Introduction

The aim of our study is to determine the formation of the recirculation zone in the snorkel. Therefore, we have to take into acount several parameters : flow rate of air in the engine, speed of the car, boundary conditions, viscosity, ...

1st case : U = 80 m/s

First, we decided to study the flow with a car velocity of 80 m/s. This value corresponds to a nominal standard velocity used by many design offices.
The first simulations gives us the following flow :

We do not notice any recirculation zone.

• Bernoulli equation

We decided to validate our simulation by checking the Bernoulli equation. Therefore, we measured the values of pressure and velocity at the intlet and the outlet of the snorkel.
Inlet : P = 105 400 Pa ; U = 44 m/s
Outlet : P = 102 250 Pa ; U = 59 m/s

• Validation of the simulation

We also decided to check the cross section of the flow by taking into account physical phenomena :
The following frames represent the cross sections of velocity and pressure :

Cross section of velocity

Cross section of pressure

We can notice that the cross section of velocity appears like parabolic, which corresponds to what we expected, regarding to Poisseuille flow results.
However, we can see that the value of velocity is not null at the wall -> problem of
boundary conditions.

In those first simulations, we did not see any recirculation zone.

2nd case : U = 200 m/s

Willing to determine the formation of a recirculation zone, we decided to increase the speed of the car.
With U = 200 m/s, we could not see any recirculationb zone.

We wondered if the problem could come from the number of iterations in time. To check wether the time was correct or not, we studied the residual graph.

Regarding to this graph, we could see that results are rather so that the number of time iteration seem to be rather correct.

3rd case : influence of physical parameters

• Boundary conditions

In order to obtain the formation of a recirculation zone, we decided to change the boundary conditions and to substitute rugosity by a sliding wall.
However, it did not really change the flow.

• Artificial viscosity

By deviding by 10 the value of artificial viscosity, we could finally see the formation of a recirculation zone. The equation of Bernoulli could not be checked anymore since the loss of load modified the cross section of velocity.

We can see this zone on the picture below :

The resprentation of the flow by velocity vectors allow us to see the reciculation zone :

We can wonder why such recirculation zone did appear. From a physical point of view, the viscosity increases the friction loss within the pipe so that this losses are rather progressive. Minor losses can be neglected. By decreasing the viscosity of the fluid, we let reciculation zone the possibility to appear through minor losses.

Study of the recirculation zone

We decided to calculate the value of the losses due to the recirculation zone and to study the influence of the number od iterations on that value.

• time = 0.12 s

number of iterations = 30 000
time step = 4.4 x 10
-6

We can take a look at the cross sections of velocity at the inlet of the snorkel :

inlet : P = 102 900 Pa ; U = 56.4 m/s
outlet : P = 102 000 Pa ; U = 59 m/s

Regarding to these values, the losses amount to 1000 mCE.

• time = 1.9 s

number of iterations = 430 000
time step = 4.4 x 10
-6

inlet : P = 102 248 Pa ; U = 50.6 m/s
outlet : P = 106 680 Pa ; U = 59 m/s

Regarding to these values, the losses amount to 3971 mCE, which is quite a lot.