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I have read on this forum that the tip vortex comes from the roll-up of the vortex sheet behind the entire wing as opposed to being a local tip phenomena.

I am interested in simulating a tip vortex numerically. Does this mean I am obliged to model the entire wing?

But this makes the simulation much more expensive! Is there a way in which it makes sense to only run CFD for the near-tip region for accurate results? For example a boundary condition to replace the rest of the wing? Any discussion or papers are appreciated.

Many thanks

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  • $\begingroup$ The cost of a simulation depends not only on the size of the domain, but also on the modeling strategy, the desired outcome, the acceptable error in the solution. Are you using RANS, URANS, LES or DNS? Which grid size? What is the purpose of tour simulation: fluid-structure interaction, aeroacustics, wake interaction, ...? You might end up with a full-wing simulation that's not so expensive $\endgroup$ Feb 8 at 10:57

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I have read on this forum that the tip vortex comes from the roll-up of the vortex sheet behind the entire wing as opposed to being a local tip phenomena

You've read good 👍

This picture (Wikipedia) summarises in a perfect way what you've read:

section lift coefficient vs Reynolds number

From the whole trailing edge of the wing a vortex (red line) is shed everywhere lift changes along the span of the wing. The strength of the vortex is proportional to this local change in the lift.

All those vortices eventually come together to form one big vortex which is the tip-vortex proper.


Does this mean I am obliged to model the entire wing?

Yes, unless the biggest changes in the spanwise lift happen only on a limited part of the wing: this is for example a common simplification for rotor blades, where the biggest change in lift happens at the tip and then only the tip vortex (or better, the vortex at the tip) can be simulated.


But this makes the simulation much more expensive!

If you are modelling only the wing with its wake, a simple panels method runs in a couple of minutes.

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By no means am I an expert on the topic, but this should be some good info for you. To answer your question directly, yes, you can just model like 1/3 of the wing. I’ve seen tons of models doing just that for wing tip purposes. Modeling in the aspect you are looking for (at least from what I can tell) is more learning based so modeling the main part you are looking to see shouldn’t be a big issue as long as you’re modeling enough to get your answer. Ideally, you’d want to get a whole model of the wing for the most data backed answer. Attached is a link of a partial wing for a tip vortex modeled how you were thinking! There are many more like this.

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  • $\begingroup$ Side comment: this simulation is the result of exascale computation ( en.wikipedia.org/wiki/Exascale_computing ). Modelling 1/10 instead of 1/3 of the wing is of limited help, if you still need 10'000s xeon cpus... To OP: the boundary conditions you would like to impose on the near tip field needs to have certain temporal/statistical properties to mimic the results of this large scale model. It is an extremely simple question to be posed: when does laminar flow transition to turbulent flow? To give an answer, however, it is one of the biggest open problem in physics/mathematics ... $\endgroup$
    – EarlGrey
    Feb 8 at 6:24
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the tip vortex comes from the roll-up of the entire sheet as opposed to being a local tip phenomena

One might question that statement. Aircraft, especially large and heavy, form large trailing vorticies from their own downwash. These vorticies result from the ambient air being drawn into the downwash flow.

A wing tip vortex is much smaller and far less energetic. It is indeed a local phenomena resulting from the pressure differential of upper and lower wing.

This means that, while there can be efficiency gains with modified wingtips under certain flight regimes, trailing vorticies from lift creation cannot be eliminated.

As far as modeling the entire wing, yes, this would provide useful information on energy balances. One might start with a seagull or albatross wing, or perhaps the DC-3.

These wings are very efficient, but suffer tip stall issues. Slats help make these wings safer.

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