# Is circulation real?

Discussion in 'Hydrodynamics and Aerodynamics' started by Mikko Brummer, Jan 25, 2013.

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### DCockeySenior Member

There is only one type of pressure in fluid. At a molecular level it is due to molecules of the fluid bouncing off of each other or off of a surface. Average the normal force exerted on a flat surface by the impinging molecules and that is the pressure.

With compressibility and gravity included the complete Navier Stokes equations (including viscous effects) and complete Euler equations (neglecting viscous effects) "govern" the flow past an airfoil, the separated flow behind a submerged transom, free surface waves and sound waves (assuming the fluid is sufficiently close to an "ideal" fluid, is not magnetic, etc). Only when the equations are simplified do distinctions need to be made between different flow situations.

The fluid that a sound wave is passing through, whether air, water or anything else, is vibrating which means the fluid is accelerating, though the amplitude of the vibrations may be very small.

But a fluid does not have to be accelerating (above the molecular level) for pressure to exist. Consider a closed container filled with air. The air exerts pressure on the walls container. If the container is connected to a pipe which in turn is connected to another container at lower pressure, air will flow out of the first container and into the second. The air in the pipe will be at lower pressure than in the first container. It accelerates while entering the pipe but the average velocity in the pipe will generally be very close to constant along the length of the pipe.

Acceleration of fluid is required to sustain a pressure gradient in the absence of viscous and gravity (hydrostatic) effects, and vice-versa. The flow over an airfoil has a pressure gradient normal to the surface of the airfoil and this pressure gradient can be directly associated with the curvature of the streamlines. But a surface itself does not have to be curved to produce a pressure gradient. Consider a thin, flat plate in a flow at an angle of attack. There will be pressure gradiants both along the plate's surface and normal to the surface.

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### quequenSenior Member

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### PetrosSenior Member

yes, this is true of course, but the pressure gradient is still generated by the acceleration of mass of the fluid, by curving the flow of that fluid. A flat plate can still accomplish that, it is just not very efficient. In fact, an areodynamacist I used to work with built a home-built aircraft using all flat surfaces, he called it the facetmobile. It flys the same way the F117 stealth fighter works, by bending or accelerating the air over a series of flat panels. So you can sail a boat or even fly and airplane with a flat surface generating the lift.

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### daiquiriEngineering and Design

There are occasions when a flat plate can be very aerodynamically efficient, and obviously your friend did know that.

RC airplanes fly at speeds which typically give Reynolds numbers around 50,000, and up to 100,000 . Unless we talk about racers, which can fly at some 8-10 times that speed (and Re).
At Re of around 60,000 and lower, a thin flat plate will be much more efficient than a common thick and streamlined airfoil, giving grossly 2 times better max. L/D ratio (data from Hoerner's "Fluid Dynamic Lift" - perhaps someone can give better numbers). Things start to change at higher Re, say higher than 100,000 , when a thick, streamlined airfoil become more efficient.

The point which becomes evident here, one more time in this thread, is that everything is relative.

Cheers

5. ### Submarine TomPrevious Member

If you add a step to that low Reynolds number plate, seemingly wonderous things happen, as can be viewed on YouTube by the guy flying his R/C airboat around in the air one summer evening at dusk.

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### PetrosSenior Member

the step is simply a means to entrain a vortex which will give it high stall resistance, it can be done at any Re but the drag penalty becomes very high and it is hardly worth the drag penalty, the cost to operate would be so high it has no practical application. The ultralight aircraft the Kasperwing used a LE flap to trap a large vortex over the wing the same way, allowing the aircraft to parachute straight down in a controlled stall. Not sure it has any practical application, but it was amazing to see a small aircraft fly forward, stall and drop vertically like an elevator, while maintaining control, and than fly out of the fall. But I admit very strange and different things happen at very low Re, that is why insects can fly the way they do.

7. ### Submarine TomPrevious Member

Yahhhh Reynold!

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### 65 NJunior Member

The popularization of science is difficult, especially when the author doesn’t fully understand the subject. Here I refer to the publication that Mikko quoted and its description of air dynamics at molecular level, including pressure and diffusion.

The expression ”two types of pressure impulses” is odd, but there is some truth in it. The pressure on a surface is always purely mechanical as DCockey explained. But there are two types of molecular movenments: the diffuse, random movement of individual molelules that exists always and causes pressure, and collective movements of molecules such as sound waves or wind. The latter ones can be treated by continuum theories.

Pressure in air is due to the kinetic energy of impinging oxygen and nitrogen molecules on surface. The speed of molecules is much higher than the wind velocity, and it depends on temperature: at 20°C the rms velocity is about 500 m/s (well above sound speed) and average speed 460 m/s. The direction of movement is random, but wind gives a small collective extra component. The velocities obey Maxwell-Boltzmann distribution (wide). The speed between collisions is not the speed of sound (as in that article).

The movements of molecules can be called diffusion. The mean free path between collisions is only 66 nanometers, but if you imagine the 0.3 nm molecules as tennis balls, the free path is about 200 m. So the image is quite different from the bouncing balls in that article. In collisions, a molecule can go to different directions, and its movements can be simulated using Random walk theory. So from the point of view of an individual molecule, there is real movement and mass transfer, but not on average, if there were no concentration, pressure, or temperature gradients. All this happens in still air, vortices, laminar flow, boundary layers, and of course inside those elements of continuum in your aerodynamics simulations. And of course, those trajectories in the linked YouTube simulations describe continuum elements, not particles or molecules.

Sound in air is a collective longitudinal vibration of continuum, but still the interactions between molecules are collisions. The molecules and intermolecular distances are several orders of magnitude smaller than the wavelength of sound, therefore there is no need to treat sound in air on molecular level. Likewise, sail aerodynamics is on different scale than molecular movements, and continuum treatment is generally valid.

Mikko Brummer and DCockey like this.
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### 65 NJunior Member

Joakim wrote:
....
"Pressure has no diffusion, but other flow variables like velocity (viscosity), temperature (conductivity) and concentrations do."
...
Expressions like diffusion of temperature, concentration or pressure are somehow odd for me. Those are properties of matter. I can't argue about terminology in aerodynamics, but generally in physics, there is diffusion of matter (e.g. air molecules in a concentration gradient), or diffusion of energy (e.g. diffusion/conduction of heat/ quanta of thermal vibrations in temperature gradient). If you can speak about diffusion of temperature, in my opinion you can speak about diffusion of pressure as well: in air the pressure at constant temperature is proportional to number of molecules/volume, and the pressure gradient is also a concentration gradient, and pressure can change by molecular diffusion.
- This comment is not related to the importance of diffusion in aerodynamics.

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### DCockeySenior Member

65N, thanks for the very good explaination of molecular motion and its relation to pressure. A couple of comments: Saying that "there are two types of molecular movenments" might be interpreted by someone as meaning that the motion of molecules switch between two types of movement. Rather it might be better to say that "molecular motion has two components" followed by "the diffuse, random movement of individual molelules that exists always and causes pressure, and collective movements of molecules such as sound waves or wind" While fluid mechanics considers averages the motion across molecules when talking about the velocity of a fluid in a continuim manner, the higher, random velocities are implicity included in the pressure and temperature of the fluid.

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### PI DesignSenior Member

That's what I've understood to be the case, and accept, but find slightly confusing. Foils have a low pressure, high velocity, upper surface but they do not have to have, in general, a high pressure, low velocity, lower surface relative to the free stream (just relative to the upper surface). As I see it, circulation superimposes a positive velocity on the upper surface, reducing pressure (so far so good), but superimposes a negative velocity on the lower surface, which implies a pressure higher than atmospheric pressure on the lower surface, which isn't necessarily the case.

If you were to run a hydrofoil in waves whose orbital velocity was equal and opposite to the expected calm water circulation around the foil, would you have zero lift?

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### 65 NJunior Member

I would be careful when deducing absolute pressure from velocity when making comparisons. IMO the upper surface and lower surface of a foil and the free flow are in different flow fields, and Bernoulli’s principle is valid within a flow field (originally something like “conservative flow along a streamline”). If those regions all were within same flow field (in Bernoullian sense) then you could not get energy from the field: no lift.
Experts in aerodynamics, please correct if false!
……
65°N

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### DCockeySenior Member

Upper surface and lower surface absolutely are in the same "flow field". Bernoulli's equation applies along a streamline as long as there are no viscous losses (or thermal input). In aerodynamics/hydrodynamics if you follow the streamlines back to upstream "infinity" the pressure and velocity are generally uniform which means that the Bernoulli equation constant is uniform across streamlines. It can also be shown that for potential flows the Bernoulli equation constant is uniform.

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### DCockeySenior Member

Continuation of reply above:

Lift on an airfoil is due to the pressure variation around the airfoil, and lift occurs with the net vertical component of the integration (summation) of the pressure acting on the surface of the airfoil is positive. Usually the discussion about "what causes lift" is actually a disucssion about why the velocity and corresponding pressure variation around an airfoil are such that lift occurs. Bernoulli's equation properly predicts the relationship between velocity and pressure outside of the boundary layer and separated flow. For attached flow the pressure across the boundary layer (normal to the surface) is essentially uniform which means the pressure on the surface is the same as the pressure just outside the boundary layer. So the pressure on the surface can be predicted from the velocity just outside the boundary layer using Bernoulli's equation. If the flow over the airfoil has large scale separation then additional information/assumptions is needed to predict the pressure at the surface within the separation zone.

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### Leo LazauskasSenior Member

Again, beautifully explained, but you should remember that these are just
models. They are not "real" as such. They make all manner of assumptions
in order to make reasonable predictions that engineers can make use of.

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