Similarity solutions are obtained for unsteady, one-dimensional self-similar flow behind a strong shock wave, driven by a moving piston, in a dusty gas. The dusty gas is assumed to consist of a mixture of small solid particles and a non-ideal gas, 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. Solutions are obtained under both the isothermal and adiabatic conditions of the flow-field. The spherical case is worked out in detail to investigate to what extent the flow-field behind the shock is influenced by the non-idealness of the gas in the mixture as well as by the mass concentration of the solid particles, by the ratio of density of the solid particles to the initial density of the mixture and by the energy input due to moving piston. A comparison is also made between isothermal and adiabatic cases.

A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

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

https://iopscience.iop.org/article/10.1088/1674-4527/10/5/005/pdf

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

One-dimensional self-similar unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in a rotational axisymmetric non-ideal gas is investigated. The medium is assumed to be non-ideal gas rotating about the axis of symmetry. The fluid velocities in the ambient medium are assumed to be varying with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account components of vorticity vector. It is found that the assumption of zero temperature gradient brings a profound change in the density and compressibility distributions as compared to that of the adiabatic case. The effect of an increase in the value of the parameter of the non-idealness of the gas is investigated. Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made. Further, it is shown that the consideration of zero temperature gradient and the effect of variation of the parameter of non-idealness of the gas decrease the shock strength and widens the disturbed region between the shock and piston. The shock waves in non-ideal gas can be important for description of shocks in supernova explosions, in the study of a flare produced shock in solar wind, central part of star burst galaxies, nuclear explosion, rupture of pressurized vessel, in the analysis of data from exploding wire experiments, and cylindrically symmetric hypersonic flow problems associated with meteors or reentry vehicles, etc. The findings of the present work provided a clear picture of whether and how the non-idealness of the gas and consideration of zero temperature gradient affect the propagation of shock and the flow behind it.

Similarity solutions for unsteady flow behind an exponential shock in an axisymmetric rotating non-ideal gas

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.

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

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law are obtained. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compare to that of the adiabatic case. Effects of the non-idealness of the gas on the flow-field between the shock and the piston are investigated. The variations of density-ratio across the shock and the location of the piston with the parameter of non-idealness of the gas $${\overline{b}}$$
 are also obtained.

Similarity solutions for the flow behind an exponential shock in a non-ideal gas

One-dimensional self-similar unsteady flow behind a strong exponential shock driven out by a piston moving with time according to an exponential law is investigated. The medium is assumed to be a mixture of small solid particles and a perfect gas. In order to get some essential features of the shock propagation, small solid particles are considered as pseudo-fluid and it is assumed that the equilibrium flow condition is maintained in the flow-field, and that the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained, in both cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compared to that of the adiabatic case. Effects of a change in the mass concentration of the solid particles in the mixture Kp and the ratio of the density of solid particles to that of initial density of the gas G1 are also obtained.

https://iopscience.iop.org/article/10.1088/0031-8949/74/4/015/pdf

J. P. Vishwakarma

Papers

A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

Similarity solutions for the flow behind an exponential shock in a non-ideal gas

Similarity solutions for unsteady flow behind an exponential shock in a dusty gas

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

Similarity solution for the flow behind a shock wave in a non-ideal gas with heat conduction and radiation heat-flux in magnetogasdynamics☆