Need calculator for Annulus flow!!

[sprintcar]

HELP!!
I need a spreadsheet (or formulas) to calculate and graph water flow thru an annulus formed by the gap between a circular orifice (square edged) surrounding a shaft. Variables will be water pressure, orifice ID, orifice thickness, and shaft OD. Temperature will be constant (probably 70F). I can dig thru Cameron’s but I figure somebody in our great group of Engineers probably already has one. (I’ll post this in a couple forums) THANKS!!


"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[daveboy]

If you are talking about fine annular clearances i.e. like a stuffing box bush there are loads of resources out there.

Depending on the length of the bush the losses along the bush may be significantly less than the entry and exit losses and therefore it is more of an oriface problem.

You'll find an iterative method in the following book

Centrifugal and Axial Flow Pumps
A. J. Stepanoff Ph.D.
Hardcover, 1992, 2
ISBN 0894647237

 

[sprintcar]

Thanks Dave
I went 'hunting' on the web and found very little that applied to stuffing box gland water flow calculations. I ran a set based on test results and the Petroleum formula, but the results were somewhat questionable.

I was hoping someone had a spreadsheet!

I'll dig around in Stepanoff to see if anything applies.

"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[sreid]

A simplification I have used is to "Flatten" the circular orfice into a gap who's width is pi x diameter. This is then a textbook problem.

 

[daveboy]

Sprintcar,

Stepanoff says

Head loss = friction factor x (( Length / Diameter) + 1.5) x (Velocity ^2 / (2 x g))

Where diameter is the diameter of a circular pipe having the same hydraulic radius as the annular channel of the clearance - for a plain bore this is equivelant to the diametrial clearance.

Stepanoff uses a modified Moddy chart for evaluating friction.

Obviously as friction and velocity are related this becomes a interative solution.

Chapter 10 in Stepanoff shows this method.

The problem I have with making avaiable a spreadsheet is that I have worked for a pump compamy for many years and the methods I use are are not strictly as presented in Stepanoff, although they are based on this there is a large degree of 'experience factors' added to correct from theoretical to actual leakage losses.

As a note high viscosity fluids tend to give errors in the friction factor and errors in the iteration.

 

[sreid]

Not exactly on topic but if you are really looking for a zero leak seal, consider a Ferrofluid seal.

http://www.ferrotec.com/

 

[sprintcar]

daveboy
Thanks!
If you could share your spreadsheet (I'm using water as the fluid) my contact is showshine at aol dot com

"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[daveboy]

Sprintcar,

I was using the Stepanoff equations for other work on axial thrust in pumps and momentum conservation around impeller casing sidewalls so I ahve extracted the section and sent it to you.

You should use it with care and your own discretion and at your own risk - you may want to add so 'experience factors' from tests.

 

[sprintcar]

Thanks Daveboy!!
I'll try it out after the holidays. I've been thru a ton of different references but there doesn't seem to be a definitive method. Maybe if I get one that seems to match test results (with 'fudge factors) I should publish a paper!
Happy Holidays

"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[daveboy]

There are loads out there - thats where I found a lot of stuff I was working on for momentum conservation.

You could try searching for old BHRA (British Hydrodynamic Research Association - not the hill walkers and ramblers) papers.

If you are looking at high flow rates then Chris Brennan at Caltech has published a few papers. As far as I know they were written and the research was done with regards to the fuel pumps in the space shuttle. The methods are very elegant but quite complicated. This method could be used for lower velocities and I think looking at the methods(although I have not tested it) that results should be fairly good.

Alternativley there is a fairly good approximate method in on of JF Gulich's papers - I can't remeber what paper it's in either the disk friction in closed turbomachinery or the surface roughness one. If you search for the author and roughly these titles you should find the papers.

The whole subject is dealt with in so many different ways there are so many variables that certain methods include and others disregard - entry and exit losses (what do you use as a coefficent), roughness in the bores, fluid entry pre whirl (as the fluid is rotating it travels further so losses are higher - this is why sreid's suggest would give some discrepancies).

I have even carried out CFD on this type of problem and results can be good and other times can be wildley different with what would seem to be insignificant changes in variables / geometry / property.

The problem is that the leakage through the annulus does not occur independantly and is effected by other parts of the system.

Hope this is of some help.

 

[sprintcar]

Good advice - Thanks!
I'm trying to equate water flow thru the stuffing box in a pump. The actual flow is very complex - 2 inlets, flow direction changes, multiple orifices in the lantern ring with a final 90 degree turn against the spinning shaft sleeve and finally exiting either thru the packing or under the lantern ring into the lower pressure area of the pump.

AES seals had an equation that was reasonably close
Q = 2.48*(d2^2 – d1^2)*V (units are gpm, inches and ft/sec)
which I set up in a spreadsheet so I could vary the velocity to match lab test values. This was pretty close.

I did pure annular area calculations for the orifice are between the lantern ring and shaft, but the results were understandably way too high.

The original flows were established using Stepanoff with a bit of 'tweaking' and the goal was to extrapolate the test results on 2 sizes over a range of 10 other sizes. Of course nothing was linear - each size had different internal clearances, etc.

In the end, it looks like the original flow rates are good enough for the application, and the result will be changes to the instructions for setup and operation.

I really appreciate the help and ideas! Someone mentioned a John Crane 410 publication. I called the packing division at Crane and they didn't have it - the sales girl was unaware of it!

Happy Holidays my friend!




"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein