HBLM for stokes drag force simulation

[Zhangshi]

Dear all，

Recently，I use the HLBM method for the simulation of a spherical
particle floating.But I found the terminal velocity of floating is not conform to the case that the sphere is under the influnece of Stokes drag force in the water.I wonder if the HLBM can act as Euler-euler for simulation of floating.

zhangshi

• This topic was modified 3 years, 10 months ago by Zhangshi.

[robin.trunk]

Dear Zhangshi,

could you explain what your setup is? When floating between two fludis stokes maybe does not hold.
The Stokes drag force is not directly applied in HLBM, but the overall hydrodynamic forces are calculated, which can give the Stokes drag force if flow regieme and geometry are chosen according to the Stokes assumptions.
What do you mean by Euler-Euler? HLBM consideres particles as distinct non-deformable objects, whereas in the Euler-Euler example case the particles are depicted by an advection-diffusion equation, describing the particles as density distribution instead of single objects. Therefore basic asumptions are differnt in this case.

Best regards
Robin

[Zhangshi]

Dear robin，

Thanks for your prompt answer.
I create a cube area in size of 600μm*600μm*720μm，and the size in lattice is50*50*60.The density of fluid and particle is 7900 and 3900 in kg/m^3.
Here are some parameters.
LatticeU=0.000904
tau=0.797
charL=0.0006 m
charU=0.00054 m/s

Conversion factors：
phyDeltaX=1.2e-05 m
phyDeltaT=2e-05 s
phyVelocity=0.5973 m/s
I set no-slip boundary condition for the wall.

Best
Zhangshi

[robin.trunk]

Dear Zhangshi,

what is the particle size, i think you need at least 10 cells per sphere diameter to depict the sphere correctly. The Stokes assumption also states that the fluid extends infinitly in all directions (i.e. there are no walls). This has been investigated in some paper finding that you need several times the sphere diameter as distance to the walls in all directions.

Best regards
Robin

[Zhangshi]

Dear Robin，

I got it!My settling of the particle size are 40μm，60μm and 80μm.Maybe the lattice is a little large.Thanks for your suggestions.
By the way,I wonder if the value of the relaxation time is necessary.Does it have a certain range?
And can I set no-slip boundary wall with the situation that I create a
larger area？

Best
Zhangshi

[Zhangshi]

Dear Robin，

I forget to tell you that I set episilon for about 1E-7m，I think it’s more similar to the sphere.Or maybe it’s not really important.
I’m waiting for your answer.Thank you so much.

Best
Zhangshi

[robin.trunk]

Dear Zhangshi,

for tau too close to 0.5 the simulation gets unstable, but a too large tau (depending on the case of application, e.g. tau=1) can lead to deviations from the physical setup.
You can apply no-slip boundaries, however the best results will be optained with a domain large enough. You might have to test that.
In your case epsilon is two orders of magnitude below the cell size physDeltaX. It will probably have almost no effect.

Best regards
Robin

[Zhangshi]

Dear Robin，

Thanks for your share.Maybe I think the less value of episilon is，the more similar to sphere the particle will be.I’ll try to understand this point.

Best
Zhangshi

[Zhangshi]

Dear Robin，

After the discussion with you the day before yesterday，I found some problems.I can‘t get any data I wanted.I thinks maybe I misunderstand the meanning of charU. When I set datas for the program.I always calculate the max velocity of the particle by stokes drag force formula at first.Then I set the charU to the value which is aqual to the max velocity of particle.I think taht’s not right.How should I set for the charU?

Best
Zhangshi

[robin.trunk]

Dear Zhangshi,

this charU enters the converter. It is only a discretisation parameter and has no influence on the settling of a sphere. You might want to look at the documentation of the converter in our user guide or the doxygen:
https://www.openlb.net/user-guide/
https://www.openlb.net/DoxyGen/html/d6/d92/classolb_1_1UnitConverter.html

Best regards
Robin

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