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July 11, 2012, 04:28 
Calculation of w component

#1 
New Member
Rob
Join Date: Jul 2012
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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 fivepoint centerdifference operator, and the integral was computed from the trapezium rule assuming that the crossstream 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! 

July 11, 2012, 06:33 

#2 
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Filippo Maria Denaro
Join Date: Jul 2010
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if you have a 3D Case, the flow being subject to the divergencefree 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 
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Rob
Join Date: Jul 2012
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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
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Quote:
Last edited by cfdnewbie; July 11, 2012 at 07:53. Reason: typo 

July 11, 2012, 07:59 

#5 
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Rob
Join Date: Jul 2012
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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
Join Date: Mar 2010
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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 
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Rob
Join Date: Jul 2012
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I'll read up and try to figure it out.
Thanks a bunch for your help! 

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