Fluid-filled Container Research Articles

Mean flow induced by longitudinal libration of a fluid-filled rotating container bounded by two conical surfaces

The problem of determining a mean flow induced by longitudinal libration of a rapidly rotating fluid-filled container bounded by the surfaces of two oppositely oriented right circular cones is considered. It is shown that the problem is reduced, through introducing a cosine of the angle between the normal to the conical surfaces and the axis of rotation, to the problem of determining a mean flow induced by libration of a fluid-filled rotating cylindrical container of infinite radius. A theoretical scenario is proposed of how the solved problem can be applied to the approximate determination of the differential mean rotation in a significant part of a rotating spherical and/or oblate spheroidal cavity under the action of longitudinal libration forcing.

Analysis of confined cavity evolution and related pressure created by hydrodynamic ram

The impact of high-velocity projectiles on fluid-filled containers can induce the hydrodynamic ram (HRAM) effect, leading to the creation of a cavity within the fluid. The evolution of this cavity is subject to the constraints imposed by the container. This study aims to investigate the decay of projectile velocity and the development of confined HRAM cavities using a combined approach involving experimental and analytical methods. In contrast to existing research, this study accounts for the varying projectile velocities during different HRAM phases. Furthermore, enhancements have been introduced to the established cavity model, encompassing refinements in pressure differentials both inside and outside the cavity, alongside adjustments to the radial extent of liquid disturbance. The effectiveness of these refinements has been substantiated through experimental evidence. The findings illuminate two prominent constraint effects exerted by the container on the dynamics of HRAM cavities. Primarily, it accentuates the disparity in HRAM cavity pressures between the interior and exterior environments, and this pressure differential follows an exponential decay with distance. Secondly, it profoundly influences the flow of liquid near the wall, resulting in a considerably slower contraction of the cavity near the wall compared to its expansion phase. The evolution of the HRAM cavity is observed to manifest across three distinct stages: the unconfined cavity expansion stage, the partial cavity confinement stage, and the full cavity confinement stage.

Inertial wave attractors in rapidly rotating tilted cuboids

Flows in rapidly rotating fluid-filled containers are strongly constrained by the restorative Coriolis force. Their responses to small amplitude perturbations may result in the excitation of regular modes of the container for some very selective geometries, but in general the response is a network of inertial wave beams. Due to the peculiar laws governing how these beams reflect, the network of reflected beams may focus onto highly localized regions of the container, where the beam energy and wavenumber become unbounded in the absence of viscous and nonlinear processes. Here, we explore in detail this focusing of wave beams in cuboids, enabling a comprehensive analysis of this intriguing process.

Experimental investigation of cavity dynamics and pressure created by cumulative hydrodynamic ram

The impact of high-velocity projectile on fluid-filled containers can cause hydrodynamic ram (HRAM) events. When multiple projectiles impact, HRAM effect is superimposed. In this paper, we presented the experimental results of cavity dynamic, pressure-time histories, and impulse-time histories caused by single and double projectiles impacting water-filled containers.

Experimental Verification of Effect of Different Fluid Properties on the Vibration Response of a Cantilever Rotor

The current analysis is an effort to obtain the vibration characteristics of a cantilever rotor shaft with an extra mass added at the free end of the rotor shaft partially immersed in a viscous medium. This work is concentrated on the theoretical analysis of the natural frequency and amplitude of the spinning cantilever rotor shaft with addition mass using the influence coefficient method. The influence of fluid forces is studied using the Navier–Stokes equation. The gap ratio (ratio of the fluid-filled container radius to the shaft radius) and viscosity of the fluid are taken as the main variable parameters.MATLAB programming is used to obtain vibration behavior from the theoretical expressions. The obtained result from the numerical analysis is validated by the comparison of the results of experimental analysis.

High velocity projectile impact of a composite rubber/aluminium fluid-filled container

When penetrated by a high-velocity projectile, a fluid-filled container can be severely damaged and ruptured due to the intense impact loading from Hydrodynamic Ram (HRAM), which causes a primary shock wave, and then a subsequent loading phase when a cavity evolves in the fluid. In the design of fuel tanks for aircraft, and other transport vehicles, the HRAM pressure is a major concern for the reliability of the structure. In this paper, experiments of high-velocity projectiles impacting two different types of fluid-filled containers, including an aluminium wall and a composite aluminium/rubber wall, were performed to study the mitigation effect of the rubber layer on the damage of the structure and the impact loading from Hydrodynamic Ram. A high-speed camera was employed to record the formation process of the cavity, and the shock wave pressure-time histories in the fluid were also obtained by pressure transducers. By comparing and analysing the experimental results, it is shown that the rubber layer of the composite wall container was able to reduce the reflected shock pressure and the deformation of the structure.

Comparison of the hydrodynamic ram caused by one and two projectiles impacting water-filled containers

High-velocity impact on fluid-filled containers is a concern associated with the vulnerability of aircraft fuel tanks due to hydrodynamic ram (HRAM). The present study compared the hydrodynamic ram caused by one and two spherical projectiles impacting water-filled containers using a previously developed and validated numerical model. Two types of comparisons were conducted to study the difference in pressure distribution inside the water and energy-time history of various parts, respectively. The propagation velocity of the superimposed shock wave in the two-projectile cases is higher than the shock wave in the one-projectile cases. The change in the energy of the entry plate is not affected by the number of projectiles, while more of the energy from water is transferred to the exit plate in the two-projectile cases compared to the one-projectile cases.

Experimental and numerical investigations of dynamic response and failure of fluid-filled container under blast loadings from a cased charge

Resulting from the hydrodynamic ram effect, a high-velocity projectile could be dramatically attenuated when penetrated into a fluid-filled container, which was usually employed as protective structures. In this paper, according to the principle of impedance mismatch, a new type of composite container was designed and manufactured, in which the container walls were consisted by steel plate with rubber layer attached, to alleviate the dynamic response and subsequent failure of fluid-filled container induced by blast loadings from a cased charge. The structural dynamic response and failure patterns of the traditional and the composite container subjected to the loadings from close-in explosion of a cased charge, including high-velocity fragments and shock wave produced by explosive, were experimentally and numerically investigated and compared. Based on the observation of experimental phenomena and numerical analysis, it is found that the rubber layer of the composite container played an important role in alleviating the damage and deformation of the container structure. The size of the damaged area, the structural deformation and the plastic strain can be significantly reduced. The result presented in this paper would be helpful in the design of protective structures.

Construction of basic functions for problems of fluid oscillations in a tank

Considerable number of studies and publications is devoted to issues of dynamic behavior of liquids, the impact on the surface tension of a liquid in partially filled tanks in particular. The study of liquid vibrations in partially fluid-filled cylindrical containers with the presence of a free surface is an important technical task. The influence of the free surface curvature of the tank filler on the oscillation frequency is taken into account. It is assumed that the liquid is incompressible and inviscid, and its motion is irrotational. The method to solve a boundary value problem for determining fluid oscillations in a reservoir has been developed, and an integral presentation of an unknown velocity potential is proposed. The geometrical characteristics of the free liquid surface have been determined. It is taken into account that the free liquid surface deviates from the equilibrium position and assumes a spherical shape. A system of singular integral equations has been obtained for unknown values of the potential and flow. The method of boundary elements with constant approximation of an unknown density on the elements has been used to solve the system numerically. The oscillation frequencies for the zero harmonic are determined in accordance with the level of the free-surface elevation. It has been determined that the deviation of the free surface shape from the flat and even a slight rise in the free surface level leads to noticeable changes in the vibration frequencies. The vibrational modes obtained in the study mostly coincide with the modes for a flat free surface and can serve as the basic system of functions in the studies of free and forced fluid vibrations in tanks, as well as, in the study of the intrinsic and forced sloshing in the reservoirs provided surface tension is taken into account.

Experimental and numerical study on the cumulative damage of water-filled containers impacted by two projectiles

High-velocity impact on fluid-filled containers is a matter of interest in the studies of aircraft fuel tank vulnerability. Most of the conducted studies have addressed this problem by considering single impact. However, the present study evaluated experimentally the cumulative damage of a water-filled container impacted by two spherical projectiles with varying velocities in the range of 1000 m/s and 1500 m/s. A specially designed aluminum sabot was used to enable a 25 mm powder gun to accelerate two tungsten projectiles simultaneously. The failure modes of the plates were also analyzed after the experiments. LS-DYNA code was used to simulate this complex fluid–structure interaction problem. The residual velocity of the projectile, pressure within the water, and plate deformation profile obtained from both the experiment and simulation were compared to verify the simulation model. The experimentally verified finite element models were further used to investigate several critical factors in cumulative damage.

The transient development of the flow in an impulsively rotated annular container

When a fluid-filled container is spun up from rest to a constant angular velocity the fluid responds in such a way that the fluid–container system is ultimately in a state of rigid-body rotation. The fluid can then be said to have traversed a trajectory in phase space from a simple stable equilibrium state of no motion to another stable equilibrium representing full rigid-body rotation. This simple statement belies the fact that during this process the fluid can undergo a series of transitions, from a laminar through a transient turbulent state, before attaining the stable motion that is rigid-body rotation. Using a combination of analytical and computational methods, we focus on the dynamics resulting from an impulsive change in the rotation rate of a fluid-filled annulus, specifically, the impulsive spin-up of a stationary annulus, or the impulsive spin-down of an annulus already in a state of rigid-body rotation. We explore the initial development of the impulsively generated axisymmetric boundary layer, its subsequent instability, and the larger-scale transient features within this class of flows, allowing us to look at the effect these features have on the time it takes for the system to spin up to a steady state, or spin down to rest.

Steady flows in an oscillating deformable container: Effect of the dimensionless frequency

A detailed and systematic investigation into the properties of steady streaming inside a fluid-filled container with oscillating deformable boundaries is presented. The results demonstrate and explain how flow reversal varies with the dimensionless vibration frequency.

The influence of rubber layer on the response of fluid-filled container due to high-velocity impact

When hit by a high-velocity projectile, a fluid-filled container might suffer from Hydrodynamic Ram. The entire tank structure can possibly rupture due to the loads from primary shock wave and a cavity developed in the liquid. In this paper, a countermeasure, of which the rubber layer is inserted on the walls of the tank, is proposed to alleviate the dynamic response of fluid-filled container under the impact of high-velocity projectile. The applicability of the numerical method in simulating the process of high speed projectile penetrates the fluid-filled container is validated by comparing the numerical results with the experimental data in the literature. Then, numerical simulations were conducted to investigate the process of projectile penetrates the fluid-filled container with rubber layer insertion between the walls of container and fluid, with the velocities of 450m/s, 600m/s, 750m/s, 900m/s and 1050m/s, respectively. The influence of rubber layer on the dynamic responses of tank walls, the change of pressure of shock wave in water and the energy absorption of structural walls and rubber layers were analyzed. The results indicate that the rubber layer has a significant effect on shock wave acting on container walls. The dynamic response of liquid tank under the loading of the shock wave and local pressure, which is caused by the high speed fragments traveling in the fluid, decreases remarkably.

Analysis on the effects of the shapes of flexible fluid-filled containers on their impact response

Analysis on the effects of the shapes of flexible fluid-filled containers on their impact response

Quasi-periodicity and multi-scale resonators for the reduction of seismic vibrations in fluid-solid systems

This paper presents a mathematical model for an industry-inspired problem of vibration isolation applied to elastic fluid-filled containers. A fundamental problem of suppression of vibrations within a finite-width frequency interval for a multi-scale fluid-solid system has been solved. We have developed a systematic approach employing full fluid-solid interaction and dispersion analysis, which can be applied to finite and periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and transient regime computations.

Numerical Methods for Interface Coupling of Compressible and Almost Incompressible Media

Many experiments in biomedical applications and other disciplines use a shock tube. These experiments often involve placing an experimental sample within a fluid-filled container, which is then placed inside the shock tube. The shock tube produces an initial shock that propagates through gas before hitting the container with the sample. In order to gain insight into the shock dynamics that is hard to obtain by experimental means, computational simulations of the shock wave passing from gas into a thin elastic solid and into a nearly incompressible fluid are developed. It is shown that if the solid interface is very thin, it can be neglected, simplifying the model. The model uses Euler equations for compressible fluids coupled with a Tammann equation of state (EOS) to model both compressible gas and almost incompressible materials. A three-dimensional (2D axisymmetric) model of these equations is solved using high-resolution shock-capturing methods, with newly developed Riemann solvers and limiters. The methods are extended to work on a mapped grid to allow more complicated interface geometry, and they are adapted to work with adaptive mesh refinement (AMR) for higher resolution and faster computations. The Clawpack software is used to implement the method. These methods were initially inspired by shock tube experiments to study the injury mechanisms of traumatic brain injury (TBI).

고속충돌에 의한 원통형 액체 용기의 유체-구조 연성해석

In this paper, fluid-structure of interaction behavior of a fluid-filled cylindrical polymer container impacted by a high speed spherical projectile was studied using ALE(Arbitrary Lagrangian Eulerian) method. The hydrodynamic ram phenomenon occurred by the impact projectile penetrating through the container was investigated by examining time histories of projectile velocity and fluid pressure and density. The analysis results were agreed reasonably well compared to those by experiments.

Oscillatory counter-centrifugation

In ordinary centrifugation, a suspended particle that is heavier than the displaced fluid migrates away from the rotation axis when the fluid-filled container rotates steadily about that axis. In contrast a particle that is lighter than the displaced fluid (e.g., a bubble) migrates toward the rotation axis in a centrifuge. In this paper, we show theoretically that if a fluid-filled container rotates in an oscillatory manner as a rigid body about an axis, at high enough oscillation frequencies, the sense of migration of suspended particles is reversed. That is, in that case particles denser than the fluid migrate inward, while those that are lighter than the fluid move outward. We term this unusual phenomenon “Oscillatory Counter-Centrifugation” or OCC, for short. Through application of the method of averaging to the equations of motion, we derive a simple criterion to predict the occurrence of OCC. The analysis also reveals that the time-average of the Coriolis force in the radial direction is the term that is responsible for this effect. In addition, we analyze the effects of the Basset history force and the Rubinow–Keller lift force on particle trajectories and find that OCC persists even when these forces are active. The phenomenon awaits experimental verification.

Numerical Study of the Effects of Metallic Plates in the Attenuation of the HRAM Phenomenon

Hydrodynamic Ram (HRAM) is a phenomenon that occurs when a high-energy object penetrates a fluid-filled container. The projectile transfers its momentum and kinetic energy through the fluid to the surrounding structure increasing the risk of catastrophic failure and excessive structural damage. In this work a numerical study of the influence of metallic plates, inside a fluid-filled aluminium tube, in the attenuation of the HRAM phenomenon effects is performed. The numerical results regarding walls displacement and pressure inside the tank will be compared with a case in which there are no barriers inside the tube. The simulations are performed with the software LS-DYNA applying the ALE technique.

Signs of magma ascent in LP and VLP seismic events and link to degassing: An example from the 2010 explosive eruption at Merapi volcano, Indonesia

The link between seismicity and degassing is investigated during the VEI 4 eruptions of Merapi volcano (Indonesia) in October and in early November 2010. Seismicity comprised a large number and variety of earthquakes including Volcano-Tectonic events, a sustained period of Long Period Seismicity (LPS), i.e., Long-Period events (LP), Very Long Period events (VLP) and tremor. LPS seismicity is ascribed to the excitation of fluid-filled cavity resonance and inertial displacement of fluids and magma. We investigate here LPS that occurred between 17 October and 4 November 2010 to obtain insights into the volcano eruption processes which preceded the paroxysmal phase of the eruption on 4–5 November. We proceed to the moment tensor inversion of a well-recorded large VLP event during the intrusion phase on 17 October 2010, i.e., before the first explosion on 26 October. By using two simplified models (crack and pipe), we find a shallow source for this VLP event at about 1km to the south of the summit and less than 1km below the surface. We analyze more than 90 LP events that occurred during the multi-phase eruption (29 October–4 November). We show that most of them have a dominant frequency in the range 0.2–4Hz. We could locate 48 of those LP events; at least 3 clusters of LP events occurred successively. We interpret these observations as generated by different fluid-filled containers in the summit area that were excited while magma rose. We also observe significant variations of the complex frequency during the course of the eruption. We discuss these changes in terms of a variable ratio of fluid to solid densities and/or by possible conduit geometry change and/or permeability of the conduit or the edifice and/or by resonance of different fluid-containers during the release of more than 0.4Tg of SO2 and large but unknown masses of other volcanic gases. Finally, we also discuss how the major explosions of the eruption were possibly triggered by passing waves resulting from regional tectonic earthquakes on 3 and 4 November.