Study of the 3-D case

 

 
 
 
 
 
 

In this case, we wanted to see the behavior of the calculation faced to the first problem we have treated (Ra = 25000) but in three dimensions.
 

Conditions of the Calculation

The domain is 3 cm length, 2 cm  width and 1 cm height.

The grid is composed of  24000 squared cells (30x40x20). That is to say half time the proportion used in the 2-D case. The fact of not keeping the same number of cells for each segment is due, of course, to the calculation time which is considerably increased.

The boundaries conditions are:
    - symmetry on the vertical boundaries
    - Temperature given on the walls

All others parameters or way of calculation are exactly the same than in the 2-D case.

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Results obtained

In the 3-D case, we obtain an extrapolation of the 2-D results. That is to say that we find the same kind of profiles for temperature (mushroom) and velocity (rolls) in a cross section.

Nevertheless, with the same conditions (boundary and initial) we find two rolls in the 3-D case, where as in the 2-D case,we found three rolls.
 
 
Temperature
Velocity

Moreover, the results obtained with the unsteady simulation are not exactly the same that for the 2-D simulation. Indeed, for the temperature there is not a smooth evolution of the mushroom and also a translation  in the x direction until reaching a steady state.
For the velocity, we can see the development of rolls (axis in the x direction) that die once the steady state is reached. This shows the competition between the different possibilities of direction that can be used by the phenomenon. Finally, this one seems to prefer the longer rolls.