Looking for a benchmark for fluid flow between cylinders

sina_mech · July 16, 2015, 16:29

Hi

I'm looking for a numerical/experimental/analytical solution for fluid flow between a rotating cylinder with vertical load inside another stationary cylinder (which resembles the fluid motion in journal bearings). I'm looking for a 2D solution for Newtonian fluid.

I appreciate your help

mprinkey · July 16, 2015, 17:51

If the cylinders are concentric, the solution is very easy. Any grad level fluid dynamics book will have it. I found this in 5 seconds of googling:

http://www.nptel.ac.in/courses/11210...ric_rotate.htm

If the cylinders are NOT concentric, as they are in a loaded bearing, you should look at the Reynolds equation. It is a reduced form of the NS equations (using assumed velocity profiles) and gives you the pressure distribution associated with the offset rotating flow.

sina_mech · July 16, 2015, 18:01

Quote:

Originally Posted by mprinkey

If the cylinders are concentric, the solution is very easy. Any grad level fluid dynamics book will have it. I found this in 5 seconds of googling:

http://www.nptel.ac.in/courses/11210...ric_rotate.htm

If the cylinders are NOT concentric, as they are in a loaded bearing, you should look at the Reynolds equation. It is a reduced form of the NS equations (using assumed velocity profiles) and gives you the pressure distribution associated with the offset rotating flow.

Thanks for your reply. The link you provided is for a basic fluid dynamics problem. As I mentioned, I'm looking for a solution that the inner cylinder is under a applied vertical force. Please see the attached photo (sorry for the quality. just took a picture by my phone).

Thanks.

mprinkey · July 16, 2015, 18:10

Then, as I said, read up on Reynolds equation solutions. You can get the pressure field from the Reynolds equations and then back calculate the velocity fields based on the assumed profiles (used to build the Reynolds equation) and the solved pressure field. I don't know that a closed-form solution exists for full incompressible NS for non-concentric rotating cylinders. Maybe there is a perturbation solution that can be constructed using the concentric solution as a base and perturbing it for small values of eccentricity.

July 16, 2015, 16:29	Looking for a benchmark for fluid flow between cylinders	#1
sina_mech Senior Member SinaJ Join Date: Nov 2009 Posts: 136 Rep Power: 16	Hi I'm looking for a numerical/experimental/analytical solution for fluid flow between a rotating cylinder with vertical load inside another stationary cylinder (which resembles the fluid motion in journal bearings). I'm looking for a 2D solution for Newtonian fluid. I appreciate your help

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July 16, 2015, 17:51		#2
mprinkey Senior Member Michael Prinkey Join Date: Mar 2009 Location: Pittsburgh PA Posts: 363 Rep Power: 25	If the cylinders are concentric, the solution is very easy. Any grad level fluid dynamics book will have it. I found this in 5 seconds of googling: http://www.nptel.ac.in/courses/11210...ric_rotate.htm If the cylinders are NOT concentric, as they are in a loaded bearing, you should look at the Reynolds equation. It is a reduced form of the NS equations (using assumed velocity profiles) and gives you the pressure distribution associated with the offset rotating flow.

July 16, 2015, 18:10		#4
mprinkey Senior Member Michael Prinkey Join Date: Mar 2009 Location: Pittsburgh PA Posts: 363 Rep Power: 25	Then, as I said, read up on Reynolds equation solutions. You can get the pressure field from the Reynolds equations and then back calculate the velocity fields based on the assumed profiles (used to build the Reynolds equation) and the solved pressure field. I don't know that a closed-form solution exists for full incompressible NS for non-concentric rotating cylinders. Maybe there is a perturbation solution that can be constructed using the concentric solution as a base and perturbing it for small values of eccentricity.