Shock jump relations for a dusty gas atmosphere

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows.     

The emergence of a spherical magnetogasdynamic shock wave at the surface of a star

The propagation of a magnetogasdynamic shock wave originating in a stellar interior, is ocnsidered when it approaches the surfaces of the star. The flow behind the shock wave is assumed isothermal rather than adiabatic to stimulate the conditions of large radiative transfer near the stellar surface. The product solution of McVittie has been used to obtain exact solution of the problem. It has been obtained that velocity, density, pressure and magnetic field increases as we move from shock surface towards the nucleus of the star.     

Magnetogasdynamic cylindrical shock wave model in an optically thin atmosphere

Similarity solutions for one-dimensional unsteady isothermal flow of a perfect gas behind a magnetogasdynamic shock wave including the effects of thermal radiation has been investigated in a uniform thin atmosphere. The flow is caused by an expanding piston and the total energy of the flow is assumed to be constant. Radiation pressure and energy have been neglected in comparison to radiation heat flux and the gas is assumed to be grey and opaque.     

Self-similar flows behind shock wave with increasing energy in magnetogasdynamics,I

Self-similar solutions for adiabatic and isothermal flows driven out by a propelling contact surface, moving into a quiet solar wind region, are investigated in the presence of magnetic field. The total energy of the flow between the shock and the contact surface is taken to be time-dependent obeying a power-law. The shock is assumed to be strong and propagating into a perfect gas at rest with non uniform density and magnetic field.     

Strong spherical magnetogasdynamic shock with radiation near the surface of a star

The propagation of a shock-wave, originating in a stellar interior, is considered when it approaches the surface of the star. The flow behind the magnetogasdynamic shock wave is assumed to be spatially isothermal rather than adiabatic to stimulate the conditions of large radiative transfer near the stellar surface. The exact shock-propagation laws obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ₀ ∝ γ^δ     

A self-similar flow behind a spherical shock wave with thermal radiation,I

Similarity solutions, for one-dimensional unsteady flow of a perfect gas behind a spherical shock wave produced on account of a sudden explosion or driven out by an expanding piston including the effects of radiative cooling, are investigated. The shock ahead of the point of explosion or piston is propagating into a transparent medium at rest with non-uniform density. The total energy of the wave is assumed to be time dependent obeying a power law.     

Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics

A self-similar flow of a perfect gas behind a strong shock driven out by a propelling contact discontinuity surface moving with time according to an exponential law in the presence of axial component of the magnetic field is investigated. The flow between the shock and the inner-expanding surface is assumed to be isothermal. The infinite electrically conductive and uniform medium has been taken into consideration.     

Propagation of magneto-radiative shock waves,II

Self-similar motion of a perfect gas behind a cylindrical shock wave with radiation heat flux in the presence of an azimuthal magnetic field have been discussed. The shock is assumed to be propagating in a medium at rest with non-uniform density. The conductivity of the gas is infinite and magnetic permeability is one everywhere. Also, the shock is assumed to be transparent and isothermal.     

An isothermal shock wave in a perfectly-conducting and non-homogeneous stellar interior

In the present paper, we have obtained some exact analytic self-similar solutions for a zero-temperature gradient behind a magnetogasdynamic shock wave produced by stellar explosions. The initial density of the medium is taken to vary as some power of the distance from the point of explosion. The solutions are obtained for the cases when the energy of the shocked gas is constant, the energy is varying, and the shock velocity is constant. General solutions are also obtained. We have also analytically obtained the position of the singular surface behind the shock wave.     

Modelling of self-similar cylindrical shock wave in radiating magnetogasdynamics,I

Self-similar flows of a perfect gas behind a cylindrical blast wave with radiation heat flux in the presence of an azimuthal magnetic field have been investigated. The effects of radiation flux and magnetic field together on the other flow variables have been studied in the region of interest. The magnetic field and density distribution vary as an inverse power of radial distance from the axis of symmetry. The electrical conductivity of the gas is taken to be infinite. The total energy of the flow between the inner expanding surface and the shock is assumed to be constant. We also have supposed the gas to be grey and opaque and the shock to be transparent and isothermal.     

Magneto-radiative shock wave propagation in a conducting plasma

Similarity solutions describing the flow of a perfect gas behind a spherical and cylindrical shock wave in a magnetic field with radiation heat flux have been investigated. The total energy of the expanding wave has been assumed to remain constant. The solutions, however, are only applicable to a gaseous medium where the undisturbed pressure falls as the inverse square of the distance from the line of explosion.     

Self-similar magnetogasdynamic cylindrical shock waves,I

Similarity solutions describing the flow of a perfect gas behind a cylindrical shock wave with transverse magnetic field are investigated in an inhomogeneous medium. The total energy of the shock wave is assumed to be constant. A comparative study has been made between the results with and without magnetic field.     

Self-similar solutions for the blast wave problem in magnetogasdynamics,II

The problem of explosion along a line in a gas cloud in the presence of transverse magnetic field has been considered. Similarity solutions of the adiabatic motion of a gas behind an infinitely strong cylindrical shock wave propagating into an infinitely conducting medium at rest is obtained. Shock radius varies exponentially with time and density is inversely proportional to fourth power of shock radius just ahead of the shock front.     

Isothermal shock waves in uniform atmospheres

Similarity solutions describing the isothermal flow of a perfect gas behind shock waves are investigated for spherical symmetry. The flow is caused by a propelling contact surface (or expanding piston) and its total energy increases as a power of the time. The shock is propagating in a medium at rest with a uniform density.     

The spectacular Supernova SN1987A: Grain evaporation and condensation

Non-similarity solutions of the equations governing the motion of a perfect gas behind a cylindrical shock wave of variable strength have been obtained. These solutions are applicable to both the weak and the strong shocks. The nature of flow and field variables are illustrated through graphs. The total energy of the wave is taken to be constant.     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.     

Propagation of plane relativistic shock waves in a slowly moving medium

Similarity solutions for the propagation of plane relativistic shock waves in a slowly moving medium, where the nucleon number density obeys an exponential law ofx/t, is obtained in this paper. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium.     

A self-similar flow in Generalized Roche model with increasing energy

The self-similar flow of a gas, moving under the gravitational attraction of a central body of fixed mass behind a spherical shock wave driven out by a propelling contact surface into quiet solar wind region, is investigated. The total energy content between the inner expanding surface and the shock front increases with time. In the last section we briefly pose the self-similar isothermal flow of a gas behind a spherical shock wave.     

Strong point-explosions in media characterized by spheroidal symmetry with zero temperature gradient far behind the shock

Strong point-explosion in an axisymmetric medium whose density is decreasing exponentially and in which the flow field has zero temperature gradient sufficiently far behind the shock, is being studied. It is found that the shock velocity is the same as in the adiabatic case in the initial stages, but after a few seconds the shock moves much faster than it would if the flow field behind were adiabatic.     

Shock waves from point-sources in a heat-conducting gas

The shock wave produced by a point source has been studied in a heat-conducting gas medium. The shock is assumed to be strong enough to neglect the ambient gas pressure and the similarity method is used. The distribution of flow quantities behind the shock have been obtained by the numerical integration of a system of ordinary differential equations using the boundary conditions at the shock wave.