# Particle Reynolds number / max entrained particle size

1. May 24, 2017

### Pete Moore

I am not a student; this is for work.

Would some kind soul:
a) direct me to an online calculator to enable answering the following or
b) give me the answer and show how you arrived at it :) or
c) advise me of the formula / process by which I can arrive at the answer? THANK YOU!

What is the maximum size silica particle (let's presume it's a sphere) that would stay entrained in flow in Jet Fuel A, in a 4' long 1/4" diameter pipe, with the fuel flowing at 40 mL/m.

Background:

Last edited by a moderator: May 24, 2017
2. May 24, 2017

### Staff: Mentor

Welcome to the PF.

Can you show us what work you have done so far? We need you to show lots of effort before we can help you, even if this is for work and not for schoolwork. It's important to learn how to do work like this whether you are in school or in your first job.

3. May 24, 2017

### Nidum

Just a few thoughts :

(1) The fluid is relatively low viscosity and the flow velocity is extremely low so the answer may depend on the orientation of the pipe .

Horizontal or vertical pipe and if vertical is fluid flowing upwards or downwards ?

(2) There are two different situations to consider for any particular arrangement of the pipe :

(a) where particle is relatively small compared to pipe diameter .

(b) where particle is nearly the same diameter as the pipe .

(3) There is a side issue to look at - with such a low flow velocity the flow may not always completely fill the pipe .

Please include a description of the actual problem that you are trying to solve when responding to @berkeman's request .

4. May 25, 2017

### Pete Moore

1) Great question!...mmm..for simplicities sake let's presume all 4' is horizontal..

2b) There is 'standard' filtration already in affect so we're very unlikely to see /anything/ a .25" in diameter! :) ...most fuel filters would only allow something a few hundred microns through..at most. I suppose, if it's easier we could just look at 'at 40mL/m in a 1/4" ID horizontal pipe how far will a 100 micron particle stay entrained in flow? (ie through all 4' or only 1.5' etc) and then take it from there. The density of course sand is ~2.65g/cm3. 100 microns = .01cm so the volume of a 100 micron sand particle would be 5.24×10-7 cm3. I believe the velocity of liquid flowing at 40ml/m in a 1/4" pipe is 1.2631 mm/m. I have not found the formula that would enable me to answer/calculate this question.

3) The system is underhung from the main fuel line and under pressure so it's very unlikely there will be any air in there.

5. Jun 5, 2017

Anyone?

6. Jun 5, 2017

### Nidum

I am not sure what there is to calculate ?

A particle introduced to the flow at one end of the pipe can only come out at the far end or get stuck somewhere along the way .

Perhaps if you explained why you need an answer to your question we'd be able to give a more helpful response .

7. Jun 5, 2017

### Pete Moore

We are trying to see particles in fuel but the analysis branch's camera needs to flow rate to be very low (40ml/m) to enable clear photos. At lower flowrates heavy particles simply sink to the bottom and /do not/ stay entrained in flow. We have not been seeing as many larger particles (>30um) as we'd expect and are wondering if that's due to our flowrate or something else (like the sampling system etc) so I'm trying to figure out how to calculate how far a certain sized/weight particle (see silicon info above) will stay entrained in flow at a velocity of 1.2631 mm/m. 'Heavy' materials routinely end up at the bottom of plumbing / sewage pipes / rivers so there must be a way to calculate (based on volume/mass / flowrate/velocity) how far a certain sized object will stay in flow before settling on the bottom (presuming it's not small enough to stay entrained forever :)

8. Jun 5, 2017

### Staff: Mentor

Can you just make this low flow rate section vertical with the flow downward? Seems like a simple solution if it would work for you.

9. Jun 5, 2017

### Pete Moore

I'm afraid not, due to space constraints the unit will most likely be under hung under the main fuel line and test section will be horizontal.

10. Jun 5, 2017

### Staff: Mentor

Then buy a better / faster camera and increase the flow rate. Not rocket science here...

11. Jun 6, 2017

### Pete Moore

That's not helpful; we're already using a \$1000 camera....and even if we doubled or tripled the flowrate the same question still remains... What is the formula for calculating how far a large/heavy particle will stay entrained in a certain fluid at a certain flowrate/velocity. I'd appreciate any help there. Thx.

Last edited: Jun 6, 2017
12. Jun 6, 2017

### Nidum

There is no simple single value answer . You would need to think in terms of the probablility of a particle of certain weight and size getting through the pipe .

Something like this :

Calculation is for spherical particles only .

The particle is relatively small compared to the pipe bore so it's presence does not alter the mean velocity of or the velocity distribution across the fluid flow .

The particle is much more dense than the carrier fluid so that it will always tend to sink .

The particle arrives at the entry plane of the pipe at a random location on the plane . This is our biggest difficulty . A particle arriving in the central or upper region is much more likely to get through than one arriving near the lower surfaces of the pipe bore ..

The particle enters the pipe with the same velocity as the local velocity of the fluid stream . This velocity will be a maximum in the central area and minimum near the pipe wall .

So the particle will be carried along by the flow and it will tend to sink at the same time .

The calculation needed is therefore to determine whether a particular particle starting from a random location on the pipe entry plane sinks so far that it contacts the lower surfaces of the pipe bore before it arrives at the exit plane of the pipe 1.

Assuming laminar flow so that the velocities are easy to determine and using some version of Stokes law to determine the particle sinking rate I think that this calculation is actually do-able .

Note 1 : We have to assume for simplicity that when a particle arrives at the pipe wall it slows down to the point where it stops for all practical purposes .

Last edited: Jun 6, 2017
13. Jun 6, 2017

### Pete Moore

Excellent, yes that all makes sense. Once we figure the sink rate in the main flow of the pipe we can know, roughly, how far a particle that starts out in the middle of the flow or nearer the top of the pipe will go. Thx!

14. Jun 6, 2017

### bigfooted

Have a look at these equations (you have probably found similar equations by now):
http://webspace.clarkson.edu/projects/crcd/me637/notes/aerosols/aerosols_page14.html
The particle relaxation time is the important quantity for your problem. If it is close to 0, the particles follow the flow perfectly.
As a reference, these authors state that if tau<0.1, the particles act as tracers to the flow if you are using them in a piv setup:
http://iopscience.iop.org/article/10.1088/0957-0233/27/9/094009/meta
If your relaxation time is larger, then you'd expect particles to sink to the bottom.
This does not take into account turbulence, particles can stay entrained for a longer time in a turbulent flow.

Regarding the probability issue mentioned by Nidum: Have a look at the section on diffusion in the same online notes.

15. Jun 26, 2017

### Pete Moore

I'd think the Particle Settling Velocity (Wso / formula 3) would be most helpful in determining how far a certain particle could stay entrained but the formulas seem circular ie to determine Wso I need to know Cd but that depends upon knowing Res which depends upon Wso?...

formula 3: Particle Settling Velocity: Wso = sqrt (4/3 * Ds50 / Cd * (Ps-Pl)/Pl * g)
formula 4: Cd = 24 / Res + 4 / sqrt (Res) + .4
formula 5: Particle Reynolds #: ReS = Wso * Ds50 / Vl

Vl = kinematic liquid viscosity. At @ 20C Kerosene = 1.25 mm2/s
ds50 = grain size at 50% passing sieve (in microns or ?)
Ps = ?
Pl = ?
g = gravity?

16. Jul 20, 2017

### Pete Moore

Using Stokes Law, max entrained particle travel distance, from top of pipe, in cm = velocity of fluid in cm/s * diameter of pipe in cm / ((1/18)*(density of sand-density of kerosene in g/cm3)*(980/0.0164)*(particle diameter in cm)^2)

...so for example, if it entered at the top of the pipe, a 20um course sand particle would travel ~109 cm in Kerosene before settling...or half that if it entered at the middle of the pipe.

17. Jul 20, 2017

### Nidum

Interesting . I haven't checked the numbers but answer seems plausible .

How does this result compare with your actual observations when testing fuel lines ?

18. Jul 21, 2017

### Pete Moore

it compares 'well' i guess...which is to say generally we don't see too many particles >30um but there are a few......even 100um particles occasionally....then again most of the contaminants don't have particles >30 so not sure how much to make of that...but the lower down in the flow we look the more particles there are and the larger they get so they're not staying entrained anyway...

19. Jul 21, 2017

### Pete Moore

then again we're seeing a mix of water and dust (even in our 'clean' tests) and are /trying/ to determine which is which... since water will stay entrained much further than anything denser and we're not 100% on what we're looking at particle by particle it's a bit less clear than my prior post suggested. :)