Reynold's Number for a Cantilever Beam

[Slayden]

Good Evening!

I've been looking at this problem for a bit and I am a little stumped on it. I asked two graduate level Fluids TAs and my other classmates and they are stumped as well. I hope that you can help...

I am doing an experiment that involves a cantilever beam and wind flow that is forcing the beam to deflect downward. The flow bench is positioned above the cantilever and is blowing the air in the same direction as the deflection. I am then taking a thermal anemometer and measuring the velocities at points just above and below the beam, starting at the center of the beam and working my way out until the velocity is zero. I hope to achieve a measured flow pattern around the beam from the anemometer.

I am trying to non-dimensionalize my flow velocities for my results and I am having an issue figuring out how to characterize the Reynolds Number for this flow. I was using D as the distance from the center line axis of the cantilever (perpendicular to the flow) but I don't think that is right. How would you calculate a Reynolds Number for this type of problem?

Let me know if you need help visualizing it.

Thank you,

C.S.

 

[Topher925]

I think I need help visualizing it. From what I understand you basically have a long rectangular object immersed in a moving fluid and you are trying to measure its velocity profile using a manometer. If this is the case then you would just calculate the Reynolds number the same way you would for any immersed body. I would just consider the sides of the beam (you don't give any info about geometry so I'm assuming its square) as flat plates and determine your Rel at the trailing edge of the side of the beam.

 

[Slayden]

http://nedyals.com/images/normalflowdiagram.jpg

If that helps a little bit.

The beam is just a regular rectangular cantilever beam that is placed in the flow. The dashed red lines signify the planes that I measured the flow velocity in at 5 millimeter increments, starting at the the mid point of the beam and moving out 50 millimeters. The top line ends up just being the freestream velocity out of the air bench. The other three is greatly changed by the body within the flow.

With the average velocity through the thermal anemometer measured, all I need is to figure out the characteristic dimension to be used...and that is which stumped me. Should every position measured have it's own Reynolds number since it is at a different location? I was using the distance from the centerline of the beam but I just have a tingle in the back of my mind that won't go away.

 

[FredGarvin]

The D in the Reynolds number is actually a convention for some characteristic length. Have you seen any tests with the RE being calculated for a flow perpendicular to a flat plate? In other flat plate tests, the characteristic length is the length along the plate. In your case the thickness of the plate is in the direction of the flow so I would think that that is your number. Try doing some looking into flat plate tests.