G. Ben-Dor

Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions

(Received 6 October 2008 and in revised form 26 December 2008) An experimental and numerical systematic study of the growth of the Richtmyer– Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15–1.45. The evolution of the mixing zone following the re-shock is found to be independent of its amplitude at the time of the re-shock and to depend directly on the strength of the re-shock. A linear growth of the mixing zone with time following the passage of the re-shock and before the arrival of the reflected rarefaction wave is found. Moreover, when the mixing zone width is plotted as a function of the distance travelled, the growth slope is found to be independent of the re-shock strength. A comparison of the experimental results with direct numerical simulation calculations reveals that the linear growth rate of the mixing zone is the result of a bubble competition process.

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.

The transition from regular to Mach reflexion and from Mach to regular reflexion in truly non-stationary flows

An experimental investigation on the IHSM 4 × 8 cm Shock Tube has confirmed the hypothesis of Ben-Dor (1978) and Ben-Dor & Glass (1979) that in truly non-stationary flows the transitions from regular to Mach reflexion (RR → MR) and from Mach to regular reflexion (MR → RR) are different. Consequently it is shown that a hysteresis loop exists in the

Shock wave interaction with cellular materials: Part II: open cell foams; experimental and numerical results

{\rm RR}\rightleftarrows {\rm MR}

Analytical and experimental investigations of the reflection of asymmetric shock waves in steady flows

transition phenomenon.

Hysteresis processes in the regular reflection↔Mach reflection transition in steady flows

In the Part I of this study, namely the analytical part in Mazor et al. (1992), the governing equations of the phenomenon in which a planar shock wave collides head-on with a cellular material and interacts with it were developed using a Lagrangian approach. In addition, the numerical approach adopted by us during the numerical course of this study was briefly outlined there. The present part reports on experimental and numerical results of the head-on reflection of a planar shock wave with an open cell polyurethane foam. Foams as mentioned by Gibson and Ashby (1988) and summerized in Part I of this study by Mazor et al. (1992), are one of the two general types of cellular materials.

The reflection of a plane shock wave over a double wedge

The reflection of asymmetric shock waves in steady flows is studied both theoretically and experimentally. While the analytical model was two-dimensional, three-dimensional edge effects influenced the experiments. In addition to regular and Mach reflection wave configurations, an inverse-Mach reflection wave configuration, which has been observed so far only in unsteady flows (e.g. shock wave reflection over concave surfaces or over double wedges) has been recorded. A hysteresis phenomenon similar to the one that exists in the reflection of symmetric shock waves has been found to also exist in the reflection of asymmetric shock waves. The domains and transition boundaries of the various types of overall reflection wave configurations are analytically predicted

The reflection of asymmetric shock waves in steady flows: a numerical investigation

Abstract Ernst Mach recorded experimentally, in the late 1870s, two different shock-wave reflection configurations and laid the foundations for one of the most exciting and active research field in an area that is generally known as Shock Wave Reflection Phenomena . The first wave reflection, a two-shock wave configuration, is known nowadays as regular reflection , RR, and the second wave reflection, a three-shock wave configuration, was named after Ernst Mach and is called nowadays Mach reflection , MR. A monograph entitled Shock Wave Reflection Phenomena , which was published by Ben-Dor in 1990, summarized the state-of-the-art of the reflection phenomena of shock waves in steady, pseudo-steady and unsteady flows. Intensive analytical, experimental and numerical investigations in the last decade, which were led mainly by Ben-Dors research group and his collaboration with Chpouns, Zeitouns and Ivanovs research groups, shattered the state-of-the-knowledge, as it was presented in Ben-Dor (Shock Wave Reflection Phenomena, Springer, New York, 1991), for the case of steady flows. Skewss and Hornungs research groups joined in later and also contributed to the establishment of the new state-of-the-knowledge of the reflection of shock waves in steady flows. The new state-of-the-knowledge will be presented in this review. Specifically, the hysteresis phenomenon in the RR↔MR transition process, which until the early 1990s was believed not to exist, will be presented and described in detail, in a variety of experimental set-ups and geometries. Analytical, experimental and numerical investigations of the various hysteresis processes will be presented.

Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results

An analysis is presented of the shock-wave configurations which will occur when a plane shock is incident on a double wedge for which the second wedge may have a greater (concave case) or a smaller (convex case) inclination than the first wedge. It is shown that seven different reflection processes may be expected depending on the Mach number of the incidnet shock Mi and the two wedge angles θ1w and θ2w. These processes may be defined by seven regiouns in the (θ1w,θ2w)-plane, for a given value of Mi. Each of the seven processes has been verified by sequences of shadowgraph and schlieren photographs.A shock-polar analysis of each of the seven processes has provided infomation about the pressure changes and the wave structures which develop immediately behind the main reflections along the wedge surfaces. These wave structures have been verified experimentally, and two types have been observed; one normal to the reflecting surface, and the other in the form of a regular reflection. The criteria to determine which of thses configurations will occur have not yet been established.It is believed that the present study will be of value in predicting the loading of shock waves on structures, and may lead to a better understanding of shock reflections form concave and convex cylindrical surfaces.

Numerical confirmation of the hysteresis phenomenon in the regular to the Mach reflection transition in steady flows

The theoretical study and experimental investigation of the reflection of asymmetric shock waves in steady flows reported by Li et al. (1999) are complemented by a numerical simulation. All the findings reported in both the theoretical study and the experimental investigation were also evident in the numerical simulation. In addition to weak regular reflection and Mach reflection wave configurations, strong regular reflection and inverse-Mach reflection wave configurations were recorded numerically. The hysteresis phenomenon, which was hypothesized in the course of the theoretical study and then verified in the experimental investigation, was also observed in the numerical simulation.