Analytic solutions for dusty shock waves

AIAA Journal ◽  
1994 ◽  
Vol 32 (5) ◽  
pp. 979-984 ◽  
Author(s):  
Jack Pike
Keyword(s):  
Shock Waves ◽  
Analytic Solutions ◽  
Dusty Shock Waves

A nondimensional analysis of dusty shock waves in steady flows

KSME Journal ◽  
1988 ◽  
Vol 2 (1) ◽  
pp. 28-34 ◽  
Author(s):  
G. Ben-Dor ◽  
M. Mond ◽  
O. Igra ◽  
Y. Martsiano
Keyword(s):  
Shock Waves ◽  
Steady Flows ◽  
Dusty Shock Waves

Dusty Shock Waves

1988 ◽  
Vol 41 (11) ◽  
pp. 379-437 ◽  
Author(s):  
O. Igra ◽  
G. Ben-Dor
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Flow Field ◽  
Gaseous Medium ◽  
Present Review ◽  
Normal Shock ◽  
Dusty Gas ◽  
Perfect Gas ◽  
Post Shock ◽  
Dusty Shock Waves

The flow field developed behind shock waves in a pure gaseous medium is well known and documented in all gasdynamics textbooks. This is not the case when the gaseous medium is seeded with small solid particles. The present review treats various cases of shock waves propagation into a gas-dust suspension (dusty shock waves). It starts (chapter 1) with basic definitions of two-phase (gas-dust) suspensions and presents a general form of the conservation equations which govern dusty shock wave flows. In chapter two, the simple case of a steady flow of a suspension consisting of an inert dust and a perfect gas through a normal shock wave is studied. The effect of the dust presence, and of changes in its physical parameters, on the post-shock wave flow are discussed. Obviously, these discussions are limited to relatively weak shock waves (perfect gas). For stronger normal shock waves, the assumption of a perfect gas no longer holds. Therefore, in chapter three, real gas effects (ionization or dissociation) are taken into account when calculating the post-shock flow field. In chapter four, the dust chemistry is included and its effects on the post-shock flow is studied. In order to emphasize the role played by the dust chemistry, a comparison between a reactive and a similar inert suspension is presented. The case of an oblique shock wave in a dusty gas is discussed in chapter five. In all cases treated in chapters two to five the flow is steady; however, in many engineering applications this is not the case. In reality, even for the simplest case of a one-dimensional flow (normal shock wave propagation into quiescent suspension—the dusty shock tube) the shock wave attenuates and the flow field behind it is not steady. This case is treated in chapter six. The cases treated in chapters two to six deal with planar shock waves. However, all explosion generated shock waves in the atmosphere are spherical. Due to the engineering importance of this case, the post-shock flow for spherical shock waves in a dusty gas is studied, in detail, in chapter seven. It is shown in the present review that the dust presence has significant effects on the post-shock flow field. In all cases studied, a relaxation zone is developed behind the shock wave front. Throughout this zone momentum and energy exchange between the two phases of the suspension takes place. Through these interactions a new state of equilibrium is reached. The extent of the relaxation zone depends upon the dust loading ratio, the dust particle diameter, its specific heat capacity, and the dust spatial density. Due to the complexity of conducting experimental investigations with dusty shock waves, the number of published experimental results is very limited. As a result most of the present review contains numerical studies. However, in the few cases where experimental data are available, (e.g. dusty shock tube flow; see chapter six) a comparison between the numerical and experimental results is given.

Blast waves propagation in magnetogasdynamics: power series method

2020 ◽  
Vol 75 (12) ◽  
pp. 1039-1050
Author(s):  
Munesh Devi ◽  
Rajan Arora ◽  
Deepika Singh
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Power Series ◽  
Shock Front ◽  
Closed Form ◽  
Analytic Solutions ◽  
Blast Waves ◽  
Series Method ◽  
Power Series Method ◽  
The Magnetic Field

AbstractBlast waves are produced when there is a sudden deposition of a substantial amount of energy into a confined region. It is an area of pressure moving supersonically outward from the source of the explosion. Immediately after the blast, the fore-end of the blast wave is headed by the shock waves, propagating in the outward direction. As the considered problem is highly nonlinear, to find out its solution is a tough task. However, few techniques are available in literature that may give us an approximate analytic solution. Here, the blast wave problem in magnetogasdynamics involving cylindrical shock waves of moderate strength is considered, and approximate analytic solutions with the help of the power series method (or Sakurai’s approach [1]) are found. The magnetic field is supposed to be directed orthogonally to the motion of the gas particles in an ideal medium with infinite electrical conductivity. The density is assumed to be uniform in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in ${\left({a}_{0}/U\right)}^{2}$, where a0 and U are the velocities of sound in an undisturbed medium and shock front, respectively. We construct solutions for the first-order approximation in closed form. Numerical computations have been performed to determine the flow-field in an ideal magnetogasdynamics. The numerical results obtained in the absence of magnetic field recover the existing results in the literature. Also, these results are found to be in good agreement with those obtained by the Runge–Kutta method of fourth-order. Further, the flow variables are illustrated through figures behind the shock front under the effect of the magnetic field. The interesting fact about the present work is that the solutions to the problem are obtained in the closed form.

Dusty Shock Waves - An Update

1996 ◽  
Vol 49 (10S) ◽  
pp. S141-S146 ◽  
Author(s):  
G. Ben-Dor
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
State Of The Art ◽  
General Area ◽  
Gas Suspensions ◽  
The Past ◽  
Planar Shock ◽  
Dust Entrainment ◽  
The Subject ◽  
Dusty Shock Waves

A review of our original article [1] is given. It describes the state-of-the art of the subject of the propagation and attenuation of planar shock waves in dust-gas suspensions. In addition, it includes a brief description of the Dust Entrainment Phenomenon. This relatively new subject in the general area of Dusty Shock Wave has been getting more and more attention in the past few years.

Investigation of shock-wave deformation history from recovered structure

1986 ◽  
Vol 44 ◽  
pp. 434-435
Author(s):  
M.A. Mogilevsky ◽  
L.S. Bushnev
Keyword(s):  
Shock Wave ◽  
Plastic Deformation ◽  
Dislocation Density ◽  
Shock Waves ◽  
Shock Front ◽  
Single Crystals ◽  
Residual Deformation ◽  
Deformation Structure ◽  
Deformation History ◽  
Deformation Velocity

Single crystals of Al were loaded by 15 to 40 GPa shock waves at 77 K with a pulse duration of 1.0 to 0.5 μs and a residual deformation of ∼1%. The analysis of deformation structure peculiarities allows the deformation history to be re-established.After a 20 to 40 GPa loading the dislocation density in the recovered samples was about 1010 cm-2. By measuring the thickness of the 40 GPa shock front in Al, a plastic deformation velocity of 1.07 x 108 s-1 is obtained, from where the moving dislocation density at the front is 7 x 1010 cm-2. A very small part of dislocations moves during the whole time of compression, i.e. a total dislocation density at the front must be in excess of this value by one or two orders. Consequently, due to extremely high stresses, at the front there exists a very unstable structure which is rearranged later with a noticeable decrease in dislocation density.

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