Stokes number and gravity

hebeldebel · March 31, 2015, 08:52

Hi,

I did not find an offtopic section, so I hope this place is OK as well.

I am about to validate some simulations of mine with PIV measurements. There are several seeding particles available and I would like to chose the right one.

I chose the Stokes number to evaluate my particles.

The test chamber is approx. 50 cm long and has several obstacles inside it. The flow is horizontal and its velocity ranges from 1 m/s to 10 m/s.

My first calculations looked like this: St = ( (d_p)² * rho_p * u) / (18 * * L_char)

d_p is particle diameter 3*10^(-6) m
rho_p is particle density 912 kg/m³
u is velocity 1 m/s
is the viscosity of air 17100 kg/(m*s)
L_char is the length of the test chamber 0.5 m

and I get St = 5*10^(-14) for 1 m/s which seems good and St = 1,48*10^(-10) for 10 m/s, which seems good as well.

But some questions remain:
- What do you usually use for the characteristic length? Is the length of the chamber the right choice?

- how do I check for the influence of gravity? As far as I understand my calculation of the Stokes number only looks at changes in direction of the flow.

Thanks for your help.

H0T_S0UP · March 31, 2015, 08:59

You want to pick something that has the closest density to the fluid as possible, as small as possible and has the least variation in shape with each particle. Obviously round is preferred because a sphere is the most studied shape.

hebeldebel · March 31, 2015, 09:02

Quote:

Originally Posted by H0T_S0UP

You want to pick something that has the closest density to the fluid as possible, as small as possible and has the least variation in shape with each particle. Obviously round is preferred because a sphere is the most studied shape.

Yep, at the moment I am evaluating, DEHS particles from 1 to 5 micrometers and hollow glass microspheres around 30 to 50 micrometers in diameter.

But I need to be sure, at least on the theoretical side, that this will work.

nvarma · April 2, 2015, 17:17

I didn't understand what exactly you are trying to do here.

However assuming it is a low Re flow, you might find this useful http://en.wikipedia.org/wiki/Galilei_number

Or try using the good old Pi theorm to find the dimensionless groups.

H0T_S0UP · April 2, 2015, 18:58

OK, I just remembered most food coloring has a specific gravity of 1. I noticed your particle density is 912 kg/m3, so I'm assuming your fluid is water?

March 31, 2015, 08:52	Stokes number and gravity	#1
hebeldebel Member Join Date: Jan 2014 Posts: 40 Rep Power: 12	Hi, I did not find an offtopic section, so I hope this place is OK as well. I am about to validate some simulations of mine with PIV measurements. There are several seeding particles available and I would like to chose the right one. I chose the Stokes number to evaluate my particles. The test chamber is approx. 50 cm long and has several obstacles inside it. The flow is horizontal and its velocity ranges from 1 m/s to 10 m/s. My first calculations looked like this: St = ( (d_p)² * rho_p * u) / (18 * * L_char) d_p is particle diameter 310^(-6) m rho_p is particle density 912 kg/m³ u is velocity 1 m/s is the viscosity of air 17100 kg/(ms) L_char is the length of the test chamber 0.5 m and I get St = 510^(-14) for 1 m/s which seems good and St = 1,4810^(-10) for 10 m/s, which seems good as well. But some questions remain: - What do you usually use for the characteristic length? Is the length of the chamber the right choice? - how do I check for the influence of gravity? As far as I understand my calculation of the Stokes number only looks at changes in direction of the flow. Thanks for your help.

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March 31, 2015, 08:59		#2
H0T_S0UP Member Alex Join Date: Jan 2014 Posts: 54 Rep Power: 12	You want to pick something that has the closest density to the fluid as possible, as small as possible and has the least variation in shape with each particle. Obviously round is preferred because a sphere is the most studied shape.

April 2, 2015, 17:17		#4
nvarma Senior Member nm Join Date: Mar 2013 Posts: 100 Rep Power: 13	I didn't understand what exactly you are trying to do here. However assuming it is a low Re flow, you might find this useful http://en.wikipedia.org/wiki/Galilei_number Or try using the good old Pi theorm to find the dimensionless groups.

April 2, 2015, 18:58		#5
H0T_S0UP Member Alex Join Date: Jan 2014 Posts: 54 Rep Power: 12	OK, I just remembered most food coloring has a specific gravity of 1. I noticed your particle density is 912 kg/m3, so I'm assuming your fluid is water?