Bubble-driven and other multi-phase flows

[raback]

Here's a question on multiphase flows that was sent to the now obsolite discussion list.

Greetings,

I would like to model liquid flow driven by bubbles -- not a few, as can
be done with level set, but hundreds or thousands, enough to use a
continuum method. The bubbles and the liquid need to have their own
separate velocity fields which are of course coupled to each other.

I don't see a suitable existing model in the Elmer Models Manual, and
can't think of a way to use say advection-diffusion, as the bubbles
might diffuse slightly, but really need to move in the direction given
by (bubble size-dependent) buoyancy plus drag due to the liquid flow.

Is there a way to do this with Elmer as it is, or would it require a new
model?

Thanks,
-Adam

Unfortunately Elmer does not have much capabilities when it comes to multiphase flows. You can have a number of passive components sitting on the flow, and maybe even have the material properties depend on the concentration. However, if the velocities of the phases differ this is not a suitable strategy as you correctly state.

The remedy would be to have separate equations for the different phases and also handle the interaction between the them. This is a considerable task considering that there is a plethora of different formulations that one can make. To my knowledge there is no ongoing work to implement true multiphase flow equations.

Apart from the continuum approach (Eulerian) one can also take a particle approach (Lagrangian). This would be fitting particularly if there is a large different between the velocity of the bubbles and the fraction of bubbles remains rather low (<10%). A Lagrangian particle tracker would allow you to follow the path of a number of particles (real or statistical). For this kind of particle tracking there has recently been some requests so we are considering implementing it. Modeling of multiphase flows could take use of it even though it needs some additional features for consistancy. Maybe this kind of approach could be feasible in your case?

BR, Peter

[hazelsct]

Hello Peter,

The Lagrangian approach sounds interesting, as long as the particles can provide a reasonable body force field for the fluid. It would probably take a lot of particles to do that accurately...

Back to the Eulerian approach, I agree that two liquids or a solid-liquid mixture would require two (or more) velocity fields.

But thinking about it a bit more, bubbles with orders of magnitude lower density than the liquid really don't need to worry about momentum or inertia changes in acceleration, and so the gas phase velocity would only depend on liquid velocity and bubble size. In this case, one might just be able to use advection-diffusion with advection velocity equal to that computed plus the rising terminal velocity. The bubble phase would then couple back to the liquid velocity by concentration dependence of density, using solutal buoyancy. One would probably need to have a small diffusivity for stability purposes, but that should not lead to major problems with accuracy. And this would only work for monodisperse bubbles, otherwise there's a distribution of terminal velocities.

How hard would it be to have the advection velocity be computed plus a constant? I'd be happy to investigate implementing this myself if needed...

-Adam

[raback]

Hi Adam,

Yes, the Lagrangian approach requires a lot of particles and its still randomized meaning that there will never be convergence in traditional sense. There are good reasons to be suspicious.

If the terminal velocity is just a function of bubble size as in http://www.bubbleology.com/Hydrodynamics.html couldn't you express this by a simple MATC expression, for example in 2D.

Code: Select all

$ vt = 2*g*r*r/(9*visc)
Convection Velocity 1 = Equals Velocity 1
Convection Velocity 2 = Variable Velocity 2
  Real MATC "tx+vt"

Note that the "convection velocity" is used when the velocity field is decleared to be "constant". If "computed" the velocity field is used internally. For coupling back the density should be made a function of bubble concentration.

You could basically use a number of instances for the same solver if you have a number of size categories. However, this may require some modification of the code since there can only be one "convection velocity" field. If you need a lot of size categories then particle tracking may start to look more interesting.

BR, Peter

[hazelsct]

Oh, of course, this sounds like a very elegant way to do this. If a non-monodisperse bubble size distribution becomes important for my application, I'll look into other methods.

Thanks!