Ionizing Cylindrical Shock Waves in a Rotating Homogeneous Non-ideal Gas

Vishwakarma, J. P.; Singh, Mahendra

doi:10.5923/j.mechanics.20120202.04

Cited by 3 publications

(4 citation statements)

References 25 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The distribution of the flow variables between the shock front (η = 1) and the inner expanding surface (η = η p ) is obtained by numerical integration of ( 46) -(52) with the boundary conditions (33) by Runge-Kutta method of fourth order. For the purpose of numerical integration, the values of the constant parameters are taken to be (Roberts and Wu [20], Elliott [3], Singh and Mishra [8], Rosenau [41], Vishwakarma and Singh [32 ], Singh and Nath [34] ρ2 are shown in tables 1 and 2 for different cases.…”

Section: Resultsmentioning

confidence: 99%

“…In addition to the shock conditions (33), the condition to be satisfied at the inner boundary surface is that the velocity of the fluid is equal to the velocity of the inner boundary itself. This kinematic condition, from (23) and (24), can be written as…”

Section: Similarity Solutionsmentioning

confidence: 99%

“…Now, the ordinary differential equations ( 46) -( 52) may be integrated, numerically, with boundary conditions (33) and the appropriate values of the constant parameters γ, b, N, d, G L , M −2 and M −2 A , to obtain the solution for the flow behind the shock surface.…”

Section: Similarity Solutionsmentioning

confidence: 99%

“…Such a shock wave is called a gas-ionizing shock or, simply ionizing shock. The propagation of a ionizing shock has been studied by Greenspan [27], Greifinger and Cole [28], Christer [29], Rangarao and Ramana [30], Singh [31], Vishwakarma and Singh [32,33] and Singh and Nath [34] in a perfect or nonideal gas.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Self-similar Cylindrical Ionizing Shock Waves in a Rotational Axisymmetric Non-ideal Gas with Radiation Heat Flux

Singh¹,

Nath²

2013

ujam

View full text Add to dashboard Cite

Similarity solutions are obtained for one-dimensional adiabatic flow behind a gas-ionizing cylindrical shock wave propagating in a rotational axisymetric non-ideal gas with radiation heat flux, in presence of an azimuthal magnetic field. The electrical conductivity in the medium ahead of the shock is assumed to be negligible, which becomes infinitely large after passage of the shock . The ambient medium is considered to have variable axial velocity component in addition to the variable azimuthal velocity. In order to obtain the similarity solutions, the initial density of the medium is assumed to be constant and the initial angular velocity to be obeying a power law and to be decreasing as the distance from the axis increases . Effects of an increase in the value of the parameter of non-idealness of the gas, in the value of radiation parameter and in the value of the index for variation of azimuthal velocity of the ambient medium ( or in the value of the index for variation of the ambient magnetic field ) on the shock propagation are investigated. It is observed that the non-idealness of the gas or radiation heat-flux has decaying effect on the shock wave.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Similarity Solutionsmentioning

confidence: 99%

Section: Similarity Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Self-similar Cylindrical Ionizing Shock Waves in a Rotational Axisymmetric Non-ideal Gas with Radiation Heat Flux

Singh¹,

Nath²

2013

ujam

View full text Add to dashboard Cite

show abstract

Propagation of cylindrical shock waves in rotational axisymmetric dusty gas with magnetic field: Isothermal flow

2021

View full text Add to dashboard Cite

In this article, the effect of the dust particles is studied on the propagation of a cylindrical shock wave in rotational axisymmetric ideal gas under isothermal flow conditions with the magnetic field. Here, magnetic pressure, azimuthal fluid velocity, and axial fluid velocity are supposed to vary according to a power law in the undisturbed medium. With the help of Sakurai's technique, we obtain approximate solutions analytically by expanding the flow parameters in the form of a power series in ϕ=(CV)2. The power series method is used to derive the zeroth and the first-order approximations. The solutions for the zeroth-order approximation are constructed in analytical form. Distributions of the hydrodynamical quantities are analyzed graphically behind the shock front. Also, the effects of shock Cowling number (co), mass fraction of the solid particles in the mixture (kp), adiabatic exponent (γ), and rotational parameter (L) on the flow variables are discussed. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero, and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods. Furthermore, the results obtained in the present work are found to be in good agreement with those obtained from the study by Nath and Singh [Can. J. 98, 1077 (2020)].

show abstract

Approximate analytical solution for ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas: isothermal flow

Nath

Singh

2020

Can. J. Phys.

View full text Add to dashboard Cite

The propagation of an ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas under isothermal flow condition with an azimuthal magnetic field is investigated. The electrical conductivity is assumed to be negligible in the medium ahead of the shock wave, which after the passage of the shock wave becomes infinitely large. The magnetic pressure, azimuthal fluid velocity, and axial fluid velocity are assumed to be varying according to the power law with distance from the axis of symmetry in the undisturbed medium. The zeroth and first-order approximations are discussed by the aid of the power series method. Solutions for the zeroth-order approximation are constructed in analytical form. Distributions of hydrodynamical quantities are discussed. The effect of flow parameters, namely, shock wave Cowling number c∗, adiabatic exponent γ, rotational parameter L, and gas non-idealness parameter [Formula: see text] are studied on the flow variables. Due to the consideration of a rotating medium or due to the presence of magnetic field, the total energy of the disturbance increases, while with an increase in adiabatic exponent γ the total energy of the disturbance decreases. Density and pressure vanish near the axis of symmetry, thus forming a vacuum there.

show abstract

Ionizing Cylindrical Shock Waves in a Rotating Homogeneous Non-ideal Gas

Cited by 3 publications

References 25 publications

Self-similar Cylindrical Ionizing Shock Waves in a Rotational Axisymmetric Non-ideal Gas with Radiation Heat Flux

Self-similar Cylindrical Ionizing Shock Waves in a Rotational Axisymmetric Non-ideal Gas with Radiation Heat Flux

Propagation of cylindrical shock waves in rotational axisymmetric dusty gas with magnetic field: Isothermal flow

Approximate analytical solution for ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas: isothermal flow

Contact Info

Product

Resources

About