scholarly journals MODELING THE INTERACTION OF A SHOCK WAVE WITH A DEFORMABLE PERMEABLE GRANULAR LAYER

2020 ◽  
Vol 82 (3) ◽  
pp. 353-363
Author(s):  
E.G. Glazova ◽  
I.A. Turygina ◽  
I.A. Modin
Keyword(s):  
Shock Waves ◽  
Granular Layer ◽  
Strong Shock ◽  
Solid Particles ◽  
Plane Shock ◽  
Friction Forces ◽  
Reflected Waves ◽  
Drag Forces ◽  
Dimensional Approximation ◽  
Granular Layers

This article presents a mathematical model that describes, in a one-dimensional approximation, the interconnected processes of unsteady deformation of flat permeable granular layers. The model consists of solid particles and wave processes in pore and surrounding gas. The model is based on nonlinear equations of dynamics of two interpenetrating continua. As interfacial forces, drag forces are taken into account when gas flows around ball particles and friction forces. The numerical solution of the equations is carried out according to the modified scheme of S.K. Godunov, adapted to the problems of the dynamics of interpenetrating media. The contact surfaces of pure gas with the porous granular layer and pore gas are the surface of the fracture of porosity and permeability. The numerical implementation of contact conditions is based on the solution of the problem of disintegration of a gap at a jump in porosity. Solutions are obtained for the effects of plane shock waves on a deformable granular layer. We study the transformation of waves passing through an elastoplastic granular layer with and without taking into account changes in the permeability of the layer. When solving problems, the dependence of the change in the permeability of a layer on its compression is used, which is also obtained numerically when modeling the compression of symmetric fragments of granular layers in a spatial setting. Numerical studies of the processes of nonlinear interaction of shock waves with deformable permeable granular layers have shown that the parameters of transmitted and reflected waves substantially depend on the degree of compression of the granular layers. Assessment of the protective properties of permeable barriers when exposed to strong shock waves should be carried out taking into account changes in their permeability due to deformation.

The refraction of shock waves at a gaseous interface

1956 ◽  
Vol 1 (5) ◽  
pp. 457-489 ◽  
Author(s):  
Robert G. Jahn
Keyword(s):  
Boundary Layer ◽  
Shock Waves ◽  
Specific Problem ◽  
Theoretical Calculations ◽  
Strong Shock ◽  
Transition Process ◽  
Plane Shock ◽  
Reflected Waves ◽  
Special Cases ◽  
Theoretical Predictions

A programme of shock tube experiments has been conducted to study the refraction of plane shock waves at interfaces between two gases. Shocks of strength ζ = 0·85 (weak) and ζ = 0·30 (fairly strong) were allowed to impinge, at various angles of incidence, on interfaces between air/CO2and air/CH4, and the resulting configurations were photographed through a Mach-Zehnder interferometer. From the interferograms, measurements were made of the strengths of the reflected waves, and of the angles of refraction, and the values were compared with the theoretical calculations of Polachek & Seeger (1951). Within the range of parameters for which the refraction model assumed by the theory is applicable–the so-called ‘regular refraction’ region–the observations were in excellent agreement with the theoretical predictions.When the study was extended to ranges of the parameters for which the theory is clearly inadequate, a succession of rather complex ‘irregular refraction’ patterns was observed. Although these configurations were highly interesting qualitatively, each of them involved curved shocks, non-uniform regions of flow, and other less simple processes which discouraged any formal theoretical analysis. On a less rigorous basis, however, it could be shown that these patterns were internally consistent, and that each represented a distortion of a regular refraction process which was reasonable under the prevailing aerodynamic conditions.Certain observations in these refraction experiments appear to be of some significance outside the specific problem. (i) The sensitivity of strong shock refractions to the values of the specific heat ratio λ for the two gases suggests a possible technique for the measurement of λ and its temperature dependence. (ii) Two of the irregular refraction patterns display a transition process which would be equally appropriate to the onset of the Mach configuration in the shock reflection problem. (iii) Some irregular refractions can be considered as special cases in the problem of the interaction of a shock and a boundary layer.

Simple Waves and Shock Waves Generated by an Incident Shock Wave in Two-Dimensional Hyperelastic Materials

1984 ◽  
Vol 51 (3) ◽  
pp. 586-594 ◽  
Author(s):  
Yongchi Li ◽  
T. C. T. Ting
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Incident Shock ◽  
Plane Shock ◽  
Developable Surface ◽  
Two Dimensional ◽  
Reflected Waves

The reflection of an oblique plane shock wave from a boundary in a two-dimensional isotropic hyperelastic material is studied. For plane strain deformations, the strain energy function W is a function of two invariants p and q of the deformation gradient. There are, in general, two reflected waves each of which can be a simple wave or a shock wave. For a special class of materials for which the strain energy function W(p, q) represents a developable surface (of which harmonic materials are particular examples), one of the reflected waves is always a shock wave. It is shown that there are materials other than harmonic materials for which the wave speeds are independent of the direction of propagation. Illustrative examples are presented to show how one can determine the reflected waves from a rigid boundary. It is also shown that for certain incident shock waves, there exists only one reflected wave.

Ionization relaxation behind strong shock waves in gases

1970 ◽  
Vol 102 (11) ◽  
pp. 431-462 ◽  
Author(s):  
L.M. Biberman ◽  
A.Kh. Mnatsakanyan ◽  
I.T. Yakubov
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Strong Shock Waves

Characteristics of Two-Dimensional Radiation behind Strong Shock Waves in Air(1st Report) Total Radiation Emission.

1997 ◽  
Vol 45 (523) ◽  
pp. 453-457
Author(s):  
Toshihiro MORIOKA ◽  
Yoshiki MATSUURA ◽  
Nariaki SAKURAI ◽  
Jorge KOREEDA ◽  
Kazuo MAENO ◽  
...  
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Two Dimensional ◽  
Total Radiation ◽  
Radiation Emission ◽  
Strong Shock Waves

Radiation Behind the Strong Shock Waves: Experiments and Modeling

2006 ◽  
Author(s):  
Eugene Anohin ◽  
Tamara Ivanova ◽  
Nikolay Koudriavtsev ◽  
Andrei Starikovskii
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Strong Shock Waves

The determination of arc temperatures from shock velocities

1957 ◽  
Vol 240 (1220) ◽  
pp. 54-66 ◽  
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Wave Theory ◽  
New Method ◽  
Shock Propagation ◽  
Plane Shock ◽  
Gas Temperature ◽  
Specific Heats ◽  
Arc Discharges

The measurement of the high gas temperatures associated with arc discharges requires special techniques. One such method, developed by Suits (1935), depends on the measure­ment of the velocity of a sound wave passing through an arc column, although in fact Suits measured the velocity of a very weak shock wave. The new method described in the present paper is one in which temperatures are determined from the measurement of the velocity of a relatively strong shock wave propagated through an arc. The new method has the merit of consistently producing accurately measurable records and of increasing the accuracy of the temperature determination. The shock velocities are measured by means of a rotating mirror camera. Within the arc, the shock propagation is observable by virtue of the increased arc brightness produced by the shock. In the non-luminous regions surrounding the arc, the shock propagation is displayed by means of a Schlieren system. The interpretation of the measurements depends upon a one-dimensional analysis given in this paper which is similar to that of Chisnell (1955) and which describes the interaction of a plane shock with a con­tinuously varying temperature distribution. In our analysis account is taken also of the continuous variation in specific heats and molecular weight which are of importance under high gas temperature conditions. In practice plane wave theory cannot adequately describe the shock propagation, since attenuation occurs both in the free gas and in the arc column. The effects of this attenuation on the temperature determinations may be accounted for by the use of an experimentally determined attenuation relationship given in the paper. The finally developed method yields temperature values to an accuracy of ± 2%. Experiments are described for carbon and tungsten arcs in air and nitrogen for currents up to 55 amperes and pressures up to 3 atmospheres. The values obtained range from 6200 to 7700° K and are in good agreement with values determined by other techniques.

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

Sign in / Sign up

Export Citation Format

Share Document