Dam Break in 3D

Problem Description

The investigated test case is based on the experimental setup of Lobovský et al ¹ shown in Figure 1, with an extension of the tank of 150 mm perpendicular to the view plane.

Figure 1. Sketch of Experimental Setup Taken from Lobovský et al (units in mm)

As shown above, the right part of the tank is filled with water (density: 997 kg/m³, kinematic viscosity: 8.9*10 ^-7 m²/s), with a height H of the water column. The experimental investigation comprise two different heights H = 300 mm and H = 600 mm, from which the former is simulated here. The setup is exposed to a gravity field with a constant acceleration of g = 9.81 m/s² in negative z-direction. After the removal of the gate in positive z-direction, the water column collapses.

Numerical Setup

The initial particle configuration is shown in Figure 2 and the measurements of the lower half of the domain corresponds to the ones of Lobovský et al. ¹ shown Figure 2.

Figure 2.

Initially, the particles are distributed on an equidistant Cartesian grid with dx = 5e^-3 m. As the air is assumed to have only a very limited influence on the collapse of the water column it is neglected in the conducted simulation. To prevent the water particles from flying away, the geometry of the tank is mirrored to the upper half to close the geometry. From the beginning of the simulation on, the gate (blue) is removed with the approximate velocity in the experimental investigations of 3.46 m/s as stated by Lobovský et al. ¹ The gate has to be chosen twice as thick as in the experiment as a representation by at least three particles is required for a wall boundary condition (see Adami et al. ²).

Results

The temporal evolution of the water shape is shown in Table 1 in comparison to the snapshots of the experiment Lobovský et al. ¹ at approximately corresponding times. The snapshots before the impact of the water lip show a qualitatively excellent agreement in the shape of the evolving water column. The splash after the impact seems to be over pronounced, although the assessment of the experimental snapshots in terms of the spray is difficult. A possible source of error in the simulation could be the neglect of the air.

Table 1. Instantaneous Time Snapshots of the Collapsing Water Column. The splash is slightly over-pronounced due to the fact that this is a single phase simulation. Consequently, after the rebound the flow begins to differ as turbulence and multiphase effects become more prominent.

Figure 3.	Figure 4.
Figure 5.	Figure 6.
Figure 7.	Figure 8.
Figure 9.	Figure 10.
Figure 11.	Figure 12.
Figure 13.	Figure 14.

These differences could also be the reason for the discrepancies in the collapsing splash, giving a secondary splash in the simulation in contrast to the experiment. Further investigations including the effect of the air could possibly shed light on these effects.

In the following graphs, the water surface was defined by the iso-Surface 0.5 of the Shepherd coefficient in the mid plane of the tank parallel to the view plane shown in Figure 1. The location of the front lip of the collapsing water column is shown in Figure 15. The agreement with the reference data of Lobovský et al. ¹ is very good. Nevertheless, the lip advances slightly slower at the beginning of the simulation, possibly due to minor differences in the gate movement.

Figure 15. Temporal Evolution of the Front Lip in comparison to Lobovský et al

The agreement with the experimental data can also be seen in the temporal evolution of the water levels at the reference positions H1 to H4 in Table 2. The collapsing water column before the splash is in excellent agreement with the reference data and even the details of the temporal evolution of the column heights are reproduced.

Table 2. Temporal Evolution of the Water Level at Reference Positions H1 to H4

Figure 16.	Figure 17.
Figure 18.	Figure 19.

The rapid increase of the water level at the arrival of the backsplash is reproduced with varying discrepancies depending on the location, but still with reasonable agreement. The most pronounced difference at position H3 is obviously due to differences in the collapsing splash as already seen in Table 1.