Is circulation real?

That's why I use the word "predict". Bernoulli's equation and it's extensions to compressible flow, etc have proven over the last to be a very, very good "model" unless mis-used.

Good to see an applied mathematician reminding us that there is a difference between math models and reality.

 

Exactly, upper, lower and free stream all started off at the same velocity, many chord lengths upstream, and it is only the presence of the foil that has caused a change of velocity over the upper and lower surfaces.

It is a fundamental necessity that:
1. The fluid speed over the upper surface is faster than the fluid speed over the lower surface.

I think it is also necessary (and unavoidable) that:
2. The fluid speed over the upper surface is faster than the free stream fluid speed.

However, there is no requirement that:
3. The fluid speed over the lower surface is slower than free stream fluid speed, (and in many cases this doesn't happen).

The 'circulation' explanation seems to require 3. to be true, otherwise how can the flow on the lower surface be going forward relative to the foil?

 

I have no illusions about what I work with. Whether equations reflect some real situation or not is immaterial

And, yes, Bernouli and its extensions work beautifully, if we ignore turbulence and a host of other phenomena we don't yet know how to handle.
Potential flow is so clean and (usually) tractable, isn't it.

 

Circulation as defined by aerodyamicists does not require the fluid speed over the lower surface to be slower than free stream speed. Positive lift by an unstalled airfoil does require that the average velocity over the top be higher than the average velocity over the bottom, and this results in a positive value of the standard definition of circulation. See daiquiri's post #4 for the standard definition of circulation.

The flow around an airfoil (other than a flat plate) is made up of more than what is sometimes called the circulatory flow. The other portions of the flow may have velocity differences from free stream which are considerably larger in magnitude than those of the the circulatory flow. Overlooking this can lead to erroneous conclusions about the flow around airfoils.

The flow over most of the lower surface does not go forward relative to the airfoil. It may do so around the leading edge, depending on the shape of the leading edge and angle of attack, and the resulting stagnation point location.

Any airfoil will have a location where the flow splits between going over the top of the airfoil and under the bottom. This location is known as the stagnation point. For a 2-D airfoil the velocity will be zero at the stagnation point. For a 3-D wing the velocity along the line on the leading where the flow splits may be greater than zero due to spanwise flow along the leading edge.

The air over the bottom of the airfoil behind the stagnation point may accelerate to higher than free stream velocity depending on combination of the the shape of the airfoil (thickness distribution and camber) and angle of attack.

The air over the top of an airfoil may slow to less than free stream velocity as it approaches the trailing edge. This also depends on the shape of the airfoil and boundary layer effects.

 

Careful, the next stage is the belief that the equations are what matters and reality is unimportant.

Minor disagreement - outside of boundary layers and separated flow Bernoulli, properly applied, is very accurate for external aerodynamics unless the scale and magnitude of the free stream turbulence is very large. Potential flow is sufficient but not necessary.

 

Hi David,

That's a very clear and concise description, and I agree with it. But the videos linked in post 63 show the air flow on the under side *is* forward relative to the foil, as indeed it would have to be to satisfy a 'circular' flow description. Which is why I struggle to see how this video (of a computer simulation), or the circulation model in general, can be an accurate description of the flow on the lower side of the foil.

Which is not to say it is wrong, but I don't get it. I had always understood that the circulation model bascially says that you superimpose circular flow onto the straight and parallel undistrubed flow, to obtain the flow around the foil. And this is what the videos appear to show. But I can not see how this is a true representation of flow underneath the foil. Please enlighten me!

 

The videos linked in post #61 and quoted in post #63 are
http://youtu.be/j_J8kNodgBQ
http://youtu.be/rLuJYHdWBJ8

The titles of the videos are incorrect. The curves in the videos are not the pathlines of particles as seen by an observer traveling at the free stream velocity. Rather the curves are the streamlines as seen by an observer traveling at the free stream velocity at the instant the airfoil is in the position shown. The particle pathlines as seen by the observer at free stream velocity would be considerably different.

These videos are based on the flow field around the airfoil with the steady, uniform freestream subtracted which is sometimes refered to as the perturbation flow field. That flow field is the same as what an observer traveling at the same velocity as the freestream velocity would sense at the instant the airfoil is in the position shown.

Pathlines and streamlines do no coincide in general unless the flow is steady. Seen by an observer traveling at the same velocity as the airfoil the flow is steady and the pathlines and streamlines coincide. Seen by an observer traveling at free stream velocity the flow is unsteady (varies with time) and the pathlines and streamlines do not coincide. There is a good discussion (at the time of this post) of streamlines, pathlines and streaklines and an animation showing the difference between them at http://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlines

Back to the animations. Confusing streamlines, particle paths and streakline for unsteady flow is a common mistake, even among aerodynamiscists. Aerodynamicists most commonly work with situations and reference frames where the flow is steady so it is understandable that the significant differences which arise with unsteady flow can be forgotten.

 

But the equations, once specified, are all that is important.

No argument there, David, if you accept the fluid as a continuum, which it isn't.

 

What you see in these videos is the result of a mathematical operation on a velocity field around the airfoil. If we call V the velocity vector in any point of a fluid domain around the airfoil, and Vx the uniform horizontal freestream velocity, what you see in those videos is the result of the following mathematical operation:
V - Vx.
In other words, what you see in the videos are simply the velocity vectors (created by the presence of the airfoil), which are obtained by subtracting the uniform freestream velocity from the actual velocity field around the airfoil.

You can get a grasp of the physical meaning of the depicted flow field by imagining the airfoil placed in a wind tunnel with glass walls. You are standing on a movable platform on the other side of the glass, and the platform is moving at exactly the speed Vx. From that position, you would see the flow field inside the wind tunnel perform that odd circular movement as the airfoil is passing in front of your eyes.

Cheers

 

That's what puzzles me about the "reality" of the circulation. You can "see" the
circulation" if you subtract off the free-stream velocity. But you can't
have that circulation in the first place without that free-stream velocity.

 

I agree with the "V-Vx" description of the basis of the flow field shown in the videos.

I would not describe curved lines which start from points and grow with time as simply the velocity vectors (created by the presence of the airfoil), which are obtained by subtracting the uniform freestream velocity from the actual velocity field around the airfoil. What is shown are streamlines, not vectors, and each streamline is tangential to the "V - Vx" velocity vectors along its length at a single instant in time.

If by seeing the flow field you mean by some means being able to see the motion of individual small particles (or "elements") of the fuild , then the videos do not show what you would see in time. You would see pathlines of the particles which are different than the streamlines shown.

I suspect this error of showing the streamlines, which are instantaneous, of the "V-VX" flow field, and labeling them as the pathlines, which are the time history of fluid particle trajectories, has occured many times over the last century. It may be a major contributor to confusion about circulation.

 

Bernoulli's equation has proven experimentally to be very accurate for external aerodynamics unless the scale and magnitude of the free stream turbulence is very large. No need for "accept the fluid as a continuum, which it isn't" unless you mean to preclude rarified gas dynamics which are irrelevant to the current discussion, unless somebody is interested in deep space exploration by sailing on the "solar wind".

The equations of classical fluid mechanics can be derived without invoking any continuum assumptions by starting with a statisctical description of the molecular motion, and then using "velocity, density, temperature" as the local average values in the same manner used in going from statistical theromodynamics to classical thermodynamics.

 

Until solutions are obtained. Then to the engineer or other user of the results how well the solutions correspond to the reality the equations are claimed to model is important.

But for some "applied mathematicians", not Leo, actual solutions don't seem to be nearly as important as proving theorems and similar.

 

I have to admit that, described in these terms, it does sound funny.

 

Why do you want to preclude Leo's access to this upper mathematical society? Nasty boy.