RPI Model, Mesh Independent study
 

It makes it very difficult when numerical models do not converge as mesh gets smaller.

My recommendation is first try to get it to converge. Use the highest quality mesh you can generate, double precision numerics and small time steps. Then refine the mesh and see if it appears to be converging.

If it does not converge then have a look at how much it is moving about. That is the likely level of error. You can take the mesh resolution which works best and use that for your simulation, but be aware this is very risky and there is nothing to guarantee it will be similar in your actual simulation.

Actually system does converge with a fixed mesh size, but when I go below that size, i.e. reducing diameter further... it doesn't converge...
means mesh independent study isn't possible... How to tackle this?

Sounds like numerical round off is causing problems. This can be helped by the suggestions I mentioned previously (highest quality mesh you can generate, double precision numerics and small time steps).

But if you you still get it then you have hit a fundamental limitation of the model. You have to consider whether the model you are doing is accurate enough to be useful.

What if RPI Model isn't useful... Can you suggest any alternatives for this? As it is written in its details that RPI model for wall boiling is strongly mesh dependent... So what should I do?

First of all - CFD of phase change is very difficult and there are few models which are universally applicable and converge easily. Most of the multi phase phase change models have a lot of empiricism in them and are very tricky to get running properly.

I would try RPI anyway and see how it goes for you. But if RPI does not work you will have to search the literature for other approaches. Be aware that it is quite possible that your simulation is not able to be modelled with current technology.