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pato January 23, 2012 13:01

permeability in porous media
 
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

papteo January 23, 2012 13:39

you can learn more information about these coefficients if you read the the solver theory guide.

pato January 23, 2012 15:51

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?

arunraj January 26, 2012 19:46

Hiii
 
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

arunraj January 26, 2012 19:48

If u r not able to find in journals use the formulaewhich has given in the manual n try to find the permeability

Dimeflow January 30, 2012 11:29

Quote:

Originally Posted by pato (Post 340667)
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

pato January 30, 2012 11:40

ooo it sounds good, thank you for all this information

pato February 3, 2012 06:53

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??

Dimeflow February 3, 2012 08:04

Quote:

Originally Posted by pato (Post 342587)
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

pato February 3, 2012 08:15

and is there any difference between S in Kozeny equation and in Kperm for CFX?

Dimeflow November 25, 2014 08:02

corrections...
 
Quote:

Originally Posted by Dimeflow (Post 341927)
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


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