RD-E: 2201 Ditching using ALE

The computation is performed using two impact velocities of 6.7 m/s and 11 m/s.

Figure 2. Problem Data

With /MAT/LAW37, the air and water are defined in the same material. The initial material is defined using Alpha_L to distinguish between liquid (water) or Gas (air).

Figure 3. /MAT/LAW37 material properties

The gas constant $\gamma \text{=1}\text{.4}$ is in LAW37. In LAW51 $C_4=C_5=\gamma -1\text{=0}\text{.4}$ for a perfect gas.

Figure 4. /MAT/HYD_VISC (LAW6) material properties

In the multi-material LAW51, the amount of each sub-material is defined. To improve numerical stability, it is recommended to define the water as 99.99% water and 0.01% air.

Figure 5. /MAT/LAW51 material properties

The boundary conditions are applied to the ALE mesh as:

• Z translation component fixed for lower and upper faces
• Y translation component fixed for lateral faces normal to Y
• X translation component fixed for lateral faces normal to X

Using LAW51 with I_form=6 it is possible to set a non-reflecting boundary without defining any parameters. The material parameters are calculated based on its neighbor element. In this case, one layer of elements needs to be defined as a non-reflecting boundary. The mesh of two corner boundary elements is recommended to be defined (Figure 6).

Figure 6. Boundary mesh treatment

The interface TYPE18 forces are computed using the penalty method. The interface stiffness is proportional to impact velocity. The results obtained by the ALE approach are dependent on the interface stiffness factor $$Stval$$, which is a function of the size of the element and fluid properties.(1) $$Stval=\frac{\rho \cdot v^2\cdot S_{el}}{Gap}$$

Where,

$\rho$

The (highest) fluid density

$$\nu$$

Estimated relative velocity of the phenomenon

$$S_{el}$$

Average surface area of the Lagrangian elements

$$Gap$$

Contact gap

Using the density of water 1e-6 $\frac{kg}{m{m}^3}$, velocity of 11 m/s, and average Lagrangian shell element area is:(2) $S_{el}=15\times 15\text{=225}$

Then (3) $$Stval=\frac{1e-6\cdot {11}^2\cdot 225}{\text{1}\text{.5}\cdot \text{15}}=\text{1}\text{.21}e-3$$

In this example, parameters are used to automatically recalculate the $$Stval$$ depending on impact velocity and mesh size. This makes it easy to study different velocities and the parameters can be used in other models. The input and calculated parameters from a simulation are printed in the Starter output file.

************************************************************************
*
*     PARAMETERS
*     ----------
*
*     EVALUATION ...
*
* GLOBAL PARAMETERS
*     Velocity
*          REFERENCE . . .= V        
*          VALUE . . . . .=  -11.00000000000    
*     fluild mesh size
*          REFERENCE . . .= mesh_f   
*          VALUE . . . . .=   15.00000000000    
*     lagrangian mesh size
*          REFERENCE . . .= mesh_l   
*          VALUE . . . . .=   15.00000000000    
*     gap =1.5*mesh_f
*          REFERENCE . . .= gap      
*          EXPRESSION  . .=  1.5*mesh_f
*          VALUE . . . . .=   22.50000000000    
*     inter18 stval =rho*V*V*S/Gap
*          REFERENCE . . .= stval    
*          EXPRESSION  . .=    1.0E-6*V*V*(mesh_l*mesh_l)/gap
*          VALUE . . . . .=  1.2100000000000E-03
*
*
************************************************************************

The following results compare LAW51 + /ALE/MUSCL + non-reflecting boundary on the left with LAW37 + /UPWIND + without the non-reflecting boundary. The LAW51 with /ALE/MUSCL results show a more distinct boundary which is more accurate. The LAW37 mesh is more diffuse with a less distinct boundary between the water and air.

Figure 7. Density results for LAW51 and LAW37

Acceleration results from the ALE simulation using LAW37 and LAW51 were filtered with a CFC 60, -3 dB filter and are compared to Von Karman theoretical solution and experimental results filtered with a CFC 60, -3 dB filter.

Figure 8. Acceleration results for 11 m/s for simulation, theoretical solution, and experimental test