Calculation of Saffman Lift Force
 

Hi all

I've got a model of a sphere (representing a small particle) attached to a wall. There is another wall a few diameters away, creating channel flow around the particle. In essence, I'm trying to numerically calculate the lift/drag on a particle to compare against the theoretical results from the literature. Re is low (<<1).

My drag force appears to be resonable, but my lift force is negative, meaning that the particle is forced towards the wall instead of away, as expected.

Has anyone played with this scenario? Any ideas on why the lift force is in the wrong direction?

Your post is not entirely clear on the problem geometry. I gather you have a spherical particle attached to wall 1, with wall 2 in close proximity. There is flow over the sphere and between the 2 walls, and the particle lift moves the particle towards wall 1(?) 2(?). Can you clarify the problem setup?

Saffman lift
 

Yes, you are correct. The particle is on wall 1, with wall 2 in proximity. (the effect of the wall-wall distance is the primary variable I am interested in) The flow is between the two walls, flowing over the particle as well. Theoretically, a lift force should exist that acts to remove the particle from the surface and entrain it into the free-stream. This is the so-called Saffman lift. (I am not trying to model the actual particle motion, just the steady-state flow field).

Pictures are attached for the case of a very close wall-wall distance. The model uses one plane of symmetry through the sphere center. Flow is from left to right in these pics.


Your ideas are much appreciated

At first galnce, I would also expect the particle lift to want to move it toward the opposite wall, due to the flow acceleration and lower pressure on top. But have you plotted the pressure distribution on the particle? I would be curious as to what the pressure looks like on the particle surface. And of course there is always the obligatory question of are you sure you don't have a sign error somewhere - only asked because I have made that mistake many times in the past.

Edit - I posted the above without fully understanding what you are interested in. Sorry about that. When I saw the term Saffman, I mistakenly thought back to work I had done years ago on Saffman vortices. I think you are probably referring to the lift due to shear. I don't know if you have seen this article, but if not it may be of some help to you -

web2.clarkson.edu/projects/crcd/me437/downloads/1_4Lift.pdf

Hope that link works