Calculating Reynolds number for a wind tunnel

[Mr.hev]

Hi All! as you can see I'm new here! i signed up in order to ask for a wee bit of help with my thesis! (now don't get me wrong I am not exactly asking anyone to write it for me!) I've found myself at a small bit of a loose end here, as a mechanical engineering student i am perfectly capable of working out reynolds numbers for pipes of any dimensions but in a square wind tunnel i haven't a clue how to go about it and it would be easier to get blood from a stone than get help from my fluids lecturer (not saying anything bad about the man, great lecturer just impossible to track down when he might have a free 5 mins to go through something! )

the last time i spoke to him about it he said something along the lines of "boundary layer, use this size, substitute this for the diameter of the pipe" this conversation lasted approximately 5 seconds before he had to shoot to his next class so i didnt have a chance to ask him for any more detail on how to do this!

So, if there is anyone amongst you here that feel like they might be able to help me out on this one and explain how one goes about calculating this either with a quick example using hypothetical figures or just a quick, logical shakedown of how to calculate what i need it would be much appreciated!

(just in case anyone feels generous about helping, could you state what you are referring to with different variables, i have found that different countries use slightly different letters etc than what i might be used to and i need to get this sorted out pretty quickly!)

Sorry for the long post and the minimal punctuation also! if anyone can help me out then thanks a bunch! :)

 

[Mr.hev]

Oh AND I seem to have forgotten to point out that this will be used for testing a small model of an airfoil (100x200 mm approx) in a wind tunnel that is about 500mm square in section give or take!

Just for the record i have a plan of sorts on how i will be mounting the part but suggestions are always welcome! thanks!

 

[boneh3ad]

Well generally for a square or rectangular duct, you use the hydraulic diameter. I don't remember the equation but a quick Google should help you there.

The issue here is why is that even an important parameter? If it's a useful wind tunnel, it will never get anywhere close to fully-developed duct/pipe flow so a full tunnel Reynolds number isn't even useful. Typically there will just be relatively thin boundary layers on the wall.

So I guess my question for you is what's your reasoning for wanting to calculate this?

 

[Mr.hev]

Basically I'm going to be running tests on lift on various permutations of the same aerofoil section. In order to calculate lift I need the Reynolds number for the velocity of the air inside the wind tunnel. If I can calculate this based on the wind tunnel itself then everything else will slot straight into place. I have everything else I need, how I work out the Reynolds number of my tunnel is the final piece of the puzzle!

 

[boneh3ad]

Basically I'm going to be running tests on lift on various permutations of the same aerofoil section. In order to calculate lift I need the Reynolds number for the velocity of the air inside the wind tunnel. If I can calculate this based on the wind tunnel itself then everything else will slot straight into place. I have everything else I need, how I work out the Reynolds number of my tunnel is the final piece of the puzzle!

Well there isn't really a useful parameter like a Reynolds number for the whole tunnel. It simply doesn't make sense since the whole point is to create a free stream that is "undisturbed" in which to test your model.

It's more common to quote a "unit Reynolds number" which is just $\rho U/\mu$ and has the units of m^-1. Then when you have something like an airfoil, you would just use that quantity along with the chord length or momentum thickness or whatever length scale of interest you have to calculate whichever Reynolds number is most relevant to you.

 

[Mr.hev]

Thanks! I'll give that a go!

 

[boneh3ad]

Just as an example, the tunnel I work in has a typical unit Reynolds number of $Re^{\prime} = 10 \times 10^6\;\mathrm{m}^{-1}$ in most of our studies. We use a model that is about 400 mm long, so the length Reynolds number of the model is 400,000. It also makes calculating the x Reynolds number along the model trivial.

 

[Mr.hev]

that sounds bang on! so for calculating this out i take my unit reynolds number" and multiply it by my chord length is it? it sounds like you just made my calculations a lot easier! :O :) thanks a million!

 

[Mr.hev]

ive just gotten around to giving this a go (had a busy weekend of work :O ) and I'm just a tad confused as to what U in the above formula is actually denoting, obviously density and viscosity are there but I'm not sure about the U if you get a chance can you fill me in? i know it's a silly question and I am sure i know what it is but I am just completely flummoxed at the moment!

 

[boneh3ad]

The wind tunnel free-stream velocity.

Of course keep in mind that including a model can and will change that velocity to a varying degree depending on how much blockage your model represents.