Pressure Created in Simple Couette Flow
 

Hello,

I have a question regarding couette flow. The problem involves the flow between two parallel plates where the top plate is moving with some velocity U and the bottom plate is stationary. There is some lubricant between the two plates.) There is no applied pressure gradient (dp/dx=0). Boundary Conditions for the problem include

u=0 @ y=0
u=U @ y=a (top moving plate)

I have not begun to the model the problem but would like to know what pressure will be created between the two plates? And will there be a pressure gradient created in the y-direction? My main objective is to analyze the pressure distribution.

I was reading my fluid mechanics book about applying bernoulli's equation to the in-viscid flow region outside the boundary layer which states dpdx=-p*U*dU/dx where p is density. I believe they got this by:

1) p1/p + V1^2/2 = p2/p + V2^2/2 (assume V1 is zero)
2) (p1-p2)=p* V2^2/2 (Taking partial with respect to x now)
3) d(p1-p2)/dx= p*V2*dV2/dx
4) dp/dx = p*V2*dV2/dx

I assume that if I want to see a pressure variation in the simulation, I will have to model it as transient.

I thank you in advance for any insight you can provide.

what do you mean for inviscid region?? the action of the moving wall is transferred to all the flow by viscous tangential stress...

Okay. Maybe I don't understand couette flow well.
I assume that a boundary layer will be created and the flow between the plates can be divided into a region where viscous tangential stresses are important and a region where they are not (invisid).

Is this wrong?

The whole flow between the plates will be influenced by viscous effects

FMDenaro,

What about the no slip condition on the stationary plate? will this not cause a boundary layer to develop? To make sure I understand, I assume the whole region is viscous because there is no region where the velocity (u) will approach the freestream velocity U at the inlet?

And will there be a pressure generated (in the x or y direction) due to the movement of the top plate?

Unless you are imposing a pressure gradient on the flow there will not be any pressure gradient. The fluid will move because it gets dragged along by the moving plate. Viscous stresses will be large over the entire domain. Thus there is no classic boundary layer. See here

http://en.wikipedia.org/wiki/Couette_flow

Agd,

Thank you for the information. I understand now.

Regarding my problem setup, I am trying to model the pressure distribution inside of a journal bearing. I was reading in my fluids book that if the gap width is small, the flow may be modeled as flow between infinite parallel plates.

Regarding journal bearings, I was reading papers who model it as the flow between two rotating cylinders. (one wall moving and the other stationary.) There is a pressure created between the rotating shaft (moving plate) and bearing (stationary plate) for this case.

Does it make sense to model this journal bearing as a couette flow if I am interested in seeing the pressure distribution? It seems that the couette case, the pressure is whatever you impose on the boundary in the initial conditions. However, if I model it as a transient case, then there might be some pressure variation I believe. As a transient case, in the beginning the velocity profile is not initially linear meaning the shear stress will not be constant everywhere.

From what I remember of journal bearings, the pressure across the fluid film is essentially constant, and the azimuthal pressure gradient is driven in large part by the eccentricity introduced by loading on the shaft. If I am remembering incorrectly then perhaps someone can provide some additional input. But if I am remembering correctly then Couette flow may not be the best approximation. Try researching journal bearings some more to see what others have done. Here is one paper I found -

http://turbolab.tamu.edu/proc/turboproc/T34/t34-16.pdf