The propagation of converging and diverging shock waves under intense heat exchange conditions

Zhuravskaya, T.A.; Левин, В. А.

doi:10.1016/s0021-8928(96)00094-9

Cited by 48 publications

(19 citation statements)

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“…Distributions of the flow variables in the flow field behind the shock front are obtained by the numerical integration of (26)- (29) in the self-gravitating case and from (26), (27), and (29) in the nongravitating case with the boundary conditions (30) by the Runge-Kutta method of the fourth order. The expression for the shock-Mach number "M" in the selfgravitating case with magnetic field (M…”

Section: Resultsmentioning

confidence: 99%

“…The piston position η p at which U = (n + 1), is obtained after numerical integration of (26) to (29) in the self-gravitating case and from (26), (27), and (29) in the nongravitating case with the boundary conditions (30) and is tabulated in Table 1 for different values of M…”

Section: −2mentioning

confidence: 99%

“…As the shock propagates, the temperature behind it increases and becomes very large so that there is intense transfer of energy by radiation. This causes the temperature gradient to approach zero; that is, the dependent temperature tends to become uniform behind the shock front, and the flow becomes isothermal [10,17,20,[23][24][25][26][27]. A detailed mathematical theory of one-dimensional isothermal blast waves in a magnetic field was developed by Lerche [28,29].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

Section: −2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Carrus et al [2], Laumbach and Probstein [24], Sachdev and Ashraf [25], Korobeinikov [19], Zhuravskaya and Levin [26], Nath [7,27], Whitham [30])…”

Section: Equations Of Motion and Boundary Conditionsmentioning

confidence: 99%

“…As the shock propagates, the temperature behind it increases and becomes very large so that there is intense transfer of energy by radiation. This causes the temperature gradient to approach zero, that is the dependent temperature tends to become uniform behind the shock front and the flow becomes isothermal (Laumbach and Probstein [24], Sachdev and Ashraf [25], Korobeinikov [19], Zhuravskaya and Levin [26], Nath [7,17,27]). A detailed mathematical theory of one-dimensional isothermal blast waves in a magnetic field was developed by Lerche [28,29].…”

Section: Introductionmentioning

confidence: 99%

Unsteady isothermal flow behind a magnetogasdynamic shock wave in a self-gravitating gas with exponentially varying density

Nath

2014

J Theor Appl Phys

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The propagation of spherical (or cylindrical) shock wave in an ideal gas with or without gravitational effects in the presence of a constant azimuthal magnetic field is investigated. Non-similarity solutions are obtained for isothermal flow between the shock and the piston. The numerical solutions are obtained using the Runge-Kutta method of the fourth order. The density of the gas is assumed to be varying and obeying an exponential law. The shock wave moves with variable velocity, and the total energy of the wave is non-constant and varies with time. The effects of variation of the Alfven-Mach number, gravitational parameter and time are obtained. It is investigated that the presence of gravitational field reduces the effect of the magnetic field. Also, the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. The shock waves in conducting perfect gas can be important for description of shocks in supernova explosions, in the study of central part of star burst galaxies, nuclear explosion, rupture of a pressurized vessel and explosion in the ionosphere. Other potential applications of this study include analysis of data from exploding wire experiments and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry vehicles etc. A comparison is made between the solutions in the cases of the gravitating and the non-gravitating medium with or without magnetic field. The obtained solutions are applicable for arbitrary values of time.

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Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

Gupta

Sharma

Arora

2021

Math Methods in App Sciences

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The purpose of this study is to obtain the solution using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self‐gravitating non‐ideal gas with the magnetic field which is taken to be axial. Here, isothermal flow is considered. In the undisturbed medium, varying magnetic field and density are taken. Out of four different cases, only three cases yield the similarity solutions. Numerical computations have been performed for the cases of power law and exponential law shock paths, to find out the behavior of flow variables in the flow field immediately behind the shock. Similarity solutions are carried out by taking arbitrary constants in the expressions of infinitesimals of the Lie group of transformations. Also, the study of the present work provides a clear picture of whether and how the variations in the non‐ideal parameter of the gas, Alfven–Mach number, adiabatic exponent, ambient magnetic field variation index, and gravitational parameter affect the propagation of shock and the flow behind it. Software package “MATLAB” is used for all the computations.

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The propagation of converging and diverging shock waves under intense heat exchange conditions

Cited by 48 publications

References 0 publications

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

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

Unsteady isothermal flow behind a magnetogasdynamic shock wave in a self-gravitating gas with exponentially varying density

Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

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