Shock wave structure in simple liquids

The shock wave structure in a liquid is studied by a molecular dynamics simulation method. The interaction between atoms is described by the Lennard-Jones (6–12) potential. In contrast to earlier works, the simulation is performed in a reference frame tied to the shock wave front. This approach reduces non-physical fluctuations and makes it possible to calculate the distribution functions of the kinetic and potential energy for several cross sections within the shock layer. The profiles of flow variables and their fluctuations are found. The surface tension connected with pressure anisotropy within the shock front is calculated. It is shown that the main contribution to the surface tension coefficient comes from the mean virial. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 722–727 (10 May 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T _eff ² behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number. Zh. éksp. Teor. Fiz. 115, 846–864 (March 1999)     

Asymmetric interaction of blast waves and shock waves with a body flying at supersonic velocity

The problems of asymmetric interaction of a blunt wedge traveling at supersonic velocity with a cylindrical blast wave from a point explosion and with a plane shock wave are investigated by numerical simulation. The evolution of the interaction flow is analyzed, and data are obtained on how the structure of the shock layer changes. Zh. Tekh. Fiz. 69, 15–19 (May 1999)     

Problems of interpretation of holographic interferograms near shock wave fronts

A method of avoiding ambiguity in the interpretation of interferograms near a shock wave front is proposed. The method is based on combining the double-exposure schlieren method and holographic interferometry. Relations for calculating, on the basis of data obtained by analyzing double-exposure schlieren photographs, both the density at the shock wave front and the gradient of the density directly behind the front, which is necessary for calculating the shifts of the interference fringes near the shock wave front, are presented. Zh. Tekh. Fiz. 68, 88–91 (September 1998)     

Effect of multiple ion reflections on the structure of an ion-sound shock wave

It is shown that multiple ion reflection, arising as a result of collisional dissipation, from a shock front can produce an ion-sound shock wave with an arbitrarily large Mach number. For an exponentially small number of reflected ions, the ion-sound shock wave “degenerates” into a collisionless quasishock wave. The comparative role of viscosity and sound dispersion with different initial nonisothermality of the plasma is discussed. Zh. Tekh. Fiz. 69, 52–56 (December 1999)     

单晶铜中冲击波阵面结构的数值模拟研究

 用分子动力学方法模拟计算了在初始温度为0 K时单晶铜中的冲击波结构,相互作用势采用铜的嵌入原子势（EAM）,模拟计算结果表明即使是在初始温度为0 K的FCC晶体中,冲击波波阵面后的区域也会向平衡态演化。局域分析表明冲击波阵面后区域的压力、粒子速度、应变和温度随时间逐步变化到稳定态,在所研究的冲击波强度（约262 GPa）下,波后区域的平均压力、粒子速度、应变均在约1 ps内逐渐上升并达到稳定值。动能温度在波阵面处始终为最大值,随着冲击波的传播,波后非零温度区域逐渐扩大,不同时刻的粒子速度分布函数说明波后区域逐渐向热力学平衡态演化,并最终达到热力学平衡,进一步的分析说明局域平衡是系统向平衡态演化的基本过程。     

Optical study of parameters of the passage of a shock wave from air to water

A study is made of the penetration of shock waves from air into water. The shock wave in air is generated as a result of dielectric breakdown induced by pulsed CO₂-laser radiation. A combination of the double-exposure shadow method and holographic interferometry is used to measure the shock-wave parameters. Density and pressure profiles behind the wave front are obtained at different times after onset of breakdown. It is shown experimentally that as the wave passes through the interface from the air to the water, there is a fourfold amplification of the pressure in the shock wave front. Estimates of the width of the shock wave front formed in the water are given in the context of studies of large-scale explosion processes. It is shown that simple empirical dependences, established in the course of studies of large-scale explosions, are also valid with certain corrections for microscopic laboratory experiments. Zh. Tekh. Fiz. 68, 39–43 (August 1998)     

Dissipative Instability of Shock Waves

A new condition is obtained for the linear instability of a plane front of an intense shock wave in an arbitrary medium, which is determined by the finiteness of the viscosity. It is shown that the shock front instability occurs due to dissipative instability of the flow behind the front, which is analogous to the flow instability in the boundary layer. It is found that in the low-viscosity limit, one-dimensional longitudinal perturbations increase much faster than two-dimensional (corrugation) perturbations. The results are compared with the available data of experimental observation and numerical simulation of instability of shock waves. The comparison shows a better agreement between the new absolute shock instability as compared to the condition of such instability in the classical D’yakov theory disregarding viscosity.     

Structure of a collisionless shock front with relativistically accelerated particles

A nonlinear self-consistent analytic theory is developed to describe the front structure of a strong magnetohydrodynamic (MHD) collisionless shock wave that generates accelerated particles (including ultrarelativistic particles). The theory is used to predict the degree of compression of matter at the plane front of such a wave, which can greatly exceed compression at an ordinary gas-dynamic front, and also the velocity, density, and pressure profiles. The energy spectrum of the accelerated particles, which is produced by the complex velocity profile at the shock transition, is determined self-consistently. New nonlinear effects are predicted that have not been discussed previously in the literature: a strong dependence of the particle acceleration regimes on the rate of injection; the existence of several regimes within a certain range of injected powers with differing spectra of accelerated particles, shapes of the shock transition profile, and magnitudes of compression of the medium; and the possibility of spontaneous jumps between different states of the shock transition. The question of stability of these states is discussed. For the values of the system parameters used here, the nonlinear regimes correspond to extremely low injection rates, of order 10⁻²–10⁻¹⁰ of the plasma flux density advancing into the front, and to exponents of the power-law spectra of accelerated particles between 5 and 3. Zh. éksp. Teor. Fiz. 112, 1584–1602 (November 1997)     

Numerical Simulation of the Formation of Granular Shock Wave Over Cylindrical Obstacle

A two dimensional (2‐D) stream of granular flow with zero initial granular temperature passing over a cylindrical obstacle is simulated by means of both molecular dynamics (MD) simulation and finite volume method (FVM). In experiments, a bow‐shaped shock wave with higher area fraction forms in front of the obstacle that was reproduced in our simulations. Due to the different circumstances to which particles are subjected, the granular flow is divided in two zones. One is undisturbed where quantities, such as space fraction (volume fraction for 3‐D and area fraction for 2‐D geometries), velocity and granular temperature are uniformly distributed and the other is called the shock wave zone. In this region, the values of the space fraction increases and the velocity of particles changes. From the MD simulation, it is found that the area fraction of the shock wave depends on surface roughness, coefficient of restitution (COR) of particles, the obstacle diameter as well as velocity of the granular stream, and a triangular region forms with almost zero velocity, and granular temperature forms in front of the cylindrical obstacle. The bigger is the size of the obstacle, the more stable this region is. In FVM simulations solid phase velocity and area fraction distributions similar to the MD simulation results are obtained for proper parameters.     

Influence of local dispersion on transient processes accompanying the generation of rf radiation by an electromagnetic shock wave

Transient processes accompanying the conversion of a video pulse into a radio pulse in a nonlinear transmission line having hysteretic properties are studied. It is established that the transition process leading to the establishment of “steady-state” (close in amplitude) oscillations has a minimum when the electromagnetic shock wave front is phase-matched with the wave excited by it at a frequency near the minimum local dispersion of the group velocity. Zh. Tekh. Fiz. 68, 89–95 (January 1998)     

Transmission times of wave packets tunneling through barriers

The transmission of wave packets through barriers by tunneling is studied in detail by the method of quantum molecular dynamics. The distribution of the arrival times of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The average position and average momentum of the packet and their spread are investigated. It is found that below the barrier a part of the packet is reflected, and a Gaussian barrier increases the average momentum of the transmitted packet and its spread in momentum space. Zh. éksp. Teor. Fiz. 115, 1872–1889 (May 1999)     

Structure and parameters of the shock layer formed when a supersonic underexpanded jet interacts with a counterpropagating hypersonic flow in the transition regime

The method of molecular dynamics (the Bird system) has been used to mathematically model a planar, strongly underexpanded supersonic jet that encounters a hypersonic flow of rarefied gas. Particular attention is paid to the structure and parameters of the shock layer close to the plane of symmetry. The results of calculations are presented for currents of a monatomic gas, simulating argon, with a Mach number of the external flow of M_∞=5.48, a Mach number at the nozzle edge of M_a=1, a ratio of the density at the nozzle edge to the density of the unperturbed flow equal to 130, and various stagnation temperatures of the external flow and of the jet. The evolution of the structure and the parameters of the shock layer as the Knudsen number Kn_∞ varies from 0.02 to 0.35 is considered. The results are compared with the data calculated for the shock layer when argon flows around thermally insulated cylinders. The main features and regularities of the relaxation of the translational degrees of freedom of the gas for external and jet flows are considered. Data are presented on the form of the distribution function over velocities and its evolution as gas moves through the shock layers. Zh. Tekh. Fiz. 68, 13–18 (July 1998)     

The characteristics of laser‐driven shock wave investigated by time‐resolved Raman spectroscopy

An accurate and simple method, Raman peak‐shift simulation, is proposed to determine the characteristics of a laser‐driven shock wave. Using the principle of the Raman peaks shifting at high pressure and the pressure distribution in the gauge layer, the profile of the Raman peak can be numerically simulated. Combined with time‐resolved Raman spectroscopy, some main characteristics of the shock wave were determined. In the experiment, polycrystalline anthracene was used as the pressure gauge. The pump–probe technique was used to obtain the time‐resolved Raman spectra of anthracene under shock loading. The velocity of the shock wave, the peak pressure and the rise time of the shock front were determined by simulating the experimental spectra numerically. The result shows that the method of Raman peak‐shift simulation is effective in obtaining the characteristics of a laser‐driven shock wave. Copyright © 2010 John Wiley & Sons, Ltd.     

Behavior of aluminum near an ultimate theoretical strength in experiments with femtosecond laser pulses

The dynamics of the motion of the free surface of micron and submicron films under the action of a compression pulse excited in the process of femtosecond laser heating of the surface layer of a target has been investigated by femtosecond interferometric microscopy. The relation between the velocity of the shock wave and the particle velocity behind its front indicates the shock compression to 9–13 GPa is elastic in this duration range. This is also confirmed by the small (≤1 ps) time of an increase in the parameters in the shock wave. Shear stresses reached in this process are close to their estimated ultimate values for aluminum. The spall strength determined at a strain rate of 10⁹ s⁻¹ and a spall thickness of 250–300 nm is larger than half the ultimate strength of aluminum.     

On the mechanism of the deflagration-to-detonation transition in a hydrogen-oxygen mixture

The flame acceleration and the physical mechanism underlying the deflagration-to-detonation transition (DDT) have been studied experimentally, theoretically, and using a two-dimensional gasdynamic model for a hydrogen-oxygen gas mixture by taking into account the chain chemical reaction kinetics for eight components. A flame accelerating in a tube is shown to generate shock waves that are formed directly at the flame front just before DDT occurred, producing a layer of compressed gas adjacent to the flame front. A mixture with a density higher than that of the initial gas enters the flame front, is heated, and enters into reaction. As a result, a high-amplitude pressure peak is formed at the flame front. An increase in pressure and density at the leading edge of the flame front accelerates the chemical reaction, causing amplification of the compression wave and an exponentially rapid growth of the pressure peak, which “drags” the flame behind. A high-amplitude compression wave produces a strong shock immediately ahead of the reaction zone, generating a detonation wave. The theory and numerical simulations of the flame acceleration and the new physical mechanism of DDT are in complete agreement with the experimentally observed flame acceleration, shock formation, and DDT in a hydrogen-oxygen gas mixture.     

Statistical characteristics of an intense wave behind a two-dimensional phase screen

An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed, in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained. Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because of random focusing effects.     

On the origin of nonequilibrium radiation from iodine molecules at the shock wave front

The direct simulation Monte Carlo (DSMC) method is used for modeling the problem on the shock wave front in the 0.7%I₂-99.3%He mixture for a shock wave Mach number of 4.85. The choice of this system is due to the fact that intense radiation peaks have been observed experimentally precisely in such systems and it has been convincingly proven that this effect is induced by high-energy collisions between I₂ molecules. The results of simulation provide additional sound arguments in favor of the conclusion that the translational nonequilibrium state at the shock wave front in a light gas with a small admixture of heavy nonreacting molecules may cause the experimentally observed nonequilibrium radiation peaks.     

On the possibility of controlling transonic profile flow with energy deposition by means of a plasma-sheet nanosecond discharge

A way of effectively affecting the gasdynamic structures of a transonic flow over a surface by means of instantaneous local directed energy deposition into a near-surface layer is proposed. Experimental investigations into the influence of a pulsed high-current nanosecond surface discharge of the “plasma sheet” type on gas fast flow with a shock wave near the surface are carried out. The self-localization of energy deposition into a low-pressure region in front of the shock wave is described. Based on this effect, a facility for automated energy deposition into a dynamic region bounded by the moving shock front can be designed. The limiting value of the specific energy deposition on the surface in front of the shock wave is found. With the help of the direct-shadow method, an unsteady quasi-two-dimensional discontinuous flow arising when a plasma sheet is initiated on the wall in a flow with a plane shock wave is studied. By numerically solving the two-dimensional nonstationary equations of gas dynamics, the influence of the energy of a pulsed nanosecond discharge, which is applied in the frequency regime, on the aerodynamic characteristics of a high-lift profile is investigated. It is ascertained that the energy delivered to the gas before the closing shock wave in a local supersonic region that is located in the neighborhood of the profile contour in zones extended along the profile considerably decreases the wave drag of the profile.     

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.