Rayleigh number for vertical cylinder with free convection

[SSeth]

Hi @ all,

i want to simulate the cooling behavior of liquid aluminum in a vertical cylinder(simplified geometry of a real transport crucible), the cylinder is cooled down by the surrounding air from all sides, from top and from buttom, i expect free convection in the liquid

to simulate this i have to decide between laminar or tubulent solvers.

i want to decide this by the rayleigh numer Ra>10^9 =turbulent

but i have a problem, i have lots of literature for the convection !around! a cylinder but zero for the convection !inside! a vertical cylinder,

so what is the characteristic length for the rayleigh number !inside! an vertical cylinder? the diameter or height? do i have to take into account the top and the buttom if yes how?


the correlation equation for D/L>=35/Gr^(1/4) is valid by the way,


if you know a relation/ literature for the nusselt number in this situation, it would be helpful

thx @ all any kind of help is welcome

 

[eljose79]

Hello,

Thank you for your post. It sounds like you have a very interesting research project on your hands. Deciding between laminar or turbulent solvers will depend on the level of accuracy and complexity you want in your simulation. In general, laminar solvers are simpler and faster, but may not capture all the nuances of the fluid behavior. Turbulent solvers, on the other hand, are more complex and computationally demanding, but can provide more accurate results.

In terms of the Rayleigh number, it is typically defined as the product of the Grashof number (a measure of the relative strength of buoyancy and viscous forces) and the Prandtl number (a measure of the relative strength of thermal diffusion and momentum diffusion). In the case of free convection in a vertical cylinder, the characteristic length for the Rayleigh number would be the height of the cylinder. This is because the height of the cylinder will have a significant impact on the buoyancy forces and thus the overall convection behavior.

As for the Nusselt number, this represents the ratio of convective heat transfer to conductive heat transfer and can be calculated using empirical correlations. I would suggest looking into the work of Nusselt himself, as well as the work of Grashof and Prandtl, for more information and literature on the subject.

I hope this helps and good luck with your simulation!