A study of transient responses of a submerged spherical shell under shock waves

Based on a procedure which couples the finite element method with the doubly asymptotic approximation, this work addresses the problem of the transient responses of a submerged spherical shell subjected to strong, plane, incident shock waves, in which elastoplastic material behavior is considered. Simulation results indicate that the procedure adopted shows good agreement with related literature, which considered linear elastic behavior of the shell. Also presented herein are the time histories of surface pressure, radial velocity and von Mises stress of the shell. Moreover, deformation diagrams and spreading of the plastic zone of the shell are described as well.     

Shock responses of a surface ship subjected to noncontact underwater explosions

In combat operations, a warship can be subjected to air blast and underwater shock loading, which if detonated close to the ship can damage the vessel form a dished for hull plating or more serious holing of the hull. This investigation develops a procedure which couples the nonlinear finite element method with doubly asymptotic approximation method, and which considers the effects of transient dynamic, geometrical nonlinear, elastoplastic material behavior and fluid–structure interaction. This work addresses the problem of transient responses of a 2000-ton patrol-boat subjected to an underwater explosion. The KSF=0.8 is adopted to describe the shock severity. Additionally, the shock loading history along keel, the acceleration, velocity and displacement time histories are presented. Furthermore, the study elucidates the plastic zone spread phenomena and deformed diagram of the ship. Information on transient responses of the ship to underwater shock is useful in designing ship hulls so as to enhance their resistance to underwater shock damage.     

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

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.     

The free vibration analysis of submerged cantilever plates

Based on empirical added mass formulation, this work presents a simple procedure to determine the vibration frequencies and mode shapes of submerged cantilever plates. Once the added mass formulation is derived, the procedure can be used to analyze free vibration response easily. An analytical and numerical study is also performed for the vibrations of cantilever plates in air and in water, with these results compared with experimental and numerical data from pertinent literature. Besides, the frequency parameters of the submerged plate for various aspect ratios and thickness ratios are given in design data sheet form and are appropriate for engineering design applications.     

Dynamic response of cylindrical shell structures subjected to underwater explosion

This study investigated the linear and nonlinear dynamic responses of three cylindrical shell structures subjected to underwater small charge explosions in a 4 m×4 m×4 m water tank. The dimensions of the cylindrical shell structures were 90 cm×30 cm×1 mm (length×diameter×thickness). Both ends of the cylindrical shell were mounted with thick plates to provide support and create an enclosed space. The three cylindrical shell structures were un-stiffened, internally stiffened and externally stiffened, respectively. The experiments involving the dynamic response of cylinders subjected to underwater explosion (UNDEX) were performed under different standoff distances, varying from 210 to 35 cm. A small quantity of explosives was used to generate the shock loading. The plastic deformation of the cylindrical shell was observed at a standoff distance of less than 50 cm. Other conditions were tested to examine cylinder linear response. Dynamic analyses were performed for the experimental model using FEM and compared with the test results. The accelerations and dynamic strains of cylindrical shells obtained from the experiment were compared with those obtained by FE analysis. Finally, problems related to small-scale UNDEX experiments performed in small water tanks were analyzed.     

The interaction of surface water waves with submerged breakwaters

This paper concerns the behaviour of nonlinear regular waves interacting with rectangular submerged breakwaters. A new series of experimental results is presented and compared with numerical calculations based upon a Boundary Element Method (BEM) that utilises multiple fluxes to deal with the discontinuities encountered at the corners of the domain. Specifically, comparisons concern both the spatial water surface profiles at various times and the spatial evolution of the harmonics generated by the breakwaters, the latter being an important focus for the paper. The BEM is shown to accurately model both the water surface profile and the harmonic generation, provided the breakwater width is sufficient to ensure that flow separation is not a controlling influence. Furthermore, evidence is provided to confirm that reflection from rectangular submerged breakwaters is fundamentally a linear phenomenon.     

The evaluation method of total damage to ship in underwater explosion

Whipping response will happen when a ship is subjected to underwater explosion bubble load. In that condition, the hull would be broken, and even the survivability will be completely lost. A calculation method on the dynamic bending moment of bubble has been put forward in this paper to evaluate the impact of underwater explosion bubble load on the longitudinal strength of surface ships. Meanwhile the prediction equation of bubble dynamic bending moment has been concluded with the results of numerical simulation. With wave effect taken into consideration, the evaluation method of the total damage of a ship has been established. The precision of this evaluation method has been proved through the comparison with calculation results. In order to verify the validity of the calculation results, experimental data of real ship explosion is applied. Prediction equation and evaluation method proposed in this paper are to be used in ship structure design, especially in the preliminary prediction of the ultimate withstanding capability of underwater explosion damage for the integrated ship in preliminary design phase.     

Simulation of the nonlinear dynamic interactions between waves, a submerged breakwater and the seabed

This study employed direct numerical simulation to simulate the fully nonlinear interaction between the water waves, the submerged breakwater, and the seabed under differing wave conditions. In the numerical simulation, the laminar flow condition in the seabed was applied to evaluate the more exact fluid resistance acting on the porous media. Varying incident wave conditions were applied to the flow field resulting from the wave–structure–seabed interaction, and the variation in the pore water pressure beneath the submerged breakwater was investigated along the cross-section of the submerged breakwater. Structural safety and scouring were also considered on the basis of the numerical results for the flow field around the structure and the variation of the pore water pressure.     

Hydrodynamic and dynamic analysis to determine the directional stability of an underwater vehicle near a free surface

A theoretical methodology to determine the open-loop directional stability of a near-surface underwater vehicle is presented. It involves a solution of coupled sway and yaw equations of motion in a manner similar to that carried out for surface ships. The stability derivatives are obtained numerically through simulation of motions corresponding to planar motion mechanism (PMM) model tests. For the numerical simulation, a boundary-integral method based on the mixed Lagrangian-Eulerian formulation is developed. The free-surface effect on the vehicle stability is determined by comparing the results with that obtained for vehicle motion in infinite fluid. The methodology was used to determine the stability of the Florida Atlantic University’s Ocean EXplorer (OEX) AUV. The presence of the free surface, through radiation damping, is found to suppress unsteady oscillations and thereby enhance the directional stability of the vehicle. With effects of free surface, forward speed, location and geometry of rudders, location of the center of gravity etc. all being significant factors affecting stability, a general conclusion cannot be drawn on their combined effect on the vehicle stability. The present computational methodology is therefore a useful tool to determine an underwater vehicle’s stability for a given configuration and thus the viability of an intended mission a priori.     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.     

Simulation of wave propagation over a submerged bar using the VOF method with a two-equation k– turbulence modeling

A two-equation k– turbulence model is used in this paper to simulate the propagation of cnoidal waves over a submerged bar, where the free surface is handled by the volume-of-fluid (VOF) method. Using a VOF partial-cell variable and a donor–acceptor method, the model is capable of treating irregular boundaries, including arbitrary bottom topography and internal obstacles, where the no-slip condition is satisfied. The model also allows the viscous sublayer to be modeled by a wall function approximation implemented in the grid nodes that are immediately adjacent to a wall boundary. The numerical model applied to the propagation of cnoidal waves over a submerged bar can produce results that are in general agreement with some laboratory measurements. Some remarks arising from the comparison between the computational and experimental results are presented.     

Three-dimensional analysis of submerged, moored, horizontal, rigid cylinders used as breakwaters

Wave attenuation by moored cylinders is considered. The cylinders are submerged with their axes horizontal. Linear potential theory is applied. Three-dimensional motions of the cylinders subjected to normal and oblique monochromatic waves are determined using potential theory and a boundary integral method. Each cylinder has length 9.1 m (30 ft) and radius 1.5 m (5 ft), with its top 1.5 m (5 ft) below the still water line and its bottom 3.0 m (10 ft) above the seabed. Free-surface elevations are obtained for a single cylinder and for two cylinders in series. These configurations are effective wave barriers for a range of wave frequencies and incident angles.     

Unsteady thermoelastic analysis of a circular disk with a hot central core and subjected to adiabatic conditions

The unsteady thermoelastic analysis of a cooling circular disk or cylinder which is originally at uniform temperature is a classical problem of the theory of thermal stresses. More recent studies consider the case of composite structural configurations. The present paper deals with a situation which, apparently, has not been previously considered: unsteady thermal stresses caused by the presence of a hot, central nucleus. The temperature field is obtained in terms of a Fourier–Bessel expansion and then, radial and tangential stresses are evaluated analytically. The problem is of basic interest in mechanical and naval engineering systems.     

A numerical study of three-dimensional wave interaction with a square cylinder

In this study, a three-dimensional numerical model is used to study the wave interaction with a vertical rectangular pile. The model employs the large eddy simulation (LES) method to model the effect of small-scale turbulence. The velocity and vorticity fields around the pile are presented and discussed. The drag and inertial coefficients are calculated based on the numerical computation. The calculated coefficients are found to be in a reasonable range compared with the experimental data. Additional analyses are performed to assess the relative importance of drag and initial effects, which could be quantified by the force-related Keulegan and Carpenter (KC) number: KC_f=UT/(4πL). Here U is the maximum fluid particle velocity, T the wave period and L the length of structure aligned with the wave propagation direction. For small KC_f, the effective drag coefficient is proportional to 1/KC_f, provided the wavelength is much longer than the structural length. When wavelength is comparable to the structure dimension, the effective drag coefficient would be reduced significantly due the cancellation of forces, which has been demonstrated by numerical results.