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Characteristics of Shock Wave Propagating over Particulate Foam
Abstract
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.
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Blast waves mitigate in foam due to various mechanisms, whose contribution to the final result is not fully understood yet. Actually, blast waves can destroy the foam barrier that is usually prone to decay and thus subsides with time. Fortunately, different time scales allow separating between these processes. The foam shattering, for example, could be completed within several milliseconds, while the foam decay lasts minutes and even hours. Recently, an increasing interest in this area has emerged, because particle-laden foams are much more stable and thus, could be applied for blast wave protection. To explore the full advantage of these new foams, the relationship between the micro-properties of the foam structure and the blast wave mitigation has to be clarified. In order to specify this relationship, little has been done. Information available in the literature on this subject clearly shows that during the test, the foam structure could be changed in a wide range, which is not usually controlled. This complicates the analysis of the occurring processes and ensures that the new factor involved in the studied problem has to be tested one by one, after the result of the previous step is well understood. To follow this strategy, this study continues our previous investigation (Britan et al in Colloid Surf A Physicochem Eng Aspects 309:137–150, 2007; Colloid Surf A Physicochem Eng Aspects 344:15–23, 2009; 2011), while mainly focusing on a single new factor, namely blast-shaped profile. To separate out the effect of the foam decay, which was discussed elsewhere (Britan et al in 2011), a special effort has been spent to ensure that the tested foam is homogeneous over its height. To exclude the bubble shattering, preference was given to weak impact conditions (Mach number of the shock generated inside the shock tube was about M
S
= 1.05). Under these circumstances, the blast wave mitigation inside the tested foam barrier solely depended on the concentration of the solid additives.
Experiments were performed to investigate the potential of water-based foams to reduce the farfield noise levels produced by demolitions activity. Measurements of the noise reductions in flat-weighted sound exposure level (FSEL), C-weighted sound exposure level (CSEL), and peak level were made for a variety of charge masses, foam depths, and foam densities (250:1 and 30:1 expansion ratio foams). Scaling laws were developed to relate the foam depth, foam density, and charge mass to noise reductions. These laws provide consistent results for reductions in the peak level, FSEL and CSEL up to a dimensionless foam depth of 2.5. A two part model for the mechanisms of sound level reductions by foam is suggested.
We present an experimental study of forced drainage through a soap foam, where a constant liquid flux at the top of a dry foam produces a downwards traveling wave with a constant velocity and uniform liquid content. The results are not consistent with existing models and we propose a new model, based upon relaxing the condition of wall rigidity throughout the network and emphasizing the importance of viscous damping in the nodes where Plateau borders meet. This model agrees well with the experimentally measured (power-law) scaling behavior of the drainage velocity, and the width of the propagating liquid front, on the imposed flow rate and bubble size.
The rheological behaviour of five fly ash samples (having different d50) collected from a thermal power plant has been investigated over a range of volumetric solids concentration (ϕ=0.32–0.4945) in shear rate range of 10–200s−1. The slurry was highly pseudo-plastic whose behavior can be described by a non-Newtonian power law model in the range of solids concentration studied. The maximum solids fraction (ϕm) at which the slurry viscosity approaches infinity, was determined for the fly ash samples using the relationship between inverse of relative viscosity (i.e.1μr) and volume fraction of solids ϕ. A model incorporating maximum solids fraction (ϕm), power law index (n), median particle size (d50), co-efficient of uniformity (CU), shear rate (γ̇) has been developed to predict the viscosity. The model predictions and the experimental data matched quite well for all five samples and it is expected to be quite helpful in evaluating the hydraulic parameters for design of commercial high concentration fly ash slurry pipelines. The most important variables such as volume fraction of solids, particle size, and size distribution, and their effect on the hydrodynamic forces in a non-Newtonian laminar flow regime are discussed.
A study was undertaken to determine how the moisture content of an aqueous foam affects its ability to attenuate an acoustic signal. The energy losses from an acoustic signal, for the series of foams considered in this study, are believed to arise principally from two causes: an increase in the density of the medium through which the signal passes (resulting in a decrease in the velocity of sound) and a viscous loss mechanism. The experimental results presented indicate that both these processes are dependent on the density or liquid content of the foam. In addition to this, the viscous loss mechanism displays a bubble size and liquid viscosity dependence. The incorporation of talc particles into the aqueous foams was found to greatly enhance the stability of the foam and its attenuation characteristics. This is believed to arise from an increase in the viscosity of the liquid phase of the foam and the enhanced signal/air and particle/liquid interactions, both of which result from the presence of the fine particles in the foam.
In the analysis of two-phase flows in which a gas carries along a large number of small particles, the volume of the particles is customarily assumed to be negligible. This assumption often is well justified, but if either the mass fraction of the particles or the gas density is sufficiently high, the particle volume fraction may become significant. It is thus important to establish the conditions at which this parameter should be included in a flow analysis. The particles may be considered as incompressible by comparison with the gas, so that a finite particle volume fraction appears as an additional variable in the basic equations. Consequences of a finite particle volume are examined for isentropic changes of the mixture, for frozen and equilibrium speed of sound, and for both the frozen flow immediately behind a shock wave and the equilibrium flow that is established further downstream. The errors that would result from neglecting the particle volume range from insignificant to large. For example, even for gas-particle density ratios as low as 10⁻³, the equilibrium flow velocity behind a shock front is quite sensitive to changes of the volume of the particles if they represent more than one-half of the mass of the mixture. © 1965 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
Mobile and easy to use barriers of aqueous foam suppress blast waves as well as the fireball that follows explosion by dissipation mechanisms and/or energy transfer into less destructive forms. Early investigations established that damping the capacity of these barriers depends on a number of factors that include the foam density and the characteristics of the blast wave. Since aqueous foams are usually subject to drain, time variation in the water content is important. To better understand the role of the foam drainage in the shock wave/foam interaction steady state experiments and numerical simulations of the drainage phenomena were combined with the results of shock tube tests. This clarified the temporal and spatial variations of the water content caused by the foam drainage that is further related to the dynamics of the shock wave propagation along an aqueous foam column.
The effects of coal fly ash dispersed in foams on the coarsening and drainage dynamics are investigated in a free drainage experiment. The growth rate of the bubbles is not significantly changed. The rates of the fluid drainage are significantly slower when powder is present, which cannot be attributed to an increase in the fluid’s viscosity associated with the dispersal of powder. Instead, the drainage process can be effectively modeled by adjusting the permeability parameters that relate the liquid fraction and drainage velocity for two-phase foams; however, the values of the adjusted parameters are considerably larger than those observed and expected for non-particulate foams indicating that new physical mechanisms are at play.
Explosions and blast control
- B E Gelfand
- M V Silnikov
Effect of thermal relaxation of attenuation of shock waves in two-phase medium
- V A Vakhnenko
- V M Kudiniv
- B I Palamarchuk
- V.A. Vakhnenko