Detonation Wave Propagation in Rotational Gas Flows

Левин, В. А.; Skopina, G. A.

doi:10.1023/b:jamt.0000030320.77965.c1

Cited by 69 publications

(23 citation statements)

References 2 publications

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“…Chaturani (1970), Ghoniem et al (1982), Levin and Skopina (2004), Nath (2010), Vishwakarma and Nath (2010) …”

Section: Fundamental Equations Andboundary Conditionsmentioning

confidence: 99%

“…Following Levin and Skopina (2004) and Nath (2010), we obtained the jump conditions for the components of vorticity vector across the shock as ,    a n     * * a n z z  The total energy 'E' of the flow field behind the shock is not constant, but assumed to be dependent on shock radius obeying a power law(Ranga Rao and Purohit(1972)…”

Section: Fundamental Equations Andboundary Conditionsmentioning

confidence: 99%

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Similarity Solution for a Cylindrical Shock Wave in a Self-gravitating, Rotating Axisymmetric Dusty Gas with Heat Conduction and Radiation Heat Flux

Bajargaan¹,

Patel²

2017

JAFM

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Similarity solutions are obtained for unsteady adiabatic propagation of a cylindrical shock wave in a self gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux in which variable energy input is continuously supplied by the piston. The dusty gas is taken to be a mixture of non-ideal gas and small solid particles. Azimuthal fluid velocity and axial fluid velocity in the ambient medium are taken to be variable. The equilibrium flow conditions are assumed to be maintained. The initial density is assumed to be constant. The heat conduction is expressed in terms of Fourier's law and the radiation is taken 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. The effects of the variation of the gravitational parameter and the heat transfer parameters on the shock strength and the flow variables such as radial velocity, azimuthal velocity, axial velocity, density, pressure, total heat flux, mass behind the shock front, azimuthal vorticity vector, axial vorticity vector, isothermal speed of sound and adiabatic compressibility are studied. It is found that the presence of gravitation effect in the medium modify the radiation and conduction effect on the flow variables.

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“…Chaturani (1970), Ghoniem et al (1982), Levin and Skopina (2004), Nath (2010), Vishwakarma and Nath (2010) …”

Section: Fundamental Equations Andboundary Conditionsmentioning

confidence: 99%

Section: Fundamental Equations Andboundary Conditionsmentioning

confidence: 99%

Similarity Solution for a Cylindrical Shock Wave in a Self-gravitating, Rotating Axisymmetric Dusty Gas with Heat Conduction and Radiation Heat Flux

Bajargaan¹,

Patel²

2017

JAFM

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“…Thus, the formulas for vorticity behind a moving curvilinear shock or detonation wave, if it is not curved, yield the formulas for vorticity in unsteady one-dimensional flows [8]. In this case, the normal component of vorticity equals zero on both sides of the discontinuity surface, and the law of conservation of the ratio of the tangential component of vorticity to density is valid for the tangential components of vorticity:…”

mentioning

confidence: 98%

“…In the general three-dimensional case, expressions for the components of the vorticity vector behind a discontinuity surface generated by a steady supersonic nonuniform flow of a combustible gas around a solid were derived in [7]. For unsteady flows, Levin and Skopina [8] obtained formulas for vorticity on a cylindrical discontinuity surface propagating in an axisymmetric swirl flow of an ideal gas away from the axis of symmetry. In the present activities, we determine the vorticity directly behind a curvilinear shock or detonation wave propagating over a nonuniform swirl flow of a combustible gas.…”

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confidence: 99%

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Behavior of the vorticity vector in a supersonic nonuniform swirl flow of a combustible gas behind a moving curvilinear shock or detonation wave

Левин

Skopina

2009

Combust Explos Shock Waves

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Expressions for components of the vorticity vector behind a curvilinear shock or detonation wave propagating in a supersonic nonuniform flow of a combustible gas are derived. Plane and axisymmetric gas flows are considered. The free stream in the general case is a vortex flow with a specified distribution of parameters. Formulas for the vorticity components in the plane of the flow for axisymmetric flows are found to have the same form as formulas for steady axisymmetric flows. As in the case of steady flows, the normal-to-wave component of vorticity is demonstrated to remain continuous across the discontinuity surface; in the case of axisymmetric flows, the ratio of the tangential component of vorticity aligned in the plane of the flow to density also remains continuous, though the quantities themselves become discontinuous.In the case of steady flows, the expression for vorticity behind a curved shock wave for a flow with constant parameters was first derived by Truesdell [1] and later by other authors. Lighthill [2] obtained formulas for components of vorticity behind an arbitrary curved wave in the general case, under the assumption of an infinite shock-wave intensity. A generalized formula was given by Hayes [3]. Maikapar [4] and Rusanov [5] obtained formulas for vorticity components behind a shock wave of an arbitrary intensity with constant free-stream parameters. Levin and Skopina [6] studied the behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a steady curvilinear shock or detonation wave. In the general three-dimensional case, expressions for the components of the vorticity vector behind a discontinuity surface generated by a steady supersonic nonuniform flow of a combustible gas around a solid were derived in [7]. For unsteady flows, Levin and Skopina [8] obtained formulas for vorticity on a cylin-1 Institute of Automation and Control Processes, Far-East Division, Russian Academy of Sciences, Vladivostok 690041; levin@imec.msu.ru.drical discontinuity surface propagating in an axisymmetric swirl flow of an ideal gas away from the axis of symmetry. In the present activities, we determine the vorticity directly behind a curvilinear shock or detonation wave propagating over a nonuniform swirl flow of a combustible gas. We study plane-parallel and axisymmetric unsteady motions of the gas, which depend only on two coordinates: x and y. The plane of the flow is the plane (x, y). The axis of symmetry coincides with the straight line x = 0. The main examined quantities (velocity vector V , pressure p, density ρ, and vorticity 2ω = rotV ) are considered as functions of the Cartesian coordinates (x, y) and time t.The velocity vector V in the coordinate system (x 1 , x 2 , x 3 ) has the components u, υ, and w. For planeparallel motion, we have x 1 = x, x 2 = y, and x 3 = z; for axisymmetric motion, we have x 1 = x, x 2 = y, and x 3 = ϕ. For a plane-parallel flow, we have w = 0.

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The propagation of strong cylindrical shock wave in a rotating axisymmetric non‐ideal gas with radiation heat flux

Yadav

Singh

Arora

2023

Math Methods in App Sciences

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In this manuscript, we studied a quasi-linear hyperbolic system of partial differential equations which describes the one-dimensional adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotating non-ideal gas, which has a varying azimuthal fluid velocity together with a varying axial fluid velocity, with radiation heat flux, and similarity solutions are obtained by using the Lie group-theoretic method. The basic idea of this method is that it changes the system of PDEs representing the one-dimensional flow through the similarity variable to the system of ODEs. The flow profiles are drawn behind the shock followed by a brief discussion on the behavior of the solutions via graphs. The effects of variation in non-ideal parameter, adiabatic index of the gas, Alfven-Mach number and ambient azimuthal velocity exponent on the flow variables are described. All numerical calculations have been performed using the "Mathematica" software.

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Detonation Wave Propagation in Rotational Gas Flows

Cited by 69 publications

References 2 publications

Similarity Solution for a Cylindrical Shock Wave in a Self-gravitating, Rotating Axisymmetric Dusty Gas with Heat Conduction and Radiation Heat Flux

Similarity Solution for a Cylindrical Shock Wave in a Self-gravitating, Rotating Axisymmetric Dusty Gas with Heat Conduction and Radiation Heat Flux

Behavior of the vorticity vector in a supersonic nonuniform swirl flow of a combustible gas behind a moving curvilinear shock or detonation wave

The propagation of strong cylindrical shock wave in a rotating axisymmetric non‐ideal gas with radiation heat flux

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