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The undewater explosion (UNDEX) example problem is based upon an experiment in which a submerged test cylinder was exposed to a shock wave produced by a 60-pound HBX-1 explosive charge (Kwon & Fox, 1993). The test cylinder is made of T6061-T6 aluminum, has an overall length of 1.067 meters, an outside diameter of 0.305 meters, a wall thickness of 6.35 millimeters and welded endcaps that are 24.5 millimeters thick. The cylinder was suspended horizontally in a 40-meter deep fresh water test quarry (sound speed =1463 meters/second). The 60-pound HBX-1 explosive charge and the cylinder were both placed at a depth of 3.66 meters, with the charge centered off the side of the cylinder and located 7.62 meters from the cylinder surface. The suspension depths, charge offset and duration of the test were selected such that cavitation of the fluid would not be significant and no bubble pulse would occur. During the UNDEX test, two pressure transducers were positioned 7.62 meters from the charge, away from the cylinder, but at the same depth as the cylinder. These transducers provided an experimental determination for the pressure vs. time history of the incident spherical shock wave as it traveled by the point on the cylinder closest to the charge.
The external fluid is meshed with 4-noded AC3D4 acoustic tetrahedral elements. The outer boundary of the external fluid is represented by cylindrical and spherical surfaces with the appropriate surface impedance absorbing conditions. The characteristic radius of the fluid outer boundary is set at 3 shell radii, thus the thickness of fluid modeled about the cylinder represents approximately 1/3 of the cylinder’s outer circumference (rigid body translational wavelength). Based upon the mesh boundary study this location should be sufficient to provide reasonably accurate results. Figure 9 shows the cylinder and first acoustic mesh that was used in the analysis, with the top half of fluid removed for clarity. The shock wave rise time is 0.0182 milliseconds, corresponding to a wave propagation distance of 0.0266 meters.
This and the next two slides are FROM::
David B. Woyak (ABAQUS Solutions Northeast, LLC), “Modeling submerged structures loaded by underwater explosions with ABAQUS/Explicit, 2002 ABAQUS User’s Conference
ABSTRACT: Finite element analysis can be used to predict the transient response of submerged structures that are externally loaded by an acoustic pressure shock wave resulting from an Underwater Explosion (UNDEX). This class of problem is characterized by a strong coupling between the structural motions and acoustic pressures at the fluid-structure wetted interface. The structural behavior is a combination of long time (low frequency) response dominated by an added mass effect, short time (high frequency) response dominated by radiation damping, and intermediate time-frequency response where both added mass and radiation damping behavior are present. For the finite element method to be useful, the analyst must develop modeling techniques and procedures that yield accurate and computationally tractable solutions. Modeling procedures and guidelines were developed for use with an explicit dynamics code that offers advanced features such as: pressure formulated acoustic elements, surface based fluid-structure coupling, surface based absorbing (radiation) boundaries, and automated incident wave loading for the fluid-structure wetted interface. The modeling guidelines address issues such as: location of the fluid acoustic domain outer boundary, meshing of the acoustic domain, representation of the shock wave, and solution efficiency. These modeling procedures and guidelines are demonstrated with an ABAQUS/Explicit analysis of an UNDEX experiment in which a submerged test cylinder was exposed to a 60-pound HBX-1 explosive charge (Kwon & Fox, 1993).
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