Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Numerical investigation of unsteady shock waves in vapor-gas-droplet mixtures

The results of mathematical modeling of the evolution of unsteady shock waves in two-phase mixtures of inert gas, vapor and suspended liquid droplets with allowance for dynamic, thermal and mass phase interaction processes are presented. The influence of interphase mass transfer effects (droplet breakdown and evaporation, vapor condensation) on the structure of unsteady shock waves in vapor-gas-droplet mixtures is analyzed. The important influence of phase mass transfer and, in particular, droplet breakdown as a result of surface layer stripping by the gas flow on the distribution of the parameters of the carrier and dispersed components of the mixture behind the shock front is demonstrated. The effect of the principal governing parameters of the two-phase mixture on the unsteady shock wave propagation process is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 67–75, July–August, 1992.     

Hydrodynamical problems of first-order phase transitions

The two-phase liquid-vapor system in a state of thermodynamic equilibrium is considered. If a shock wave propagates in this medium, during its passage the material undergoes shock compression and transforms into a new equilibrium state. Not only the initial velocity changes in this case, but so does the quantitative composition of the phases. Due to the complication of the process, analytic results have practically not been available so far. Calculations of parameters behind the shock discontinuity were carried out approximately by using various tables and nomograms, restricted basically to only one two-phase system, H₂O. Thus, condensation jumps were treated in [1–4] in two-phase supersonic flows within the single-velocity model and a low content of the liquid phase in the mixture. Using the assumptions mentioned, the various parameters were found at the front of the shock wave by numerical solution of the conservation equations of mass, momentum, and energy at the discontinuity. The thermodynamic parameters are usually given in tabulated form as a function of pressure or temperature for equilibrium conditions of the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–87, September–October, 1977.     

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.     

Initial stage of the collision of blast waves

The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions.     

Amplification of shock waves in a bubble-filled liquid with gas concentration gradient

The properties are studied of the propagation of unsteady shock waves in a gas-liquid system of bubble structure in the case when the volume concentration of the gas changes in the direction of motion of the shock wave. It is established that when there is a sufficiently rapid drop in the gas content, an effect of amplification of the shock wave is observed which is due to the deceleration of the medium behind the shock wave. A study is made of the laws of the evolution of long- and short-wave pulsed perturbations in such systems. The authors consider processes of reflection of waves from obstacles and their passage from a gas into a bubble liquid, from a two-phase mixture into a pure liquid. The contribution is determined of nonequilibrium effects to the process of amplification of a wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–54, January–February, 1988.The authors wish to express gratitude to R. I. Nigmatulin for his interest in the study and for useful discussions.     

On regular reflection of detonation waves

The boundaries of regular reflection of detonation waves by a rigid wall are calculated. It is assumed that detonation is initiated at the point of reflection when a shock wave is incident on the wall at a finite angle in a gas fuel mixture, the detonation propagating instantaneously along the reflected front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–180, March–April, 1983.     

Nonequilibrium viscous flow of a multicomponent gas in the vicinity of the stagnation point of a blunt body

This paper gives the results of numerical calculations characterizing the effect of variation of the shock layer parameters on the heat transfer in the case of a multicomponent nonequilibrium-dissociating air on a wall with finite catalycity in the vicinity of the stagnation point of a spherical blunt body. Similar results for the case of a binary mixture can be found in [1–3]. It is shown that a consideration of the variation of the parameters in the nonequilibrium shock layer leads to a significant increase in heat flux to the noncatalytic wall in comparison with the theory of an asymptotically thin nonequilibrium boundary layer with equilibrium parameters on its outer boundary.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–147, March–April, 1971.The author thanks V. V. Lunev for useful comments in the discussion of this work.     

Supersonic two-phase flow around a wedge

Supersonic two-phase flow around bodies is encountered in calculating the flow around the last stages of blades of condensing turbines, in studying the motion of airplanes under cloudy conditions, etc. In the latter case, there is, along with erosion of the forward edges of the wing profiles, a change in the wave structure and interference situation in the flow about the airplane, leading to off-design regimes of motion. Supersonic flow of a two-phase mixture around a wedge, without taking account of the influence of the particles on the flow, was investigated in [1–3]. In [4], also in this kind of simplified setting, a study was made of the interaction of particles with the surface of a wedge in which reflection of the particles from the wall was taken into account. Morganthaler [5] made an experimental study of the flow of a mixture of air and aluminum oxide particles around a wedge. In [6] a theoretical study was made of a supersonic two-phase flow around thin flat axially-symmetric bodies. In particular, for the flow around a wedge, closed form solutions were obtained for the form of the shock wave, the gas streamlines and particle paths, and the distribution of all the parameters along the surface of the wedge. On the basis of the equations given in [7] and the method of characteristics, which were developed for flows consisting of a mixture of a gas and heterogeneous particles in nozzles [8,9], we present below a study of a supersonic two-phase flow around a wedge.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 83–88, March–April, 1972.     

A theory of hydroshock in a two-phase gas-liquid mixture

A hydroshock in a two-phase gas-liquid mixture is usually calculated by an analog of the Zhukovskii formula for a mixture (see, for example, [1, 2]) which establishes the relation of the hydro-shock intensity to the velocity of sound in the mixture. However, as the experimental data [1] show, the hydroshock intensity in the mixture can significantly exceed the calculated values, a fact which is explained by the increase in the propagation velocity of the perturbation wave in comparison to the velocity of sound in the mixture [3, 4]. In the present paper, an equilibrium model of shock transition, similar to [5, 6], is used to calculate the attenuation of the hydroshock as the gas content of the mixture increases in a bubble flow regime. It is shown that owing to the high compressibility of the mixture the effect of the elasticity of the pipe-line walls is small, and the dependence of the propagation velocity of the perturbation wave on the intensity and gas content becomes the main effect. A simple dependence of the hydroshock intensity on the gas content and two similarity parameters is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 202–204, September–October, 1984.     

Population inversion behind a detonation wave propagating in a variable-density medium

The creation of an active medium by means of detonation has been investigated on a number of occasions. It was suggested that one could use the expansion of the detonation products of an acetylene-air mixture in vacuum [1] or the cooling of the detonation products of a mixture of hydrocarbons and air through a nozzle [2, 3]. In [4], the detonation of a solid high explosive was used to produce population inversion in the gas mixture CO₂-N₂-He(H₂O). Stimulated emission from HF molecules was observed in [5] behind the front of an overdriven detonation wave propagating in an F₂-H₂-Ar mixture in a shock tube. Population inversion behind a detonation wave was studied in H₂-F₂-He mixtures in [6–8] and in H₂-Cl₂-He mixtures in [9] with energy release on a plane and on a straight line in a medium with constant density. Similar problems were solved for shock waves propagating in both a homogeneous gaseous medium [7, 10] and in the supersonic part of an expanding nozzle. In the present paper, we study theoretically population inversion behind an overdriven detonation wave propagating in a mixture (fine carbon particles + acetylene + air) which flows through a hypersonic nozzle. The propagation of detonation in media with variable density and initial velocity was considered, for example, in [11, 12]. Analysis of the gas parameters behind a detonation wave propagating in a medium with constant density (for a given fuel) showed that the temperature difference across the detonation front is insufficient to produce population inversion of the vibrational levels of the CO₂ molecule.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 65–71, January–February, 1980.I am grateful to V. P. Korobeinikov for a helpful discussion of the results.     

Force action of a shock wave on a sphere or a cylinder in numerical and physical experiments

The results of an investigation of the unsteady and steady stages of the action of a plane shock v/ave on a sphere or a cylinder are given. The volume compression force which determines the signal amplitude of a nondirectional spherical transducer [1] and the force acting on the body in the direction of the shock wave motion are analyzed. Good agreement of the results is obtained between the numerical and physical experiments and with the data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 134–139, November–December, 1985.The authors are grateful to B. I. Zaslavskii for the discussion of the results and to O. V. Zonovaya for the formulation and presentation of the calculated material.     

Transition from regular reflection to mach reflection when a shock wave interacts with a wall in a two-phase gas—liquid medium

A study is made of the transition from regular reflection to Mach reflection when a plane moderately strong or weak shock wave interacts with a wall in a two-phase gas—liquid medium. An equilibrium model that differs from the model of Parkin et al. [1] by the introduction of the adiabatic velocity of sound is used to investigate shock wave reflection in the complete range of gas concentrations. For the reflection of weak shock waves, nonlinear asymptotic expansions [2] are used. In the limiting cases, the results agree with those already known for single-phase media [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 190–192, September–October, 1983.     

Plane-parallel supersonic flow with a discontinuity

This article considers a plant-parallel supersonic flow, with a shock wave terminating within the flow; the shock wave is regarded as a distortion. A line of discontinuity is located ahead of the shock wave in the supersonic zone. The problem is solved by the method of indeterminate coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 95–100, July–August, 1970.The authors thank S. V. Fal'kovich for his valuable advice and for his evaluation of the results obtained.     

Interaction of a Shock Wave with a Spherical Gas–Liquid Cluster

Experimental studies were performed of the interaction of a plane shock wave with a spherical gas–liquid cluster (polyurethane foam ball saturated with a bubbly liquid) in a vertical shock tunnel filled with a liquid. The cluster was shown to generate a solitary pressure wave of large amplitude.     

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.     

Diffraction of a spherical acoustic wave on a cone

An exact analytic solution of the problem of diffraction of a plane acoustic wave on a cone of arbitrary aperture angle was obtained and studied in [1]. For the case of spherical wave diffraction on a cone a formula is known [2] which relates the solutions of the spherical and plane wave diffraction problems. This study will employ the results of [1, 2] to derive and investigate an exact analytical solution of the problem of diffraction of a spherical acoustic wave on a cone of arbitrary aperture angle. Results of numerical calculations will be presented and compared with analogous results for a plane wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 200–204, March–April, 1976.The author is indebted to S. V. Kochura for her valuable advice.     

The reflection of a plane shock wave from a body with groove

When a plane shock wave impinges on bodies with grooves and when a supersonic stream of gas flows past such bodies a complicated flow pattern develops. In a number of cases oscillations of the bow wave [1–3] and an anomalous heating of the gas in the groove [4–6] have been observed. Unsteady reflection of shock waves from bodies with grooves and the processes occurring inside the grooves have been investigated comparatively little.Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Zhidkosti 1 Gaza, No. 5, pp. 180–186, September–October, 1935.The authors wish to thank V. I. Ivanov for carrying out the calculations.     

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.     

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.