Study of the initial condition influence in Steady flow


    We noticed during our simulation that the initial condition influenced  the type of solution we obtained.
Using a configuration formerly defined and a difference of temperature of 3 °K, we obtained three different results with three different initial conditions.
The walls temperatures are 300 K for the top wall and 303 K for the bottom wall. The fluid used is water.
The correspondent Rayleigh number (Ra) is approximately 25000.


- In the firs case, we assume that the velocity is equal to zero in the domain and that the temperature is equal to a constant fixed to 301.5 K.
We obtain three rolls.
Static temperature in the domain
Velocity vectors

On the animation of the static temperature (obtained with an unsteady study), the temperature in the layer evoluates first into a gradient configuration and then splits into a mushroom shape.


 
- Now, we keep the velocity equal to zero but we assume that the distribution of temperature is linear between the two plates at the initial time. We cannot observe any rolls. The solution of the computation is a linear distribution of the temperature.

 
Initial condition in temperature 
  Result of the computation

The calculation converges in 21 iterations.
This configuration correspond to a stable result of the problem. However, the Boussinesq effect, that is supposed to give an important buoyancy to the fluid particle at the bottom, seems to be missing. It is quite strange if we consider that for the first case studied (initial temperature in the domain), the temperature distribution goes first to gradient and then evoluates to an atomic mushroom shape. This evolution is not present here.
 
 

    If we keep the same type of initial conditions, which means a velocity field initially equal to zero and a temperature with a linear distribution, but with a modification of the gradient value, we notice that the result of the computation is not the same.
The difference of temperature between the two plates is now 5 °K. The reason why we have decided to increase the gradient value is that we wanted to know if  the initial condition in temperature as a gradient was "blocking" the code, which means that no rolls could be computed, even with a large Rayleigh number.
 
 
 

Initial condition in Temperature

 
 
Results of the computation  
Static Temperature
                      Velocity field

Obviously, the result are not the same. We don't know why the computation gives a result in that case and if there is a critical difference of temperature that has to be considered in that case of initial condition to allow a result of Fluent including a flow motion. Furthermore, it makes us become very critical to the solutions given by the calculating codes. In several complex cases, we need to know exactly the type of solving and the approximations of the code to decide if whether or not we trust the computation.

It is also to notice that the rolls are not centered . Why?  we don't know either.

   



 
 
- In another case, we decide to keep a constant temperature in the domain at the initial time, but we give a condition to the velocity vectors inside the domain, similar to the velocity field observed for two rolls.

 
Initial condition in velocity
Result of the computation


As a conclusion, we can say that the initial conditions seem to be important .  Indeed we have noticed that our results are directly linked to these ones.

To achieve these different configurations, we have used the custom field function provided in Fluent.