Turbulence models
In Fluent, turbulence is modeled using one of two "twoequation" turbulence models, or the Reynolds stress model. In twoequation models, effects of turbulence are represented by an isotropic turbulent viscocity which is evaluated using two quantities, k and e, are obtained from the solutions of "modeled" transport equations. In the Reynolds stress model, transport equations ( 6 in 3D, 4 in 2D) are explicitly solved for the Reynolds stresses.Fluent provides the following choices of turbulences models :
Before starting any simulation, we have to determine a critic temperature difference DT_{c }to have a turbulent flow. The following picture gives the rate of flow for differents values of e :
According to this scale, the flow is turbulent for e_{turbulent }>2000, i.e., DT _{turbulent }> 2001.DT_{c }.But with a critical temperature difference about 0,2 degree, we should have DT _{turbulent }= 500 degrees. Consequently, if we use liquid water, this conditions will be unachievable because the computation time will be very high and the fluid might boil ! So we found a case nonlaminar by starting with low DT and increasing it untill the results were not physical because the flow was no longer laminar.We can see it with the temperature field with a laminar study :
D T = 0,1 e ~0,5
no rolls 

DT = 0,2 e ~0
2 rolls 

DT = 5 e ~24
2 rolls


DT = 10 e ~49
4 rolls


DT = 20 e ~99
2 rolls

In this last caseI, the computations are converged with 39 iterations
!
All this part , we will work with these conditions :
In these previous equations, five constants appears. The ke standard model is based on the following values :
The simulation are done with 20 degrees between the two walls.
Turbulent cinetic energy  
Velocity field  
Temperature 
We can see that a kind of roll lices on. This phenomena is due to the oversight the term pu' in the kequation.
In order to avoid these problems, we added the following option :
The results are :
Turbulent cinetic energy  
Velocity field  
Temperature 
The convection rolls don't appear. Moreover if we
look at the turbulent cinetic energy, we find that the highest is localised
inthe center of the box although it is near the wall that there are gradient
of temperature.
Actually, this model gives good results for Reynolds numbers of the turbulence
Re_{T} >>1 and far from any partitions. In fact, the velocity
can be descirbed by a logarithmic law :
The validity field is y^{+}>30. But an estimation of y^{+}
can be done with the following values :
y =10^{3} u^{*} =10^{2} v =10^{6} so
y^{+}=10 < 30.
Moreover if we try to optimise the mesh by increasing the number of nodes,
y+ will decreased .
Renormalization group (RNG) methods are a general framework for "model building" in which the complex dynamics of physical problems is described in terms of ''coarsegrained" equations of motion governing a large scale, longtime behavior of the physical system. The mathematics of RNG theory allows similar coarsegraining of physical phenomena and has been applied to a range of physical processes including critical phenomena, highenergy particle physics, and, in the context of fluid dynamics, turbulence, combustion, and heat transfert. The key idea is that the RNG method is applicable to scaleinvariant phenomena lacking externallyimposed characteristic length and time scales. For turbulence, this means that the method can describe the small scales that should be statistically independent of the external initial conditions and dynamical forces that create them through various kinds of instability phenomena.
Turbulent cinetic energy  
Velocity field  
Temperature 
We can see that the differents field have the same than previously. But if we look at the maximum of turbulent cinetic energy and velocity , we find:
Model 
E_{c} (m^{2}/s^{2 )} 
V (m/s) 
ke standard 
10^{5}

2,24.10^{3}

ke standard 
6,79.10^{3}

3,30.10^{8}

RNG 
3,5.10^{4}

3,5.10^{4}

The problems encounted with this last model can be partly explained with stricted mesh conditions .