scholarly journals An Exact Analytical Solution of the Strong Shock Wave Problem in Nonideal Magnetogasdynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
S. D. Ram ◽  
R. Singh ◽  
L. P. Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Shock Front ◽  
Total Energy ◽  
Wave Motion ◽  
Exact Analytical Solution ◽  
Strong Shock ◽  
Strong Shock Wave ◽  
Wave Problem

We construct the solutions to the strong shock wave problem with generalized geometries in nonideal magnetogasdynamics. Here, it is assumed that the density ahead of the shock front varies according to a power of distance from the source of the disturbance. Also, an analytical expression for the total energy carried by the wave motion in nonideal medium under the influence of magnetic field is derived.

Magnetic field compression by a strong shock wave

1975 ◽  
Vol 15 (3) ◽  
pp. 427-429
Author(s):  
A. I. Bertinov ◽  
D. A. But ◽  
V. I. Yudas
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Strong Shock ◽  
Strong Shock Wave

The initial ionization of hydrogen in a strong shock wave

1969 ◽  
Vol 36 (4) ◽  
pp. 695-720 ◽  
Author(s):  
A. N. Belozerov ◽  
R. M. Measures
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Cross Section ◽  
Theoretical Calculations ◽  
Strong Shock ◽  
Operating Conditions ◽  
Strong Shock Wave ◽  
Relaxation Length ◽  
Single Temperature ◽  
The Cross

A theoretical and experimental investigation has been made of the initial ionization processes in a strong shock wave in hydrogen. The relaxation length for ionization, which is principally determined by the rate of excitation, was measured and from a comparison with the theory an estimate was obtained for the cross-section for atom-atom excitation collisions.Detailed theoretical calculations showed that the electron temperature approaches to within 1 % of the atomic temperature in a distance that is small compared with the total relaxation length for ionization. This enabled considerable simplification, for it indicated that a single-temperature model could be used in calculating the theoretical relaxation profile over the experimental range of operating conditions. An electromagnetic shock tube, with a Philippov pinch to create the driver plasma, was employed to produce shock waves of the required velocity. The ionization behind the shock front was studied by means of a double-frequency Mach-Zehnder interferometer, with a ruby laser and a K.D.P. crystal as the light source. A close agreement between the theoretical and experimental electron density profiles, behind the shock front, was obtained for small relaxation lengths, when the cross-section for the atom-atom excitation collisions was assumed to be about 7 × 10−2 times that of the corresponding cross-section for electron-atom excitation collisions.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

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