Propagation of weak shock waves

An asymptotic method is developed in order to treat the evolution of weak shock waves. One obtains a geometrical theory according to which weak shock waves propagate along rays and satisfy a transport law.     

Propagation of shock waves in nonuniform plasma

Results of numerical simulation of the propagation of one-dimensional magnetohydrodynamic shock waves in a nonuniform plasma containing a magnetic field are discussed. Possible uses for the production of high velocities and temperatures and astrophysical applications are considered. The essential effect of the magnetic field is shown; acceleration of a shock wave is intensified in a medium with decreasing density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 22–26, March–April, 1976.In conclusion, the authors are grateful to S. K. Godunov for a detailed discussion of the computational aspects and of the results, and to A. E. Voitenko for a discussion of experimental possibilities and of the results.     

Propagation characteristics of shock waves driven by gaseous detonation waves

We experimentally investigated propagation characteristics of the shock wave driven by a gaseous detonation wave emerging from the open end of a cylindrical detonation tube. In the present study, we visualized the shock wave and exhaust flowfields using a shadowgraph optical system and we obtained peak overpressure in the tube axial direction and the continuous shape transformation of shock waves around the tube open end. We also obtained overpressure histories of the shock wave using piezo-pressure transducers within 201 m from the open end of the tube. We normalized and classified these results by four regions using non-dimensional pressure and distance which are independent of variety of mixture and tube diameter. In the vicinity of the open end of the tube, the shock wave is nearly planar and does not significantly attenuate, and the peak overpressure maintains approximately C–J pressure. Subsequently, the shock wave attenuates rapidly, transforming from quasi-spherical to spherical. Farther from the tube open end, the shock wave propagates with approximately sound characteristic so that the peak overpressure decreases proportional to 1/r. Eventually, the shock wave begins to attenuate more rapidly than ideal sound attenuation, which may be due to the viscous effect.     

Propagation of cylindrical shock waves in a gravitating medium

We study gas motion behind the front of a cylindrical shock wave created by the motion of a piston in a gravitating medium. The problem is self-similar, but the solution cannot be obtained in closed form. A numerical calculation is made for various Mach numbers. The calculation shows that the central part of the configuration is displaced a definite distance from the axis of symmetry.Cylindrical shock waves through a compressible homogeneous medium in a gravity field have been examined by Sedov [1] and Lin [2], However, these studies contain the essential assumption that the total energy (i. e., the sum of the kinetic and thermal energies) within the region bounded by the expanding shock wave is independent of time.In the following we extend the previous studies to the case of shock waves in nonhomogenous media, which propagate in the fluctuating gravity field created by the disturbed mass itself. The shock wave is created by the motion of a piston whose velocity varies as some power of the time, i. e., v. The total energy of the configuration also depends on the time.The authors wish to thank M. P. Murgai for cooperation and assistance and C. D. Ghildyal for valuable advice, as well as L. I. Sedov and G. I. Petrov for their critical comments.     

Propagation of steady shock waves in non-linear thermoviscoelastic solids

This paper is concerned with the dynamic response of a class of thermoviscoelastic solids. In particular a specific one-dimensional model, consistent with the laws of continuum thermodynamics, is proposed and applied to the problem of the propagation of steady shock waves. The governing equations are written in terms of material response functions which can be determined from shock wave, thermophysical, and bulk response data. The results of the analysis are compared with experimental steady wave studies involving the solid polymer, polymethyl methacrylate.     

Propagation of weak shock waves in a magnetic field

This paper gives a solution of the problem of the propagation of weak shock waves in an inhomogeneous conducting medium in the presence of a magnetic field. The width of the perturbed region is taken to be small compared with the characteristic dimensions of the problem. The magnetic Reynolds number is also assumed small, which allows one to neglect the induced magnetic field. The method of solution employed is similar to that used in [1–3],The author is grateful to B. I. Zaslavskii for useful advice and for discussing the paper.     

Propagation of planar shock waves in an exponential atmosphere

We consider planar explosions in a medium with an exponential density distribution. In contrast to the so-called sectorial approximation [1] we take into account the overflow of energy from a lower region to an upper region, so that our solution of the problem considered here gives a truer picture of the flow of the gas at a later stage of a point explosion in a nonhomogeneous atmosphere. The numerical solution in both upper and lower regions of the flow merges into the corresponding limiting self-similar regime [2, 3]. The calculations are carried out up to a gap in the atmosphere [4]. The computational method is based on implicit difference approximations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 5, pp. 31–35, September–October, 1971.The authors are deeply grateful to L. A. Chudov for his constant interest in our work and for useful discussions, and they also wish to thank É. I. Andriankin for meaningful discussions of the paper.     

Propagation of shock and detonation waves in dust-laden gases

This article examines the flows of a two-phase mixture of a gas with solid particles arising as a result of the propagation of shock waves or detonation waves through a homogeneous medium at rest. It is assumed that the basic assumptions of the mechanics of mutually penetrating continua hold [1], whereby it is possible to describe the flow of each phase of the mixture within the framework of the mechanics of a continuous medium. We assume that the solid phase consists of identical, incompressible, and nondeformable particles of spherical shape. It is assumed that the temperature inside the particles is homogeneous. Collisions between particles and their Brownian motion are ignored. It is assumed that the carrier phase is an ideal gas (the viscosity is only allowed for in the interaction forces between phases). The contribution of the volume of the particles is not considered. On the basis of these assumptions, the following problems are considered: the propagation of a detonation wave in a mixture of a detonating gas and chemically inert particles and the motion of a dust-gas mixture in a shock tube in the presence of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 93–99, November–December, 1984.     

Propagation of magnetohydrodynamic shock waves in a medium of decreasing density

It is explained under what condition instability develops in the wave front when a shock wave travels in a medium whose density is decreasing. It is shown that under laboratory conditions the buildup of such an instability may be suppressed by a diffusion of wave front segments into the walls of the system. Such an instability can occur, for example, in certain astrophysical bodies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 24–27, May–June, 1972.     

Propagation of shock waves in a medium with exponentially varying density

The results of Raizer [1], Hays [2], and Chernous'ko [3] are generalized to-the case of self-similar propagation of shock waves in a gas with exponentially varying density and constant pressure. A solution is found by the method of successive approximations. The zero-order approximation coincides with the Whitham method [4]. The first-order approximation is in good agreement with numerical calculations in [2]. The non-selfsimilar motion of a weak shock wave is investigated in the framework of linear theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 48–54, November–December, 1970.     

Propagation of converging and diverging shock waves under isothermal condition

In this article the flows of perfect gas behind converging and diverging strong shock waves under isothermal condition in the cases of spherical and cylindrical symmetry are examined. A diverging shock wave is formed by energy supply according to a power law. These waves propagate in a uniform medium at rest and all conservation laws hold at the fronts of these shock waves. It was established that in the case of converging waves for any value of the ratios of specific heats the solution of the problem under consideration exists and is unique. When the problem has more than one solution. In the case of diverging shock waves the solution exists and is unique for any from the interval and any value of power in the energy input law. Received 4 August 1996 / Accepted 28 May 1996     

接触爆炸荷载作用下带孔防护结构内冲击波的传播规律

采用有限元分析软件ATUODYN,对接触爆炸荷载作用下带孔防护结构内冲击波的传播进行了数值模拟,得到了防护结构孔口和内部中心处冲击波超压－时间曲线;分析了炸药量和爆心距孔口距离对防护结构内部超压、正压冲量的影响;以数值计算结果为基础,结合量纲分析,拟合得到了结构内部中心处爆炸冲击波特征参数的预估公式。     

Propagation of nonlinear waves in gas-liquid media with a gas content variable in space

A study is made of the propagation of nonlinear waves in gas-liquid systems of bubble structure with a gas content which is variable in the direction of propagation of the wave. It is shown that it is possible in a number of cases to amplify the pressure waves. Restrictions on the degree of homogeneity of the gas content are obtained such that, when they are fulfilled, this amplification is possible. The study also covers the effect of inhomogeneity in the gas content on the structure of nonlinear steady waves of the soliton and shock wave types.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 180–183, January–February, 1986.     

Propagation of shock waves in a two-phase mixture with different pressures of the components

The process of propagation of shock waves in two-component mixtures is considered. The studies were performed within the framework of the two-velocity approximation of mechanics of heterogeneous media with account of different pressures of the components. The stability of propagation of all types of stationary shock waves (fully dispersed, frozen-dispersed, dispersed-frozen, and frozen shock waves of two-front configuration) to infinitesimal and finite perturbations is shown numerically, using the method of coarse particles. The problem of initiation of shock waves (the formation of different types of shock waves from stepwise initial data) is solved. Flows in the transonic range relative to the speed of sound in the first component are obtained. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 55–63, January–February 1999.     

Propagation of free waves in a composite plate with elastic coupling between the layers

Zaporozh'e Industrial Institute, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 31, No. 2, pp. 48–55, February, 1995.