Flow of an Incompressible Fluid Around a Solid Object

[gandersen]

Dear Participants:

I am not sure that this is the right forum, but can anyone point me in the direction of a diagram that would show the flow lines (flow paths) of an incompressible fluid in rectilinear flow (parallel flow lines) as it flows past a solid plate barrier that is oriented perpendicular to the flow lines? I would like to assume that the flow is laminar. Also, assume that the problem is a 2-D flow field.

In particular, I would like to be able to assess the flux at various positions behind the obstruction to get a measure the effectiveness of the barrier in decreasing the amount of fluid flowing behind it.

I am a geotechnical engineer (Civil Engineer) that is looking at the potential effectiveness of placing a barrier (slurry cutoff wall) to decrease the groundwater flowing into a particular site.

Have I asked the question appropriately?

Thank you in advance for your time.

 

[jmw]

I suggest you look into the problem from the perspective of vortex shedding.
There are many program around which deal with different geometries, you may be able to find some through a web search.
I would suggest a start at

http://home.hccnet.nl/m.dijk/pressure_drop_calculator/calcs/calcs.html;

http://www.euronet.nl/users/e_wesker/et.html#1;

http://tigger.uic.edu/~mansoori/Thermodynamic.Data.and.Property_html;

http://www.cheresources.com/indexzz.shtml

 

[zdas04]

Ganderson,
The language of your post was very clear and precise, but I missed something - is the flow "past" (I read that as the wall surface is parallel to the flow) or "over" the wall? The "perpendicular" term confused me.

If you're looking for laminar flow along a wall, then your flow profile is a parabola with zero velocity at the wall and maximum velocity in the mid-stream. Stream lines will all be parallel to the wall.

If the flow is over the wall, then it is a wier problem that should be explained very well in standard CE references.

jmw,
Laminar flow is inconsistent with vortex formation or shedding.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

 

[prex]

If I understand correctly your problem, this is what is called the flow of viscous fluids through a porous medium in seepage problems. It is governed by the same equation as for the incompressible flow of a fluid outside the viscous boundary layer.
The equation is simply the well known Laplace equation, that governs many physical problems (thermal conduction, torsion of a beam, magnetic induction and others) and represents essentially a condition of continuity of the flow of some physical quantity. This equation together with the boundary conditions (represented by the available head in your case) fully describes the physical situation.
The problem is that there are no simple solutions for the Laplace equation, even for very simple geometries. Hence a numerical approach is required: this may be by means of a FEM program, but it is also not difficult to set up a finite difference calculation scheme, if you have some experience with this.

prex

http://www.xcalcs.com

Online tools for structural design

 

[jmw]

zdas04, assuredly so, but the math around it may provide some useful understanding.

 

[gandersen]

Thank you for the input:

This is an excellent forum.

As a point of clarification. I am referring to a 2-dimensional flow with a wall that completely obstructs the flow paths. In otherwords, the fluid must flow around the wall and converge again on the other side. It does not flow over the wall but rather around the wall.

The flow paths are heading directly towards the wall. At some point they begin to diverge and go around the wall (on the two sides) and then they converge behind the wall and at some distance behind the wall, the flow becomes rectilinear again.

I currently do not have access to a numerical code. I did do finite difference coding in school but that has been 17 years ago. Is there a shareware 2-D finite difference code that I could get easily?

What I need is a diagram where someone has either solved LaPlace's Equation and drawn flow lines, or has made experimental measurements where flow lines have been measured for the case where a flat plate completely obstructs the rectilinear flow and it has to pass around the plate and converge on the other side.

I have seen graphical solutions for flow around a circular object and around an airfoil and I was hoping to find a quick reference for flow around a flat plate.

Thank you again for your time.

 

[gandersen]

Dear Forum Members:

I found a free finite element code for steady state groundwater flow that is able to solve my problem. The software is written for Windows and it is pretty good considering the price

It can be downloaded for free from Arnold Verruijt's web page

http://geo.verruijt.net

and is called GEFEM1.

Thanks again for the advice.

Glen