Shock Hugoniot for Biological Materials

This paper presents shock Hugoniot compression data for several bio-related materials by using flat plate impact experiments. Shock pressure covered in this study ranges at least up to 1 GPa. It is emphasized here that spatial and temporal uniformity of pressure distribution behind a shock wave front is very important and it can be realized in these materials by the impact method, and their precise shock propagation characteristics have been obtained by the application of the procedure developed previously by our group. Hugoniot measurements for different and systematic data for various samples are compared with shock Hugoniot curve for water. Samples used in the experiment include water gel of gelatin, NaCl aqueous solution, and finally chicken breast meat. Several samples with different initial density were used for gelatin and NaCl solution. Shock Hugoniot function for all the specimens tested can be summarized as u _s =A+B u _p , B ~ 2Value of the intercept of the relationship, A, which has the meaning of the sound velocity, is apparently dependent on the material and ambient temperature. Physical meanings of the obtained results have been discussed.     

Particle morphology and packing effects on the shock loading of powders

A physically based model for the shock Hugoniot of a powdered material is described which allows separate identification of the cold and thermal contributions to pressure and specific internal energy. Special features of this model are provision for the effects of porosity on the stress state and an empirically determined cold loading contribution to pressure. The model was tested against published Hugoniot data for iron and gave excellent agreement for shock pressures ranging from low to high values.This shock Hugoniot was used to explore the shocked state of 4 samples of iron powder derived from commercially available material. The purpose of this study was to investigate the effect of powder particle characteristics and initial starting densities on the shocked state.The powder samples investigated had a range of morphologies and sizes. Powders with either a large shape factor or high internal friction, as determined in shear cell experiments, exhibited a higher stiffness in the cold loading curve. In the shocked state, this translated into a higher cold component of pressure and energy than found in the other powders.The effect of initial powder density was studied by applying the Hugoniot model to two impact initiated shock loadings, one for a stainless steel flyer impacting at 0.5 km/s and one at the higher velocity of 2.0 km/s. Both were applied to iron powder targets preloaded to a range of initial densities. For a given impact event, the proportion of shock energy in the thermal mode was found to decrease with increasing initial density. This decrease was more pronounced at higher shock strengths. As a result of the decreasing component of thermal energy with higher initial density, there was a reduction in the continuum temperature behind the shock. However, the corresponding increase in the component of cold energy with the falling relative contribution from the thermal energy lead to increasing density behind the shock suggesting that there is a trade off in terms of temperature and density achievable with a given impact event.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.     

On the structure of the Hugoniot relation for a shock-induced martensitic phase transition

The Hugoniot curve relates the pressure and volume behind a shock wave, with the temperature having been eliminated. This paper studies the Hugoniot curve behind a propagating sharp interface between two material phases for a solid in which an impact-induced phase transition has taken place. For a solid capable of existing in only one phase, compressive impact produces a shock wave moving into material, say, at rest in an unstressed state at the ambient temperature. If the specimen can exist in either of two material phases, sufficiently severe impact may produce a disturbance with a two-wave structure: a shock wave in the low-pressure phase of the material, followed by a phase boundary separating the low- and high-pressure phases. We use a theory of phase transitions in thermoelastic materials to construct the Hugoniot curve behind the phase boundary in this two-wave circumstance. The kinetic relation controlling the evolution of the phase transition is an essential ingredient in this process.      

Shock waves in molecular solids: ultrafast vibrational spectroscopy of the first nanosecond

A novel technique which uses a microfabricated shock target array assembly is described, where the passage of a shock front through a thin (0.5μm) polycrystalline layer and the subsequent unloading process is monitored in real time with ultrafast coherent Raman spectroscopy. Using a high repetition rate laser shock generation technique, high resolution, coherent Raman spectra are obtained in shocked anthracene and in a high explosive material, NTO, with time resolution of ∼ 50 ps. Spectroscopic measurements are presented which yield the shock pressure (up to 5 GPa), the shock velocity (∼ 4 km/s), the shock front risetime (t _r < 25 ps), and the temperature (∼ 400°C). A brief discussion is presented, how this new technique can be used to determine the Hugoniot, the equation of state, the entropy increase across the shock front, and monitor shock induced chemical reactions in real time. Received 28 October 1996 / Accepted 12 November 1996     

Evidence for shock wave effect of meteoritic impact

There is material evidence for the existence of shock waves generated by meteoritic impact. This is demonstrated by the pressure and temperature dependent formation processes that exist in the memory of constituent minerals. Stishovite of high-pressure type silica mineral can be observed to be a relict of the compression stage of shock impact. Almost all of the silica minerals evolved from shock impact phenomena are -quartz crystals of a low-temperature type silica polymorph. By using precise measurements of cell parameters and the corresponding calculated density of the quartz crystal grains collected by an ultrasonic cutter method, shocked quartz grains can be interpreted as the principle relict of meteoritic impact from natural impact craters, artificial impact craters and Cretaceous-Tertiary (K/T) boundary samples.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Effect of overtaking disturbances on strong cylindrical shock in a self-gravitating gas

The effect of overtaking disturbances on the propagation of strong cylindrical shock in a self-gravitating gas has been studied by an approximate technique developed by Yadav (1992). Assuming an initial density distribution law ase _o=er^–w , wheree is the density at the axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strengths modified by overtaking waves have been obtained. The results accomplished here have been compared with those for freely propagating shock.The conclusions arrived here agreed with experimental results.Finally, the modified expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived.     

Shock reaction of hexane at 77, 193, and 273 K with special reference to shock pressure

Shock waves generated by projectile impacts were transmitted into hexane and the shocked hexane was analyzed by TCD-GC, FID-GC, GCMS, and FABMS for produced aliphatic hydrocarbons. The projectile length and its velocity were varied from 10 to 40 mm and from 220 to 1040 m/s, respectively. The initial temperature of the hexane was 77, 193 and 273 K. The major products detected throughout the reactions were hydrogen, light alkanes from C to C, and light alkenes from C to C. The minor products were heavy alkanes from C to C and soot-like materials. Experiments with varied projectile length revealed that the shock reaction occurred only while the shock wave was transmitted through hexane (about seconds). This short reaction time may be responsible for a lower yield of branched products in the shock reaction compared with yield produced by hexane pyrolysis in previous studies. In the shock reaction of hexane, the dehydrogenation was one of the important reactions and the recombination of hexyl radicals might play a role in the formation of -C. Experiments with varied initial temperature suggested that the molar yield of products depends not on the shock temperature but on the shock pressure, and that the reaction mechanisms for solid hexane and for liquid hexane are not identical. As the shock pressure increased, the relative yield of heavy products increased while that of light products decreased. This could be interpreted mainly by considering the activation volumes of the reaction involved. Received 12 September 1997 / Accepted 14 October 1997     

Shock response of a heavy tungsten alloy

This article describes the results of shock wave experiments performed on a heavy tungsten alloy containing W, Ni, and Fe in the ratio of 92.85:4.9:2.25 by weight. These experiments provide information about the shear strength under compression and tensile strength, as measured by the spall threshold, of this alloy to 24 GPa. The results of these experiments show that: (i) the magnitude of its Hugoniot elastic limit (HEL) is 2.76±0.26 GPa; (ii) this alloy deforms plastically above its HEL and thus retains its shear strength to 24 GPa; (iii) the spall strength of the alloy is found to be 1.9±0.4 GPa and is independent of the impact stress and duration of the shock compression pulse; and (iv) the tensile impedance of the alloy, determined from a new experiment designed to measure this impedance, is 68±10 Gg/m² s.     

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.     

Search for conditions of compressive fracture of hard brittle ceramics at impact loading

In this paper we discuss three different experimental configurations to diagnosing the modes of inelastic deformation and to evaluating the failure thresholds at shock compression of hard brittle solids. One of the manifestations of brittle material response is the failure wave phenomenon, which has been previously observed in shock-compressed glasses. However, based on the measurements from our “theory critical” experiments, both alumina and boron carbide did not exhibit this phenomenon. In experiments with free and pre-stressed ceramics, while the Hugoniot elastic limit (HEL) in high-density B₄C ceramic was found to be very sensitive to the transverse stress, it was found relatively less sensitive in Al₂O₃, implying brittle response of the boron carbide and ductile behavior of alumina. To further investigate the effects of stress states on the shock response of brittle materials, a “divergent flow or spherical shock wave” based plate impact experimental technique was employed to vary the ratio of longitudinal and transversal stresses and to probe conditions for compressive fracture thresholds. Two different experimental approaches were considered to generate both longitudinal and shear waves in the target through the impact of convex flyer plates. In the ceramic target plates, the shear wave separates a region of highly divergent flow behind the decaying spherical longitudinal shock wave and a region of low-divergent flow. Experiments with divergent shock loading of alumina and boron carbide ceramic plates coupled with computer simulations demonstrated the validity of these experimental approaches to develop a better understanding of fracture phenomena.     

Investigation of possibility of flow field diagnostics by laser induced biacetyl phosphorescence

Experimental results of laser induced phosphorescence of biacetyl triplet³A _u in a mixture of biacetyl and N₂ show that: the lifetime of phosphorescence is a function of temperature and independent of density and concentration; the initial phosphorescence intensity is a linear function of density and insensitive to the variation of temperature. The temperature and density distribution of gas flow could be measured by observing the phosphorescence lifetime and initial intensity of biacetyl mixed with N₂ respectively. The velocity distribution could be measured by observing the time-of-flight of the gaseous phosphorescent spot under pulsed laser excitation. Compared with Doppler anemometer, it, to a great extent, avoids the particle lag problem in flow field with large velocity gradient. The phosphorescence decay mechanism is also analysed and the analytical results agree with experimental ones. The project supported by National Natural Science Foundation of China and The Third World Academy.     

Dynamics of a single bubble in a liquid in the presence of chemical reactions and interphase heat and mass exchange

The influence of inert and chemically reactive additives in the form of microdrops on the dynamics of a single bubble filled with an active gas mixture and collapsing under the action of a shock wave is considered. The development of a reaction during formation of the mixture is analyzed for instantaneous and dynamic evaporation of drops with allowance for various phases of their injection t _inj . It is shown that in instantaneous evaporation, an increase in the fraction of gaseous argon in the H₂+O₂ system raises the final temperature of the system under cryogenic conditions, lowers it under ordinary conditions, and causes appreciable oscillations of the values of γ, heat release, and molecular weight. It is noted that there are values of t _inj and D₀ at which the final temperature of the mixture decreases practically to the initial temperature. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 119–127, March–April. 1999.     

Numerical study of unsteady compressible flow driven by supersonic jet injected into elliptical cell with small exit hole

The unsteady behavior of flow driven by a jet suddenly injected into an elliptical cell is numerically studied by solving the axisymmetric two-dimensional compressible Navier–Stokes equations. This system is a model of laser ablation of a certain duration followed by a discharging process through the exit hole at the downstream end of the cell. The parameters for the calculations are the exit diameter of the cell, the Mach number and duration of the injected jet. The injected jet becomes a traveling plume approaching the downstream end of the elliptical cell and discharges from the cell through an exit hole. The plume generates and interacts with a shock wave in the elliptical cell. The unsteady flow properties downstream of the cell are found to be attenuated by the combination of the phenomena occurring in the cell and at the exit. Monitoring the velocity at the exit hole is used to clarify the characteristics of the flow and apply them to applications in pulse laser ablation. The results show that the vortex in the plume head with the same radius as the exit diameter (i.e., D_e/D_j = 2.7, where D_e is the exit diameter and D_j is the injected jet diameter) causes a relatively constant velocity at the exit for about 10 μs. In the downstream flow characteristics, the suddenly injected jet makes a single or double peak in the velocity variation outside the cell depending on the combination of parameters. This suggests that a single laser pulse might generate two beams through the exit hole of a cell, which could increase the efficiency of beam generation with the combination of an elliptical cell and the laser ablation. It is also found that the wave form of the variations and their level are roughly determined by the durations of the jet and the exit diameters of the cell exit, respectively. PACS 51.35.+a; 47.40.Nm     

Shock wave solution of the Boltzmann kinetic equation in a 13-moment approximation

We consider the classic problem of a one-dimensional steady shock-wave solution of the Boltzmann kinetic equation utilizing a new type of 13-moment approximation proposed by Oguchi (1997). The model, unlike previous ones, expresses the collision term in an explicit function of the molecular velocity. This enables us to examine directly the nature of the singularity of the distribution function to this particular problem caused by the vanishing molecular velocity. We can thus obtain moment integrals directly because of its explicit expression. The principal value is utilized for the moment integral to cope with the singularity, and we can have five relations for five unknown functions to be determined with respect to the coordinate x. These relations can be reduced to a first-order differential equation that is solved to provide the familiar smooth monotonic transition from the upstream supersonic state to the subsonic downstream state. Computed values of shock thickness for various shock Mach numbers agree well with existing results obtained by different methods to the certain Mach number beyond which no solution exists.Received: 17 May 2002, Accepted: 1 May 2003, Published online: 15 August 2003PACS: 51.10. + y     

Shock tunnel flow visualization using planar laser-induced fluorescence imaging of NO and OH

Temporal sequences of planar laser-induced fluorescence (PLIF) images of several high-speed, transient flowfields created in a reflection-type shock tunnel facility were acquired. In each case, the test gas contained either nitric oxide or the hydroxyl radical, the fluorescent species. The processes of shock reflection from an endwall with a converging nozzle and of underexpanded free jet formation were examined. A comparison was also made between PLIF imaging and shadow photography. The investigation demonstrated some of the capabilities of PLIF imaging diagnostics in complex, transient, hypersonic flowfields, including those with combustion.Nomenclature A spontaneous emission rate - A _las cross sectional area of laser sheet - B laser absorption rate - C _opt constant dependent on optical arrangement, collection efficiency, etc. - D nozzle throat diameter - E _p laser pulse energy - f _J Boltzmann fraction of absorbing state - g spectral convolution of laser and absorption lineshapes - k Boltzmann constant - M _s incident shock Mach number - N noise, root-mean-square signal fluctuation - P static pressure - P ₁ initial pressure of test gas in shock tube - P _a free jet ambient pressure - P _s stagnation pressure - Q electronic quenching rate of excited state - S PLIF signal - t time between shock reflection and image acquisition - T static temperature - T _s stagnation temperature - _a mole fraction of absorbing species     

Stability of a hypersonic shock layer on a flat plateStabilité d'une couche de choc hypersonique sur une plaque plane.

Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine–Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM by the method of electron-beam fluorescence and with theoretical data of other authors. To cite this article: A.A. Maslov et al., C. R. Mecanique 332 (2004).     

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.     

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.     

Mechanisms of detonation transmission in layered H2-O2 mixtures

When a plane detonation propagating through an explosive comes into contact with a bounding explosive, different types of diffraction patterns, which may result in the transmission of a detonation into the bounding mixture, are observed. The nature of these diffraction patterns and the mode of detonation transmission depend on the properties of the primary and bounding explosives. An experimental and analytical study of such diffractions, which are fundamental to many explosive applications, has been conducted in a two channel shock tube, using H₂-O₂ mixtures of different equivalence ratios as the primary and bounding or secondary explosive. The combination of mixtures was varied from rich primary / lean secondary to lean primary / rich secondary since the nature of the diffraction was found to depend on whether the Chapman-Jouguet velocity of the primary mixture,D _p, was greater than or less than that of the secondary mixture,D _s. Schlieren framing photographs of the different diffraction patterns were obtained and used to measure shock and oblique detonation wave angles and velocities for the different diffraction patterns, and these were compared with the results of a steady-state shock-polar solution of the diffraction problem. Two basic types of diffraction and modes of detonation reinitiation were observed. WhenD _p>D _s, an oblique shock connecting the primary detonation to an oblique detonation in the secondary mixture was observed. WithD _p<D _s, two modes of reinitiation were observed. In some cases, ignition occurs behind the Mach reflection of the shock wave, which is transmitted into the secondary mixture when the primary detonation first comes into contact with it, from the walls of the shock tube. In other cases, a detonation is initiated in the secondary mixture when the reflected shock crosses the contact surface behind the incident detonation. These observed modes of Mach stem and contact surface ignition have also been observed in numerical simulations of layered detonation interactions, as has the combined oblique-shock oblique-detonation configuration whenD _p>D _s. WhenD _p>D _s, the primary wave acts like a wedge moving into the secondary mixture with velocityD _p after steady state has been reached, a configuration which also arises in oblique-detonation ramjets and hypervelocity drivers.     

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