Pressure drop through sand (Ergun equation?)

[ione]

I’d need to estimate the pressure drop of an air stream through a cylinder of sand.
After a brief research I’ve bumped into Ergun equation (new stuff to me) and I’ve thought it could be fine for my needs.
The Ergun equation gives the pressure drop for unit length of a fluid flowing through granular media. Pressure drop depends on a series of factors such as void fraction, media particles diameter, Reynolds number, fluid density and velocity. If the fluid were a liquid I think Ergun equation would be the right way to go. Now since I’m dealing with a gas (air specifically), I was wondering if this could affect in any way Ergun equation. In particular I’m thinking of density and velocity variations due to pressure changes as air flows through the sand.
Any input from those already familiar with Ergun equation and its application would be appreciated. If by chance anyone had approached a similar problem in a different way, his/her comments would be welcome as well.

 

[BigInch]

I have always avoided studying "flow of fluids through a porous media", since that would be just one more subject in which I could never expect to master, but your question inspired me to at least search the quoted text. Scanning articles appearing in the search results would appear to indicate that there are many problems that will come up using that equation, not only for gas, but even for liquids that exceed Darcy flow regimes and that there also appear to be a number of equations developed for gas flow through sand and dusty gas flow through sand which should yield superior results. The Ergun equation seems to have a foundation in liquid flow through packed catalyst beds. Branch out into the geological field and I think you will find a number of alternatives that are not so limited as the Ergun equation appears to be.

I hate Windowz 8!!!!

 

[braddles90]

Is this a vertical column of sand that you're forcing air through? You could find some more information if you look for terms like 'fluidised bed'. Looking back quickly through my pneumatic conveying notes, it looks like Mainwaring and Reed (1997) was a reference for a paper where they experimentally tested columns of different bulk materials to determine at what air velocity the bed becomes 'fluidised', i.e. the powder starts to act like a fluid. An example of similar test data can be seen in the following picture:

http://www.scielo.org.za/img/revistas/jsaimm/v113n7/09f04.jpg

From memory (it's been a couple of years since those courses) there is no real great way of predicting the pressure drop without knowing specific material data for the type of sand you're using, by which you'd need to do testing to determine anyway. They really drilled into us at uni how different all material samples are, and that to work stuff like this out properly each sample needs to be tested.

Is there any kind of direct messaging function on this site? If you could somehow get me an email address I'd be happy to email a copy of my course notes, which has (one of) Erguns equations for the pressure gradient through a packed bed, in which case you might find you could knock together some kind of estimate before testing. There's an example of a test rig that has been used as well which might help. If you don't want to email thats fine, I'll dig up the rest of my notes and attach them in this thread.

 

[EnergyMix]

Braddles90 (and ione),

Posting e-mails is a site "no-no", but it is acceptable to provide a tag line link to your Linked In account or a web page through your profile (Look at the button on the top, right hand side labeled My Stuff ... if you click on it, you'll get the option to go to My Profile ... which you can then update to provide a tag line.)

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[Latexman]

I've used the Ergun equation a few times in my career. It works great if you do some small scale experimental tests. If you lump all the solid particle parameters together into two constants (a and b) it takes the form:

dP/L = a[μ]V + b[ρ]V²

Easy to curve fit with just a few test runs. Try to run the tests to span the actual operating range.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[Latexman]

Oh yeah, the Ergun equation doesn't extrapolate from the compacted state to the fluidized state. So, keep the dP/L < 85% of the bed bulk density!

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[ione]

Thanks to all for your input