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 Bivan May 22, 2002 19:17

Help for a Moving Boundary Problem

I'm simulating a bottle with a flexible bottom and hard wall. If we push the bottom, the liquid in the bottle will go out, if we pull it, the bottle will take in water(the bottle is immersed in the water). Since the water mass in the bottle will change, and the boundary at the bottle bottom is some kind of vibration, I really have no idea to set up the model and get the mesh. Can you give me some suggestion? Thanks.

 Wen Long May 23, 2002 12:24

Re: Help for a Moving Boundary Problem

Hi:

I think you can look into any book/text dealing with moving boundary. Simply look for Kinematic Fress Surface Boundary Condition.

For example, if your bottle looks like:

z....---\_ .........._ /--- --- z=f(x,t)

^....|......... -..-...........|............

.|....|...........~.~...........|............

.|....|..........................|............

.|....|.........water........|............

.|....|.........................|............

.|....|.........................|---------->x

.........\_................_/..............

............\_........._/................

...............\..../..................

.................-.-...................

.................|.|....................

.................|.|....................

.................|.|...................

.................|.|.....................

Hope it's not a bad drawing, given any displacement function of the bottle bottom f(x,t), then the boundary condition for the water at the bottom is:

w(x,z,t)= f(x,t)_t+ u(x,z,t)*f(x,t)_x ; at z=f(x,t)

where w is the vertical velocity, u is the horizontal velocity, _t,_x means partial derivatives.

For 3D lay out, should be:

w(x,y,z,t)= f(x,y,t)_t

+ u(x,y,z,t)*f(x,y,t)_x

+ v(x,y,z,t)*f(x,y,t)_y

if you use polar cylinerical coordinate, you need do a transform to turn x y into (theta,r)

good luck

wen

 Bivan May 23, 2002 17:01

Re: Help for a Moving Boundary Problem

Thanks. Then how to model the fluid and use what kind of grid?

 Yanhu May 23, 2002 17:05

Re: Help for a Moving Boundary Problem

You can use ALE(arbitrary-lagrangian-eulerian)

method.

 Bivan May 23, 2002 21:21

Re: Help for a Moving Boundary Problem

Thanks for your reply. Is ALE a CFD or FEM method? I prefer pure CFD method. Can you recommend a good book about ALE to me?

 wen long May 23, 2002 22:13

Re: Help for a Moving Boundary Problem

Hey Bivan:

How much do you want get out of the simulation by CFD codes? What's the purpose of the problem?

I would guess if the bottle is circular, and the water volume is big enough, also the process of intaking water is not very fast, then an analytical solution can be obtained once we do some linearization to the N-S equation.

I would suggest some students to do this in Fluid Mechanics Course.

Wen

 Bivan May 24, 2002 11:14

Re: Help for a Moving Boundary Problem

You are faculy? I do not think the problem is as simple as what you said.

Consider the modelling of a heart, the heart will compact and expand with time goes, the mass in the heart will change, the boundary will move, my problem is like this but not the same. I want to model a pump with a actuator attached at the bottom. the actuator will press the bottom of the bottle to let fluid in it go out,or pull the bottom to intake fluid, and only the mouth of the bottle is immersed in the fluid.So both the boundary at the bottom and the mass in the the bottle will change.

I want to find the flowrate and the velocity field in the pump.

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