[Rabsyboi]

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!

[FMDenaro]

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

[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

[cfdnewbie]

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!

[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.

[cfdnewbie]

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?

[Rabsyboi]

I'll read up and try to figure it out.
Thanks a bunch for your help!