Slamming is a term that is often used in a maritime context to describe the sudden impact of the ship hull on a water surface. It leads to pressure spikes on the hull along with rapid and intricate deformations of the fluid surface. Physical testing, especially for large-scale applications in the maritime world, is not only time-consuming and expensive but often even unfeasible. Computational fluid dynamics can complement real-world experiments and hence reduce costs as well as accelerate development. However, simulating the water entry of solid bodies is no easy task. Using traditional grid-based methods requires periodical remeshing due to the moving geometry and discretizing the entire simulation domain. Particle-based simulation methods on the other hand can generate insights without these inconveniences, saving valuable computation time. This article aims to show how PreonLab can be used to simulate the water entry of free-falling rigid bodies.
To capture scenarios like this correctly, various physical aspects must be covered. It involves two-way coupling of rigid body dynamics, violent fluid splashing, and complex pressure distributions – all of that on a very small timescale. Managing computational resources is an additional challenge. While the simulation domain must be big enough to minimize the effects of the boundaries, a high spatial resolution is advisable too in order to obtain high quality results. These demands make the use of PreonLab’s Continuous Particle Size (CPS) feature a key component for this simulation.
Before considering more advanced cases, we will validate the Preon Solver by means of an established benchmark test which involves a cylinder that is dropped into a reservoir filled with water. Greenhow and Lin  provide experimental data that is used as a reference in many publications (e.g., [2-4]). As shown in Figure 1, the described experiment consists of a cylinder with a diameter of 11 cm which is positioned 50 cm above the water surface inside a tank. It is then dropped into the water to examine the total displacement of the cylinder over time and the free surface effects during the water entry. The cylinder is a half-buoyant body, i.e., its density is 50% of the water density. Hence, it will decelerate and eventually return to the water surface.
Figure 1: 2D setup for the simulation of a free-falling horizontal cylinder
By reducing the simulation to 2D, we can compare the data among different solvers, as well as the experimental results within a matter of only a few minutes. In Figure 2, PreonLab is compared against experimental data  as well as another SPH solver  and a Boundary Element Method (BEM) approach . The graph shows the vertical position of the cylinder after penetrating the water surface.
Figure 2: Cylinder displacement over time after water entry
By conducting a resolution study with particle sizes ranging from 15 to 2 mm, the convergence towards the experimental data with decreasing particle size was confirmed. Another metric to evaluate is the splashing phenomena that occur during the entry phase of the cylinder. In Figure 3, images of the experimental results are shown on the left and results with PreonLab are visualized on the right. Both images are overlaid by the prediction of the free surface according to the BEM used in  as an orange line. The PotentialForce cohesion model enables PreonLab to capture splashing phenomena better than the BEM approach, even for a 2D model. PreonLab and the experimental data show a close correlation regarding the position of the free surface, while the entry depth of the cylinder is similar across all three approaches.
Another common benchmarking method for free surface impact is the free-falling symmetrical wedge. This test is of importance since a wedge can be seen as a simplification of the cross section of a ship hull. For this reason, Yettou et al.  performed large-scale experiments with free falling wedges entering water in a 30×2 m water tank. In the following section, PreonLab will be validated against this experimental data in a series of 3D-simulations.
Ship hulls come in many different shapes, depending on their purpose and size. A characteristic metric to describe them is the so called deadrise angle. It describes the angle between the surface of the boat and a horizontal plane. Depending on the type of boat, it can vary in a wide range and even change along the hull. The wedge used in this study measures 1.2×1.2m at the top surface and has a deadrise angle of 25°, as shown in Figure 4. The wedge is attached to a vertical sliding mechanism. The dropping weight, consisting of the wedge and the moving parts of the sliding system, is 94kg. The water level is 1m and the drop height is 1.3m above the water surface.
Figure 4: Sensor positions on the wedge
The simulation of such a case is especially challenging, since around 80% of the kinetic energy of the wedge dissipates within less than 100ms after the initial contact with the water surface. Another difficulty arises regarding the spatial resolution. Fine particles are required near the wedge surface to capture the small-scale hydrodynamic phenomena of the water entry properly. However, the large total water volume would lead to an unfeasibly high particle count. The use of local particle refinement in proximity to the wedge surface is crucial. Thankfully, PreonLab offers a powerful and easy to use solution with Continuous Particle Size (CPS). For this study, particle refinements were implemented based on the proximity to the wedge surface, as shown in Video 1. Three refinement levels were used, ranging from 6.25mm near the wedge surface to 25mm in the far-field. During a resolution study, even a fourth layer was added, which only had a negligible effect on the results, indicating that the fluid is already well resolved.
By looking at the velocity of the wedge over time shown in Figure 5, the strong correlation between experimental data and the results of the simulation in PreonLab can be seen. After the initial free fall period, the wedge hits the water surface at around 0.5s and decelerates rapidly. The wedge continues to decelerate and eventually floats back to the surface because of its lower density. It should be noted that according to  the fluctuations in the experimental data in Figure 5 arise from vibrations of the potentiometric cable extension transducer, which was used to determine the instantaneous positional data. Similar to the first benchmark test, the results obtained with PreonLab are in very good agreement with the experimental data.
Figure 5: Vertical velocity profile for the free-falling wedge
The expected surface pressure is an important metric when designing a ship hull. Hence, this was experimentally measured for the free-falling wedge by means of 11 individual pressure transducers along the side (see Figure 4).
We can obtain the same measurement data in PreonLab by simply adding solid planes at the corresponding positions, connecting each of them with a force sensor, and coupling their movement with that of the wedge. The sample rate in PreonLab is chosen at 10 kHz, identical to the experimental setup. Each sensor measures a strong peak the moment it initially reaches the water surface after which it flattens out. Now, we can compare these maximum values and the time at which they occur between experiment and simulation. This is visualized in Figure 6 for multiple wedges with different deadrise angles. The simulation results obtained with PreonLab are in good agreement with the experimental data in . Conclusively, PreonLab enables us to gain insight into the structural load that the wedge must withstand during slamming, even for smaller deadrise angles.
Figure 6: Comparison of the peak surface pressure between PreonLab and experimental data  for multiple deadrise angles
After two successful benchmark tests, we can now take this even further. The following simulation of an entire ship hull was performed within less than 17 hours on 32 cores (2x Intel(R) Xeon(R) Gold 6130), using up to 4.7 million particles. We can monitor how the alignment of the boat changes, visualize the pressure distribution on the entire geometry, and even evaluate how much water is splashing onto the top of the vessel. This slamming simulation is set up similar to the benchmark tests before. We use CPS to improve computational efficiency with three refinement layers in proximity to the boat hull. With a hull length of 39.6m, a beam of 5.3m, and a minimum particle size of 0.0625m, the fluid domain around the vessel is well resolved, even for this large-scale application. To add additional complexity, the boat is slightly tilted in all three directions (roll, yaw, and pitch) at its initial position. The results are illustrated in Video 2.
PreonLab is a valuable tool for simulating the water entry of rigid bodies. Established benchmark tests for free-falling cylinders and wedges have proven that PreonLab is capable of accurately predicting the behavior of two-way coupled dynamic rigid bodies in complex scenarios. The setup of such scenarios is straightforward and intuitive. PreonLab comes with powerful methods to improve computational efficiency such as CPS. This enables the user to utilize high resolution discretization in the area of interest without compromising performance when resolving large simulation domains. The extensive capabilities of its built-in post-processing features help to extract valuable information from the simulation data effortlessly. With its particle-based simulation approach PreonLab offers a highly efficient alternative to conventional mesh-based methods for water entry simulations. It can complement physical testing to reduce costs and boost development times significantly.
 Greenhow M., Lin WM., Nonlinear-Free Surface Effects: Experiments and Theory, Report no. 83-19, Department of Ocean Engineering, MIT, 1983
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