[MaticG]

Dear All,

I am trying estimate average relative velocity of 3 microne, 30 microne and 100 microne particles (density 1590 kg/m3) in mixing vessel (water as medium).

I obtain relative velocity by integrating it over time. Results which are obtained are: 3 microne: 7 cm/s, 30 microne: 5.8 cm/s and 100 microne: 6 cm/s.

Results are not expected since I would expect larger particles would have doue to their higher inertia higher relative velocity. I would expect smaller particles follow liquid flow trajectories better than larger particles.

Could you suggest what could be wrong?

Thank you for any information!

[FMDenaro]

It depends on the mathematical model you are using for computing those values...generally the computation is done by using quite complex models for the particle integration (for example using the Maxey equation).

Thus, if you do not specify how you are computing no one can help you

[Bmalgil]

If the medium is water, most probably they don't have any relative velocity at all since they have very similar densities.

Control like this, solve problem without the particle (depends on particle concentration) you will have velocities.

Solve simple Stoke drag for velocities and reynolds.

I have some experience for air for same particles with same size. Even for this we need enormous force to act on particle to have a relative velocity.

[MaticG]

Hi FMDenaro and Bmalgil,

Thank you for your answers.

I could not find in help, what is exact model behind particle trajectory calculation. I know, that model uses on-way coupling however (it calculates infuence of fluid on particles and not vice versa). I beleive it calculates sum of forces (drag, bouyancy and gravity) on particle. Forces are used to calculate acceleration, acceleration is used to calculate velocity and velocity to calculate increment change in particle position. Calculations are repeated until entire trajectory length is calculated.

Model also does not account for inter particle interactions, so their concentration does not have influence on their trajectories.

Results I mentioned were exported and integrated over manually in Excel
(v_rel=sum((t(i+1)-t(i))*0.5*(v_rel(i)+v_rel(i+1))/max(t(i))).

I agree, that so small particles with density similar to water should follow liquid flow closely with small relative velocities. Newertheless I think larger particles should have higher relative velocities due to their higher inertia.

Best regards,

Matic

[FMDenaro]

there are many papers on journals like PoF, JFM and so on