Added mass

Hi
Does anyone know of a programme that can calculate added mass coefficients for arbitrary shapes? We have a variety of software at work including NX, paramarine, CFX, ADAMS, etc, but nothing seems able to do this. I always end up estimating coefficients based on simple geometries from text books.

 

WAMIT will do it for wave flow, but they are frequency dependent and so-so for other things as they are rather incursive with the wave potential. For general linear flow I know that some have tried CFX with still water-moving body and extracted it. For the most part, I work it up by hand when I need it from Brennen's NFESC report.

http://authors.library.caltech.edu/233/1/BRE052.pdf

 

Thanks Jehardiman. Great link. That's pretty much where I'm at, but I'm suprised there isn't more knowledge/info available. I would have thought that some CAD packages would be able to make an estimate. I reckon there's a PhD there for someone.

 

The problem is that the problem is recursive."Added mass" is the pressure caused by the acceleration of the flow around the body...which is effected by the added mass.

Sometimes you really can't get there from here.

 

All the discussions I've seen about added mass concern linearized motion about a straight-line, constant speed equilibrium. What about quasi-steady accelerated motion?

For example, consider a multihull that is in a steady turn. An outer hull experiences a constant centripetal acceleration. Is there added mass associated with the centripetal acceleration? And if so, is it the same as would be experienced with the same lateral acceleration of the hull from traveling in a straight line?

 

Tom
Not sure what you mean by constant speed equilibrium? Added mass only applies when the body is accelerating - as far as I know that can be a change of speed or direction so your turning cat would have added mass. As best I can make out added mass is similar to drag(but associated with acceleration not velocity) and would have intuitively thought that a shape with a low Cd would also have low added mass coefficient? But there appears to be very little work on the subject.
In Orcaflex (an offshore dynamics package) you anter the full 6*6 matrix of terms. It is hard enough estimating the translational values, the rotational terms are pure guesswork!

 

Meant to add:
the added mass of the turning (therefore accelerating) multihull would be different to the same boat accelerating the same amount due to chage of speed. The added mass coefficient is a function of shape and therefore the presented face into the flow. The turning hull would not be presenting it's bow to the flow so I would expect the added mass to be higher.

 

Tom;
As PI said, it is better to think of it in the 6x6 directional velocity matrix of u,v,w,p,q,r for some small differintal element of the fluid.

The first derivative if the directional matrix (x,y,z,phi,theta,psi ) would give you the velocity matrix for viscious forces of drag and damping; i.e. viscious drag = F( u,v,w,etc.).

The second derivative if the directional matrix would give you the acceleration for the forces of pressure; i.e. form drag = F(u dot, v dot, etc.).

The third derivative if the directional matrix would give you the jerk (yes, position triple dot is jerk, see ISO 2041) for the value of added mass; i.e. added mass= F(u double dot, v double dot, etc.)>

So the jerk (1,6) term would be used to calculate the added mass in the x direction due to the time derivative of rotational acceleration about the yaw axis. Likewise the jerk (2,1) to calculate the added mass in sway due to change in acceleration in the x direction. These becomve very important in the determination of the stability derivatives for controlability.

 

In matter of fact I have developed an internet based application witch calculates added mass and damping coefficient in heave motion.
http://88.213.199.107/Ship Dynamics/ - there it is ...

I hope if you can say your oppinion for the calculation results, too.
I am looking forward your reply!

 

What about 'Entrained water' which is also added mass isn't it?

 

Entrained water is a seperate mass, not related to added mass. Lets say I had an AUV with a space frame structure, some buoyancy blocks, and fairing panels. The total hydrodynamic mass would be the actual mass of the AUV plus the mass of the water entrained inside the envelope. Added mass is an additional force, proportional to acceleration, required to accelerate the accelerated flow around the exposed parts of the AUV. Entrained water is the mass of the free flooding water contained within the AUV envelope and not subjected to accelerated flow.

 

Thanks for explaining that.