About the stokes drag on a sphere (mph attached)

Topics: 5.0, Fluid Flow

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Leo Mechelle

Leo Mechelle

September 12, 2015 9:03am UTC

About the stokes drag on a sphere (mph attached)

Dear All,

I am trying to find the drag coefficient of a sphere in a stokes flow. Since this 3D problem can be simplified into a 2D problem, I use the creeping flow module in 2D to simulate this case. Attached please find the mph file.
creeping flow BCs: As shown in the attachment, inlet velocity is 10^(-5)m/s, and outlet pressure to be 0. The two side walls are symmetric boundary condition and circle (2d section of sphere) surface velocity to be 0 (no slip).

Then I plot the pressure on the circle and I found it is proportional to cos(theta) (The result is deleted due to the limited attachement size requirement). In theoretical analysis, the form of pressure shound be 3/2*viscosity*velocity*cos(theta)/R^2. Then I check my result and I found the coefficient in front of the cos(theta) is much lower than the theoretical calculation.
And this coefficient becomes lower when I enlarge the simulation box size.

I just wonder if pressure is dependent on box size, can I get a correct result of stokes drag 6*Pi*viscosity*radius*velocity of a sphere using 2D simulation? Should I throw away 2D results and focus on 3D in order to get a correct stokes drag result?

Any help will be greatly appreciated!

Thank you!

Best,
Leo

Attachments:   Q1-43493.mph  

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Ying Tang

Ying Tang

June 19, 2017 5:24pm UTC in response to Leo Mechelle

Re: About the stokes drag on a sphere (mph attached)

Hi Leo,

I am also face the problem of simulation stoke drag on a sphere. Have you solve the issue already?

Best regards,

Ying

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Jeff Hiller

Jeff Hiller
COMSOL Employee
USA
Moderator

June 19, 2017 6:22pm UTC in response to Leo Mechelle

Re: About the stokes drag on a sphere (mph attached)

Hi Leo,
Since you worked in 2D, your model represents flow around a cylinder, I am afraid.
To model flow around a sphere, you would need to use 2D axisymmetry.
Best regards,
Jeff

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Leo Mechelle

Leo Mechelle

June 25, 2017 3:14am UTC in response to Jeff Hiller

Re: About the stokes drag on a sphere (mph attached)

Dear Jeff,

Thank you so much for your suggestion. It is exactly where my problem lies.

Best Regards,
Leo

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Leo Mechelle

Leo Mechelle

June 25, 2017 3:16am UTC in response to Ying Tang

Re: About the stokes drag on a sphere (mph attached)

Dear Ying,

Yes. Just set the system to be 2D rotation symmetry as Jeff suggested would solve this problem.

Best Regards,
Leo

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