Jump relations across a shock in non-ideal gas flow

Yadav

2016

Acta Phys. Pol. A

This work presents the structure of viscous shock front in a non-ideal gas. The analytical expressions for the particle velocity, temperature, pressure and change-in-entropy within the shock transition region are derived taking into consideration the Landau and Lifshitz equation of state for non-ideal gas. The effects on the structure of shock front due to the variations of the coefficient of viscosity, Mach number, adiabatic exponent and parameter of non-ideality of the gas are investigated. The model developed in the paper is valid only for small values of Mach number M i.e., M < 2.5.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Effects of Viscosity on the Structure of Shock Waves in a Non-Ideal Gas

Yadav

2016

Acta Phys. Pol. A

“…Obviously, this approximation is inadequate, and it is necessary to take account of the deviations of an actual gas from the ideal state which result from the interaction between its component molecules. A short description of the equation of state for non-ideal gas presented here was given in the recent paper of the author [36]. The information given in that paper is repeated here for completeness.…”

Section: Equations Of Motion and Shock Jump Relationsmentioning

confidence: 99%

“…(10) - (13) to write the quantities in it, which are those immediately behind the shock, in terms of those ahead of the shock and the shock velocity. The shock jump relations we use here are the shock conditions for the non-ideal gas [36] rather than the ideal gas shock conditions used by Whitham [34]. Now, substituting the shock jump relations given by Eqs.…”

Section: The Geometrical Shock Dynamics Theory and Analytical Solutionsmentioning

confidence: 99%

Shock dynamics of strong imploding cylindrical and spherical shock waves with non-ideal gas effects

2013

Wave Motion

Shock dynamics of strong imploding cylindrical and spherical shock waves with non-ideal gas effects R K Anand Wave Motion (2013), http://dx.Abstract In this paper, the generalized analytical solution for one dimensional adiabatic flow behind the strong imploding shock waves propagating in a non-ideal gas is obtained by using Whitham's geometrical shock dynamics theory. Landau and Lifshitz's equation of state for non-ideal gas and Anand's generalized shock jump relations are taken into consideration to explore the effects due to an increase in (i) the propagation distance from the centre of convergence, (ii) the non-idealness parameter and, (iii) the adiabatic index, on the shock velocity, pressure, density, particle velocity, sound speed, adiabatic compressibility and the change in entropy across the shock front. The findings provided a clear picture of whether and how the non-idealness parameter and the adiabatic index affect the flow field behind the strong imploding shock front.Keywords Imploding shock waves, Non-ideal gas, Shock jump relations, Non-idealness parameter, Adiabatic index PACS numbers: 47.40-X, 45.55.kf Shock dynamics of strong imploding cylindrical and spherical shock waves with non-ideal gas effects R K Anand Wave Motion (2013), http://dx.Shock wave phenomena also arise in astrophysics, hypersonic aerodynamics and hypervelocity impact. An understanding of the properties of the shock waves both in the near-field and the far-field is useful with regard to the characteristics such as shock strength, shock overpressure, shock speed, and impulse.The first study on converging shock waves was performed by Guderley [2], who presented his well-known self-similarity solution of strong converging cylindrical and spherical shock waves close to focus. The problem was also studied independently by Chester [3], Chisnell [4], and Whitham [5] with approximate methods, specifically geometrical shock dynamics. In their solutions, the exponent in the expression for Mach number as a function of shock radius for the spherical case is exactly twice that for the cylindrical case. This approximate result differs from the exact solution by less than one percent. The geometrical shock dynamics approach is both simple and intuitive while providing fairly accurate results. Sakurai [6,7], Sedov [8], Zel'dovich and Raizer [9], Lazarus and Richtmeyer [10], Van Dyke and Guttmann [11] and Hafner [12]presented high-accuracy results adopting alternative approaches for the investigation of the implosion problem under consideration. A numerical solution for a converging cylindrical shock wave was presented by Payne [13]. The problem of contracting spherical or cylindrical shock front propagation into a uniform gas at rest was studied by Stanyukovich [14]. The effects of overtaking disturbances on the motion of converging shock waves were studied by Yousaf [15]. The problems of implosion of a spherical shock wave in a gas and collapse of a spherical bubble in a liquid are discussed by Zel'dovich and Raizer [9] by using a self simila...

“…Wu (1996, 2003) have used an equivalent equation of state to study the shock theory of sonoluminescence. The internal energy e per unit mass of the non-ideal gas is given as (see Anand, 2012) ( )( )…”

Section: The Equation Of State For Non-ideal Gasmentioning

confidence: 99%

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

2012

Astrophys Space Sci

Self Cite

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of nonidealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.