Compressed Air Turbulent Annular flow

[klchurch]

I've been studying Crane 410, trying to figure out an equation to determine pressure drop in a tubular annulus (tube within a tube). Crane page 1-4 under Hydraulic Radius mentions vaguely that the Hydraulic radius would be 1/2 the width of the passage. Does this mean 1/2 the annular wall or does this possibly mean we can use the opposite side of the annular wall also, since the cross-section would flow through both sides. Pressure drop calculations would be greatly effected. I've searched through out this forum and found much technical data on annular flow, but I believe not much on the Crane 410 discussion of annular flow. Any comments will be greatly appreciated.
Kris Church
Conroe, Texas

 

[sailoday28]

Hydraulic DIAMETER is defined as the flow 4*area/wetted perimeter.
For flow in an annulus the flow area is PI(r2^2-r1^2)
= PI(r1+r2)(r1-r2)
The wetted perimeter is 2PI(r1+r2)
Hydraulic diameter=2(r2-r1)

where r2 is the inside radius of the large tube and r1 is the outside radius of the inner tube.

 

[zdas04]

I've found the standard Hydraulic Diameter calc to significantly overstate pressure drop in annular flow. The equation that I've found to allow the use of normal hydraulics equations is:

d(eff) = [(d1+d2)^2*(d1-d2)^3]^0.2

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"

 

[klchurch]

Thank you zdas04 and sailoday28 for the comments. It is greatly appreciated!!!!!!!!
I’m more mechanical than verse in fluids.
In pursuing the same subject, I would like to explain further do-loops I’m going through. In Crane 410 the equations seem to deal mostly with a single pipe and tailor the equations respectively. Especially so, in compressed fluids. With annular flow, the annular cross-sectional area and the equivalent diameter are some what related, which it seems that one will need to be very careful and leery on which equation to use. I have labored through the related compressible equations, and found quite different values when utilizing annulus values and equivalent diameters. I believe, the reason for the differences are directly related with the values of “D” = (Equivalent Diameter derived from a equation with inputs of the two annulus diameters) and “d” = (inside diameter derived from the annulus area equivalent diameter as stated under Hydraulic Radius). With this in mind, it seems that a relevant equation should include the use of “D” and “d”, not “D” or “d”. There is an equation in Crane that seems applicable, Page 3-3 second equation of 3-7. I can solve for P1 because all of the other values are known even though the equations solve directly for mass flow. However if I use the equation just above the second equation, the value for P1 is greatly different when we are looking at 10,000 ft of pipe at high pressures and normal friction factors. The basic difference, in my situation, between the two equations are the inputs of “D” & “A”, and “D” & “d”. When solving for P1, the second equation is anywhere from 40 to 50 % less pressure drop (P1 – P2), than the first equation. By using zdas04’s adjustment, the pressure drop would be less in both equations but still not within let say, 10% of each other equations solution.
My situation has the downstream pressure and CFM required (known) and the upstream pressure and pipe sizing to be supplied and figured out (unknown). In one calculation I need multiple compressors and boosters or larger diameter pipes, and the other equation, one compressor and booster. At $300.00 of diesel a day per machine, the economics are drastic between the equations. The question is, am I on the right track if I utilize the equations with “D” and “d” instead of “D” and “A”? Or am I completely on the wrong track all together? Above variables are in accordance with using Crane’s Nomenclature and Units?
Your comments again are greatly appreciated.
Kris Church
TorqueLock Corp

 

[sailoday28]

For normal pipe flow, with liquids, the accepted engineering practice is to use the Moody diagram to relate friction factor and Reynolds number.
However, for flow in an annulus, I would be careful about using the Moody diagram with a definition of hydraulic raduius or equivalent diameter.
For example, I don't believe that using equivalent diameter for an annulus with laminar flow and the Moody diagram will match closed form solutions.
Perhaps other readers as(zdas04 )could give their experience with annular flow, both for compressible and incompressible flow.