Porous medium coefficients

cfdkorea · February 6, 2019, 01:10

Hi,
I am modelling a porous medium in starccm. in order to determine the inertial and viscous coefficients of the i have plotted a velocity vs pressure drop curve and get an equation like dp=av+bv2. I van calculate the values of 1/alpha and C2.

as 1/alpha=a/(Dynamic Viscossity) and C=(2*b)/Rho

Now how i could determine the values of Pi and Pv.

Carno · February 6, 2019, 04:09

Write your equation in the form,

deltaP/L = Pi*V2+Pv*V, You will get the values.
Where,

substrate length (L)
Pressure drop (deltaP)
porous inertial and viscous resistance (Pi; Pv) and velocity (V)

cfdkorea · February 6, 2019, 04:42

Quote:

Originally Posted by Carno

Write your equation in the form,

deltaP/L = Pi*V2+Pv*V, You will get the values.
Where,

substrate length (L)
Pressure drop (deltaP)
porous inertial and viscous resistance (Pi; Pv) and velocity (V)

thanks Carno for yous response.

when I fit my equation on the curve I get

DP=312.72v2+2.7232V
which makes Pi=312.72 and Pv=2.7232

is length of substrate equals to the length of porous medium. Additionally, I was looking for different examples in the text they always qoute Pi < Pv. even in the starccm tutorial Pi<Pv. than how this will work.

fluid23 · February 6, 2019, 12:12

Make sure your units are consistent, too. Use Pa and m/s or psf and ft/s. I suggest doing a dimensional analysis and working out the units so you make sure that what you are inputting agrees with the input units in star/ccm.

Pi and Pv really can depend on the shape of the DP curve so it is possible that you have low Pv. However, in my experience Pv is usually the larger of the two.

cfdkorea · February 6, 2019, 14:40

Quote:

Originally Posted by fluid23

Make sure your units are consistent, too. Use Pa and m/s or psf and ft/s. I suggest doing a dimensional analysis and working out the units so you make sure that what you are inputting agrees with the input units in star/ccm.

Pi and Pv really can depend on the shape of the DP curve so it is possible that you have low Pv. However, in my experience Pv is usually the larger of the two.

Thanks, in the quadratic equation like y=ax+bx2

I am sure about "a" that its unit will be (pascal/m/sec) but can you please confirm the units of "b"

Additionally for a second order polynomial your b will be always higher than a. therefore I am confused.

fluid23 · February 7, 2019, 11:17

you might have a/b and Pi/Pv swapped and your units for 'a' are wrong. Consider it this way:

dp/l = Pi * V^2 + Pv * V

or

y = a * x^2 + b * x

Where y=dp/l, a = Pi, b = Pv and x = V

The units of a * x^2 and the units of b* x must be the same as dp/l (i.e Pa/m).

Therefore, the units of a or Pi must be Pa-s^2/m^3 and the units of b or Pv must be Pa-s/m^2.

(Pa - s^2 / m^3) * (m^2 / s^2) = Pa / m

(Pa - s / m^2) * (m / s) = Pa /m

These actually simplify further into kg/m^4 and kg/m^3-s respectively. If you are using SI units in your file, then these are the preferred default units for inertial and viscous resistance.

February 6, 2019, 01:10	Porous medium coefficients	#1
cfdkorea New Member anonymus Join Date: Apr 2016 Posts: 11 Rep Power: 10	Hi, I am modelling a porous medium in starccm. in order to determine the inertial and viscous coefficients of the i have plotted a velocity vs pressure drop curve and get an equation like dp=av+bv2. I van calculate the values of 1/alpha and C2. as 1/alpha=a/(Dynamic Viscossity) and C=(2*b)/Rho Now how i could determine the values of Pi and Pv.

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February 6, 2019, 04:09		#2
Carno Member carno Join Date: Mar 2009 Posts: 70 Rep Power: 17	Write your equation in the form, deltaP/L = PiV2+PvV, You will get the values. Where, substrate length (L) Pressure drop (deltaP) porous inertial and viscous resistance (Pi; Pv) and velocity (V)

February 6, 2019, 12:12		#4
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 18	Make sure your units are consistent, too. Use Pa and m/s or psf and ft/s. I suggest doing a dimensional analysis and working out the units so you make sure that what you are inputting agrees with the input units in star/ccm. Pi and Pv really can depend on the shape of the DP curve so it is possible that you have low Pv. However, in my experience Pv is usually the larger of the two.

February 7, 2019, 11:17		#6
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 18	you might have a/b and Pi/Pv swapped and your units for 'a' are wrong. Consider it this way: dp/l = Pi * V^2 + Pv * V or y = a * x^2 + b * x Where y=dp/l, a = Pi, b = Pv and x = V The units of a * x^2 and the units of b* x must be the same as dp/l (i.e Pa/m). Therefore, the units of a or Pi must be Pa-s^2/m^3 and the units of b or Pv must be Pa-s/m^2. (Pa - s^2 / m^3) * (m^2 / s^2) = Pa / m (Pa - s / m^2) * (m / s) = Pa /m These actually simplify further into kg/m^4 and kg/m^3-s respectively. If you are using SI units in your file, then these are the preferred default units for inertial and viscous resistance.