[mohamedh]

I am using ANSYS FLUENT to model a two-phase flow of liquid and gas where the surface tension force is included.
In the theory of the VOF model, the surface tension force is added to the momentum equation as a source term.

However, in the Eulerian model, we have two momentum equations, one for the liquid and one for the gas. How is the surface tension force included? is it added to the liquid momentum equation?is it added to the gas momentum equation? is it split between the two phases?

If it is split, is it split by two volume averaged factors or two mass averaged factors?

Unfortunately, the theory manual does not mention related information under the Eulerian model theory.

[BlnPhoenix]

This is a very interesting question! I always wondered if and how the surface tension force in an Eulerian-Eulerian framework is modelled. My current view on this is, that it is actually non relevant in E-E framework, since it is the force that describes interface curvature. This is only relevant in a VOF type simulation. In E-E the interfaces are not simulated.

I would be very happy if anyone could confirm this.

[mohamedh]

I found the answer. It is split by two volume averaged factors. In other words, it is multiplied by the volume fraction of the given phase and added to its momentum equation as a source term.

[BlnPhoenix]

Originally Posted by mohamedh

I found the answer. It is split by two volume averaged factors. In other words, it is multiplied by the volume fraction of the given phase and added to its momentum equation as a source term.

Do you have a source for this?

[mohamedh]

Originally Posted by BlnPhoenix

Do you have a source for this?

I asked the same question in the ANSYS Student Community, someone from ANSYS stuff answered it.

The answer does make sense for me. If you looked at a momentum equation for the Eulerian model, you will find that each term ( pressure force, shear force ...etc) is multiplied by the volume fraction so that if you add the two momentum equations of the phases the volume fractions add up and become unity. .
.
They deal with the surface tension force in a similar manner.

[BlnPhoenix]

Originally Posted by mohamedh

I asked the same question in the ANSYS Student Community, someone from ANSYS stuff answered it.

The answer does make sense for me. If you looked at a momentum equation for the Eulerian model, you will find that each term ( pressure force, shear force ...etc) is multiplied by the volume fraction so that if you add the two momentum equations of the phases the volume fractions add up and become unity. .
.
They deal with the surface tension force in a similar manner.

Yes, but still i don't understand why modelling the Surface Tension is important in an E-E type simulation. When you have a dispersed like flow and the interface is not resolved why should i include surface tension in my simulation? To my knowledge the surface tension describes the bubble shape and therefore the drag, the drag force is modelled in E-E. So the effect of surface tension force is embedded in the drag force calculation. What extra force is acting in the momentum exchange, when i include the surface tension? It would make sense to use it if i actually resolve an interface but for a fully dispersed (under-resolved) situation it's not a force acting like Lift, drag or Virtual Masse force imho..

Am i missing something? Thx!

[mohamedh]

Originally Posted by BlnPhoenix

Yes, but still i don't understand why modelling the Surface Tension is important in an E-E type simulation. When you have a dispersed like flow and the interface is not resolved why should i include surface tension in my simulation? To my knowledge the surface tension describes the bubble shape and therefore the drag, the drag force is modelled in E-E. So the effect of surface tension force is embedded in the drag force calculation. What extra force is acting in the momentum exchange, when i include the surface tension? It would make sense to use it if i actually resolve an interface but for a fully dispersed (under-resolved) situation it's not a force acting like Lift, drag or Virtual Masse force imho..

Am i missing something? Thx!

The effect of surface tension is not included in the drag!

The drag force is a result of the friction at an interface separating two phases. If the two phases are solid and air, we do not have surface tension! Surface tension only exists on liquid free surfaces.

Moreover, the flow does not have to contain bubbles. You may have cases like stratified flow where you have a wavy interface between the two phases with no bubbles exist! The surface tension is there at the liquid-gas interfaces either bubbles exist or not.

One difference between the drag and the surface tension is that the drag force is in the direction of the relative velocity, while the surface tension force is always normal to the interface. For an air bubble in water, for example, the surface tension force on the bubble surface add up to the pressure force acting on the bubble surface. So if the surface tension is so small compared to the inertia force, it can be neglected.

[BlnPhoenix]

Originally Posted by mohamedh

The effect of surface tension is not included in the drag!

It depends on the drag Force model. If i use Schiller-Naumann it's only for rigid objects without shape deformation. If i use Ischii-Zuber, the bubble shape is calculated with influence of the surface tension.

Originally Posted by mohamedh

The drag force is a result of the friction at an interface separating two phases. If the two phases are solid and air, we do not have surface tension! Surface tension only exists on liquid free surfaces.

I agree! It's basically what i said above.

Originally Posted by mohamedh

Moreover, the flow does not have to contain bubbles. You may have cases like stratified flow where you have a wavy interface between the two phases with no bubbles exist! The surface tension is there at the liquid-gas interfaces either bubbles exist or not.

I agree. It's what i meant, when i said, it's used when there is an interface modelled in the E-E simulation.

Originally Posted by mohamedh

One difference between the drag and the surface tension is that the drag force is in the direction of the relative velocity, while the surface tension force is always normal to the interface.

The drag force acts against the relative velocity. It slows down rising or sinking velocity of an object other than that, i fully agree.

Originally Posted by mohamedh

For an air bubble in water, for example, the surface tension force on the bubble surface add up to the pressure force acting on the bubble surface. So if the surface tension is so small compared to the inertia force, it can be neglected.

Ok, but this does not contribute anything extra to interface shape, does it.
So in total: if i assume rigid spheres and do not resolve any wavy interface, surface tension Force does not contribute anything to momentum exchange between the E-E phases and i do not need to include it.

[yylaw]

Originally Posted by mohamedh

I found the answer. It is split by two volume averaged factors. In other words, it is multiplied by the volume fraction of the given phase and added to its momentum equation as a source term.

Hi there, my case is similar with your problem, but I set "none" surface tension from window "Phase Iteraction" , how fluent will react then ?

Then, How can I calculate / generate result of finding value of surface tension ?