One of the
first things learned by Fluid Dynamics Engineers is how to know if a fluid
is laminar or turbulent. All the equations describing the behaviour of
the fluid depend on it. In the study of the instabilities of Rayleigh-Benard,
the unitless number that is the most often used is the number of Rayleigh,
whose equation was given in a previous chapter. This number depends, for
a given fluid and a given geometry, on the difference of temperature between
the two walls. When we did several calculations with a difference of temperature
getting higher and higher, the fluid became quickly turbulent. So we decided
to see which information FLUENT could give us when a turbulent fluid was
simulated with a laminar model.

1)The previous cases were donc for a cell whose dimensions were 1cm*2cm. To get a Rayleigh number high enough to reach turbulent regime, this cell was too small because the difference of temperature needed would be very high. So we decided to study a cell with dimensions of 1m*1m. Indeed we have chosen a cell not too big to have a reasonable time of calculations.Presentation of the simulation case

Since the fluid moves due to a thermal effect, it is better to use the Nusselt number to quantify the turbulence instead of the Reynolds number, normaly used.

with

: heat transfer passing through the walls (W)

: thermal conductivity (W/m/K)

e : layer thickness (m)

: difference of temperature between the two walls (K)

S : plate area (sq.m)

The data of this case are:

d = 1 m

= 10 K

= 0.6 W/m/K

The Rayleigh number calculated with these parameters is:
**Ra = 125 e 9**

2)Results with the turbulent model

The turbulent model used for this calculation is the two-equations k-epsilon model. The initial parameters for this model are chosen as:

k ~ 1e-6 m2/s2 (Turbulence Kinetic Energy)

~ 1e-9 m2/s3 (Turbulence Dissipation Rate)

Velocity vectors (m/s):

Temperature (K):

The turbulence entails a homogeneisation of the physical properties of the fluid, as it is shown in the previouscontour. Since we will lately have to compare the turbulent results with the laminar ones, we have chosen some values to do this comparison: the heat flux through the fluid (), the highest velocity in the fluid (Vmax) and the Nusselt number (Nu). Here are the values for the turbulent model:

~ 2300 W

Vm ~ 1.7e-2 m/s

Nu ~ 380

3)This case has the same parameters and th same initialization as the "turbulent case". The only thing we changed was of course the model, that became laminar. Here are the results we got:Results with the laminar model

Velocity vectors (m/s)

Temperature (K)

The temperature profile shows the turbulence of the flow because of the
homogeneous temperature in almost the whole cell. So, if we consider only
the contours as the results, it seems correct to conclude that the laminar
model gives the same results as the tubulent one, which is obviously wrong.
And that is why it was interesting to choose some specific values to compare
these two models. For the calculations done with the laminar model, the
parameters described previously are:

~ 115 W

Vm ~ 2.4 e -2 m/s

Nu ~ 20

This study shows us that from the contours, the two models seem to give the same results. But if we consider the heat flux through the fluid, or even the Nusselt number, hopefully we notice that these two models don't give the same results at all. This conclusion is not really new. Nevertheless it was interesting to notice that, first of all, the laminar model could converge even if the fluid was turbulent. And secondly, it was important to draw the attention of FLUENT's users that it is better to know pretty well the case they want to simulate because the results of a simulation are just numerical solutions. The mistake will be to consider these results as what happens physically. FLUENT just solves equations and if the results have no physical meaning, only the user can check it.

4)Conclusion