Propagation of shock waves in a dusty gas with heat conduction, radiation heat flux and exponentially varying density

Vishwakarma, J. P.; Nath, G.; Singh, Kehar

doi:10.1088/0031-8949/78/03/035402

Cited by 36 publications

(38 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Values of initial volume fraction Z o for some values of k p and σ are calculated from the equation (13).Initially taking shock strength U/a o =12 at r=1.1 for k p =0.1, σ=50, b̅ =0.02, Z o =0.00222, β=0.16, =1.4=1, λ=1.1 and Γ=1.36 the variation of shock velocity, shock strength, non-dimensional pressure and non-dimensional flow velocity with propagation distance(r) have been calculated and displayed through figures (1)(2)(3)(4)(5)(6)(7)(8)(11)(12)(13)(14). It is observed that shock strength increases asymptotically as cylindrical shock implodes in the medium.…”

Section: Resultsmentioning

confidence: 99%

“…The governing equations for one dimensional, unsteady, adiabatic and cylindrical symmetrical flow of a mixture of real (non-ideal) gas and small spherical solid particles can be written as [12]- [14] u u 1 p u 0 t r r …”

Section: Basic Equationsmentioning

confidence: 99%

“…To represent the quantities u, p,  and Z in terms of their undisturbed values, the jump conditions across the strong shock are given by [12], [14] and [23] …”

Section: Basic Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of Cylindrical Imploding Shock Wave in Dusty Real Gas with Exponential Varying Density

Gangwar¹

2017

IJRASET

View full text Add to dashboard Cite

In this paper, the effect of overtaking disturbances has been estimated on the propagation of cylindrical imploding strong shock wave in a real dusty gas. 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. Considering the exponential varying initial density distribution, analytical expressions for shock strength and shock velocity immediately behind the shock have been derived for freely as well as under the influence of overtaking waves. The modified expressions for the non-dimensional pressure and flow velocity have also been obtained. The variations of all the flow variables have been computed and discussed through graphs. It is observed that the presence of dust particles has a significant role in the shock wave propagation and the shock is strengthened, as the non-idealness (realness) of the gases mixture increases. Finally the results obtained here are compared with earlier results as well as those for ideal dusty gas having uniform initial density distribution. Keywords: Effect of overtaking disturbances, CCW, dusty, imploding, real gas, shock. I. INTRODUCTIONPropagation of shock wave 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. Severalauthors (Carrier solution in dusty ideal gashaving exponentially varying initial density distribution, using a non-similarity method and obtained that the presence of small spherical dust particles in the gaseous medium has significant effects on the variation of shock strength and other flow variables. Vishwakarma and Nath [11] have found the self-similar solution of the problem of exponential shock in a dusty gas. Propagation of shock wave in a mixture of ideal gas and small dust particles with radiation heat flux and exponentially varying density has been investigated by Vishwakarmaet. al.[12] using similarity method. Using CCW method, Yadav et al. [13] have explored the problem of propagation of weak cylindrical shock in the mixture of ideal gas and dust particle in presence of constant axial magnetic field. Singh and Gogoi [14] have use the equation of state for non-ideal gases simplified by Anisimov and Spiner [15], to study the propagation of spherical shock wave in the mixture of non-ideal gas and dust particles by similarity solutions. Recently, the effect of self-gravitation on the propagation of cylindrical imploding strong shock wave in dusty ideal gas is analysed by using CCW method by Deepak et. al.[16]. Neglecting the effect of overtaking disturbances, Prakashet. al. [17] have investigated the problem of shock wave propagation in a real gas having uniform initial density distribution. Very recently, Gangwar [18] has studied theoretically the effect of overtaking disturbances on adiabatic propagation of cylindrical strong shock waves in mixture of small spherical inert dust particles and a real gas having power varying i...

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Cylindrical Imploding Shock Wave in Dusty Real Gas with Exponential Varying Density

Gangwar¹

2017

IJRASET

View full text Add to dashboard Cite

show abstract

“…al. [8] and Viashwakarma [9] using similarity method. He found that the presence of small solid particles in the medium has significant effect on the variation of density and pressure.…”

Section: Introductionmentioning

confidence: 99%

Effect of Gravitation on the Motion of Cylindrical Imploding Shock Wave in Dusty Gas

Kumar¹

2017

ijetst

View full text Add to dashboard Cite

Abstract:In the present paper, the propagation of cylindrical imploding strong shock waves in a self-gravitating dusty gas has been investigated by Chester-Chisnell-Whitham method. The dusty gas is assumed to be a mixture of small solid spherical particles and a perfect gas. The effect of overtaking disturbances on freely propagating shock has been estimated by using Yadav technique [Mod. Mes. Cont. B, 46(4), 1(1992)]. Assuming an initial density distribution o log( r)     , where µ is the density at the axis of symmetry and φ is a constant, the variation of shock velocity, shock strength, pressure and particle velocity with propagation distance, density parameter (φ), mass concentration of solid particles in the mixture and the ratio of solid particles to the initial density of gas have been computed and discussed through figures. The effect of self-gravitation is also calculated. Maintaining equilibrium flow conditions, it is found that the presence of dust particles in the gases medium has significant effects on the variation of flow variables and the shock is strengthened under the influence of overtaking disturbances. The role of the acceleration due to gravity on propagation of shock wave is also calculated numerically and depict through graphs. Finally, the results obtained here have been compared with those for pure perfect gas as well as those for freely propagating shock.

show abstract

“…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.…”

mentioning

confidence: 99%

Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

Prakash¹

2017

IJRASET

View full text Add to dashboard Cite

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...

show abstract

Propagation of shock waves in a dusty gas with heat conduction, radiation heat flux and exponentially varying density

Cited by 36 publications

References 41 publications

Analysis of Cylindrical Imploding Shock Wave in Dusty Real Gas with Exponential Varying Density

Analysis of Cylindrical Imploding Shock Wave in Dusty Real Gas with Exponential Varying Density

Effect of Gravitation on the Motion of Cylindrical Imploding Shock Wave in Dusty Gas

Cylindrical Imploding Strong Shock Wave in Uniform Real Dusty Gas

Contact Info

Product

Resources

About