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January 23, 2012, 13:01 
permeability in porous media

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albert
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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, 13:39 

#2 
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Theodoros Papadopoulos
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you can learn more information about these coefficients if you read the the solver theory guide.


January 23, 2012, 15:51 

#3 
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albert
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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 
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Arun raj.S
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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 
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Arun raj.S
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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  
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Quote:
I've used porous regions for various apps in the past from packed columns to pond reed, and nearly always reconfuse 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 multipurpose (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 xsectional 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)/((1epsilon)^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*(1epsilon)^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*(1epsilon)/(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 multipurpose, 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 
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albert
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ooo it sounds good, thank you for all this information


February 3, 2012, 06:53 

#8 
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albert
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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)/((1epsilon)^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*(1epsilon)^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*(1epsilon)/(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 

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


November 25, 2014, 08:02 
corrections...

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Quote:
**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*(1epsilon)^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*(1epsilon)/(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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