Dynamic displacement ?

There is a concept called dynamic displacement. As I understand it, or not understand it, There is a body of water surrounding a moving waterborne object. It has finite dimensions. That body of water moves at the same rate as the floating object. The implication is that the body is larger than the boundry layer attached to the moving object. In a perfect world the ratio of static displacement divided by dynamic displacement would be equal to one. Not a perfect world.

Are we dealing with some sort of pressure differentials? If so, are the dimensions a function of velocity, density, viscosity? I, sort of, understand the kinetic/potential energy principle that causes transverse waves. Are there clues buried in that division of physics?

Can anyone help me understand this concept?

 

Messabout, there is a ton of stuff on dynamic displacement. I have some reading to do. It appears in physiology and tsunami science too. You have opened a can of worms here.

Just for starters.:
http://www.springerlink.com/content/8836657r43t07232/
http://portal.acm.org/citation.cfm?id=1660165.1660405

 

I think the concept you are looking for is "added mass".

When a boat is moving at a constant speed and angular rate (running straight or turning in a circle), the flowfield has a quasi-steady character, with the water flowing in streamlines that have the same shape relative to the boat. A gob of water moving along a streamline will be accelerated (slowed, sped up, pushed to the side), and this is the source of many of the fluid dynamic forces on the boat.

However, if the boat is accelerating (changing its speed, changing its angular rates, or operating in a seaway), the streamlines have to change, too, and there are forces associated with making those changes that are over and above the "normal" fluid dynamic forces. Since they are proportional to the acceleration of the boat, they can be lumped with the same force & moment bookkeeping as the mass of the boat. Hence the moniker, "added mass".

You can equate the forces and moments due to added mass with an equivalent volume of water. But that is only a way to visualize the magnitude of the added mass. In fact, the water nearest the boat will be most affected and the effects will die off with distance, so it's not like there is a discrete volume of water that constitutes the added mass and the rest of the water does not. Some authors get confused by this point and think that if, say, the added mass has the same magnitude as a cylinder of water whose diameter is the same as the beam, that must mean that there is a literal cylinder of water that constitutes the added mass. That's not the case.

The forces due to added mass do show up as pressures on the hull. Seakeeping programs can calculate these pressures, given the hull shape, the boat speed, the wave speed and direction, and how the boat is moving. It's a lot simpler to do the computations for a 2D shape than for a 3D boat, so many of these codes compute the flow a section at a time, under the assumption that most of the change in velocity of the flow is directed outward from the hull and the changes in velocity in the longitudinal direction are much smaller by comparison.

So while calculating the effects of added mass on the boat are complicated, the physics are pretty well understood.

 

EDIT: This was cross posted with Tom, he handled added mass which was not my take on messabout's question, and takes on the idea of the "viscous boundary layer correction".

Whos concept from where? The term "dynamic displacement" is not one I have heard of as a standardrized term; are we talking about the physical displacement of a plaing boat on plane or "added mass" of any body.

Yes, that's what makes it waterborne...ba-da-boom. But in a narower sense, there is an area of effect of the fluid distrubances in pressure and viscosity that a body makes while moving through a fluid.

Yes and no. As a moving body interacts with a fluid, it makes a pressure, and corresponding flow, distrubance in the fluid that causes a pressure face to be generated. That pressure face moves out radialy form the point of disturbance subject to the laws of physics (a function of fluid density, viscosity, depth, and gravity). The pressure face advances at a set rate, but will eventually advance to the infinite ends of the fluid if the fluid was that large. Toss a rock in a still pond, it will generate a ring wave of a fixed total energy. As that wave expands the total energy remains the same (assuming we don't drill down into molecular interactions and Brownian effects). However, the amount of energy in a single foot of wave front will quickly decrease as the size of the ring become large.

Again yes and no. On one hand, there is at a very small level a viscous "bound" turbulent layer that moves along at "nearly" the same speed as the body, but the mass of this layer is much, much, less than the mass of the body. In the larger sense, while it appears there is a moving pressure wave train with the body, this is not so. Consider the rock analogy from above. As a body moves forward, it is like tossing a rock into the water just ahead in course and behind in time. Because the speed of pressure disturbance propagation is fixed, the wave train "appears" to be fixed to the body but in reality is not.

Maybe. There are a lot of "ifs" and matematical contrivinces going on here. Over the speed regieme we go from where the kinematic viscosity dominates the distrubances to where we have enough energy available so as to tear the fluid apart molecule from molecule (i.e. cavitation). Also in question is were you draw line for what is "in" and what is "out" of the bound layer. In most cases of real world applications for vessels of useful sizes, the body is considered only very slightly "larger" as you describe. Maybe 1-4% of the ships mass in water is contained in the bound turbulent layer. This is actually just a "near field" correction that allows correlation with "far field" results.

Yes, only in an inviscid fluid would there not be a "bound" turbulent boundary layer or need for correction.

Actually it is the ratio of where the energy is going, into turbulence or into the pressure wave.

And gravity and water depth and body dimensions including surface roughness.

Yes, there are clues, but they are way buried in stoichastics at a molecular level

Go see the papers of Sir Thomas Havelock and the text Hydrodynamics by Lamb for a more through discussion of the assumptions and derivation which lead to modern CFD.

 

jehardiman and tspeer have given very good explanations of some senses of the term "dynamic displacement".

I use the term to mean the apparent displacement of a "squatted" hull, i.e. when the sinkage force is downwards and tending to increase the displaced volume with respect to the undisturbed free-surface.

The term is sometimes used in other context, e.g. in this report to the Int. Navigation Association.

http://www.pianc.iwr.usace.army.mil/workinggroups/docs_wg/marcom-wg41.pdf

All the best,
Leo.

 

Thanks all. You have made my day. We are priveleged to have so many very bright and generous people who participate here. I use the plural pronoun, we, advisedly. Unfortuneately some of the "we" fail to understand the value of learned council. Happily there are many of us who do appreciate these gifts.

This line of questioning came up as a result of bits and pieces of information that has crossed my path....... performance of a boat sailing over very shallow water is different from the performace in deep water, even for little boats like kayaks. ....Test tank depth versus model draft or displacement.......ships running parallel to one another or in a triangular pattern, or echelon pattern influence one another in different but meaningful ways. That last bit came from some papers published by one of the Aussie universities. Adelade Univ. maybe?

Hoyt; I did not mean to open a can of worms. I'm just a sincerely curious old dude who is trying to delay the onset of senility. (mental cardio training). I promise never to ask questions, here, about black holes or dark matter.

Thanks again gentlemen.

 

This is also where the tsunami behaves differently. In deep water, almost unnoticeable; in shallow water, BIG problem.

 

That'd be right. A few years ago there was some bozo at that university who obsessed over waves made by weird arrangements of hulls.

All the best,
Leo.