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Old   April 9, 2009, 21:55
Default Who can help me with orthotropic resistance
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wu
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hello, everyone
I am a freshman in CFD. i want to calculate the flow resistance of monolith according to the equation which is provide in STARCD methodology volume, but i meet some trouble. anyone can give some hints to solve this trouble.
In the methodology volume of Star CD(in Chapter 8,Example 2), it gives a formula to calculate the friction factor. in this equation, how to get the value of C1, C2 and n?

Can I calculate the flow resistance of monolith by ergun equation ? but ergun equation is derived for isotropic resistance!


thank you in adavance
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Old   April 13, 2009, 04:15
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Anton Lyaskin
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Look for some engineering books on hydraulics - as it is written in the Methodology, these coefficients come from simple relations for "hydraulic resistance" vs Reynolds number. You'll need to calculate Reynolds number for the single channel within your monolith.
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Old   April 13, 2009, 12:12
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A while back I did some automotive catalyst modeling. I directly calculated the A & B coefficients for the channel direction from the measured pressure drop vs. flow rate curve (eq. 8-1 & 8-2). I then set the orthogonal direction's coefficients to arbitrarily large values (4 orders of magnitude larger).

I was also able to replicate the pressure drop vs flow rate curve by computing the pressure drop along one representative channel. For this you need to be careful with appropriately capturing inlet & exit losses.

Follow the useful points for relative values and limits on the B coefficient. The on-line help (Nav-Center help button once inside the porous media panel) has a decent summary. Make sure you understand the superficial velocity concept.
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Old   April 13, 2009, 23:49
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Quote:
Originally Posted by A_Lyaskin View Post
Look for some engineering books on hydraulics - as it is written in the Methodology, these coefficients come from simple relations for "hydraulic resistance" vs Reynolds number. You'll need to calculate Reynolds number for the single channel within your monolith.
Dear A_Lyaskin
Thanks for you answerm,would you please tell me the title of this kind book?

does you mean I must calculate the reynold number for single channel and then derive the formula for porosity factor
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Old   April 14, 2009, 03:55
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Right now I have a pretty old book by Daugherty and Ingersoll, "Fluid Dynamics with Engineering Applications" lying on my desk, but there should be plenty of such books.

Yes, you're right about Reynolds number for single channel. Consider a simple example - channel with a circular cross-section. Reorganizing the formula from methodology we have
\Delta p = - 4f \frac{L}{D} \frac{\rho V^2}{2}
So you can see that in this case f = \lambda / 4, where \lambda is friction factor. If your Re < 2300, then \lambda = 64 / Re, which gives you n = -1, C_1 = 16, C_2 = 0(well, actually it's not a good example, because you can also take n = 0, C_1 = 1, C_2 = 16). If your Re > 2300, then there are different theoretical formulas for smooth pipes. The simplest is
\lambda = 0.3164 / Re^{0.25}
This gives you n = -0.25, C_1 = 0.0791, C_2 = 0

There are also approximations for transition region, which will give you both C_1 and C_2 \neq 0
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Old   April 14, 2009, 04:50
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Quote:
Originally Posted by Pauli View Post
A while back I did some automotive catalyst modeling. I directly calculated the A & B coefficients for the channel direction from the measured pressure drop vs. flow rate curve (eq. 8-1 & 8-2). I then set the orthogonal direction's coefficients to arbitrarily large values (4 orders of magnitude larger).

I was also able to replicate the pressure drop vs flow rate curve by computing the pressure drop along one representative channel. For this you need to be careful with appropriately capturing inlet & exit losses.

Follow the useful points for relative values and limits on the B coefficient. The on-line help (Nav-Center help button once inside the porous media panel) has a decent summary. Make sure you understand the superficial velocity concept.
thanks Pauli, now we have estimated the pressure loss through your method,but we want to develop a theoretical model to estimate the pressure loss in different monolith.
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Old   April 14, 2009, 05:27
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Quote:
Originally Posted by A_Lyaskin View Post
Right now I have a pretty old book by Daugherty and Ingersoll, "Fluid Dynamics with Engineering Applications" lying on my desk, but there should be plenty of such books.

Yes, you're right about Reynolds number for single channel. Consider a simple example - channel with a circular cross-section. Reorganizing the formula from methodology we have
\Delta p = - 4f \frac{L}{D} \frac{\rho V^2}{2}
So you can see that in this case f = \lambda / 4, where \lambda is friction factor. If your Re < 2300, then \lambda = 64 / Re, which gives you n = -1, C_1 = 16, C_2 = 0(well, actually it's not a good example, because you can also take n = 0, C_1 = 1, C_2 = 16). If your Re > 2300, then there are different theoretical formulas for smooth pipes. The simplest is
\lambda = 0.3164 / Re^{0.25}
This gives you n = -0.25, C_1 = 0.0791, C_2 = 0

There are also approximations for transition region, which will give you both C_1 and C_2 \neq 0
A_Lyaskin

thank you very much for your quick response.

according to your comment, I could deal with monolith channel as a simple pipe to calculate the pressure loss of the whole monolith without considering the monolith porosity. That is to say, the pressure loss caused by friction in the monolith is only related to the parameter of the monolith channel, and has nothing to do with the monolith porosity.

Can I understand your comment in this way ?

By the way if I take n = 0, C_1 = 1, C_2 = 16), I can not get f = 16/ Re.

Thanks again!
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Old   April 14, 2009, 11:06
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Quote:
Originally Posted by lilyshining View Post
according to your comment, I could deal with monolith channel as a simple pipe to calculate the pressure loss of the whole monolith without considering the monolith porosity. That is to say, the pressure loss caused by friction in the monolith is only related to the parameter of the monolith channel, and has nothing to do with the monolith porosity.
Yes, pressure drop is caused by friction in the channels, but porosity \chi also comes to play when you calculate \alpha and \beta coefficients (see formulas 8-15 and 8-16)

And yes, I've screwed with a math a little bit
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Old   April 14, 2009, 23:17
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I understand it .
thank you very much
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Old   April 24, 2009, 09:05
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Have you tried using STAR CCM+ for the pressure curve? You can use field functions and other polynomial functions or tables for modelling the alpha and beta (or A and B). You can also accomodate the porosity accordingly or have something to the effect of C2 and alpha that Fluent uses.

STAR CD may not be able to do this directly, but you can get these effects using some user sub-routines in STAR CD.
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