RD-E: 5000 INIVOL and Fluid Structure Interaction (Drop Container)

The aim of this example is to introduce /INIVOL for initial volume fractions of different materials in multi-material ALE elements, /SURF/PLANE for infinite plane, and fluid structure interaction (FSI) with a Lagrange container.

Input Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this example are available in:

Model Description

A hex mesh is created that fully encloses the structural container. The mesh size of the hex mesh should be ½ the size of the structural mesh. Ideally the hex mesh should also be ¼ of the structural mesh size in the direction of impact. To simplify this example, the hex mesh in this model does not adhere to the ¼ mesh size guideline.

A container partially filled with water is simulated being dropped from a height of 1 meter. The container is partially filled with water with the remainder filled with air.

Boundary Conditions

Each outer side of the hex mesh is constrained to prevent displacement in the direction normal to the side. For example, the top and bottom of the hex mesh is constrained in the z translation DOF (Figure 2). The same is done for the other four sides. The velocity at impact of a drop from 1 meter would be 4429 mm/s. Since the simulation is started right before impact, an initial velocity of 4429 mm/s is applied to the container and the fluid hex mesh (Figure 2).

Units: mm, s, Mg, N, MPa

In one /MAT/LAW51 card, three different phases can be defined. The two phases are: Air and Water

Air is defined with the following characteristics:
Reference density used in E.O.S (equation of state)
1.2e-12
Initial density of air
1.2e-12
Initial energy per unit volume
0.25
Hydrodynamic cavitation pressure
-1e-20
Hydrodynamic coefficient C41
0.4
Hydrodynamic coefficient C51
0.4
Water is defined with the following characteristics:
Initial density of water
1e-9
Hydrodynamic cavitation pressure
-1e-20
Hydrodynamic coefficient C03
0.10
Hydrodynamic coefficient C13
2250 (Liquid bulk modulus)
/ALE/MAT should also be defined for the /LAW/MAT51 material, to indicate that is an ALE model.

Coupled Euler_Lagrange (CEL) Interface

To define the contact between the fluid and the structure a visco-elastic penalty formulation /INTER/TYPE18 interface is defined as:
• Main is the Lagrange structure
• Secondary is the ALE fluid nodes
Gap is the Interface gap. The recommended value is 1.5 times fluid element size along the normal direction to contact.(1) $Stfac=\frac{\rho \cdot {v}^{2}\cdot {S}_{el}}{Gap}$
Where,
$\rho$
The (highest) fluid density
$\upsilon$
Velocity.
• For incompressible models (ditching, sloshing, etc.), use the velocity of the event.
• For compressible but not supersonic, use the speed of the sound in the material.
• Compressible and transonic (Mach 0.8 to 1.0), replace the term ${\nu }^{2}$ with $v\cdot c$
Where,
$\upsilon$
Speed of the sound in the material
$c$
speed of sound in air
• Compressible and supersonic, use the velocity of the event
• For an explosion, use the Chapman Jouguet velocity
$v\cdot c$
Surface area of the Lagrangian elements
$Gap$
Interface gap, as defined above
For this example:(2) $Gap=1.5fluid\begin{array}{c}\end{array}element\begin{array}{c}\end{array}size=1.5×2.5=3.75\left[\mathrm{mm}\right]$ (3) $Stfac=\frac{\rho \cdot {v}^{2}\cdot {S}_{el}}{Gap}=\frac{1×{10}^{-9}×{4429}^{2}×\left(5×5\right)}{3.75}=0.131$

Simulation Iterations and Modeling

Fill Container with /INIVOL.

With /INIVOL, the water line can be defined in this part.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/INIVOL/part_ID/inivol_ID
inivol_title
surf_ID ALE_PHASE FILL_OPT ICUMU FILL_RATIO
surf_ID ALE_PHASE FILL_OPT ICUMU FILL_RATIO
etc etc etc etc etc
surf_IDn ALE_PHASE FILL_OPT ICUMU FILL_RATIO
/INIVOL uses successive filling actions of the initial background multi-material ALE mesh, to get the final configuration of the initial volume fractions (three containers and three ALE phases). Initially the volume is filled by the first material defined in the /MAT/LAW51 field. In this case, the first material is air, so the entire hex mesh is first filled with air. Next, a surface is defined from the container part ID.
/SURF/PART/998
Vessel_Surf_Part
85
Since the surface normal of container part point outside, use FILL_OPT = 1 to fill the water (phase 3) inside the container (filling the side which against surface normal direction).
/INIVOL/86/10003507
INIVOL
#  Surf_ID ALE_PHASE  FILL_OPT     ICUMU          FILL_RATIO
998         3         1         0                 1.0
Now, ALE mesh is filled with ALE material 1 (air) from /MAT/LAW51 on the outside of the container and material 3 (water) inside the container. Lastly, define a surface plane, /SURF/PLANE to define the fill height. The normal of this plane points upward, use FILL_OPT = 0 to fill the air (phase 2) above the plane (filling the side along normal direction).
#  Surf_ID ALE_PHASE  FILL_OPT     ICUMU          FILL_RATIO
9999         2         0         0                 1.0
To check the initial fill, the following animation options can be used in the Engine file.
• /ANIM/ELEM/DENSITY
• /ANIM/ELEM/VFRAC

You can contour the model and use section cut to see inside, or use iso-surface, as shown in Figure 4.

/ALE/MUSCL - Anti-diffusive Technique

/ALE/MUSCL allowing for a better localization of the interface between fluids, and much less numerical diffusion. In this example, use default for Beta.

/ALE/GRID/DONEA - ALE Grid Velocity

This activates the J. Donea Grid Formulation, where the velocity of a given grid node depends on velocity and displacements of neighboring grid nodes.

Engine Control

It is recommended to use time step scale factor 0.5 for ALE in /DT/BRICK in order to keep computation stable, and use fac=1.0 in /UPWM/SUPG. This option provides better velocity field in Cartesian grids when ALE material velocity is not normal to brick faces.

Results

To see the movement of the water in the container, and iso-surface plot of results type "density” can be done. If the simple averaging method is used in HyperView, the results will look smoother.

Also notice that water is starting to splash up the sides of the container at the end of the simulation.