Swept Volume Theory

Discussion in 'Hydrodynamics and Aerodynamics' started by Sailor Al, Aug 2, 2022.

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Sailor AlSenior Member

I don't think so. Babinsky's video doesn't show it, my observations don't show it, Bernoulli worked with water.

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Doug HalseySenior Member

Let's not complicate things by discussing rotors, windmills, flapping wings or other unsteady flows. I haven't been able to find measured flowfield data for simple cases, possibly because it's expensive to test and usually not considered necessary because the computations are usually pretty good.

There are some papers with results for airfoils with simulated ice on the leading edges. These complicate the situation by having large separated areas behind the ice, but they clearly show higher speeds going above the ice. Unfortunately they don't show the measured flows without the ice or the flow below the airfoil. (I've attached a pdf of the paper this figure came from.)

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Doug HalseySenior Member

Because the pressure has a minimum (i.e. speed is maximum) somewhere on the upper surface, it has to decelerate aft of the point, until at the trailing edge, the speeds are the same above & below.

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Doug HalseySenior Member

I can possibly find comparisons of the same airfoil tested in both air and water. Would you expect the results to be much different?

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Sailor AlSenior Member

I agree, I was responding to your rather open question. I certainly wasn't talking about flapping wings or other unsteady flows.
I can't believe you would expect me to respond to that. It has absolutely nothing to do with the issue at hand.
Well, until you can I think you have start to doubt your confidence on the matter. It wouldn't be the first time in history that a widely held perception was wrong.
After all you, yourself stated "On average, the speed is higher than on the windward side. That's all that matters."
I agree, that is all that matters.
It's a cracked record but:
Babinsky's video doesn't show it, my observations don't show it, Bernoulli worked with water.

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Doug HalseySenior Member

I have no doubts about the validity of Bernoulli's equation in both air & water, or the general feature of flows above & below airfoils. My doubts are only what published data is available to see.

For what it's worth though, I can write a flow solver without making use of the pressure or Bernoulli's equation at all, but I can't write one that doesn't involve the velocities.

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Doug HalseySenior Member

Comparing results in air and water certainly is relevant. If you're claiming that Bernoulli's equation works in water but not in air, then they could have the same pressure distributions with different velocity distributions.

Plus, perhaps I can find some cavitation predictions compared to experiments that could be used to prove to you that the speed is higher on the upper surface.

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Sailor AlSenior Member

Yes, I know. And the lack of published data is the issue.
It can't be that expensive or difficult to demonstrate, Babinsky had a really neat setup, there's lots of labs with wind tunnels, smoke generators, smart scientists and engineers. I can't be the first person to challenge the theory.
Doesn't any of that raise any doubts in your mind?
I'm sure you can, but I wonder if you can do it for a gas where PV=RT as opposed to density = constant?
And anyhow would I understand it well enough to check your algorithms?
Cavitation only occurs in a liquid. Air is already a gas, it is already 100% "cavitated" !
[add] Cavitation is caused by low pressure, not accelerated velocity.

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Doug HalseySenior Member

In the theories I'm talking about, the velocities come first. Then they are fed into Bernoulli's equation to give the pressures. Those pressures show good agreement with the experimental data. Why would you suspect that the velocities were wrong, yet they gave the correct pressures?

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Sailor AlSenior Member

If the velocities come first, what is the experimental evidence of the velocities?
That's my question, plain and simple.

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Doug HalseySenior Member

Why do you keep referring to "accelerated velocity
That the pressures computed from them agree with experiments.

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Sailor AlSenior Member

Because that's what Bernoulli's theory requires to generate a pressure difference.
OF COURSE THEY DO!
Since the velocities are computed according to Bernoulli from the measured pressures, of course the pressures can be validated by the computed velocities! OF COURSE THEY DO.
That is the circular argument I identified in #128

The argument fails if the computed velocities differ from measured velocities.

It doesn't help to explain the source of the pressures.

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Doug HalseySenior Member

Bernoulli's equation says nothing about acceleration and it isn't used in computing the velocities in the flow solvers.

It is not a circular argument.

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Sailor AlSenior Member

Of course it is.
Quoting Encyclopaedia Britannica:"Bernoulli's theorem implies, therefore, that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity."
Any increase in velocity is ACCELERATION. v = u + at. You can't get an increased velocity with out acceleration. That's what acceleration means!!!
I was using acceleration as a shortcut for increased fluid velocity. Come on, you can do better than that.
Oh come on! What is not circular about the argument:
"The velocity is calculated by applying Bernoulli to the measured pressure which, when input to Bernoulli, matches the measured pressure"?
You are letting the side down.

If you can't demonstrate an increase in velocity (acceleration) then the argument that the pressure difference is due to increased velocity fails.

It's bizarre that I am having to appeal for counter evidence. If it were so obvious you should be burying me with evidence.

Please take a deep breath. You may be wrong.

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Doug HalseySenior Member

Okay, let's back up to the graph I showed in post #117:

The theory used in this case is explained in great detail in Chapter 3 of Theory of Wing Sections so it should be easy to verify that it doesn't use Bernoulli's equation at all.

The flow regime to which it applies is 2D inviscid incompressible potential flow, for which the relevant flow equations reduce to Laplace's equation - a well-known partial differential equation that is also involved in electrostatics, gravitation, and other fields. The key feature of the theory is that certain exact solutions of Laplace's equation exist (in this case for flow about a circular cross section with specified circulation) and that a particular kind of purely geometric transformation (conformal mapping) can be applied to the exact solutions to get solutions for flows about airfoils of almost any shape. The velocity at any point on or outside the circle can be transformed to get a velocity on or outside the airfoil.

The transformations are such that the flows at large distances from the circle (or airfoil) are not affected, which means that any numerical errors that might be made in the calculations are largest on the airfoil's surface. Away from the airfoil is also the area where the theory ought to be most applicable (being totally outside the viscous boundary layer). If the flow on the surface is accurate, the flow out in the field will be even more accurate, giving little incentive to measure those flows experimentally.

So the theoretical velocity distributions represented by the solid curves in the figure resulted directly from the conformal-mapping process. The axis is labelled "(v/V)^2)" because that was what was actually computed. They are casually referred to as "pressure distributions" because Bernoulli's equation (which is brought into the discussion for the 1st time), in its nondimensional form, is simply Cp = 1-(v/V)^2.

That's what I meant when I said that the velocities came first. The theoretical velocities. The plotted curves represent the results of the calculation. The experimental points are obtained by applying the operation (v/V)^2 = 1-Cp to the raw data of the experiment (not shown). The velocities and the pressures are only trivially different.

It is not a circular argument to make note of the agreement between the curves and the points and to assert that the method used in the calculations would give flowfield values in good agreement with whatever measurements could have been made. I'm sure such data must exist among the mountains of data acquired by the aircraft companies, but I'm not worried that they haven't bothered to post it on the Internet. The theory is solid!

As a footnote, I hope you can see that the upper-surface velocities are higher than the lower-surface ones and that both upper and lower surfaces have areas where the flow is accelerating and areas where it is decelerating. (taking the axis label literally as giving the velocities).

You can always argue that more experimental data would be desirable, and that's fine. But there are hundreds of airfoils designed by similar processes and that perform very much as expected by the calculations. There really is no reason to suspect that there's any fundamental problem that would invalidate all of that experience. The ball is in your court if you claim there's something that's been done wrong and that you have a theory that can do better. So far, I've seen nothing from you that bolsters that claim.

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