Motion of low-density gaseous bodies in the atmosphere

The problem of motion of low-density deformable bodies in an atmosphere is interesting in reference to the hypothesis that the Tungussk catastrophe of 1908 resulted from atmospheric deceleration of a body of large size and low density (less than 0.01 g/cm³) [1]. Article [2] investigated the region of earth destruction caused by the shock wave formed ahead of a meteorite body. The motion of the meteorite is modeled here by explosion of a linear charge of variable cross section. Article [3] examined deceleration in an exponential atmosphere of a body whose shape and size are given functions of time. It was shown that under certain conditions the shock wave separates from the body and detaches. However, the body shape is not known beforehand, in fact, and a law for its variation can be obtained only by simultaneous consideration of flow in the shock layer, the wake, and the gas cloud. With an initial cloud velocity on the order of 40 km/sec this is a difficult problem. The present author knows of no attempt to solve the problem formulated in this way. The present paper addresses the problem of motion of a gas cloud in an exponential atmosphere with large initial velocity. The cloud gas and the atmospheric gas are assumed to be perfect and ideal. The problem is solved numerically by the direct finite-difference method of Godunov [4], using a moving mesh and isolated discontinuities. The objective of the work is to elucidate the basic aerodynamic effects arising when a low-density body enters the atmosphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 89–93, March–April, 1978.The author thanks G. I. Petrov for guidance of the work.     

A Model for the Determination of the Resisting Torque of the Rolling Bearing Cage Motion of Slow-Speed Kinematic Pairs

A simplified, plane model for determination of resisting torques of the rolling bearing cage motion of low speed kinematic pairs is presented. The considerations are devoted to an arbitrary character of the point contact of a rolling element–cage pairs lying in a plane which is crossing the rolling elements in their geometrical centre. The model has been developed on the basis of the analysis of motion kinematics of a bearing track and rolling elements. The proposed algorithm allows for continuous tracking the resisting torque of the cage and its components during the kinematic pair motion.     

Periodic dislocation motion in a relaxing medium

We consider periodic helical dislocation motion in a para-elastic medium under variable external stresses. The para-elastic properties of the medium are determined by the short-range-order parameters between atoms of the different components of the alloy. The solution of the nonlinear dislocation equation of motion is obtained in four different regions of the amplitude-frequency space. The conditions are indicated under which dislocation motion is viscous and is in the nature of breakaway from the polarization atmosphere.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 79–85, November–December, 1970.     

Self-similar axisymmetric thermal in a variable-density medium

A model of a turbulent axisymmetric thermal rising in a medium whose density varies with height is proposed. An analytic solution describing the self-similar stage of ascent of the thermal is constructed. The effect of the density stratification of the atmosphere on the structure of the thermal during its motion is analyzed, and relations describing the characteristic points of the thermal and the smearing of its leading edge are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–53, July–August, 1991.     

Propagation of acoustic perturbations along a supersonic jet flowing out into the atmosphere

The propagation of acoustic perturbations (specified in the outlet cross section of a particular channel) along a supersonic jet flowing out of the channel is considered; also considered is acoustic emission from the surface of the jet into the atmosphere. The solution of these problems is obtained by a numerical method on the linear approximation. The laws governing the propagation of the perturbations as a function of the perturbation frequency and other determining parameters are investigated; these parameters include the velocity and temperature of the jet, the velocity of the subsonic accompanying flow in the external medium, and the character of the perturbation in the initial cross section of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 92–99, March–April, 1977.     

Certain magnetohydrodynamic flows associated with the propagation of waves

The propagation of waves in an absorptive medium is accompanied by unidirectional motion of this medium — a flow which develops due to the fact that the wave loses a portion of its momentum along with energy loss. It is this loss which is compensated by the flow by virtue of the momentum-conservation law. In a conducting medium the momentum losses via the waves are associated not only with the viscosity and thermal conductivity but also with the Joule-heat losses. Moreover, the magnetic field itself also affects the configuration and character of the flow in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 30–33, July–August, 1970.The authors thank N. A. Roi for his useful comments.     

Numerical investigation of the phenomenon of “blocking” with the flow of a stratified liquid around an obstacle

An investigation is made of the phenomenon of blocking with the laminar flow of an incompressible viscous liquid around periodically arranged obstacles. The character of the motion is followed under conditions of temperature stratification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 151–153, July–August, 1976.     

Formation of a vortex ring during the rise of a heated air mass in the stratified atmosphere

The motion of a strongly heated air mass in the earth's atmosphere is studied numerically. The turbulence effects are modeled by the assignment of constant coefficients of viscosity and thermal conductivity. It is shown that a vortex torus is formed during the rise of a hot mass initially having a spherical shape. The velocity, density, and temperature distributions over the significant time interval are obtained for a series of variants differing in the values of the Reynolds and Prandtl numbers. A satisfactory correspondence between the integral characteristics (altitude of rise, dimensions of disturbed region) and the data obtained by the approximate method of A. T. Onufriev [1] is established for several variants.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 186–189, March–April, 1978.The author thanks L. A. Chudov for guidance of the work.     

Nonmonotonic dependence of the convective heat flux on the rate of blowing of opaque admixtures into a radiating H-He shock layer

The results are given of calculations of radiative and convective heat transfer in a radiating H-He shock layer in the neighborhood of the stagnation point of a blunt body when graphite ablation products are blown from the surface. It is found that under the conditions in the shock layer characteristic for motion of the body in the atmosphere of Jupiter [3] the dependence of the convective flux on the blowing rate is essentially nonmonotonic. The maximal value is comparable with the radiative flux to the surface under these conditions. It is shown that a decisive part in the mechanism which increases the convective flux is played by the presence near the surface of particles which effectively absorb radiative energy in the spectral regions in which an appreciable radiation flux reaches the boundary layer; the difference between the transport properties of the blown and the oncoming gases is also important.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 106–113, May–June, 1981.     

Generators of the product of two Schoenflies motion groups

Schoenflies motion is often termed X-motion for conciseness. A set of X-motions with a given direction of its axes of rotations has the algebraic properties of a Lie group for the composition product of rigid-body motions or displacements. The product of two X-subgroups, which is the mathematical model of a serial concatenation of two kinematic chains generating two distinct X-motions, characterizes a noteworthy type of 5-dimensional (5D) displacement set called double Schoenflies motion or X–X motion for brevity. This X–X motion set is a 5D submanifold of the displacement 6D Lie group. Such a motion type includes any spatial translation (3T) and any two sequential rotations (2R) provided that the axes of rotation are parallel to two fixed independent vectors. This motion set also contains the rotations that are products of the foregoing two rotations. In the paper, some preliminary fundamentals on the 4D X-motion are recalled; the 5D set of X–X motions is emphasized. Then implementing serial arrays of one-dof Reuleaux pairs and hinged parallelograms, we enumerate all serial mechanical generators of X–X motion, which have no redundant internal mobility. Based on the group-theoretic concepts, one can differentiate two families of irreducible representations of an X–X motion. One family is realized by twenty-one open chains including the doubly planar motion generators as special cases. The other is generally classified into eight major categories in which one hundred and six distinct open chains generating X–X motion are revealed and nineteen more ones having at least one parallelogram are derived from them. Meanwhile, these kinematic chains are graphically displayed for a possible use in the structural synthesis of parallel manipulators.     

Influence of the atmosphere on the magnitude of the hydrodynamic forces in the case of a disk in a flat encounter with the surface of a compressible liquid

If the velocities with which bodies enter liquids are small, and the bodies are not too blunt, the magnitudes of the hydrodynamic forces can be satisfactorily determined in the framework of the approximation of an incompressible liquid and depend on the density of the liquid, the velocity of entry, and the geometrical parameters (shape of the body, angles of entrance and attack). If the velocity is increased or the encounter with the surface becomes nearly flat, the compressibility of the liquid and the presence of an atmosphere begin to influence the hydrodynamic forces significantly. The influence of the compressibility on the magnitude of the impact loads has been investigated theoretically and experimentally [1–8]. The influence of the atmosphere in the case of an incompressible liquid has also been taken into account [9–11]. In the case of a flat encounter the two factors (compressibility of the liquid and presence of the atmosphere) simultaneously influence the development of the impact process. The present paper reports experimental results and computer calculations of the impact loads in the case of a flat encounter of a disk and the surface of a compressible liquid in atmospheres of helium, air, and freon.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 15–20, May–June, 1984.     

Calculation of the discharge of underground explosion gases into the atmosphere

Nonstationary gas filtration from the cavity of a camouflaged underground explosion through a disaggregated porous medium is calculated. The computations were carried out for a spherically symmetric gas experiencing two-dimensional motion. A two-term law of filtration was used. The space-time pressure distribution of the gas within the medium was obtained. Motion hodographs of the front of filtration and the interface between the explosion products and air were constructed. The influence of the soil filtration characteristics and pressure in the cavity was investigated. The time at which gas is discharged into the atmosphere is determined based on well-known data on the permeability of certain types of rocks that have undergone the effects of an explosion. The variation of gas flow with time as a function of explosion depth is established.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 111–120, January–February, 1976.     

Nonsteady motion of a transverse-shear crack across the interface between elastic media

This article examines the motion of a crack along the line joining two different elastic half-planes under the influence of variable shear stresses. Analogous to the case of a homogeneous medium [1–3], the law of motion of the edge is assumed to be known. Among the features of the physical situation being examined are the nonsymmetrical character of the solution with a symmetrical load distribution and the dependence of the number of Rayleigh wave which can be generated (two, one, none) on the ratios of the elastic parameters. The problem decomposes in the image space into a scalar problem of conjugating two functions reflecting the connection between the displacement discontinuity on the crack and the shear stress on the crack extension. The formula must then be inverted to represent the normal stress. The solution is constructed by the method of factorization, which was used in [2, 3] for a problem with a movable separation point for the boundary conditions. The properties of the Rayleigh boundary function for contacting elastic bodies are also studied. It is shown that the Holder continuity condition for the input functions is sufficient to determine the asymptotes at the edge of the crack, analogous to the case of steady crack movement [4]. With transformations of the convolutions, we used the methods of contour integration and applied the residue theorem. This made it possible to somewhat simplify the results [2]. The subject of crack starting is addressed in an examination of special types of loading. The solution of a similarity problem was given in [5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 129–138, November–December, 1986.     

Growth of a main crack under the influence of gas moving inside it

The motion of a gas or liquid in a growing main crack is examined in connection with the problem of the hydraulic fracture of an oil-bearing bed [1, 2] and evaluation of the quantity of gaseous products escaping from the cavity formed by the underground explosion into the atmosphere by way of the crack [3]. The studies [1, 2] formulated and solved a problem on the quasisteady propagation of an axisymmetric crack in rock under the influence of an incompressible fluid pumped into the crack. An exact solution was obtained in [4] to the problem of the hydraulic fracture of an oil-bearing bed with a constant pressure along the crack. The Biot consolidation theory was used as the basis in [5] for an examination of the growth of a disk-shaped crack associated with hydraulic fracture of a porous bed saturated with fluid. A numerical solution to a similarity problem on the motion of a compressible gas ina plane crack was obtained in [6]. Here we examine the problem of the propagation of a main crack (plane and axisymmetric) under the influence of a gasmoving away from an underground cavity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 116–122, July–August, 1986.We thank V. M. Entova for his remarks, which helped to improve the investigation.     

Numerical simulation of the two-phase flows with viscous carrier phase

The motion of a dilute mixture of two incompressible phases with viscous carrier phase is investigated theoretically in the two-velocity approximation. The numerical solution of the mass and momentum conservation equations is used to analyze the influence of the parameters of the phases on their joint motion for two specific problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 49–54, May–June, 1931.I thank L. G. Loitsyanskii for interest in the work.     

Stability of the motion of a rigid body in an unsteady flow

The problem of rigid-body motion in an unsteady gas flow is considered using a flow model [1] in which the motion of the body is described by a system of integrodifferential equations. The case in which among the characteristic exponents of the fundamental system of solutions of the linearized equations there are not only negative but also one zero exponent is analyzed. The instability conditions established with respect to the second-order terms on the right sides of the equations are noted. The problem may be regarded as a generalization of the problem of the lateral instability of an airplane in the critical case solved by Chetaev [2], pp. 407–408.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–22, May–June, 1989.     

Problem concerning a plane explosion in a heterogeneous atmosphere with account taken of the post-breakthrough stage

The problem is considered concerning a plane explosion in an exponential and standard atmosphere. The heterogeneity of the medium exerts an extremely marked influence on the gas flow. As shown in [1], under the conditions of an exponential atmosphere the upper part of the shock-wave front recedes to an infinite distance, after a finite time. This phenomenon has received the name breakthrough of the atmosphere. A numerical investigation of a powerful plane explosion in an exponential atmosphere at the stage before breakthrough is contained in [2]. In [3], asymptotic boundary conditions are proposed which permit the gas flow after breakthrough to be calculated. In the present paper, a numerical solution of this problem is obtained at an interval of time which exceeds by a factor of 10–15 the time of break-through. The effect of counterpressure and gravity is studied. Some results are given for a plane explosion in a standard atmosphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–131, May–June, 1976.The authors thank L. A. Chudov for attention to the project and for useful advice.     

Calculation of the flow of a two-phase mixture in a Laval nozzle,allowing for the turbulent diffusion of the particles

The flow of a mixture of gas and condensed particles in an axisymmetric Laval nozzle is considered. The motion of the particles is calculated in a specified field of gas flow, with due allowance for their turbulent diffusion. The results of calculations indicating the necessity of allowing for this phenomenon when considering the motion of particles toward the wall of a profiled nozzle are presented.Translated from Izvestiya Akademii Nauk SSSR, No. 2, pp. 161–165, March–April, 1973.     

Radiative heating of bodies entering the atmosphere of venus

The problem of the trajectory of a blunt body in a CO₂+N₂ gas mixture simulating the atmosphere of Venus is considered.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 135–139, July–August, 1992.     

Influence of an elastic plate on the motion of an inhomogenfous fluid

The influence of a thin elastic isotropic plate on the wave motion of an inhomogeneous fluid originating under the effect of external periodic perturbations is investigated. The fluid density increases constantly with depth. Analogous problems have been examined for an inhomogeneous fluid without a plate in [1, 2] and with a plate on the surface of a homogeneous fluid in [3–5].Sevastopol'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 60–67, January–February, 1972.