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

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.

Figure 1. Problem Description

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).

Figure 2. Boundary Condition of Container in z-direction

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.

To define the contact between the fluid and the structure a visco-elastic penalty formulation /INTER/TYPE18 interface is defined as:

• Master is the Lagrange structure
• Slave 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

$\upsilon$

The 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

$$v\cdot c$$

The surface area of the Lagrangian elements

$$Gap$$

The interface gap, as defined above

For this example:(2) $$Gap=1.5fluid\begin{array}{c}\end{array}element\begin{array}{c}\end{array}size=1.5\times 2.5=3.75[\mathrm{mm}]$$ (3) $$Stfac=\frac{\rho \cdot v^2\cdot S_{el}}{Gap}=\frac{1\times {10}^{-9}\times {4429}^2\times \left(5\times 5\right)}{3.75}=0.131$$

/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

Figure 3.

To check the initial fill, the following animation options can be used in the Engine file.

• /ANIM/ELEM/DENSITY
• /ANIM/ELEM/VFRAC

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

Figure 5.