Detonation Wave Propagation in Rotational Gas Flows

This paper studies the propagation of detonation and shock waves in vortex gas flows, in which the initial pressure, density, and velocity are generally functions of the coordinate — the distance from the symmetry axis. Rotational axisymmetric flow having a transverse velocity component in addition to a nonuniform longitudinal velocity is considered. The possibility of propagation of Chapman–Jouguet detonation waves in rotating flows is analyzed. A necessary conditions for the existence of a Chapman–Jouguet wave is obtained.     

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.     

Sudden Blocking of a Subcritical Open–Channel Flow

This paper reports results of experiments in which a steady nonuniform flow in a rectangular channel with an even horizontal bottom was blocked by a rapidly falling shield. Data on the height of the splash–up of water on the shield and the shape, propagation speed, height, and internal structure of the upstream propagating wave of the bore type are obtained for various liquid flow rates at the channel entrance. It is established that the bore produces a strong stratification in the liquid particle velocity, and under particular conditions, the speed of propagation and height of the bore, and the height of the water splash–up on the wall are constant and are determined only by the critical depth for unperturbed flow, i.e., by the specified flow rate.     

Determination of particle charge and size from the propagation of ultrasound in suspensions

The propagation of small perturbations in raulticomponent disperse media consisting of an uncharged dispersion fluid, positive and negative ions and charged particles or droplets of another fluid is investigated. When weak waves pass through emulsions and suspensions, because of the difference in the velocities of the ions and charged particles a non-uniform distribution of electric potential develops in the medium [1–3]. Expressions relating the amplitude of the electric potential and the amplitude of the fluid velocity in the wave, the particle charge and the parameters characterizing the medium are derived. Relations are obtained for the phase shift between the values of the electric potential and the fluid velocity. It is proposed to use the expressions obtained, which describe the propagation of ultrasound, for the experimental determination of the particle charge and other parameters of the disperse medium, in particular, the particle size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1988.     

Shock wave in a gas-liquid medium

The propagation of weak shock waves and the conditions for their existence in a gas-liquid medium are studied in [1]. The article [2] is devoted to an examination of powerful shock waves in liquids containing gas bubbles. The possibility of the existence in such a medium of a shock wave having an oscillatory pressure profile at the front is demonstrated in [3] based on the general results of nonlinear wave dynamics. It is shown in [4, 5] that a shock wave in a gas-liquid mixture actually has a profile having an oscillating pressure. The drawback of [3–5] is the necessity of postulating the existence of the shock waves. This is connected with the absence of a direct calculation of the dissipative effects in the fundamental equations. The present article is devoted to the theoretical and experimental study of the structure of a shock wave in a gas-liquid medium. It is shown, within the framework of a homogeneous biphasic model, that the structure of the shock wave can be studied on the basis of the Burgers-Korteweg-de Vries equation. The results of piezoelectric measurements of the pressure profile along the shock wave front agree qualitatively with the theoretical representations of the structure of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 65–69, May–June, 1973.     

Energy analysis of the stability of plane-parallel flows with an inflection in the velocity profile

Energy estimates are obtained for the critical Reynolds numbers for a number of flows having velocity profiles with an inflection point. Flows with a cubic velocity profile, a free submerged jet, and a jet in a channel are examined. It has been detected that the energy estimates are not more than two- to threefold less than the corresponding critical Reynolds numbers computed by linear theory.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhmcheskoi Fiziki, No. 6, pp. 86–93, November–December, 1971.The authors are grateful to M. A. Gol'dshtik for attention to the research.     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

On the Stability of a Laminar Wall Jet with Heat Transfer

The hydrodynamic stability of a low speed, plane, non-isothermal laminar wall jet at a constant temperature boundary condition was investigated theoretically and experimentally. The mean velocity and temperature profiles used in the stability analysis were obtained by implementing the Illingworth–Stewartson transformation that allows one to extend the classical Glauert solution to a thermally non-uniform flow. The stability calculations showed that the two unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. Heating is destabilizing the flow while cooling is stabilizing it. However, the large-scale instabilities associated with the inflection point of the velocity profile still amplify in spite of the high level of the stabilizing temperature difference. The calculated stability characteristics of the wall jet with heat transfer were compared with experimental data. The comparison showed excellent agreement for small amplitudes of the imposed perturbations. The agreement is less good for the phase velocities of the sub-harmonic wave and this is attributed to experimental difficulties and to nonlinear effects.     

Wave front in the blunt body immersion problem

The immersion of a three-dimensional blunt convex body in a compressible fluid with nonpositive acceleration is considered in the linear formulation. It is shown that at every instant the perturbation zone will be convex. The fluid particle velocity and pressure are calculated at each point on the wave front. At every instant the wave front is wholly determined by the initial supersonic stage of propagation of the boundary of the body-fluid interaction zone.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 5–11, July–August, 1992.The author wishes to thank A. G. Khovanskii for his constant interest.     

Calculation of the pressure at the critical point when a shock wave is incident on a body moving with supersonic velocity

The interaction of a shock wave with a blunted body moving with supersonic velocity is considered. It is shown that under certain conditions the reflection pressure at the critical point of the body can be determined on the basis of one-dimensional theory of shock waves. The error due to the application of this theory is investigated. Equations are obtained for the maximum error as asymptotically large values of the number M of the unperturbed stream incident on the body. Conditions under which secondary reflections of the discontinuities at the critical points are possible are analyzed.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–101, November–December, 1972.     

Effect of the Conductance and Thickness of a Conducting Plate on the Signal from a Material–Velocity Inductive Transducer

The perturbation problem of the magnetic field of a constant–current turn located above a conducting plate set into motion by a plane shock wave with a rectangular profile is considered. It is shown that not only the velocity of the plate but also its dynamic conductivity can be determined on the basis of the electromotive force of induction recorded by means of the turn. For the case where the conductance of the plate is known for both the conducting half–space and for a plate whose thickness is comparable with the skin–layer thickness, approximatecalculated dependences for the velocity of the plate are obtained. A comparison with experimental data and the clarification of the calculated dependences allows one to conclude that the approaches proposed can be used for determining the conductance of metals in shock–wave processes.     

On the expansion into a vacuum of a rarefied plasma with two sorts of ions

The one-dimensional expansion of a plasma with different temperatures and two sorts of ions into a vacuum is examined. When the ion velocity distribution in the plasma is Maxwellian, propagation of a rarefaction wave is observed, the boundary of which is a weak discontinuity moving with the velocity of ionic sound in the plasma. The value of this velocity is found for the plasma in question. Attention is mainly focused on finding the first two moments of the distribution functions, i.e., the mean velocities and the densities of the heavy particles. An approximate asymptotic solution is obtained for the system of transport equations in the case when the two kinds of ions have similar masses, and the system is solved numerically by computer. Some features of the solutions, typifying a plasma in which the different sorts of ions have different masses, are analyzed in detail.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 1, pp. 32–38, January–February, 1970.In conclusion the author thanks N. T. Pashchenko for suggesting the problem and showing unfailing interest.     

Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

Existence and Uniqueness of Traveling Waves for Fully Overdamped Frenkel–Kontorova Models

In this article, we study the existence and the uniqueness of traveling waves for a discrete reaction–diffusion equation with bistable nonlinearity, namely a generalization of the fully overdamped Frenkel–Kontorova model. This model consists of a system of ODEs which describes the dynamics of crystal defects in lattice solids. Under very weak assumptions, we prove the existence of a traveling wave solution and the uniqueness of the velocity of propagation of this traveling wave. The question of the uniqueness of the profile is also studied by proving Strong Maximum Principle or some weak asymptotics on the profile at infinity.     

Turbulent air flow over a moving curved surface

A numerical model of turbulent air flow over a curved surface is described. The model is based on two-dimensional nonlinear Reynolds equations and continuity equations written in a coordinate system moving with the profile of the curved surface. The Reynolds stresses are represented in the form of the product of the isotropic turbulent viscosity coefficient, which increases linearly with height, and the deformation tensor of the mean velocity field. Flow over a stationary sinusoidal surface and a sinusoidal gravity wave on water is simulated. The structure of the velocity and pressure wave fields is obtained. The differences in flow over stationary and moving surfaces are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–24, September–October, 1986.     

Thermal mechanism of wave damping in a gas-liquid mixture

The effect of interphase heat transfer on the process of propagation of a wave in a monodisperse gas-liquid mixture is investigated. A three-wave equation of the Boussinesq type is derived and formulas for the dependence of the thermal components of the dissipative coefficients on the thermophysical parameters of the mixture are obtained. The limits of applicability of the short-wave method are determined. The theoretical and experimental values of the phase wave velocity are compared and found to be in good agreement.Yerevan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 75–83, November–December, 1994.     

Korteweg-de vries-type equations in the theory of surface waves in electrically conducting liquids

Equations are obtained which describe the propagation of long waves of small, but finite amplitude in an ideal weakly conducting liquid and on the basis of these equations the influence of MHD interaction effects on the characteristics of the solitary waves is investigated. The wave equations are derived under less rigorous constraints on the external magnetic field and the MHD interaction parameter than in [1–3]. It is shown that the evolution of the free surface is described by the KdV-Burgers or KdV equations with a dissipative perturbation, and that the propagation velocity of the solitary waves depends on the strength of the external magnetic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 177–180, November–December, 1989.     

Nonlinear wave motions on liquid surfaces

A study is made of the formation of a shock wave (bore), produced by the movement of an initially weak discontinuity in the spatial derivatives of velocity and liquid depth in an area of stationary current in a channel of constant inclination. The formation of shock waves from compression waves was first studied by Riman [1]. Frictional resistance was considered in the Chezy form. The equations obtained therein for determination of the moment in time and spatial coordinates of the point at which the shock wave is formed, as well as the laws for propagation of shock waves are applicable to the problem of one-dimensional transient motion in a gas, the pressure of which is dependent on density. Instantaneous collapse of waves, as well as formation and movement of bores in rivers for an idealized flow model in a channel with horizontal bottom, neglecting friction, were described by Khristianovich, Mikhlin, and Devison [2], and Stoker [3]. Recently in the work of Sachdev and Bhatnagar [4], using numerical integration of the equation for bore intensity, the problem of shock wave propagation in a channel of constant inclination with consideration of fluid resistance in the Chezy form was studied. Gradual wave collapse and the bore formation mechanism were studied by Stoker [3] on the basis of the shallow-water theory. Neglecting friction on the horizontal channel bottom, he calculated the moment of time and coordinates of the point at which the shock wave is formed in the case where the initial disturbance is sinusoidal. The dependence of these values on wave amplitude for a channel of constant inclination was obtained by Jeffrey [5], who also neglected friction on the channel bottom and considered the initial disturbance to be sinusoidal. Lighthill and Whitham [6] discovered that for Froude numbers greater than two, the linear theory led to unlimited growth in the intensity of the flood wave. We note that the studies of flood-wave motion in the region of the first characteristic, performed in [3, 6], differ only in the forms of the resistance laws and dependences of the unknown functions on the variables. Physical peculiarities of various liquid wave motions were also examined by Lighthill in [7].Saratov. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 62–66, March–April, 1972.     

Reflection of a strong shock wave from an ellipsoid

The reflection from an ellipsoid of a strong shock wave (with uniform parameters behind the wave) moving along one axis of the ellipse is considered. Viscosity and thermal conductivity of the gas are not considered. A solution is sought in the vicinity of the critical point using the small parameter method [1]. The nonlinear differential equations for the dimensionless components of the gas velocity in this region are solved by the method of separation of variables with the additional condition of [2]. Analytical expressions are found for the flow parameters, which for the cases of an elliptical cylinder and ellipsoid of revolution coincide with the corresponding expressions obtained previously in [2].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 19–23, November–December, 1980.