__4-STUDY OF THE MESH CONSTRICTED AROUND
THE VEHICLE.__

__5-COMPUTATION OF THE DRAG COEFFICIENT.__

__1.1 Presentation of the
problem :__

The aim of this task is to calculate numerically the drag coefficient of a solar vehicle by simuling a flow around a sketch of the vehicle. In order to do this simulation we have used the computation code FLUENT and its generator of grid PREBFC.

We began at first to generate a geometry and several mesh. Our task aiming more on the study of the flow around the solar vehicle than on the realisation of the mesh itself, we have been satisfied with a 2-dimension geometry. Then, we have generated 2 types of unstructured mesh : one composed of mails of regular size, the other more constricted around the vehicle in order to compare the eventual differences of the results.

The drag coefficient (Cx ) is thorically defined by the formula :

with :

Fx : strentgh exerted on the car in the direction x.

A : lateral surface of the solar vehicle.

V : reference speed ( speed at infinite )

r : volumic mass of the fluid.

n : cinematic viscosity of the fluid.

t _{p}(x): shearing
at walls.

__Expression of the drag coefficient for some geometries
:__

Plane plate : Cx = 0.664*Re(x)^{-0.5}

Sphere (for Re small) : Cx = 24 / Re

We have chosen to generate two unstructured meshes, more adapted to the particular geometry of our problem.

We have chosen to mail a domain of quite big dimension in comparison with the vehicle. The length of the domain is 10 meters and its heigth is 4 meters. the vehicle is seen in profile, it measures 2 meters long and 0.8 meter high. It is situated at 0.5 meter of the ground.

In order to obtain good results, we had to chose a grid sufficiently constricted to have several mails between the bottom of the car and the ground. Indeed, we have noticed than with meshes not enough constricted in this zone ( only one mail ) , the results were roughly falsified by the influence of the wall.

As conditions at the limits, we have taken walls to modelise the the ground and the car: an inlet and an outlet at each side of the domain; and in order to limit the domain in height we have taken a condition of symmetryin order to obtain an horizontal direction of the fluid.

In entry , we impose a condition of constant velocity (VELOCITY-INLET). At the exit we take a condition of conservation of the flow of the fluid (OUTFLOW) and then a condition of constant pressure : P = Patmospheric (PRESSURE-OUTLET). In order to simulate the ground we define a wall moving at the same speed than the air.Thus, we reproduce the conditions of a moving vehicle in an immobile fluid.

__Second mesh : constricted mesh.__

In a second time, we generated a grid more constricted in the zone which interested us more specifically : the neighbourhood of the solar vehicle.

Indeed it is around the car that we observe the more important variations of the physical values. We have been able, then, to compare the results obtained with this grid and the precedent grid.

In the case of the regular mesh, we have simulated several cases of flow at different Reynolds. Our aim being to determine the drag coefficient for different values of the number of Reynolds, we had first to calculate the fields of pressure and velocity of the flow in order to verify the validity of our case.

It is possible with Fluent to modelise the viscosity of the flowI. We have thus, in a first time worked out the simulations in a stationary laminar flow, then we have studied the case, more realistic, of a turbulent flow with the standard K-Epsilon model.

Aspect of the field of velocity for V0 = 20 m/s.

Aspect of the field of pressure for V0 = 20 m/s.

The laminar model is valid only for small Reynolds, but it became false when we increase the velocity of the flow. Indeed, it doesn`t take into account the turbulences near the walls and the calculation of the drag coefficient is thus false. It is thus necessary, if we want to approach of the real conditions of the use of the vehicle, to modelise a turbulent model.

We have chosen to modelise the turbulence with the standard K-Epsilon model.

n _{t} is defined by
the relation : n _{t }= Cm
* K^{2} / eps

We initialise K and eps with the values : K = 0.1 et eps = 0.03.

We obtain, for V0 = 20 m/s, the aspect of the field of velocities :

Field of pressure, for V0 = 20 m/s.

__4-STUDY OF THE MESH CONSTRICTED
AROUND THE VEHICLE.ETUDE DU MAILLAGE RESSERRE AUTOUR DE LA VOITURE.__

Aspect of the field of velocity for V0 = 20 m/s.

Aspect of the field of pressure for V0 = 20 m/s.

Aspect of the field of velocity for V0 = 20 m/s.

Aspect of the field of pressure for V0 = 20 m/s.

__5-COMPUTATION OF THE DRAG COEFFICIENT.__

The calculation code Fluent dispose of an instance allowing to compute the drag coefficient ( cf : manual ).

For the different cases studied, we have computed Cx in function of the velocity of the flow.

This is the drag strength in function of the velocity :

We observe that, contrarily to the case of the cylinder or of the plane plate with an incidence angle equal to zero ( classical cases seen in class ) where the drag coefficient decreases when the Reynolds increases, Cx is here approximatively constant. The drag strength, thus increases proportionnaly to the square of the velocity.

This is due to the singular geometry of the car which presents an incidence angle to the flow not equal to zero, and which create a depression behind it.

We observe that the drag coefficient in laminar is lower than the turbulent one. Indeed, in turbulent the shearing on the walls is greater than in laminar.

The computation of the drag coefficient depend also of the grid used, the more the grid is narrow around the walls and the more the calculation of the shearing, of the fields of velocity and pressure and of the drag coefficient is precise. In our case, the more narrow is the grid, the more the drag coefficient decrease.

This task allowed us to have a good learning of fluent and its grid generator PREBFC. We could familiarise ourselves with the technics of grid and see their importance in a numerical simulation.

Moreover, the aim of this task was very interseting because it was a real engineer problem. It showed us what could be asked to an engineer in order to improve the characteristics of a vehicle.