Introduction

This test case aims at validating the numerical accuracy and stability of numerical solvers for simulating flow impact on an elastic structure, which corresponds to the dam breaking flows interacting with an elastic plate. In this benchmark experimental data, FEM results (Liao et al., 2015) and SPH results (Lyu et al., 2021; Sun et al., 2019) are provided. In particular, for the SPH results both single-phase and multiphase simulations are considered. The former is devoted to emphasizing the importance of using Tensile Instability Control (TIC) or Particle Shifting Techniques (PST) to prevent the unphysical flow separation between the fluid-structure interface, while the latter aims to highlight the effects of air phase when the air cavity is formed.

Fig. 1. Schematic diagram of the test case

Flow phenomena

Incompressible Flow

Multiphase Flow

Fluid-structure Interaction

Water Impact

Geometry

This benchmark is a classical FSI problem originating from the experimental work conducted by Liao et al. (2015), in which the structural deformations of the elastic plate and the free-surface evolutions during impact were recorded and investigated in detail. The schematic diagram of the experiment is displayed in Fig. 1 above, where the length of the water column is 𝐿3=0.2 m, while the initial heights of the water column are 𝐻=0.2, 0.3 or 0.4 m. The water column is initially restricted by a rigid gate. The elastic plate, with the height and thickness respectively being 0.09 m and 0.004 m, is installed at 0.2 m in front of the rear wall. In order to study the structure deformations of the elastic plate during flow slamming, three markers are installed on the elastic plate with the heights being 0.04 m, 0.065 m, and 0.0875 m, respectively.

Boundary conditions

1. This test is characterized only by free-slip solid boundary conditions on all walls of the tank and the elastic plate.

2. As reported by Liao et al. (2015), the initial vertical movement of the gate has significant effects on the forming of the dam-breaking flow. Consequently, during the simulation, the motion of the gate must be strictly controlled according to its time-displacement curve recorded in the experiment (see Fig.2 or the ASCII file in attachments named Gate_motion_time_vertical_position.dat).

Fig. 2. Rising-up law of the gate

Initial conditions

• The initial pressure field of the water column is simply considered as hydrostatic distribution.

• The material properties of the elastic plate are density 𝜌0𝑠=1161.54 kg/m3, Young's modulus 𝐸𝑠=3.5×1E6 Pa, and Poisson's ratio 𝜈𝑠=0.45, respectively.

Discretization

The entire computational domain can be easily discretised as particles in a Cartesian pattern because all objects have a regular shape. In terms of the initial particle spacing, 𝛥𝑟 = 0.001 m is sufficient to provide convergent numerical results.

Results specifications

1. It is suggested to validate the numerical results by comparing with experimental measurements of the x-displacements of the markers (see the ASCII files in the folder named “Liao_exp_&_FEM_data_APOR_2015”).

2. It is also recommended to compare your results with other numerical (FEM and SPH) results (see the ASCII files in the folder named “Liao_exp_&_FEM_data_APOR_2015” and “Sun_et_al_EABE_2019_Multiphase_SPH_results”).

3. Since plenty of experimental snapshots are provided by Liao et al. (2015), one may also compare the flow evolutions and structure deformations at different time instants (experimental snapshots can be accessed from the reference paper).

Results format

1. For all provided ASCII files, the first column is time (unit: s) and other columns are featured by length (unit: m).

2. In the folder named “Liao_exp_&_FEM_data_APOR_2015”, the ASCII file named “Gate_motion_time_vertical_position.dat” contains the rising-up law of the gate in which Col.1 is time and Col.2 is the vertical motion of the gate, while other ASCII files contains the FEM results of the three markers (i.e. horizontal displacements) simulated by Liao et al, 2015.

3. In the folders named “Sun_et_al_EABE_2019_Multiphase_SPH_results”, different SPH reference results of the case H=0.4m for the three markers (i.e. horizontal displacements) are provided with an ASCII format.

Benchmark results

Herein two results respectively related to single-phase SPH simulations (from Lyu et al., 2021) and multiphase SPH simulations (from Sun et al., 2019) are reported.

Fig.3. Results of single-phase SPH simulations for the dam breaking of H=0.3m

Fig. 4. Results of multiphase SPH simulations for the dam breaking of H=0.4 m

Download

You can download the full test case below:

Publications using this test case as a benchmark

   Martínez-Estévez, I., Tagliafierro, B., El Rahi, J., Domínguez, J. M., Crespo, A. J. C., Troch, P., & Gómez-Gesteira, M. (2023). Coupling an SPH-based solver with an FEA structural solver to simulate free surface flows interacting with flexible structures. Computer Methods in Applied Mechanics and Engineering, 410, 115989

References

Liao, K., Hu, C., & Sueyoshi, M. (2015). Free surface flow impacting on an elastic structure: Experiment versus numerical simulation. Applied Ocean Research, 50, 192-208.

Sun, P. N., Le Touzé, D., & Zhang, A. M. (2019). Study of a complex fluid-structure dam-breaking benchmark problem using a multi-phase SPH method with APR. Engineering Analysis with Boundary Elements, 104, 240-258.

Lyu, H. G., Sun, P. N., Huang, X. T., Chen, S. H., & Zhang, A. M. (2021). On removing the numerical instability induced by negative pressures in SPH simulations of typical fluid–structure interaction problems in ocean engineering. Applied Ocean Research, 117, 102938.