# Calculation of w component

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July 11, 2012, 04:28
Calculation of w component
#1
New Member

Rob
Join Date: Jul 2012
Posts: 4
Rep Power: 7
Hi Guys,

I currently preparing a paper on secondary currents and am having some difficulty with some data calculations. The data I have has been measured using LDA equipment in a rectangular flume. I have accurate data for u and v components but need to calculate the w component mathematically.
I have been told that this is possible using the equation shown in the attachment.
Apparently the differential is calculated using a standard five-point center-difference operator, and the integral was computed from the trapezium rule assuming that the cross-stream velocity at the wall was zero.
I hope that someone on here can make sense of this as it is really doing my head in.
Thanks for your help!
Attached Images
 equation.jpg (5.0 KB, 5 views)

 July 11, 2012, 06:33 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,499 Rep Power: 40 if you have a 3D Case, the flow being subject to the divergence-free contraint, then: dW/dz=-(dU/dx + dV/dy) thus, if you have U and V fields you can integrate anc compute W

 July 11, 2012, 07:18 #3 New Member   Rob Join Date: Jul 2012 Posts: 4 Rep Power: 7 Yeah you've hit the nail on the head! I am just not sure how to perform the maths. The conditions are such that there is no variation is streamwise, u, velocity, so that term can be removed. The v data I have is in the following form (the top row is the z locations and the left column are the y locations): v 14.3203 27.88824 41.45621 55.22419 68.59216 8.5 0.000597 0.001682 0.003992 0.010048 0.008707 10 0.000297 -0.00017 0.005296 0.010319 0.009262 12 0.000935 -0.00093 0.004421 0.009234 0.010913 15 0.000514 -0.00107 0.004239 0.010468 0.01063 18 0.000483 -0.00249 0.004134 0.011069 0.011067 20 0.000898 -0.00229 0.003639 0.011235 0.012193 If you could help me out with the calculation that would be amazing! Thanks

July 11, 2012, 07:53
#4
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cfdnewbie
Join Date: Mar 2010
Posts: 557
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Quote:
 Originally Posted by Rabsyboi Yeah you've hit the nail on the head! I am just not sure how to perform the maths. The conditions are such that there is no variation is streamwise, u, velocity, so that term can be removed. The v data I have is in the following form (the top row is the z locations and the left column are the y locations): v 14.3203 27.88824 41.45621 55.22419 68.59216 8.5 0.000597 0.001682 0.003992 0.010048 0.008707 10 0.000297 -0.00017 0.005296 0.010319 0.009262 12 0.000935 -0.00093 0.004421 0.009234 0.010913 15 0.000514 -0.00107 0.004239 0.010468 0.01063 18 0.000483 -0.00249 0.004134 0.011069 0.011067 20 0.000898 -0.00229 0.003639 0.011235 0.012193 If you could help me out with the calculation that would be amazing! Thanks
well, just determine dv/dy from your data by using a central stencil (and one-sided at the boundary), then integrate along z, noting that z=0 at the wall to fix the constant. voila!

Last edited by cfdnewbie; July 11, 2012 at 07:53. Reason: typo

 July 11, 2012, 07:59 #5 New Member   Rob Join Date: Jul 2012 Posts: 4 Rep Power: 7 You make it sound so easy! If you could dumb this down and give me an example for 1 of the points I will be that stoked I'll do a seated backflip.

July 11, 2012, 08:07
#6
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cfdnewbie
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Quote:
 Originally Posted by Rabsyboi You make it sound so easy! If you could dumb this down and give me an example for 1 of the points I will be that stoked I'll do a seated backflip.
Well, read up on how to compute a finite difference stencil on equidistant nodes, thats a very basic technique, you will find it in every textbook! Just plug your values in, the equation gives you the derivatives you need... Then integrate along z.... Dont know, maybe you can explain your difficulties in more detail?

 July 11, 2012, 08:11 #7 New Member   Rob Join Date: Jul 2012 Posts: 4 Rep Power: 7 I'll read up and try to figure it out. Thanks a bunch for your help!

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