Spherical Containment Vessels Research Articles

Improved theory of the elastic-plastic response of spherical containment vessels subjected to internal blast loading and its application

Baker built the displacement equations of motion for a thin spherical shell to spherically symmetric internal blast loading, and further provided the analytical solution of the elastic-plastic response under a triangular decaying pressure, neglecting shell thinning and radius variation [1], which was widely used in the fields of analysis and design of explosion containment vessels. However, it appears that some improvements and corrections are needed when we revisit this classic problem. In this paper, the elastic-plastic response of thin spherical shells is investigated mathematically. The complete equations of motion for three models are developed. Then the main ideas of the analytical and numerical methods are presented, as well as some important procedures and results by using Laplace transform techniques, which are convenient to use and generalize. Three typical examples are solved to exhibit differences between our improved theory and Baker’s [1]. Furthermore, our models are employed to gain some insights into response regularities, including the effect of various degrees of strain-hardening on maximum displacements under impulsive loading, and the effect of loading duration on the shell displacement for a perfectly plastic material.

Quasi-static gas pressure generated by explosive charge blasting in a spherical explosion containment vessel

Quasi-static pressure is important for the design of explosion containment vessels. Experiments of the spherical vessel under blast loading, in which the quasi-static pressure was measured by the pressure sensors of two different installations, i.e. flush installation and guide-hole installation, were carried out. The data obtained by the pressure sensors are consistent with each other. Based on the formula form derived theoretically, the empirical formula was obtained by fitting the data. The main results are as follows:(1) the pressure in the vessel goes into quasi-static state after the blast wave reflects back and forth three times in the vessel; (2) the quasi-static pressure in the spherical vessel is proportional to the explosion equivalent-to-vessel volume ratio, and the empirical coefficient is 1.10 MPa·m3/kg TNT.

Engineering Design of a Multiple-Use Spherical Explosion Containment Vessel Subjected to Internal Blast Loading From 25 kg TNT High Explosive

Explosion containment vessels have been widely used to contain the internal blast effects. In this paper, we present engineering design and experimental results of a real multiple-use spherical explosion containment vessel, which has been employed to withstand internal blast loading from 25 kg trinitrotoluene (TNT) high explosive in the past 10 years. It is shown that strain growth should be considered in the analysis and design of multiple-use explosion containment vessels, and the dynamic load factor (DLF) method with the consideration of strain growth may achieve a safe and proper design.

Interactive mechanisms between the internal blast loading and the dynamic elastic response of spherical containment vessels

The interactive mechanisms between internal blast loading and dynamic elastic response of spherical containment vessels are studied in this paper. The blast loading history in containment vessels can be divided into three periods, i.e. the primary-shock period, the shock-reflection period and the pressure-oscillation period. It is shown that the initial response of the containment vessel depends on both the impulse and the shape of the primary-shock depending on the ratio of the loading period to the breathing mode period. However, during the shock-reflection period, the response of the containment vessel can be coupled with the reflected shock waves in the vessel, especially when the dominant frequency of reflected shock waves is close to the breathing mode frequency of the vessel. During the pressure-oscillation period, the dynamic loading is mainly the oscillation of the internal pressure due to the oscillatory volume change of the vessel, which couples dissipatedly with the vibration of the vessel leading to reduced vibration amplitudes. The effects of the influential non-dimensional parameters on the resonant interaction in shock-reflection period are discussed, based on which guidelines are recommended for avoiding the strain growth in the shock-reflection period in the design of spherical containment vessels.

Further study on strain growth in spherical containment vessels subjected to internal blast loading

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading, which is featured by the increased vibration amplitude of the vessel in a later stage. Previous studies attributed the strain growth in spherical containment vessels to the structural perturbation, the beating between two close vibration modes and the interactions between the vessel vibration and the reflected shock waves. In this paper, it is shown that nonlinear modal coupling is another important cause of strain growth in spherical containment vessels. Based on the understanding of the vibration modes in a complete spherical shell, the nonlinear modal coupling in the nonaxisymmetric response of complete spherical shells are studied using finite element method. Methods for preventing the strain growth due to nonlinear modal coupling are discussed, which provide guidelines for the engineering design of spherical containment vessels.

Measurement of Neutrino Oscillation with KamLAND: Evidence of Spectral Distortion

Measurement of Neutrino Oscillation with KamLAND: Evidence of Spectral Distortion

Strain growth in spherical explosive chambers subjected to internal blast loading

Spherical pressure vessels are used to fully contain the effects of high explosions. In this paper, the vibrations of a spherical containment vessel undergoing elastic response are investigated. Vibration modes of containment vessels are of particular interest, as it is the superposition and interaction of different modes of response with closely spaced frequencies (beating) that has been reported to be the mechanism of ‘strain growth’. The modal frequencies of a complete spherical shell for both axisymmetric and nonaxisymmetric response modes are discussed, based on a sequence of papers that have appeared in the open literature. Analytical predictions are then compared with finite element numerical simulations. It is found that the numerical simulations accurately predict both the axisymmetric and nonaxisymmetric modal frequencies for the complete spherical shell. Next, numerical simulations of modal frequencies for the more complex spherical containment vessel (with nozzles) are compared with the spherical shell results. These simulations for the spherical containment vessel reveal that frequencies are similar to the complete spherical shell, although a splitting of the degenerate frequencies (associated with nonaxisymmetric modes) occurs when progressing from a perfect spherical shell to the containment vessel. As a result, the vibrational response of the spherical containment vessel can be interpreted as a perturbation on the response of a perfect spherical shell. Limited comparisons with experimentally recorded frequencies for participating modes of vessel dynamic response during high explosive containment testing are presented as well. Participating modes potentially capable of beating together to produce ‘strain growth’ are isolated and are found to agree within 4 percent with frequencies determined from beating frequency measurements.

Spherical vessel subjected to explosive detonation loading

The following work utilizes a calculation method for the design of spherical containment vessels for pressure gases likely subjected to internal detonation. A centrally initiated explosion within the vessel is taken into account and the history of pressures on the internal vessel wall is investigated by means of the fundamental compressible fluid dynamics, for which a non-viscous perfect gas is assumed. The obtained differential equations are integrated with explicit finite difference techniques, introducing artificial viscosity. The response of vessel is decoupled from the fluid and it is determined by a dynamic finite element code of explicit type; the investigated material is considered to have an elastic-plastic behaviour. Comparison with data found in references on PBX-9404 high-explosive induced explosions confirms the calculation method developed.

On the bi-directional toroidal field of a spherical rotamak

In many rotamak experiments performed in spherical containment vessels a self-generated toroidal field of substantial magnitude, and opposite polarity in the upper and lower hemispheres, has been observed. In addition, several experiments have observed the formation of a doublet poloidal flux configuration in which the toroidal plasma current flows predominantly above and below the equatorial plane. The authors analyse these phenomena theoretically by considering a spherical uniform density plasma bounded by an insulating wall and immersed in a uniform magnetic field which has both a rotating component (for current drive) and a constant vertical component (for MHD equilibrium). They use both a multiple-order perturbation technique and a general numerical technique to solve the vector spherical harmonically expanded MHD equations under the approximation of negligible ion velocity.

Fracture Mechanics Aspects of the Structural Integrity Technology of Spherical Aluminum Containment Vessels for LNG Tankers

The Kvaerner-Moss spherical tank design offers significant economic advantage for the shipboard transport of liquefied natural gas. An analytical and experimental approach based on fracture mechanics concepts was used to assist the designer in providing answers to the following basic questions: (1) Might a discontinuity smaller than detectable by nondestructive inspection lead to catastrophic fracture; (2) How fast would such a discontinuity grow under fatigue loading likely to occur during the lifetime of the tank; (3) Could a fatigue crack growing part way through the tank wall precipitate catastrophic fracture before it grows through the wall and is detected as a leak; and (4) If leakage develops, how much time is available to get the ship safely to port for discharge and repair? Both “critical” locations in the tank, i.e., the highest stressed region of the membrane and the equatorial ring, are examined. Available data indicating the safety of spherical tanks fabricated of aluminum alloy 5083-0 is documented.