The Problem of a Strong Explosion with Energy Loss or Deposition at the Front of the Shock Wave and the Problem of an Impulsive Load: Self-Similar Solutions of the Second Kind

1979 ◽  
pp. 63-85
Author(s):  
G. I. Barenblatt
Keyword(s):  
Shock Wave ◽  
Energy Loss ◽  
Impulsive Load ◽  
Self Similar ◽  
Strong Explosion ◽  
Similar Solutions

Inviscid hypersonic flow on cusped concave surfaces

1966 ◽  
Vol 24 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Philip A. Sullivan
Keyword(s):  
Shock Wave ◽  
Surface Pressure ◽  
Leading Edge ◽  
Pressure Change ◽  
Inviscid Flow ◽  
Small Region ◽  
The Body ◽  
Cubic Surface ◽  
Self Similar ◽  
Similar Solutions

An analysis of the exact equations of the inviscid flow of a perfect gas over cusped concave bodies is described. The field is examined in the limit of infinite free-stream Mach numberM∞. The slope of the shock wave in a small region adjacent to the leading edge is strongly dependent onM∞, while much further downstream the shock-wave slope is controlled primarily by the body slope. Consequently the region near the leading edge introduces into the field downstream a thin layer of gas, adjacent to the body, where the entropy is much lower than that of the gas above it. This layer is so dense that the gas velocity along it is not appreciably slowed by the pressure gradient along the body. However, it is so thin that there is little pressure change across it.The well-known self-similar solutions to the hypersonic small-disturbance equations have previously only been used to study the flow on blunted slender convex surfaces. They are known to behave singularly at the body. It is shown that there is a region on concave power-law shapes where the self-similar solutions are the correct first approximation to the exact inviscid equations in the limitM∞→ ∞; and that, further, they predict the correct first-order surface pressure.Numerical results for surface pressure from the similar solutions are presented, and comparisons are made with certain approximate theories available for more general shapes. Pressure measurements taken on a cubic surface in the Imperial College gun tunnel are presented and compared with the theoretical distributions.

scholarly journals Shock Wave in Condensed Matter Generated by Impulsive Load

1985 ◽  
Vol 40 (1) ◽  
pp. 8-13 ◽  
Author(s):  
S. I. Anisimov ◽  
V. A. Kravchenko
Keyword(s):  
Shock Wave ◽  
Shock Loading ◽  
Condensed Matter ◽  
Laser Pulses ◽  
Self Similarity ◽  
Impulsive Load ◽  
Self Similar Solution ◽  
Short Laser Pulses ◽  
The Media ◽  
Self Similar

A shock wave in condensed matter generated by impulsive load ("shock loading") is considered. A self-similar solution of the problem is presented. The media are described by the equation-of-state of the Mie-Grüneisen type. Values of the self-similarity exponent and the profiles of gas-dynamical variables have been calculated. The problem of generation of shock waves by ultra-short laser pulses is discussed.

scholarly journals Self Similar Shocks in Atmospheric Mass Loss Due to Planetary Collisions

Atmosphere ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 445
Author(s):  
Almog Yalinewich ◽  
Andrey Remorov
Keyword(s):  
Shock Wave ◽  
Mass Loss ◽  
Equations Of State ◽  
Impact Angle ◽  
Planetary Cores ◽  
Self Similar Solution ◽  
Self Similar ◽  
Similar Solutions ◽  
The Impact ◽  
Atmospheric Mass

We present a mathematical model for the propagation of the shock waves that occur during planetary collisions. Such collisions are thought to occur during the formation of terrestrial planets, and they have the potential to erode the planet’s atmosphere. We show that, under certain assumptions, this evolution of the shock wave can be determined using the methodologies of Type II self similar solutions. In such solutions, the evolution of the shock wave is determined by boundary conditions at the shock front and a singular point in the shocked region. We show how the evolution can be determined for different equations of state, allowing these results to be readily used to calculate the atmospheric mass loss from planetary cores made of different materials. We demonstrate that, as a planetary shock converges to the self similar solution, it loses information about the collision that created it, including the impact angle for oblique collisions.

Self-similar explosion waves of variable energy at the front

1980 ◽  
Vol 99 (4) ◽  
pp. 841-858 ◽  
Author(s):  
G. I. Barenblatt ◽  
R. H. Guirguis ◽  
M. M. Kamel ◽  
A. L. Kuhl ◽  
A. K. Oppenheim ◽  
...  
Keyword(s):  
Energy Deposition ◽  
Density Ratio ◽  
Blast Waves ◽  
Ambient Atmosphere ◽  
Pressure Profiles ◽  
Integral Curves ◽  
Self Similar ◽  
Strong Explosion ◽  
Similar Solutions ◽  
Variable Energy

A set of self-similar solutions for blast waves associated with the deposition of variable energy at the front is presented. As a consequence of self-similarity, the results are applicable when the ambient atmosphere into which the wave front propagates is at a negligibly low pressure and temperature. Besides the class of (1) blast waves associated with energy gain that covers a regime bounded on one side by the well-known solution for adiabatic strong explosion waves (ASE) and, on the other side, by the solution for waves having the Chapman–Jouguet condition established immediately behind the front, included within the scope of our analysis are two others: (2) blast waves associated with energy loss that occupy a regime between the ASE solution and the case of infinite density ratio across the front, and (3) a non-unique class of solutions for blast waves associated with energy deposition that may have either locally sonic or supersonic flow immediately behind the front, extending over the regime between the waves headed by the Chapman-Jouguet detonation and the case of infinite rate of energy deposition. Specific results for a number of representative cases are expressed in terms of integral curves on the phase plane of reduced blast wave co-ordinates, as well as in the form of particle velocity, temperature, density, and pressure profiles across the flow field.

The propagation upward of the shock wave from a strong explosion in the atmosphere

1968 ◽  
Vol 32 (2) ◽  
pp. 317-331 ◽  
Author(s):  
Wallace D. Hayes
Keyword(s):  
Shock Wave ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Axial Symmetry ◽  
Approximation Scheme ◽  
The Self ◽  
Parabolic Approximation ◽  
Propagation Law ◽  
Self Similar ◽  
Strong Explosion

A method is established for the calculation of the trajectories of shocks moving upward in the atmosphere, on the basis of the assumption that they are of the self-propagating type. The results of calculations for self-similar motions are given, and these are used to establish a propagation law based upon the concepts of the Chisnell, Chester and Whitham (CCW) approximation. This propagation law enters a characteristics law based upon that proposed by Whitham, but reformulated for the computation of axisymmetric shocks with varying density.An asymptotic self-preserving shock shape is investigated, and is computed for the case γ = 1·4. A parabolic approximation scheme suggested by the self-preserving solution is developed, in which the solution near the axis is reduced to the solution of a system of ordinary differential equations. Finally, the governing equation for the general case without axial symmetry (but without winds) is presented.

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