In this paragraph, we are going to study, in a first point, the temperature for which the steady rolls appear. In a second part, we'íll study the meshing influence on the computation.
Rac is defined as the number for which the steady rolls appear. So to
determined it, we are going to simulate some cases for different temperature
and calculate the heat flow between the two walls. Indeed, we are going
to use the Nusselt number:
This number is the ratio of two heat flux: the actual and those exchanged as if the exchange was only made by conduction. Then we have:
In our case:
So, to determine Rac, we just have to plot Ra, in function of Nu. This have been made for a grid containing 800 cells (20x40):
We find: Rac=1743
To check our calculations, we plot the contour of temperature at Ra=1763 and Ra=1723.
So, our computations seem to be correct:
Now, we are trying to determine the influence of the grid on Rac. We have realised new computations on a 10x5 grid. A new critical Rayleigh Rac has been calculated by using the same method:
This time, we find Rac=1565
We check this result by plotting the contour of temperature at Ra=1603 and Ra=1522:
For the same physic case, we didnít found the case result: the grid has a heavy influence on the computations. Then, to find the actual Rac, a investigation would be to lead the simulation on grids more and more fine, until Rac donít depend on the mesh.