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Terminal Velocity of a Falling Sphere

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Message 1 of 11
hs.simanto
854 Views, 10 Replies

Terminal Velocity of a Falling Sphere

Hi!

I would like to determine the "Terminal Velocity of a Falling Sphere" problem which was discussed in Verification part of Autodesk Simulation CFD 2015 help. (http://help.autodesk.com/view/SCDSE/2015/ENU/?guid=GUID-0E465614-E97B-424B-9C82-27A82320B1DE)

How can i setup this problem? Should i assign free moton to the Sphere?

Thank You!

Simanto
10 REPLIES 10
Message 2 of 11
Jon.Wilde
in reply to: hs.simanto

Yes, use free motion.

How much have to set up so far?

 

Kind regards,

Jon

Message 3 of 11
hs.simanto
in reply to: Jon.Wilde

Hi!

I tried to solve the verification problem, designed a CAD model in 2D,applied all the boundary conditions indicated there. But when i clicked to solve, it rejected to mesh showing improperly formed elements. Problem window and support file is attached below. Please let me know whats going wrong with my procedure.

Thanks!

Simanto
Message 4 of 11
OmkarJ
in reply to: hs.simanto

A quick tip, have you tried modelling your domain in XY plane, as axisymmetric and with X as axis? I see it is in YZ plane and is modelled as Cartesian 2D coordinate system that may be a cause of problem.

Message 5 of 11

To do this you could do free motion or you could do flow driven linear and assign the appropriate force to represent gravity acting on the sphere.

 

2D axisymmetric would be recommended and it is required to be on the XY plane (Z=0) for any 2D model

Message 6 of 11
hs.simanto
in reply to: OmkarJ

Hi!

Thanks for your suggestion on CAD design, i fixed that prblm and tried to run the main simulation. which was like this.
TV2.JPG

So i designed my CAD using following dimensions

Assem1.JPG

I set all the boundary conditions according to the verification guideline! But my results are showing quite different!

TV1.JPG

I achieved a velocity like 0.46m/s and remained more or less constant for the rest of the time steps.

But actual terminal velocity is Vt (m/s) = 6.469 !

Couldnt find out what is wrong in my approach. Please help!

Attached my CFZ file for your review. Thanks!

Simanto
Message 7 of 11

Please go back and fix your cad

 

I stated this in my message - This must be on the XY Plane (Z=0)

 

Not to mention we also mention to represent a 'sphere' this would have to be axisymmetric. If you were to do that with the current model (which does not have the centerline aligned with either the X or Y axis) we would create an annular domain and annular solid).

 

 

Move the geometry to the Z=0 and then align the center line of the geometry to the Y axis

 

If you cannot easily 'move' your geometry a quick trick would be to take this part in to an assembly and mate it accordingly as we'll then use the assembly's origin.

 

XYPlane.png

Message 8 of 11

Also - another comment taht I made was taht for axisymmetric you will have better luck doing Linear Flow driven motion and applying a force that would be equivalent to gravity acting on the body. This will be more stable than trying to use Free motion

Message 9 of 11

Hi apolo.vanderberg

Thanks for your review on my CAD. You guys are really helpful. Sorry for being slow to understand your points, but i fixed my CAD this time according your message.
TV3.JPG

I doubled the length of my domain to 80m. sphere radius was 0.25m. I used free motion to moving solid as i couldn't understand the volume of the solid in 2D [if it was in 3D i could measure mass = (density)*(volume)  and then could calculate the force acting on it]

now my this try i found this result from motion review
TV1.JPG


Which is showing terminal velocity Vt = 4.4 m/s (approximately)

The verification problem didn't indicate any radius of the sphere, i assumed it to 0.25m. And also due to lack of stability for using free motion might cause the deviation from actual result which was stated abt  Vt = 6.1m/s. Or would my setup show this result if i have made my domain more longer ??

I also attached my CFZ file below.

Thanks for you help in advance 🙂

Simanto
Message 10 of 11
OmkarJ
in reply to: hs.simanto

As has been pointed out earlier, you need axisymmetric model for this (yours is still 2D Cartesian)

Also, you can not hope for accurate results if your model doesn't have adequate refined mesh and timestep. You need to do some sensitivity study for these.

 

Also, I just thought you can be innovative about this problem, by modelling the sphere at the center position of the cylinder column (instead of at the top as you initially model). From then on, you can run steady state simulations for different velocities of the flow close to the terminal velocity you calculate by hand. If for one of these velocities, the (Weight-Buoyancy) force equals the drag you measure from CFD, then these two forces are equal (or nearly equal), indicating you have found terminal velocity. Here, you are keeping the sphere stationary but mobilising the fluid, essentially obtaining the force balance. And since after terminal velocity, the acceleration is zero, this can be treated as steady state. Just thinking aloud, Autodesk personnel may confrm if this will work though.

 

Also, it wouldn't hurt to "feel the physics" of this problem by reading through the reference given in the Help documentation from which this has been picked up. 

http://science.fire.ustc.edu.cn/download/download1/book/fluid%20dynamics/massey_-_mechanics_of_fluid...

Message 11 of 11
hs.simanto
in reply to: OmkarJ

Hi! OmkarJ!

Thanks for your review. I thought about your different approach,and was confused too. Thanks,i will try the force balance different method other times. And thanks for the book link. Will be back with some new problems 🙂

Simanto

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