Cylindrical Shock Waves Research Articles

Positive Pulsed Streamer in Supercritical Carbon Dioxide

A positive pulsed streamer in a needle-to-plane gap in supercritical carbon dioxide was observed by using a laser schlieren method. The treelike streamer is initiated at a needle electrode when the electric field reaches approximately 9 MV/cm and propagates spatially toward a plane electrode. The streamer is accompanied by the cylindrical and spherical shock waves. A low-density region along the streamer channel decays with time, and no bubble formation occurs finally.

A Self-Similar Flow behind a Magnetogasdynamic Shock Wave Generated by a Moving Piston in a Gravitating Gas with Variable Density: Isothermal Flow

The propagation of a cylindrical (or spherical) shock wave in an ideal gas with azimuthal magnetic field and with or without self-gravitational effects is investigated. The shock wave is driven out by a piston moving with time according to power law. The initial density and the initial magnetic field of the ambient medium are assumed to be varying and obeying power laws. Solutions are obtained, when the flow between the shock and the piston is isothermal. The gas is assumed to have infinite electrical conductivity. The shock wave moves with variable velocity, and the total energy of the wave is nonconstant. The effects of variation of the piston velocity exponent (i.e., variation of the initial density exponent), the initial magnetic field exponent, the gravitational parameter, and the Alfven-Mach number on the flow field are obtained. It is investigated that the self-gravitation reduces the effects of the magnetic field. A comparison is also made between gravitating and nongravitating cases.

Self-similar flow of a rotating dusty gas behind the shock wave with increasing energy, conduction and radiation heat flux

A self-similar solution is obtained for one dimensional adiabatic flow behind a cylindrical shock wave propagating in a rotating dusty gas in presence of heat conduction and radiation heat flux with increasing energy. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The heat conduction is expressed in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α R are assumed to vary with temperature only. In order to obtain the similarity solutions the initial density of the ambient medium is assumed to be constant and the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameters and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.

Landau—Stanyukovich Rule and the Similarity Parameter of Converging Shock Waves in Magnetogasdynamics

Second-kind self-similar solutions to a problem of converging cylindrical shock waves in magnetogasdynamics are investigated. Two trial functions suggested by Chisnell and the shooting method of Landau—Stanyukovich are used to determine the similarity exponent for different values of specific heat ratio γ and the parameter k, where k ∊ (0, 1]. Detailed analyses of flow patterns for different values of adiabatic heat exponent and magnetic field strength are carried out. It is observed that the general behavior of the velocity and density profiles is not affected in a magnetogasdynamics regime whereas there is an increase in the absolute value of the flow parameters with an increase in the magnetic field strength. However, the pressure profiles are greatly affected by the magnetic field interaction.

Simulation of converging cylindrical GPa-range shock waves generated by wire array underwater electrical explosions

Results of one-dimensional numerical simulations of the parameters of the converging strong shock wave generated by electrical underwater explosions of a cylindrical wire array with different array radii and different deposited energies are presented. It was shown that for each wire array radius there exists an optimal duration of the energy deposition into the exploding array, which allows one to maximize the shock wave pressure and temperature in the vicinity of the implosion axis. The simulation results agree well with the 130-GPa pressure in the vicinity of the implosion axis that was recently obtained, which strongly indicates the azimuthal symmetry of the converging shock wave at these extreme conditions. Also, simulations showed that using a pulsed power generator with a stored energy of ~200 kJ, the pressure and temperature at the shock wave front reaches ~220 GPa and 1.7 eV at 0.1 mm from the axis of implosion in the case of a 2.5 mm radius wire array explosion. It was found that, in spite of the complicated equation of state of water, the maximum pressure at the shock wave front at radius r can be estimated as P ≈ (P*(r*/r)α, where P* is the known value of pressure at the shock wave front at radius r* ≥ r and α is a parameter that equals 0.62±0.02. A rough estimate of the implosion parameters of the hydrogen target after the interaction with the converging strong shock wave is presented as well.

Planar and cylindrical magnetosonic solitary and shock waves in dissipative, hot electron-positron-ion plasma

Planar and cylindrical magnetosonic solitary and shock structures are studied in a hot and dissipative plasma consisting of electrons, positrons, and ions. By employing the reductive perturbative method, a modified Korteweg-de Vries Burgers (mKdVB) equation is derived in the limit of low frequency and long wavelength by taking into account viscous dissipation of the three species. The effects of variation of various plasma parameters on the profiles of planar and cylindrical solitary and shock structures are discussed. In the limit, when certain terms of the mKdVB equation are small enough to be treated as perturbation, analytical solutions are obtained and compared with the corresponding numerical ones.

Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux

The propagation of shock waves in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux, which has a variable azimuthally fluid velocity together with a variable axial fluid velocity, is investigated. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The fluid velocities in the ambient medium are assume to be vary and obey power laws. The density of the ambient medium is assumed to be constant, the heat conduction is express in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α R are assumed to vary with temperature and density. In order to obtain the similarity solutions the angular velocity of the ambient medium is assume to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameter and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.

Modeling thunder propagation and detectability on Titan.

This research is part of a study investigating the characteristics of thunder on Saturn’s largest moon, Titan. In tandem with electromagnetic signatures, thunder can corroborate and quantify lightning discharges. A physical model for the propagation of thunder on Titan, based on the most recent data collected by the Cassini–Huygens mission, is being developed. The model approximates a tortuous 20 km cloud-to-ground lightning channel by an angle-wise random walk of small discharge segments, each generating a strong cylindrical shock wave, which acquires an N-wave shape after it travels through the relaxation radius, into the acoustic regime. These acoustic waves are then propagated to the far-field detector where they are added linearly to form long-range thunder. The detectability of thunder signatures by a sensor in Titan’s lower atmosphere depends on the moon’s atmospheric structure. In order to constrain the fraction of acoustic energy reaching a detector in Titan’s troposphere, the model accounts for the upward-refracting sound speed profile up to the inversion point at ∼45 km and also for ground effects. The sound speed and attenuation are computed along the length of the lightning channel (20 km) using altitude-dependent pressure, density, and temperature measurements by Cassini–Huygens, as well as thermophysical parameters (specific heats, viscosity, thermal conductivity, and diffusivity) extracted from NIST’s Chemistry WebBook.

Magnetogasdynamic shock wave generated by a moving piston in a rotational axisymmetric isothermal flow of perfect gas with variable density

The propagation of a strong cylindrical shock wave in an ideal gas with azimuthal magnetic field, and with or without axisymmetric rotational effects, is investigated. The shock wave is driven out by a piston moving with time according to power law. The ambient medium is assumed to have radial, axial and azimuthal component of fluid velocities. The fluid velocities, the initial density and the initial magnetic field of the ambient medium are assumed to be varying and obey power laws. Solutions are obtained, when the flow between the shock and the piston is isothermal. The gas is assumed to have infinite electrical conductivity and the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. It is expected that such an angular velocity may occur in the atmospheres of rotating planets and stars. The shock wave moves with variable velocity and the total energy of the wave is non-constant. The effects of variation of the initial density and the Alfven-Mach number on the flow-field are obtained. A comparison is also made between rotating and non-rotating cases.

Shock wave initiated by an ion passing through liquid water

We investigate the shock wave produced by an energetic ion in liquid water. This wave is initiated by a rapid energy loss when the ion moves through the Bragg peak. The energy is transferred from the ion to secondary electrons, which then transfer it to the water molecules. The pressure in the overheated water increases by several orders of magnitude and drives a cylindrical shock wave on a nanometer scale. This wave eventually weakens as the front expands further; but before that, it may contribute to DNA damage due to large pressure gradients developed within a few nanometers from the ion's trajectory. This mechanism of DNA damage may be a very important contribution to the direct chemical effects of low-energy electrons and holes.

Shock dynamics of strong imploding cylindrical and spherical shock waves with real gas effects

Strong cylindrical and spherical shock implosion in a monatomic gas is considered. A simple solution is obtained by Whitham’s geometrical shock dynamics approach modified to account for the real gas effects. The real gas effects are introduced by jump relations over the shock and include several levels of ionization, Coulomb interaction as well as internal energy of the excited electrons. It is shown that ionization has a major effect on temperature and density behind the converging shock as well as on the shock acceleration. The temperature and acceleration being substantially reduced and density substantially increased as compared to the ideal nonionizing case. The ionization effect on the pressure behind the converging shock is less pronounced. It is also shown that for the considered test case of initial Mach number M0=8 the gas becomes completely ionized behind the spherical shock at approximately 1% of the initial radius from the focal point and its speed being decreased by a factor of 1.8 as compared to the ideal case.

Analytical Solution of Converging Shock Wave in Magnetogasdynamics

In this paper, a similarity solution to a problem in magnetogasdynamics with strong converging cylindrical shock wave is examined. An analytical description of converging shock waves is presented by replacing the previous approach for numerical solutions of the ordinary differential equations with a theoretical study of the singular points of the differential equations. A study of singular points of the system of differential equations leads to an analytic description of the flowfield and a determination of the similarity exponent. The influences of adiabatic heat exponent and magnetic field strength on the flow pattern for various cases are assessed. The general behavior of the velocity and density distribution remains unaffected. However, the pressure profiles are greatly affected by the magnetic field interaction.

Similarity solutions for imploding shocks in non-ideal magnetogasdynamics

In the present article, similarity solutions of second kind to a problem of imploding cylindrical shock wave in non-ideal magnetogasdynamics are investigated. The equation of state of the medium is assumed to be in the form of the Mie-Gruneisen type. A numerical study of singular points of the differential equations leads to determination of the similarity exponent. Numerical description of the flow field has been presented in non-ideal magnetogasdynamics. The results obtained are compared with the numerical solution obtained by using CCW approximation method. Detailed studies are carried out for two different physically meaningful non-ideal medium in the presence of magnetic field. Also, the effect on magnetic field of flow variables such as density, velocity, pressure and magnetic pressure behind the wave front is illustrated through figures.

A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

A self similar method is used to analyze numerically the one-dimensional, unsteady flow of a strong cylindrical shock wave driven by a piston moving with time according to an exponential law in a plasma of constant density. The plasma is assumed to be a non-ideal gas with infinite electrical conductivity permeated by an axial magnetic field. Numerical solutions in the region between the shock and the piston are presented for the cases of adiabatic and isothermal flow. The general behaviour of density, velocity, and pressure profiles remains unaffected due to presence of magnetic field in non-ideal gas. However, there is a decrease in values of density, velocity and pressure in case of magnetogasdynamics as compared to non-magnetic case. It may be noted that the effect of magnetic field on the flow pattern is more significant in case of isothermal flow as compared to adiabatic flow. The effect of non-idealness, specific heat exponent and magnetic field strength on the variation of shock strength across the shock front is also investigated.

Extreme water state produced by underwater wire-array electrical explosion

The generation of an extreme water state (130 GPa, 5000 K, and 3.4 g/cm3) which is characterized as dense plasma at the axis of a converging shock wave is reported. A 4 kJ pulse generator was used to explode a 40 Cu-wire array, generating a cylindrical shock wave. The measured shock wave trajectory and energy deposited into the water flow were used in hydrodynamic simulations coupled with the equation of state to determine the water parameters. The temperature estimated using the emission data of water in the vicinity of the implosion axis agrees with the simulation results, indicating shock wave symmetry in such extreme conditions.

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas, which has a variable azimuthal and axial fluid velocity. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equilibrium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. The fluid velocities in the ambient medium are assumed to obey exponential laws. The shock wave moves with variable velocity. The effects of variation of the mass concentration of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times. Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.

Thermal radiation from a converging shock implosion

High energy concentration in gas is produced experimentally by focusing cylindrical shock waves in a specially constructed shock tube. The energy concentration is manifested by the formation of a hot gas core emitting light at the center of a test chamber at the instant of shock focus. Experimental and numerical investigations show that the shape of the shock wave close to the center of convergence has a large influence on the energy concentration level. Circular shocks are unstable and the resulting light emission varies greatly from run to run. Symmetry and stability of the converging shock are achieved by wing-shaped flow dividers mounted radially in the test chamber, forming the shock into a more stable polygonal shape. Photometric and spectroscopic analysis of the implosion light flash from a polygonal shock wave in argon is performed. A series of 60 ns time-resolved spectra spread over the 8 μs light flash shows the emission variation over the flash duration. Blackbody fits of the spectroscopic data give a maximum measured gas temperature of 5800 K in the beginning of the light flash. Line emissions originating in transitions in neutral argon atoms from energy levels of up to 14.7 eV were also detected.

Propagation of a cylindrical shock wave in a rotating dusty gas with heat conduction and radiation heat flux

A self-similar solution for the propagation of a cylindrical shock wave in a dusty gas with heat conduction and radiation heat flux, which is rotating about the axis of symmetry, is investigated. The shock is assumed to be driven out by a piston (an inner expanding surface) and the dusty gas is assumed to be a mixture of non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The heat conduction is expressed in terms of Fourier's law and radiation is considered to be of diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient αR are assumed to vary with temperature and density. Similarity solutions are obtained, and the effects of variation of the parameter of non-idealness of the gas in the mixture, the mass concentration of solid particles and the ratio of density of solid particles to the initial density of the gas are investigated.

Self Similar Solution of Strong Cylindrical Shock Wave in Magnetogasdynamics: Lagrangian Description

In the present paper the self similar solution of strong cylindrical shock wave in magnetogasdynamics using Langrangian mass co-ordinate has been studied. Analytic solutions of governing equations in closed form are obtained. The strong cylindrical shock wave generated by sudden line source explosion in an inhomogeneous medium of infinite electrical conductivity has been studied. The influence of specific heat ratio and magnetic field strength on flow variables for various cases is assessed. The general behaviour of velocity distribution remains unaffected. However, the density and pressure profiles are significantly affected in presence magnetic field interaction.

Cylindrical and spherical dust-acoustic shock waves in a strongly coupled dusty plasma

Cylindrical and spherical dust-acoustic (DA) shock waves propagating in a strongly coupled dusty plasma are theoretically investigated. The generalized hydrodynamic model, in which highly charged dust are treated as strongly coupled, but electrons and ions are treated as weakly coupled, is employed. The modified Burgers equation, which is derived by using the reductive perturbation technique, is numerically solved to examine the effects of nonplanar cylindrical and spherical geometries on the basic features of the DA shock waves that are formed due to a strong correlation among highly negatively charged dust. It is shown that the effects of nonplanar cylindrical and spherical geometries significantly modify the basic properties of the DA shock structures. The implications of our results in laboratory dusty plasma experiments are briefly discussed.