Numerical simulations
Numerical simulations
The studied geometry is an airplane part which lies between the wing and the turboreactor. This part is called fuel container.
Figure: Position of the studied geometry in red
source: http://photos.linternaute.com/photo/1457769/1553166946/2092/elements-d-avion-de-ligne-boeing-757/
It is crossed by the fuel pipes which supply the engine of the reactor. Sometimes, it occurs a leak of fuel in this part of the airplane. The fuel is then gathered in the container and evacuated by its bottom. The fuel may be evaporated there and the concentration of fuel may increases. An air flow is also kept in this structure to make sure that the concentration of fuel does not increase too much.
Even though the security of the passenger in the airplane is guarantee, Airbus wants to understand the mechanism which drives the evaporation and want to know if CFD is adapted to a such problem.
Geometry
Airbus, the industrial partner, has given the following geometry
Figure: Initial geometry given by the industrial partner
It's composed by two circular holes at the left hand side situated at the two extremities of the fuel container. Each hole measures 20 mm. To capture the flow inside the geometry, the flow at the inlet and at the outlet has to be correctly solved and involve a large number of cells in this regions.
To avoid meshing problems the inlet and the outlet of the flow have been redefined. Plus the baffles have been enlarged for the same reason avoid meshing problems.
Here below is shown the geometry used for the numerical simulation:
Figure: Simplified geometry
Numerical simulations
IcemCFD meshing
The meshing is one of the critical points of CFD. Numericians are aware that to obtain good simulation results, a clever meshing has to be done.
Enseeiht's teacher used to say that meshing represents 90% of the time dedicated to the simulation.
The geometry is meshed with tetrahedon and cells has been refined near the wall to capture the wall shear stress. The mesh is composed by 306814 elements.
The following two figures show the mesh. The first gives an overview of the general mesh and the second one is a cut plane of the mesh. It illustrates the mesh refinement near to the wall.
Figure: Overview of the mesh
Figure: Cut plane of the mesh with refinement near the wall
Then, when the mesh is created, the mesh has to be qualify. And to do so, three different meshes are going to be tested:
Mesh number | Total number of elements |
1 | 31 013 |
2 | 115 142 |
3 | 306 814 |
Numerical simulations
meshing sensitivity
The mesh has to be qualified. The results must be independent from the mesh, so the results can be valid and used for further analysis.
Three different meshes have be chosen to the "mesh convergence". Here follows the total number of elements for each one.
Mesh number | Total number of elements |
1 | 31 013 |
2 | 115 142 |
3 | 306 814 |
The most interessant regions are the ones where the fuel is more likely to evaporate: the region, separated between the two baffles, which defined one part of the geometry's bottom.
The following picture shows the geometry, the velocity on a slice and the line along where the mesh sensitivity is done.
Figure: Velocity on the slice geometry and line over which the sensitivity will be done
The mesh sensitivity along this line brings up to the light that the mesh used is not the best one. The maximal velocity (Position = 0.1m) is obviously not the same for the different meshes. Although, the velocity elsewhere along the line seems to be good for both mesh 2 and 3. Mesh 1 can not be used for an analysis because it gives strange results for the maximal velocity. On the other hand, mesh 2 and 3 have a parabolic shape which is what it's expected for a flow between two walls. Even if these two meshes seem to be good they are not perfect.
Although for a matter of time and CPU capacity, it has been here chosen to go on with mesh number 3.
Figure: mesh sensitivity along the white line
This study underlines the fact that the mesh is not ideal. But we are not pretending to have perfect results. the project's goal is to set up a path which can be used for further analysis.
Numerical simulations
Once the mesh sensitivity has been done, the parametric study can be processed. The following figure shows the three flight conditions used. For each flight condition, the industrial partner has given the Reynolds number and the density.
We note that the following results correspond to the "lift off" flight's conditions. The next figure shows a screenshot of the temperature field in the container:
Figure: The temperature field in the container
1- $ \delta_T $ and $ h_c$
The first step to estimate the evaporation rate $W_v$ is to compute $ \delta_T $ and $ h_c$. For this, the simulations gave us $ \delta_T $ and $ h_c$. The figure below explains how we have done to extract these values from the simulation results:
Figure: numerical estimation of $ \delta_T $ and $ h_c$
2- Evaporation rate $W_v$
We remind that we have found the expression of the evaporation rate $W_v$ on account density, the boundary layer thickness $ \delta_T $ and $ h_c$
$$W_v(x)=\frac{b\lambda}{C_p} ln\left( 1+\frac{W_v(x)}{b}\frac{C_p}{h_c(x)}\right)\frac{1}{\delta_T(x)-\delta}$$ |
Then with this formula established previously, $W_v$ is processed.
To better understand the distribution of the evaporation model, here there is the following figure:
Figure: distribution of the evaporation model
Otherwise, the following table gave the values of the evaporation rate in different flight cases:
It's important to note that the most accurate result is the one of the lift off flight case because all the simulations were done in this case.
Otherwise, the mass vapor rate seems to be very high. What can be interesting to validate this approach is to compare it to available experimental data but it doesn't exist yet.