Ship Slamming Analysis
Ship Slamming: Theoretical Foundations
Physics of Slamming
What is the slamming phenomenon for ships?
It is a phenomenon where an extremely large impact pressure occurs in a very short time when the bottom of a ship navigating in waves strikes the water surface. It is classified into bow flare slamming at the bow, bottom slamming at the bottom, and stern slamming at the stern. The impact pressure reaches the order of MPa, causing local structural damage and whipping vibration.
Governing Equations
Is there a theoretical solution for the impact pressure?
Wagner's (1932) theory is classical. For the water impact of a 2D wedge shape,
Here, $V$ is the impact velocity, $\beta$ is the deadrise angle, and $c(t)$ is the wetted width. As $\beta \to 0$, the pressure diverges to infinity, so a modified model considering the air cushion effect is necessary.
On the fluid side, the incompressible (when impact velocity $V \ll c_{water}$) or compressible Navier-Stokes equations are solved. The free surface is tracked using the VOF method.
On the structural side, it is elastoplastic FEM. The relationship between the time scale of the impact load (order of milliseconds) and the natural period of the structure determines whether the response is dynamic or quasi-static.
Wagner's Wedge Water Entry Theory—Why is the "Water Wall" so Hard?
At the moment a ship's bottom slams against the sea surface, the local pressure can be tens to hundreds of times the hydrostatic pressure. H. Wagner first theorized this in 1932, deriving the relation p_max ≈ ½ρ(πV/2tanβ)² for the maximum pressure when a wedge-shaped cross-section enters water at velocity V (β is the half-apex angle). The key point is that "the smaller the entry angle, the more explosively the pressure increases." For example, with β=5° and an entry speed of 5m/s, the peak pressure reaches several MPa. This is why the bottom panels of small high-speed FRP boats dent with a "bang!" sound after repeated slamming. This theory is still used as the starting point for slamming design today.
Computational Methods for Ship Slamming
Numerical Methods
What methods are used for slamming CFD-FSI?
Explicit methods are fundamental due to the impact.
| Method | Fluid | Structure | Features |
|---|---|---|---|
| CFD-VOF + FEM Explicit | OpenFOAM/Fluent | LS-DYNA/Abaqus Explicit | General-purpose. FSI often uses weak coupling |
| SPH + FEM | SPH | FEM | Mesh-free. Strong for spray/splashing |
| ALE (LS-DYNA) | ALE fluid | FEM | *CONSTRAINED_LAGRANGE_IN_SOLID |
| BEM + FEM | Panel method | FEM | Efficient but cannot represent spray |
Is the SPH method suitable for slamming?
SPH is mesh-free and can naturally track large deformations and spray of free surfaces. However, numerical oscillations (noise) in the pressure field are prone to occur, so improved versions like Riemann SPH or δ-SPH are used. LS-DYNA has a built-in SPH solver and can directly couple with FEM structures.
Spatiotemporal Resolution
What resolution is needed to accurately capture impact pressure?
Since the slamming pressure peak disappears in about 0.1~1 ms, a time step below 0.01 ms and a spatial mesh below 1~5 mm near the impact surface are required.
| Parameter | Recommended Value |
|---|---|
| Impact surface mesh size | 1~5 mm |
| Time Step | Below 0.01 ms |
| VOF interface resolution | Minimum 5 cells/water film thickness |
| Pressure sampling | Below 0.001 ms |
The "1000x Wall" Between Tank Tests and CFD—The Reality of Slamming Analysis
Numerical analysis of slamming is a continuous struggle with time step issues. The slamming peak pressure occurs within a few milliseconds, so a time step Δt below 0.01ms is needed to resolve it. On the other hand, an actual ship takes several seconds to pass over one wave. This time scale difference is the "1000x wall." In practice, a one-way coupling approach is mainstream, separating "CFD for slamming alone" and "long-term FEA for the entire hull," and mapping the slamming pressure. In comparison with tank tests, a practical sense is that being within ±20% of the peak pressure is acceptable. The main cause of differences between CFD and experiments is often the "air entrainment effect," which can reduce pressure by 10~30%.
Ship Slamming in Practice
Analysis Procedure
What is the procedure for conducting slamming analysis in practice?
A two-stage approach is common.
Phase 1: Full Ship Seakeeping Analysis
- Calculate ship motions using potential flow BEM or CFD
- Identify slamming occurrence conditions (relative velocity, relative displacement)
Phase 2: Local Slamming Analysis
- Extract impact velocity and angle from Phase 1 results
- Calculate impact pressure and structural response using local CFD-FSI or SPH-FEM
Why separate into two stages?
Because ensuring spatiotemporal resolution for slamming at the full ship scale would lead to astronomical computational costs. Phase 1 identifies "when, where, and at what speed" the impact occurs, and Phase 2 analyzes only that local event with high precision.
Verification Data
Are there benchmark problems available for verification?
The water impact problem for wedge shapes is standard.
| Benchmark | Shape | Verification Target |
|---|---|---|
| Wagner theory | 2D wedge | Impact pressure distribution |
| Zhao & Faltinsen experiment | 2D wedge (β=30°) | Pressure time history |
| Aarsnes elastic wedge | 2D elastic panel | FSI response |
| Luo experiment | 3D bow section | 3D pressure distribution |
Container Ship "Whipping"—The Entire Ship Shakes After Slamming
Immediately after slamming occurs, the entire hull vibrates longitudinally like a plucked guitar string, a phenomenon called "whipping." For large container ships, the natural period is about 2~4 seconds, and bending stress spikes of several hundred MPa repeat 5~10 times at the ship's midsection after slamming. In the 2013 MOL Comfort sinking accident (where a container ship broke in two), it was suggested that this whipping stress may have exceeded design assumptions. Following this accident, the International Association of Classification Societies (IACS) revised regulations to explicitly incorporate whipping stress into container ship design criteria (UR S11A). This was a turning point where slamming-whipping coupled analysis became essential for design.
Ship Slamming: Software & Solver Comparison
Tool Comparison
What software is suitable for slamming analysis?
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators| Tool | Method | Features |
|---|---|---|
| LS-DYNA |