Is circulation real?

I wouldn't contradict you there.

But would it not be exiting if there was a physical explanation to vorticity and circulation, that corresponds well to the msimple mathematical model?

These vortices are convective, transporting physical particles, but what about vorticity as predicted by CFD in general, it doesn't appear to have a physical counterpart, unless the one described in the paper as diffusion?

 

Be very careful mixing the "vorticity" of singularities used in mathematical models of airfoils, and the "vorticity" of viscous flow.

The leading edge singularity is an artifact of the simplifications made in the mathematical models. Real flows do not have singularities.

 

Or perhaps - the answer, my friend, is blowin’ in the wind.

 

I think you may have hit the nail on the head there Daiqu!

 

I think the term "circulation" only confuses people, it is a poor way to explain how lift is generated. It was developed by people studying the pure physics of what is happening, and yes, the mathematical models do predict nicely what we see in nature. The problem I think is trying to get a feel for what is happening by those that do not study fluid mechanics is made more difficult by such terminology.

All anyone needs to keep in mind is these simple facts: 1) air has mass, 2) when you accelerate a mass you get a force; F=ma, 3) curving a fluid over a surface (such as what happens on an airfoil) accelerates that mass of air and you get a lift force.

This is basically how wings, sails, propellers, etc all operate. The idea that you can separate the free stream velocity from the curved path leads to the idea of circulation. The more circulation you have the more lift you generate. That circulation is just another way of measuring or calculation the mass of the air you accelerate over the curved surface.

Keep this in mind will make it easier to follow all the fancy numerology that devines the fate of your new design.

 

I agree, David.
I was commenting on one flaw of VLM as a mathematical method.
(Personally I have no interest in "reality".)

 

Is there no standardised "patch test" for this elements?

Are you both ostensibly referring to what in FEA circles is a basic ‘singularity’ like at a sharp corner?

In the sense that to converge on an exact solution, every element must becomes arbitrarily small. (IN FEA the h-convergence and p-convergence if I recall). However, going from a coarse to a fine mesh, a finite error remains, which inevitably means a finite error will remain. Which also relates to the patch test of ensure a constant gradient across the section with ever decreasing element size. But usually when interpreting FEA results one tends to ignore the localised displacement or stresses, which can be infinite under a single node, but at some distance away and globally, is acceptable.

I recall in FE there are singular integration elements that can assist in such difficult situations. (Although I’m pushing the limits of my memory on FE now…). Is this not a similar situation you’re both referring too?

 

Yes, there are tests one can perform to assess the accuracy,
but they are not always apparent. It depends on what you are
looking for. Vortex Lattice Methods can have remarkable
accuracy for the lift, but their deficiencies appear when
trying to calculate pressures and other point loadings.

The attached shows the behaviour of the vorticity (multiplied
by the square root of the distance from the leading-edge)
using different numbers of panels for a square wing near the
centre of the wing. The LE is at x=0 and the TE is at x=1.

Increasing the number of panels just moves the kink closer to
the LE, but does not eliminate it. The situation is worse
for curved wings, and much worse as we approach the wing tip.

The "kink" does not have much effect on the lift because that
is calculated by integration, and integration is a smoothing
operator. It does, however, matter for calculation of the LE
singularity and this is important in estimating the induced
drag of planar wings. We are also interested in the rate of
vorticity production approaching the wing tips (and corners
of rectangular wings) because this also has a bearing on
induced drag and other quantities.

There are remedies for the deficiency, but they are not always
appreciated. In fact, mathematicians are not appreciated these
days. (I nearly cried then, but I managed to hold it in.)

 

I'm a dumby when it comes to VLM etc. But isn't this the same thing as a patch test and singularity found in FEA? Since what you're describing sounds like the same problems one finds in FEA. But assuming that the FEA has elements that "work correctly", i.e. passes the patch test, then the analyst just needs to recognise where the errors might creep in, from such irregularities (from a singularity) which are not always so easy to over come.

 

A VLM solution is a global superposition of vortex filaments which have strongly singular ( ~ 1/r ) velocity fields. It's like having one finite element on the whole domain (h=1), but one which has a very complex geometry (the whole wing or airplane), with hundreds or thousands of highly-singular basis functions (p=1000 or more). You can't define an FEA-style patch test for a general VLM case, since there's no known exact solution to compare to. About the only thing that can be done is grid-refinement studies on very simple geometries which happen to have effectively-exact solutions from other sources.

 

Mark

Thanks for the explanation, make sense now. If there is no known exact solution, I see where the issues arise.

Would it therefore come down to, an “acceptable” level of tolerance? Since using simple geometry for verification is then asking too much once beyond such limitations of “exact” solutions.

 

Well put. I thought AdHoc was referring to some accuracy test on a single panel.

That's why the circular wing is important - it's the only known planform for which exact solutions can be constructed.

VLM and panel methods don't seem capable of estimating the wingtip
singularity strength. They incorrectly give a strength of zero at the wingtip
when it is actually about 0.46 in Jordan's and Boersma's solution.
Furthermore, their behaviour as the wingtip is approached is wrong. They
show the strength rising to a maximum inboard of the tip and then dropping
rapidly to zero. The correct behaviour is that the strength increases to a
finite value at the tip and the slope of the strength is infinite.

I doubt anyone is really nerdy enough to try it, but the problem
is to find the coefficients in the behaviour of the circulation
given by:
Gamma(y) = A*sqrt(y) + B*y*log(y) - C*y + ...

Jordan gives A=3.186 and B = -0.2819.
Hauptman and Miloh claimed their solution was exact with
A=2.813 and B = -0.497, but they finally admitted that their
wing was twisted at the tips to satisfy the Kutta condition.
Standingford's panel method gives A = 3.21 and B = -0.58.
VLM is unlikley to get anywhere close to those values.

 

Arvel Gentry describes his "bathtub" experiment (paper attached, point 7) to demonstrate circulation. Not shure if this is related to what Mikko calls a possible "physical connection between molecules communicating via vorticity". My own vague idea about circulation was about a mathematical artifact to explain something complex in a more simple way, but this experiment confused me a little...

 

Good question. In the sentence above I was referring to the singularity which occurs in the "exact" solution to incompressible and subsonic potential flow around a sharp corner. (Actually, the flow only needs to be invisicid, not potential, for the singularity to occur but for the present discussion that is not an important distinction.) I'm not familar with terminology used in FEA circles but it sounds like it would be called a basic singularity. Potential flow around a 180 degree corner such as the leading edge of a flat plate at an angle of attack will have a singularity with the velocity proportional to the inverse of the square root of the distance from the edge.

Another use of the term "singularity" in aerodynamics is in reference to fundamental solutions such as sources, dipoles, vortices (point in 2D, filament in 3D), etc. Panel methods, vortex lattice methods, and related methods represent the flow as a distribution of these singularities on the boundary with the strength of the singularities determined during the solution process. The flow properties at desired locations can then be found as intergrals of the singularity distributions. Such methods are a sub-set of or related to Boundary Element Methods, depending on choice of terminology. This is a fundamentally different approach than that of Finite Element Methods, Finite Difference Methods and Finite Volume Methods in which the entire flow field is discretized and determined during the solution process.

 

Presumably you mean your velocity relative to the sailboat is the apparent wind velocity relative to the sailboat. That would be the same as flying relative to the earth at the velocity of the wind. In other words flying so that the air and you are moving at the same velocity, ie the apparent wind speed relative to you is zero. Perhaps it would better to be suspended from a ballon drifting with the wind since airplanes don't fly well at zero airspeed.

As the boat passes by you will feel a disturbance of the air. In aerodynamic terms some of what you feel will be the portion of the flow field that is due to lift generation (assuming that lift is being generated), and the remainder of the flow field which will be due to other factors including displacement of the air by the the boat. You won't be able to determine how much of disturbance velocity is caused by lift without measurement and analysis.

Another example of the same phenomena has been felt by anybody who has stood by the side of the road on a calm day while trucks are passing by. The disturbance flow field can be felt and observed if there is dust on the ground.

Or consider going to the local airport and standing on the runway while an aircraft makes a low pass and misses you by a few feet. In that case you will feel a disturbance flow field, part of which will be due to the lift of the wing, part due to the propeller, and part due to displacment of the air by the finite size of the aircraft. http://www.youtube.com/watch?v=8qRkSKwJpKo