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Peter Nagy January 9, 2004 15:41

Marangoni VS Rayleigh-Bernard
Dear Community:

I am trying to model and observe the competition between the Marangoni/buoyancy driven flow inside a small droplet (3mm dia) sitting on a heated solid support. From a simple solid-free boundary condition, Rayleigh number may be sufficient to kick the thermal instability. However, thermo-capillarity effect dominates in real life and buoyancy effect is not well observed. This is pretty much what I am trying to show with Fluent by using different thermo-capillary coefficient values(d(sigma)/dT).

I am considering thermocapillarity to be modeled through UDF, and buoyancy with Boussinesque approx.

The initial idea was to place the half-hemispherical drop on the solid and let it "sit" and deform under gravitaty until the "steady-state" is achieved. Then switch on the energy equation with appropriate boundary condition to observe the thermally and capillarity-driven flow inside the dorp.

The problem is that the solution never reaches the steady state, but oscillates due to the "parasitic error" at the interface. The magnitude of the error is O(mm/s) at the surface, and this is comparable to the magnitude of the thermo-capillary induced velocity inside the drop (which I observed from an experiment) of O(mm/s). Does this indicate that Fluent is not capable of modeling Marangoni flow ?

Or is there any other way to model this with Fluent?

I am considering to investigate different parameters but it seems that the parasitic error is always present...

Also, I have run some numerical testing: I placed a hemispherical drop (2D-axisymm) with no gravity and let it iterate. The parasitic error deformed the droplet until the liquid drop splits and eventually the solution diverged.

time step is taken to be very very small (1e-6) which is 2 orders magnitude smaller than the capillary time scale.

Thanks for the help

ozgur January 10, 2004 17:59

Re: Marangoni VS Rayleigh-Bernard
hi peter,

could you explain a bit about the "parasitic error". I have the similar problem when simulating a free falling 1mm drop for inner and outer velocity field investigation. I expect spherical drop under the physical conditions I have, but the drop deforms, and splits as you have said. the model is 2D VOF. I need about 1e-5 s. time step.

Peter Nagy January 12, 2004 10:53

Re: Marangoni VS Rayleigh-Bernard
it's the error associated with CSF scheme. My output from the testing: spherical volume in a chamber with no body force (no gravity), yields a dynamic system due to this parasitic current (where it should not do anything). From what I heard, this is the result of the addition of surface tension term to the momentum equation and faulty estimation in the curvature of the interface...

I can only think of 2 directions. Find better software package that can do the job or write your own???

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