What is the mathematical model behind the Coanda Effect?

[jfierro]

Hello everyone!

We have a physics project at school for which we can choice the subject... my teammates and I have decided to make a 'flying saucer' exploiting the Coanda effect. Although this project seems to be fairly popular, we have been unable to find a good technical explanation of the Coanda effect, we are specially looking for a mathematical model... we've been trying to find this kind of information to no avail, which has led us to believe that there is no such thing as a Coanda model but it is rather a combination of other models involving Vector fields and Viscosity.

Sorry for this long writting for such a trivial question, but I wanted some of you experienced people to emphasize a little more with our science quest , so, do you know of any good source, book, abstract, etc. that contains a model of the coanda effect, or that explains it a lil bit more mathematically?

Your help will be very much appreciatd!

 

[Terry Day]

The "state of the art" re Coanda Effect is found in the book "APPLICATIONS OF CIRCULATION CONTROL TECHNOLOGY" published by American Institute of Aeronautics and Astronautics. ISBN 1-56347-789-0. Get it through Amazons. In there you will find all you can digest on the subject. The chapters of the book are based on presentations at the NASA, ONR, 2004 Circulation Control workshop in Hampton, Virginia. The workshop proceedings can also be downloaded. here are the links. http://hdl.handle.net/2002/15755 and
http://hdl.handle.net/2002/15756 A failure just now to upload two attachments( probably too big) means you will have to go to my website www.newfluidtechnology.com[/URL] Go to[U] "Lift and the Coanda Effect"[/U] and [U]"Chanins thesis"[/U] Lift and the Coanda Effect is 100% non mathematical aimed at decision makers but I'm sure you will be surprised. Chanins thesis involves [U]Wind turbine[/U] work done in the NASA Ames 40 X 80 feet wind tunnel on the Coanda form of [U]Circulation Control (CC)[/U].

In the book APPLICATIONS OF CIRCULATION CONTROL TECHNOLOGIES, Chapter 3 page 85 V, describes the work done by Office of Naval Research (ONR) on the "circular wing" (CC.Disc). Page 100, "Conclusions" Quote, "The successful omnidirectional demonstrations of the CC-disc suggest future application to very maneuverable low AR vehicles or to appendages. It is helpful to know that analysis of the low AR investigations determined that there are no basic effects unique to wing lift developed by means of the Coanda form of CC, as compared to the classical lift development approaches."

There is a short video of a disc hovering in ground effect on my website. The explanation is given in the above book in my own chapter, 24.

So all you need to know to build your "flying saucer" is available to you. You can get it above ground effect and if you run into trouble re yaw control get in touch with me.

Terry Day

 

[Phrak]

...which has led us to believe that there is no such thing as a Coanda model but it is rather a combination of other models involving Vector fields and Viscosity.

It's called an 'effect' because it is an observed phenomena, rather than something that explains why. So you are right in that it's explained by other models.

Wikipedia, http://en.wikipedia.org/wiki/Coanda_effect" has something on cause.

It's not a very satisfying answer in my opinion. A good answer would make evident, for instance, how a detached airflow over a wing section in stall, should reattach as the angle of attack were decreased.

 

[rcgldr]

Assuming skin friction isn't a significant factor, isn't part of Coanda effect due to the fact if the fluid or gas didn't follow a convex surface a void would be developed (what I called void abhorence theory towards the end of this thread (I found 2 other sources for using void). So the main issue is if the fluid or gas follows this surface smoothly enough (it's never truly laminar except at relatively slow speeds) to generate lift without a lot of drag penalty.

https://www.physicsforums.com/showthread.php?t=237423

It's my understanding that the first diagram at:

http://www.aviation-history.com/theory/lam-flow.htm

is exaggerated, but an accurate model of wings in the real world (full scale aircraft at reasonable speeds as opposed to tiny wings at slow speeds). Even though it's turbulent, the air will still follow a convex surface. I would assume that the speed of the air in those mini vortices represents an increase in kinetic energy, but at the same time, the faster air speed also translates into lower pressure, so less angle of attack would be needed, and I'm not sure how overall efficiency is affected.

For the boundary layer streamline, it's sometimes better to trip up the air into turbulent flow and control it since it happens anyway. For gliders, oil flow testing is done to see where the air flow detaches, transitions from laminar into turbulent flow, then reattaches:

http://www.standardcirrus.org/Turbulators.html

I'm trying to figure out how all this plays into Coanda effect.

 

[jfierro]

Thank you all for your promplty replies.
I will look trhough all this documentation and will try to come up with some ideas, Terry, thank you for your support, I will ask you if i get in trouble :)

 

[ccrummer]

Dear jfierro,

Phrak makes a good point about the Coanda effect. I have a paper on ArXiV that may help in your study: http://arxiv.org/abs/nlin.CD/0507032 . The Coanda effect, the seeming attraction of a smoke stream in a wind tunnel to a surface curving away from the flow, is caused by a pressure at the surface that is below the free-stream pressure. (This is a no-brainer.) This pressure difference could not exist if the air had no viscosity. Check out the work of Marco Colombini at the University of Genoa in Italy. Beware the usual mathematical models that assume zero viscosity and "steady" flow. Study a good book on Fluid Dynamics, like Landau and Lifgarbagez. This stuff isn't easy but there are some easy experiments that will make you think. Good luck.