# Is circulation real?

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

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### Alan CattelliotSenior Member

Well, in a sense, you are right, the model itself of circulation is barly discutable, because mathematician theoricists have paved the way.

The circulation concept is indeed a mathematical tool, used to solve any integral calculations, a trick that a good scholar will learn ages before encounting any physical model. In fact, when doing the maths of basic integral equations, it is obvious that any closed domain of integration can be used, as long as the constitutive equations are conservatives. Which is the case of the Navier-Stokes equations.

Adding to your comment, I must say that the sensibility to initial conditions is not the reason why we are not able to produce results. It's like saying that your porridge is not good because of the oats of your neighbor... An excuse that fit every situation is no excuse at all.

And because we don't like, in general, weak excuses, we develop the amplification theory + the optimal control theory, that cares about initial conditions, building on our own special conditions, inside of which we can work, while managing the propagation of any kind of field value.
There is also a class of differential equations that are not sensitive at all to boundary conditions. Even when the class of equations are non linear and subject to chaos, are we, today, here and now, able to compute any integral value.
For instance, any scientific presentation of the global warming phenomenon will begin by explaining, why, although the governing equations are chaotic, we are able to mathematically extract prediction values of the temperature field.

Wake up, boys ! We made progress since 1967 and the Lorenz's butterfly. This progress may be the reason why you can find recent publications on this old subject, together with the fact that numerical demonstration is more accepted as a proof ( which is discutable, in my opinion, but this is not the subject )
Enlighted with this progress, it seems natural to re-view the subject, and make interpretations converge.

Last edited: May 31, 2022
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### DogCavalrySoy Soylent Green: I can't believe it's not people

Word salad, comparing apples and aardvarks. Me out.

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### Alan CattelliotSenior Member

Sorry to ear that, DogCavalry. I can't leave you like this. The elliptical theory of circulation say it all :
The lift coefficient is mostly equal to 0.11*alpha*Aspect_ratio_coefficient. Best approximation ever, to my opinion !!!!!! You can make everything with that, and besides looking colored pictures or boring maths, it will be useful your whole life.

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### philSweetSenior Member

Things were going along so nicely until this -
This contains a cart before a horse and the beating of a dead horse just for good measure.

In airfoil action, the magnitude of the circulation is determined by the behavior of real fluids. The Kutta condition provides a crutch to ideal fluid models which only then can associate a unique circulation value to each foil geometry and flow combination. As a matter of habit, we choose a Kutta condition that makes the circulation-lift relation simple; and we select foil geometries that make choosing a Kutta condition simple. All in all, a poster child for optimized mediocrity.

With the Magnus effect, we aren't so lucky. Although the sentence doesn't actually say the air being dragged around by the cylinder is part of the circulation, that is certainly how most people interpret it, and that is wrong. It is only the air outside the the captive boundary layer that is considered in terms of circulation. Fluid shear stresses play no part in inducing circulation and don't exist in ideal fluids. It is only the asymmetrical shape of the boundary layer around the rotor that induces circulation. That is again due to real gas phenomena, but there isn't anything akin to the Kutta condition which lets us relate circulation to the Magnus rotor geometry, rotor velocity, and fluid state of this system. While the relationship between circulation, freestream velocity, and lift is valid for a Magnus rotor, it is also pointless because there is no simple way to relate it to geometry, or to scale the results from a tested geometry to account for changes in diameter, rotor speed, freestream speed, or fluid properties. We are nowhere near attaining mediocrity regarding the Magnus effect.

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### Alan CattelliotSenior Member

PhilSweet,

I feel really sorry for the horse also !

Fact is that I only made a snapshot of the beginning of the Wikipedia page that shows nice green picture like those one find in every chapter talking about integral.

For the rest, as You, I feel deeply depressed by such explanations of the Magnus effect. I intentionally do not put the Wikipedia link, because it is not a trustable source in general. Some scientific publications are at another level regarding this subject, basics are always to be kept as rear mirror :
So the circulation concept is not very much understood.
I've been teached the fluid mechanics primarily by the boundary layer theory. My school was aeronautical & space, under direct command of the ministry of defense, and I had the chance to see real time applied supercomputed CFD on real hardcore cases. In real time, in a special amphitheater, we were able to directly connect the field value visualisation, and were able, in a matter of second, to optimize the air intake of the A380 motor from General Electric Motor, jumping from test case to test case. Great experience !

It is interessant to see also the parallel between the circulation theory and the boundary layer theory. Both rest on the prescription of a given initial field. In the case of the circulation, the source distribution. In the case of the boundary layer theory, a surface with a "culot". You can play with them an infinite time to create some specific "real" fluid behaviour. For instance, I can very easily take account into fences on a rudder or wing using a simple lifting line, but zeroing the right terms. I can also force numerically one fluid to stall by imposing a initial partial friction coefficient on a particular zone of a boundary layer code.

Still, I'm bothering....if we can re arrange the flow so easily, is it because there is no unique solution to the Navier Stokes equations ?

As I know, the Millennium challenge has not be conquered for the Navier Stokes equations. So till today, whether circulation , boundary layer, we are bound to make what we can with our tools.

Millennium Problems | Clay Mathematics Institute https://www.claymath.org/millennium-problems

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### philSweetSenior Member

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### Doug HalseySenior Member

You might want to check that "best approximation ever". As written, it says that wings with aspect ratio greater than 1 have larger lift-curve slopes than 2D sections.

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### Alan CattelliotSenior Member

Well... That's will be not the case if Aspect_ratio_coefficient value is between zero and one.
Thanks for the precision.

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### Doug HalseySenior Member

My point is that the equation is wrong. Even between zero & one. (You forgot the denominator)

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### Alan CattelliotSenior Member

In radian or in degree is the angle, again ?
Please find a not so bad as mine definition.

Find it better ?

PS:
I recall
CL = 2 x pi x Angle_of_incidence[rad] x Aspect_ratio_coefficient
= 2 x pi² / 180 x Angle_of_incidence[deg] x Aspect_ratio_coefficient
# 0.1096622711 x Angle_of_incidence[deg] x Aspect_ratio_coefficient
with
Aspect_ratio_coefficient = AR / (AR + 2), with the figure notation.
There is many talk on this single subject of aspect ratio coefficient, because it's a very practical entry point to make any measurement fits with numerical simulation. So, there should be in this forum, experienced users that has many other formulas for this coefficient, some very specific to certain shapes,
What Aspect_ratio_coefficient should we use ?

Last edited: Jun 1, 2022
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### Doug HalseySenior Member

Sorry - I had never heard the expression "Aspect_ratio_coefficient" and was assuming you meant simply "Aspect ratio."

The equations you show are for lifting-line theory. You might be interested to see how those compare to lifting-surface theory:

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### Alan CattelliotSenior Member

You're absolutely right, Doug. Very popular codes are VS_areo, Apame, AVL, PANAIR - the two last have my preference, I should say, because of their very detailed documentation and validation -. Today, I used mainly EF codes, as it is more straightforward to input directly CAD files, but not every time.

For those who are interested, down below is an extract of a code I was using in 2008, when pushing hard a version of the A40, architect B. Nivelt.

For those you would be interested to do something with this code, there is maybe something we could achieve together... I've got lot of ideas... What you have here is a simple surface lifting code that you can use on quad meshed wing.

Code:
% determine surface area and outward pointing normal vectors at control points (assumes counter clockwise around compass by RH rule points out of surface)
ac=0.5*v_cross(r(:,sw)-r(:,ne),r(:,se)-r(:,nw));nc=ac./v_mag(ac);

%determine influence coefficient matrix
npanels=length(rc(1,:));coef=zeros(npanels);
for nn=1:length(bp)
n=bp(nn);
cmn=ffil(rc(:,n),r(:,nw),r(:,sw))+ffil(rc(:,n),r(:,sw),r(:,se))+ffil(rc(:,n),r(:,se),r(:,ne))+ffil(rc(:,n),r(:,ne),r(:,nw));
coef(n,:)=nc(1,n)*cmn(1,:)+nc(2,n)*cmn(2,:)+nc(3,n)*cmn(3,:);
end
for nn=2:length(wp)
n=wp(nn);
coef(n,ea(n))=1;coef(n,we(n))=-1;coef(n,n)=1;
end

%determine result matrix
rm=(-nc(1,:)*vinf(1)-nc(2,:)*vinf(2)-nc(3,:)*vinf(3))';
rm(wp)=0;
coef(end+1,bp)=1;rm(end+1)=0; %prevents singular matrix - sum of panel strengths on closed body is zero
ga=coef\rm;

Last edited: Jun 2, 2022
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### Sailor AlSenior Member

Circulation Theory, developed by Kelvin in 1869 applies to barotropic fluids. Liquids are barotropic, gases are not barotropic. Air is a gas. Circulation Theory does not apply to air and is not relevant to the investigation of the aerodynamic force on a sail. See Aerodynamic force on a sail to see how the force is entirely due to the compressibility of air.

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### Alan CattelliotSenior Member

Well.... I may look a deep further into you "views" ( since there is no real theories in Physics, right ?) .

Still, i'm very surprised by what I am reading at the beginning :

Hi don't get it ? Is there any confusion here between static and dynamic pressure ? Water is rather incompressible in the application of sailing yachts, so can't we generate lift with our daggerboard or keel ?

Compressed air tends to higher their temperature. Do you think (besides the energy loss due to friction drag), that you really ramp up the temperature of the air in front of the sail and cool it down at the trailing edge ? In that case, I won't race against you, your speed on water must be freaky !! Typically, one consider the air incompressible for Mach number under 0.3....

Last edited: Aug 3, 2022
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### patzefranpatzefran

Obviously, you are right ! compressibility is negligible here, he (who ?) should replace "compresses the air" by "slow down the air" and "decompresses the air " by "accelerate the air " to get the right physics.

Looks Nessie is back again !

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