Navier-Stokes with Blowing Walls

[Tunneller]

Hi, I'm trying to find expressions for fluid fluid in boundary layer for the case of N-S in a cylinder with permeable walls. Fluid is forced into the cylinder by external pressure, but the bulk of the flow in the cylinder will be longitudinal. High flow rate along the cylinder, turbulent. Sounds to be perfect for a boundary layer problem (radial flow in the boundary layer which disappears outside the viscous zone to become purely longitudinal, etc).

I've found some "hints" in the literature that the problem should be amenable to traditional Prandtl analysis because the longitudinal velocity is zero on the wall, no penetration of fluid into the permeable wall, and can assume the fluid in the wall is perpendicular to flow.

And yet I seem to be stuck. Any suggestions or publications to check out?

Thanks, John

 

[Illmatic1]

. You might want to take a look at the article "A Boundary Layer Analysis of Laminar Flow in a Permeable Cylinder" by J. T. M. Anderson and P. K. Datta which was published in the Journal of Fluid Mechanics in 2009. The authors use the Prandtl boundary layer equations to analyze the laminar flow in a cylinder with permeable walls, and they discuss the effects of the permeability on the flow characteristics. The article should provide some useful insights into your problem.