I need to calculate the forces caused by vortex shedding(or vortex induced vibrations) on a tapered cantilever structure under wind loading.
I did some reading and some researchers suggests to calculate the response using some empirical equations to include the motion induced forces due to lock in and negative damping as I understood.
Your advice and suggestions will be appreciated.
If your structure is tapered, you should get a slightly different VIV frequency excited along the length and so lock on will probably not be an issue. However if the taper is slight, and any of the frequencies excited are near a structural resonance you could get a resonant amplification. OrcaFlex software from Orcina.com can do some VIV modeling but I don't know if that would fit your application or not. VIV happens in normal flow and when the flow angle is near perpendicular to the object, but is largely absent as the shape becomes more tangential to the flow so can you mitigate the problem by sweeping your shape aft? There are many types of fairings that have been developed over the years for everything from cables to smoke stacks to pipes. There are two "families", those that break up or absorb the vortex street, and streamlined wing like shapes. The disruptors like fringes and helixes actually increase the basic drag coefficient and area but mostly eliminate the VIV. The wings reduce the drag dramatically from a coefficient as high as 4 or 5 when strumming to a routine 0.4 with the wing fairings on cables. The wings shed no vortex as the flow reattaches smoothly in the wake. Good Luck
Hi Sean,
Thank you very much for your answer.
Initially, on my tapered cylindrical tower, I need to investigate whether the vibrations due to VIV forces are significant.
Hence, I need a closed form analytical equation which computes the VIV forces. I was wondering if you are of any of that ?
Later on, I can look at spoilers to mitigate the effect of VIV.
Best Regards,
Mahmoud
I would look on line for the Strouhal number of similar structures at similar Reynolds numbers to see what is already been done. When in doubt 0.22 is a good first guess at the Strouhal number. From there I would set up an excel spreadsheet with different heights above the base plane, then do a 1/7th power law for the boundary layer effect and calculate the wind velocity in 10 or so different points up the height. From there you should be able to get the vortex shedding frequency as a function of wind speed and height to compare to your structural resonances. Figuring out the unsteady lift force is more problematic from first principles but I bet there is a lot out there in the published technical literature. Good luck
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