Basset–Boussinesq–Oseen equation (Added Mass and Basset Force)

[K41]

I've been studying the Basset-Boussinesq-Oseen (BBO) Equations and I don't really understand the unsteady forces terms which are:

- Added Mass Effect
- Basset Force

It says the unsteady forces arise from an acceleration to the relative velocity vector. Can someone explain with an example? I'm, having difficulties really picturing what relative velocities are in this context.

Also, the added mass effect comes from the fact that the particle does work on the surrounding fluid. I don't understand this because isn't this how lift/ drag is created? Why is this any different from that?

Finally, regarding the Basset force, if there was a relative velocity (i.e. u-v was non-zero), wouldn't there be a lag in the boundary layer anyway without the need for an acceleration?

As a sidenote, can someone elaborate why form drag and Buoyancy are different? I've read from another thread here that form drag is to do with the dynamic pressure and Buoyancy the static pressure, yet all the formulae to work these out appear to be exactly the same which is the integral of a pressure gradient around the surface :s.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[SteamKing]

As a sidenote, can someone elaborate why form drag and Buoyancy are different? I've read from another thread here that form drag is to do with the dynamic pressure and Buoyancy the static pressure, yet all the formulae to work these out appear to be exactly the same which is the integral of a pressure gradient around the surface :s.

Buoyancy is inherently a static phenomenon. You can generate a buoyant force with an object which is not moving, by virtue of the object's displacement of fluid, but you must be moving in order to generate a drag force, the magnitude of which depends on the velocity of the object relative to the fluid.

 

[RandomGuy88]

As a sidenote, can someone elaborate why form drag and Buoyancy are different? I've read from another thread here that form drag is to do with the dynamic pressure and Buoyancy the static pressure, yet all the formulae to work these out appear to be exactly the same which is the integral of a pressure gradient around the surface :s.

In most cases a fluid can only generate a force on an object in one of two ways: Pressure and friction. A portion of the drag is generated by the pressure differences from one side of the object to the other. The buoyancy also generates a force through a pressure difference between one side of the object and the other. The difference between drag and buoyancy has to do with how these pressure differences are generated which SteamKing mentions above. Also a portion of the drag is generated by frictional forces. There is no friction component to buoyancy.

Apparent mass effect is additional drag felt by an object when it accelerates relative to a fluid. Imagine a sphere moving at a constant velocity in a fluid. It is experiencing a certain amount of drag. In order to accelerate the sphere a net force must be applied (F = ma). But when the sphere accelerates in a fluid, in addition to the sphere accelerating some of the surrounding fluid must accelerate as well. As a result you need to apply a larger force in order to get a given acceleration. So you can think of it as you are trying to accelerate a sphere in a vacuum but the sphere has more mass than the sphere in the fluid. Since it has more mass more force must be applied to obtain a given acceleration.

F = (Mass_Sphere + Mass_fluid)*Acceleration

So you can see where the term "apparent mass" comes from. The apparent or effective mass of the object is larger.

 

[fireflyxox]

Buoyancy is typically thought of as an ideal fluid effect (viscous effects are ignored, so no separation). You are correct in that the buoyant force on an object can be found by integrating the pressure around the surface, and the general application of this is the difference in hydrostatic pressure between the top and bottom of an object, which creates an upward force on a positively buoyant object. However, in dynamic environments (such as a wave field), the pressure can be more spatially variant, which can result in any kind of force. Form drag is a result of separation around the object, which cannot be modeled by potential flow (ideal fluid). While it is also a pressure effect, the pressure results from a different mechanism.

Added mass is an acceleration effect, and can be described most simply as the additional mass that must be "pushed out of the way" when an object accelerates. We can all agree that a sphere would be harder to move underwater than in the air, and this is due to a) drag (which is proportional to velocity squared), and b) added mass (which is proportional to acceleration, and greater for more bluff bodies).

Hope that helps!