The simplest estimated value to use is the width of channel, which defines the flow domain, while for the velocity value one can take the initial (inlet) value that is set as a boundary condition. Nevertheless, the value of velocity as well as the full flow area changes spatially as the fluid is redirected through densely packed medium. Could we define such a value as "effective" Re? What would be some benefits of it?
It all depends on the type of physics that you are trying to capture (describe) with the flow system.
For example, if you are trying to describe the pressure drop across a packed bed, then the typical definition for the Reynolds number is:
Re=(\rho U_s D_p)/(\mu(1-\epsilon))
where U_s is the superficial velocity, \rho the fluid density, \mu the fluid viscosity, \epsilon the void fraction of the packed bed and D_p the characteristic diameter of a equivalent spherical particle. This form of the Reynolds number appears in the Ergun equation for the friction factor:
f=150/Re+1.75
which can be related to the pressure drop \Delta P across the packed bed of length L:
f=(\Delta P}{L)(D_p)/(\rho U_s)(\epsilon^3/(1-\epsilon))
If on the other hand you are interested in two-phase flow in which capillary effects are important in assessing flows in constricted passages, then defining the Reynolds number based on a length scale related to the constricted passage might be relevant so that one can assess inertial effects on meniscus curvature, which in turn dictates the local pressure drop required to move fluid blobs through a constricted passages.
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3 Recommendations
Alexander J. Babchin
Alberta Research Council (ARC)
Brian knows too much for a simple answer. No one should forget that in old good America West at Cawboys time, Bob killed Jack in a bar for a correct answer two times two = 4.
Jack was too smart for Bob's liking.
So, the simplest choise of internal lengh scale within homogineous porous media is either
L = (Absolute Permeability / Porosity) ^ (1/2), or 1/Sv, where Sv is the specific surface, having dimention [m ^ 2 / m ^ 3]. Both should result to the same scale, if measured correctly.
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4 Recommendations
Nevena Perovic
Technische Universität München
Dear Mr. Higgins,
I appreciate very much, that you wrote such detailed explanation! At the moment I would like to concentrate on the first case, where no capillary forces are taken in the consideration. The formulae for the friction factor, which can be treated as a correlation between Re and expected pressure drop, can be useful in my case, as a double check, as I currently use slightly different approach.
Thank you so much,
Best regards!
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Nevena Perovic
Technische Universität München
Dear Mr. Babchin,
I would not mind being killed by Bob, if I knew the exact answer to this question. That's why I appreciate both yours and Brian's help.
The main problem in my case is that I cannot measure any variable, especially not such ones like specific surface or permeability. I may though use some previous cases and measurement in order to validate, what I am actually working on. The equation that you provided can be nevertheless easily used as a correction mechanism in an iterative procedure between chosen characteristic length and absolute permeability, within algorithm that I already have. Thank you very much for this contribution!
Best regards!
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2 Recommendations
Brian G Higgins
University of California, Davis
Ha, Ha; I see Alex has not lost his humor!
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2 Recommendations
Alexander J. Babchin
Alberta Research Council (ARC)
Brian, you better ask a dark skinned Mexican fellow, you workred with him and Jim Davis in IPC., Tito Banano.. Some day in 1980 I took him for MUD RESLING. Jim tells me that the fellow still consieders this day as a fanniest one in his entire live.
You want to have fan, just visit me, your Hotel room is on me.
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1 Recommendation
Brian G Higgins
University of California, Davis
Yes I do remember Tito, and back to the subject of this discussion. I like your response.
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1 Recommendation
António Manuel Abreu Freire Diogo
University of Coimbra
Reynolds number is a dimensionless parameter proportional to the quotient between the inertial and viscosity forces. In fact, for a liquid with a given kinematic viscosity, you can choose arbitrarily any characteristic velocity and characteristic length you wish (only changes the absolute values according to your choice). In hydraulics, it is frequent the simple use of the apparent velocity and the average diameter of the particles of the porous medium.
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1 Recommendation
Nian-Sheng Cheng
Zhejiang University
Part of the paper attached may help.
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1 Recommendation
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