# -nano-scale treatment in CFD

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 January 16, 2013, 08:49 #2 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 The navier-stokes equations are derived assuming continuum assumption (Knudsennumber -> 0). If your flow has a high Knudsen number, the validity of this assumption becomes weak, and any code solving the navier stokes equations will get into trouble. There are some extensions to rarefied or extended gas dynamics, but I doubt that they have been included in a commercial solver, in fact, most of this topic is still very current research.

 January 16, 2013, 10:16 #3 Senior Member     Alex Join Date: Jun 2012 Location: Germany Posts: 1,506 Rep Power: 25 Fluent comes with a boundary condition suitable for extending the applicability of the NS-equations to about Kn=0.1. See "slip boundary formulation for low pressure gas systems" in the fluent documentation.

 January 16, 2013, 13:09 #4 Senior Member   Join Date: Dec 2011 Location: Madrid, Spain Posts: 134 Rep Power: 8 Hi, I don't see such problem. The nano particles are transported by a continuous phase (helium), which is not rarefied, so that NS holds perfectly. The transport of nano particles can be modelled by seeding the flow with a discrete number of particles and tracking their trajectories individually (Lagrangian approach) or using an Eulerian formulation, which also holds if the nano particles are diluted in the main gaseous phase. This will allow you to obtain the velocity of the particles. As far as I know, FLUENT allows you to include the Brownian motion effect. I would suggest that you calculate the Stokes number of the particles beforehand. If it is sufficiently small the particles will accelerate right away and attain the velocity of the gaseous stream. Otherwise, if St~1 or higher, the inertia of the particles is not negligible. Cheers, Michujo.

 January 16, 2013, 17:37 #5 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 13,732 Rep Power: 106 Hi JGG: You asked me to comment on this thread but the comments here already are a good summary of the issues to consider. Other than to say that if you are looking at the length by which the particle accelerate to flow velocity - this is easily worked out through the stokes number and you do not need CFD for that.

January 17, 2013, 06:00
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Alex
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Quote:
 Originally Posted by michujo The nano particles are transported by a continuous phase (helium), which is not rarefied, so that NS holds perfectly.
I disagree with that. If the Knudsen number evaluated from the mean free path of the fluid and the characteristic length of the particles is high, the NS-equations are no longer valid.

January 17, 2013, 08:36
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 Originally Posted by flotus1 I disagree with that. If the Knudsen number evaluated from the mean free path of the fluid and the characteristic length of the particles is high, the NS-equations are no longer valid.
Out of curiosity I calculated the Knudsen numbers of the gas relative to the tube diameter (1 mm) and to the particles diameter (1e-7 to 1e-8 m). The mean free path of the gas is calculated for p=1 bar and T=273 K. I get:

Kn_tube ~ 2e-4

Kn_particles ~ 2e1 to 2e0

In light of these results I think we can say that NS hold for the gas, since the Kn relative to the tube characteristic dimension is small. However, for the particles it is not.

Do the concept of Stokes number or drag force still hold for this case, where the particles are travelling through the interstices of the helium gas particles? How would you compute the drag force of the solid particles then?

Thanks,
Michujo.

January 17, 2013, 09:14
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Quote:
 Originally Posted by michujo In light of these results I think we can say that NS hold for the gas, since the Kn relative to the tube characteristic dimension is small. However, for the particles it is not. Michujo.
We can definitely agree on that.

Quote:
 Do the concept of Stokes number or drag force still hold for this case, where the particles are travelling through the interstices of the helium gas particles
The drag force experienced by a particle travelling through a rarefied gas is lower than the force one would expect for creeping flow.
But it should still be possible to calculate the drag through some kind of algebraic expression.
I havent done any research on this particular topic, but i am sure that there exists literature about it.

 January 28, 2013, 17:45 #9 Super Moderator   Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 13,732 Rep Power: 106 You definitely should check the Knudsen number is in the range where the NS equations apply. If that is OK, then you should check the stokes number of your particles and work out the terminal velocity/range of the particles and see if that is much smaller than your region of interest. For nanoparticles this is usually the case.

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