One-dimensional spherical shock waves in an interstellar dusty gas clouds

2021 ◽  
Vol 76 (5) ◽  
pp. 417-425
Author(s):  
Astha Chauhan ◽  
Kajal Sharma
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Differential Equations ◽  
Shock Propagation ◽  
Dusty Gas ◽  
Shock Strength ◽  
Efficient System ◽  
One Dimensional ◽  
Arbitrary Strength ◽  
Spherical Shock

Abstract A system of partial differential equations describing the one-dimensional motion of an inviscid self-gravitating and spherical symmetric dusty gas cloud, is considered. Using the method of the kinematics of one-dimensional motion of shock waves, the evolution equation for the spherical shock wave of arbitrary strength in interstellar dusty gas clouds is derived. By applying first order truncation approximation procedure, an efficient system of ordinary differential equations describing shock propagation, which can be regarded as a good approximation of infinite hierarchy of the system. The truncated equations, which describe the shock strength and the induced discontinuity, are used to analyze the behavior of the shock wave of arbitrary strength in a medium of dusty gas. The results are obtained for the exponents from the successive approximation and compared with the results obtained by Guderley’s exact similarity solution and characteristic rule (CCW approximation). The effects of the parameters of the dusty gas and cooling-heating function on the shock strength are depicted graphically.

scholarly journals Propagation of Shock Waves in a Polytrope with a Toroidal Magnetic Field. I. Simplified Solution of Differential Equations

1969 ◽  
Vol 22 (5) ◽  
pp. 589
Author(s):  
NK Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Shock Waves ◽  
Differential Equations ◽  
Toroidal Magnetic Field ◽  
Spherical Shock Wave ◽  
Simplified Solution ◽  
Spherical Shock

The propagation of an initially spherical shock wave in a polytrope with a magnetic field has been studied. The model chosen for the purpose was that of a poly trope with a toroidal magnetic field given previously by Sinha. Butler's method has been extended to transform the set of governing partial differential equations into a set of ordinary differential equations involving derivatives in the direction of propagation of the shock element at any point. An approximate solution is obtained and the effect of the toroidal magnetic field on the geometry of the front as well as on the effects brought about by the shock is discussed.

Shock Wave Kinematics in a Relaxing Gas with Dust Particles

2019 ◽  
Vol 74 (9) ◽  
pp. 787-798 ◽  
Author(s):  
Sonu Mehla ◽  
J. Jena
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Cross Section ◽  
Dust Particles ◽  
One Dimensional ◽  
Wave Kinematics ◽  
Relaxation Parameters ◽  
Arbitrary Strength ◽  
Spatially Varying ◽  
Relaxing Gas

AbstractIn this article, we considered the evolutionary behaviour of one-dimensional shock waves propagating through a relaxing gas with dust particles in a duct with spatially varying cross section. We adopted the procedure based on the kinematics of a one-dimensional motion to derive an infinite hierarchy of transport equations, which describe the evolutionary behaviour of shock of arbitrary strength propagating through the medium. The first three truncation approximations are considered, and the results are compared with existing results in the absence of relaxation and dust particles. The effects of dust particles and relaxation are studied using numerical computations. The results are depicted for different values of dust and relaxation parameters.

IMPLODING CYLINDRICAL AND SPHERICAL SHOCK WAVES IN A NON-IDEAL MEDIUM

2004 ◽  
Vol 01 (03) ◽  
pp. 521-530 ◽  
Author(s):  
G. MADHUMITA ◽  
V. D. SHARMA
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Low Density ◽  
Similarity Parameter ◽  
One Dimensional ◽  
Ideal Medium ◽  
Converging Shock Waves ◽  
Gas Molecules ◽  
Internal Volume ◽  
Spherical Shock

Converging shock waves in an almost ideal medium are considered. The kinematics of one-dimensional motion have been applied to construct an evolution equation for strong cylindrical and spherical shock waves propagating into a low density gas at rest. The approximate value of the similarity parameter obtained from there is compared with those derived from Whitham's Rule and the exact similarity solution at the instant of collapse of the shock wave. The above computation is carried out for different values of the parameter α, which depends on the internal volume of the gas molecules.

Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Swati Chauhan ◽  
Antim Chauhan ◽  
Rajan Arora
Keyword(s):  
Shock Waves ◽  
Mass Fraction ◽  
Strong Shock ◽  
Dust Particles ◽  
Excluded Volume ◽  
One Dimensional ◽  
First Order ◽  
Nonideal Gas ◽  
Spherical Shock ◽  
Strong Shock Waves

Abstract In this work, we consider the system of partial differential equations describing one-dimensional (1D) radially symmetric (i.e., cylindrical or spherical) flow of a nonideal gas with small solid dust particles. We analyze the implosion of cylindrical and spherical symmetric strong shock waves in a mixture of a nonideal gas with small solid dust particles. An evolution equation for the strong cylindrical and spherical shock waves is derived by using the Maslov technique based on the kinematics of 1D motion. The approximate value of the similarity exponent describing the behavior of strong shocks is calculated by applying a first-order truncation approximation. The obtained approximate values of similarity exponent are compared with the values of the similarity exponent obtained from Whitham’s rule and Guderley’s method. All the above computations are performed for the different values of mass fraction of dust particles, relative specific heat, and the ratio of the density of dust particle to the density of the mixture and van der Waals excluded volume.

Shock waves in a liquid containing gas bubbles

1958 ◽  
Vol 243 (1235) ◽  
pp. 534-545 ◽  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Rarefaction Wave ◽  
Temperature Rise ◽  
Compression Wave ◽  
Liquid Mixture ◽  
Propagation Speed ◽  
Plane Wall ◽  
Shock Propagation ◽  
Wide Range

Considerations of continuity, momentum and energy together with an equation of state are applied to the propagation of plane shock waves in a gas + liquid mixture. The shock-wave relations assume a particularly simple form when the temperature rise across a shock, which is shown to be small for a very wide range of conditions, is neglected. In particular, a simple relation emerges between the shock propagation speed and the pressure on the high-pressure side of the shock, the density of the liquid and the relative proportions, by mass and volume, of gas and liquid in the mixture. It is shown from entropy considerations that a rarefaction wave cannot propagate itself without change of form, and it is argued that a compression wave can be expected to steepen into a shock wave. Consideration of the collision between two normal shock waves, moving in opposite directions, suggests that the strengths of the two shocks are unaltered by the interaction between them. This implies, in particular, that, when a shock impinges normally on a plane wall, the pressure ratio across the reflected shock is equal to that across the incident shock. When the mass ratio of gas to liquid in the mixture is allowed to tend to infinity, the various shock-wave relations for a mixture, derived with the temperature rise across the shock neglected, assume the same limiting form as the corresponding relations for a perfect gas when the ratio of specific heats tends to unity. The theoretical discussion has been illustrated by experiments with a small gas + liquid mixture shock tube. Samples of the records, obtained when the passage of a shock changes the amount of light transmitted through the mixture to a photoelectric cell, illustrate the steepening of a compression wave and the flattening of a rarefaction wave. Measurements confirm the theoretical relation for the propagation speed of shock waves. Reasonably good experi­mental confirmation is also reported of the theoretical predictions for the pressure which arises following the normal impact of a shock wave on a plane wall.

scholarly journals Propagation of Shock Waves in a Polytrope with a Toroidal Magnetic Field. II. Solution of Complete Differential Equations

1969 ◽  
Vol 22 (5) ◽  
pp. 605
Author(s):  
NK Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Differential Equations ◽  
Toroidal Magnetic Field ◽  
Initial Values ◽  
Made In

The differential equations for the shock parameters along shock rays in the case of propagation of a spherically developed shock wave in a polytrope with a toroidal magnetic field, obtained in Part I, have been integrated numerically for a particular set of initial values. The results are compared with the corresponding results in Part I obtained by neglecting certain small terms and it is found that the effect of this omission is not significant. This substantiates the results and justifies the simplification made in Part 1.

Probing of Flow Fields with Shock Waves—The Swing Probe

1971 ◽  
Vol 49 (10) ◽  
pp. 1340-1349 ◽  
Author(s):  
J. D. Strachan ◽  
B. Ahlborn
Keyword(s):  
Shock Waves ◽  
Source Term ◽  
Flow Fields ◽  
Inhomogeneous Media ◽  
Shock Propagation ◽  
Local Velocity ◽  
One Dimensional ◽  
Density Distributions ◽  
The One ◽  
Velocity Pressure

The one dimensional equations governing shock propagation into inhomogeneous media have been developed to allow a shock to be used as a probe. Shock waves which collide with unknown gas or plasma flow fields suffer a change in velocity. Pressure, density, particle velocity, and local energy input at the edge of an unknown flow can be determined from the measurement of unknown flow. The steady variation of the velocity of strong probing shocks reveals details of the local velocity and density distributions inside the unknown flow field. One further result is the extension of the general theory of shock propagation into inhomogeneous media to cover the case when an energy source term appears at the front.

scholarly journals Normal Reflection Characteristics of One-Dimensional Unsteady Flow Shock Waves on Rigid Walls from Pulse Discharge in Water

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Dong Yan ◽  
Jinchang Zhao ◽  
Shaoqing Niu
Keyword(s):  
Shock Wave ◽  
Hydrostatic Pressure ◽  
Shock Waves ◽  
Pulse Discharge ◽  
Weak Shock ◽  
Rigid Wall ◽  
Wave Source ◽  
One Dimensional ◽  
Normal Reflection ◽  
Rigid Walls

Strong shock waves can be generated by pulse discharge in water, and the characteristics due to the shock wave normal reflection from rigid walls have important significance to many fields, such as industrial production and defense construction. This paper investigates the effects of hydrostatic pressures and perturbation of wave source (i.e., charging voltage) on normal reflection of one-dimensional unsteady flow shock waves. Basic properties of the incidence and reflection waves were analyzed theoretically and experimentally to identify the reflection mechanisms and hence the influencing factors and characteristics. The results indicated that increased perturbation (i.e., charging voltage) leads to increased peak pressure and velocity of the reflected shock wave, whereas increased hydrostatic pressure obviously inhibited superposition of the reflection waves close to the rigid wall. The perturbation of wave source influence on the reflected wave was much lower than that on the incident wave, while the hydrostatic pressure obviously affected both incident and reflection waves. The reflection wave from the rigid wall in water exhibited the characteristics of a weak shock wave, and with increased hydrostatic pressure, these weak shock wave characteristics became more obvious.

On converging shock waves of spherical and polyhedral form

2002 ◽  
Vol 454 ◽  
pp. 365-386 ◽  
Author(s):  
DONALD W. SCHWENDEMAN
Keyword(s):  
Shock Waves ◽  
Numerical Study ◽  
Stability Result ◽  
Shock Propagation ◽  
Initial Shape ◽  
Regular Polyhedra ◽  
Converging Shock Waves ◽  
Geometrical Shock Dynamics ◽  
The Stability ◽  
Spherical Shock

The behaviour of converging spherical shock waves is considered using Whitham's theory of geometrical shock dynamics. An analysis of converging shocks whose initial shape takes the form of regular polyhedra is presented. The analysis of this problem is motivated by the earlier work on converging cylindrical shocks discussed in Schwendeman & Whitham (1987). In that paper, exact solutions were reported for converging polygonal shocks in which the initial shape re-forms repeatedly as the shock contracts. For the polyhedral case, the analysis is performed both analytically and numerically for an equivalent problem involving shock propagation in a converging channel with triangular cross-section. It is found that a repeating sequence of shock surfaces composed of nearly planar pieces develops, although the initial planar surface does not re-form, and that the increase in strength of the shock at each iterate in the sequence follows the same behaviour as for a converging spherical shock independent of the convergence angle of the channel. In this sense, the shocks are stable and the result is analogous to that found in the two-dimensional case. A numerical study of converging spherical shocks subject to smooth initial perturbations in strength shows a strong tendency to form surfaces composed of nearly planar pieces suggesting that the stability result is fairly general.

Precursor shock waves at a slow—fast gas interface

1976 ◽  
Vol 76 (1) ◽  
pp. 157-176 ◽  
Author(s):  
A. M. Abd–El–Fattah ◽  
L. F. Henderson ◽  
A. Lozzi
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Shock Wave ◽  
Shock Waves ◽  
Plane Shock ◽  
One Dimensional ◽  
Irregular Wave ◽  
Irregular Systems ◽  
Theory And Experiment ◽  
Good Agreement

This paper presents experimental data obtained for the refraction of a plane shock wave at a carbon dioxide–helium interface. The gases were separated initially by a delicate polymer membrane. Both regular and irregular wave systems were studied, and a feature of the latter system was the appearance of bound and free precursor shocks. Agreement between theory and experiment is good for regular systems, but for irregular ones it is sometimes necessary to take into account the effect of the membrane inertia to obtain good agreement. The basis for the analysis of irregular systems is one-dimensional piston theory and Snell's law.

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