Grid

The hypothesis is that the upper
rolls need more room to developp, so we mqde a higher mesh.

Viscosity

/*user define function*/

/* udf pour viscosite*/

#include "udf.h"

DEFINE_PROPERTY(viscosite,cell,thread)

{

real nu;

real temp;

temp=C_T(cell,thread);

if (temp<300.5)

nu=0.1;

else if (temp<300.75)

nu=-0.396*temp+119.098;

else

nu=0.001;

return nu;

}

Initial Velocity, |v|=1, delta T=1

If we simulate this case without
any viscosity gradient, the convergence is to 2 rolls, one above the other.

Velocity

We can notice the developpement
of the lower roll and the motion of the fluid above, but still not one
real roll.

Velocity, |v|=10, delta T=1

Even with a greater velocity initialisation, the convergence is similar to the last one.

Velocity, |v|=10, delta T=10

The solution could have been to take a bigger Rayleigh number, but , as we can see, the researched case is unstable and with a greater Rayleigh, the case converges to one single roll.

Velocity, |v|=1, delta T=5