The uniqueness of the solution of boundary-value problems of a thermal model of discharge

The paper is devoted to a nonlinear analysis of superheating [1, 2] instability of an electric discharge stabilized by electrodes [3] in the framework of a thermal model [4] where the stability of the discharge relative to the long-wave and short-wave perturbations is proved in a linear approximation. Similar boundary-value problems arise in the theories of chemically and biologically reacting mixtures [5–7], thermal breakdown of dielectrics [8], thermal explosion [9], in the investigation of nonlinear waves in semiconductors and superconductors [10, 11], and in the investigation of Couette flow with variable viscosity [12]. The uniqueness of the one-dimensional steady solutions of the thermal model of discharge and the stability relative to the small spatial perturbations, respectively, for the exponential and step dependence of the electrical conductivity on the temperature are proved in [3, 13]. The uniqueness of the solutions in the one-dimensional case for the same electrode temperature and arbitrary dependences of the electrical and thermal conductivity on the temperature is established in paper [14]. In the present paper, the existence and uniqueness of steady solutions of the thermal model of discharge in a three-dimensional formulation for arbitrary fairly smooth electrical and thermal conductivity functions of the temperature in the case of isothermal isopotential electrodes are proved analytically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 140–145, January–February, 1986.The author expresses his gratitude to A. G. Kulikovskii and A. A. Barmin for the formulation of the problem and their discussions.     

两自由度振动系统的斜碰撞分析

研究斜碰撞振动系统动力学的一个关键问题是对系统在碰撞前后的状态进行合理描述和正确计算．针对两弹性体斜碰撞问题，基于瞬间碰撞假设，提出了采用步进冲量来分析和求解斜碰撞前后的状态关系；并以弹簧摆和振子组成的两自由度斜碰撞振动系统为例，具体介绍了该算法如何实现．用解析方法讨论了该系统在斜碰撞过程中可能出现的各种力学现象，将冲量步进算法得到的数值解与解析结果进行对比，取得了完全一致的结果．该数值方法能适应多种斜碰撞问题的计算．     

Method of calculation of interaction of wall flows

A flow of viscous compressible fluid in the neighborhood of the line of interaction of wall flows is considered. A method of calculating the line of interaction and the direction of the self-induced secondary flow is developed. Papers [1–3] are devoted to the simulation of a separation flow with singularities in the neighborhood of singular lines and points, where boundary-layer equations are invalid. However, the theories of local separation used at present have mainly been developed only for two-dimensional problems, while the models of viscous-inviscid interaction have restrictions in application for turbulent flows with developed separation. The interaction of three-dimensional wall turbulent flows is considered below. It is assumed that the thickness of the boundary layers and the scales of the interaction zones are small in comparison with the characteristic dimension of the system, while the line of discontinuity of the solutions of the three-dimensional boundary layer equations is the same as the line of interaction of the wall flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–59, March–April, 1987.The author is grateful to G. Yu. Stepanov and V. N. Ershov for their interest in my work and their valuable remarks.     

Theory of the combustion of small drops of metal

The article discusses the combustion of small drops of metal. It is postulated that the formation of an oxide in the liquid phase starts with the origin of a condensed phase and continues as the result of a reaction between the vapors of the drop and the oxidizer at the surface of the forming particles of the condensed phase. It is shown that the process of the formation of particles of condensed oxide in the gas, for very small drops, has an essentially unsteady-state character. Under these circumstances, a considerable fraction of the vaporization products of a drop does not succeed in condensing after the complete gasification of the drop and remains in the gaseous state.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 47–53, March–April, 1976.     

Solution of variational problems of gasdynamics of supersonic nonequilibrium flows

The problem of the optimization of the supersonic portion of a nozzle for gas flow in the case of certain nonequilibrium processes was solved in [1, 2]. The authors examined the flow scheme in which the closing Mach line of the first family arrives at the initial rarefaction wave fan. At the same time, in [3] in the solution of the analogous problem for the case of gas flow with foreign particles it was shown that it is advisable to consider also a different scheme, in which the closing characteristic arrives at the axis of symmetry outside the initial rarefaction wave fan. In the following we present results of a study of such a scheme for gas flow with nonequilibrium processes taking place. The necessary conditions which define the optimum contour are obtained and, in particular, the conditions which define the coordinate x and the magnitude of the angle at the corner points.     

Homogenization of the equations of the Cosserat theory of elasticity of inhomogeneous bodies

The paper deals with the homogenization of a boundary value problem for an inhomogeneous body with Cosserat properties, which is referred to as the original problem. The homogenization process is understood as a method for representing the solution of the original problem in terms of the solution of precisely the same problem for a body with homogeneous properties. The problem for a body with homogeneous properties is called the accompanying problem, and the body itself, the accompanying homogeneous body. As a rule, a constructive homogenization procedure includes the following three stages: at the first stage, the properties of the inhomogeneous body are used to find the properties of the accompanying homogeneous body (efficient properties); at the second stage, the boundary value problem is solved for the accompanying body; at the third stage, the solution of the accompanying problem is used to find the solution of the original problem. This approach was implemented in mechanics of composite materials constructed of numerous representative elements. A significant contribution to the development of mechanics of composites is due to Rabotnov [1–3] and his students. Recently, the homogenization method has been widely used to solve problems for composites of regular structure by expanding the solution of the original problem in a power series in a small geometric parameter equal to the ratio of the characteristic dimension of the periodicity cell to the characteristic dimension of the entire body. The papers by Bakhvalov [4–6] and Pobedrya [7] were the first in the field. At present, there are numerous monographs partially or completely dealing with the method of a small geometric parameter [8–14]. Isolated problems for inhomogeneous bodies with nonperiodic dependence of their properties on the coordinates were considered by many authors. Most of such papers published before 1973 are collected in two vast bibliographic indices [15, 16]. General methods were considered, and many specific problems of the theory of elasticity of continuously inhomogeneous bodies were solved in Lomakin’s papers and his monograph [17]. The theory of torsion of inhomogeneous anisotropic rods was considered in [18]. In 1991, in his Doctoral dissertation, one of the authors of this paper proposed a version of the homogenization method based on an integral formula representing the solution of the original static problem of inhomogeneous elasticity via the solution of the accompanying problem [19, 20]. An integral formula for the dynamic problem of elasticity was published somewhat later [21]. This integral formula was used to develop a constructive method for the homogenization of the dynamic problem of inhomogeneous elasticity, which can be used in the case of both periodic and nonperiodic inhomogeneity of the properties [22]. The integral formula in the case of the Cosserat theory of elasticity was published in [23]. The present paper briefly presents constructive methods for homogenizing the problems of the Cosserat theory of elasticity based on the integral formula.     

Experimental verification of the theory of thixotropy of viscoelastic polymer media

Previous studies [1, 2] were devoted to the formulation of a phenomenological theory of the reversible changes (thixotropy) in the physicomechanical properties of viscoelastic media, in particular, polymer systems. The basis of this theory is the idea that the reversible changes in the structure and properties of viscoelastic thixotropic media under the influence of mechanical action are due to a change in their relaxation spectrum. In this case the behavior of the mechanical properties is entirely and uniquely determined by two material functions which completely characterize the given material: the relaxation time (frequency) distribution function, which describes the behavior of the material in the linear region of deformation, and the thixotropy function, which determines the nature of the changes compression) of the relaxation spectrum on transition to the nonlinear region. The object of this approach is to reflect the effect of the change in supramolecular and molecular structures associated with the flow of polymer system, or in the bonds and orientation of the particles in disperse systems, on the viscoelastic and viscosity properties of the systems concerned. The essential validity of this approach was demonstrated in [3], where it was shown that at sufficiently high strain rates changes occur in the structure of the polymer leading to a change in mechanical properties. In [4] the basic structural functions were found. These, in conjunction with the proposed theory of thixotropy, characterize the behavior of a broad group of polymer systems in both the linear and the nonlinear regions of deformation. In this connection it should be noted that whereas for the linear region the accuracy of the laws obtained lies within the limits ± 100%, on transition to the nonlinear region the error may increase, Therefore, for the purposes of a rigorous quantitative verification of the theory we shall use not the universal functions obtained in [4], but the more precise characteristics of the specific material on which the experiments are performed, since those effects with respect to which it is desired to test the theory usually lie within the limits of 30% of the measured quantities.The authors thank G. V. Vinogradov for organizing and discussing their work.     

Experiments of free vibration of shells of revolution

This paper presents experimental techniques used in and results obtained during a series of experiments performed to investigate the free-vibration behavior of 15-in. base-diameter spherical and paraboloidal shell models of various geometric parameters and boundary conditions. The models were manufactured from polyvinyl-chloride (P.V.C.) sheets by a thermo-vacuum process using special molds and templates. To provide the necessary excitation power, a variable control amplitude/frequency audio oscillator was used to drive a loudspeaker which was mounted underneath the models. A recently developed noncontact fiber-optics instrument, referred to as the “Fotonic Sensor”, was employed in determining the motion of the models. Thirty-two models of different configurations and boundary conditions were tested in the series. The natural frequencies were observed for all models, while the mode shapes associated with the first four-to-six resonant frequencies were mapped only for some of the models, using special scanning devices.     

SWT-120风洞稳定段的性能测量

在普通超音速风洞中,由于受到噪声干扰,很难进行有效的边界层转捩特性试验研究,针对超声速流动特点发展较低噪声风洞十分必要,而稳定段设计的好坏直接影响到下游试验段噪声水平。本文介绍一座低噪声风洞稳定段的结构和性能测量结果。先对稳定段的结构设计做了简单介绍,然后对实验结果进行分析,实验结果表明在大角度扩散段内装置孔锥,稳定段安装消音夹层和阻尼网组等部件后,气流的速度脉动和压力脉动明显降低,其中压力脉动降低一个量级,速度脉动为1%。进一步优化设计和改进工艺,速度脉动还可进一步降低。测量结果表明SWT-120稳定段的设计是成功的,对我们以后发展更高性能的静风洞有借鉴和参考价值。     

Development and design of new methods of measurement of state of strain of structures

The present paper deals with development and design of new methods utilizing Wiedemann's effect for determination of state of strain in building structures. Wiedemann's effect and some features of torsional strain of magnetic field are the basis of new experimental method. Especially the point electromagnetic strain gages using the effect of pure torsion of electromagnetic field to enable universal examination. For strain-gage measurements, almost all physical quantities are used which can be related to the variation in length of the structures. From the electric strain measurements, the most commonly used methods are the measurements by resonance-wire strain gages or by electric-resistance strain gages. In this paper, electromagnetic strain gages are discussed using the Wiedemann effect, and the author describes some new measuring equipment and his own suggestions and methods based on an application of this effect.     

Saturation of absorption of the powerful radiation of a system of anharmonic oscillators

Recently, the theory of nonequilibrium systems simulated by a set of anharmonic oscillators has received significant development. The investigation of such kinds of systems is especially important in the study of problems associated with the stimulation of chemical reactions and the development of effective molecular lasers. The systematic analysis of the kinetics of anharmonic oscillators assumes the simultaneous solution of a large number of nonlinear equations describing the population balance of the vibrational levels. Realization of this approach is associated with cumbersome numerical calculations and does not permit obtaining a qualitative picture of the behavior of the system as a function of the different parameters (pressure, temperature, etc.). An approximate analytical theory has been formulated in [1, 2] which permits finding the distribution function over the vibrational states with the effects of anharmonicity taken into account. We will employ the approach developed in these papers to describe a system of anharmonic oscillators under conditions of powerful optical pumping. This problem was discussed in [3], where it was found that such a system changes into a saturation mode in the case of high pumping levels. The existence of this mode is explained by the fact that the maximum rate of energy input into a vibrational degree of freedom is determined by the rate of distribution of this energy over all the vibrational levels, i.e., by the constant of V—V-exchange. For sufficiently large pumpings the approximation of the Boltzmann distribution function adopted in [3] in connection with the calculation of the saturation parameters is too crude. The goal of this paper is to derive in explicit form expressions for the vibrational energy supply, the absorbed power, and so on, under saturation conditions without the use of the approximation indicated above [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 10–15, September–October, 1978.     

大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

A study of influence of gravity on bulk behaviour of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method （DEM）. Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions. The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

Mathematical simulation of hydrodynamic generators of oscillations

Unsteady turbulent swirled water flow in a channel in the presence of cavitation is calculated. It is shown that in the near-axial channel zone a fluctuating vapor region, or cavity, arises and variations in the cavity shape and dimensions lead to the onset of undamped pressure fluctuations. The amplitude-frequency characteristics of the oscillations are obtained in different channel cross-sections. The amplitude maximum position in the channel expansion zone is in agreement with the available experimental data. The dynamics of toroidal vortices formed in the hydrodynamic generator channel and in the expansion zone at its exit are established.     

Assessment of the performance of different classes of turbulence models in a wide range of non-equilibrium flows

The performance of thirteen benchmark turbulence models within the RANS framework has been assessed in classical non-equilibrium flows. Linear and non-linear eddy-viscosity schemes, Reynolds stress transport models and single- and two-time-scale approaches have been considered in the investigation. Among the test cases studied are homogeneous shear and normally strained flows, adverse-pressure-gradient, favourable-pressure-gradient and oscillatory boundary layer flows, fully developed oscillatory and ramp up pipe flows and steady and pulsated backward-facing-step flows. The main advantages and drawbacks of the models in each of the test cases are discussed. These discussions provide a reasonably wide understanding of the expected behaviour of the models for future applications in non-equilibrium flows, and also result in suggestions on how the effectiveness of existing models can be further improved.     

A study of influence of gravity on bulk behavior of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method (DEM). Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions.The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.