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

Vishwakarma, J. P.; Nath, G.

doi:10.1007/s11012-008-9166-y

Cited by 94 publications

(85 citation statements)

References 16 publications

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“…Expressions for non-dimensional pressure and particle velocity in the region behind the strong shock can be obtained by using (22), (23), (25) and (33), respectively…”

Section: Resultsmentioning

confidence: 99%

“…The gas is assumed to be so rarefied that its molecules interact only through binary collisions, while triple, quadruple etc collisions are negligible. Therefore, the equation of state of the mixture of perfect gas and small solid particles is given by [13] and [ 22] …”

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confidence: 99%

“…The speed of sound in unperturbed medium a o ' is given by the relation (22) To represent the quantities u, p, and Z in terms of their undisturbed values, the jump conditions across the strong shock are given by [18], [13]and [26] …”

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Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

Prakash¹

2017

IJRASET

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Chester-Chisnell-Whitham method has been used to study the behavior of dusty real gas on adiabatic propagation of cylindrical imploding strong shock waves. It is assumed that the dusty gas is the mixture of a real gas and a large number of small spherical solid particles of uniform size. Neglecting the effect of overtaking disturbances, the analytical expressions for shock strength and shock velocity immediately behind the shock have been derived for uniform initial density distribution. The expressions for the pressure and particle velocity have also been obtained. The variation of the flow variables have been calculated numerically and discussed through graphs. Finally the results accomplished here are compared with earlier results as well as those for ideal dusty gas. Keywords: CCW, dusty, imploding, real gas, shock. I.INTRODUCTION The study of the shock wave propagation in a dusty gas has received considerable attention due to its application to space science, bomb blast, lunar ash flow, coal mine explosions, nozzle flow, missiles and other engineering problems. Many scientists (Sedov . Vishwakarma [7] generalized Ray and Bhowmik[8] solution in gas to the mixture of gas and small solid particles with exponentially varying density, using a nonsimilarity method. He found that the presence of small dust particles in the gaseous medium has significant effects on the variation of flow variables. The problem of propagation of shock wave in dusty ideal gas have been tackled by Vishwakarma[9] using similarity method. Vishwakrma and Pandey[10] have studied one-dimensional unsteady self-similar adiabatic flow of a dusty ideal gas behind a spherical shock wave with time-dependent energy input. Motion of shock wave in a mixture of ideal gas and small dust particles with radiation heat flux and exponentially varying density has been studied by Vishwakarma et. al. [11]. Yadav et al. [12] studied the propagation of weak cylindrical shock in the mixture of ideal gas and dust particle in presence of constant axial magnetic field. Singh and Gogoi [13] have found similarity solution for the propagation of spherical shock wave in the mixture of non-ideal gas and small solid dust particles. They use the equation of state for non-ideal gases simplified by Anisimov and Spiner [14], which describes the behavior of non-idealness of gas on the problem of strong shock explosion. The aim of the present study is to investigate the motion of cylindrical imploding shock in a real dusty gas having uniform initial density distribution by using CCW ) method, without considering the effect of overtaking disturbances. It is assumed that the real (non-ideal) dusty gas is the mixture of real gas and a large number of small spherical solid particles of uniform size. The particles are inert and uniformly distributed in the gas. Initial volume fraction of the solid particles is also assumed constant in this particular study. The particles do not interact with each other therefore their thermal motion is nigligble. Initial density of the m...

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“…Expressions for non-dimensional pressure and particle velocity in the region behind the strong shock can be obtained by using (22), (23), (25) and (33), respectively…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

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Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

Prakash¹

2017

IJRASET

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“…As the shock is strong, we assume (q 2 − q 1 ) to be negligible in comparison with the product of p 2 and V [10,17,18,23,27,31,32]. Therefore, (10) reduces to…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…In aerodynamics, the analogy between the steady hypersonic flow past slender-blunted (planar or axisymmetric) power-law bodies and the one-dimensional unsteady selfsimilar flow behind a shock driven out by a piston moving with time according to a power-law is well known (see, e.g., [1,8,10,[12][13][14][15][16][17][18][19]). …”

Section: Introductionmentioning

confidence: 99%

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

Nath

Sinha²

2011

Physics Research International

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The propagation of a cylindrical (or spherical) shock wave in an ideal gas with azimuthal magnetic field and with or without selfgravitational 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.

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An analysis of shock wave propagation in a dusty gas

Singh

Arora

2022

Math Methods in App Sciences

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The present work uses a power series method to investigate the propagation of shock waves with generalized geometries generated by an intense explosion in a dusty gas. A mathematical model using a system of partial differential equations (PDEs) is presented for the considered problem. The density of the undisturbed medium is assumed to be constant. Approximate analytic solutions to the considered problem are obtained using the power series method by extending the power series of the flow variables. This work discusses the first‐order and second‐order approximate solutions and provides closed‐form solutions for the first‐order approximation. The behavior of the flow variables is depicted via figures behind the shock front for the first‐order approximation. Furthermore, the effects of geometry factor α, adiabatic exponent γ, and various dusty gas parameters such as Kp (the mass fraction of the dust particles), G0 (the ratio of the density of the dust particles to the initial density of the gas), and σ (the relative specific heat) are analyzed on the flow variables and total energy of disturbance J0 for the first‐order approximation. It is observed that an increase in any of the parameters Kp or σ causes the fluid velocity to increase and density and pressure to decrease. Increase in the parameter G0 causes the density and pressure to increase, whereas the fluid velocity does not get affected. An increase in the value of α results in a decrease in the density and pressure, while the fluid velocity remains the same. An increase in the value of γ results in a decrease in the fluid velocity; however, it has opposite effect on the pressure. The density decreases near the shock front and increases as we move towards the axis/center of symmetry with an increase in γ. Also, it is observed that J0 increases on increasing the value of G0 or σ, while it decreases on increasing the value of Kp, γ or α.

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

Cited by 94 publications

References 16 publications

Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

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

An analysis of shock wave propagation in a dusty gas

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