Mechanical seals with oscillating stator

This paper presents theoretical analyses and experimental investigations of a mechanical seal subjected to axial impulses of one of its mating rings (stator). The amplitude of oscillations of stator depends on the pressure of sealed fluid. The frequency of oscillations is influenced by the geometry of frontal faces of the seal rings and depends on the rotational speed of rotor. The analytical models include the analyses of the static equilibrium of the investigated mechanical seal and the dynamic response of stator. The experimental analysis implies the conception of the testing system, the experimental estimation of the leakage and the measurements of amplitude and frequency of oscillations. During operating time, the experimental variations of leakage of a mechanical seal with oscillating stator are monitored for different rotational speed of rotor. Finite element analysis is used to visualize the stress distribution of stator as a function of the applied forces.     

Solution of the direct problem of the flow of a two-phase mixture of a gas and foreign solid or liquid particles in a laval nozzle

Within the framework of a two-liquid (two-velocity and two-temperature) model of a continuous medium, the article considers the flow of a mixture of a gas and foreign particles in the subsonic, transonic, and supersonic parts of a Laval nozzle. In the case of a thin layer of pure gas near the wall, the problem is solved in two stages. First, the method of establishment is used to calculate the core of the flow, where the gas with the particles is flowing; under these circumstances, the parameters in the layer of pure gas are determined approximately; then simplified equations (of the type of the equations of the boundary layer) are used to find the distribution of the parameters in the zone of pure gas, and the flow in the core of the stream is refined. Examples of the calculation are given. Use of the method developed permitted establishing some of the special characteristics of the flow of a mixture of gas with particles in a Laval nozzle in the case of Stokes flow around the foreign particles.     

Unsteady Liquid Jets

The behaviour of unsteady liquid jets in a gas atmosphere is mainly governed by the conservation of momentum and the interaction with the environment. In this article it will be shown that many of the particular effects in the propagation and desintegration of unsteady jets are simply explained by the conservation of initial momentum. Many of the distortions and peculiar shapes of the liquid elements of the jet can be explained by a time and space development of weak initial distortions of momentum in travelling waves during propagation.The first part of the paper is devoted to the droplet formation in liquid jets of moderate Weber numbers in the order of ten. In this regime and higher the surface tension is not the governing influence of instability of jet decomposition and hence of the droplet formation.If there is a high frequency distortion of the velocity which is artificially implemented in our experiments by a special device, but under usual conditions also existing by turbulence or source distortions of the nozzle flow, the concentration of mass in packets in a kind of shock formation is the main reason for droplet formation. The frequency of droplets in space and time is given by the frequency of the distortion. The amplitude and phase is also given by the initial values of the driver for these quantities.For large amplitudes and low frequencies the jets are decomposed in very peculiar shapes, which can be very simply explained by the collision of packets of concentrated mass on the axis of the jet motion.The whole range of phenomena can be understood in a theoretically elegant manner by a Lagrangian transform of the nonlinear equations of motion together with some plausible considerations about the lateral motion. Solutions for the droplet formation and the formation of liquid films in different shapes can be achieved this way.As an illustration of the whole range of beautiful and regularly reproducible details of jet decomposition some photographs will be shown which summarize the phenomena and give an idea of the importance of systematic investigation of the sometimes very confusing appearance of fluid jets.     

Development of analytical methods in three-dimensional problems of the statics of anisotropic bodies (Review)

The main results of scientific research carried out at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in the field of three-dimensional problems of the statics of anisotropic bodies are stated in a systematic form. The results include the structural method of constructing the exact analytical solutions of equations of the elastic and thermoelastic equilibrium of rectilinearly orthotropic bodies and approximate analytical methods of solving three-dimensional boundary-value problems for curvilinearly orthotropic bodies of canonical and noncanonical form. Results of solution of specific boundary-value problems for orthotropic and transversally isotropic bodies are analyzed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 3–38, February, 2000.     

随机-模糊处理方法在岩石力学指标统计及岩组划分中的应用

探讨了随机 模糊处理方法在岩石力学指标统计和岩组定量划分中的应用。文中对计算中的隶属函数取值及迭代方式进行了深入讨论。通过计算结果的比较分析, 认为随机 模糊处理方法更符合实际, 并优于其他方法。最后作者提出了岩组定性划分 岩石样本参数的随机 模糊统计分析 岩组定量划分及参数重新统计的分析程序。     

EFFECT OF STRESS-STRAIN CURVE OF MATERIAL ON SOLUTION OF PLANE-STRESS PROBLEMS WITH LARGE PLSTIC DEFORMATION

本文首先将以前所得到的关于两个轴对称塑性平面应力问题(薄圆环和旋转盘)的有关方程和计算结果作了一个简单的叙述.这些计算结果是根据两种不同硬化特性的材料和一种理想塑性材料的应力应变曲线在不同负荷下计算得到的.这些结果指出这三种不同材料的应力应变曲线和负荷对于这两个问题的主应力比值和比例应变的影响很小,而对于比例应力的影响则很大.之后,分析了二维的塑性平面应力问题的方程;这些方程考虑了大应变,但不包括体积力(body force).分析这些方程中的包括材料应力应变曲线项和载荷数项的结果,认为假若在边界上的主应力的比值和比例应变不变,则材料的应力应变曲线和载荷对于主应力比值和比例应变的分布的影响可能不大,而对于比例应力的影响则很大.这种边界条件在实际问题中的普通加减下,满足的可能想是很大的.薄圆环和旋转盘的边界条件及所得的结果和这分析的结果是完全一致的.从这些结果并可提出一个简单而相当准确的近似解,最后并将本文所得的结果和依留辛(Ильюшии)的理论——关于小应变下三维问题形变理论的应用条件——作了比较.     

Inverse approach and sensitivity analysis for identification of ingot-mould thermal resistance in continuous casting of metals

The problem of appropriate location of the sensors for identification of ingot – mould thermal resistance during continuous casting of metals is the subject of the paper. Analysed problem belongs to the group of inverse problems. The present work shows also the method of identification of unknown thermal resistance using the temperature measurements at the number of sensors located in the wall of the mould. The influence of the location of the sensors on the results of identification is analysed. The best location of the sensors results from the sensitivity analysis for the steady-state inverse heat conduction problem. Validation of the proposed inverse method is realized by comparison of the results taken from solution of inverse and direct problems. Several numerical examples are presented and analysed.     

Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Determination of dynamic sizes during the process of impact of railway wagons

The objective of research in this paper refers to the theoretical and experimental determination of dynamic sizes that occur during the process of impact of railway wagons. At the process of wagons impact as well as at the time of changes of movement regime (starting, stopping, and braking), the longitudinal forces that significantly affect the stress-deformational state of the supporting wagon structure occur. In the process of developing and designing new types of wagons and in the process of identifying the behavior of existing types of wagons, it is necessary to know the values of the most important dynamic sizes that occur during the process of impact. In this paper, a method for determining these sizes is formed by using the theoretical models of impact of wagons. Results of numerical simulation of impact are compared with the results of experimental tests, which were conducted according to international regulations. Research has shown that the results of numerical simulations coincide with the results of experimental tests, with certain exceptions. It is concluded that theoretical model can be used in determining the most important dynamic sizes that occur during the process of wagons impact.     

Rayleigh-type waves in a water-saturated porous half-space with an elastic plate on its surface

The paper deals with the plane problem of steady-state time harmonic vibrations of an infinite elastic plate resting on a water-saturated porous solid. The displacements of the plate are described by means of the linear theory of small elastic oscillations. The motion of the two-phase medium is studied within the framework of Biot's linear theory of consolidation. The main interest is focused on the investigation of properties of the Rayleigh-type waves propagating alongside of the contact surface between the plate and the porous half-space. In particular, the dependence of the phase velocity and attenuation of the waves on the plate stiffness, mass coupling coefficient, and degree of saturation of the medium is studied. Besides, for the limiting case of an infinitely thin plate, the comparison of the wave characteristics is carried out with those of the pure Rayleigh waves.     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)——BASIC EQUATIONS

This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four simultaneous basic equations, i.e., equation of interest rate and amount of circulating fund, equations of purchasing and selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate, have been established. Discussions mainly on the solution and its simple applications of the equation of interst rate and amount of circulating fund are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping and the influence of amount of circulating fund with exponential attenuation due to the decreasing of banking interest rate.     

On Isotropic Invariants of the Elasticity Tensor

Isotropic invariants of the elasticity tensor always yield the same values no matter what coordinate system is concerned and therefore they characterize the linear elasticity of a solid material intrinsically. There exists a finite set of invariants of the elasticity tensor such that each invariant of the elasticity tensor can be expressed as a single-valued function of this set. Such a set, called a basis of invariants of the elasticity tensor, can be used to realize a parametrization of the manifold of orbits of elastic moduli, i.e. to distinguish different kinds of linear elastic materials. Seeking such a basis is an old problem in theory of invariants and seems to have been unsuccessful until now. In this paper, by means of the unique spectral decomposition of the elasticity tensor every invariant of the elasticity tensor is shown to be a joint invariant of the eigenprojections of the elasticity tensor, and then by utilizing some properties of the eigenprojections a basis for each case concerning the multiplicity of the eigenvalues of the elasticity tensor is presented in terms of joint invariants of the eigenprojections. In addition to the foregoing properties, the presented invariants may also be used to form invariant criteria for identification of elastic symmetry axes.     

Critical points in the formulation of pharmaceutical swellable controlled release dosage forms-Influence of particle size

Swellable matrix represents one of the most employed controlled release systems. These dosage forms provide slow release of drugs to reduce the fluctuation of drug concentration in plasma in order to improve the efficiency of treatment and/or to reduce adverse effects. The application of the concepts of statistical physics has allowed discovering the existence of critical points in the formulation of swellable matrices. These points, representing the volume fractions of the tablet components where the properties of the matrix diverge or change suddenly, provide important knowledge of how to rationalize the design of swellable matrices. The critical points are generally related to the percolation threshold of one of the components of the formulation, which corresponds to a geometrical phase transition of this component, passing from isolation to spanning the whole system. The last section of the paper is devoted to more recent findings concerning the influence of particle size of the components on the percolation threshold of the matrix forming polymer, and therefore on the release behaviour of the matrix. Knowledge of the excipient percolation threshold allows a more rational design of swellable matrices, according to the guidelines of the regulatory authorities concerning science-based formulation and quality by design.     

Investigation of the microstructure a turbulent jet in a wake

The study of the characteristics of the turbulence in the boundary layer and in free jets is one of the most important problems of the aerodynamics of viscous fluids. The accumulation of information on the pulsation characteristics of jet flows and the establishment of the corresponding governing laws may serve to verify the basic hypotheses of the semiempirical theories of turbulence, and also for the development of more advanced computational methods. In many cases the measurement of the pulsation characteristics of turbulent jets is of practical interest.The studies made up till now [1–5] of the microstructure of turbulent flow in the primary region of submerged axisymmetric jets have made it possible to obtain several interesting results. In particular, in addition to the average velocity profiles, hot-wire anemometric equipment has been used to measure the normal and tangential Reynolds stresses and also the intermittency factor in cross sections of the jet, the distribution of the intensity of the longitudinal and lateral velocity pulsations along the axis, the correlation coefficients and the corresponding integral turbulence scales, etc. These measurements have made it possible to draw several important conclusions on the mechanism of turbulent exchange, on the order of the terms omitted in the equation of motion, and on the semiempirical theories of turbulence [6–9].The common deficiency of the studies mentioned above is that near the boundary of a submerged jet, where the average velocity is practically equal to zero, the intensity of the pulsations is so great that it makes the reliability of the results obtained by means of the hotwire anemometer questionable. In this connection Townsend [6] indicated the advisability of studying the microstructure of a turbulent jet issuing into a low-velocity ambient flow.The present study had as its objective the investigation of the microstructure of the primary region of an axisymmetric jet in a wake flow over quite a broad range of the flow ratio parameter m=u/u₀;here u₀ is the average velocity at the nozzle exit, u is the velocity of the ambient stream. For various values of the parameter m in the primary region of the jet measurements were made of the profiles of the three components of the pulsation velocity and the Reynolds shear stresses, and also the values of the average velocity and two components of the pulsation velocity at a large number of points on the jet axis. The measured profiles of the Reynolds shear stresses were compared with the corresponding profiles calculated on the basis of the boundary layer equations from the experimentally determined average velocity profiles. For two values of the parameter m, in one of the sections of the jet measurements were made of the correlation coefficients of the longitudinal components of the pulsation velocity and the variation across the jet of the integral turbulence scale was determined.The results obtained give an idea of the influence of the parameter m on the characteristics of the turbulent jet in an ambient stream.     

The equations of motion of a mechanical system in matrix form

This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the investigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D'Alambert-Lagrange, Hamilton-Ostrogradski and Gauss.     

Dynamic contact angle for etting of a surface by a van der waals fluid

We consider the creeping motion of a thin layer of a nonvolatile viscous fluid spreading due to capillary forces over a rigid surface covered by a thin homogeneous film (microfilm). The influence of van der Waals forces on the asymptotic slope of the free boundary of the layer is studied in the region of large thickness, where capillary forces dominate. A solution of the problem of the slope angle is obtained for the entire possible range of the microfilm thickness. In the limit of small thickness of the microfilm, this solution is in agreement with the well-known solution of the problem of the dynamics of wetting of a dry surface in the presence of a precursory film and van der Waals forces. The role of the condition at the end of the precursory film is studied. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences. Tyumen' 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika. Vol. 41, No. 4, pp. 101–105, July–August. 2000.     

A two-phase stream containing liquid particles in the sub- and transonic regions of plane nozzles

The results of experimental studies of the influence of the entrance conditions, the particle size, the profiles of the sub- and transonic parts of the nozzle, and the initial concentration on the distribution of the solid discrete phase in the exit cross sections of axisymmetric nozzles were analyzed in [1]. The results of a study of the influence of the profiling of the nozzle and the size of the particles at the nozzle entrance on the formation of the distribution fields of the discrete liquid phase and its size at the cut of a plane nozzle are presented in the present report, which is a continuation of [1]. The experimental data presented permit a deeper understanding of the mechanism of flow of a two-phase medium in a nozzle and are required for an evaluation of efficiency of the calculation methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 167–170, March–April, 1978.     

Capture of small drops by large drops in an electric field

In the investigation of the process of the breakdown of emulsions by the coalescence of drops, up to the present time, use has been made of the theory of the coagulation of colloids (for example, [1]). However, there is a considerable difference between colloids and emulsions. Forces of attraction, bringing about the coalescence of two colloidal particles, become predominant at distances much greater than the particle size, so that, in a hydrodynamic sense, it can be assumed that colloidal particles do not interact. On the contrary, the disperse phase in emulsions consists of molecularly smooth spherical drops with a size from a few tenths of a micron or more and, with approach of the drops, forces of hydrodynamic interaction, inhibiting coalescence, become substantial. As a rule, the drops can be regarded as rigid undeformed spheres since their surface is stabilized by surface-active substances. With the approach of such spheres, the layer of liquid between them generates a braking force proportional to the rate of approach of the drops and inversely proportional to the distance between their surfaces. As a result, the approach of drops under the action of a finite force takes place over an infinite time. It follows from this that the process of the coalescence of drops requires the presence of a force of attraction, rising to infinity with approach of the drops, and any theory of coalescence must take simultaneous account of the forces of attraction of the drops and of the hydrodynamic forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–68, September–October, 1973.