L. P. Singh

The progressive wave approach analyzing the decay of a sawtooth profile in magnetogasdynamics

An asymptotic approach is used to analyze the main features of weakly nonlinear waves propagating through an electrically conducting gas permeated by a transverse magnetic field. The analysis leads to an evolution equation, which characterizes the wave process in the high‐frequency domain. The growth equation for an acceleration front is recovered as a special case. The influence of the magnetic field on the decay behavior of a sawtooth profile, which is headed by a weak shock front and ends with a magnetosonic disturbance, is investigated. A remarkable difference between the plane and cylindrical wave profiles is noted; for instance, when the adiabatic index γ is 2, the field does not affect the decay behavior of plane waves but does affect cylindrical waves.

An Approximate Analytical Solution of Imploding Strong Shocks in a Non-Ideal Gas through Lie Group Analysis

The method of Lie group transformation is used to obtain an approximate analytical solution to the system of first-order quasilinear partial differential equations that govern a one-dimensional unsteady planer, cylindrically symmetric and spherically symmetric motion in a non-ideal gas, involving strong shock waves. Invariance groups admitted by the governing system of partial differential equations, which are indeed continuous group of transformations under which the system of partial differential equations remains invariant, are determined, and the complete Lie algebra of infinitesimal symmetries is established. The infinitesimal generators are used to construct the similarity variables. These similarity variables are used to reduce the governing system of partial differential equations into a system of ordinary differential equations.

Flow pattern induced by a piston impulsively moving in a perfectly conducting inviscid radiating gas

A self‐similar method is used to study numerically the flow pattern resulting from the impulsive motion of a plane and a cylindrical piston through a perfectly conducting inviscid radiating gas permeated by a transverse magnetic field. The effects of thermal radiation are treated by the differential approximation to the radiative transfer equation. Numerical solutions in the region between the shock and the piston are presented for the cases of general opacity and the transparent limit. The influence of thermal radiation, the magnetic field strength, and the adiabatic heat exponent on the flow pattern for various cases are assessed. The general behavior of the velocity and density distribution remains essentially unaffected by the interaction between the radiative and magnetogasdynamic phenomena. However, the pressure profiles are greatly affected by the interaction; the effect of the magnetic interation is to diminish the effects of radiative transfer.

Propagation of weak shock waves in a non-ideal gas

This paper investigates the problem of propagation of planar and non-planar weak shock waves in a non-ideal medium. The mathematical formulation developed in this work leads to a closed system of coupled transport equations which efficiently describes the strength of a shock wave and the first order discontinuities induced behind it. The influence of the parameter of non-idealness and the non planar configuration of the wavefront on the nonlinear distortion, attenuation and shock formation of pulses, are discussed in detail. An analytical expression for the shock formation distance is obtained and a direct comparison between the ideal versus the non ideal gas flow is established. Also, the usual asymptotic decay laws for weak shock are recovered.

Steepening of waves in radiative magnetohydrodynamics

Abstract Singular surface theory is used to determine the modes of wave propagation and development of discontinuities at planar and cylindrical wave fronts. It is investigated as to how the effects of thermal radiation and magnetic field strength influence the steepening and flattening of wave fronts. Although the effect of magnetic field, whether axial or azimuthal, is to increase the shock formation distance, it, unlike the effect of thermal radiation, cannot offset the tendency of a compression wave-head, carrying a jump discontinuity (no matter how weak initially), to grow into a shock wave after a finite running length. In an optically thick gas with negligible radiation pressure and energy, an increase in the radiative flux reduces the shock formation distance; this is in contrast to the corresponding result for an optically thin gas where an increase in the radiative flux causes shock formation distance to increase. However, numerical calculations show that in a temperature range 9 × 10 4 T 5 , the combined effect of radiation pressure, energy and flux is to delay the formation of a shock wave. It is found that the decaying of expansion waves is enhanced (slowed down) due to the presence of thermal radiation (magnetic field).

Analytical Solution of the Blast Wave Problem in a Non-Ideal Gas

An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium. It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave. Also, an analytical expression for the total energy in a non-ideal medium is derived.

Landau-Stanyukovich Rule and the Similarity Parameter of Converging Shock Waves in Magnetogasdynamics

Second-kind self-similar solutions to a problem of converging cylindrical shock waves in magnetogasdynamics are investigated. Two trial functions suggested by Chisnell and the shooting method of Landau—Stanyukovich are used to determine the similarity exponent for different values of specific heat ratio γ and the parameter k, where k (0, 1]. Detailed analyses of flow patterns for different values of adiabatic heat exponent and magnetic field strength are carried out. It is observed that the general behavior of the velocity and density profiles is not affected in a magnetogasdynamics regime whereas there is an increase in the absolute value of the flow parameters with an increase in the magnetic field strength. However, the pressure profiles are greatly affected by the magnetic field interaction.

Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.

Analytical Solution of Converging Shock Wave in Magnetogasdynamics

In this paper, a similarity solution to a problem in magnetogasdynamics with strong converging cylindrical shock wave is examined. An analytical description of converging shock waves is presented by replacing the previous approach for numerical solutions of the ordinary differential equations with a theoretical study of the singular points of the differential equations. A study of singular points of the system of differential equations leads to an analytic description of the flowfield and a determination of the similarity exponent. The influences of adiabatic heat exponent and magnetic field strength on the flow pattern for various cases are assessed. The general behavior of the velocity and density distribution remains unaffected. However, the pressure profiles are greatly affected by the magnetic field interaction.

Wave propagation in a steady supersonic flow of a radiating gas past plane and axisymmetric bodies

SummaryUsing the method of wavefront analysis the paper presents an analysis of shock wave formation in a two-dimensional steady supersonic flow of a radiating gas past plane and axisymmetric bodies such as a beak and sharp edged ring. Transport equations are derived which lead to the determination of the shock formation distance and also to conditions which insure that no shock will ever evolve on the wavefront. It is assessed as to how the shock formation distance is influenced by the presence of thermal radiation, the initial body curvature and upstream flow Mach numberM0>1.