RD-E: 0602 Fluid Flow

Fuel tank overturning with simulation of the fluid flow. The reversing tank is modeled using horizontally-applied gravity. The tank container is presumed without deformation and only the water and air inside the tank are taken into consideration using the ALE formulation.

The fluid flow is studied during the fuel tank overturning. This example uses the ALE (Arbitrary Lagrangian Eulerian) formulation and the hydrodynamic bi-material law (/MAT/LAW37) to simulate interaction between water and air. The tank container is presumed without deformation and it will not be modeled.

Options and Keywords Used

Regarding the ALE boundary conditions (/ALE/BCS), constraints are applied on:
  • Material velocity
  • Grid velocity

All nodes inside the border have grid and material velocities fixed in the Z direction; the nodes on the left and right sides have a material velocity fixed in the X and Z directions, while the nodes on the high and low sides have a material velocity fixed in the Y and Z directions. The grid velocity is fully fixed on the border, just as the material velocity is fixed on the corners.

A function defines gravity acceleration in the X direction compared with time in order to simulate the rotation effect. Gravity is activated by /GRAV. Two cases are studied depending on the acceleration function selected:

ex6-fig9and10
Figure 1. Left: Variable Acceleration Function 1; Right: Constant Acceleration Function 2
Gravity is considered for all nodes.
  • Both ALE materials air and water must be declared as ALE using /ALE/MAT. Lagrangian material is automatically declared as Lagrangian.
  • The /ALE/GRID/DONEA option activates the J. Donea grid formulation in order to compute grid velocity. See the Radioss Theory Manual for further explanation about this option.

Input Files

The input files used in this example include:
Fluid_flow_gravity_1
<install_directory>/hwsolvers/demos/radioss/example/06_Fuel_tank/2-Tank_overturning/Fluid_flow_1/PFTANK*
Fluid_flow_gravity_2
<install_directory>/hwsolvers/demos/radioss/example/06_Fuel_tank/2-Tank_overturning/Fluid_flow_2/PFTANK*

Model Description

A rectangular tank is partially filled with water, the remainder being supplemented by air. The tank turns once around itself on the Y-axis. The overturning is achieved by defining a gravity field in the X direction, which is parallel to the liquid gas interface. All gravity is applied in other directions. The initial distribution pressure is already known and supposed homogeneous. The tank dimensions are 460 mm x 300 mm x 10 mm.

rad_ex_fig_6-7
Figure 2. Problem Description

The example deals with two loading cases: an instantaneous rotation of the fuel tank by 90 degrees (gravity function 1) and a progressive rotation (gravity function 2).

The main material properties for the ALE bi-phase air-water are:
Material Properties
Air density
1.22x10-6 [ g m m 3 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadEgaaeaacaWGTbGaamyBamaaCaaaleqabaGaaG4maaaa aaaakiaawUfacaGLDbaaaaa@3BBC@
Water density
0.001 [ g m m 3 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadEgaaeaacaWGTbGaamyBamaaCaaaleqabaGaaG4maaaa aaaakiaawUfacaGLDbaaaaa@3BBC@
Gas initial pressure
0.1 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@

Model Method

The bi-material air-water is described in the hydrodynamic material law (/MAT/LAW37). See previous section for information about this law, including full input data.

This loading case does not require a tank container mesh and the model, air and water are only comprised of the brick element using an ALE formulation.

rad_ex_fig_6-8
Figure 3. Air and Water Mesh (ALE bricks)

Using the ALE formulation, brick mesh is only deformed by the tank deformation, the water flowing through the mesh. The Lagrangian shell nodes still coincide with the material points, while the elements are deformed with the material: this is the Lagrangian mesh. For the ALE mesh, nodes on boundaries are fixed to remain on the border, while the interior nodes are moved.

Results

Curves and Animations

Table 1. Model with Constant Acceleration (Gravity function 1) - Time = 170 ms
Density

ex6_density-170_zoom53
Velocity

velocity-50_zoom59
Table 2. Model with Constant Acceleration (Gravity function 1) - Time = 280 ms
Density

ex6_density-280_zoom59
Velocity

velocity-70_zoom59
Table 3. Model with Variable Acceleration(Gravity function 2) - Time = 50 ms
Density

ex6_density-50_zoom62
Velocity

velocity-170_zoom61
Table 4. Model with Variable Acceleration (Gravity function 2) - Time = 70 ms
Density

ex6_density-70_zoom61
Velocity

velocity-280_zoom59

Conclusion

This example studied hydrodynamic bi-material using LAW37 in Radioss, using ALE and Eulerian formulations. The application of boundary conditions in ALE formations and handling the fluid-structure interaction were discussed. Furthermore, the results obtained correctly represent the physical problem.