Turbulent concentric annular flow

[Atholl]

Hi all,

I've done some Computational Fluid Dynamic(CFD) simulations of turbulent flow of a Newtonian fluid in a concentric annulus. I want to compare the results in terms of velocity distribution with explicit analytical predictions. I know there are numerous analytic expressions for the calculation of laminar flow velocity distribution in concentric annuli, but does anyone know if there are equivalent equations for turbulent flow? My search so far has come up with nothing; the subject seems to be avoided in an explicit analytical sense.

Yours hopefully,

A.

 

[desertfox]

Hi Atholl

I have several fluid mechanics books here which show formula for velocity distributions for laminar flow but as you found nothing for turbulent flow.
It appears that the velocity in turbulent flow is approximated to be constant throughout the annulus even though there is a small laminar boundary layer at the wall of the annulus.
Sorry I am unable to help further.

Regards desertfox

 

[Atholl]

Thanks Desertfox, you've confirmed what I've suspected!

Atholl

 

[quark]

I concur with DesertFox. There is an excellant coverage in Foundations of Fluid Mechanics by SW Yuan about laminar flow velocity distribution for annular pipe and even for flow between two rotating cylinders. These are derived from Navier-Stokes equation.

Not a single word about turbulent flow.

I feel you can use Prandtl's one seventh law for some approximation(works good for normal pipe flow).

Regards,

 

[zdas04]

I've used the 1/7 power law for turbulent flow in a vertical annulus (flow up) and got good correlation to observed data.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The Plural of "anecdote" is not "data"

 

[Atholl]

Thanks for the input, guys. Believe it or not, I found an expression for turbulent velocity profiles in concentric annuli; It's a modified version of the Karman-Prandtl universal logarithmic velocity distribuation for pipes.

For anyone who's interested, it's in the new (2nd) edition of 'Transport Phenomena' by Bird, Stewart and Lightfoot pages 174 - 175. They refer to a paper in the AIChE Journal, Volume 7, Issue 1 , Pages 41 - 45 (1961), which I'll try to get hold of:


Turbulent newtonian flow in annuli
Donald M. Meter, R. Byron Bird
University of Wisconsin, Madison, Wisconsin

Abstract
In recent years there have been quite a few experimental studies on turbulent flow in annuli. In this paper a Prandtl mixing-length approach is applied to give a friction factor vs. Reynolds number expression for annuli [see Equation (22) and Table 1]; this expression describes tube flow and slit flow as special cases. No new adjustable constants appear in the final result other than those determined earlier for tube flow. The final expression is found to predict friction factors within the accuracy of the existing experimental data. The mixing-length friction-factor expression is thus substantially more accurate than the usual hydraulic-radius procedure and of comparable accuracy to other recent annulus friction-factor treatments.

Received: 18 January 1960; Revised: 9 May 1960; Accepted: 10 May 1960



Thanks again,

Atholl