Evaluation of T and V at each iteration.
 

The lack of reliability of previous methods let us esperate to reach better accuracy taking into acount the evolution of box center values of Tadim and V during iteration process.
On the graph just below, we can see that after a transient evolution, Tadim and V reach a levelled state.
To determine the critical Ra number using Tadim curves, we use the same preceeding idea that is Tadim should yields to 0.5 for critical and under-critical Ra.
To determine the critical Ra number using V curves, we use the idea that V should yields to 0 for critical and under-critical Ra.
 
 
 
Box center vertical velocity : 1565< Rac <1577 (dT=0.129<  dTc  <dT=0.128)
Box center dimensionless temperature  : 1565< Rac <1577 (dT=0.129<   dTc <dT=0.128)

1) Determination of Rac using V.

We are here using the resulsts obtained for a 10x20 nodes mesh.

We are going to explain the procdure to determine the Rac . For this the user should be able to store on disk a point value at each iteration.

Firstly choose an arbitrary over-critical Ra number. e.g.~1850. Then produce a series of curves with decreasing Ra.
    We can then determine a major boundary value for the Rac. On the graph below it is clear that : Rac <1758 (grey curve)
    For an accurate determination we must zoom to low speeds area.
 
 
Box center vertical velocity

 
 


Zoom to low speeds area:
 

We plot curves with decreasing Ra number up to reach a value of Ra for which the mean value of the velocity is about null. We have reached the 1589 Ra number.
The main problem of this type of determination is the difficulty to say if the mean value of the velocity curve can be considered as 0.
If the curves are well ordered ,i.e. the mean value of the velocity deacreases with Ra number, we can then obtain a more accurate result.
Looking at the graph we can say that 1589< Rac <1711   i.e. Rac = 1650 +/-60.
Nevertheless the monotonic placement of the red, green and blue curves let us to say that Rac ~1711.
It should be noticed that the differenciation between curves near critical Ra number becomes more and more diffcult as the mesh is finer.
 
 
 
Box center vertical velocity

 
 

2) Determination of Rac using Tadim.
 

A seek to next graph let see that for critical and under-critical Ra numbers Tadim does not tend to 0.5 but to 0.45. This problem comes from the manner of FLUENT to interpolate temperature at a point when this point does not match with a grid point. No matter this artificial shifting value effect the user will compute a far under-critical Ra number simulation to get the limit value of Tadim. Here it is 0.452.
 

The observation of the set of Tadim curves yields to the same conclusion as done studying V : We can then determine a major boundary value for the Rac. On the graph below it is clear that : Rac <1758 (grey curve)
    For an accurate determination we must zoom to low speeds area.
 
Box center dimensionless temperature


Zoom to low speeds area:

We can see that the determination of  critical Ra number is more difficult tham with V , since the curves placement is not monotonic.
Looking at the graph we can say that 1589< Rac <1753   i.e. Rac = 1671 +/-80
It should be noticed that the differenciation between curves near critical Ra number becomes more and more diffcult as the mesh is finer.
 
 
 
 
 
Box center dimensionless temperature

 
 
 
 

3) Conclusion

At first, we noticed that the determination of Rac is less accurate using Tadim than with V.
The use of these methods should leads to some problems of accuracy for fine meshes because of the difficulty to separate curves behaviors.