Why do flags flutter? 1

[nobog]

- instead of sticking straight out? I would like to understand it better to apply that to a fluid dynamics issue. Any input appreciated, Jim, Minnesota

 

[GregLocock]

So you are claiming that an infinitely thin flag with no pole (just a tensioned forward edge) would not flutter?



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[saksmito]

I´m an engineer. I´ve never seen that.

 

[rb1957]

think maybe about the fore-sail on a boat, with the boat head-to-wind ...

 

[saksmito]

Would like to apologize for the bad temper of the answer before.
Of course the material matters. Air has viscosity, and any surface will produce a vortex. The question is that regardless of the material this vortex is created within the leading edge of the flag. If you had a wooden mast and a flag made of a material that couldn´t generate any vortex you would have fluttering.
The opposite case, a flag with the leading edge extremely thin and with no rugosity, and a normal flag attached to it would probably produce two different vortex streets not related at all. Downwater you would have different conditions depending on the material, size, etc. and may you have another VKVS generated by the flag, but the reason why flags flutter is because of the mast.
You can see this in the period of the oscillations of the flag with a thick and a thin mast and the same fabric for the flag.

 

[rb1957]

i thought you were questioning greg's proposition of a flag without a mast

 

[GregLocock]

The point I was making was that there may be more than one mechanism that generates flutter. A Karman vortex street generated by the flagpole is certainly a possibility, but the mechanism proposed earlier, where psoitive feedback causes a ripple, needs no flagpole. I'm not saying either is right, I suspect both are contributors.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MadProf]

Hi Greg, Saskimoto, Nobog, Rb1957;
Some responses to offer:
1. Greg is correct. There are many mechanisms and they operate on a variety of scales.
2. Saskimoto's vortex street operates on a macro scale, but I hold it to be a bit superficial. It's a mechanism that can cause the flag to flutter, but Vortex streets and indeed vortices themselves don't merely exist. They are caused.
3. Obviously, the presence of a body in a fluid mass flow will do this.
4. Its bulk is just as obviously a cause, if it possesses bulk, because the fluid mass is displaced and this remains true even at very low RE numbers in purely laminar flow conditions.
5. But when it doesn't have bulk, vortices are still produced. The flag could have absolutely no thickness whatsoever, yet it would still flutter. If its leading edge did NOT oscillate, it would still flutter.
6. Eliminate every large scale cause from the equation and the flag would still flutter. Eliminate the mast; eliminate the leading edge thickness; eliminate whatever you like. It hardly matters.
7. When you have an entity in a fluid mass flow, the fluid's viscosity plays a role. There is adhesion to the body. At the skin of the body, the velocity of the fluid is virtually that of the body and progressively approaches that of the fluid mass flow with increasing distance from the body's surface until, at a given distance, it matches that of the greater volume of the fluid mass. Between these two "altitudes", the velocity of the fluid mass is somewhere in-between that of the body and that of the greater fluid mass. This zone is the Boundary Layer and within it, the relative velocity of the fluid mass obeys the inverse square law as a function of the distance from the body's skin.
8. The very presence of the body in a fluid mass flow MUST change the velocity of the fluid close to itself and it DOES. Two mechanisms operate here.
9. The first mechanism is Bernoulli Effect. Change in velocity causes change in pressure perpendicular to the flow. That causes curvature of the flow and cannot fail to set up oscillations and vortices.
10. The second mechanism is on the micro scale. Tolmien-Schlichting Waves are generated in the boundary layer and are responsible for boundary layer growth. In an expanded boundary layer, vortices WILL occur and increase in magnitude downstream - which they DO. Although there is no officially recognised cause known for these TS Waves, I can tell you all with authority that THE CAUSE IS MOLECULAR SHEAR, according to my own choice of terminology. I claim the right to that terminological liberty, because I claim its discovery and as a result, the body of knowledge in this field has been EXPANDED.
11. Vortex streets are small potatoes. They're the product of other causalities.
Cheers, everyone!

 

[saksmito]

Madprof.
I´m talking about the flag fluttering, not the nature of turbulences (I thought this was the question).
On the other side.
If you want to demonstrate that viscosity is the responsible for turbulences I think that you are late (unless you are Prandtl or Glauert by night).
Congrats for the discovery. Please, tell us when you get the Nobel. We´ll all be there with flags and no masts fluttering in the wind. DD

Cheers.

 

[MadProf]

Hi Saskimoto,
The natures of turbulences are underpinned by causes. Turbulences cause the flag to flutter, obviously enough. Ipso facto, whatever causes turbulence also causes the flag to flutter. Merely a different depth of analysis applied to the phenomenon.
Prandtl's and Glauert's work should hardly need to be re-demonstrated, though it surprised me a little that something so critical to the whole question's body of answers would be in any way refuted in favour of the vortex street phenomenon: a causality factor, certainly - but itself a secondary cause-and-effect-combined at best, which itself has more basic and fundamental causalities, that actually take place at molecular level within the boundary layer.
Collectively, have we not all been aiming after the nitty-gritty causalities of flag flutter?
The discovery of Molecular Shear might hardly be enough to win a PhD - far less a Nobel Prize, but thanks for the vote of confidence. In a limited range of applications which unfortunately cannot include flags, perhaps I may cut-and-paste your confidence vote to my work on attenuating Tolmien-Schlichting Waves in the boundary layer? Realising that TS Waves cannot be eliminated because they're intrinsic to the boundary layer phenomenon, I nevertheless have something that will reduce their effect quite considerably - more so, I believe, than 3M's Micro Riblet contact sheet. Micro Riblet is known to reduce drag by about 7% through direct passive containment of vortex growth. My concept achieves something very similar, but through the active elimination of progressive wave amplification, instead. It's a different approach, tackling the phenomenon at a different level by different means. The two are not incompatible, either. They can be used in conjunction with each other, possibly yielding overall drag reductions of up to 20%, optimistically.
In the meantime, I've been studying an altogether different set of interrelated phenomena for almost four years now - those of Gravity, Unified Field, Over-Unity, Scalar Energy, the Zero Point Field and Spacetime. This links with the work of Nikola Tesla, James Clerk Maxwell, J.J. Searle, Thomas Townsend-Brown, Werner Von Braun, Faraday, Beifeld, Poynting and Einstein.
As was the case with TS Waves, in-depth study led to invention/design and also more recently to development of my own theory concerning these things - Gravity and its direct causality in particular. I believe I have the answer to the cause of Gravity at the level of the relationship between Baryons and Leptons, though this is presently unproven.
The theory is in its early stages of evolution presently, but looks good and is now progressing more rapidly than I can test experimentally. If the theory proves correct and the prototype I will commence constructing early next year tests successfully, both the PhD and the Nobel will be in the bag, plus a lot more. There should be far-reaching implications in the Quantum and Cosmic realms, plus much more. And one should not ignore the possibility that the speed of gravity may actually be the speed of light squared.
Furthermore, IF I am correct in any reasonable measure and the prototype works as expected, Mankind will have its "Next Wheel". A primitive one, but a Gravitron, nevertheless.
Now, this is entirely outside the scope of aerodynamic engineering.
So is the question, "What causes Gravity?" though I'd welcome attempts to answer it other than, "Oh, come on! Everybody KNOWS that Mass causes Gravity - right?"
Because IF I am right - then "everybody" is very wrong.
Cheers, all!

 

[pja]

I think one of the the basic questions here is whether or not the oscillation of the flag is fundamentally a forced oscillation or self-excited instability. If it is the former than the flag should be fluttering with a frequency near one of the fluid frequencies. For example if it is due to vortex streets generated from the flag pole then the frequency of oscillation should be near that of the shedding frequency of the vortex street and would be a function of the geometry of the pole. If it is due to a self-excited instability, as in a true flutter problem, then the oscillation of the flag would be near that of the first couple modes of the flag, ie quite low.

These things could probably be checked fairly simply by going out and measuring the frequency of oscillation, approximating the wind speed and measuring the geometry of the pole.

I have a paper due on Thurs though so I don't have time now... : )

 

[MadProf]

Oh, just one other thing regarding vortices shed by a mast. Yes, they'll determine periodicity of the dominant flutterings in the flag, but conditional upon the Reynolds Number (flow condition) operating about the mast. The biggest amplitudes are produced at relatively low RE numbers in the rough order of 500, where the flow is "Turbulent Laminar". The vortices are big, rhythmical and geometric, while the point of flow stagnation on the mast's leading surface correspondingly cycles from left to right.
When the RE < 50 and the flow condition is "Laminar", the flag must generate most of its own vortices and flutter, because the mast will not shed any significant turbulence at all.
When the flow condition is in the other extreme - say RE > 1,000,000 and "Turbulent Separation" is occurring about the mast, the amplitude and periodicity of ripples in the flag are very different: being very much less and very much shorter. They're also far more complex, reflecting the flag's presence in the mast's totally chaotic turbulent wake.
It's interesting that the flag operates as a very good visual downstream indicator of the Reynolds flow condition about the mast.
But there is another consideration. The flag is a second entity in the same stream, but may well behave as though it were very much a contiguous part of the mast in some respects. In cases of "Laminar Separation" and "Turbulent Separation", the flag may be either partially or fully in the shredded wake of the mast. It is possible that at some wind velocities, "Turbulent Reattachment" of the mast's shed boundary layer may occur at the flag's surface. It would again show such a thing visually with very small ripples of short periodicity upstream, but with larger ripples of longer periodicity in the trailing part of its length.

 

[MadProf]

Thanks PJA!
Good observation!

 

[GregLocock]

Three points, in decreasing order of banality

1) The flag starts off drooped, ie in a somewhat chaotic geometry. It seems to me that expecting something that starts off with an ill defined geometry is unlikely to attain a nice rectangular shape under the influence of an unstable set of forces.

2) Real world winds vary in direction and strength, contnuously. Around here I'd guess that the variation in strength is around 30% over the course of 5 minutes, and the wind direction changes by 20 or 30 degrees in the same timeframe.

3) If the flag is limp then the only way that forces can be transmitted are in the local plane of the material, ie membrane forces with no bending. A flag that is streaming perfectly is not in stable equilibrium, as soon as the free upper corner moves out of plane it will start to descend. As it does so a pleat forms, which will create lift. This tends to move the material back up into plane, but will inevitably do so a bit too much, in an underdamped system. So as the upper free corner returns to position it will have an upward velocity. This will then create tension pleats in the material, which create a downward lift. And so it goes.

If we put the flagpole horizontally it is possible for the flag to assume a somewhat stable shape. Do you think the free corners will point up - because they locally develop more lift than local weight, or down, because they don't generate enough lift, or horizontal? Will they flutter around a stable position, or just sit there, or does this stable shape never form in practice? Obviously it can if the material is sufficiently stiff.

So, my prediction is that the flutter pattern will be dependent on g, and Et^4, as well as all the usual suspects.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MadProf]

Yes, in the real system where there are so many variables and different mechanisms operating, the influence of gravity as Greg indicates cannot be ignored and neither can the vortex street per RB1957 & Saskimoto be dismissed.
And streaming the flag in the horizontal plane should produce interesting behaviour to compare with the vertical. In either plane, transverse and diagonal ripples in the flag are certainly another consideration.
Something has just occurred to me here, where the corners of the flag at the trailing edge are concerned. I haven't examined it in detail yet, but I'll resort to geometry for a moment in pointing this out.
1. Mark a midway point between top and bottom of the flag on its leading edge.
2. Use that point as the origin of a series of concentric circular arcs described across the fabric of the flag.
3. Make the radial increments small enough to isolate each of the corners in its own arc radius.
4. Now do the same, using the top and bottom corners of the flag's leading edge as the origins of two similar sets of arcs, increasing by the same increments.

Do they tell us anything about the role of the trailing edge corners? I think they might.

 

[MadProf]

Oh, and apologies to all for throwing in a change-of-subject and non-related question.
Greg's pointing out 731-376 is noted.
It wasn't intended to corrupt the thread, but purely in response to the Nobel Prize reference. Whether I'll put the question to the forum in a different category remains undecided, yet.

 

[MadProf]

If I can take us back to the vortex street phenomenon one more time, there is something to remark concerning the alternating nature of the vortices that would shed from a mast at an RE of about 500.
Assuming dead-steady wind of a velocity that would create the particular flow condition called "Turbulent Laminar", what actually causes the asymmetry in flow that sets up the vortical pattern?
Obviously, some condition within the boundary layer must generate that - otherwise the flow either side of the mast would simply meet downstream of it with equal pressure and cancel, exactly per the "Laminar" flow condition. Presto! No vortices shed by the mast!
But this is Turbulent Laminar flow, brought on by a higher wind velocity than would cause the purely Laminar condition, so what is the mechanism operating that cycles the downstream flow into a vortex street in this particular way?
I think that it only takes a very small asynchronous perturbation in the flow to trigger it and the flow volume/velocity/density equation in turn supplies the amplification and determines the periodicity (in its relationship to the thickness of the mast and consequent measure of flow displacement) in a naturally elastic system.
I strongly suspect that Molecular Shear around the mast may be responsible for that asymmetry at grass roots level - in other words, the TS Wave phenomenon.
Also, there would be comparatively little tension in the fabric of the flag, since the vortices impress a very slowly moving boundary layer upon the fabric, due to "upstream" direction of helical flow at the periphery of each vortex where it is in contact with the flag, as opposed to the downstream flow direction farthest from the flag on the opposite side of each vortex.
I think of it as a kind of "false boundary layer condition" imposed upon the flag by the mast, transmitted by the vortices it sheds.
Therefore, in the presence of the mast, the flag's behaviour would be rather languid compared with its behaviour in an air mass flow of the same velocity without the mast being there to disturb the flow from upstream.
And molecular shear at the flag's surface itself would play almost no significant part, since it is highly dependent upon flow velocity to produce the laminar tearing effect in sufficient strength. About the mast itself, this tearing effect would be significantly stronger.
Another thing of interest is the manner in which the vortices dissipate themselves in the downstream wake.

 

[MadProf]

I overlooked one other thing to mention where the vortex street is concerned.
There is a flow condition of the Turbulent Laminar kind where the vortices do not alternate, but occur in pairs downstream from the mast. The RE number applicable is higher than that of a purely Laminar flow, but lower than that of the Turbulent Laminar with alternating vortices.
There is enough low pressure behind the mast to curve the flow sufficiently to set up the vortices by drawing flow from either side into an upstream direction to fill the void created by the mast, but not enough to force the vortices to alternate. Several factors appear to contribute to this condition: velocity change and consequent pressure variation is sufficient to curve the flow enough, but velocity is insufficient to generate vortices of a larger diameter - ones big enough to interfere directly with one another in the mast's wake. These vortices can be seen to be of a diameter of less than half the mast's thickness, where the alternating vortices are about twice that diameter, approaching the full thickness of the mast in diameter.
Asymmetry, on the assumption of a TS Wave origin is not forced, presumably due to lack of molecular shear in that relatively low airflow velocity range. So there is insufficient disturbing energy to vary the pressure differential from one side to the other and so set the vortices to alternating with each other.
And the flag's behaviour in this stream?
Very, very languid, I would say; and the huge vortex street ripples of the alternating street would have to be altogether absent.