Waves from an underground explosion

The problem of the propagation of a spherical detonation wave in water-saturated soil was solved in [1, 2] by using a model of a liquid porous multicomponent medium with bulk viscosity. Experiments show that soils which are not water saturated are solid porous multicomponent media having a viscosity, nonlinear bulk compression limit diagrams, and irreversible deformations. Taking account of these properties, and using the model in [2], we have solved the problem of the propagation of a spherical detonation wave from an underground explosion. The solution was obtained by computer, using the finite difference method [3]. The basic wave parameters were determined at various distances from the site of the explosion. The values obtained are in good agreement with experiment. Models of soils as viscous media which take account of the dependence of deformations on the rate of loading were proposed in [4–7] also. In [8] a model was proposed corresponding to a liquid multicomponent medium with a variable viscosity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 34–41, May–June, 1984.     

Shock waves in soils and in water near the point of explosion

This paper gives a solution to the problem of the propagation of a plane shock wave in soils and in water; the solution was obtained by the method of characteristics using an electronic computer. Here, the soils were regarded as multicomponent media, in accordance with a previously proposed model [1, 2]. A comparison is made between the parameters of the waves and the dimensions of the gas cavity in soils with a different content of their components and in water.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 151–159, May–June, 1972.The authors thank S. S. Grigoryan and N. I. Polyakov for their evaluation of the work.     

Calculation of viscous and plastic properties by the solution of wave problems

Models of elastoplastic media are applied to soils and rocks [1, 2]. In conformity with experimental data [3–5] a model of soils and rocks as a viscoplastic medium has been proposed [6]. Below we give a solution, based on this model, of the problem on the propagation of a plane one-dimensional wave. As the basis of computer programs we propose a finite-difference representation of the equations of motion of a continuous medium in Lagrange coordinates and the differential equations governing the behavior of the medium. A direct calculation procedure with pseudoviscosity is applied. It is shown that the damping of plane waves is connected with two energy-dissipating mechanisms, determined by the viscous and plastic properties of the medium. The washing out of a discontinuity can occur in the absence of a segment of the dynamical compression curve that is concave to the strain axis. Under certain conditions the maximum strain is attained during the phase of decreasing stress. These results agree with the experimental data [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 114–120, March–April, 1973.The authors thank S. S. Grigoryan for his discussion of the work.     

Experimental investigations of the interaction of shock waves in soils containing obstacles

A model of water-saturated soil as an ideal liquid has already been proposed [1], Experimental investigations of shock waves [2] have shown that for small stresses in water-saturated soil features of a solid plastic body begin to manifest themselves. As regards its properties the soil approximates to the model proposed in [3].The results of tests on the interaction of a plane shock wave in the soil with a moving obstacle are given below. As a development of papers [2,4, 5] an approximate solution is given for the problem of the interaction of waves with an obstacle. At high pressures the ground is regarded as nonlinearly elastic, and at low pressures as a plastic medium. A similar approach may be applied to water-saturated and nonsaturated soils when the wave is a shock wave. Experimental values of the parameters of motion of the obstacle are compared with the results of calculation.The authors are grateful to S. D. Mizyakin for participating in the tests.     

Wave propagation in the combustion of a low-concentration aerial suspension

In the general case the convective combustion of aerial suspensions is described by the equations of mechanics of multiphase media [1]. If the volume particle content is neglected and it is assumed that in the initial stage of convective front propagation the particles are stationary, and that during combustion their temperature is constant, then the equations for describing the combustion process reduce to the equations of gas dynamics for a distributed supply of heat and mass [2, 3]. The equations and model constant mass burning rate kinetics are used to solve the plane one-dimensional problem of the combustion of an aerial suspension in part of a region bounded on one side by a fixed wall. A small parameter proportional to the mass concentration and the heat value of the fuel is introduced. The method of matched asymptotic expansions [4] is used to construct a uniformly applicable first approximation. The solution obtained describes the wave propagation in aerial suspension combustion processes. The resulting pattern includes an inclined compression wave propagated with the speed of sound followed by a convective hot reaction product front whose propagation velocity is much less (in conformity with the small parameter introduced) than the speed of sound.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 63–73, March–April, 1986.     

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.     

Theory of convective combustion of an aerosuspension of fuel which contains an oxidant

In earlier papers [1, 2], the author and Nigmatulin developed a theory of the unsteady propagation of combustion in aerosuspensions of a unitary fuel (a fuel containing an oxidant) at low subsonic velocities of the gas. The assumption of low velocities permits a number of simplifications which reduce the equations describing the mechanics of multiphase reacting media [3, 5] to the equations of unsteady homobaric (with uniform pressure [1, 3, 4, 6]) motion of gas with distributed blowing and heat release. At a constant mass rate of combustion of the particles, these equations have a class of analytic solutions describing the initial stage of convective combustion of aerosuspensions in open and closed regions with allowance for the possible formation of weak shock waves. In the present paper, these solutions are generalized to the case of a more realistic law of combustion of a particle of a unitary fuel [7]. The results are given of a numerical solution to the problems, and these results make it possible, in particular, to analyze the conditions of applicability of the model with a constant mass rate of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–155, October–December, 1981.     

Wave flow regimes of a thin layer of viscous fluid subject to gravity

The studies of Kapitsa initiated the detailed experimental and theoretical study of the flow of a thin layer of viscous liquid (liquid film) over a solid surface [1–2]. Extensive experimental data on this question have now been accumulated. As a rule, the existing theories are based on linearization of the problem and diverge considerably from the experimental results. The present paper is also addressed to the theoretical solution of this problem. The solution method used enables consideration of the wave flow of the liquid as a nonlinear problem and on this basis permits determining all the parameters of the wave regime-amplitude, wavelength, wave propagation speed, frequency.     

The detonation burning of a fuel mixture resulting from a double explosion

A study is made of the propagation of a multifront detonation burning in a fuel mixture consisting of a gaseous fuel and an oxidant with additions of combustible solid or liquid particles arising as a result of a double point explosion. In such combustible media it is possible for there to be propagation of several detonation or burning fronts following one after the other. The easily igniting gaseous fuel burns in the first detonation wave, which propagates in the gaseous mixture with particles which are heated by the products of the explosion, ignite and burn in the second detonation wave or in the flame front. Self-similar regimes of propagation of such waves in an idealized formulation were studied in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–131, March–April, 1985.     

Acoustics of a Bubbly Liquid with a Weak Chemical Reaction in the Gaseous Phase

The influence of the composition and thermophysical properties of gas-liquid bubbly systems with a dissociating component in the gaseous phase on the laws of small-disturbance propagation and attenuation is investigated. It is found that the reacting gas component in the bubbles significantly affects the sonic-wave attenuation coefficient in the bubbly liquid. This follows from the fact that when a gas bubble is compressed isothermally, a recombination reaction occurs which prevents pressure growth in the bubble.Small-disturbance propagation in bubbly liquids was investigated in a number of publications discussed in review [1]. The acoustics of a bubbly liquid with a gas phase containing active admixtures are of both methodical and practical interest. The dynamics of such multicomponent bubbles were investigated in [2].     

Self-similar solutions describing the propagation of solitary waves above underwater ridges and troughs

The nonlinear ray method [1] is used to investigate the propagation of solitary waves over an uneven bottom. In the process of nonlinear evolution of the wave front, singular points develop in it; these are treated in the given model as discontinuities [2, 3]. In contrast to earlier studies, it is not assumed here that the intensity of the discontinuity is weak. Boundary conditions at the discontinuities are introduced on the basis of the results of Miles and Bakholdin [4–6], and this makes it possible to take into account the energy loss at a discontinuity and the effects of wave reflection and construct a number of new self-similar solutions for the propagation of a wave above a ridge and trough. The main attention is devoted to considering how the type of solution depends on the parameters of the wave and the relief. For certain values of the parameters, the self-similar solution of the encounter of a homogeneous wave with a ridge is not unique. The reason for this is the singularity of the relief at the end of the ridge. A numerical investigation has therefore also been made of the encounter of a wave with a ridge having a smooth relief at its end. For an under-water trough and a ridge—trough system, self-similar solutions with complete or partial reflection or transmission of the wave energy into the trough are found. A reflected wave can also arise from an encounter with a ridge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 137–144, September–October, 1985.I thank A. G. Kulikovskii and A. A. Barmin for their interest in the work and for valuable comments made as the paper was being prepared for press.     

Three-dimensional waves on the surface of a viscous fluid

The study of the effect of viscosity on the propagation of surface waves has traditionally been confined to the consideration of plane (two-dimensional) waves [1, 2]. So far the effect associated with taking the transverse modulation of the wave profile into account have not been studied. In what follows, a solution is constructed and analyzed for linear three-dimensional periodic waves in an infinitely deep fluid. Their distinguishing property is the presence of a vorticity in the direction of propagation. An expression for the average (over the wavelength) velocity of horizontal particle drift is found in the quadratic approximation in the small wave steepness.     

Impact of a strip of compressible liquid on a barrier

The exact solution of the plane problem of the impact of a finite liquid strip on a rigid barrier is obtained in the linearized formulation. The velocity components, the pressure and other elements of the flow are determined by means of a velocity potential that satisfies a two-dimensional wave equation. The final expressions for them are given in terms of elementary functions that clearly reflect the wave nature of the motion. The exact solution has been thoroughly analyzed in numerous particular cases. It is shown directly that in the limit the solution of the wave problem tends to the solution of the analogous problem of the impact of an incompressible strip obtained in [1]. A logarithmic singularity of the velocity parallel to the barrier in the corner of the strip is identified. A one-dimensional model of the motion, which describes the behavior of the compressible liquid in a thin layer on impact and makes it possible to obtain a simple solution averaging the exact wave solution, is proposed. Inefficient series solutions are refined and certain numerical data on the impact characteristics for a semi-infinite compressible liquid strip, previously considered in [2–4] in connection with the study of the earthquake resistance of a dam retaining water in a semi-infinite basin, are improved. The solution obtained can be used to estimate the forces involved in the collision of solids and liquids. It would appear to be useful for developing correct and reliable numerical methods of solving the nonlinear problems of fluid impact on solids often examined in the literature [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 138–145, November–December, 1990.The results were obtained by the author under the scientific supervision of B. M. Malyshev (deceased).     

Transmission of waves in a liquid through absorbing layers and subsequent interaction of the waves with an obstacle

The propagation of waves in porous media is investigated both experimentally [1, 2] and by numerical simulation [3–5]. The influence of the relaxation properties of porous media on the propagation of waves has been investigated theoretically and compared with experiments [3, 4]. The interaction of a wave in air that passes through a layer of porous medium before interacting with an obstacle has been investigated with allowance for the relaxation properties [5]. In the present paper, in which the relaxation properties are also taken into account, a similar investigation is made into the interaction with an obstacle of a wave in a liquid that passes through a layer of a porous medium before encountering the obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–53, March–April, 1983.     

Effect of viscosity on the propagation of nonlinear Alfvén waves along a tangential magnetohydrodynamic discontinuity in an incompressible fluid

It is proposed to consider the propagation of surface waves along a tangential magnetohydrodynamic discontinuity in the particular case where the fluid velocities on both sides of the interface are equal to zero. In [1] it was shown that waves called surface Alfvén waves may be propagated along the surface separating a semi-infinite region without a field from a region with a uniform magnetic field. The linear theory of surface Alfvén waves in a compressible medium was considered in [2]. In [3] the damping of surface Alfvén waves as a result of viscosity and heat conduction was investigated. The propagation of low-amplitude nonlinear surface Alfvén waves in an incompressible fluid in the absence of dissipative processes is described by the integrodifferential equation obtained in [4]. By means of a numerical solution of this equation it was shown that a perturbation initially in the form of a sinusoidal wave will break. The breaking time was determined. In this paper the equation derived in [4] is extended to the case of a viscous fluid. It is shown that the equation obtained does not have steady-state solutions. The propagation of periodic disturbances is investigated numerically. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–104, November–December, 1986. The author wishes to thank L. S. Fedorov for assisting with the calculations.     

Method of outer and inner asymptotic expansions in the theory of Brownian motion of aerosol particles

We examine the Brownian motion of particles in a gaseous medium, complicated by the influence of inertial forces. The equation for the distribution function in phase space describing motion of this type was obtained in [1]. Also presented in [1] are the solutions of this equation for certain simple particular cases. The approximate equations of motion of aerosol particles in coordinate space were first obtained in [2] and solved for certain concrete problems in [3,4]. More exact equations of motion in coordinate space, and also the limits of applicability of the equations of [2], are presented in [5].     

Interaction of rarefaction waves with wet foam

The interaction of rarefaction waves of different shapes with wet water foams is studied experimentally. It is found that the observed values of the pressure are greater, while the surface velocity is lower than the corresponding values predicted by the pseudogas model. The foam breakdown starts as the pressure decreases by 0.3 atm relative to the initial pressure. During downstream propagation of the rarefaction-wave leading edge the propagation velocity decreases.Using of water-based foams as effective screens for damping blast waves in different technological processes has caused considerable interest in studying wave propagation in such systems. The pressure wave dynamics in a foam have been investigated in much detail, both experimentally and theoretically [1–3]. However, the interaction of rarefaction waves with foam has practically never been studied, although it was mentioned in [4] that the unloading phase following the compression wave phase is one of the factors defining the damaging action of blast waves. Besides blast-wave damping, rarefaction wave propagation takes place if such waves are used to breakup foam in oil-producing wells [5].Below, the interaction of rarefaction waves of different shapes with wet water foams is studied. The vertical shock tube described in detail in [3] was used in these experiments.Brest. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–82, March–April, 1995.     

Effect of a shock wave on heat propagation

The nature of the propagation of a thermal wave produced by a powerful explosion was described in a number of papers, for example, [1–6]. It was shown by a numerical method [4] that a shock wave is present together with the thermal wave. In this paper, the effect of a homothermal shock wave on heat propagation is evaluated by an approximate method.     

Numerical simulation of explosion processes in fronzen soil

At present, there are numerous experimental and theoretical papers concerned with the behavior of soft soils under explosive loading; e.g., see [1–5]. The case of frozen soils is quite different. There are known only a few papers presenting the results of experimental [6–8] and numerical [9, 10] studies. The numerical results were obtained by solving one-dimensional problems on the explosion of a spherical charge. In the present paper, we give the results of numerical studies of wave processes caused by the explosion of a spherical charge in a homogeneous or layered frozen soil with allowance for the free surface and the finite depth of the freezing boundary. Frozen and soft soils are modeled by Grigoryan’s medium with irreversible bulk and shear strains. We analyze how the free boundary and the interface affect the wave parameters. The results of numerical calculations are compared with known experimental data.