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.     

环肋圆柱壳体在水下冲击波作用下的动力弹塑性屈曲

本文以加肋圆柱壳体为对象建立力学模型，在水下爆炸产生的冲击波作用下，考虑流体与结构的耦合效应，研究加肋圆柱壳体的弹塑性失稳变形量及动力响应特性。数值分析显示出的最终变形形状和压力变化过程与实验资料一致的     

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.     

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.     

壳体厚度对战斗部爆炸气泡特性影响的数值模拟研究

采用LS-DYNA软件,对装药半径为0.15m、0.42m、0.55m的战斗部有、无壳体的爆炸特性进行数值模拟研究,分析了炸药在有无壳体的水下爆炸时的冲击波压力、气泡脉动压力等特性参数,对比总结了不同当量、不同装药半径及有无壳体的数值计算结果。结果表明:壳体对水下爆炸气泡脉动的影响是较为显著的。壳体厚度对气泡形成时间没有太多影响,但对气泡压力峰值影响较大。因此,研究战斗部水下爆炸威力时必须考虑壳体因素,不能简化。     

On the determination of the mesh size for numerical simulations of shock wave propagation in near field underwater explosion

It is well known that the accuracy of mesh-based numerical simulations of underwater explosion strongly relies on the mesh size adopted in the analyses. Although a numerical analysis of underwater explosion can be performed with enough accuracy by using considerably fine meshes, such fine meshes may lead to substantially increase in the CPU time and the usage of computer memory. Thus, how to determine a suitable mesh size in numerical simulations is always a problem confronted when attempting to study the shock wave propagation resulting from underwater explosion and the subsequent response of structures. Considering that there is currently no universally accepted method for resolving this problem, this paper aims to propose a simple method to determine the mesh size for numerical simulations of near field underwater explosion. To this end, the mesh size effects on the shock wave propagation of underwater explosion are carefully investigated for different charge weights, through which the correlation between mesh sizes and charge weights is identified. Based on the numerical study, a dimensionless variable (λ), defined as the ratio of the radius of charge to the side length of element, is introduced to be the criterion for determining the mesh size in simulations. It is interesting to note that the presented method is suitable for various charge weights. By using the proposed meshing rule, adequate balance between solution accuracy and computational efficiency can be achieved for different blast scenarios in numerical simulations of underwater explosion.     

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.     

Parametric study for underwater blast-induced pipeline response embedded in marine sediments

Abstract

Blast response of submerged pipelines has been a research focus in recent years. In this article, a three-dimensional numerical model is established to investigate dynamic response of pipelines due to underwater explosion. The u–p approximation is integrated into finite element method (FEM) to simulate pore water effect in the seabed. Numerical continuity between hydraulic pressure in the flow field and pore pressure in the marine sediment is guaranteed to realize the blast response of submerged pipelines in ocean environment. Both fluid–structure interaction (FSI) and pipeline–seabed interaction (PSI) have been considered in the proposed model simultaneously. A comprehensive parametric study is carried out after validation of the present model with test data from underground explosion and underwater explosion, respectively. The effect of embedment depth, TNT equivalent, stand-off distance, pipeline diameter, and pipeline thickness to blast response of the submerged pipelines is investigated based on numerical results. Variation of deformation patterns and stress distribution of the pipeline with various installation and structure parameters has been illustrated and discussed to facilitate engineering practice.     

Displacements induced by breaking waves on axially loaded cylindrical shells

Forced vibrations of the walls of a vertical cylindrical shell under the impact of a breaking wave are studied theoretically. The wave action is modelled as a pressure distribution which varies in time and space. A linear dynamic analysis of the transient response is carried out by means of the modal superposition technique, in which the static stresses are considered. The results show that in thin shells, the transient displacements could be of the order of the thickness of the shell. It is suggested that these large displacements could play an important role in eroding the buckling capacity of the structural component. The problem of limiting the dynamic displacements is discussed by interaction diagrams for static axial load-dynamic lateral pressure, and by examination of the confluence of shell and wave parameters for which the transient displacements do not exceed a given value.     

Experimental investigation on a two-part underwater towed system

An experimental set-up is developed and proved to be effective for laboratory study of an underwater towed system. The experimental technique gives a practical method for monitoring the kinematic and dynamic performance of an underwater towed system in a ship towing tank. Both the theoretical and experimental results in the investigation indicate that the hydrodynamic response of a towed vehicle to the wave induced motion of a towing ship can be significantly reduced by applying a two-part tow method. A comparison of the numerical and experimental results in the investigation demonstrates that the numerical simulation results are close to the experimental data, overall agreement between experimental and theoretical results is satisfactory. The results qualitatively verify the mathematical model of a two-part underwater towed system proposed by Wu and Chwang [Wu, J., Chwang, A.T., 2000. A hydrodynamic model of a two-part underwater towed system. Ocean Engineering 27 (5), 455–472].     

Investigation on the Cavitation Effect of Underwater Shock near Different Boundaries

When the shock wave of underwater explosion propagates to the surfaces of different boundaries, it gets reflected. Then, a negative pressure area is formed by the superposition of the incident wave and reflected wave. Cavitation occurs when the value of the negative pressure falls below the vapor pressure of water. An improved numerical model based on the spectral element method is applied to investigate the cavitation effect of underwater shock near different boundaries, mainly including the feature of cavitation effect near different boundaries and the influence of different parameters on cavitation effect. In the implementation of the improved numerical model, the bilinear equation of state is used to deal with the fluid field subjected to cavitation, and the field separation technique is employed to avoid the distortion of incident wave propagating through the mesh and the second-order doubly asymptotic approximation is applied to simulate the non-reflecting boundary. The main results are as follows. As the peak pressure and decay constant of shock wave increases, the range of cavitation domain increases, and the duration of cavitation increases. As the depth of water increases, the influence of cavitation on the dynamic response of spherical shell decreases.     

A dynamic two-dimensional calculation of underwater lines

On the basis of a lumped mass method in two-dimension, we derive a dynamic calculation method for a system including both extensible and inextensible underwater lines. The Newmark beta method is used in numerical integration with respect to time. The Newton Raphson method is applied so that the numbers of iterations are reduced. A transient response of a line during deployment is calculated.     

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H_s and T_z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.     

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.     

深海采矿转场工况平台—水下系统耦合动力响应特性研究

针对水深6.0 km深海采矿装备,研究其转场工况平台—水下系统耦合动力响应特性。建立深海采矿平台—输浆管—中继站一体化耦合动力模型,其中采用有限元方法离散输浆管,采用势流理论计算平台水动力,基于Kalman滤波对动力定位系统进行参数整定,优化动力定位系统推力。考虑动力定位系统,计算水动力和采矿平台—输浆管—中继站的频域响应和平台—水下系统耦合时域运动响应,计算得到了平台时域运动响应、水下系统动力响应及动力定位系统推力响应。结果表明：建立的一体化耦合动力分析模型是可行的,可以有效预报平台及水下系统响应;转场0°浪向动力定位系统可以有效控制平台运动;中继站运动较小,输浆管轴力较大,建议将输浆管的浮力材料移动到流速较小的水下范围,可降低拖曳力,有利于输浆管的强度性能。     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

Estimation of Depth and Yield of Underwater Explosions From First and Second Bubble-Oscillation Periods

In this communication, a method is described for estimating the order of magnitude of energy yield and detonation depth for underwater explosions, based on the acoustical signals radiated. The method determines the ratio of the periods of the first two oscillations made by the gas bubble formed by an explosion, with bubble-oscillation periods being extracted from the cepstra of signals recorded on hydrophones. The results of laboratory studies, taken from the literature [H. G. Snay and R. V Tipson, “Charts for the parameters of migrating explosion bubbles,” Tech. Rep., NOLTR 62–184 (1963)], are used to convert this ratio into a measure of the maximum bubble radius achieved during the first oscillation, expressed as a fraction of the detonation depth. This fraction, combined with the period of the first oscillation, allows detonation depth and explosion energy yield to be estimated on an order-of-magnitude basis. The method is applied to signals gathered in the Pacific Ocean, at ranges of thousands of kilometers from a series of chemical explosions. Reported values of detonation depths and explosion yields are shown to agree with the order-of-magnitude estimates derived using the method. The method is shown to have a bias towards underestimating explosion energy yield. It is hypothesized that this bias results from the different scales of the at-sea explosions and the laboratory measurements on which the estimation method is based. The uncertainty associated with the method's estimation of charge yield is comparable with those of seismic methods for the estimation of energy yields of underground nuclear tests.      

Review of flexible risers and articulated storage systems

The anchorage system for mid-ocean loading or production consists of an articulated tower for mooring the tanker. Flexible risers are also essential components of the anchorage system. The present paper provides a state-of-the-art review on articulated storage systems and flexible risers, giving theoretical background for the development of computer software for the static analysis of flexible risers.In the state-of-the-art review for flexible risers, various analysis techniques for elastic lines and flexible risers under self-weight, current and wave forces are presented. The dynamic response of the flexible riser, including vortex-induced oscillations, is also outlined.The literature concerning the articulated tower and tanker is relatively scarce. Available works related only to dynamic responses of articulated towers. The combined response of tower and tanker is only studied by Chakrabarti and Cotter [(1978), Analysis of a tower-tanker system. In Proceedings of the 10th Offshore Technology Conference, OTC 3202, pp. 1301–1310] in a limited sense. The review of these works is summarised relevant to this paper.In the end, the static analysis of the flexible riser under its self-weight and current is presented using a finite difference approach. The problem essentially involves geometrical non-linearity, which is tackled with the help of an iterative solution based on modified Newton-Raphson technique. The theoretical formulation presented is being used to develop the computer software for the static analysis of the flexible risers.     

Transient sea-ice polynya forced by oceanic flow variability

In the Weddell Sea during the winters of 1974–1976 a significant opening in the sea-ice cover occurred in the vicinity of a large bathymetric feature — the Maud Rise seamount. The event is commonly referred to as the Weddell Polynya. Aside from such a large-scale, relatively persistent polynya in the Weddell Sea, transient, small-scale polynya can also appear in the sea-ice cover at various times throughout the winter and at various locations with respect to the Maud Rise. The underlying causes for the occurrence of such transient polynya have not been unambiguously identified. We hypothesize that variations in the mean ocean currents are one major contributor to such variability in the sea-ice cover. Analysis of the sea-ice equations with certain idealized patterns of ocean currents serving as forcing is shown to lead to Ekman transports of sea ice favorable to the initiation of transient polynya. Aside from the actual spatial pattern of the idealized ocean currents, many other factors need also be taken into account when looking at such transient polynya. Two other such factors discussed are variations in the sea-ice thickness field and the treatment of the sea-ice rheology. Simulations of a sea-ice model coupled to a dynamical ocean model show that the interaction of (dynamical) oceanic currents with large-scale topographic features, such as the Maud Rise, does lead to the formation of transient polynya, again through Ekman transport effects. This occurs because the seamount has a dynamic impact on the three-dimensional oceanic flow field all the way up through the water column, and hence on the near surface ocean currents that are in physical contact with the sea ice. Further simulations of a sea-ice model coupled to a dynamic ocean model and forced with atmospheric buoyancy fluxes show that transient polynya can be enhanced when atmospheric cooling provides a positive feedback mechanism allowing preferential open-ocean convection to occur. The convection, which takes hold at sites where transient polynya have been initiated by sea-ice–ocean stress interaction, has an enhancing effect arising from the convective access to warmer, deeper waters. To investigate all of these effects in a hierarchical manner we use a primitive equation coupled sea-ice–ocean numerical model configured in a periodic channel domain with specified atmospheric conditions. We show that oceanic flow variability can account for temporal variability in small-scale, transient polynya and thus point to a plausible mechanism for the initiation of large-scale, sustained polynya such as the Weddell Polynya event of the mid 1970s.     

Long-term measurement of temperature variabilities off Mindanao Island by the ocean acoustic tomography

Oceanic variabilities off Mindanao Island, Philippines where the North Equatorial Current branches into the Kuroshio and the Mindanao Current were measurerd for a period from 14 Feb.–1 Jun. 1992 by the oceean acoustic tomography (OAT). From the beginning of April, the travel time of acoustic rays propagating over a horizontal distance of about 250km, through the depth range of 80–4700 m around the underwater sound channel began to decrease, implying a warming of water. This variability was also confirmed with the results of temperature measurement at the sites where a sound source and receiver were located. The TOGA/TAO array data show that the OAT experiment was done when the 1991–1992 El Nino was at a decaying stage and the resulting warming-up of water occurred at the western Pacific. This study provides us a first evidence of ENSO-related variabilities detected by the OAT.