Swept Volume Theory

In your bubble experiment you move the foil so slowly, that you get stokes flow (or creeping flow), where the inertia forces are negligible. This has nothing to do with the flow around a sail, where the Reynolds-number is higher by a factor of one million. You can see, that the rear stagnation point in your experiment is not on the trailing edge, but on the lee side of the foil. All similarity rules are violated in this experiment.

 

I recorded the video in slo-mo on my phone.
The foil was moving at ~1m/s over around .3 m giving an experimental Re of around 10^4.

According to an unreliable source Stokes Flow occurs when I think that means very much less than 1.
Not a sail's Re I agree, but way out of range for Stokes Flow.

Thanks for that. I can see that I need to provide a lot more information about the experiment.

 

In response to all the feedback received on this and a number of other channels, I have completely reworked and re-published the paper into the form of a thesis.
It is available as a PDF from this location with a link to a video of the experiment of which the following image is a frame and is fully explained in the PDF.


I invite you all to review the paper and look forward to receiving further valuable comments.

 

That video tells a much clearer story than normal.

It shows the air being slowed down by both surfaces (pushed to the right when we're watching from the initial rest frame of the air) with different deceleration rates. The air underneath is decelerated most strongly at the front, to the point that some is forced to go over the top of the wing instead. In the later stages of passing under the wing it is accelerated again instead of being decelerated, and both of these forces in opposite directions are caused by the underside of the wing compressing the air. When looking at the air going over the top, it's decelerated all the way, and may be decelerated more strongly the further back it is, so it's moving most quickly relative to the wing when it's at the front end. This is caused by the wing generating a vacuum over the wing by moving away from the air that's sitting over it. Higher pressure underneath and lower pressure above drives lift directly, while these accelerations and decelerations are just consequences of the generation of the compression and the vacuum rather than drivers of lift.

At the front end we have lift of the wing upwards towards air that's moving faster relative to the wing, but at the back end we have lift of that part of the wing upwards away from the air that's moving faster relative to the wing, and we can see that this faster moving air (faster relative to the wing) at the back is pushing upwards on the wing more strongly than the air over the wing is pushing down on it because the air moves upwards once the wing's out of its way. So it isn't the horizontal speed of the air relative to the wing that tells you how much pressure it's applying to the wing surface. The air under the back of the wing must be denser that the air over the top at the back because it's being squeezed.

 

When this thread started last August I wondered if we were having our legs pulled but as time went on I realised the depth of research and thought you have put into it, culminating in your latest thesis.

I shall study it.

Meanwhile I give you 100% for effort.

 

Bubbles squished, and bubbles stretched. This is excellent. 15 minutes and it’s getting better. Are the bubbles particles or waves? Or something in between?

And how much am I learning about bubbles vs flow?

 

Might this stir the gray matter?

A variational theory of lift | Journal of Fluid Mechanics | Cambridge Core https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/variational-theory-of-lift/A8F0A5954BCE9BD9D42BF34482E9251D

possibly a parallel conversation?
The mysteries of aerodynamic lift https://news.ycombinator.com/item?id=22237528

 

Interesting, but could we use this thread to review/analyse/criticise the issues in the paper ?

 

Having read your paper, I find a number of assertions which appear to be unfounded. One of particular note is, quote:

"The venturi is offered as an example of the link between pressure and flow speed, but its
relevance to air flowing over an aerofoil is at best obscure, when, in a venturi the low
pressure occurs at the throat whereas on an aerofoil, the low pressure region would appear
to occur well downstream of anything resembling the throat of a venturi."

The section I have highlighted in bold is profoundly erroneous. Countless properly conducted experiments have demonstrated that the lowest pressure occurs at or very near the leading edge of the aerofoil, the region which would correspond with the throat of a venturi.

Further, you assert that, quote:

"The sailing literature leaves a gap in the explanation of the source of the pressure difference
which is not filled from the aerodynamics literature.
It is apparent that there is no consensus on the subject and that there is no satisfactory
documented explanation for the source of the pressure difference."

The phenomena of lift and the pressure differential at the root of it has been well understood for around a hundred years (circulation theory). The problem lies in explaining it in laymen's terms, without resorting to calculus.

Regarding your experiment, I like it. It's very clever. It does appear have a flaw though, but I think it can be rectified. More on that later.

Where I have an issue is with your interpretation of the results. The video clearly shows: the upwash ahead of the foil; the high velocity fluid moving upwards and over the leading edge; the low velocity, if not stagnated flow under the leading edge; stagnation of the flow on the upper trailing edge; fluid wrapping around from the lower trailing edge into the stagnated region of the upper trailing edge; some stagnation of the flow in a small region on the top surface immediately behind the leading edge (separation bubble); small bubbles being generated on the top surface near the leading edge, indicating low pressure. These are all things I would expect to see. Given that the experiment shows regions of vastly different fluid velocity and direction, I find it hard to understand your assertion that fluid velocity changes are not required to produce lift. I suspect that if you summed the velocities around the foil and subtracted the free stream velocity, you would probably find a net circulation effect, as described in circulation theory.

Regarding the flaw in the experiment, it would appear from the video and the photo of the apparatus that you have, in effect, a free surface above the foil. What you are modelling is akin to a hydrofoil close to the water surface. The video clearly shows, at one point, the surface wave being generated by the foil. We know that there is a loss of lift for foils close to the water surface, which would imply that the fluid flow is affected in some way. In that case, your experiment is not truly representative of fully immersed flow. I would suggest that you may be able to remedy this by having the top surface of the bubble region bounded in the same way as the lower surface (if I'm understanding your setup correctly).

 

"We know that there is a loss of lift-----"
I was under the impression that a foil working close to the water exhibits more lift due to the ground effect condition.
Perhaps you can support your comments

 

Thank you for your thoughtful review.
I realise that the paragraph on the venturi is unnecessarily contentious and adds nothing to the hypothesis. In the revised May 26 version of the paper I have removed that paragraph without adding or subtracting from the hypothesis. Thank you for the observation.
I will respond to your other points separately.

 

With respect, and having spent a great deal of time and effort exploring circulation theory, which originated with Prandtl, was popularised by Gentry and massacred by Marchaj and many others, I am confident that, whilst circulation theory does claim to explain lift it, does not claim to explain the pressure differences around a sail.
As you are aware, the origin of the pressure differences is the subject of my paper.

 

Thank you, I thought it was a pretty neat experiment too.

 

To be clear, I'm talking about a hydrofoil working close to the water surface (free surface effect), which is different to an airfoil working close to a water or ground surface, or a hydrofoil working close to a ground surface (ground effect).

Here's one study picked at random (there are many) - https://hal.science/hal-03963200/document

Edit: Here is an example of a technology that uses the free surface effect to control the ride height of a foil assisted boat - Hydrofoil Boat Technology | Center Consoles, RIBs, & More | Hysucat https://hysucat.561dev.com/hysucat-hydrofoil-boat-technology/#:~:text=The%20Hysucat's%20efficient%20main%20hydrofoil,boat%20out%20of%20the%20water.

 

The "free surface above the foil" you are referring to is an experimental error.
In that particular video, I started the run before the bubble raft was fully established.
I create the bubble raft by activating the air pump for a few minutes to allow a sufficient number of bubbles to rise under the glass and spread out beyond the boundaries of the glass. I then stop the pump and run the experiment. On this particular run, I started the run before the bubble raft had fully developed to what you describe as the top surface, but is the left side of the glass closest to the tub.
I can assure you that I have performed many runs where there is no evidence of any "wave" forming above the foil.
With a little more experimental experience I could do better.
You suggest that the lower surface is bounded. That is not the case. I think you are referring to the side close to the tub. That is in fact the "top surface". In the photo, the foil carriage (a fancy name for the toy buggy!) is sitting on top of the glass for the photo shoot, to show the foil of the buggy which is normally rather obscured under the glass. It is not in its operational configuration, which is with it rotated around 90° clockwise from the the photo position, with the wheels running on the glass and parallel to the long edge, and the foil extending under the glass .
I have attempted to show a frame from the video appropriately oriented relative to the apparatus:. The wave occurs along the left side of the glass.

My editor has suggested that I make a detailed drawing of the apparatus, and I think she may be right.