Diffraction of normal shock for monoatomic gases

In the present investigation, vorticity distribution of a particle over the normal diffracted shock has been obtained for monoatomic gases, CO₂ and SF₆. Further some results using Lighthill’s theory (Lighthill in Proc R Soc A 198:454–470, 1949) and Whitham’s theory (Whitham in J Fluid Mech 2:145–171, 1957) have been obtained.     

On the vorticity distribution over a normal diffracted shock for small and large bends

Vorticity distributions over the diffracted shock both from Lighthill’s theory (Proc R Soc A 198:454–470, 1949) applicable for small bends and Sakurai and Takayama’s theory (Shock Waves 4:225–230, 2005) applicable for larger bends have been investigated for Mach numbers 1.80 and 1.95. Furthermore, Mach reflection effects for both theories for the same Mach numbers 1.80 and 1.95 have been investigated.     

Normal shock interaction with a yawed wedge moving at supersonic speed

In this article, the interaction of a normal shock with a yawed wedge moving at supersonic speed has been considered. The vorticity distribution of a particle over the diffracted shock wave for various combinations of yawed angles, Mach number of the shock wave and Mach number of the moving wedge have been obtained. Further triple point angle χ in Mach reflection has been calculated for the various parameters.      

Type of reflection of a near-wall shock wave in the process of diffraction from a square channel

The results of an experimental and numerical investigation of the process of diffraction of shock waves from a square channel at a ninety-degree convex corner are presented for various incident shock wave Mach numbers M₀ (1.4<M₀<7). The type of reflection of the near-wall fragment of the diffracting shock wave from the wall and the wave velocity are determined as functions of M₀, direction, and time. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 145–151, January–February, 2000. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 96-02-16170a).     

Application of underwater shock wave and laser-induced liquid jet to neurosurgery

Paper deals with applications of underwater shock waves to medicine. A historical development of underwater shock wave generation by using pulsed Ho:YAG laser beam irradiation in water is briefly described and an overview is given regarding potential applications of shock waves to neuro-surgery. The laser beam irradiation in a liquid-filled catheter produces water vapor bubble and shock waves intermittently produces micro-liquid jets in a controlled fashion from the exit of the catheter. Correlations between shock dynamics and bubble dynamics are emphasized. To optimize the jet motion, results of basic parametric studies are briefly presented. The liquid jet discharged from the catheter exit has an impulse high enough to clearly exhibit effectiveness for various medical purposes. In liquid jets we observed reasonably strong shock waves and hence invented a compact shock generator aiming to apply to microsurgery. We applied it to a rat's bone window and developed an effective method of brain protection against shock loading. The insertion of Gore-Tex® sheet is found to attenuate shock waves drastically even for very short stand off distance and its physical mechanism is clarified. The laser-induced liquid jet (LILJ) is successfully applied to soft tissue dissection. Animal experiments were performed and results of histological observations are presented in details. Results of animal experiments revealed that LILJ can sharply dissect soft tissue with a minimum amount of liquid consumption, while blood vessels larger than 0.2 mm in diameter are preserved. Shock waves and LILJ have a potential to be indispensable tools in neuro-surgery.This paper was based on work that was presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan, March 1–3, 2005.Communicated by K. Takayama PACS 42.62.Be, 47.40.-x, 42.62.-b     

Radiative shock solutions with grey nonequilibrium diffusion

This study describes a semi-analytic solution of planar radiative shock waves with a grey nonequilibrium diffusion radiation model. The solution may be used to verify radiation-hydrodynamics codes. Comparisons are made with the equilibrium diffusion solutions of Lowrie and Rauenzahn (Shock Waves 16(6):445–453, 2007). The solution also gives additional insight into the structure of radiative shocks. Previous work has assumed that the material temperature reaches its maximum at the post-shock state of the embedded hydrodynamic shock (Zel’dovich spike). We show that in many cases, the temperature may continue to increase after the hydrodynamic shock and reaches its maximum at the isothermal sonic point. Also, a temperature spike may exist even in the absence of an embedded hydrodynamic shock. We also derive an improved estimate for the maximum temperature.      

Atmospheric pressure waves in the field of volcanology

Atmospheric pressure waves are a notable phenomenon associated with explosive volcanic eruptions. They can provide us with information about eruption processes that are useful both scientifically and practically. In this paper, we give a brief review of studies that have been carried out on this phenomenon in the field of volcanology. Then, we introduce a prototype tool called ‘MOVE’ (Mobile Observatory for Volcanic Explosions). It is a remote-controlled vehicle carrying various instruments to observe pressure waves and the eruption processes. PACS 91.40.Dr · 91.40.Ft · 93.65.+e · 93.85.+qThis paper was based on work presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan on March 1–3, 2005.     

Modeling of the unsteady force for shock–particle interaction

The interaction between a particle and a shock wave leads to unsteady forces that can be an order of magnitude larger than the quasi-steady force in the flow field behind the shock wave. Simple models for the unsteady force have so far not been proposed because of the complicated flow field during the interaction. Here, a simple model is presented based on the work of Parmar et al. (Phil Trans R Soc A 366:2161–2175, 2008). Comparisons with experimental and computational data for both stationary spheres and spheres set in motion by shock waves show good agreement in terms of the magnitude of the peak and the duration of the unsteady force.      

Slow Eigenvalues of Self-similar Solutions of the Dafermos Regularization of a System of Conservation Laws: an Analytic Approach

The Dafermos regularization of a system of n hyperbolic conservation laws in one space dimension has, near a Riemann solution consisting of n Lax shock waves, a self-similar solution u = u _ε(X/T). In Lin and Schecter (2003, SIAM J. Math. Anal. 35, 884–921) it is shown that the linearized Dafermos operator at such a solution may have two kinds of eigenvalues: fast eigenvalues of order 1/ε and slow eigenvalues of order one. The fast eigenvalues represent motion in an initial time layer, where near the shock waves solutions quickly converge to traveling-wave-like motion. The slow eigenvalues represent motion after the initial time layer, where motion between the shock waves is dominant. In this paper we use tools from dynamical systems and singular perturbation theory to study the slow eigenvalues. We show how to construct asymptotic expansions of eigenvalue-eigenfunction pairs to any order in ε. We also prove the existence of true eigenvalue-eigenfunction pairs near the asymptotic expansions.     

Application of the method of direct separation of motions to the parametric stabilization of an elastic wire

The paper considers the application of the method of direct separation of motions to the investigation of distributed systems. An approach is proposed which allows one to apply the method directly to the initial equation of motion and to satisfy all boundary conditions, arising for both slow and fast components of motion. The methodology is demonstrated by means of a classical problem concerning the so-called Indian magic rope trick (Blekhman et al. in Selected topics in vibrational mechanics, vol. 11, pp. 139–149, [2004]; Champneys and Fraser in Proc. R. Soc. Lond. A 456:553–570, [2000]; in SIAM J. Appl. Math. 65(1):267–298, [2004]; Fraser and Champneys in Proc. R. Soc. Lond. A 458:1353–1373, [2002]; Galan et al. in J. Sound Vib. 280:359–377, [2005]), in which a wire with an unstable upper vertical position is stabilized due to vertical vibration of its bottom support point. The wire is modeled as a heavy Bernoulli–Euler beam with a vertically vibrating lower end. As a result of the treatment, an explicit formula is obtained for the vibrational correction to the critical flexural stiffness of the nonexcited system.     

Visualization of shock-wave formation processes during shock reflection at obstacles with multiple steps

According to standard textbooks on compressible fluid dynamics, a shock wave is formed by an accumulation of compression waves. However, the process by which an accumulated compression wave grows into a shock wave has never been visualized. In the present paper, the authors tried to visualize this process using a model wedge with multiple steps. This model is useful for generating a series of compression waves and can simulate a compression process that occurs in a shock tube. By estimating the triple-point trajectory angle, we demonstrated visually that an accumulated compression wave grows into a shock wave. Further reflection experiments over a rough-surface wedge confirmed the tendency for the triple point trajectory angle to reach the asymptotic value _s in the end.This work was first presented at the Symposium on Shock Waves, Japan 2002     

Investigation of high-speed combustible gas ignited by a hot gas jetproduced in the shock tube

The high-speed combustible gas ignited by a hot gas jet, which is induced by shock focusing, was experimentally investigated. By use of the separation mode of shock tube, the test section of a single shock tube is split into two parts, which provide the high-speed flow of combustible gas and pilot flame of hot gas jet, respectively. In the interface of two parts of test sections the flame of jet was formed and spread to the high-speed combustible gas. Two kinds of the ignitions, 3-D “line-flame ignition” and 2-D “plane-flame ignition”, were investigated. In the condition of 3-D “line-flame ignition” of combustion, thicker hot gas jet than pure air jet, was observed in schlieren photos. In the condition of 2-D “plane-flame ignition” of combustion, the delay time of ignition and the angle of flame front in schlieren photos were measured, from which the velocity of flame propagation in the high-speed combustible gas is estimated in the range of 30–90m/s and the delay time of ignition is estimated in the range of 0.12–0.29ms. PACS 47.40.Nm; 82.40.FpPart of this paper was presented at the 5th International Workshop on Shock/Vortex Interaction, Kaohsiung, October 27–31, 2003.     

A State-of-the-Knowledge Review on Pseudo-Steady Shock-Wave Reflections and their Transition Criteria

The distinguished philosopher Ernst Mach published the first known paper on the phenomenon of planar shock-wave reflections over straight wedges over 125 years ago in 1878. In his publication he presented two wave configurations that could result from this reflection process, a regular reflection (RR) and a configuration that was later named after him and called Mach reflection (MR) in the early 1940s. In 1945, Smith reported on an additional wave configuration, which had a reflected shock wave that was slightly different from that of the just-mentioned Mach reflection. Smith (OSRD Rep. 6271, Off. Sci. Res. Dev., 1945) did not ascribe any special importance to the wave configuration that he observed. The wave configuration that was observed and reported by Smith (OSRD Rep. 6271, Off. Sci. Res. Dev., 1945) was recognized as an independent one only about 5 years later when White (Tech. Rep. II-10, Princeton Univ. Dept. Phys., 1951) reported on the discovery of a new wave configuration that was named double-Mach reflections (DMR) because it had similar features to that of the Mach reflection wave configuration but all the features were doubled. For this reason the Mach reflection wave configuration has been re-named single-Mach reflection (SMR). (Until the late 1970s it was called simple-Mach reflection although nothing is simple about it.). The discovery of the double-Mach reflection revealed that the wave configuration that was first observed by Smith was an intermediate wave configuration between the SMR and the DMR wave configurations. For this reason it was named transitional-Mach reflection (TMR) (Until the early 1980s it was called complex-Mach reflection although it is not the most complex one.). Since the discovery of the DMR many investigations were aimed at elucidating the exact transition criteria between the above-mentioned four different wave configurations as well as some additional configurations and sub-configurations that were discovered later. In 1991 Ben-Dor published a monograph, entitled “Shock Wave Reflection Phenomena”, that was, in fact, a state-of-the-knowledge review of the phenomena. This state-of-the-knowledge will be referred to in the followings as the “old”-state-of-the-knowledge (This state-of-the-knowledge existed until the mid 1990s. A few years later Li and Ben-Dor (Shock Wave 5(1/2), 59–73, 1995) modified the analytical approach for evaluating the transition criteria from the single-Mach to the transitional- Mach reflection (SMR, ,TMR) and from the transitional-Mach to the double-Mach reflection (TMR, ,DMR) and presented some modified and new criteria for the formation and termination of both the TMR and DMR wave configurations. Experimental results from various sources revealed that the transition boundaries between the SMR, TMR and DMR wave configurations that were based on the modified analytical approach were better than those of the “old” state-of-the-knowledge that as mentioned earlier was summarized in Ben-Dor’s (Shock Wave Reflection Phenomena, Springer, 1991) monograph. Unfortunately, however, the results of Li and Ben-Dor’s (Shock Wave 5(1/2), 59–73, 1995) modified analytical approach have not been internalized, and publications by various scientists in the past decade neglected the revised and better transition criteria and kept on referring to the old and wrong criteria that appeared in Ben-Dor’s (Shock Wave Reflection Phenomena, Springer, 1991) monograph. For this reason, a state-of-the-knowledge review that is based on the above-mentioned 10-year-old findings of Li and Ben-Dor (Shock Wave 5(1/2), 59–73, 1995) is presented herein. At the first step, the “old” state-of-the-knowledge is presented.This paper was based on work that was presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan, 1–3 March 2005.     

On dislocation models of grain boundaries

Dislocation models of grain boundaries was suggested by Bragg (Proc Phys Soc 52:54–55, 1940) and Burgers (Proc Phys Soc 52:23–33, 1940). The first quantitative study of these models was given by Read and Shockley (Phys Rev 78(3):275–289, 1950). They obtained a formula for the dependence of the grain boundary energy on the misorientation of the neighboring grains, which became a cornerstone of the grain boundary theory. The Read–Shockley formula was based on a proposition that the grain boundary energy is the sum of energies of the two sets of dislocations that come from the two neighboring grains. This proposition was proved under an assumption on a quite special geometry of the slip planes. This paper aims to show that the assumption is not necessary and the proposition holds for arbitrary geometry of slip planes. Another goal of this paper is to provide all basic formulas of the theory: though the dislocation model of grain boundaries is considered in all treatises on dislocation theory, a complete analysis, including the relations for lattice rotations and displacements, has not been given. This analysis shows, in particular, that continuum theory does not yield the proper relations for the lattice misorientations, and these relations must be introduced by an independent ansatz.     

The effect of shock pressures on the inactivation of a marine Vibrio sp.

The effect of shock pressures on the inactivation of a marine Vibrio sp. was studied experimentally and numerically. In the experiment, an aluminum impactor plate accelerated by a gas gun was used to induce shock waves in a sealed aluminum container with cell suspension liquid inside. The shock pressures in the container were measured by a piezofilm gauge. Several 10–100 MPa of pressure were measured at the shock wave front. An FEM simulation, using the Johnson–Cook model for solid aluminum and the Tait equation for the suspension liquid, was carried out in order to know the generation mechanism of shock pressures in the aluminum container. The reflection, diffraction and interaction of shock waves at the solid–liquid boundaries in the aluminum container were reasonably predicted by the numerical simulation. The changes in shock pressures obtained from the computational simulation were in good agreement with those from the experiment. The number of viable cells decreased with the increase of peak pressures of the shock waves. Peak pressures higher than 200 MPa completely inactivated the cells. At this pressure, the cell structures were deformed like the shape of red blood cells, and some proteins leaked from the cells. These results indicate that the positive and negative pressure fluctuations generated by shock waves contribute to the inactivation of the marine Vibrio sp.      

Nonideal effects behind reflected shock waves in a high-pressure shock tube

Abstract. Shock tubes often experience temperature and pressure nonuniformities behind the reflected shock wave that cannot be neglected in chemical kinetics experiments. Because of increased viscous effects, smaller tube diameters, and nonideal shock formation, the reflected-shock nonidealities tend to be greater in higher-pressure shock tubes. Since the increase in test temperature () is the most significant parameter for chemical kinetics, experiments were performed to characterize in the Stanford High Pressure Shock Tube using infrared emission from a known amount of CO in argon. From the measured change in vibrationally equilibrated CO emission with time, the corresponding ddt (or for a known time interval) of the mixture was inferred assuming an isentropic relationship between post-shock temperature and pressure changes. For a range of representative conditions in argon (24–530 atm, 1275–1900 K), the test temperature 2 cm from the endwall increased 3–8 K after 100 s and 15–40 K after 500 s, depending on the initial conditions. Separate pressure measurements using a shielded piezoelectric transducer confirmed the isentropic assumption. An analytical model of the reflected-shock gas dynamics was also developed, and the calculated 's agree well with those obtained from experiment. The analytical model was used to estimate the effects of temperature and pressure nonuniformities on typical chemical kinetics measurements. When the kinetics are fast (s), the temperature increase is typically negligible, although some correction is suggested for kinetics experiments lasting longer than 500 s. The temperature increase, however, has a negligible impact on the measured laser absorption profiles of OH (306 nm) and CH (216 nm), validating the use of a constant absorption coefficient. Infrared emission experiments are more sensitive to temperature and density changes, so nonuniformities should be taken into account when interpreting ir-emission data. Received 25 April 2000 / Accepted 8 September 2000     

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.      

High-pressure minerals in shocked L6-chondrites: constraints on impact conditions

We have studied the high-pressure phases observed in Yamato 791384 and ALH78003 L6-chondrites. Host meteorite consists mainly of olivine, pyroxenes, and plagioclase glass. Mineral fragments observed in the veins and the vein margin region of these meteorites were partially or totally transformed into high-pressure phases wadsleyite, ringwoodite, majorite, akimotoite, NaAlSi₃O₈ hollandite and jadeite. Whereas matrix of the shock vein contains majorite-pyrope solid solution in both meteorites. The spatial distribution indicates that high-pressure phases are present in the shock veins and host rocks adjacent to the shock veins. Investigation of the high-pressure phases revealed that, in Y791384, fragments and adjacent matrix were subjected to pressures around 18–23 GPa and the vein experienced temperatures around 2,000–2,300°C during the shock event. ALH78003 experienced the shock pressure of about 15–18 GPa at 2,000°C. Ringwoodite lamellae were observed in the host olivine adjacent to the vein in Y791384. Kinetic investigation for ringwoodite lamellar growth in olivine indicates that the meteorite experienced an impact with a pressure around 20 GPa for more than 4 s of the pressure pulse indicating a large impactor with the size greater than 10 km. ALH78003 contains wadsleyite–ringwoodite aggregates in the shock veins. The ringwoodite grains have wadsleyite rim enriched in Mg₂SiO₄ component. The compositional profiles of wadsleyite rim and ringwoodite core of the fragments in the shock veins in ALH78003 cannot be explained by a simple Mg–Fe inter-diffusion process.This paper was based on the work that was presented at the 2nd International Symposium on Interdisciplinary Shock Wave Research, Sendai, Japan, March 1–2, 2005.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.