Dynamics of fluids

As it is mentioned somewhere in another thread that I've posted, I am doing an experiment that investigates keel shapes for the one with the least water drag.
This experiment being done, I am now working on analysing the data obtained. I have gotten to the part where dynamics of fluids has to be taken into acount to explain how the water runs along the keels.
I would be greatful if someone had any [good] URL that would help me in my work.

Thank you in advance

Pierre Badin

 

Don't know about urls but there are some specialised software manufacturers out there that design software just for this type of work. I think something like Star CD.

 

Have a look at
http://www.vacantisw.com/

Leave a message, David is a good person to ask about this, they have done a lot of work with their foils and wings analysis software.

 

Thanks for the help, but I'm more looking at a theory website rather than for a program doing the calculation for me.
To explain a bit better what I'm looking for: I need to explain how come the results have come up this way, therefore, why did the water run along the keel this way, and not another, and how come this keel drags more than this one.

Thank you

PB

 

The flow around a keel is pretty much the same as the flow around a wing, so maybe you'll be able to find something if you Google with these words: airfoils, downwash, lift, drag.
BTW: Dave Vacanti has written some good articles on the subject. You can find them on his website.

 

D. j .PIERROT
Are you talking about displacement hulls, Planing surfaces or simply fully submerged objects. If I knew which one maybe I can help you with some simplified theory and algorithims. John David

 

The keels that I'm investigating are fully submerged. Only the hull (which is constant for all) is partially immerged

 

DJ, Since the keels are attatched to the hull, of course the hull portion of drag is comon to all and in theory can be subtracted out.However this only provides information on the differential drag of the different keel designs compared to the baseline configuration.I think this is difficult since you will probably be subtracting two large numbers looking for a small differential. Ignoring this potential difficulty for now, fully submerged drag has two components form (or pressure) drag and skin friction drag. The former comes from the underwater body, "pushing' on the water as it moves through.The velocity of the stream is converted to pressure on the "nose" of the body.
The pressure acts on the body to produce a drag force.Water flowing at a velocity, V,
has the potential of generating a pressure of 1/2 rho v squared.This is called dynamic pressure,often designated as "q".
However the actual average pressure can be much less, being modified by the shape of the body. The drag force is obtained by multiplying the frontal area by "q" and a drag coefficient. Highly faired bodys have small fractional coeficients,flat nosed or buff bodys have coeficients closer to one. With a long slender object like a keel, skin friction is probably much more important, creating most of the drag. This drag takes the same mathematical form as pressure drag, except the area is the wetted area along the flow versus that perpendicular to it. The skin friction coeficients are typically .002 to .005. and vary with Reynolds number,roughness and turbulence.Since both of these drags vary with q which in turn varies with velocity squared they are sometimes called "Square Law drag".

I hope this helps you. Sorry I don't know how to type math formulas.

 

I don't think there is a link on the net that explains everything to you in a few minutes. I would get some good books. If you want to approach the problem from the aircraft side you shouldn't have problems finding very good literature. In the end the only difference between water and air lies in a few constants and one is incompressible and the other isn't. Once you understand wings you shouldn't have problems understanding keels. Start with 2D problems (wing sections, boundary layers) and then try to get into the 3D stuff (inducted drag). The standard aerodynamic books are:

Schlichting H. Boundary Layer Theory,
McGraw-Hill, New York, 1968.
Review: MUST HAVE. The boundary layer book par excellence. Although much progress has been made since it appeared in its last editions, it is one of the most quoted books in aerodynamics, fluid dynamics and related fields.

Schlichting H, Truckenbrodt E. Aerodynamics of the Airplane, McGraw-Hill, New York, 1979.
Review: MUST HAVE. Very well organized, with clear charts, figures and drawings, as in the German engineering tradition. The book is placed between a text of aerodynamics and one of aerodynamic design of the airplane. It includes chapters on wings, fuselage and tail.

Abbott IH, Von Doenhoff A. Theory of Wing Sections, Dover Publ. Inc., New York, 1959.
Review: It has been a reference for airfoil data for over 40 years. You can find a lot of more recent publications, but this book set a standard. Besides airfoils data in a range of Reynolds and Mach numbers, there is some related aerodynamic theory (airfoils definitions, boundary layers, compressibility effects).

Hope your math is up to scratch.

Cheers,
Karsten