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.

Options and Keywords Used

Solid element (/BRICK)
Material laws (/MAT/LAW51 (MULTIMAT) and /MAT/LAW6 (HYDRO or HYD_VISC))
Property (/PROP/TYPE14 (SOLID) with ALE property formulation I_ale = 1)
Load (/INIVEL)
Define initial volume (/INIVOL)
Infinite surface plane (/SURF/PLANE)
Fluid structure contact (/INTER/TYPE18)

Input Files

Before you begin, copy the file(s) used in this example to your working directory.

RD-E-5000_Inivol_FSI.zip

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.

ex_50_container — Figure 1. Problem Description

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).

ex_50_container_bc — Figure 2. Boundary Condition of Container in z-direction

Units: mm, s, Mg, N, MPa

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

Air is defined with the following characteristics using sub-material /MAT/LAW6:

EoS_Options_input (IDEAL_GAS): Value
Reference density: 1.22e-12
Initial density: 1.22e-12
Heat Capacity Ration (Gamma): 1.4
Initial Pressure (P0): 0.1

Water is defined with the following characteristics using sub-material /MAT/LAW6:

EoS_Options_Input (LINEAR): Value
Initial density: 1e-9
Initial Pressure (P0): 0.1013
Bulk Modulus (B): 2089.0

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.

The contact stiffness is calculated as:

S t f v a l = \frac{ρ \cdot v^{2} \cdot S_{e l}}{G a p}

Where,

$ρ$

The (highest) fluid density

$υ$

Velocity.

For incompressible models (ditching, sloshing, and so on), 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 $ν^{2}$ with $v \cdot c$
Where,

$υ$

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

$S_{e l}$

Surface area of the Lagrangian elements

$G a p$

Interface gap, as defined above

For this example:

G a p = 1.5 f l u i d \begin{matrix}  \end{matrix} e l e m e n t \begin{matrix}  \end{matrix} s i z e = 1.5 \times 2.5 = 3.75 [mm]

S t f v a l = \frac{ρ \cdot v^{2} \cdot S_{e l}}{G a p} = \frac{1 \times 10^{- 9} \times 4429^{2} \times (5 \times 5)}{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)
/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_ID`_n	`ALE_PHASE`	`FILL_OPT`	`ICUMU`	`FILL_RATIO`

part_ID

Part ID of ALE hex mesh

surf_ID_n

3-nodes or 4-nodes surfaces only or /SURF/PLANE

ALE_PHASE

Phase of the multi-material ALE material

FILL_OPT

= 0: Filling the side which along normal direction
= 1: Filling the side which against normal direction
Figure 3.

ICUMU

Remove the previous material and then fill new material or mixed

FILL_RATIO

Ratio of filling material

/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         2         1         0                 0.0

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         1         0         0                 0.0

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

/H3D/ELEM/DENS
/H3DE/ELEM/VFRAC

You can contour the model and use section cut to see inside, or use iso-surface, as shown in Figure 5.

Engine Control

It is recommended to use time step scale factor 0.5 for ALE in /DT/ALE in order to keep computation stable.

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.

Water is starting to splash up the sides of the container at the end of the simulation.