The structure of shock fronts in various gases

The optical reflectivity of shock fronts in A, N₂, O₂, CO, CO₂, N₂O, CH₄, Cl₂ and HCl have been studied. The thickness of shock fronts in A up to the Mach number M = 1·55 is in agreement with the theory of Gilbarg and Paolucci. The rotational relaxation time is about 5·5 collisions in N₂ and equal to or less than that in the other gases. However, for stronger shocks N₂ does not appear to reach rotational equilibrium in the shock front and a qualitative theoretical discussion of this phenomenon is presented. In HCl there appears to be over-excitation of rotation in the shock front. There is no vibrational excitation of any of the gases.     

Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats

Specific features of shock wave interaction in a viscous heat-conducting gas with a low ratio of specific heats are numerically studied. The case of the Mach reflection of shock waves with a negative angle of the reflected wave with respect to the free-stream velocity vector is considered, and the influence of viscosity on the flow structure is analyzed. Various issues of nonuniqueness of the shock wave configuration for different Reynolds numbers are discussed. Depending on the initial conditions and Reynolds numbers, two different shock wave configurations may exist: regular configuration interacting with an expansion fan and Mach configuration. In the dual solution domain, a possibility of the transition from regular to the Mach reflection of shock waves is considered.     

Grid turbulence and its interaction with a shock wave

Turbulent fluctuations of density and pressure in air and argon in a shock tube have been investigated as well as their interaction with a shock wave reflected from a perforated plate at the end of a shock tube. Air and argon were used as test gases. The Mach number of the incident shock was 1.9–3.9, that one of the reflected shock was 1.4–2.4. The turbulent length scale behind the incident shock was measured as well as that one behind the reflected shock. The last value is a few times less than the former. It was established that there is overpressure in the turbulent flow behind the reflected shock. The value of the overpressure is 12% in argon and 9% in air.     

Molecular dynamics simulations of microscopic structure of ultra strong shock waves in dense helium

Hydrodynamic properties and structure of strong shock waves in classical dense helium are simulated using non-equilibrium molecular dynamics methods. The shock speed in the simulation reaches 100 km/s and the Mach number is over 250, which are close to the parameters of shock waves in the implosion process of inertial confinement fusion. The simulations show that the high-Mach-number shock waves in dense media have notable differences from weak shock waves or those in dilute gases. These results will provide useful information on the implosion process, especially the structure of strong shock wave front, which remains an open question in hydrodynamic simulations.     

Stationary collisionless shock waves in an initial plasma with high ion temperature

Stationary collisonless shock waves propagating perpendicularly to an initial magnetic field are produced by the fast-rising magnetic field \((\dot B = 7 \cdot 10^{10} G/sec)\) of a theta pinch (coil diameter 16 cm, coil length 60 cm). The initial plasma is produced by a fast theta pinch discharge (810 kHz). At filling pressures between 5 and 15 mtorr H₂ or D₂ the degree of ionization is about 50%. By choosing the filling pressure properly it is possible to trap a homogeneous magnetic field. The ions of this plasma have a temperature of a few 10 eV. This value is much higher than the electron temperature and results in a local plasmaβ between 0.3 and 5. In this initial plasma stationary collisionless shock waves with Mach numbers between 1.5 and 5 are observed. The snow-plough model is used to derive conditions for the stationary state, attainable Mach number, and velocity of the front which relate the external magnetic field and the parameters of the initial plasma. Strong collisionless dissipation can be demonstrated by measuring the profiles of magnetic field, density, and electron temperature of the shock waves. For the electrons this dissipation mechanism can be described by an effective collison frequency. This phenomenologically introduced frequency determines the width of the shock front at least for subcritical shock waves. It exceeds the classical electron-ion collision frequency by 1–2 orders of magnitude and is roughly equal to one-third of the ion plasma frequency. The ion temperature can be estimated from the steady state conservation relations. The ions are heated in the two degrees of freedom perpendicular to the magnetic field. For shock waves with Mach numbers below the critical one the ions seem to be heated merely adiabatically. In strong shock waves this heating is considerably exceeded, and for high Mach numbers it yields ion temperatures up to about 500 eV. Finally, semi-empirical formulas are derived to estimate the possible temperatures of electrons and ions behind the shock front.     

Time evolution of collisionless shock in counterstreaming laser-produced plasmas

We investigated the time evolution of a strong collisionless shock in counterstreaming plasmas produced using a high-power laser pulse. The counterstreaming plasmas were generated by irradiating a CH double-plane target with the laser. In self-emission streaked optical pyrometry data, steepening of the self-emission profile as the two-plasma interaction evolved indicated shock formation. The shock thickness was less than the mean free path of the counterstreaming ions. Two-dimensional snapshots of the self-emission and shadowgrams also showed very thin shock structures. The Mach numbers estimated from the flow velocity and the brightness temperatures are very high.     

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)     

Three-dimensional reactive shock bifurcations

We model interactions of a premixed flame with incident and reflected shocks in a rectangular shock tube using three-dimensional (3D) reactive Navier–Stokes numerical simulations. Shock-flame interactions occur in the presence of boundary layers that cause the reflected shock to bifurcate and form a reactive shock bifurcation (RSB), which contains a flame in the recirculation zone behind the oblique shock. The recirculation zone acts as a flame holder thus attaching the flame to the shock in the vicinity of the wall, and providing a mechanism for a detonationless supersonic flame spread. The accelerated burning induced by an RSB, and Mach stems that may result from RSB–RSB interactions, promote hot-spot formation, and eventually accelerate deflagration-to-detonation transition. Schlieren-type images generated from the simulation results show that the 3D structure of an RSB may not always be easily recognized in experiments if the RSB is attached to the surface of the observation window. The main 3D effect observed in the simulations is caused by the presence of the second no-slip wall in a 3D rectangular channel. Two RSBs that form at adjacent walls interact with each other and produce an oblique Mach stem between two oblique shocks. The oblique Mach stems then interacts with a central Mach stem that forms near symmetry plane, and this interaction creates a hot-spot that leads to a detonation initiation.     

Shock Wave Propagation in Gases and Low Temperature Plasma Under Subatmospheric Pressure

Results of investigation of the shock wave dynamics under subatmospheric pressure in neutral gases and weakly ionized low temperature plasma are presented. The characteristics of spherical and plane configuration shock wave excitation and propagation in gases in the pressure region 1 Torr < p <100 Torr are studied. The same is done for the plane configuration shock wave in weakly ionized plasma in the pressure region 1 Torr < p <10 Torr. It is shown that when p = 3 Torr it is still possible to fix successfully the shock wave appearance and propagation in various neutral gases. The pressure dependence of the shock wave propagation velocity and amplitude is determined experimentally. It is shown that when the pressure decreases the shock wave amplitude decrease and the increase of the Mach number take place. In the case of plane shock wave Mach number reaches the value M = 5.2 under the pressure p = 3 Torr. As for shock wave propagation in low temperature plasma, our experiments showed a significant decrease of wave amplitude and simultaneous increase of its velocities up to 35 wave velocity is related to the heating of neutral gases in plasma.     

Waves in interplanetary shocks: a wind/WAVES study

We describe results from the first statistical study of waveform capture data during 67 interplanetary (IP) shocks with Mach numbers ranging from approximately 1-6. Most of the waveform captures and nearly 100% of the large amplitude waves were in the ramp region. Although solitary waves, Langmuir waves, and ion acoustic waves (IAWs) are all observed in the ramp region of the IP shocks, large amplitude IAWs dominate. The wave amplitude is correlated with the fast mode Mach number and with the shock strength. The observed waves produced anomalous resistivities from approximately 1-856 Omega.m (approximately 10(7) times greater than classical estimates.) The results are consistent with theory suggesting IAWs provide the primary dissipation for low Mach number shocks.     

Double-diaphragm shock tube at the Ioffe Physicotechnical Institute

Results of numerical calculations of the flow in a double-diaphragm shock tube with a tailored contact surface are reported. The calculations were carried out using a model of an ideal shock tube allowing for the real properties of the driver gas at high pressures and equilibrium thermodynamics of the processes behind the shock waves at Mach numbers M _s1 of the shock wave in the working gas varying in the range 5–25. Flow regimes with a tailored contact surface were obtained for Mach numbers M _s1=6.3, 11, and 15 using the double-diaphragm shock tube at the Ioffe Physicotechnical Institute. Under these conditions, the parameters of the working gas were kept constant for more than 1 ms. The calculated data were compared with the experimental results and it was shown that the calculated data may be used to determine the section lengths in a double-diaphragm shock tube and to estimate its operating time. The calculated values of the initial pressure in the sections of the tube were substantially lower than those achieved experimentally. Measurements were made of the static pressure along the axis of a conical nozzle during the expansion of hydrogen (initial temperature T ₀=293 K) and shock-heated nitrogen (T ₀=4000 K). It is found that the expansion of hydrogen is accompanied by deactivation of the rotational degrees of freedom, and that partial freezing of the vibrational degrees of freedom takes place in the nitrogen stream. Zh. Tekh. Fiz. 67, 88–95 (November 1997)     

Study of shock waves interacting with Ar and N<Subscript>2</Subscript> low pressure dc discharges

Acoustical shock waves (Mach number <2) generated in situ by spark gap are propagated in weakly ionized dc discharges working at low pressure (399 Pa) and containing either Ar or N₂ gas. The electrical characterization and the laser deflection technique are used to measure the characteristics of dc discharge (such as voltage, resistance and power of discharge) and the structure and velocity of shock wave, respectively. The results stress the importance of atomic and molecular nature of the gases in affecting the power deposition and the shock wave properties.     

Shock wave propagation in gases under subatmospheric pressure

In the present paper the results of the experiments on the shock wave dynamics under subatmospheric pressure in neutral gases are presented. The characteristics of spherical and plane configuration shock wave excitation and propagation are studied in the pressure region 1 torr<p<760 torr. It is shown that whenp=3 torr it is still possible to fix successfully the shock wave appearance and propagation in various neutral gases. The pressure dependence of the shock wave propagation velocity and amplitude is determined experimentally. It is shown that when the pressure decreases the shock wave amplitude decreases and an increase of the Mach number takes place. In the case of plane shock wave the Mach number reaches the valueM=5.2 under the pressurep=3 torr.     

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

We study the propagation of anisotropic sound and shock waves in dipolar Bose-Einstein condensate in three dimensions (3D) as well as in quasi-two (2D, disk shape) and quasi-one (1D, cigar shape) dimensions using the mean-field approach. In 3D, the propagation of sound and shock waves are distinct in directions parallel and perpendicular to dipole axis with the appearance of instability above a critical value corresponding to attraction. Similar instability appears in 1D and not in 2D. The numerical anisotropic Mach angle agrees with theoretical prediction. The numerical sound velocity in all cases agrees with that calculated from Bogoliubov theory. A movie of the anisotropic wave propagation in a dipolar condensate is made available as supplementary material.     

入射激波诱导环氧丙烷爆炸特征研究

用自行设计激波管点火测试技术,实验研究了温度范围760-1380K间入射激波诱导下环氧丙烷的点火机理。利用激波管压力传感器测定了H*(486.1) 和O (470.5nm)随激波诱导强度变化的点火时间特征。实验结果表明：在低马赫数下氢氧自由基出现时间较接近,1.5-2.5马赫间随激波诱导强度增大而线性减小;而马赫大于2.5后,氧自由基的出现时间迅速减小,是由于高活化能的氧自由基的点火时间对强激波较敏感,而诱导强度大于3.5马赫后对两者点火影响区别就下明显了。实验数据将有益于含能材料点火时间的研究。     

入射激波诱导环氧丙烷爆炸特征研究

用自行设计激波管点火测试技术,实验研究了温度范围760-1380K间入射激波诱导下环氧丙烷的点火机理。利用激波管压力传感器测定了H*(486.1) 和O (470.5nm)随激波诱导强度变化的点火时间特征。实验结果表明：在低马赫数下氢氧自由基出现时间较接近,1.5-2.5马赫间随激波诱导强度增大而线性减小;而马赫大于2.5后,氧自由基的出现时间迅速减小,是由于高活化能的氧自由基的点火时间对强激波较敏感,而诱导强度大于3.5马赫后对两者点火影响区别就下明显了。实验数据将有益于含能材料点火时间的研究。     

On a supersonic flow of ions in a light gas

The possibility of attainment of large Mach numbers is analyzed for the case of heavy ions drifting in a light gas. Under conditions typical of experiments with dust structures in plasmas, the use of the mixture of light and heavy gases is shown to make it possible to suppress the ion heating in the electric field and to form supersonic flows characterized by large Mach numbers. The drift of xenon ions in helium is considered as an example.     

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

A kinematic approach is considered whereby the wavenumber jump conditions in conjunction with the appropriate dispersion relations is applied to the investigation of the normal and oblique interaction of a plane acoustic wave with a plane shock wave. For the normal interaction of an acoustic wave with a stationary plane shock a logarithmic shift in the wave spectra is obtained. For the normal interaction with a moving shock front it is shown that for shock Mach numbers above a critical value, the frequency of the transmitted wave becomes negative. This results in the fact that the crests of the transmitted signal arrive at a fixed observer in a reverse order to their generation. Finally, the oblique interaction of an acoustic wave with a stationary shock is considered. The “Snell's Law” for the transmitted wave is derived and two special angles of incidence are identified. The first is a no-refraction angle: i.e., the transmitted wave angle is the same as the incident wave angle. The second is a critical angle such that for incident angles greater than this critical angle there is no transmitted wave. A necessary and sufficient condition for the existence of a transmitted wave is derived in terms of the speed of sound and Mach number of the fluid and the frequency and tangential wavenumber component of the incident wave.The dynamics aspects of the interaction concerning the determination of the frequency independent transmission coefficients and shock displacements are determined for the simple case of the normal interaction with a moving shock as an illustration.     

Flow visualization and density measurement of compressible flows by a laser speckle method

Laser speckle method is a well known technique that is useful for both visualization and quantitative measurement. This technique was applied to the density measurement of Mach reflection of shock waves in the present experiment. The Object of the measurement is the density field of simple Mach reflection in relatively low shock Mach number. The non-uniform flow field is divided into three regions by incident, Mach and reflected shock waves. A shock tube was employed in the present experiment. Wedges of 20 degrees and 45 degrees were placed in the test section. YAG laser was employed as a light source. Speckle photograph was taken by a digital still camera. Simple subtraction between the reference and flow images shows a shock pattern and a degree of the correlation of speckle pattern in the flow field. Thus, we can obtain a visualized flow image showing a configuration of Mach reflection from speckle photograph. Speckle photographs which was obtained in the experiments were processed with cross-correlation method. A reconstructed density gradient vector map of Mach reflection was obtained. Comparing the experimental result with numerical one, the measured density gradient shows a good agreement with theoretical prediction.     

Surface tension and instability of shock waves in gases

The pressure anisotropy within a shock layer results in an additional property of the shock wave: the surface tension. Its value amounts to 10³ dyn/cm for Mach number 10. The surface tension term in the characteristic equation causes an absolute shock wave instability in the spontaneous sound emission regime.