Effect of acoustic oscillations on the stability of a plane jet

The problem of the effect of acoustic oscillations on the stability of a compressible ideal-fluid jet flow is examined in the case of a plane jet with standing acoustic waves superimposed across it. The method of dividing the motion into fast and slow with allowance for nonlinear acoustic effects is employed. The acoustic oscillations are found to affect the growth rate of unstable hydrodynamic disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 54–60, July–August, 1991.     

Nonlinear interaction of longitudinal—Transverse acoustic waves in a circular cylinder

The limiting amplitudes of acoustic oscillations in a cylindrical volume of a heat releasing medium in which one or several modes are unstable in the linear approximation are determined. One of the mechanisms limiting the amplitudes of unstable acoustic modes is the transfer of energy from them to damped modes by nonlinear interaction. The nonlinear interactions of plane acoustic waves in a long channel have been considered by Artamonov and Vorob'ev [1]; in the present paper, the interaction of mixed longitudinal—transverse acoustic modes in a closed cylindrical volume is considered. The equations describing the interaction of two and three longitudinal—transverse modes are derived and investigated in the quadratic approximation by the method of slowly varying amplitudes and phases of the oscillations [2]. The treatment is applicable to a high-temperature gas, for which general stability conditions in the linear approximation have been formulated by Artamonov [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–9, September–October, 1982.I should like to express my thanks to K. I. Artamonov (deceased) for suggesting the problem and for scientific supervision and A. P. Vorob'ev for constant interest in the work and helpful advice.     

Nonlinear magnetoacoustic waves in a conducting liquid containing gas bubbles

The propagation of long waves in an incompressible conducting liquid saturated with nonconducting gas bubbles is considered on the basis of the equations of magnetohydrodynamics of a homogeneous gas-liquid medium. It is shown that the propagation of weakly nonlinear MHD waves in such a medium is described by the Burgers-Korteweg-de Vries (BKdV) equation. The influence of MHD interaction effects on the parameters of fast and slow weak magnetoacoustic shock waves is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 142–147, March–April, 1991.     

Frequency characteristics of a laminar flame

A theoretical study is made of the effect of harmonic pressure oscillations on a flat laminar flame. Frequency characteristics of the flames are obtained at amplitudes of the pressure oscillations which are small compared with the average pressure. It is established that in a broad range of frequencies the disturbances in the integral rate of heat release occur in phase with the pressure oscillations and depend weakly on the frequency.Translated trom Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 84–94, January–February, 1974.The authors thank V. E. Doroshenko for attention to the work and discussions.     

Waves in an inhomogeneous plasma with Hall dispersion

The evolution of steady-state periodic solutions of the Korteweg-de Vries equation (the socalled cnoidal waves), propagating along the direction of the gravitational force with an arbitrary orientation of the magnetic field, is studied for plasma characterized by Hall dispersion and Joule dissipation, using the magnetohydrodynamic approximation. The wavelength is regarded as much shorter than the characteristic scale of the inhomogeneity. The dependence of the wave amplitude on the distance to the source of the wave is considered for various limiting cases. The behavior of the wave depends on the temperature distribution in the medium. In the particular case of an isothermal atmosphere, the problem is solved analytically for a cold plasma in the absence of dissipation. The amplitude of both fast and slow waves increases when the wave travels upward and diminishes when the wave travels downward. The nonlinearity of the wave (i.e., the parameter characterizing the deviation of the wave from sinusoidal form) diminishes in the case of fast magnetoacoustic waves when the wave travels upward and increases when the wave travels downward. The situation is reversed for slow magnetoacoustic waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–144, September–October, 1976.The author is grateful to V. B. Baranov for constant interest in the work and valuable comments.     

Convective stability of a horizontal rotating fluid layer with distributed heat sources

The results of investigating the convective instability of a horizontal layer of rotating fluid, created by a temperature difference applied at the boundaries of the layer and by heat sources distributed according to various laws, are presented. It is shown that, when the other parameters of the problem are fixed, an increase in the internal heat release lowers the limits of both monotonic and oscillatory stability of the layer, increases the wave number and reduces the neutral oscillation frequency. An increase in source concentration towards the center of the layer intensifies the effect. As the strength of the internal heat sources and their concentration towards the center of the layer increase, the oscillating convection that develops at the stability limit when the Prandtl number is low and the rotation fairly fast is first replaced by monotonic convection and then ceases altogether.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–28, January–February, 1989.     

Escape of a turbulent jet under the effect of acoustic perturbations

Results are presented of experimental investigations of the local effect of acoustic oscillations of different frequency and constant intensity on the root part of a nonisothermal axisymmetric subsonic turbulent jet escaping from a gas jet atomizer at a different velocity in the S = 0.053–3.84 range of Strouhaille numbers. Data have been obtained indicating the presence of unstable escape modes of a subsonic turbulent jet in an acoustic field; experimental dependences are presented of the relative aperture of the turbulent jet flowing in an acoustic field as a function of various parameters.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 58–62, January–February, 1972.The author is grateful to A. S. Ginevskii and B. S. Burikov for discussing the results of this paper, and also to A. S. Modnov and R. A. Arkhipova for assistance in conducting and processing the experiments.     

Oscillations of a gas-vapor bubble in an acoustic field

It is shown that at large vapor contents, as a result of the combined action of phase transitions and capillary effects, the small radially symmetric oscillations of gas-vapor bubbles in an acoustic field are unstable in amplitude. The critical vapor concentration in the bubble separating regions of qualitatively different bubble behavior in the acoustic field is determined. Expressions are obtained for the decay rate of the radial oscillations of the gas-vapor bubble and the growth rate characterizing the rate of increase of oscillation amplitude in the region of instability. It is shown that adding only a slight amount of gas to the vapor bubble leads to a marked decrease in the growth rate. It is found that in the particular case of a vapor bubble the tine growth rate characterizing the development of the instability is of the same order as the second resonance frequency of the vapor bubble. This may serve to explain why in the case of vapor bubble oscillations the second resonance effect, which has been established in a number of theoretical studies and is widely discussed in the literature, has not yet been experimentally confirmed. The problem of spherically symmetrical processes around gasvapor bubbles was posed in [1], and their small oscillations are investigated in detail in [2–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 79–33, May–June, 1986.The authors are grateful to R. I. Nigmatulin for useful discussions.     

Interaction between a supersonic boundary layer and acoustic disturbances

The development of disturbances in a boundary layer that have been induced by an external acoustic field are investigated. The problem is considered in the linear formulation. It is shown that the oscillations inside the supersonic boundary layer can have several times the intensity of the external disturbances. The susceptibility of the boundary layer to the acoustic disturbances increases with increasing Mach number. Cooling of the surface leads to a small decrease in the intensity of the longitudinal velocity oscillations in the layer. The effect of the parameters of the acoustic wave is considered, i.e., the effect of the frequency and phase velocity on the development of the disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1977.     

Sound propagation in a plane wave guide with an elastic wall section

Problems of acoustic wave propagation in a plane wave guide whose walls are assumed to be undeformed with the exception of a section of finite length whose bending is described by the thin plate theory equations in the framework of the Kirchhoff-Love hypotheses are considered. The sound-proofing characteristics of the wave guide described and the stability of the forced oscillations of the system considered are investigated. Formulations of the problem of active vibroacoustic protection and the problem for the peristaltic pump are given. Soundproofing in wave guides has been considered in a number of papers, a fairly complete review of which is given in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 1, pp. 132–139, January–February, 1986.     

Conservation laws and invariants of differential equations in some problems relating to a nonhomogeneous medium

We examine the relationship between conservation laws and invariants of differential equations in problems dealing with the transformation of waves in a plasma and also the relationship of the invariants with the stability of oscillations locked in a nonhomogeneous medium and with the stability of oscillations of connected oscillators whose parameters vary randomly with time.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 9–17, November–December, 1970.The author wishes to thank S. S. Moiseev and V. D. Shapiro for valuable advice and consultation.     

Stable nonlinear waves in a poiseuille flow

Nonlinear Tolmin-Schlichting waves are studied [1–8]. The investigation is carried out by means of a modified Stuart-Watson method [1–3]. In the case of a rigid regime of excitation terms to the fifth order are taken into account in expansions with respect to the amplitude of self-excited oscillations. The stability of self-excited oscillations with respect to two- and three-dimensional disturbances is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 40–45, September–October, 1978.The author thanks S. Ya. Gertsenshtein for attention to the work and discussion of the results.     

Simple waves in a plasma with anisotropic pressure

Fast and slow simple waves are studied in the framework of the anisotropic magnetohydrodynamics of Chew, Goldberger, and Low [1]. Baranov [2] has constructed fields of integral curves for fast and slow waves and in two special cases has shown that such waves break in the compression section. The possibility of breaking of a slow wave in a rarefaction section was noted by Akhiezer et al. [3]. However, their general relations in simple waves [3] have been shown to be incorrect [2, 4]. In the present paper the nature of the variation of the longitudinal and transverse plasma pressures is determined, and the problem of the breaking of fast and slow waves is completely solved. Conditions under which a slow wave breaks in a rarefaction section are found. A fast wave always breaks in a rarefaction section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 181–183, July–August, 1988.     

Nonsteady burning of a solid propellant in a gaseous oxidizer flow

The burning of a solid propellant is investigated for nonsteady heat propagation in the induction zone. The equation of heat conduction in the propellant is solved in finite form for the case of a sharp change in burning rate; the time dependence of the temperature gradient at the propellant surface is obtained and used to investigate the mechanism of collapse of the diffusion flame above the surface. The combustion stability of a propellant burning in a channel with a large free volume is analyzed. The perturbations of the gas-dynamic quantities are related with the perturbations of the burning rate and hence with the properties of the induction zone in the solid phase. An analysis of the dispersion relation for the limiting case of propagation of acoustic waves in a stationary gas shows that the longitudinal acoustic perturbations that develop in the channel may grow with time, interacting with the heated subsurface layer of propellant.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fizikt, No. 4, pp. 44–52, July–August, 1971.In conclusion the author thanks B. V. Librovich for formulating and discussing the problem and A. G. Istratov and V. G. Markov for their valuable comments.     

Effect of the acoustic regularization of initial perturbations on the development of ordered structures

Mechanisms are considered by which acoustic oscillations influence the structure of subsonic shear flows. Analysis of the experimental data [1–7] confirms the assumption made in [6] that the regularization of initial perturbations, which causes a higher degree of ordering and an increase in the life of vortices formed because of the development of instability waves or interaction of acoustic oscillations with the edge of the nozzle, is one of the mechanisms by which acoustics influences various shear flows. Photographs are given which show the regularizing effect of acoustics on the development of vortices in the wake behind the edge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–174, January–February, 1986.     

Thermomechanical oscillations of a fluidized bed

Within the framework of the simplest one-dimensional model of a fluidized bed as a medium consisting of two interpenetrating interacting fluids, it is shown in the paper that linear thermomechanical oscillations can occur if the gas viscosity depends on the temperature and a nonisothermic chemical reaction takes place in the fluidized bed. The conditions under which oscillations occur and their frequencies are determined and their dependence on the fluidization parameters, the heat loss (or supply) rate, the rate and heat of the reaction, and quantities characterizing the dependence of the gas viscosity on the temperature and the force of the interphase interaction on the concentration of the solid particles is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 75–80, September–October, 1984.     

Stability of combustion of powder in a phenomenological model with nonadiabatic flame

A stability criterion for combustion of powder is obtained, taking into account the effect of the processes in the gas phase. It is shown that consideration of the effects of a nonadiabatic flame leads to the stability reserve of combustion being reduced and the natural frequency of vibrations being lowered. The effects thus found are physically explained by the radiation of a part of energy from the combustion zone with thermal and acoustic waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 82–87, November–December, 1973.Deceased.     

Numerical analysis of oscillations of a gaseous cavity in a compressible liquid

The radial oscillations of a gas-filled spherical cavity in an infinite compressible ideal liquid are investigated. The numerical solution of the equation of motion of a gaseous sphere is used for the comparison of acoustic and energy characteristics of underwater trotyl explosion and small-amplitude explosion sound sources (detonation of explosive gaseous mixture, expansion of a compressed inert gas).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–182, March–April, 1971.     

Stability of a spherical cavity in a sound field

The linear theory of the stability of the spherical shape of a cavity and the stability of its radial oscillations in a sound field are discussed. An equation is derived for the amplitudes of the spherical harmonics with allowance for surface tension, viscosity, and compressibility of the surrounding liquid in the Herring-Flynn approximation. The radial pulsation stability is analyzed in the same approximation. The equations derived in the article are subjected to numerical analysis.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 109–114, November–December, 1973.     

Decay rates of oscillations and effective heat transfer coefficients for bubbles pulsating radially in a liquid

Vapor (gas) bubbles executing free radial oscillations in a liquid are considered. Expressions are obtained for the frequency and decay rate of small free oscillations of the bubbles. The effective coefficients of heat transfer between the radially pulsating bubbles and the liquid are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 80–87, November–December, 1980.