Application of the ALE technique for underwater explosion analysis of a submarine liquefied oxygen tank

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Abstract

The design of submarines has continually evolved to improve survivability. Explosions may induce local damage as well as global collapse to a submarine. Therefore, it is important to realistically estimate the possible damage conditions due to underwater explosions in the design stage. The present study applied the Arbitrary Lagrangian–Eulerian (ALE) technique, a fluid–structure interaction approach, to simulate an underwater explosion and investigate the survival capability of a damaged submarine liquefied oxygen tank. The Lagrangian–Eulerian coupling algorithm, the equations of state for explosives and seawater, and the simple calculation method for explosive loading were also reviewed. It is shown that underwater explosion analysis using the ALE technique can accurately evaluate structural damage after attack. This procedure could be applied quantitatively to real structural design.

Introduction

Due to the development of increasingly advanced and threatening underwater weapons (Fig. 1), it has become more important for submarines to be protected from enemy attack and damage so that they can accomplish their given tasks. Put another way, their survivability must be maximized, where survivability is the relationship between susceptibility, vulnerability, and recoverability (Said, 1995), as shown in Fig. 2.

To this end, it is important for modern submarines to establish countermeasures of vulnerability. As submarine size has increased, so has their chances of being damaged by enemy attack. Therefore, it is crucial to design submarines to protect the main hull and vital equipment against various underwater weapons. To effectively design a submarine for survivability, designers should simulate reasonable attack scenarios, and realistically estimate the possible damage conditions that could result based on the simulations. The present study assessed the potential damage to a liquefied oxygen tank, one of the most important structures of a submarine, following a simulated underwater explosion.

Simulations of fluid–structure interactions (FSI) are complex, and several advanced software programs have been developed specifically for such intricate and complicated analyses, including LS-DYNA (Hallquist, 1999) and MSC/DYTRAN (MSC Software Corporation, 1999). These so-called hydrocodes are used in multiple industries for a wide variety of analyses, including airbag and tire–water dynamics in the automobile field, the impact of bird strikes on aircraft, and the effects of sloshing on ships (Kim et al., 1994).

FSI techniques are regularly applied in the ship-building field (Chung et al., 1992, Chung et al., 1997; Lee et al., 2001), and have recently been used in naval architecture and ocean engineering to enhance the survivability of naval ships and ocean plants such as FPSO by estimating explosion loadings. Fig. 3 shows the various applications of FSI techniques (Hallquist, 1999; MSC Software Corporation, 1999). The present study used an FSI (Souli, 2003) technique, the Arbitrary Lagrangian–Eulerian (ALE) method, to simulate an underwater explosion using the explicit hydrocode of LS-DYNA.

Section snippets

ALE technique and methodology

Purely Lagrangian methods are typically used only for structural deformation. The mesh moves in space. The computational expense of this method is determined by the amount of mesh deformation that occurs. If large deformations occur and mesh distortion is high, the calculation will terminate and the mesh will need to be repaired manually in order to continue the calculation. This process is necessary every time the mesh becomes too distorted for the calculations to continue. Therefore,

Shockwave by an underwater explosion

There are four characteristics associated with the shockwave produced by an explosion that are of primary interest when using similitude: peak pressure, pressure–time history, shockwave impulse, and shockwave energy flux density. The peak pressure is given by both Cole (1948) and Swisdak (1978) asPmax=K1(W1/3R)A1,where R is the point of interest from the center of the charge in ft., and W is the charge weight in pounds-force. To determine the pressure–time history of point R for the shockwave,

The scenario of underwater explosion analysis

The shock severity in the simulation is given by a keel shock factor (NAVSEA, 1985; Scavuzzo and Pusey, 2000), which is defined by Eq. (14) and is illustrated in Fig. 9:KSF=WR×(1+sinθ2),where W is the weight of the explosive, R is the minimum distance from the explosive to the keel, and α is the angle of attack.

In general, submarines are designed for ultimate strength, which is equal to a shock factor value of 1.0. Therefore, a shock factor value of 1.0 (W=100 kgf, R=10 m, and α=0°) was used in

Conclusion

This study applied the ALE fluid–structure interaction technique to analyze the impacts of an underwater explosion on a submarine liquefied oxygen tank design. The ALE technique was confirmed as a useful method for underwater explosion analysis. It allowed direct modeling of the explosion and the seawater as a fluid element and the tank structure as a structure element. The analyses were sensitive to the mesh size of the fluid element, where the smaller the mesh size of the seawater, the better

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