The propagation of a normal shock wave along a coupled convex–concave surface of equal radii has been analysed experimentally and numerically in this study. The experimental and numerical studies were conducted using a similar geometry as of that used by Ram et al. (J. Fluid Mech., vol. 768, 2015, pp. 219–239) for studying the shock wave transition from regular reflection to Mach reflection. Many interesting flow features such as shock wave transitions over the ramp, characteristics of the induced flow behind the shock wave and the development of a stationary separation shock wave have been observed in the study. The numerical results are validated with experimental data. While the shock wave transitions over the ramp are found to depend mainly on the ramp geometry, the characteristics of the stationary shock wave and the flow separation in the concave region of the ramp surface have been found to vary with the shock wave Mach numbers.

Shock-wave reflection over concave surfaces poses a difficulty in its analysis due to the unsteady nature of the reflection process and the occurrence of various types of Mach reflections caused by it. In a pseudo-steady flow, the reflection's configuration is self-similar since the shock wave reflects over a surface with constant inclination. The unsteady Mach reflection introduces an additional complexity as it is affected by the changing inclination of the surface, forcing the reflection to continuously adjust itself to the varying boundary condition. In this study, validated simulations of Mach reflection (MR) over cylindrical concave surfaces with different radii were performed for three inviscid perfect gases with moderate incident shock Mach numbers (M-s) ranging from 1.3 to 1.5. The reflection was investigated up to the point of transition from MR to transitioned regular reflection. A similar behaviour of the configuration and evolution of the Mach stem was observed, one that is independent of the surface radius and type of gas. With regards to different gases, the speed of sound a(0) is a dominant factor since it dictates the propagation of wall disturbances. A universal condition of the rate of surface change was found, accounting for different radii, different gases and M-s variation. Analysis based on shock dynamics is employed to explain how disturbances caused by surface variations play a significant role in the behaviour of the reflection. This method successfully supports the similarity that was demonstrated and facilitates a more informed perception of the MR process.

In spite of the worldwide recognition of the importance of testing blast effects on dummy humans, there is a lack of blast simulators that are capable of generating realistic blast conditions in the laboratory. The objective of the present study was to design, construct and test a blast tube that is able to accurately reproduce loading histories of actual explosions in the laboratory. The design combines some advantages of existing blast-wave generating facilities. Using numerical simulations, a 5-m long blast tube was designed. The blast tube is large enough to enclose dummies including torso and head, wearing vests and/or helmets. The system generated blast waves equivalent to those of a spherical explosion of about 3.5 kg TNT with an over pressure of 0.64 bar and a positive phase of 4 ms. The repeatability of the experiments was very good. The blast tube’s open end is square of 1.57 m × 1.57 m and although designed for experiments on human dummies, it could be used for testing even full-scale structural components. High quality high-speed photography was demonstrated through the designed windows. Our preliminary study on the effect of a helmet on a dummy’s head revealed that the tested helmet amplified by a factor of 2 and more the peak pressure in the back side of the head. The newly designed blast tube is capable of simulating close range blast waves, manifested with short positive durations. Experiments with and without helmets revealed the importance of blast testing for improving helmet design.

A detailed Loss of Coolant Accident (LOCA) analysis in an AP1000 NPP was performed, followed by a definition of the vulnerability analysis principles, and analysis of blast loads and fragments impact created by a nearby explosion. The AP1000 NPP performs excellently to small-break LOCA due to in-structure shock, with the 10 CFR 50.46 Acceptance Criteria fully accomplished. Impulsive dynamic loads resulting from blast waves and fragments impact of GBU-28 (Guided Bomb Unit) were considered for a nearby explosion. We model the structure and the main reactor components using the MSC/Dytran code to obtain accurate internal acceleration levels at critical points. We account for the appropriate blast wave interaction with the soil and the soil interaction with the containment structure, rather than using empirical formulas. The model includes the shielding structure with its concrete base, the support structures for the reactor, the steam generators, and the pressurizer. The combined effect of bomb fragmentation and blast loading was also considered using a cylindrical fragmentation model and the blast model of Kingery-Bulmash, assuming a hemispherical charge. A comprehensive risk assessment methodology composed of four phases was developed. The methodology is comprised of: (I) System analysis, (II) Hazard analysis, (III) Damage assessment, and (IV) Risk analysis of the in-structure shock consequences. Using seismic fragility curves for analysis of the expected failure modes according to explosion events faced difficulties since no published data was found. Adjustments to these fragility curves were made using median acceleration limits on components designed to withstand airplane crash, together with standard deviations taken from the given earthquake fragility tables. The findings reveal that the probabilities of failure of the reactor coolant system components resulting from a GBU-28 nearby hit, namely the pressurizer, the cooling pumps, and valves are quite high (greater than 1.10(-4)).

Within its 2050 energy plan, Israel examines the demographic implications of a Nuclear Power Plant (NPP) in Shivta Rogem site in the Negev.NPP would have a great contribution to the diversity and robustness of energy sources in Israel.A Small Modular Reactor (SMR) is designated to be safer than existing NPPs and will have better resistance to external hazards due to inherent passive safety features.This study develops a risk assessment methodology for a Nuclear Power Plant (NPP), in particular, SMR, to withstand a large conventional warhead explosion (GBU-28).The methodology comprises: hydro-dynamic simulations, validation of the dynamic simulations using numerical analysis compared to the simulations, risk analysis and damage assessment given the reference scenario of a detonation of a GBU-28 inside the underground water pool of a NuScale SMR.Discrete fragility curves were developed to evaluate the capacity of the SMR critical components.The overall probability of failure was assessed based on a Fault-Tree-Analysis (FTA).Results of the 3 m explosion from the reactor bay wall showed a displacement of 13 cm, breaching of the SMR bay wall and the water pool wall, and 12 cm deflection of the Containment Vessel (CNV).Sensitivity analyses of the uncertainty values were carried out by posting HCLPF (High Confidence Low Probability of Failure) values to the fragility curves.Combination of the results of the study with the failure criteria of NuScale for seismic hazards reveals that given the hazard scenario, core damage is expected accompanied by release of radioactive materials to the atmosphere.The study concludes that building the SMR in Israel will require adapted protective solutions.Future research may examine protective alternatives such as adding a reinforced concrete protecting layer or the possibility to set the SMR at a deeper underground elevation.

A simplified analysis can be employed to predict the pressure buildup behind a porous barrier fairly accurately without resorting to numerical modeling. A macroscopic approach is used in which the pressure buildup behind the porous barrier is analyzed in relation to the load inflicted on its front face thus allowing finding the effects of the different parameters of the porous barrier. This method was successfully employed to study the impingement of shock waves and blast waves on stiff silicon carbide foams and more recently on buildings that had enough internal divisions as to be considered as a low porosity medium. In this study, the methodology is employed to study a porous barrier comprised from an array of perforated plates with various porosities to determine the parameters affecting the pressure buildup behind it. Perforated plates were chosen since the geometry of the barriers assembled from the plates is simple enough so it can be exactly defined, and still the shock structure and the developing fields are so complicated that only few studies attempted to deal with similar scenarios in the past. In fact, previous studies were limited to one or two perforated plates. In the experiments presented, 3 mm plates were placed 8 mm apart inside a 32 mm by 32 mm shock tube. The last plate was mounted 10 mm from the end wall. The plates were drilled to accommodate various blockage ratios (defined as blocked to open area ratio) ranging from 50% to 80%. It was found that the volume of air confined inside the porous medium undergoes an adiabatic process, and thus the pressure buildup time at the end wall depends on the volume to the power of the heat capacities ratio.

Experiments and inviscid numerical computations were performed in air at an incident shock wave Mach number of 1.3. The incident shock waves were reflected over cylindrical convex surfaces. The models differed in the radii and initial angles. Great agreement was obtained between the high-resolution computations and the high-resolution experiments. Examination of the flow Mach number distributions revealed a fundamental difference between pseudo-steady and unsteady reflections. As the radius of the surface increases, the orientation of the reflected shock wave, with respect to the incident shock wave, approaches its orientation in a pseudo-steady reflection. This means that the radius of curvature does play a rule in the RR reflection. Therefore, it is reasonable to assume that the RR→MR transition is also affected by the radius of curvature. This observation is in contrast with the claim that variation between the RR→MR unsteady and pseudo-steady transitions is a result of optical limitations as was previously suggested by several studies. The problematic estimation of the RR→MR transition is also discussed. This study is a section of an extensive ongoing research dealing with the unsteady mechanism that leads to transition.

The reflection pattern over a convex cylindrical surface followed by a concave cylindrical surface is studied using a high spatial resolution and high temporal resolution experimental setup. This fully automated setup enabled the repetition of experiments many times while retaining extremely high repeatability. For the investigated moderate shock strengths (1.2–1.4), the repeatability was less than 0.01 in the incident shock wave Mach number. Each experiment produced a single schlieren image with a pixel size of 0.03 mm. Thus, it was possible to distinguish minuscule flow features of size 0.06 mm. All the images were later combined into a detailed description of a single reflection process. The process was analyzed using an automatic image processing procedure that located the triple point in each image. The tested model enabled studying both the evolution of the RR → MR transition over the convex segment and the evolution of a complicated shock pattern reflection over the concave part. It was found that the RR → MR nonstationary transition is closer to the pseudo-steady criterion in comparison to previous experimental studies. Yet, based on error estimation analysis and in contrast to Kleine et al. (J Fluid Mech 740:47–60, 2014) the pseudo-steady criterion will remain 3o–8o higher than the dynamic transitions investigated. Over the concave segment, we observed the evolution of a newly three-shock configuration established on the Mach stem of the original reflection (MRMR). This double Mach configuration explains the enhancement in the pressure when using blunt entry reflectors. The transition of the newly formed MR to regular reflection (MRRR) was also investigated. The reflection process over the concave segment depends on the first reflection process. Since the later dictates a specific relative angle between the incident shock wave and the original Mach stem. This angle can be later used to adjust the MRMR → MRRR transition angles. Even though this three-shock configuration originated from the Mach stem, it was found that the adjusted transition angles were close to the MR → RR transition angles reported in the literature.

This chapter summarized results of experiments performed for many years and eventually we reached a conclusion. A stationary Mach reflection is a typical reflection pattern that exists in steady supersonic flows, whereas a similar reflection pattern appears over a double wedge and is temporally maintained. The consisted presence of the stationary MR in shock tube flows contradicts the self-similarity of the shock tube flows. The chapter discusses experimentally whether or not the stationary Mach reflection can exist over a double wedge in shock tube flows.

This survey includes, mainly, investigations that Were published during recent years and a few earlier studies that were not included in the review by the same authors published in 2012. The survey covers analytical, numerical and experimental studies in which the effect of layering, spacing and change of the order of the plates on the protective performance of metallic shields against high-speed impact is investigated, and also studies that suggested analytical methods for optimization of multilayered shields. (C) 2016 Elsevier Ltd. All rights reserved.

The effort invested in improving our understanding of the physics of high energy explosion events has tremendously increased in the past few decades. Moreover, the dramatic increase in computer capabilities over the last two decades made the numerical simulation approach the dominant tool for investigating blast wave related phenomena and their effects. However, both large- and small-scale field tests are still in use. In the following, we present an experimental tool capable of better resolving and studying the blast–structure interaction phenomenon. In addition, this experimental tool can assist in validating numerical simulations of these phenomena prior to applying them to simulate large-scale events. The experimental tool uses an exploding wire technique to generate small-scale cylindrical and spherical blast waves. This approach permits safe operation, high repeatability, and usage of advanced diagnostic systems that cannot be used in large-scale field experiments. The system was calibrated using an analytical model, an empirical model, and a numerical simulation. To ensure that spherical blast geometry was achieved, a set of free air blast experiments in which high-speed photography was used to monitor the blast wave structure was conducted. Furthermore, by using similitude analysis the results obtained from small-scale experiments can be applied to full-scale problems. It has been clearly shown that an exploding wire system offers an inexpensive, repeatable, safe, easy to operate, and effective experimental tool for studying phenomena involving blast–structure interactions.

The response of metallic foams to a high strain or high stress rate loading has received increased attention in recent years due to their potential to absorb large amounts of energy during plastic deformation and crushing (see, e.g., Thornton and Magee [1]). Research of the mitigation of blast effects indicates that the high-energy absorption characteristic of metallic foams makes them very useful as protective layers of critical structural elements. Consequently, understanding the material dynamic properties of metallic foams will enable engineers to better utilize their energy absorption characteristics. Aluminum foam (Al-foam) is a lightweight material with excellent plastic energy absorbing characteristics [2]. The implementation of bare Al-foam as a protective layer is not practical. The material needs to be a part of a multilayer structure (see, e.g., Seitzberger et al. [3]. The foam layer can be exploited as a protective layer in military vehicles where both lightweight and good energy absorption are needed. The ability of aluminum foams to reduce the explosion-generated blast-induced damage from concrete slabs has been demonstrated in the course of high-explosive (HE) field experiments (see, e.g., Hanssen et al. [4, 5] and Sadot et al. [6]). Several studies have been conducted in order to investigate the constitutive model parameters of Al-foams during the past three decades. The effect of the strain rate was one of the important issues needed to be resolved [7]. A constitutive numerical model was validated in the work of Hanssen et al. [4, 5]. The validation procedure was based on three levels: (a) material calibration; (b) non-uniformed compression test at the material level; and (c) numerical validation at the structural interaction level. Several material models from the LS-DYNA library were calibrated. However, discrepancies between the models were found even for relatively simple load configurations. The most important conclusion noted by the authors was the need for further development of more robust fracture models for the Al-foam. This conclusion is crucial especially since there are increasing numbers of Al-foam manufacturers. Various experimental facilities were used to dynamically load the Al-foam at large ranges of strain and stress rates. In the work of Dannemann and Lankford Jr. [8], closed-cell Al-foams were assessed under static and dynamic loads in the strain rate range of 400–2500 s−1. This range was achieved by using split Hopkinson bar apparatuses. It was found that the strain rate effect is significant in high density Al-foams. Deshpande and Fleck [9] suggested that the initial elastic modulus was lower than that of fully dense alloys. Deformation in the cell walls led to stress concentration around the deformation zones, which resulted in a decrease of the modulus. Some inconclusive results regarding the dependence of the stress–strain curve on the strain rate were presented. Deshpande and Fleck [9] and Paul and Ramamurty [10] did not notice any strain rate dependency, in contrast to the findings of Dannemann and Lankford [8] and Paul and Ramamurty [10]. In a later work by Wang et al. [11], experiments were done using an Instron compression machine at strain rates ranging from 10−3 s−1 up to 450 s−1. Strain–stress curves constructed and distinct strain rate dependency was noted. In the work of Bastawros et al. [12] efforts were made to understand the morphology of the Al-foam during its collapse. Explanation was given to the cell deformation. However, some observations have been ignored and not fully explained even though some key elements of the deformation were identified. The dynamic behavior of Hydro/Cymat Al-foam material was investigated by Tan et al. [13] under different load conditions. The plastic collapse, the plateau range, and the strain at which the deformation occurred were found. It was demonstrated that the dynamic response depends on the direction of the load with respect to the plate manufacturing orientation. Some load enhancement was observed and was explained by micro-inertial effects. Postimpact observation of partly crushed specimens revealed that the deformation is through crush bends. Feng et al. [14] conducted experiments to investigate the rate dependence of Al-foams having different relative densities. They found that the effect of strain rate increases while increasing the Al-foam density as was found by others. For Al-foams with a relative density of 15 % there was little effect of the strain rate while for heaver foams significant strain rate effect was noted.

Numerical simulations were conducted to understand the different wave configurations associated with the shock-wave reflections over double-concave cylindrical surfaces. The reflectors were generated computationally by changing different geometrical parameters, such as the radii of curvature and the initial wedge angles. The incident-shock-wave Mach number was varied such as to cover subsonic, transonic and supersonic regimes of the flows induced by the incident shock. The study revealed a number of interesting wave features starting from the early stage of the shock interaction and transition to transitioned regular reflection (TRR) over the first concave surface, followed by complex shock reflections over the second one. Two new shock bifurcations have been found over the second wedge reflector, depending on the velocity of the additional wave that appears during the TRR over the first wedge reflector. Unlike the first reflector, the transition from a single-triple-point wave configuration (STP) to a double-triple-point wave configuration (DTP) and back occurred several times on the second reflector, indicating that the flow was capable of retaining the memory of the past events over the entire process.

Small-scale modeling of explosive events has become an important tool in the investigation of blast wave-structure interactions. In this approach, a full-scale model is miniaturized and subjected to “gram-scale” explosions from detonated micro-charges. While offering a cheaper, faster, and ultimately more manageable alternative to full-scale field tests, small-scale testing also offers better reliability and accuracy in more complex scenarios where numerical simulations become limited. Nevertheless, small-scale experiments introduce other difficulties due to the reliance on the well-known Cranz-Hopkinson “cube-root” scaling law. This scaling relationship is suitable for self-similar open-field experiments but does not necessarily apply to urban scenarios. Additionally, chemical explosive charges of such small quantities might be susceptible to changes in parameters such as the explosive compound compression strength, the humidity of the explosive and of the surrounding atmosphere, the method of ignition, etc. Logistically, the handling and preparing of the experimental setup with these small chemical explosives requires specially trained personnel and permits. To overcome these challenges, the exploding wire (EW) technique offers an elegant substitute to using small chemical charges in scaled-down modeling.

A wide analysis and risks assessment has been carried out to understand the variety of the influences of a standard nuclear explosion or an Improvised Nuclear Explosion Device (INED) on a representative model of a structure of an emergency department in an urban acute care medical center. Emergency departments are most important after the occurrence of a nuclear event and their continuous performance is significant in reducing the consequences of the nuclear explosion. The research compares the influences and the resultant damage of un-protected and protected of a typical emergency department consisted from Reinforced Concrete (RC) framed structure in various methods. The scenarios carried out analyzed ground nuclear explosions of 1 kiloton in various distances. Each of which is matching a different probability of occurrence. All of the above-mentioned scenarios are aimed towards the medical center as well as other targets in the area. The calculated and summarized consequences based on a deep literature survey are the blast and its characteristics (reflected pressure, reflected impulse, positive duration, etc.) on the front wall and on the other facades of the emergency department, thermal radiation, fire ball and potential fires and the immediate & residual radioactive radiation (ground shock and cratering are neglected). The consequences will be expressed as functions of the distance, real and scaled. The structural and nonstructural damages and the vulnerability due to the blast will be estimated according to the literature. The physical findings will be expressed in terms of casualty rate and damage to the medical center systems as well as the consequences of lack of performance of the medical center. The collected data will lead to a risk assessment that will point out to the profitability of retrofit as against an as-is unprotected emergency department and its recommended scope. The outcome of the research will be a Decision Support tool that may be applicable for other infrastructures exposed to a nuclear explosion.

The pressure buildup behind an array of perforated plates following a shock wave impingement was experimentally studied. The experiments were performed in a shock tube facility and the arrays were varied in the number of their perforated plates and the porosities of the plates. It was found that the pressure buildup behind all of the configurations that were examined displayed similar characteristics. Using simplified assumptions about the nature of the flow through the perforated plates array, we could account for the influence of the volume confined between the plates, and the porosity of the plates. Once accounted for, experiments were performed with argon and SF6, in addition to air, in order to examine the effect of the gas. It was found that the pressure buildup depended on a constant parameter, which was gas-dependent. The constant parameter for each gas was found in this study experimentally. To the best of our knowledge this result has never been reported before. The large spread of different experiments performed throughout the present study enabled the separation of the effects facilitated by the perforated plates array into two distinct processes that affected the pressure buildup at the end-wall. The first was the diffraction of the incident shock wave and subsequent shock reverberations that were found to depend on the number of perforated plates in the array and their porosity. The second was the inhibition of the flow through the perforated plate that was found to depend on the confined volume, type of gas and the porosity of the plates.

On the basis of generalization of the Florence model to several ceramic layers, it is proved that arranging the ceramic plates in order of increasing material density implies the maximum the ballistic limit velocity of the armor in comparison with other arrangements.

Light aluminum closed-cell foams (4% relative density to solid aluminum) were experimentally studied in order to determine the added dynamic compressive strength facilitated by the trapped gas. A compression machine, an impact pendulum, and a shock tube were used to compress foam samples in strain rates varying from 10−3s−1 to 700s−1. Very similar results were recorded from the compression machine and the impact pendulum experiments. The shock tube results exhibited a significantly higher compressive strength. An experiment was designed to isolate the compressive strength contribution from the gas trapped inside the foams. It was shown that, in light aluminum foams, gas compression contributes the additional dynamic stress. It was also shown that, in the samples used in this study, gas compression caused as much as 50% of the dynamic compressive strength. An isentropic model was used to analytically explain the gas contribution to the dynamic compression stress recorded in the experiments.