High-speed videocamera investigation of the wave structure development on an unstable cavity boundary

The formation of wave structures on an unstable (in the Rayleigh-Taylor criterion) boundary of a plane cavity is studied using high-speed video filming. It is shown that at the head of the cavity a quasiperiodic wave regime develops, with a mean wavelength similar to that obtained from a linear stability analysis for the cavity boundary. Observations of the initial-regime breakdown show that its scenarios are similar to the development of subharmonic instability in the one-mode regime. The waves are classified with respect to the wave development rate. It is shown that the large-wave amplitude growth law is on average closely approximated by a quadratic parabola, with the total gas entrainment from the cavity being proportional to the square of the cavity length. The existence of a scaling effect is detected, which in the case considered reduces mainly to a dependence of the gas entrainment coefficient on the Weber number. It is shown that with decrease in the Weber number the gas entrainment coefficient may significantly increase.     

Three-dimensional boundary layer on a plane delta wing in the intermediate hypersonic interaction regime

The results of calculating the three-dimensional boundary layer on a plane delta wing of finite length in the intermediate hypersonic interaction regime are presented. The effect of the hypersonic interaction parameter on the gas flow in the boundary layer and the aerodynamic characteristics is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–116, May–June, 1991.     

Application of a Virtual-Boundary Method for the Numerical Study of Oscillations Developing Behind a Cylinder Near A Plane Wall

The conditions of onset and the character of the oscillations developing behind a circular cylinder located above a plane wall (screen) in a flow with a velocity profile of the boundary layer type are studied numerically. The dependence of the critical Reynolds number (at which a steady flow regime in the wake behind the cylinder is replaced by an oscillatory regime) on the cylinder-wall gap and the free-stream boundary layer thickness is found.     

Quasiperiodic structures in the problem of fluid convection between horizontal planes

A steady flow induced by quasiperiodic temperature distributions at the boundaries is considered with reference to the example of fluid convection in a plane horizontal layer heated from below. A spectral-finite-difference method is employed to obtain convective vortex structures varying quasiperiodically along the horizontal coordinate. The properties of the quasiperiodic solutions, together with their spectra and integral characteristics (Nusselt number) are studied as functions of the Grashof number and the boundary conditions of the problem.     

The effect of hydrodynamic friction on the stability of a wall layer in annular two-phase flow

This note is concerned with annulat flow in a vertical tube when the gas stream in the central portion of the tube is separated from the wall by an annular layer of liquid. The friction at the interface may have either a stabilizing or destabilizing effect on such a flow regime with respect to small disturbances of the interface. The liquid-layer thickness is assumed small, which permits direct use of the results of [1] in studying the stability. The analysis is applicable to laminar and developed turbulent gas motions; in both cases the motion in the liquid layer is assumed laminar.     

Transition of plane overdriven detonation wave to the Chapman-Jouguet regime

The asymptotic laws of behavior for plane, cylindrical, and spherical infinitely thin detonation waves were found in [1, 2] for increasing distance from an igniting source in those cases in which the waves changed into Chapman-Jouguet waves as they decayed. It was shown that the plane overdriven detonation wave approaches the Chapman-Jouguet regime asymptotically, while the transition of the cylindrical or spherical strong detonation wave into the Chapman-Jouguet wave may occur at a finite distance from the initiation source.Similar conclusions are valid for the propagation of stationary steadystate detonation waves which arise with flow of combustible gas mixtures past bodies.However, numerous experiments [3, 4] on firing bodies in a detonating gas show that the overdriven detonation wave which forms ahead of the body decays and decomposes into an ordinary compression shock and a slow combustion front. To establish why the wave does not make the transition to the Chapman-Jouguet regime, in the following we consider the propagation of a plane detonation wave and account for finite chemical reaction rates. We use the very simple two-front model (ordinary shock wave and following flame front). Conditions are found for which transition to the Chapman-Jouguet regime does not occur. We first consider the propagation of an unsteady plane wave and then the steady plane wave. It is found that for all the mixtures used in these experiments transition to the Chapman-Jouguet regime is not possible within the framework of the assumed model.     

Asymptotic Analysis of Plastic Flow along the Generatrix in a Thin Cylindrical Layer

An analytical solution is found for the problem modeling quasistatic compression and flow of an ideal rigid plastic (under the Mises-Hencky criterion) material along the generatrix in a thin cylindrical layer. This problem is a generalization of the classical Prandtl problem. The small asymptotic parameter is the ratio of the layer thickness to its length. The radii of the cylinders can have any intermediate order of smallness. It is shown that when the radii and thickness of the layer are of the same order of smallness, the solution is asymptotically exact in the sense that the number of terms of the series describing the kinematic and dynamic parameters of the flow is finite. Limiting transitions to the classical Prandtl solution are investigated.     

Investigation of the Process of Compression of a Magnetic Field by a Strong Ionizing Shock Wave in a CsI Single Crystal

A mathematical model is proposed for the process of compression of a magnetic field by a strong ionizing shock wave in a single crystal when a compressible electroconducting medium is formed behind the shock. The detailed physical pattern of the process is obtained numerically. It is shown that in the final stage different magnetic field compression regimes are possible: cumulation on the axis, an oscillatory regime in which the magnetic field and gas dynamic quantities change sharply, and a quasi-steady regime with smooth slow variation of all the parameters. In previous studies the possibility of this regime was not noted. For the dimensionless parameters characterizing the process of compression of the magnetic field as a whole domains corresponding to different compression regimes are obtained.     

Large deformation mechanics of a soft elastomeric layer under compressive loading for a MEMS tactile sensor application

The study is motivated by the need to develop highly sensitive tactile sensors for both robotic and bionic applications. The ability to predict the response of an elastomeric layer under severe pressure conditions is key to the development of highly sensitive capacitive tactile sensors capable of detecting the location and magnitude of applied forces over a broad range of contact severity and layer depression. Thus, in this work, a large deformation Mooney–Rivlin material model is employed in establishing the non-linear mechanics of an elastomeric layer of finite thickness, subjected to uniform displacement of controlled compression. Thus, an analytical non-linear model for the above described problem which is validated numerically via the method of finite elements is developed. Two dimensional, plane strain conditions of an infinitely long and of finite thickness elastomeric layer are assumed. The layer is subjected to a uniform vertical large displacement with symmetry conditions applied at the contact center. Cauchy normal and shear stress profiles as well as displacement profiles are established over a broad range of a layer compression including up to 40% of layer thinning. The model allows for the determination of the non-linear relationship between the relative separation of embedded conducting electrodes and thus the sensor capacitance during touch, to the force magnitude of the force concentrated at the symmetry plane or sensor center. The current model is expected to further improve the sensitivity and range of polymeric tactile sensors currently under development (Charalambides and Bergbreiter, 2013) [1]. As shown elsewhere (Kalayeh et al., 2015) [2], capacitance–force model predictions are found to be in remarkable agreement with experimental measurements for a broad family of self-similar pressure sensors.     

Self-oscillation regimes in a liquid jet curtain separating gas regions with different pressures

The results of an experimental investigation of the self-oscillation regimes of liquid jet outflow into a plane channel with air injection in its dead end are presented. The effect of the volume of the cavity, or the air cushion, and its thickness (or channel width) on the flow is studied on a wide range of the gas injection rate and the liquid outflow velocity. The self-oscillation flow regimes are realized at a constant pressure of water in the supply tank and a constant mass flow rate of the air injected into the cushion. With increase in the air injection rate the self-oscillation regime realized at lower injection intensities is replaced by a higher-frequency regime. High-speed videofilming shows that the difference from the low-frequency regime consists in the absence of the direct interaction between the out flowing jet and the channel wall. It is found that in both low-frequency and high-frequency regimes the self-oscillation frequency and amplitude are independent of the cushion thickness but the moment of the regime changeover is determined by this parameter. It is established that there exists a threshold value of the cavity volume, behind which the low-frequency regime does not occur at any air injection rates.     

Bifurcation phenomena in the plane compression test

A basic, compression, bifurcation problem is studied by methods similar to those used by R. Hill and J. W. Hutchinson (1975) for the corresponding tension problem. Bifurcations from a state of homogeneous in-plane compression loading are investigated for a rectangular block of incompressible material constrained to undergo plane deformations. The sides of the block are tractionfree, and it is loaded compressively by a uniform, shear-free, relative displacement of its ends. For a wide class of incrementally-linear time-independent materials only two instantaneous moduli enter into the analysis. Diffuse modes of both symmetric and antisymmetric bifurcation are examined in the elliptic regime of the governing equations, and the possibility of localized modes is considered both inside and outside this regime. Lowest bifurcation stresses are computed for essentially the entire range of possible combinations of material properties and geometry, and these are compared with results obtained by Hill and Hutchinson for the tension problem. The limiting case of large thickness (the semi-infinite block) is considered, confirming the results of M. A. Biot (1965).     

Effects of a countercurrent gas flow on falling-film mode transitions between horizontal tubes

A liquid film falling between horizontal tubes is known to take the form of droplets, jets or sheets, depending on the liquid flow rate; the form of the flow is the so-called “falling-film mode”. Although previously neglected in studies of mode transition, a countercurrent gas flow often exists in falling-film heat exchangers, and its effect on the liquid flow might be important: it could impact the flow regime, lead to local “dryout,” and decrease the heat transfer rate. Experiments are conducted to explore the effects of a countercurrent gas flow and liquid feeding length on falling-film mode transitions for a liquid flowing over horizontal tubes. The effects on mode transition are shown to depend on fluid properties and are explained in terms of unsteadiness and film thickness. In general, transition hysteresis is reduced with an increasing gas velocity. A correlation is developed to predict the countercurrent gas flow effects on falling-film mode transitions. The liquid feeding length can affect mode transitions in quiescent surroundings and when a countercurrent gas flow imposed.     

Plane acoustic wave propagation through a composite of elastic and Kelvin–Voigt viscoelastic material layers

The problem of plane wave propagation through a plane composite layer of thickness h is considered. The composite consists of periodically repeated elastic and Kelvin–Voigt viscoelastic material layers, and all layers are either parallel or perpendicular to the incident wave front. Moreover, it is assumed that the thickness of each separate layer of the composite is much less than the acoustic wave length and the thickness h of the entire composite. We study the problem by using a homogenized model of the composite, which allows us to find the reflection and transmission factors and the variation in the sound intensity level as it propagates though the composite layer of thickness h.     

Nature of the surface heart transfer fluctuation in a hypersonic separated turbulent flow

This paper presents the results of an experimental study of the unsteady nature of a hypersonic separated turbulent flow. The nomimal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5×10⁷/m. The separated flow was generated using finite span forward facing steps. An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make multi-channel measurements of the fluctuating surface heat trtansfer within the separated flow. Conditional sampling analysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness. The compression waves converge into a single leading shock beyond the boundary layer. The shock structure is unsteady and undergoes large-scale motion in the streamwise direction. The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave. There exists a wide band of frequency of oscillations of the shock system. Most of the frequencies are in the range of 1–3 kHz. The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave. This intermittent phenomenon is considered as the consequence of the large-scale shock system oscillations. Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed. The project supported by National Natural Science Foundation of China     

Parameters of shock waves with emission in gases

Parameters of emitting shock waves in gases are investigated in the limiting case when there is no screening of emission from the shock front by the precursory layer. The one-dimensional quasi-steady-state formulation of the problem with deceleration of high-speed gas flow against a plane fixed obstacle under conditions of strong emission is given. The case of the shock waves of large optical thickness is analytically considered over a wide range of variation of the obstacle reflectivity. The parameters of emitting shock waves generated in experiments in shock tubes in the inert argon gas are estimated using the methods developed and compared with the measurement results. The shock “adiabats” of optically thick shock waves are considered with allowance for the radiation energy losses. The calculations are carried out for aluminium plasma.     

Expansion of monatomic and diatomic gases from a spherical source into a vacuum in a gravitational field

Steady monatomic and diatomic gas flows from a spherical source into a vacuum in a gravitational field are studied using direct statistical simulation. The qualitative gravitation effect on the flow is shown to be independent of the intermolecular collision model. Three characteristic Jeans parameter ranges can always be distinguished, namely, the subcritical range, on which the flow in a weak gravitational field is similar with the outflow in the absence of gravitation, the supercritical range, on which the outflow velocity remains small even at large distances from the source, and a narrow transitional range between the two former ranges. The presence of internal degrees of freedom of gas molecules displaces the transitional range toward the greater values of the Jeans parameter and leads to an increase in the outflow velocity and the gas temperature; however, in the initial region the latter effect is expressed only slightly. The normalized escape flow is a nonmonotonic function of both the Jeans parameter and the Knudsen number and is different for monatomic and diatomic gases within 50% on the parameter range considered.     

A receding contact plane problem between a functionally graded layer and a homogeneous substrate

In this paper, we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress–strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using integral transforms, the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half-length. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half-length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.     

非平整、多孔介质海底上波浪传播的复合方程

为了反映近岸区域实际存在的多孔介质海底效应，并且考虑到波浪在刚性海底上传播模型的 最新研究进展，运用Green第二恒等式建立了波浪在非平整、多孔介质海底上传播的复合方 程. 假设水深和多孔介质海底层厚度均由两种分量组成：慢变分量，其水平变化的长度尺度大于 表面波的波长；快变分量，其水平变化的长度尺度与表面波的波长等阶，但其振幅小于表面 波的振幅. 另外，多孔介质层下部边界的快变分量比水深的快变分量小1个量级. 针对水体层和多孔介质层，选择Green第二恒等式方法给出了波浪传播和渗透的复合方程， 它在交接面上满足压力和垂直渗透速度的连续性条件,可充分考虑波数变化的一般连续性， 并包含了某些著名的扩展型缓坡方程.     

On the influence of the gravity force on the stability of an inhomogeneous layer under biaxial extension-compression

In the present paper, in the framework of the three-dimensional nonlinear theory of elasticity, we study the stability of a heavy layer under biaxial extension-compression. The elastic properties of the layer are assumed to be inhomogeneous along thickness and are described by a semilinear material model. We study the stability by using the bifurcation approach. By solving the linearized equilibrium equations, we obtain the critical curves and the stability domain in the plane of the loading parameters, for which we take the material elongation ratios along the coordinate axes lying in the layer plane. We analyze the influence of the layer thickness, specific weight, and material parameters on buckling. In particular, we find that, when studying stability, it is expedient to take the gravity force into account only if the layer rigidity decreases with increasing depth.     

Quasiperiodic solutions of the Navier-Stokes equations induced by the quasiperiodic shape of the boundaries of a two-dimensional flow domain

Steady quasiperiodic solutions of the Navier-Stokes equations in an infinite two-dimensional layer with quasiperiodic boundaries are obtained on the Reynolds number range 0 < Re* < 200. The calculations are performed using a spectral-difference method based on the representation of the quasiperiodic solutions in the form of convergent double Fourier series. The properties of these solutions and the distinctive features of their spectra are studied and their fundamental differences from periodic solutions are shown. The possibility of applying the quasiperiodic solutions for modeling flows in fractal layers is discussed.