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



4 Replies Last Post 2017年6月24日 GMT-0400下午11:16
COMSOL Moderator

Hello Leo Mechelle

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Posted: 4 months ago 2017年6月19日 GMT-0400下午1:24
Hi Leo,

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

Best regards,

Ying
Hi Leo, I am also face the problem of simulation stoke drag on a sphere. Have you solve the issue already? Best regards, Ying

Jeff Hiller COMSOL Employee
Posted: 4 months ago 2017年6月19日 GMT-0400下午2:22
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
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

Posted: 4 months ago 2017年6月24日 GMT-0400下午11:14
Dear Jeff,

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

Best Regards,
Leo
Dear Jeff, Thank you so much for your suggestion. It is exactly where my problem lies. Best Regards, Leo

Posted: 4 months ago 2017年6月24日 GMT-0400下午11:16
Dear Ying,

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

Best Regards,
Leo
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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