Control of separation phenomena in a high-speed flow by means of the surface electric discharge

The results of an experimental and theoretical investigation of the interaction between a surface electric discharge and a supersonic air flow in a constant cross-section channel are given. The features of the generation of the surface discharge in the flow are described. A model of the interaction is proposed. The regime of gasdynamic screening of a mechanical obstacle on the channel wall is investigated. Data on the change in the main flow parameters as a result of the generation of a surface discharge are given. The experimental results are compared with the results of calculations based on a simplified model of the interaction.     

压电体椭圆孔边的力学分析

基于复变函数的方法,以PZT-4材料为例,分别采用精确电边界条件和非导通电边界条件进行了远场均匀载荷作用下的横观各向同性压电体椭圆孔的力学分析并与相关结果进行对比。结果表明当椭圆孔退化为圆孔时,无论在远场作用力载荷或电载荷,两种电边界条件下的结果均能完全吻合。随着椭圆孔的愈加尖锐化,非导通电边界条件逐渐不能适用。     

The Blasius and Sakiadis flow with variable fluid properties

A theoretical study of the effect of variable fluid properties on the classical Blasius and Sakiadis flow is presented in this paper. The investigation concerns engine oil, water and air taking into account the variation of their physical properties with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented, as well as values of wall shear stress and wall heat transfer, for a variety of temperatures between the plate and the ambient fluid. It is found that the variation of fluid properties and especially viscosity have a strong influence on the results. The results of oil and water are, in general, similar and are generalized to liquids whereas air results are different and are generalized to gases. Except of the new results found in the present work some inaccurate results existing in the literature have been identified.     

Scaling theory of adsorption-induced stresses in polymer brushes grafted onto compliant structures

The lateral forces exerted on a substrate by a layer of end-grafted polymer molecules are calculated on the basis of simple scaling arguments. The results are cast in terms of an equilibrium surface stress and an elastic constant, which describes the rate of change of the surface stress upon deformation of the substrate. This allows for straightforward integration of the present results into a continuum framework describing the response of a compliant structure, which facilitates device design and analysis. The results are illustrated with calculations for end-grafted poly(styrene) and poly(ethylene oxide), and the implications for building micromechanical devices based on adsorption-induced deformation are discussed.     

Axisymmetric shells and plates on tensionless elastic foundations

This paper first describes a finite element method for the large deflection analysis of axisymmetric shells and plates on a nonlinear tensionless elastic foundation. Through the use of discrete data points, any form of nonlinear elastic foundation behaviour can be easily modelled. The analysis is then validated by comparison with existing results for circular plates and beams as the only existing results for shells on tensionless foundations are found to be in error. Following this verification, the analysis is applied to investigate the behaviour of shallow spherical shells subject to a central concentrated load on tensionless linear elastic foundations. A number of insightful conclusions regarding the behaviour of such structure-foundation systems are drawn. The numerical results for shells are believed to be the first correct results, which may be useful in benchmarking results from other sources in the future.     

Three Dimensional Vibration Transmission of a Plate on a Layer of Porous Medium Due to a Moving Load

Three-dimensional (3D) transmission of vibration in an infinite elastic thin plate on a layer of poroviscoelastic medium, due to a harmonic, rectangular moving load, is investigated theoretically based on Biot’s theory. The material of the medium is idealized as a uniform, fully saturated poroviscoelastic layer on bedrock. By introducing four scalar potential functions and Helmholtz decomposition theorem, analytical solutions of stress, displacement, and pore pressure with and without thin plate are derived using Fourier transform technique. Numerical results are obtained with the help of inverse Fourier transform and are used to analyze the influence of load velocity, porosity, permeability, relative stiffness of plate versus ground, and the thickness of plate on the vibration. Furthermore, the results are compared with the available dynamic response results of a non-moving load on a layer of viscoelastic material.     

Experimental investigation of rarefied gas flow through rectangular slits and nozzles

The flow of a rarefied gas through rectangular configuratons of different geometries has been experimentally studied to determine their discharge coefficient characteristics. The configurations used are a set of sharp-edged slit orifices, a smooth converging nozzle and a tube. The range of the Reynolds number based on the throat conditions varied from 0.01 to 100. The equivalent Knudsen number range based on the upstream conditions and inlet diameter varied from 0.0521 to 2.521. The results for the smooth nozzle are compared with calculations using a numerical method with one-dimensional stream tube approximation based on integrated boundary layer equations. The slit and the tube results are compared with the experimental results of Sreekanth and Davis [1988].     

Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions

The problem of formulating minimal conditions on input data that can guarantee the existence and uniqueness of solutions of the boundary value problems describing non-one-dimensional ideal incompressible fluid flow is considered using as an example the initial boundary value problem in a space-time cylinder constructed on a bounded flow domain with the nonpenetration condition on its boundary (which corresponds to fluid flow in a closed vessel). The existence problems are considered only for plane flows, and the uniqueness issues for three-dimensional flows as well. The required conditions are obtained in the form of conditions specifying that the vorticity belongs to definite functional Orlicz spaces. The results are compared with well-known results. Examples are given of admissible types of singularities for which the obtained results are valid, which is a physical interpretation of these results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 130–145, July–August, 2008.     

Some asymptotic results for a class of stochastic systems with parametric excitations

Systems of stochastic ordinary differential equations dependent on a small parameter are studied. The equations are assumed to depend on two time scales: they are stochastic in a fast time t and they are deterministic in a slow time t. The method of analysis is based on a generalization of the Method of Averaging. Mathematical results are given valid for all t for sufficiently small. The mathematical results are applied to several examples of parametrically excited dynamical systems.     

Rotating Waves in Neutral Partial Functional Differential Equations

General results on the existence and global continuation of rotating waves are established for partial neutral functional differential equations defined on the unit circle. These results are applied to a class of coupled lossless transmission lines.     

Heat transfer by conduction,natural convection and radiation across a rectangular cellular structure

This paper describes results on the effects of wall conduction and radiation heat exchange among surfaces on laminar natural convection heat transfer in a two-dimensional rectangular cavity modelling a cellular structure. Parametric heat transfer calculations have been performed, and numerical results are presented in graphical and tabular form. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The findings suggest that the local or the average Nusselt number is one of many parameters that control conjugate heat transfer problems. The results indicate that natural convection heat transfer in the cavity is reduced by heat conduction in the walls and radiation exchange among surfaces. The results obtaibed for the total heat transfer rate through the system using the two-dimensional model are compared with those based on a one-dimensional model.     

An error analysis of holographic strains determined by cubic splines

Holographic measurements of an idealized cantilever beam under end-loading and uniform-loading conditions are simulated on a computer. Cubic splines are fitted to the simulated data and then used to evaluate the shear strain and bending moment. Controlled data errors are introduced into the simulated measurements and the strain and bending-moment results are compared with the known analytic results. When the data are not resolution limited, the accuracy of the results increases as more cubic splines are taken. However, when the data are resolution limited, the accuracy of the results is a maximum for an optimum number of cubic splines and the use of more splines actually decreases the accuracy.     

预扭转钨合金杆弹侵彻钢靶的数值模拟

在实验的基础上 ,对预扭转钨合金长杆弹提出了一个唯象的本构模型和破坏准则 ,并针对预扭转钨合金长杆弹侵彻厚钢靶进行二维有限元计算 ,得到了侵彻过程中的主要物理图象和曲线 ,进而对计算结果进行了分析讨论。计算结果表明 ,侵彻过程中的主要物理数据与实验测量结果基本一致。     

岛津试验机高温剪切蠕变试验装置的研制与实验研究

介绍了作者研制的在岛津试验机上进行高温剪切蠕变实验装置的原理和结构，利用此装置进行了碳钢和铝合金在高温下的剪切蠕变实验，结果表明，该装置有较高的实验精度。有关此类实验结果的报导尚不多见。     

Forced convection with laminar pulsating flow in a tube

The heat transfer model of laminar pulsating flow in a tube in rolling motion is established. The correlations of velocity, temperature and Nusselt number are obtained. The effects of several parameters on Nusselt number are investigated. The theoretical results are consistent with experimental data. Then the results are evaluated with Nield and Kuznetsov’s results. It is found that Nield and Kuznetsov’s results are not applicable for the laminar pulsating flow in nuclear power systems in ocean environments.     

Propagation of harmonic perturbations in a thermoelastic medium with heat relaxation

The propagation of plane harmonic waves in a thermoelastic medium with heat-flux relaxation is studied; in particular, the dependences of the temperature and displacement on the coordinate are analyzed in a coupled formulation. The dependences of the group and phase velocities on frequency are investigated. The influence of the frequency and parameters of the material on the amplitude of thermoelastic waves is examined. The results are compared with the available results obtained using classical thermoelasticity theory.     

Braking of a Body by a Soft Inflatable Shell on Impact on a Surface

The results of mathematical simulation of a solid velocity damping by a soft skeleton fabric shell filled with air on impact on a hard surface are given. The equations of motion of a falling body and of the loading dynamics of membrane shells and the reinforcement rings in the fabric shell are considered together. Themathematical model and the numerical algorithm for solving the spatial problem of the dynamics of inflation of a shell with reinforcement rings are explicitly realized by the finite difference method. The boundary conditions are posed with regard to the contact of the shell elements in compression near the ring belts. The results of numerical experiments considering the interaction of the falling body with the deformable skeleton shell are discussed. The parameters influencing the process of the body braking on impact on a surface are determined.     

Steady Groundwater Flow to Drains on a Sloping Bed: Comparison of Solutions Based on Boussinesq Equation and Richards Equation

Analytical expressions for the scaling factor (A) in the Wooding and Chapman (J Geophys Res 71:2895–2902, 1966) solution for steady-state flow to drains on a sloping bed are presented. Otherwise A needs to be obtained by matching numerical and solutions. Corrections to various errors in other analytical solutions are given. The HYDRUS2D numerical model was used to generate results for steady-state flow to drains on a sloping bed which were compared to published Hele-Shaw cell results. The numerical results were used to compute both the pressure head on the bottom and the height of the phreatic surface. The numerical results for maximum water-table height are almost exactly the same as the published Hele-Shaw cell results and are greater than the numerical values for the maximum pressure heads on the sloping base. These HYDRUS2D model results were then compared with various analytical solutions, and it was found that Towner’s (Water Resour Res 11:144–147, 1975) solution gave the best results for both estimation of the maximum height of the phreatic surface and the position on the slope where this occurs.     

Stochastic analysis of groundwater flow in a bounded domain by spectral methods

A saturated flow problem with spatially varying conductivity is studied in a rectangular domain. An expansion of the flow equation with respect to small perturbations of the conductivity is given. Discrete spectra are used to calculate the expected flux across the outflow boundary and its variability. The results obtained are compared with results based on Monte Carlo studies. Another way to deal with heterogeneous soils is to replace the actual conductivity by a smooth, so-called, effective conductivity. A comparison is made between results based on that approach and our results.     

Fractal porous media

The transport properties of continuous deterministic fractals are reviewed. The method of construction, the fractal dimension, and the major features of transport are summarized. Then the major single-phase transports are addressed; attention is focused on the numerical results and on the analytical arguments which may be used to derive these results in a simple way, whenever it is possible.