The normal motion of a shock wave through a non-uniform one-dimensional medium

1955 ◽  
Vol 232 (1190) ◽  
pp. 350-370 ◽  
Keyword(s):  
Shock Wave ◽  
Density Distribution ◽  
Contact Discontinuity ◽  
Initial Density ◽  
Incident Shock ◽  
Shock Strength ◽  
Total Strength ◽  
Reflected Wave ◽  
Uniform Medium ◽  
Initial Density Distribution

The non-uniform medium is regarded as a succession of small-density discontinuities separated by uniform regions. Consideration of the interaction of a shock wave with a weak contact discontinuity gives a first-order relationship between change in shock strength and change in density across the discontinuity, which is integrated to give the shock strength as a function of the initial density of the non-uniform medium in closed form. Due to the passage of the shock, a wave is reflected back through the non-uniform medium, generating in turn a doubly reflected wave which eventually catches up the shock. A complete description of the flow as modified by the first reflected wave is obtained. The modifications to the flow caused by the doubly reflected wave are more difficult to formulate, and a complete description of the flow so modified is not given. The extra difficulty is partly due to the dependence of the doubly reflected wave on the initial density distribution, whereas the motion of the incident shock, and the flow behind it as modified only by the first reflected wave, are found to have the useful property that they are independent of the particular density-distance distribution being considered. Calculations of the total strength of the doubly reflected wave, and the strength of the incident shock when this wave has fully merged with it, have been made for a particular density distribution. A comparison of this calculated strength with the strength of the shock transmitted, after the interaction of a shock wave and a contact discontinuity, suggests that a description of the flow which takes account only of the single and double reflexions is satisfactory, even if the initial density distribution varies considerably.

EFFECTS OF INITIAL INHOMOGENEOUS DENSITY DISTRIBUTION AND VOID SHAPE ON POWDER FORGING OF POROUS METAL

2013 ◽  
Vol 27 (19) ◽  
pp. 1341008
Author(s):  
TAIQING DENG ◽  
LIANXI HU ◽  
YU SUN ◽  
XIAOYA LIU
Keyword(s):  
Density Distribution ◽  
Initial Density ◽  
Porous Metal ◽  
Major Axis ◽  
Average Density ◽  
Semi Major Axis ◽  
Punch Force ◽  
Inhomogeneous Density ◽  
Void Shape ◽  
Initial Density Distribution

The deformation behavior during axisymmetric upsetting of sintered metals has been studied based on the finite-element method. The investigation on the effects of the initial density distribution, void shape and die friction on the density distribution and punch force during deformation have been conducted. It was found that under low-friction conditions, the initial density distribution affects the deformation geometry and the density distribution. However, the effect of the initial density distribution was found to be negligible under high-friction conditions. The initial density distribution did not affect the punch force or the average density, regardless of the friction conditions. When the force is perpendicular to semi-major axis of elliptical void, it is not only good for densification but also decrease the punch force in forging of porous metal.

IV.—Expansion of a Finite One-dimensional Gas Cloud into a Vacuum

1953 ◽  
Vol 64 (1) ◽  
pp. 57-70
Author(s):  
A. G. Mackie
Keyword(s):  
Density Distribution ◽  
Analytical Solutions ◽  
Initial Density ◽  
Initial Distribution ◽  
One Dimensional ◽  
Gas Streams ◽  
Subsequent Motion ◽  
Gas Cloud ◽  
Initial Density Distribution ◽  
Stationary Period

SynopsisAn investigation is made of the motion of a one-dimensional finite gas cloud which is initially at rest and is allowed to expand into a vacuum in both directions. The density of the gas at rest is assumed to rise steadily and continuously from zero at the boundaries to a maximum in the interior of the cloud.If the subsequent motion is continuous, it is completely specified by analytical solutions in seven different regions of the x-t plane joined together along characteristics. The motion of one of the boundaries is discussed, and conditions found for it to have (i) an initial stationary period or (ii) a final constant velocity of advance into the vacuum. The gas streams in both directions from a dividing point at zero velocity. This point ultimately tends to the mid-point of the initial distribution.The possible breakdown of the continuity of the motion is discussed, and a condition on the initial density distribution found for shock-free flow to be maintained.

Paper 14: On the Reflection of Shock Waves from Deflector Plates

1965 ◽  
Vol 180 (10) ◽  
pp. 245-259
Author(s):  
W. A. Woods
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Reflected Shock Wave ◽  
Reflected Wave ◽  
Reflected Shock ◽  
Pressure Time ◽  
Wave Travel ◽  
Wave Region

The paper first explains the importance of the reflection of shock waves in the design of certain chemical plant. The theory of the reflection of shock waves is also discussed in the first part of the paper. It is shown that when a shock wave travelling along a pipe containing stationary gas reaches the outlet end of the pipe there may be ( a) a reflected expansion wave, ( b) a reflected shock wave, ( c) a reflected sound wave, ( d) no reflected wave at all, ( e) a standing shock wave situated at the end of the pipe, depending upon the strength of the incident shock wave and the amount of blockage present at the outlet end of the pipe. The conditions for each kind of reflection are determined, and in the case of the reflected shock wave region the strengths and speeds of the reflected shock waves are established throughout the region and the results are presented graphically. In the second part of the paper the results are given of experiments carried out on a shock tube fitted with various kinds of deflector plates. The experiments were performed to study the reflection of shock waves from the deflector plates by measuring pressure/time indicator diagrams near the outlet end of the pipe. The indicator diagrams revealed the approximate pressure amplitudes of the incident and reflected shock waves and also the wave travel times for the shock waves. This information was used in conjunction with the charts given in the first part of the paper to establish the deflector geometry and spacing needed in order to avoid the occurrence of a reflected shock wave.

scholarly journals The Ionization and Expansion of a Globule of Interstellar Gas overun by a Weak R Type Ionization Front

1977 ◽  
Vol 32 (7) ◽  
pp. 692-696
Author(s):  
J. S. Berry
Keyword(s):  
Density Distribution ◽  
Similarity Solution ◽  
Spherical Symmetry ◽  
Initial Density ◽  
Neutral Hydrogen ◽  
Ionization Front ◽  
Interstellar Gas ◽  
Ionized Gas ◽  
Initial Density Distribution

Abstract The flow of the ionized gas behind a contracting ionization front is investigated for spherical symmetry. A similarity solution is given when the initial density distribution in the neutral hydrogen is ω0/rα- where r is the distance from the centre of contraction.

scholarly journals The Evolution of Young Supernova Remnants

1983 ◽  
Vol 101 ◽  
pp. 119-124
Author(s):  
A. C. Fabian ◽  
W. Brinkmann ◽  
G. C. Stewart
Keyword(s):  
Density Distribution ◽  
Stellar Wind ◽  
Supernova Remnants ◽  
Initial Conditions ◽  
Numerical Models ◽  
Variable Mass ◽  
Initial Density ◽  
X Ray ◽  
Cassiopeia A ◽  
Initial Density Distribution

Einstein X-ray observations of the young supernova remnants Cassiopeia A (Murray et al. 1980) and Tycho (Seward, Gorenstein and Tucker 1982) indicate that the swept-up mass does not much exceed that of the observed ejecta. The initial density distribution of the ejecta and surrounding material is then important in determining the X-ray structure and evolution. Some aspects of this behaviour have been dealt with in previous numerical (e.g. Gull 1973; Itoh 1977; Jones, Smith and Straka 1981) and analytical (e.g. Chevalier 1982a,b) studies. We present here results obtained from numerical models covering a wider range of initial conditions. In particular, we consider the effect of a constant stellar wind from the progenitor star on the expansion of the remnant. We have previously suggested that variable mass loss from SN1006 may explain its warm filled interior (Fabian, Stewart and Brinkmann 1982).

Cylindrical shock wave in a self-gravitating perfect gas with azimuthal magnetic field via Lie group invariance method

2020 ◽  
Vol 17 (10) ◽  
pp. 2050148
Author(s):  
G. Nath ◽  
Arti Devi
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Initial Density ◽  
Density Variation ◽  
Shock Strength ◽  
Adiabatic Exponent ◽  
Perfect Gas ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
Variation Index

In this paper, we have studied the propagation of cylindrical shock waves in a self-gravitating perfect gas under the influence of azimuthal magnetic field. The method of Lie group invariance is used to construct some special class of self-similar solutions in the presence of the azimuthal magnetic field. The different cases of solutions with a power law and exponential law shock paths are obtained with the choice of arbitrary constants appearing in the expressions for the infinitesimal generators. The similarity solution for cylindrical shock wave with power law shock path is discussed in detail. The effects of variation of Alfven-Mach number, gravitation parameter, initial density variation index and adiabatic exponent on the flow variables are analyzed graphically. It is obtained that the increase in the values of Alfven-Mach number, gravitation parameter and adiabatic exponent have decaying effect on the shock strength. Also, the shock strength increases with an increase in the values of initial density variation index. A comparison is also made between the solutions in gravitating and non-gravitating cases in the presence of magnetic field.

The initiation of condensed explosives by shock waves from metals

1958 ◽  
Vol 246 (1245) ◽  
pp. 284-288 ◽  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Detonation Wave ◽  
Mild Steel ◽  
Delay Time ◽  
Incident Shock ◽  
Shock Strength ◽  
Solid Explosive ◽  
Condensed Explosives

When a shock wave is transmitted from a metal to a solid explosive a pure shock wave is transmitted into the explosive. The shock generally builds up to a complete detonation wave but in some cases it fails to initiate the explosive. In the former case an effective delay time in the initiation of the explosive is observed. Initiation delays have been measured in 2 in. diam. sticks of 60/40 RDX/TNT as a function of incident shock strength in mild steel and aluminium .

scholarly journals Confinement effects on regular–irregular transition in shock-wave–boundary-layer interactions

2018 ◽  
Vol 853 ◽  
pp. 171-204 ◽  
Author(s):  
Ilan J. Grossman ◽  
Paul J. K. Bruce
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Incident Shock ◽  
Oblique Shock Wave ◽  
Shock Strength ◽  
Wave Boundary Layer ◽  
Separation Shock ◽  
Shock Generator ◽  
Expansion Fan ◽  
Wave Boundary

An oblique shock wave is generated in a Mach 2 flow at a flow deflection angle of$12^{\circ }$. The resulting shock-wave–boundary-layer interaction (SWBLI) at the tunnel wall is observed. A novel traversable shock generator allows the position of the SWBLI to be varied relative to a downstream expansion fan. The relationship between the SWBLI, the expansion fan and the wind tunnel arrangement is studied. Schlieren photography, surface oil flow visualisation, particle image velocimetry and high-spatial-resolution wall pressure measurements are used to investigate the flow. It is observed that stream-normal movement of the shock generator downwards (towards the floor and hence the point of shock reflection) is accompanied by (1) growth in the streamwise extent of the shock-induced boundary layer separation, (2) upstream movement of the shock-induced separation point while the reattachment point remains nearly fixed, (3) an increase in separation shock strength and (4) transition between regular and irregular (Mach) reflection without an increase in incident shock strength. The role of free interaction theory in defining the separation shock angle is considered and shown to be consistent with the present measurements over a short streamwise extent. An SWBLI representation is proposed and reasoned which explains the apparent increase in separation shock strength that occurs without an increase in incident shock strength.

Computed Dynamic Compaction of a Two-Layered Copper Powder Medium

1979 ◽  
Vol 101 (2) ◽  
pp. 122-128
Author(s):  
Yukio Sano ◽  
Kiyohiro Miyagi
Keyword(s):  
Density Distribution ◽  
Layered Medium ◽  
Initial Density ◽  
Dynamic Compaction ◽  
Volume Distribution ◽  
Green Density ◽  
Compaction Process ◽  
Density Distributions ◽  
Powder Medium ◽  
Initial Density Distribution

In the paper presented a dynamic compaction of a two-layered powder medium is analyzed. A two-layered medium is used because it is the simplest form of layered medium available. The layers are differentiated not in terms of different powdered materials but rather a difference in terms of initial-density (initial specific volume) distribution, that is a higher initial density distribution and a lower initial density distribution. Again for these initial density distributions, two forms of arrangement can be considered; for the first situation, the layer to be impacted has a lower initial density distribution, while for the second situation the arrangement is reversed. The objective of this paper, therefore, is to examine the effect that the initial density sequence has on the compaction process and on the green density of a layered powder medium, especially in terms of shock wave and elastic wave influence.

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