A. Britan

Shock waves attenuation by granular filters

Abstract Proper design of protecting filters mitigates the effect of blast and shock waves and thereby makes such filters effective protection against both accidental and planned explosions. The main goal of the present study was to clarify the filter performance in reducing the loading on structures as well as reducing the strength of the transmitted shock. While most of the granular filters used for protection in the past were composed of sand or rock particles, in the present study the investigated granular filters were composed of small spherical particles. This was done in order to exclude the influence of the particle shape and to ease the numerical simulation of the filter performance. Moreover, in the simulations we neglected real effects such as particles movement and its rearrangement during the shock wave propagation and only discussion regarding the dependence of the granular filter performance on its length and composition is provided. Based on a comparison between experimental results and appropriate numerical simulations obtained for the pressure profiles inside and downstream of the filter it was found that the attenuation performance of the filter can be well predicted using a simple one-dimensional approach to the real, more complicated problems.

Gas filtration during the impact of weak shock waves on granular layers

Abstract This paper deals with the unsteady gas filtration through a granular layer attached to a rigid end-wall when impacted head-on by a weak shock wave in a shock tube. The main goal of the present work is to study the gas pressure field developed inside the granular layer during its compression by the shock wave. A physical model is proposed for simulating the phenomenon and solved numerically. The numerical results are compared with the measured gas pressure at different locations inside the sample and at the end-wall covered by the granular layers. Good agreement is found between the calculated gas pressure signals and those measured at the shock tube end-wall covered by a granular layer at the final stage when the gas pressure is mostly governed by gas filtration. In the initial, unsteady part of the signals, large deviations exist between the calculated and the experimental results. The only reason for the agreement or discrepancy between the theoretical predictions and the experiments is the compaction effect associated with the formation of the gas pressure profile at the shock tube end-wall covered with a granular layer.

The contribution of shock tubes to simplified analysis of gas filtration through granular media

A hybrid method for the problem of transient shock-induced filtration of the gas flow through granular media is developed. The hybrid method combines a controlled shock-tube test and Morrison’s simplified approach to the problem of gas filtration. It is demonstrated that most pressure traces that have been recorded in various laboratories with a large variety of granular material samples and under different conditions are limited to situations in which the pressure losses in the flow are dominated by the Forchheimer mechanism. The hybrid method enables these results to be described by a single, universal pressure curve, and specification of the Forchheimer coefficient which is one of the two key parameters responsible for the correct simulation of the filtration-flow behaviour. The second key parameter, the Darcy coefficient, cannot be evaluated by the available experimental results. To overcome this shortcoming, a new controlled laboratory test that provides a wider range of the flow conditions, from the Forchheimer to the developed mixed flow, was conducted. In turn, a comprehensive gas dynamic analysis of the transient flow inside the shock tube enables us to define, from the single controlled laboratory test, the two coefficients of the Forchheimer resistance law, a and b.

Weak Shock Wave Interaction with Inert Granular Media

This chapter discusses the dynamics of stress phenomena inside granular materials as well as inside those modeled by random packing of monodisperse disks or cylinders. It outlines developments and focuses on the main experimental methods, materials used during various investigations, and results that are obtained with respect to the following points: mechanics of stress propagation through granular media and the role of the sidewall friction, effect of the shock wave induced gas filtration, unsteady waves and contact stress performances inside a granular medium, shock wave damping caused by granular filters, and recent physical models and methods used for computer simulation to predict experimental findings

Head-on collision of a planar shock wave with a granular layer

An experimental study was conducted in a vertical, 31×31 mm2 cross-section, shock tube. The investigation included measurements of the gas pressure and the compressive stress; based on the observed measurements the trajectories of the principal disturbances inside the granular layer were reconstructed. Results of this study show that two different effects, gas filtration and mechanical response of a granular layer to the weak shock wave loading, are of paramount importance and depend on the layer characteristics.An experimental study was conducted in a vertical, 31×31 mm2 cross-section, shock tube. The investigation included measurements of the gas pressure and the compressive stress; based on the observed measurements the trajectories of the principal disturbances inside the granular layer were reconstructed. Results of this study show that two different effects, gas filtration and mechanical response of a granular layer to the weak shock wave loading, are of paramount importance and depend on the layer characteristics.

Development of a general approach for predicting the pressure fields of unsteady gas flows through granular media

Two approaches for treating the shock-induced gas filtration, namely, a solution of the complete system of the conservation equations, and a solution of a simplified version of the conservation equations, which was originally proposed by Morrison [Ind. Eng. Chem. Fundam. 11, 191 (1972); Trans. ASME J. Fluids Eng. 8, 567 (1976); Trans. ASME J. Fluids Eng. 12, 779 (1977)] are examined and analyzed. The capability of these approaches in accurately simulating the dynamic parameters of the gas filtration process through granular columns is investigated. A simple and practical reconstruction method of the gas pressure history inside long granular columns is proposed and verified experimentally by shock tube data with rather long (2.5m) granular columns, which was obtained in the course of the present study. Several important features based on Morrison’s simplified approaches are demonstrated. Applying a dimensional analysis to the complete system of the governing equations resulted in a dimensionless presentati...

Drainage and attenuation capacity of particulate aqueous foams

It is well established, nowadays, that if the particles added to aqueous foams are hydrophilic, have proper size and shape they concentrate within the Plateau borders and decrease the liquid drainage. The fact that solid additives can increase the protective performances of a particulate aqueous foam is also well known and even patented. This study bridges the gap between these two different features, which have been investigated to date independently. The experimental finding that small particles (about 45μm coal fly ash) slow down temporal and spatial variations of the liquid fraction clarified in the drainage tests was further related to the dynamics of the shock wave propagation in a shock tube. To the best of our knowledge, the results that are reported for the first time can help in better understanding the fundamentals of shock wave/particulate foam interaction.

Experimental investigation of the stress wave propagation along a single straight chain of photo-elastic discs

The propagation of stress waves through a chain of discs has been studied experimentally using a high-speed photoelastic diagnostic technique and strain gauge measurements. An optically transparent single straight chain of 20-mm diameter discs, made of epoxy, was impacted in a vertical shock tube by an air shock wave. The fringe patterns of the stress field were recorded using a Q-switched YAG laser, a transmission polariscope and a CCD cameras. The incident shock wave reflected head-on from a puncher plate that was placed on top of the discs chain inducing behind it a fairly uniform step-wise pressure pulse. The duration of this pressure pulse acting over the puncher surface lasted for about 6 ms. Experiments indicated that inside the discs-chain the step-wise pressure pulse was broken into several oscillating cycles composed of transmitted and reflected stress waves that were followed by transmitted and reflected rarefaction waves. The back and forth bouncing of these waves continued until the overall stress within the discs-chain reached equilibrium with the compression force acting on the puncher plate. The stress wave propagation velocity along the discs chain was significantly lower than the appropriate speed of sound of the material from which the discs were made.

Characteristics of Shock Wave Propagating over Particulate Foam

For many applications where solid and heavy protections against blast are inoperative, the mitigation of the blast wave loading in a cost-effective manner could be achieved using aqueous foam. The protective behavior of aqueous foam is mainly ascribed to high compressibility of the gas bubbles, which is generally accomplished with energy losses due to side wall friction, viscous losses, evaporation, foam shattering and acceleration of the resulted droplets [1, 2, 3]. As transient processes, these factors introduce uncertainty into the predicted behavior of the foam based protection [4]. Recently it has been established that solid additives slow down the foam decay due to the increase in the liquid viscosity [5, 6] as well as enhance the mitigation performance of the foam barriers [7]. A diversity of physical mechanisms responsible for the final effect complicates the issue, and to obtain reliable data, one has to use specially designed tests.

Dynamics of the Load Transfer in a Single Straight Chain of Disks: FEM Simulations

The wave propagation phenomenon in a single straight chain of disks made of PSM9 was simulated numerically using the finite element code ABAQUS. The results yield information on the stress wave propagation along the chain. Qualitative agreement with experimental data that was obtained using an optical method of dynamic photo‐elasticity and strain gages was obtained. The results of the comparison clearly demonstrate that the stress propagation phenomena are largely governed by the quality of the contacts between the disks. Based on the obtained results justifications for further research efforts on this subject are presented.