Underwater Explosion Analysis
Underwater Explosion Analysis: Theoretical Foundations
What is an Underwater Explosion (UNDEX)?
Professor, what kind of problem is underwater explosion analysis?
UNDEX (Underwater Explosion) is the problem of shock waves from an underwater explosion acting on the hulls of ships and submarines. It is the most important shock resistance evaluation in naval hull design.
Physics of Underwater Explosions
Characteristic phenomena of underwater explosions:
1. Shock Wave (primary shock wave) — Propagates spherically from the source. Travels at the speed of sound in water (1500 m/s)
2. Bubble Pulse — Repeated expansion → contraction → re-expansion of the gas bubble. Low-frequency pressure pulsation
3. Cavitation — Negative pressure near the water surface due to shock wave reflection → water boils (cavitation) → secondary shock upon collapse
It's different from in air, isn't it?
Water is 800 times denser than air. The energy of the shock wave is orders of magnitude greater, causing several times more damage for the same TNT equivalent compared to in air.
Analysis Methods in FEM
Can the DAA method be used in Nastran?
Define FLUIDEX (external fluid field) in Nastran's SOL 109/112, and input the underwater explosion shock wave into the structure using the DAA approximation. This is the standard method of the U.S. Navy.
Summary
Key Points:
- Underwater explosions have orders of magnitude more energy than in air — Water density is 800 times greater
- Shock Wave + Bubble Pulse + Cavitation — Three phenomena
- DAA Method (Nastran), ALE Method (LS-DYNA), BEM-FEM — Analysis methods
- Most important in naval hull design — Shock resistance performance evaluation
Bubble Collapse in Underwater Explosions Destroys Structures
In underwater explosions (UNDEX), after the initial shock wave, the "bubble pulse" of repeated expansion and contraction of the explosion gas bubble delivers a secondary shock to the structure. The period of this bubble pulsation can be estimated by T=K(W^(1/3)/(D+10)^(5/6)) seconds (K is the TNT constant, D is explosion depth in meters). A typical explosion (100kg TNT, 30m depth) shows a period of about 0.5 seconds. It was later discovered that many cases of ships sunk during World War II were due to keel breaking caused by this bubble pulse.
Computational Methods for Underwater Explosion Analysis
Implementation of DAA Method
DAA (Doubly Asymptotic Approximation) is a method that simultaneously approximates low-frequency added mass effects and high-frequency acoustic radiation. DAA boundary conditions are set on the structure's wetted surface (surface in contact with water).
Which Nastran solution is used?
Add FLUIDEX (external fluid field) to SOL 109/112. The explosion shock wave is calculated using formulas like Cole's equation and input as an incident wave to the structural surface. Scattered waves are calculated using DAA approximation.
ALE Method (LS-DYNA)
Simultaneously solves water and explosive with Eulerian (ALE) mesh, and ship hull with Lagrangian mesh. Directly simulates all phenomena: shock wave propagation, reflection, and cavitation.
Is the ALE method more accurate?
The ALE method is the most accurate, but requires enormous water mesh (millions to tens of millions of elements). For distant explosions, the DAA method is efficient. For close-range explosions, the ALE method is necessary.
Summary
DAA (Delayed Acoustic Approximation) is Key to Fluid-Structure Coupling
For fluid-structure interaction in UNDEX analysis, DAA (Doubly Asymptotic Approximation), which approximates scattered waves in infinite water domains, is widely used. DAA2 (second-order accuracy) developed by DeRuntz and Geers in 1978 continuously switches between asymptotic solutions for both far-field and near-field, and has been adopted in the U.S. Navy's ship UNDEX certification code USA (Underwater Shock Analysis). The USA code is still managed by the Naval Research Laboratory (NRL) as an external fluid solver for Nastran and Abaqus.