Simulation parameters

For the test cases, the following parameters were taken :

External air speed : 50 km/h

External air temperature: 278 K

Ventilation speed : 1 m/s

Ventilation temperature : 313 K

These parameters seemed us good to validate our model, especialy the boundary conditions and the characteristic time of the heating of the cabin. They introduce indeed strong convection on the external boundaries of the car (glasses, roof and floor), and strong temperature gradients.

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 Case tests in 2 dimensions

In order to validate our modelization, we performed two-dimensional simulations with the 2D mesh and the right boundary conditions.

The different results are presented for t = 100s.

The velocity simulation seems to be correct with a larger velocity in the upper part of the cabin. We can observe vortexs in the car, on the seats and under the console.

The vortexs are better visible on the following picture, which displays velocity vectors coloured by temperature.

We can observe that the repartition of temperature in the cabin is quite homogen after a very short time: 100s.

We can observe the appearance of boundary layers on the wall and glasses, which permits to think that the thermal boundary conditions are correctly modellized. But the lack of data did not allow us to modelize the heat losses on the seats and on the console.

This modelling seems then to reflect correctly the real phenomena, except about the time needed to heat the cabin of the car. But as we consider that all the windshields are pulsing hot air, we need to perform 3D calculations to evaluate our model.

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 Three dimensional simulation

To evaluate the influence of the three dimensional modelling, we used the mesh created with ICEM-CFD. The same parameters were used as in the two-dimensional simulation, except the use of the porous media.

The influence of 3D is then obvious. The following picture represent the isothermal curve with a temperature of 307 K. The different flows produced by the windshields are visible, and also the ifluence of the bottom windshields.

Some cuts show clearly the influence of 3D modelling, with a different repartition of temperature in the cabin versus the z coordinate :

longitudinal cut on the middle of the left front seat

longitudinal cut on the middle of the cabin

The boundary layer on the roof and glasses is also visible, with transversal cuts. We can observe some dissymetries in the flow, probably due the interaction between vortex:

transversal cut, x = 1.5 m

The evolution of the temperature in the middle of the cabin is shown by the pictures below (time step 20s):

After 20s:

After 40s:

After 60s:

After 80s:

After 100s:

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 Discussions and problems

A more rigorous analysis has permitted us to detect some problems with the 3D case.

The graphic of the path lines show clearly that the flow is going out too rapidly of the car.

Another problem is clearly visible: the density of the mesh at the boundary faces is not sufficient to observe clear boundary layers. But we could not refine the mesh, because of calculation time.

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