[The_Provost]

Hello,

I am performing a simulation (2-D), where a stationary vapor bubble is placed inside a super-heated liquid (water). The temperature, density, viscosity of the bubble is kept constant. I find that inside the bubble, there are two counter-rotating vortex structures when plotting the velocity vectors. Could anybody help me with what could be the possible reasons behind the presence of these vortex structures?

PS 1: I am running the simulation to plot the growth of the bubble as a function of time and compare with the analytical solution. That part is done, and it the results match the analytical ones.

PS 2: I am simulating only a quarter of a bubble, as it is axisymmetric, and two vortex like structures are present in one-quarter. Please see the attached image

Let me know if you need any other information.

Thanks,
The_Provost

[FMDenaro]

I have no experience on this specific flow problem, from the pattern of the velocity field seems to me that the bubble is expanding.. This is a steady state solution?

[The_Provost]

Originally Posted by FMDenaro

I have no experience on this specific flow problem, from the pattern of the velocity field seems to me that the bubble is expanding.. This is a steady state solution?

Yes, the bubble is expanding, the bubble is placed inside super-heated liquid, so the liquid at the interface is evaporating, and thus the vapor mass increases, which in turn increases the size of the bubble.

What i do not understand is the presence of the two counter-rotating vortices inside the bubble.

[FMDenaro]

Originally Posted by The_Provost

Yes, the bubble is expanding, the bubble is placed inside super-heated liquid, so the liquid at the interface is evaporating, and thus the vapor mass increases, which in turn increases the size of the bubble.

What i do not understand is the presence of the two counter-rotating vortices inside the bubble.

Well, therefore you are simulating a transient problem... What do you expect inside the bubble? The increasing of the interface should correspond to a change in pressure. Do you start from fluid at rest?

[The_Provost]

Originally Posted by FMDenaro

Well, therefore you are simulating a transient problem... What do you expect inside the bubble? The increasing of the interface should correspond to a change in pressure. Do you start from fluid at rest?

Yes, fluid is at rest initially. I want to confirm if my thinking is correct, i.e. if it is the pressure difference which creates the vortices. Is there any way you can suggest by which I can modify the simulations (may be changing some parameters) to get a proof that it is indeed being caused by the pressure difference? I don't think changing the bubble radius will help, may be reducing the temperature of the liquid?

[FMDenaro]

I am not sure about the physics of your problem, you wrote that you take constant temperature and density inside the bubble...pressure is therefore costant...maybe you should give us more details about your formulation

[The_Provost]

Originally Posted by FMDenaro

I am not sure about the physics of your problem, you wrote that you take constant temperature and density inside the bubble...pressure is therefore costant...maybe you should give us more details about your formulation

Yes, temperature and density is constant inside the bubble, but the volume is changing (due to increase in bubble size), which makes the pressure change.

[FMDenaro]

Originally Posted by The_Provost

Yes, temperature and density is constant inside the bubble, but the volume is changing (due to increase in bubble size), which makes the pressure change.

Therefore the term div v inside the bubble is not zero and you are using a compressible flow model. How do you get pressure? From the state equation it would be constant....

[The_Provost]

Originally Posted by FMDenaro

Therefore the term div v inside the bubble is not zero and you are using a compressible flow model. How do you get pressure? From the state equation it would be constant....

I am using incompressible flow, and solving the continuity, NS, and energy equations for both vapor and liquid phases, I employ a jump condition for the interface which encapsulates the velocity and the pressure change at the interface. When you say div v, you mean the velocity, right? Yes, the divergence of the velocity should be zero as per the continuity equation.

[FMDenaro]

I tried to understand your model, but I cannot realize how you can take constant density and temperature and having an increase of the volume of gas with the divergence-free constraint...
For example, this paper shows a differen model
https://www.researchgate.net/profile...crochannel.pdf

[The_Provost]

Originally Posted by FMDenaro

I tried to understand your model, but I cannot realize how you can take constant density and temperature and having an increase of the volume of gas with the divergence-free constraint...
For example, this paper shows a differen model
https://www.researchgate.net/profile...crochannel.pdf

Check the paper: On the dynamics of bubble growth by L.E. Scriven (1958), this paper gives the analytical solution of the problem I am solving.

[FMDenaro]

The analytical model is 1D (along r) so that no vorticity can be compared ... you have a 2D model that develop convection and vorticity... You can just compare approximatively fine the surface tension development and the radius increasing...

[The_Provost]

Originally Posted by FMDenaro

The analytical model is 1D (along r) so that no vorticity can be compared ... you have a 2D model that develop convection and vorticity... You can just compare approximatively fine the surface tension development and the radius increasing...

Yes, I am comparing the radius increase, that works fine, I am just trying to determine the source of the vorticity.

[FMDenaro]

Originally Posted by The_Provost

Yes, I am comparing the radius increase, that works fine, I am just trying to determine the source of the vorticity.

writing the vorticity equation from your momentum equation shows that it is possible to produce recirculating region by means of the movement of the interface

[jbreunig]

Sounds like you may have your answer. I do have to agree with FMDenaro though that you seem to be increasing volume. If mass stays the same, then density must change by simple definition. Not sure incompressible is the way to go, but you know more about your problem than we do. Just giving my own opinion.

[Benben]

If i understand correctly, some of the surrounding liquids is changing to vapour phase, hence the volume increase without a density change.

As for the vorticity, your buble seems to grow faster at the extremities (along the x axis and y axis), than at the rest of the interface : The shape of your interface is not a quarter of sphere cap.
That might be why you have some recirculation.