Content  Introduction  Global parameters  Simulation parameters  Thermal boundary conditions  Outlet modelization  Problems
The present part describes the modelization used for our calculations.
As we did not have any documentation on this subject, we were obliged to create our modelization.
The parameters and boundary conditions presented here are the results of different attempts, and are sometimes not linked with physics. For instance, we chose the coefficients for the outlet boundary condition experimentally, with visual observation of the results.
A better modelization could be off course possible, but with a larger time and documentation.
To perform the calculations, we considered that the car was running, with a speed of 50 km/h.
The temperature of the external air is fixed and is a parameter of the simulation.
For every simulation the inner temperature of the car is equal to the temperature of the external air and there is an equilibrium between the exterior and the interior of the cabin at the initialisation time.
For the simulations, two solid materials have been used, glass and aluminium. The physical parameters for aluminium were taken in the Fluent database and for the glass in Aide mémoire du thermicien (Elsevier, 1997)
The windshields are designed in the mesh to reflect the real windshields of the Twingo, as shown in the picture below:
This section describes the parameters chosen for our simulations. The computational code used for the calculations was Fluent.
Solver 
To perform our study, we decided to use the kepsilon model. The flow which goes out of the vent nozzles is indeed turbulent. This can be explained by the different bundles, filters and pumps placed in the aeration system of a car.
The energy model of Fluent was used.
The standard options proposed by Fluent were conserved for the calculations.
Time step 
The simulations were performed with transcient calculations in order to visualize the evolution of the temperature in the cabin. The time step was chosen as 0.1s, to be small enough to allow a good accuracy for the result and avoiding numerical problems.
One of the greatest problem encountered during this project was the definition of the right thermal boundary conditions.
Theoretical approach 
The main encountered phenomenon is the thermal convection. That is to say that we had to evaluate the convection coefficient of each boundary surface.
In fact, because of lacks of documentation, it was only possible to define this coefficient for the glasses and the bottom and upper part of the car. The lateral walls and the seats were considered as adiabatic walls.
To evaluate this coefficient, we used the following formula for the Nusselt number, valuable for turbulent flows :
avec et
This formula is valuable for a plane plate. That means that the local Reynolds number of the plate is used instead of the global car Reynolds number.
To calculate the convection coefficient, we used the formula :
Parameters 
As the air is the external fluid, we took the following parameters :
Results for thermal boundary conditions 
The results are detailed in the following table:

Length (m) 
Re 
Nu 
H (W/m2/K) 
Width (mm) 
Foreward window 
1 
9.54e10^{5} 
2011 
48.6 
3 
Backward window 
0.66 
6.3e10^{5} 
1443 
52.9 
3 
Roof 
1.51 
1.44e10^{6} 
2796 
44.8 
30 
Floor 
1.4 
1.33e10^{6} 
2624 
45 
50 
These results were inputs for the definition of the thermal convective conditions in Fluent
The other problem encountered was the modelization of the outlet.
In a car, there are indeed losses because the cabin is not completely closed. For instance, with defective joints, or special aeration nozzles.
It was very difficult to modelize these parameters, and also quite impossible without data. So we decided to create holes in the coffer of the meshed cabins.
The problem was, after the first simulations, that all the repartition of the heat was not correct: the most part of the heated air was going out through the windshields. A better modelling was needed.
We tried to put losses of pressure on the outlets, but this solution has not given the awaited results: the repartition of heat was the same. The other problem was that the speed of convergence of our calculations was very slow.
The solution to date in our simulations is to place a porous media in the coffer, to slow the outgoing of heat. This porous media is made of aluminium, and the value of the porosity was taken at 50%.
Unfortunately, some parts of the model could not be applied to the 3D mesh. It was indeed designed before the elaboration of the outlet modelization. Because of its complexity, the division of the inner fluid into two zones was impossible and thus, the use of porous media.
For 3D mesh the outlet consists then in two little holes in the rear part of the coffer.