# Modelling Thin film lubrication in a thrust bearing

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December 13, 2015, 22:44
Modelling Thin film lubrication in a thrust bearing
#1
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arvind prabhakar
Join Date: Nov 2014
Posts: 2
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Hi Everyone,

I am new to this forum. I am trying to model a 2-dimensional incompressible flow in a thin air lubricating film i.e. a in 1d bearing (Re between 100 to 1000) but, I am not getting the resulting correct pressure profile.
The model geometry and flow conditions are essentially a couette flow problem (Only top wall moves causing velocity profile, I have attached image of flow domain for your reference) however, the bottom wall is stationary and non parallel to the top wall ( This I believe requires grid transformation OR non-dimensionalizing the equations as per geometry, in my case I have non dimensionalized as per film thickness to length ratio (epsilon) ).
I have written the code for couette flow for solving 2 dimensional Navier stokes equations (using simple algorithm on staggered grid which was also available on this forum) and it works correctly when epsilon is set equal to 1 for a standard couette flow geometry as per results from John Anderson's book "CFD - Basics with Applications", section 9.4. (I have attached the matlab code as well as a pdf file) However, The section does not discuss anything about the pressure field output from couette flow so I have no idea about what kind of pressure field should be generated.
I would really appreciate help from you guys on this forum to guide me in solving this problem on the geometry I have attached.

Thanks and Regards,
Arvind
Attached Images
 1d bearing geometry.png (23.5 KB, 42 views)
Attached Files
 couette flow.pdf (140.5 KB, 38 views)

December 17, 2015, 06:47
#2
Senior Member

Troy Snyder
Join Date: Jul 2009
Location: Akron, OH
Posts: 219
Rep Power: 18
Quote:
 Originally Posted by arvind9008 Hi Everyone, I am new to this forum. I am trying to model a 2-dimensional incompressible flow in a thin air lubricating film i.e. a in 1d bearing (Re between 100 to 1000) but, I am not getting the resulting correct pressure profile. The model geometry and flow conditions are essentially a couette flow problem (Only top wall moves causing velocity profile, I have attached image of flow domain for your reference) however, the bottom wall is stationary and non parallel to the top wall ( This I believe requires grid transformation OR non-dimensionalizing the equations as per geometry, in my case I have non dimensionalized as per film thickness to length ratio (epsilon) ). I have written the code for couette flow for solving 2 dimensional Navier stokes equations (using simple algorithm on staggered grid which was also available on this forum) and it works correctly when epsilon is set equal to 1 for a standard couette flow geometry as per results from John Anderson's book "CFD - Basics with Applications", section 9.4. (I have attached the matlab code as well as a pdf file) However, The section does not discuss anything about the pressure field output from couette flow so I have no idea about what kind of pressure field should be generated. I would really appreciate help from you guys on this forum to guide me in solving this problem on the geometry I have attached. Thanks and Regards, Arvind
More commonly, the slider bearing is solved via the thin film equation, i.e. Reynolds eqn. (Couette and Poiseuille velocity profiles dumped into continuity eqn.). See the solution for the plane slider in the following link (includes plots of pressure profile):

http://rotorlab.tamu.edu/me626/Notes...D_bearings.pdf

I have not looked at your code in detail but I suspect your issue may lie in the boundary conditions. What are the boundary conditions for the momentum and pressure correction equations at the inflow and outflow?

 December 18, 2015, 20:47 #3 New Member   arvind prabhakar Join Date: Nov 2014 Posts: 2 Rep Power: 0 Hi, Thanks for the reply. I have the codes for reynold's equation applied to thin films. It predicts pressure profile well however, due to neglection of inertia terms the pressure predicted is not as accurate as the one predicted by solution of complete navier stokes. the case i am analyzing is for Re=1000 and higher. inertia effects become predominant therefore, requiring modelling of complete navier stokes. although, I have to model the compressible form of navier stokes equations but i want to ensure I have results for the incompressible modelling first so I can be sure and move to modelling the compressible system of equations. This is kind of stressing me out because, This is to form part of my thesis that I have to defend in spring 16. Any inputs from you guys will be of help to me. Thanks, Arvind

 December 19, 2015, 04:29 #4 New Member   Syed Aaquib Hazari Join Date: Apr 2015 Location: Delft Posts: 16 Rep Power: 11 Hi, It maybe that turbulence may affect your case. Are you sure there's no turbulence affecting your case? Since Re is around 1000 there could possibly be traces of turbulence.

 December 19, 2015, 05:17 #5 Senior Member   Troy Snyder Join Date: Jul 2009 Location: Akron, OH Posts: 219 Rep Power: 18 Arvind, Getting back to your original post, I was under the impression that the only issue was that you were unsure if your pressure profile was 'correct'. Please clarify your issues as the Reynolds codes should give you an idea of what your pressure profile should look like. If your concern is inertia or turbulence muddying the waters, simply run a case with smaller film height, lower sliding velocity, or higher viscosity (take your pick) to drop the Re # and then compare with the Reynolds code results.