = area of particle So how does this fit together in CFX? You have to input a POROSITY, PERMEABILITY COEFFICIENT and RESISTANCE LOSS COEFFICIENT. The porosity is simply the % VOID of the region. The Permeability Coeff governs low speed viscous losses. If Erguns equation is to be adopted, this term can be calculated as: Kperm = [(Dp^2)*(epsilon^3)*(S^2)]/[150*(1-epsilon)^2] where: Dp = equivalent spherical diameter of particle = 6*(Volume of Particle/Surface Area of Particle) The Resistance Loss term governs inertia effects and can be calculated as: KLoss = 2[1.75*(1-epsilon)/(S*Dp*(epsilon^3)] The above terms were found by rearranging the Ergun Equation in to the form of: deltaP/L = -(viscosity/Kperm)Vs - KLoss(density/2)Vs^2 (as per Help Page // Theory Guide // 1. Basic Solver Capability Theory // 1.7. Sources // 1.7.1. Momentum Sources) I know I commented above saying Ergun's Equation to be multi-purpose, and I have applied it myself to many scenarios, but I strongly recommend you read up and see if it is suitable for your diffuser. All the best Dimeflow

**corrections**

The Permeability Coeff governs low speed viscous losses. If Erguns equation is to be adopted, this term can be calculated as:

Kperm = [(Dp^2)*(epsilon^3)/[150*(1-epsilon)^2]

where:
Dp = equivalent spherical diameter of particle
= 6*(Volume of Particle/Surface Area of Particle)

The Resistance Loss term governs inertia effects and can be calculated as:

KLoss = 2[1.75*(1-epsilon)/(Dp*(epsilon^3)]

Dp = Equivalent Spherical Diam of Particle

The above terms were found by rearranging the Ergun Equation in to the form of:

deltaP/L = -(viscosity/Kperm)Vs - KLoss(density/2)Vs^2

 Tags porous media

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Bernard Van FLUENT 27 June 7, 2016 08:21 Axius FLUENT 2 August 7, 2014 10:34 sean FLUENT 4 October 25, 2011 01:25 Alex FLUENT 0 April 25, 2007 02:00 Igor Main CFD Forum 0 December 5, 2002 16:16

All times are GMT -4. The time now is 13:16.