Shock Wave Driven Out by a Piston in a Mixture of a Non-ideal Gas and Small Solid Particles Under the Influence of Azimu
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GENERAL AND APPLIED PHYSICS
Shock Wave Driven Out by a Piston in a Mixture of a Non-ideal Gas and Small Solid Particles Under the Influence of Azimuthal or Axial Magnetic Field P. K. Sahu1 Received: 28 March 2020 © Sociedade Brasileira de F´ısica 2020
Abstract One-dimensional self-similar unsteady flows behind a spherical or cylindrical shock wave driven out by a piston moving with time according to a power law in a dusty gas is investigated. The medium is assumed to be the mixture of small solid particles of micro-size and a non-ideal gas. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by the inner surface (piston). It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock waves in non-ideal dusty gas can be important for the description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, the central part of starburst galaxies, nuclear explosion, rupture of the pressurized vessel, in the analysis of data from exploding wire experiments, and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry vehicles, etc. The findings of the present work provided a clear picture of whether and how the non-idealness of the gas and the presence of the magnetic field affect the propagation of shock and the flow behind it. It is interesting to note that in the presence of azimuthal magnetic field, the pressure and density vanish at the piston and hence a vacuum is formed at the center of symmetry for both the isothermal and adiabatic flows, which is in excellent agreement with the laboratory condition to produce the shock wave. Keywords Fluid-solid interactions · Magnetogasdynamics · Similarity method · Shock wave · Non-ideal gas · Adiabatic and isothermal flows
1 Introduction Shock waves are essentially the waves propagating at the velocities which are higher than the speed of sound. Shock waves sharply raise the pressure and temperature of the medium. Shock waves are very thin, and the thickness of shock wave is about 10−7 m for air at ambient conditions (see [1–3]). Shock wave studies are of great importance from the standpoint of both practical applications and fundamental research. Shock wave phenomena arise due to the deposition of large amounts of energy in a very small region over short intervals, as in the case of P. K. Sahu
[email protected] 1
Department of Mathematics, Government Shyama Prasad Mukharjee College Sitapur, Sitapur, Chhattisgarh, 497111, India
explosion or spark discharges in air. High-speed multiphase flows containing shock or blast waves occur in a wide variety of natural and engineered systems as well across various length scales (Frost[4]). At astrophysical scales, multiphase insta
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