Effects of internal heat transfer on the structure of self-similar blast waves

Ghoniem, A. F.; Kamel, Mohamed H.; Berger, Stanley A.; Oppenheim, A. K.

doi:10.1017/s0022112082001724

Cited by 57 publications

(54 citation statements)

References 12 publications

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“…Also, Abdel-Raouf & Gretler (1991) obtained the non-self-similar solution for the blast waves with internal heat transfer effects. Ghoniem et al (1982) obtained a self-similar solution for spherical explosions taking into account the effects of both conduction and radiation in the two limits of Rosseland radiative diffusion and Plank radiative emission. In these works, where both the radiation and conduction effects are considered, the density of the medium ahead of the shock is taken to be uniform and effects of self-gravitation of the medium are not taken into consideration.…”

Section: Introductionmentioning

confidence: 99%

A self-similar flow behind a shock wave in a gravitating or non-gravitating gas with heat conduction and radiation heat-flux

Vishwakarma

Singh

2009

J Astrophys Astron

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The propagation of a spherical shock wave in an ideal gas with heat conduction and radiation heat-flux, and with or without self-gravitational effects, is investigated. The initial density of the gas is assumed to obey a power law. The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density, and the total energy of the wave to vary with time. Similarity solutions are obtained and the effects of variation of the heat transfer parameters, the variation of initial density and the presence of self-gravitational field are investigated.

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Section: Introductionmentioning

confidence: 99%

A self-similar flow behind a shock wave in a gravitating or non-gravitating gas with heat conduction and radiation heat-flux

Vishwakarma

Singh

2009

J Astrophys Astron

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“…Consequently, similarity models for classical blast wave problems have been extended taking into account radiation (see [8][9][10][11][12][13][14][15]). Elliot [9] considered the explosion problem, introducing a radiation fl ux in its diffusion approximation.…”

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Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

Vishwakarma

Patel

2015

J Eng Phys Thermophy

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A similarity solution is presented for a cylindrical magnetogasdynamic shock wave in a rotating nonideal gas in the presence of a variable axial magnetic fi eld in the case where the radiation heat fl ux is of importance. The initial angular velocity of the medium is assumed to vary as some power of the distance from the symmetry axis. The radiation heat fl ux is evaluated from the equation of motion without explicit use of the radiation transfer equations. It is shown that the gas nonidealness increases the shock strength but decreases the shock velocity. On the other hand, the presence of a magnetic fi eld decreases the shock strength but increases the shock velocity. Moreover, the shock velocity increases with the ratio of specifi c heats. The total energy of the shock wave increases with time.Keywords: cylindrical shock waves, self-similar fl ow, rotating nonideal gas, radiation heat fl ux, axial magnetic fi eld.Introduction. Formulation of self-similar problems and some examples describing the adiabatic motion in the context of nonrotating gas models of stars are considered by Sedov [1], Zel'dovich and Raizer [2], Lee and Chen [3], and Summers [4]. Experimental studies and astrophysical observations show that the outer atmosphere of planets rotates due to their rotation. Macroscopic motion with a supersonic speed occurs in an interplanetary atmosphere, so that shock waves are generated there. Thus, rotation of planets or stars signifi cantly affects the processes occurring in their outer layers; therefore, questions connected with explosions in a rotating gas atmosphere are of defi nite astrophysical interest. Chaturani [5] studied the propagation of cylindrical shock waves through a gas with solid body rotation and obtained solutions by the similarity method adopted by Sakurai [6]. Nath, Ojha, and Takhar [7] derived similarity solutions for the fl ow behind spherical shock waves propagating in a nonuniform rotating interplanetary atmosphere with increasing energy. Gangualy and Jana [8] studied a theoretical model of propagation of strong spherical shock waves in a self-gravitating atmosphere with a radiation fl ux in the presence of a magnetic fi eld. They also considered that the medium behind the shock rotated, but neglected rotation of the undisturbed medium. In all the works mentioned, the medium is taken to be a gas satisfying the equation of state of a perfect gas.The radiation infl uence on a shock wave and on a fl ow fi eld behind the shock front has always been of great interest, for instance, in nuclear power and space research. Consequently, similarity models for classical blast wave problems have been extended taking into account radiation (see [8][9][10][11][12][13][14][15]). Elliot [9] considered the explosion problem, introducing a radiation fl ux in its diffusion approximation. Wang [10] discussed the piston problem with radiation heat transfer in the thin and thick limits, as well as in the general case with an idealized two-direction approximation. Ashraf and Sachdev [12] did not explicitl...

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“…The counter pressure (the pressure ahead of the shock) is taken into account. The radiation pressure and radiation energy are neglected [13,14,17]. The assumption of an optically thick gray gas is physically consistent with such a neglect [15].…”

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confidence: 99%

“…The fundamental equations for one-dimensional, unsteady, adiabatic, and cylindrically symmetric fl ow of a nonideal gas, which is rotating about the axis of symmetry and in which the effects of the heat conduction and radiation heat fl uxes are taken into account, may be expressed as [11,16,17,22] …”

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confidence: 99%

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Similarity Solutions for the Flow Behind an Exponential Shock in a Rotating Nonideal Gas with Heat Conduction and Radiation Heat Fluxes

Singh

Nath

2014

J Eng Phys Thermophy

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A self-similar solution for the propagation of a shock wave driven by a cylindrical piston moving according to exponential temporal law in a nonideal rotating gas with heat conduction and radiation heat fl uxes is investigated. The density and angular velocity of the ambient medium are assumed to be constant. Heat conduction is expressed in terms of the Fourier law, and radiation is considered to be of diffusion type for an optically thick gray gas model. The thermal conductivity and absorption coeffi cient are assumed to vary with temperature and density. Similarity solutions are obtained, and the effects of variations in the heat transfer parameters and gas nonidealness on the fl ow variables in the region behind the shock are investigated.Introduction. In the aerodynamics, the similarity between a steady hypersonic fl ow past slender blunted (planar or axisymmetric) power-law bodies and a one-dimensional unsteady self-similar fl ow behind a strong shock driven by a plane or cylindrical piston moving with time according to a power law is well known [1][2][3][4]. Sedov [5] indicated that a limiting case of a self-similar fl ow fi eld with a power-law shock is the fl ow fi eld formed with an exponential shock (see also [6]). Ranga Rao and Ramana [6] and Singh and Vishwakarma [7] obtained solutions for the problem of unsteady self-similar motion of a perfect gas behind an exponential shock.However, under extreme conditions that prevail in most of the problems associated with shock waves, the assumption that the gas is ideal is no longer valid. In recent years, several studies have been performed concerning the problem of strong shock waves in a nonideal gas, in particular, by Anisimov and Spiner [8], Ranga Rao and Purohit [9], Wu and Roberts [10], and Vishwakarma and Nath [11]. Anisimov and Spiner [8] investigated the problem of point explosion in a nonideal gas by taking the equation of state in a simplifi ed form to describe the behavior of the medium. Ranga Rao and Purohit [9] analyzed self-similar fl ows of a nonideal gas driven by an expanding piston. Wu and Roberts [10] studied the problem of structure and stability of a spherical shock wave in a sonoluminescence bubble. Vishwakarma and Nath [11] obtained similarity solutions for a nonideal gas fl ow behind a strong exponential shock driven by a piston (cylindrical or spherical) moving according to an exponential temporal law.Marshak [12] studied the radiation effect on the shock propagation by introducing the radiation diffusion approximation. Using the same mode of radiation, Elliott [13] discussed the conditions leading to self-similarity with a specifi ed functional form of the mean free path of radiation and obtained a solution for self-similar spherical explosions. Wang [14], Helliwell [4], and Nicastro [15] treated the problems of radiating walls, either stationary or moving, generating shocks at the head of self-similar fl ow fi elds. Gretler and Wehle [16] studied the propagation of blast waves with exponential heat release, taking into account inte...

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Effects of internal heat transfer on the structure of self-similar blast waves

Cited by 57 publications

References 12 publications

A self-similar flow behind a shock wave in a gravitating or non-gravitating gas with heat conduction and radiation heat-flux

A self-similar flow behind a shock wave in a gravitating or non-gravitating gas with heat conduction and radiation heat-flux

Magnetogasdynamic Cylindrical Shock Waves in a Rotating Nonideal Gas with Radiation Heat Flux

Similarity Solutions for the Flow Behind an Exponential Shock in a Rotating Nonideal Gas with Heat Conduction and Radiation Heat Fluxes

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