CFD Online Logo CFD Online URL
Home > Forums > Software User Forums > OpenFOAM > OpenFOAM Verification & Validation

Stokes Flow arround a single sphere

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Search this Thread Display Modes
Old   November 8, 2021, 09:38
Default Stokes Flow arround a single sphere
New Member
Join Date: Jan 2021
Posts: 3
Rep Power: 4
NFisc is on a distinguished road
Dear Foamers,

I am currently simulating Stokes Flow arround a single sphere and try to compare the results to the analytical solution.

Analytical Solution/Theory: We have incompressible flow at very low Reynolds numbers (< 1) in a cube geometry with a single sphere in the middle with periodic BC at all cube sides and noSlip on the sphere's boundary (Image attached). A force is added to the N-S-Eqn to enforce fluid flow solved with a steady-state solver (simpleFoam):
\bf{v}\cdot \nabla\bf{v}= -\nabla p - \bf{S}
Since the flow is at very slow flow, one can neglect the left-hand-side and the pressure drop should be equal to the added source term:
\nabla p \approx \bf{S}

We can compare the results with the analytical solution of Sangani (1982, "Slow Flow Through A Periodic Array of Spheres") by calculating the incompressible pressure and viscous force, which are used to calculate the non-dim drag K for spheres with different diameter via:
K = \frac{F_{D}}{6\pi \mu U r}
with F_{D}= F_{pressure}+F_{viscous} which we will get from postProcess -func forcesIncompressible, U is the darcy velocity and r the radius of the sphere, \mu the viscosity.
With this we can calculate the non-dim K which is in very good agreement with the analytical solution (Image attached).

So here is the problem: Even though the K values are correct, the calculated pressure drop is not even close to the added source term as mentioned above in the N-S-Eqn. Further, the pressure field does not look correct as it should be a linear gradient through the domain, but this is not what it looks like (Image attached).

Here is what I tried (next to refine the mesh): mappedOutlet BC for the inlet velocity, with zeroGradient velocity at the outlet and set a fixed pressure gradient between inlet (uniform 1E-3) and outlet (uniform 0). With this I get the correct pressure drop gradient and pressure field but the non-dim K is completely off (calculated again with postProcess -forcesIncompressible).
This leads to my dilemma: Either a correct non-dim K or a correct pressure gradient....

Any explanation or help is appreciated. Am I missing something regarding the BC or the theory?
Attached Images
File Type: jpg Sphere.jpg (31.3 KB, 25 views)
File Type: png K_Sim_Analytical_VolumeAveragedUx.png (20.6 KB, 26 views)
File Type: jpg Pressure_Comparison.jpg (46.6 KB, 29 views)
NFisc is offline   Reply With Quote

Old   March 12, 2022, 01:07
Senior Member
piu58's Avatar
Uwe Pilz
Join Date: Feb 2017
Location: Leipzig, Germany
Posts: 743
Rep Power: 14
piu58 is on a distinguished road
Cyclic b.c. arise problems. I recommend working first with an ordinary inlet and outlet first.
Uwe Pilz
Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)
piu58 is offline   Reply With Quote


Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Water Sphere reacting to flow of air modelling Jacee FLUENT 0 May 25, 2018 09:29
Symmetry Boundary Condition for Flow Past a sphere Qkarl Main CFD Forum 14 March 6, 2018 03:32
Flow in canal with solid sphere obstacle Gandel FLUENT 0 May 3, 2017 04:59
superSonic Flow around sphere prapanj OpenFOAM Running, Solving & CFD 0 March 17, 2009 01:20
Stokes Flow george FLUENT 3 July 30, 2001 05:33

All times are GMT -4. The time now is 20:58.