Gas combination for shock wave enhancement

It was recently demonstrated that shock wave enhancement could be achieved when a shock propagates in a constant cross-section duct through pairs of air–helium layers having a continually decreasing width (Igra and Igra in Shock Waves 16(3):199–207). A parametric study was conducted aimed at finding a two-layered, light–heavy gas arrangement that yields maximal shock enhancement; the heavy and the light gases used were air and helium, respectively. Effects associated with changes in following parameters were investigated: the number of alternating heavy/light gas layers, the applied reduction ratio between successive layers thickness, and the initial shock wave Mach number.      

Specific features of incident and reflected blast waves

On the basis of numerical modeling specific features of shock wave reflections were analyzed. It was found, that after diaphragm rupture self-modeling pressure and velocity distributions nearby the shock front establish. But in some special cases the temperature behind the shock front can rise. This peculiarity should be taken into account when performing experiments with high reactive gaseous mixtures. The temperature on the shock front and the velocity gradient behind it are uniform in the case of strong blast wave reflections. This effect is observed in the zone with an elevated temperature profile behind the incident blast wave. The reflected triangular waves conserve a quasi-self-modeling character by pressure. Typical experiments were carried out to verify the theoretical predictions. The effects of reflected wave acceleration in the case of triangular waves and the self-similar character of the pressure profiles were observed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The effect of porosity on shock interaction with a rigid, porous barrier

This work investigates the pressure amplification experienced behind a rigid, porous barrier that is exposed to a planar shock. Numerical simulations are performed in two dimensions using the full Navier–Stokes equations for a M = 1.3 incoming shock wave. An array of cylinders is positioned at some distance from a solid wall and the shock wave is allowed to propagate past the barrier and reflect off the wall. Pressure at the wall is recorded and the flowfield is examined using numerical schlieren images. This work is intended to provide insight into the interaction of a shock wave with a cloth barrier shielding a solid boundary, and therefore the Reynolds number is small (i.e., Re = 500 to 2000). Additionally, the effect of porosity of the barrier is examined. While the pressure plots display no distinct trend based on Reynolds number, the porosity has a marked effect on the flowfield structure and endwall pressure, with the pressure increasing as porosity decreases until a maximum value is reached.      

Detonation Initiation by Shock Reflection from an Orifice Plate

Results from an experimental investigation of the interaction of a “non-ideal” shock wave and a single obstacle are reported. The shock wave is produced ahead of an accelerated flame in a 14 cm inner-diameter tube partially filled with orifice plates. The shock wave interacts with a single larger blockage orifice plate placed 15–45 cm after the last orifice plate in the flame acceleration section of the tube. Experiments were performed with stoichiometric ethylene–oxygen mixtures with varying amounts of nitrogen dilution at atmospheric pressure and temperature. The critical nitrogen dilution was found for detonation initiation. It is shown that detonation initiation occurs if the chemical induction time based on the reflected shock state is shorter than the time required for an acoustic wave to traverse the orifice plate upstream surface, from the inner to the outer diameter. The similarity between the present results and those obtained from previous investigators looking at detonation initiation by ideal shock reflection produced in a shock tube indicates that the phenomenon is not sensitive to the detailed structure of the shock front but only on the average shock strength.This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

Experimental investigation of the interaction of shock waves with textiles

Experimental studies have been performed to investigate the pressure amplification experienced behind a textile when exposed to a shock wave. Three textiles with different masses and air permeabilities were studied. Mach numbers for tests varied between 1.23 and 1.55. The distance between the back wall and the textile was varied between 3 and 15 mm. It was found that in most cases the presence of the textile led to a pressure amplification at the back wall. This amplification was dependent on the textile, Mach number and distance from the back wall. The processes causing the pressure amplification were identified by analysing pressure traces and contact shadowgraphs. It was found that when the incident wave impinges on the textile, a part is reflected upstream and a part is transmitted through the textile. The transmitted portion reflects back and forth in the gap between the textile and the back wall leading to a back wall pressure trace with a stepped profile. In addition, the textile moves towards the back wall causing compression waves to propagate towards the back wall. The combination of the stepped profile and the compression waves cause the pressure amplification. The contribution of each mechanism depends on the textile properties. Approximate wave diagrams have been constructed. Tests involving multiple layers of textiles are also discussed. Received 17 October 2000 / Accepted 2 February 2001     

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Flow visualization of shock/water column interactions

The breakup of a liquid droplet induced by a high speed gas stream is a typical multiphase flow problem. The shock/droplet interaction is the beginning stage of the droplet breakup. Therefore, investigation of the shock/droplet interactions would be a milestone for interpreting the mechanism of the droplet breakup. In this study, a compressible multiphase solver with a five-equation model is successfully developed to study shock/water column interactions. For code validation, interface-only, gas–gas shock tube, and gas–liquid shock tube problems are first computed. Subsequently, a planar shock wave interacting with a water column is simulated. The transmitted wave and the alternative appearances of local high- and low-pressure regions inside the water column are observed clearly. Finally, a planar shock wave interacting with two water columns is investigated. In this work, both horizontal and vertical arrangements of two water columns are studied. It is found that different arrangements can result in the diversity of the interacting process. The complex flow structures generated by shock/water column interactions are presented by flow-visualization techniques.      

Application of background oriented schlieren for quantitative measurements of shock waves from explosions

This paper describes application of a background oriented schlieren technique in order to obtain quantitative measurements of shock waves from explosions by processing high speed digital video recordings. The technique is illustrated by an analysis of two explosions, a high explosive test and a hydrogen gas explosion test. The visualization of the shock front is utilized to calculate the shock Mach number, leading to a predicted shock front pressure. For high explosives the method agreed quite well with a standard curve for side-on shock pressures. In the case of the gas explosion test we can also show that the shock front is non-spherical. It should be possible to develop this technique to investigate external blast waves and external explosions from vented gas explosions in more details. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

The quasi-stationary structure of radiating shock waves. I. The one-temperature fluid

We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an implicit adaptive grid. We show that this code successfully resolves the shock wave in both the subcritical and supercritical cases and, for the first time, we have reproduced all the expected features – including the optically thin temperature spike at a supercritical shock front – without invoking analytic jump conditions at the discontinuity. We solve the full moment equations for the radiation flux and energy density, but the shock wave structure can also be reproduced if the radiation flux is assumed to be proportional to the gradient of the energy density (the diffusion approximation), as long as the radiation energy density is determined by the appropriate radiative transfer moment equation. We find that Zel'dovich and Raizer's (1967) analytic solution for the shock wave structure accurately describes a subcritical shock but it underestimates the gas temperature, pressure, and the radiation flux in the gas ahead of a supercritical shock. We argue that this discrepancy is a consequence of neglecting terms which are second order in the minimum inverse shock compression ratio [, where is the adiabatic index] and the inaccurate treatment of radiative transfer near the discontinuity. In addition, we verify that the maximum temperature of the gas immediately behind the shock is given by , where is the gas temperature far behind the shock. Received 21 September 1998/ Accepted 2 February 1999     

Shock waves in water with Freon-12 bubbles and formation of gas hydrates

The evolution of a shock wave and its reflection from a wall in a gas-liquid medium with dissolution and hydration are experimentally investigated. Dissolution and hydration behind the front of a moderate-amplitude shock wave are demonstrated to be caused by fragmentation of gas bubbles, resulting in a drastic increase in the area of the interphase surface and in a decrease in size of gas inclusions. The mechanisms of hydration behind the wave front are examined. Hydration behind the front of a shock wave with a stepwise profile is theoretically analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 58–75, May–June, 2007.     

Shock wave propagation in a branched duct

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. Received 15 July 1996 / Accepted 20 February 1997     

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 15–21, November–December, 2007     

On shock wave propagation in a branched channel with particles

The problem of wave propagation in a dust–air mixture inside a branched channel has not been studied widely in literature, even though this topic has many important applications especially in process safety (dust explosions). In this paper, a shock wave interaction with a cloud of solid particles, and the further behaviour of both gas and particulate phases were studied using numerical techniques. The geometry mimicked a real channel where bends or branches are common. Two numerical approaches were used: Eulerian–Eulerian and Eulerian–Lagrangian. Using Eulerian-Lagrangian simulation, it was possible to include the effects of particle–particle and particle–wall collisions in a realistic and direct manner. Results are mainly shown as snap-shots of particle positions during the simulations and statistics for the particle displacement. The results show that collisions significantly influence the process of particle cloud formation. PACS47.40.Nm, 02.60.Cb, 47.55.kf     

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.      

Penetration of Cylindrical Projectiles into Saturated Sandy Media

The time and depth of vertical one-dimensional projectile penetration into sandy media in the near shore region are derived. A precise definition for the physical properties and for the behavior of the sandy medium following the projectile impact are evaluated. Three separate time intervals following projectile impact are identified. During the first 3 ms of penetration, the deviatoric friction stress is shown to be negligible and the integrated Mie–Grüneisen equation of state (or, equivalently, the Hugoniot-adiabat) may be applied to compute the normal penetration resistance force from the sand pressure. In order to compute sand pressure as a function of the sand density D by the integrated Mie–Grüneisen equation of state, the Mie–Grüneisen dimensionless constants γ₀ and s and the dimensional speed of sound C ₀ in the sandy medium are required. In order to illustrate the one-dimensional shock wave propagation in both wet and dry sands, Hugoniot data for wet and dry silica sands are evaluated by a three degrees of freedom algorithm to compute these required constants. The numerical results demonstrate that the amplitude of the shock wave pressure in the wet silica sand (41% porosity) is approximately one-third of the shock wave pressure amplitudes in the dry silica sands (22% and 41% porosity). In addition, the shock wave pressure dampens quicker in the wet sand than in the dry sands.     

Attenuation of shock waves propagating in polyurethane foams

Shock wave attenuation in polyurethane foams is investigated experimentally and numerically. This study is a part of research project regarding shock propagation in polyurethane foams with high-porosities = 0.951 ~ 0.977 and low densities of ρc = 27.6 ~55.8 kg/m³. Sixty Millimeter long cylindrical foams with various cell numbers and foam insertion condition were installed in a horizontal shock tube of 50 mm i.d. and 5.4 mm in length. Results of pressure measurements in air/foam combination are compared with CFD simulation solving the one-dimensional Euler equations. In the case of a foam B fixed on shock tube wall, pressures at the shock tube end wall increases relatively slowly comparing to non-fixed foam, free to move and a foam A fixed on shock tube wall. This implies that elastic inertia hardly contributes to pressure build up. Pressures behind a foam C fixed on shock tube wall decrease indicating that shock wave is degenerated into compression wave. Dimensionless impulse and attenuation factor decrease as the initial cell number increases. The momentum loss varies depending on cell structure and cell number.     

A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for unsteady, one-dimensional self-similar flow behind a strong shock wave, driven by a moving piston, in a dusty gas. The dusty gas is assumed to consist of a mixture of small solid particles and a non-ideal gas, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. Solutions are obtained under both the isothermal and adiabatic conditions of the flow-field. The spherical case is worked out in detail to investigate to what extent the flow-field behind the shock is influenced by the non-idealness of the gas in the mixture as well as by the mass concentration of the solid particles, by the ratio of density of the solid particles to the initial density of the mixture and by the energy input due to moving piston. A comparison is also made between isothermal and adiabatic cases.     

Measurement of He II evaporation induced by impingement of a thermal pulse on a He II–vapor interface

The transient evaporation phenomenon in a pure superfluid helium (He II)–vapor system was experimentally studied. Evaporation is caused by the impingement of a second sound thermal pulse onto a He II–vapor interface. The resulting gas dynamic phenomena are visualized with the aid of a laser holographic interferometer, and are also measured with a pressure transducer and a superconductive temperature sensor. It is clearly seen in the interferograms that a clear shock wave is formed at the front of an evaporation wave. We obtained the condensation coefficient of He II as being 0.70 ± 0.05 in the temperature range between 2.04 K and 1.74 K by the comparison of the experimental data with the kinetic theory results. Received: 24 June 1999/Accepted: 28 March 2000     

Focusing of a shock wave in a rarefied gas A numerical study

The process of focusing of a shock wave in a rarefied noble gas is investigated by a numerical solution of the corresponding two dimensional initial–boundary value problem for the Boltzmann equation. The numerical method is based on the splitting algorithm in which the collision integral is computed by a Monte Carlo quadrature, and the free flow equation is solved by a finite volume method. We analyse the development of the shock wave which reflects from a suitably shaped reflector, and we study influence of various factors, involved in the mathematical model of the problem, on the process of focusing. In particular, we investigate the pressure amplification factor and its dependence on the strength of the shock and on the accommodation coefficient appearing in the Maxwell boundary condition modelling the gas-surface interaction. Moreover, we study the dependence of the shock focusing phenomenon on the shape of the reflector, and on the Mach number of the incoming shock. Received 25 May 1998 / Accepted 4 January 2000