Density distribution in rarefaction wave produced by rupture of diaphragm in a shock tube

The effect of the finite time of opening of the diaphragm in a shock tube on the formation of the rarefaction wave was investigated experimentally. The density distribution in the rarefaction wave was measured in relation to the coordinate and time and was compared with the known self-similar solution.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 130–131, March–April, 1972.     

Self-consistent approach to the problem of nonlinear waves on the surface of a vertically flowing film

An unsteady nonlinear equation, more accurate than those derived in previous studies, is obtained for the process of wave formation on the surface of a vertically flowine film. Perturbation theory is used to investigate the solutions of this equation. The wave cnaracteristics ot the steady-state flow regime are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–75, July–August, 1986.     

Formation and Amplification of Shock Waves in a Bubble “Cord”

The structure and dynamics of the wave field generated by a bubble system in the form of an axial bubble cylinder (cord) excited by a plane shock wave propagating along the axis in an axisymmetric shock tube are numerically examined. It is shown that consecutive excitation of oscillations of the bubble zone results in formation of a quasi-steady shock wave in the cord and in the ambient liquid. Results of the numerical analysis of the maximum amplitude of the resulting wave as a function of problems parameters are described.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 46–52, September–October, 2005.     

Instability of streaky structure in a Blasius boundary layer

An experimental study was performed to analyze the stability of localized streaky structure in a Blasius boundary layer. An artificial streaky structure was created by using suction or blowing through a thin spanwise slot at the wall. The velocity gradient generated by the suction or blowing was controlled by a damper. The Reynolds number based on the displacement thickness ₁ was =280 at the slot. The behavior of the artificial streaky structure was scrutinized by damping the velocity gradient. It was found that the local streamwise and spanwise velocity gradients play a significant role in the formation of different types of instability. Artificial Tollmien–Schlichting (T–S) wave packets were created by a loudspeaker to elucidate the interaction of the streaky structure with the T–S wave packets. The T–S wave packets imposed on the streaky structure become unstable when the frequency of the T–S wave packets exceeds a certain critical frequency. The development of the T–S wave packets was investigated on the basis of the neutral stability curve.     

Interaction between a vertical wall and a wave propagating in a channel of parabolic cross section

The reflection of a long wave from a vertical wall is studied on the assumption that the wave travels in a channel or river of parabolic cross section. According to [11], such cross sections are found in river beds formed in noncohesive soils. Expressions describing the evolution of the height of the wave at the vertical wall are obtained on the assumption that the exponent of the parabola takes the values k=2/(2n – 1). The conditions corresponding to the formation of a bore at the vertical wall are described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 102–105, January–February, 1987.The author wishes to thank E. N. Pelinovskii for his interest in the problem.     

Propagation of solitary waves over a semi-infinte underwater trough

Self-similar solutions describing the incidence of a uniform solitary wave on a semi-infinite linear trough are obtained on the basis of the nonlinear ray method [1]. Previously, in investigating the incidence of a wave on a trough [2] the conditions at the discontinuities present in the solutions were derived on the assumption that they are of low intensity. In the present study the use of the conditions at the discontinuities obtained by investigating soliton interaction [3–5] has made it possible to construct a series of new solutions and take into account wave reflection effects and the formation of a shadow zone beyond the trough. The types of solutions that occur are established in terms of the relations between the wave parameters and the relative depth of the trough. To ensure that self-similar solutions exist for all values of the parameters it was necessary to introduce a type of discontinuity not previously encountered [5–7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 102–107, July–August, 1987.The author wishes to thank A. G. Kulikovskii and A. A. Barmin for discussing the work.     

Shock wave formation as a result of interaction with a weak discontinuity on the boundary of a local subsonic zone

A self-similar solution, which explains the formation of a strong-family shock wave (Mach number behind the wave less than unity) on the sonic line, is obtained for the Tricomi equation of plane potential flow in hodograph variables. A characteristic with a discontinuity of the derivatives of the gas dynamic parameters arrives at the formation (interaction) point, while the characteristic of the other family leaving this point does not contain a singularity. The intensity of the shock wave varies along its generator in accordance with a power law with an exponent close to unity. At the interaction point the discontinuity of the derivatives along the streamline is equal to infinity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 152–158, July–August, 1990.The results were presented at the G. G. Chernyi seminar. The author is grateful to the seminar director and the participants for useful discussions.     

Nonlinear evolution of waves in forced decaying capillary jets

The investigation of nonlinear waves in decaying capillary jets is of great interest both from the point of view of nonlinear wave processes in media and for practical applications associated with the generation and propagation of flows of monodisperse droplets [1–4]. The formation and dynamics of satellite droplets are particularly important in the study of the decay of thin capillary jets [5–8]. Investigation of the conditions of formation of satellites open up important prospects for the preparation of monodisperse microscopic granules with diameters appreciably less than the diameter of the original jet. This is of great importance in modern technologies based on the use of materials in disperse form [9–13]. The present paper is devoted to the investigation of nonlinear waves in decaying capillary jets.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 54–60, May–June, 1993.     

Wave packet formation in an incompressible boundary layer under the influence of impulsive vibration of the wall

The formation of a Tollmien-Schlichting wave packet excited by the impulsive motion of a localized area of the boundary surface is investigated. A solution of the mixed problem for the linearized system of Navier-Stokes equations is constructed by the Fourier method for a parallel main flow. The initial stage of the disturbed motion is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 56–60, May–June, 1989.     

Mass transfer in a liquid layer of variable thickness on a rotating archimedes spiral taking account of the entrance region

In [1] the method of integral relations was used to investigate the hydrodynamics and mass transfer in a liquid layer on a rotating Archimedes spiral in the absence of wave formation. In the present article we use the work method [2, 3] to investigate the hydrodynamics and mass transfer in the entrance region in a liquid layer of variable thickness on a rotating Archimedes spiral.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 91–98, November–December, 1977.     

The existence of a discontinuity in the profile of a slow shock magnetohydrodynamic wave

An analysis is made of the structure of the profile of a slow shock magnetohydrodynamic wave of arbitrary intensity in a nonviscous medium. It is shown that the condition for the formation of a discontinuous profile coincides with the condition for the creation of an isothermal discontinuity in conventional gas dynamics.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 2, pp. 3–9, March–April, 1971.The authors thank G. Ya. Lyubarskii for useful advice and discussions of the questions touched upon in this paper.     

Propagation of nonlinear waves in a fluidized bed in the presence of interaction between the particles of the dispersed phase

A model of a fluidized bed as a medium consisting of two interacting interpenetrating ideal fluids is used to investigate the propagation of one-dimensional linear and nonlinear perturbations of the particle concentration in a gas-fluidized bed. The interaction of the particles with each other is taken into account by introducing into the momentum conservation equation for the dispersed phase an effective pressure that depends on the local porosity of the bed and the relative velocity of the dispersed and dispersion phases. The conditions of hyperbolicity of the system of equations describing wave propagation are determined. The stability of the uniform state is investigated. Dispersion effects in the fluidized bed are considered. The propagation of a steady dispersed-phase concentration wave is investigated. The conditions of formation of concentration discontinuities at the steady wave front are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 81–89, March–April, 1987.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Effect of shock–wave loading on the properties of cryogenic TiNi — a shape–memory alloy

Results of an experimental study of the shock–wave deformation of TiNi and its effect on the crystallographic structure and temperature of austenite–martensite transformations are given. It is found that, for pressures of up to 2 GPa, shock–wave loading changes the defect structure and parameters of the lattice; however, this does not lead to a noticeable change in the temperature of the austenite–martensite transformation and the manifestation of the shapeNdash;memory effect.     

Numerical simulation of shock wave intersections

A large number of papers, generalized and classified in [1, 2], have been devoted to unsteady gas flows arising in shock wave interaction. Experimental results [3–5] and theoretical analysis [6–9] indicate that the most interesting and least studied types of interaction arise in cases when there are several shock waves. At the same time, nonlinear effects, which depend largely on the nature of the shock wave intersections, become appreciable. Regions of existence of different types, of plane shock wave intersections have been analyzed in [10–13]. It has been shown that in a number of cases the simultaneous existence of different types of intersections is possible. The aim of the present paper is to study unsteady shock wave intersections in the framework of a numerical solution of the axisymmetric boundary-value problem that arises in the diffraction of a plane shock wave on a cone in a supersonic gas flow. Flow regimes that augment the experimental data of [3–5] and the theoretical analysis of [9] are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–140, September–October, 1986.     

Effect of particle size on nonlinear wave propagation in a fluidized bed

The effect of particle size (Archimedes number) on the propagation of a kinematic particle concentration wave in a fluidized bed is investigated. The dependence of the characteristic wave velocity on the porosity of the bed (particle concentration) and the Archimedes number (or the Reynolds number for flow past individual particles of the dispersed phase) is determined. The evolution of a nonlinear perturbation of the bed porosity is investigated and the formation of discontinuities in the concentration of the dispersed phase is studied in relation to the particle size (Archimedes number). It is shown, in particular, that, as distinct from a bed of small particles, in a bed of large particles with quadratic interphase interaction only compression discontinuities can be formed. The results obtained can be used to analyze the formation of inhomogeneities (slugs and bubbles) in a fluidized bed in relation to the particle size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 96–100, May–June, 1987.     

Localized Coherent Structures in the Boundary Layer

A Blasius laminar boundary layer and a steady turbulent boundary layer on a flat plate in an incompressible fluid are considered. The spectral characteristics of the Tollmien—Schlichting (TS) and Squire waves are numerically determined in a wide range of Reynolds numbers. Based on the spectral characteristics, relations determining the three–wave resonance of TS waves are studied. It is shown that the three–wave resonance is responsible for the appearance of a continuous low–frequency spectrum in the laminar region of the boundary layer. The spectral characteristics allow one to obtain quantities that enter the equations of dynamics of localized perturbations. By analogy with the laminar boundary layer, the three–wave resonance of TS waves in a turbulent boundary layer is considered.     

Pressure wave breakdown of a gas film in a liquid-filled slit

In [1–4] the results of investigating the breakdown of gas bubbles by medium-intensity pressure waves are presented and various bubble breakdown mechanisms are proposed. It is shown that breakdown may occur as a result of the formation of a cumulative jet on the boundary of the bubble or as a result of instability due to the relative motion of the bubble in the wave. In [5] experimental data on the pressure wave breakdown of a gas film in a liquid on a solid wall are reported. It is shown that at wave amplitudes p/p₀1 a liquid jet is formed at the edge of the gas film. The jet, traveling along the wall, strips off the film and carries it into the surrounding liquid. Below we investigate the pressure wave behavior of a gas film in a liquid-filled slit.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 175–178, September–October, 1992.     

Two-Phase Models of Formation of Cavitating Spalls in a Liquid

The dynamics of the structure of a liquid layer structure (with microbubbles of a free gas) behind a rarefaction wave front is studied numerically using the two-phase Iordansky–Kogarko–van Wijngaarden model and the frozen mass-velocity field model. An analysis of the initial stage of cavitation by the Iordansky–Kogarko–van Wijngaarden model showed that tensile stresses behind the rarefaction wave front relax quickly and the mass-velocity field in the cavitation zone turns out to be frozen. This effect is used to describe the late stage of the development of the cavitation zone. These models were combined to study the formation of cavitating spalls in a free-surface liquid under shock-wave loading.     

Reflection of a plane shock wave from a rigid concave wall

We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 33–39, July–August, 1970.