Propagation of strong cylindrical shock wave in a self-gravitating rotational axisymmetric mixture of small solid particles and perfect gas with density varying exponentially

2019 ◽  
Vol 162 ◽  
pp. 447-460 ◽  
Author(s):  
G. Nath
Keyword(s):  
Shock Wave ◽  
Solid Particles ◽  
Perfect Gas ◽  
Cylindrical Shock Wave

Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
G. Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Mass Concentration ◽  
Solid Particles ◽  
Dusty Gas ◽  
Perfect Gas ◽  
Rotational Parameter ◽  
First Approximation ◽  
Isothermal Flows ◽  
Flow Variables

Abstract The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

Cylindrical shock wave in a self-gravitating perfect gas with azimuthal magnetic field via Lie group invariance method

2020 ◽  
Vol 17 (10) ◽  
pp. 2050148
Author(s):  
G. Nath ◽  
Arti Devi
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Initial Density ◽  
Density Variation ◽  
Shock Strength ◽  
Adiabatic Exponent ◽  
Perfect Gas ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
Variation Index

In this paper, we have studied the propagation of cylindrical shock waves in a self-gravitating perfect gas under the influence of azimuthal magnetic field. The method of Lie group invariance is used to construct some special class of self-similar solutions in the presence of the azimuthal magnetic field. The different cases of solutions with a power law and exponential law shock paths are obtained with the choice of arbitrary constants appearing in the expressions for the infinitesimal generators. The similarity solution for cylindrical shock wave with power law shock path is discussed in detail. The effects of variation of Alfven-Mach number, gravitation parameter, initial density variation index and adiabatic exponent on the flow variables are analyzed graphically. It is obtained that the increase in the values of Alfven-Mach number, gravitation parameter and adiabatic exponent have decaying effect on the shock strength. Also, the shock strength increases with an increase in the values of initial density variation index. A comparison is also made between the solutions in gravitating and non-gravitating cases in the presence of magnetic field.

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