For a convection problem with lets say a rectangular mesh, if there is a free surface at the top while insulated at the bottom, with the two sides kept at 1.0 and 0. What sort of vorticity and stream function plots can i expect? Can i expect something like many many little vortices throughout the mesh? Please advice.

I assume that 0.0 and 1.0 are non-dimensional temperatures and the fluid properties are such that the Grashof number is in the laminar range.

If that's the case, I would 'expect' one major circulation cell, with the hot fluid (the 1.0 wall) rising, flowing across the top, and flowing down the 0.0 wall as it cools. I would not be surprised to see small vortices in the lower two corners, maybe several of decreasing size in each corner if your mesh is fine enough. I would not expect 'many little vortices.'

That's what I would expect. Don't actually know what I would get!

Your assumptions are correct. However what i am unsure of are my boundary conditions for temperature and vorticity. For the topsurface, being a free surface, vorticity is 0, but what are temperature?I am also assuming that the bottom surface temperature can remain insulated.

You can also take the temprature on free surface as insulating from envorimental gas. Because surface tension depends on temperature, the unbalanced surface tension should be coded if you want a better solution. The final temeperature distribution on free surface depends on your geometrical condition, Rayleigh number, and Marangoni number in you case.

Supposing if i leave my surface temperature at a certain temperature...lets say 0.5 (non dimensionless) while my left wall is at 1.0 and the right wall at 0. With the bottom remaining insulated, what sort of plots should i expect? Right now i am getting very weird plots. And i am not sure if it is my program being unstable due to the scheme i am using or the values of Rayleigh'snumber i am using or my conditions are simply just not correct. Please advice. Thanks.

(1) Even if you want to ignore unbalanced free surface tension, treat free surface as adibatic and slip velocity boundary. I think adibatic temperature boundary condition is more reasonable than a fixed temperature boundary condition. (2) The temperature contour plot depends on Rayleigh and Marangoni numbers with a fixed geometrical condition and specified material (Prandtl number). (Only Rayleigh number if free surface tension is ignored). If you have set adibatic B.C. for top and bottom, for a very small Re, the temperature contour lines are almost parallelized, and it deviate parallel line with trend that temperature line on free surface is compressed to cold wall with increment of Ra.

Good luck

Zeng

Hello, I need help to solve Navier-Stokes Eq. using FEM-3D, to simulating of standing waves in a rectangular basin. Just a simple case. But I don,t know how it is. For Driven Cavity, it's easy. But there is no free surface in that case. Anybody could help me ? What kind of books I have to read, or papers, website etc. I don't need the source code anyway. Thank you.

me, student of Civil Eng. Gadjah Mada University -Yogyakarta, Indonesia

Hi

Perhaps you can try a method called "sigma transformation"

Regards Levent