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The interaction between a planar shock wave propagating in air and a polygonal bubble (composed of two triangles) containing two different gases is studied numerically. Studying the interaction between an oncoming shock wave with front- and rear-facing triangles containing light and heavy gases is of great importance in understanding the complex shock wave propagation, interaction and hydrodynamic instabilities as well as their effect on mitigating or enhancing the colliding shock/blast wave. Two different cases were studied: in the first case, the front triangle contained sulfur hexafluoride (SF6) and the rear one contained helium (He); while in the second case, He is in the front and SF6 in the rear triangle. As the speed of sound in He is significantly higher than that in SF6 and in air, different flow fields were evolved. When SF6 is placed in the front triangle, the shock wave transmitted through the SF6 is reflected back from the interface separating the two gases and starts propagating downstream; over the He segment of the bubble, the incident shock wave (in the open air) is already seen over the He section and it submits compression waves into the He gas. These compression waves travel upstream and downstream; in their upstream movement they generate compression waves into the ambient air ahead of the incident shock wave. The part moving downstream will hit the interface separating SF6 and He, resulting in a complex wave pattern. A completely different wave pattern is visible when He is placed in the front triangle. Now the fastest shock is the transmitted shock wave in the He section; it reaches the membrane separating the two gases well before the incident shock wave reaches this location. Unlike the previous case, now the resulting flow in the rear triangle of the bubble is affected not only by the incident shock wave but also by the transmitted compression waves from the helium section. Furthermore, when helium is placed in the front section of the bubble, the compression waves in the He impacts the rear triangle of the bubble (containing SF6) almost like a planar shock wave. This is different from the previous case where SF6 was in the front section; then the shock wave impacting on the rear bubble containing He had a completely different shape due to its propagation into the SF6 bubble. This resulted in completely different peak pressures.

Multi-element ducts are used to improve the aerodynamic performance of ducted wind turbines (DWTs). Steady-state, two-dimensional computational fluid dynamics (CFD) simulations are performed for a multi-element duct geometry, consisting of a duct and a flap; goal is to evaluate the effects on the aerodynamic performance of the radial gap length and the deflection angle of the flap. Solutions from inviscid and viscous flow calculations are compared. It is found that increasing the radial gap length results in an augmentation of the total thrust generated by the DWT, whereas a larger deflection angle has an opposite effect. A reasonable to good agreement is seen between the inviscid and viscous flow calculations, except for multi-element duct configurations characterized by large flap deflection angles. The viscous effects become stronger at large flap deflection angles, and the inviscid calculations are incapable to take into account this phenomenon.

Propagation of shock waves through a set of plate barriers is studied numerically. It is found that the studied barrier sets are very effective in attenuating transmitted shock waves. All transmitted shock waves through the proposed barrier sets are reduced to mild compression waves upon exiting the sequence of inclined or vertically placed barrier plates.

The present work shows that weak blast waves that are considered as being harmless can turn to become fatal upon their reflections from walls and corners inside a building. In the experimental part, weak blast waves were generated by using an open-end shock tube. A three level building model was placed in vicinity to the open-end of the used shock tube. The evolved wave pattern inside the building rooms was recorded by a sequence of schlieren photographs; also pressure histories were recorded on the rooms' walls. In addition, numerical simulations of the evolved flow field inside the building were conducted. The good agreement obtained between numerical and experimental results shows the potential of the used code for identifying safe and dangerous places inside the building rooms penetrated by the weak blast wave.

Flows in which shock wave interact with a rigid boundary are found in many engineering applications and therefore draw a lot of attention during the past seven decades. The rigid boundary may have different geometry, a building where an explosive air blast took place, a mine tunnel in which an accidental blast propagates, an internal combustion engine where inflow and outflow valves are periodically opened and closed, etc. In order to correctly predict the loads acting on the rigid boundary and to reduce it, if possible one has to understand the complex flow evolved during this interaction. A relatively simple example is the flow resulted from the diffraction of a planar shock over a square cavity installed in a duct; this was studied experimentally and numerically in [1]. Later, a similar geometry was studied numerically in [2]; in that case the square cavity was filled with small dust particles in order to reduce the pressure acting on the square cavity walls. The present chapter is a further step in this topic; it investigates numerically the case when an incident shock wave propagates in a duct, shown in Fig. 1; black square indicates the location where pressure was computed. In the present case, the square cavity was filled with either Helium, Argon, Air, or SF6 while the rest of the duct contained only Air.

Results of experiments investigating shock wave reflections from wedges having sawtooth roughness of 0.1 mm, 0.2 mm, 0.8 mm, and 2.0 mm are presented. Observations based on direct shadowgraph diagnostic revealed that for wedges whose inclination angle was close to the critical transition angle, the foot of the incident shock interacted locally with the sawtooth steps and merged with the part of shock waves reflected from the sawtooth walls. This trend was observed for all the sawtooth wedges.

Consider a shock tube configuration with a sharp transition between a wide driver segment and a much narrower driven segment. The flow commencing upon the rupture of the diaphragm that separates the two segments is studied both numerically and by analytic modeling. This analysis is aimed in particular at understanding the converging flow through the sharp area contraction, noting the vena-contracta formed by the separation bubble that evolves as the flow negotiates the sharp corner at the entrance to the driven segment. For a high driver-to-driven pressure ratio (typically 100) the large-time flow at the entrance to the driven segment is found to be nearly steady. The separation bubble downstream of the corner seems to produce a choked vena-contracta flow with a smooth transition from subsonic to supersonic velocity (at high driver-to-driven pressure ratio). It is this flow that drives the shock wave into the long driven segment. The numerical study was performed on an axisymmetric configuration with an area ratio 36 and initial pressure ratio 100, first by solving the Euler equations (using the GRP method), then by a commercial code (FLUENT) based on the compressible Navier-stokes equations. On the Mach number flow map, a sonic surface (M = 1) is clearly visible at the entry to the driven segment, just ahead of a separation bubble. While CFD solutions do provide a detailed view of the flow field, it is generally difficult to get an understanding of the observed phenomena in terms of well-known concepts of fluid dynamics. Here we seek such insight by resorting to analytic modeling where the large-time flow model is based on simple one-dimensional fluid-dynamical “building blocks”, such as steady quasi-one-dimensional isentropic flow, or simple waves: centered rarefaction wave, shock discontinuity, and contact discontinuity. The resulting flow-field consists of a fixed-length isentropic flow producing a steady sonic or supersonic flow. A self-similar set of flow segments (CRW, constant flow segments, contact discontinuity) is “matched” to the steady flow and produces the (constant intensity) driven shock wave.

Experimental studies conducted during the 70s and 80s of the previous century are numerically simulated. We examine a horizontal duct with a vertical branch having a circular cross section whose diameter is 5 cm. These experiments were conducted by the late Dr Heilig in the Ernst-Mach-Institute (private communication). In both segments of the branched duct pressure transducers were installed. They were used for recording the pressure histories and for deducing the traveling shock wave speed. These results were compared with the present numerical simulation. The numerical simulations were conducted using the commercial code Fluent with the density-based AUSM solver. The solver is second order in both space and time. It is apparent from the results obtained that good agreement exists between the recorded pressure histories and their simulations. Based on the good agreement between recorded and simulated pressures a numerical study was conducted by comparison between two similar branched ducts, one having a circular cross section while the other has a rectangular cross section. Also, the effect that changes in the branched segment orientation have on the resulting flow field were investigated.

For evaluating the motion of a solid body in a gaseous medium, one has to know the drag constant of the body. It is therefore not surprising that this subject was extensively investigated in the past. While accurate knowledge is available for the drag coefficient of a sphere in a steady flow condition, the case where the flow is time dependent is still under investigation. In the present work the drag coefficient of a sphere placed in a shock tube is evaluated numerically. For checking the validity of the used flow model and its numerical solution, the present numerical results are compared with available experimental findings. The good agreement between present simulations and experimental findings allows usage of the present scheme in nonstationary flows.

This comprehensive and carefully edited volume presents a variety of experimental methods used in shock waves research. In 14 self contained chapters this [...] volume [...] presents the experimental methods used in shock tubes, shock tunnels and expansion tubes facilities. Also described istheir set-up and operation. The uses of an arc heated wind tunnel and a gun tunnel are also contained in this volume. Whenever possible, in addition to the technical description some typical scientific results obtained using such facilities are described. Additionally, this authoritative book includes techniques for measuring physical properties of blast waves and laser generated shock waves. Information about active shock wave laboratories at different locations around the world that are not described in the chapters herein is given in the appendix, making this book useful for every researcher involved in shock/blast wave phenomena. [Source : 4 de couv.]

We consider a classical shock tube with Helium-filled driver section, and a driven section filled with a He– Ar gaseous mixture of continuously varying composition. We simulate a shock tube experiment, where the driven section composition starts out with pure Ar and ends with pure He (denoted ‘ − ’), or vice versa (denoted ‘+’). The initial pressures are 2 and 0.01 MPa. Two alternate initial species compositions are assumed: ‘Molar fraction’ – a linear distribution of the molar fraction; ‘Mass Fraction’ – a linear distribution of the mass fraction. Wave patterns arising in every case are presented and discussed.

The interaction between a planar shock wave and square and triangular bubbles containing either SF6, He, Ar, or CO2 is studied numerically. It is shown that, due to the existing large differences in the molecular weight, the specific heat ratio, and the acoustic impedance between these gases, different wave patterns and pressure distribution inside the bubbles are developed during the interaction process. In the case of heavy gases, the velocity of the shock wave propagating along the bubble inner surface is always less than that of the incident shock wave and higher than that of the transmitted shock wave. However, in the case of the light gas (He), the fastest one is the transmitted shock wave and the slowest one is the incident shock wave. The largest pressure jump is witnessed in the SF6 case, while the smallest pressure jump is seen in the helium case. There are also pronounced differences in the deformation of the investigated bubbles; while triangular bubbles filled with either Ar, CO2, or SF6 were deformed to a crescent shape, the helium bubble is deformed to a trapezoidal shape with three pairs of vortices emanating from its surface.

A simple model is proposed for simulating the flow field developed in porous foam as a result of its head-on collision with a planar shock wave. In the model, the foam is simulated by a suspension composed of air and small, rigid spheres. The sphere's drag coefficient is increased beyond its regular level in order to account for the drag acting on the foam resulting from the air being forced to flow through the tortuous passages in the foam. The obtained numerical results are compared with appropriate experimental findings. Based on the obtained good agreement between experiments and simulations, a parametric study on the foam—shock-wave interaction process is conducted. It is shown that although the proposed dusty-gas model is very simple and might not simulate accurately all experimental findings, it certainly represents the main features and mechanism of the considered interaction process.

The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding shock waves.

The drag coefficient of a sphere placed in a non-stationary flow is studied experimentally over a wide range of Reynolds numbers in subsonic and supersonic flows. Experiments were conducted in a shock tube where the investigated balls were suspended, far from all the tube walls, on a very thin wire taken from a spider web. During each experiment, many shadowgraph photos were taken to enable an accurate construction of the sphere's trajectory. Based on the sphere's trajectory, its drag coefficient was evaluated. It was shown that a large difference exists between the sphere drag coefficient in steady and non-steady flows. In the investigated range of Reynolds numbers, the difference exceeds 50%. Based on the obtained results, a correlation for the non-stationary drag coefficient of a sphere is given. This correlation can be used safely in simulating two-phase flows composed of small spherical particles immersed in a gaseous medium.

The propagation of stress waves through a chain of discs has been studied experimentally in Part I (Glam et al. [1]) and is completed here with numerical investigation using the standard package ABAQUS. A fair agreement is found between experimental findings and their simulations. Based on this agreement, parametric study of wave propagation through disc-chains was conducted. Specifically, effects associated with changes in the disc diameter, material density, stiffness/rigidity and the number of discs in the chain on the stressed chain have been studied. It was found that the propagation velocity of the evolved waves increases with improving contacts between the chain’s discs by exposing the chain to a static load before its dynamic loading. The wave- propagation velocity decreases with increase in the discs material density and it increases when its diameter increases. In case of a chain composed of small diameter discs and/or small material density, the transmitted stress wave is first strengthened and only at discs further down the chain it starts decaying. When checking the influence of the dynamic-loading duration it was found that long dynamic-load duration dissolves quickly into short pulses. It was also found that there is a ‘characteristic’ wave for a given chain. This wave propagates with minimal dispersion. Dynamic loads having shorter time duration than the ‘characteristic’ one experiences significant attenuation.

It is well known that the pressure jump across a given shock wave increases when it propagates in a conduit whose cross-section is continually reduced [1], or in a case of spherically imploding shock wave [2]. In both cases the flow cross-section is reduced toward zero. A question arises whether or not this is a necessary condition for pressure amplification. The present paper demonstrates that pressure amplification is possible, for a planar shock in a one-dimensional unsteady flow, when the pre-shocked gas has either of the following characters

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.

In order to shed light on the initial mechanism of dust entrainment behind a moving shock wave, the particles' motion behind a planar shock wave was investigated using horizontally placed shock tubes and a direct photographic technique synchronized with the shock wave motion. The drag coefficient measurement of an accelerating spherical particle (0.3–5.57 mm in diameter) was performed. The obtained drag coefficients were found to be higher than those from the standard drag curve. On average, the difference was about 20% for a relative Reynolds number from 103 and 105. The initial motion of a particle just lifted-up from the wall was also examined using the other shock tube. The results indicated that the velocity and speed of rotation of particles were strongly affected by the floor conditions. It was also found that the particle's initial rotation does not play a major role in the particle rise.

The present paper contains a detailed study of shock wave reflection from a wedge placed in various suspensions. In past works, the incident shock propagated initially in pure gas and the suspension started only at the leading edge of the deflecting wedge. However, in the present case the entire flow field is filled with a gas-dust suspension and the initial shock wave has steady-state structure relative to the shock front. In former studies the transmitted shock wave starts its propagation into the suspension and is reflected from the wedge at the same time. It is therefore obvious that the two unrelated processes of (2D) reflection and (1D) "transitional" relaxation occur simultaneously. In the present case the suspension behind the incident shock wave has reached steady state (i.e., it is a traveling wave) before the shock reaches the wedge leading edge. The reflection process from the deflecting wedge is studied for different dust mass loadings and different dust-particle diameter. It is shown that when the dust loading is low and the dust particle diameter is small the wave reflection pattern is similar to that observed in a similar pure gas case. In addition, an equilibrium state is reached, behind the evolved waves, very quickly. On the other hand, when the dust loading is relatively high and/or the dust particle diameter is relatively large, the observed reflection wave pattern is very different from that seen in a similar pure gas case. In such cases it takes much longer time to reach an equilibrium state behind the reflecting waves. It is also shown that the dust presence significantly affects the (gas) pressure on the wedge surface. The higher the dust loading is, the higher the pressure on the wedge surface. Suspensions composed of solid particle of different size, but having the same dust mass loading, will approach the same equilibrium pressure. However, it will take longer time to reach an equilibrium state for suspensions having large diameter particles. (C) 2004 Elsevier Ltd. All rights reserved.

The flow developed behind shock wave transmitted through a screen or a perforated plat is initially highly unsteady and nonuniform. It contains multiple shock reflections and interactions with vortices shed from the open spaces of the barrier. The present paper studies experimentally and theoretically/numerically the flow and wave pattern resulted from the interaction of an incident shock wave with a few different types of barriers, all having the same porosity but different geometries. It is shown that in all investigated cases the flow downstream of the barrier can be divided into two different zones. Due immediately behind the barrier, where the flow is highly unsteady and nonuniform in the other, placed further downstream from the barrier, the flow approaches a steady and uniform state. It is also shown that most of the attenuation experienced by the transmitted shock wave occurs in the zone where the flow is highly unsteady. When solving the flow developed behind the shock wave transmitted through the barrier while ignoring energy losses (i.e., assuming the fluid to be a perfect fluid and therefore employing the Euler equation instead of the Navier-Stokes equation) leads to non-physical results in the unsteady flow zone.

While a lot of attention was given to shock wave reflections from wedges during the past four decades, only little work was published regarding the similar case of blast wave reflection from wedges. In the present paper this subject is studied experimentally and theoretically/numerically. The obtained results show that the geometry of the reflected wave pattern is similar in the two cases when both incident waves have the same initial pressure jump across their fronts. However, different reflected pressure signatures (history) are observed in these two cases. The pressures obtained behind a reflected shock wave are always higher than those obtained behind the corresponding similar blast wave. In the present case differences as high as 17% were observed.

Using conduits in which a transmitted shock wave experiences abrupt changes in its direction of propagation is an effective means for shock wave attenuation. An additional attenuation of the transmitted shock wave is obtained when the medium contained inside the conduit (through which the shock wave is transmitted) is a suspension rather than a pure gas. The present numerical study shows that adding small solid particles (dust) into the gaseous phase results in sharp attenuation of all shock waves passing through the conduit. It is shown that the smaller the dust particles diameter is, the higher the shock attenuation becomes. Increasing the dust mass loading in the suspension also causes a quick attenuation. By proper choice of dust mass loading in the suspension, or the particles diameter, it is possible to ensure that the emerging wave from the conduit exit channel is a (smooth) compression wave, rather than a shock wave.

An experimental investigation was conducted examining the option of using branched duct geometry for shock wave attenuation. Experiments were done in an 80 mm $$\times $$ 80 mm square section shock tube to which a 20-mm diameter pipe was added vertically. Pressures were recorded along the shock tube wall (static pressure) and at the branched pipe end wall (stagnation pressure). Experiments were repeated with a constant incident shock wave Mach number ( $$M_\mathrm{s}=1.47$$ ) and with different pipe lengths. It was found that the length of the branched pipe has a significant effect on the flow inside the branched pipe and that in the present experimental configuration, the stagnation pressure recorded at the branched pipe end wall surpasses the pressure in the main channel behind the original incident shock wave. Finally, simulations were carried out using a commercial program, Star-CCM+, to complete the description of the flow studied here. The computed pressure profiles and shock wave locations agree quite well with the present experimental data.

The behavior of an aluminum door hanging at the exit of an open shock tube at different angles, from 5\(^\circ \) to 85\(^\circ \), and thereby providing partially open space for the exiting flow, was investigated experimentally. Experiments were conducted with an incident shock wave Mach number of \(M_\mathrm{is}=1.1\) impinging on the partially opened door. Both pressure measurements in the vicinity of the door, on its center and inside the shock tube, and schlieren visualization were undertaken for studying the door movement and its maximum opening angle relative to its initial position. It was found that for an initial opening angle smaller than 25\(^\circ \) the door opened completely while for larger angles its motion is marginal. In addition, for an initial door opening angle of about 10\(^\circ \) the lowest pressures were recorded inside the shock tube behind the evolving waves after exiting of the incident shock wave. The present experimental results may be useful to numerical studies of fluid–structure interactions, e.g., in designing safety valves in jet engines. Such a device is needed for preventing rupture in the case when a sudden overpressure pulse is generated inside the aircraft engine compartment.

The complex flow and wave pattern following an initially planar shock wave transmitted through a double-bend duct is studied experimentally and theoretically/numerically. Several different double-bend duct geometries are investigated in order to assess their effects on the accompanying flow and shock wave attenuation while passing through these ducts. The effect of the duct wall roughness on the shock wave attenuation is also studied. The main flow diagnostic used in the experimental part is either an interferometric study or alternating shadow–schlieren diagnostics. The photos obtained provide a detailed description of the flow evolution inside the ducts investigated. Pressure measurements were also taken in some of the experiments. In the theoretical/numerical part the conservation equations for an inviscid, perfect gas were solved numerically. It is shown that the proposed physical model (Euler equations), which is solved by using the second-order-accurate, high-resolution GRP (generalized Riemann problem) scheme, can simulate such a complex, time-dependent process very accurately. Specifically, all wave patterns are numerically simulated throughout the entire interaction process. Excellent agreement is found between the numerical simulation and the experimental results. The efficiency of a double-bend duct in providing a shock wave attenuation is clearly demonstrated.

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.

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over Aat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were M-s = 1.30 and M-s = 2.032, dust loading ratios were alpha = 1 and alpha = 5, and particle diameters were d = 1, 10 and 50 mum. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure historics were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension.

The reflection of planar shock waves from straight wedges in dust-gas suspensions is investigated numerically. The GRP shock capturing scheme and the MacCormac scheme are applied to solve the governing equations of the gaseous and solid phases, respectively. These two schemes have a second-order accuracy both in time and space. It is shown that the presence of the dust significantly affects the shock-wave-reflection-induced flow field. The incident shock wave attenuates and hence unlike the shock wave reflection phenomenon in a pure gas, the flow field in the present case is not pseudo steady. The presence of the dust results in lower gas velocities and gas temperatures and higher gas densities and gas pressures than in dust-free shock wave reflections with identical initial conditions. It is also shown that the smaller is the diameter of the dust particle the larger are the above-mentioned differences. In addition, the smaller is the diameter of the dust particle the narrower is the width of the dust cloud behind the incident shock wave. Larger dust velocities, dust temperatures and dust spatial densities are obtained inside this dust cloud for smaller dust particles. The results provide a clear picture of whether and how the presence of dust particles affects the shock-wave-reflection-induced flow field.

The flow in a converging-diverging nozzle is studied numerically. The flowing medium is a suspension composed of gas seeded with small, spherical, solid particles. The solution covers the entire flow history, from its initiation and until a steady state flow is reached. The covered flow domain includes both the flow field inside the nozzle and part of the free jet flow outside of the nozzle exit plane. The solution is repeated for different solid particle diameters, ranging from 0.5 μm to 50 μm, and different dust loading ratios. It is shown that the presence of solid particles in the flow has a significant effect on the developed flow field, inside and outside the nozzle. In particular, by a proper choice of particles diameter lateral pressure waves and the secondary shock wave can be significantly attenuated. The solid particles size has also a marked effect on the position and size of the Mach disk appearing in the free jet flow. It is also shown that in a suspension case a steady state flow is reached faster than in a similar pure gas flow.

The propagation of a planar shock wave in a 90° branched duct is studied experimentally and numerically. It is shown that the interaction of the transmitted shock wave with the branching segment results in a complex, two-dimensional unsteady flow. Multiple shock wave reflections from the duct's walls cause weakening of transmitted waves and, at late times, an approach to an equilibrium, one-dimensional flow. While at most places along the branched duct walls calculated pressures are lower than that existing behind the original incident shock wave, at the branching segment's right corner, where a head on-collision between the transmitted wave and the corner is experienced, pressures that are significantly higher than those existing behind the original incident shock wave are encountered. The numerically evaluated pressures can be accepted with confidence, due to the very good agreement found between experimental and numerical results with respect to the geometry of the complex wave pattern observed inside the branched duct.

The starting process of the flow in a wedge-like expansion nozzle of a shock tunnel is simulated by an unsplit 2-D GRP scheme on an unstructured grid. The scheme is briefly outlined and results are presented and discussed in comparison to the experimental (shadowgraph) findings obtained by Amann. The simulated pattern of reflected and transmitted shock waves in the nozzle inlet region and inside the nozzle is found to agree well with the experimental data.

A comparative study of the interaction of shock wave or rarefaction wave with a converging duct separating long constant cross-section segments is presented. Quasi-one-dimensional computations are compared with fully two-dimensional computations. It is observed that in some cases the two-dimensional results approach the respective one-dimensional approximations over long times, while in other cases the two-dimensional computed flow is genuinely two-dimensional and cannot be reduced to a one-dimensional equivalent. In the latter cases, significant errors are incurred by analysing the flow using the quasi-one- dimensional duct flow approximation.

We propose a new formulation of the fourth-difference artificial dissipation coefficient needed for the Navier–Stokes solutions. This coefficient is scaled by a damping function which is expressed in terms of the Baldwin–Lomax algebraic turbulence model. The suggested scaling function damps the artificial dissipation across the boundary layer. The objective of this paper is to test the ability of the suggested damped scaling coefficient to provide (a) a given accuracy on a coarser grids and (b) an accurate computing of turbulent boundary layers. To accomplish this, attached and separated transonic flows over the NACA 0012 airfoil, and turbulent flow over a flat plate have been considered.

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.

Certain aspects of wave propagation and the dynamic reaction of a granular material when subjected to a long-duration impulse load are studied. In the majority of studies published on this subject the unsteady pressure behavior at the end-wall covered by a layer of granular material was observed and documented. However, up to now little attention was given to explaining the physical mechanism of this process.

The paper describes new experimental results regarding the pressure fields in front of and inside granular layers of different materials during their collision with weak shock waves. A variety of waves result from the shock wave-granular layer interaction. The pressure behind the reflected wave from the material interface approaches the equilibrium value, P5, which would have been reached had the shock wave reflected from a solid end-wall.

International audience; Quick and reliable shock wave attenuation is the goal of every protection facility and therefore it is not surprising that achieving this has drawn much attention during the past hundred years. Different options have been suggested; their usefulness varying from a reasonable protection to the opposite, a shock enhancement. An example for a suggestion for shock mitigation that turned out to be an enhancement of the impinging shock wave was the idea to cover a protected object with a foam layer. While the pressure behind the reflected shock wave from the foam frontal surface was smaller than that recorded in a similar reflection from a rigid wall [25], the pressure on the ``protected'' surface, attached to the foam's rear-surface, was significantly higher than that recorded in a similar reflection from a bare, rigid wall [11]. In protecting humans and installations from destructive shock and/or blast waves the prime goal is to reduce the wave amplitude and the rate of pressure increase across the wave front. Both measures result in reducing the wave harmful effects. During the past six decades several approaches for achieving the desired protection have been offered in the open literature. We point out in this review that while some of the suggestions offered are practical, others are impractical. In our discussion we focus on recent schemes for shock/blast wave attenuation, characterized by the availability of reliable measurements (notably pressure and optical diagnostics) as well as high-resolution numerical simulations. (c) 2012 Elsevier Ltd. All rights reserved.