On hysteresis in elasto-plasticity and in ferromagnetism

We define hysteresis as rate-independent memory, illustrate some of its properties, and review some scalar models of elasto-plasticity: the stop, the play, the Prandtl–Ishlinski models. In particular we study the Prager model of linear kinematic hardening, which encompasses stops and plays. We then couple the latter model with the dynamic equation for a one-dimensional system, show existence of a weak solution, and deal with its homogenization. We also discuss the extension to tensors and to three-dimensional systems.

We then deal with ferromagnetic hysteresis. We review the classic Preisach model and a vector extension. Finally, we formulate a model of vector ferromagnetic hysteresis, couple it with the magnetostatic equations, and discuss its homogenization. The latter consists in a two-length-scale model, and corresponds to a variant of the vector Preisach model.     

Heating zone dynamics in in situ combustion

The integrodifferential equation of the quasisteady regime of a moving in situ combustion front is obtained and its exact solution is constructed in a particular case; the possibility of the heat generated at the combustion front being projected into the region ahead of the front is analyzed and the heating zone dynamics in the reservoir and the surrounding rock are investigated. In a number of studies of in situ combustion it is assumed that an increase in the water-air factor or, what amounts to the same thing, an increase in convection velocity in the reservoir leads to the total transfer of the heat into the region ahead of the combustion front [1–3]. In [3] the area of the heating zone ahead of the combustion front was calculated in accordance with the Marx-Longenheim model [4]. Below, on the basis of exact solutions of model problems it is shown that in the case of quasisteady Newtonian heat transfer between the surrounding medium, when the latter is assumed to be a thermal reservoir, i.e., maintain a constant temperature, this projection of heat is possible if the convection velocity exceeds the velocity of the combustion front. In the case of unsteady heat transfer in accordance with the Leverrier model there is no total projection of heat into the region in question; in the steady-state regime a limited heating zone, proportional in depth to the square of the difference of the convection and combustion front velocities, is formed ahead of the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–172, July–August, 1987.The author wishes to thank V. M. Entov for his valuable advice and useful discussions.     

Genetic disorders in haematological practice in India

Haemoglobinopathies represent a significant national health burden in India. The distribution of specific disorders varies geographically and by community. Heterozygote frequencies of beta-thalassaemia range from 1 to 15%, resulting in an estimated 20 million carriers. HbS is mainly present in tribal and non-caste communities, with carrier prevalences of up to 40%. By comparison, alpha-thalassaemia carriers are found in both the caste and tribal communities, and can reach a frequency of >90% in the latter case. Community control of haemoglobinopathies relies mainly on out-reach education programmes and genetic counselling, with antenatal diagnosis offered in specific major centres. Only partial data are available on the prevalence of haemophilia, but it has been estimated that there are some 50,000 affected individuals nationwide, with an additional 1,500 new cases born each year. RFLP-based techniques have been established to detect mutations in the factor VIII and IX genes, enabling the limited introduction of carrier detection and antenatal diagnosis.     

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

A two-dimensional problem of the flow of a gas containing an impurity through a porous medium is considered. At the initial time, the gas containing a uniformly distributed impurity is at a high pressure in a spherical cavity in a porous medium at a certain distance from a flat surface. It is assumed that for t > the motion of the carrier gas is described by the system of equations for flow in a porous medium and the dispersion of the impurity is described by the equations of convective diffusion and nonequilibrium adsorption. A numerical method for solving the problem is discussed. Some results of calculations are given. The influence of the flat surface on the flow of the gas and the dispersion of the impurity is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1982.We thank V. N. Nikolaevskii for comments which permitted a significant improvement in the paper.     

Transition process in a fluid layer in a rotating paraboloid in response to a sudden change in its angular velocity

The process of establishment of the rigid-body rotation state in a liquid layer in a rotating paraboloid upon a sudden increase in its angular velocity is studied theoretically and experimentally. The theoretical study is performed within the framework of linear shallow-water theory with account for the bottom Ekman friction. Analytical solutions describing the transition process are obtained and the dependence of the establishment time on the liquid depth and the radius of curvature of the paraboloid is investigated. It is shown that the effect of free surface deformation may lead to a significant increase in the establishment time. Good agreement with the results of special laboratory experiments is found.     

Fluctuations in cavities in a supersonic gas flow

Numerical calculations are carried out within the framework of the ideal compressible gas model for the unsteady flows in rectangular cavities exposed to a supersonic external stream. The Euler equations are integrated by means of Godunov's finite-difference method [6]. On the basis of an analysis of the calculation results an expression is proposed for determining the possible frequencies of the flow rate oscillations in the cavity as a function of the free-stream Mach number M and the geometry of the cavity. The results obtained are compared with the experimental data and calculations of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–127, March–April, 1990.     

Gas-Dynamic Processes in Two-Phase Flows in MHD Generators

A plane problem of a two-phase monodisperse flow of combustion products of plasma-forming composite solid propellants in the duct of a Faraday's MHD generator with continuous electrodes, including an accelerating nozzle, MHD channel, and diffuser, is considered. An algorithm based on the pseudo-transient method is developed to solve the system of equations describing the two-phase flow. Gas-dynamic processes in the channels of the Pamir-1 setup are numerically studied. It is shown that shock-free deceleration of a supersonic flow to velocities close to the equilibrium velocity of sound in a two-phase mixture and significantly lower than the velocity of sound in the gas is possible in two-phase flows.     

Self-sustained global oscillations in a jet in crossflow

A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier?CStokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.     

Capillary effects in steady-state flow in heterogeneous cores

Effects of capillary heterogeneity at the macroscopic scale have previously been analyzed for static conditions or in the context of outflow end-effects. This paper presents a systematic study for the case of one-dimensional, steady-state flow, that complements recent work on transient displacement. We consider the saturation response to various forms of heterogeneity. Included are analytical results for certain model cases, some general results, and numerical solutions for variously correlated spatial variations. The sensitivity to process parameters, such as rate, heterogeneity length scale and correlation, is studied. Physical interpretations are offered and potential applications in the estimation of heterogeneity are discussed.     

Erosion in conical diffusers in particulate-laden cavitating flow

This paper highlights the serious damage that can occur in diffusing sections of pipework in which a cavitating particulate-laden fluid is flowing. The combined effects of particle erosion and cavitation are shown to remove considerably more material than would be expected from summing the effects of the individual mechanisms. It is demonstrated that, to be sure of avoiding this accelerated surface erosion, the transition from a smaller flow section to a larger one needs to be an abrupt expansion. If pressure recovery is important, a possible design solution is proposed. In the case of swirling flow, the expansion again needs to be abrupt. Evidence was also obtained which showed that, by allowing air to be entrained into the low pressure region in the flow, the cavitation and the erosion can be substantially reduced.     

Experiments in mechanical and optical coincidence in photoplasticity

In the extension of the shear-difference method to the separation of interior principal stresses in the elasto-plastic state¹, a basic question arises whether the optical isoclinics give the directions of the principal stresses, i.e., whether optical coincidence exists. Experiments are described aiming to answer this question, and preliminary results are given for cellulose nitrate as a model material. Experiments are also described dealing with mechanical coincidence.     

Mixing in Circular and Non-circular Jets in Crossflow

Coherent structures and mixing in the flow field of a jet in crossflow have been studied using computational (large eddy simulation) and experimental (particle image velocimetry and laser-induced fluorescence) techniques. The mean scalar fields and turbulence statistics as determined by both are compared for circular, elliptic, and square nozzles. For the latter configurations, effects of orientation are considered. The computations reveal that the distribution of a passive scalar in a cross-sectional plane can be single- or double-peaked, depending on the nozzle shape and orientation. A proper orthogonal decomposition of the transverse velocity indicates that coherent structures may be responsible for this phenomenon. Nozzles which have a single-peaked distribution have stronger modes in transverse direction. The global mixing performance is superior for these nozzle types. This is the case for the blunt square nozzle and for the elliptic nozzle with high aspect ratio. It is further demonstrated that the flow field contains large regions in which a passive scalar is transported up the mean gradient (counter-gradient transport) which implies failure of the gradient diffusion hypothesis.     

Mean stress in a granular medium in dynamics

In this paper we propose to construct a mean stress tensor for a granular medium, valid in static and in dynamics, which takes into account the contact reactions and the body forces acting at the grain level. A simple analytical example shows that taking account of inertia forces is essential to insure the symmetry of the mean stress tensor in dynamics. Finally, numerical simulations illustrating this definition of the mean stress tensor are presented for a granular medium ensiled.     

Recent research activities in experimental mechanics in China

A brief review is presented of the recent activities in the field of experimental mechanics in the People's Republic of China. The current research work covers the following subjects: (1) photoelastic phenomena, such as the classical three-dimensional photoelasticity, the scattered-light technique, birefringent coatings, birefringent materials; (2) holography, holographic interferometry, speckle interferometry and their applications; (3) moiré method; (4) strain-gage techniques and strain indicators.     

Turbulent transport in an inclined jet in crossflow

The present study experimentally investigates a turbulent jet in crossflow relevant to film cooling applications. The jet is inclined at 30°, and its mean velocity is the same as the crossflow. Magnetic resonance imaging is used to obtain the full three-dimensional velocity and concentration fields, whereas Reynolds stresses are obtained along selected planes by Particle Image Velocimetry. The critical role of the counter-rotating vortex pair in the mixing process is apparent from both velocity and concentration fields. The jet entrainment is not significantly higher than in an axisymmetric jet without crossflow, because the proximity of the wall inhibits the turbulent transport. Reynolds shear stresses correlate with velocity and concentration gradients, consistent with the fundamental assumptions of simple turbulence models. However the eddy viscosity is strongly anisotropic and non-homogeneous, being especially low along the leeward side of the jet close to injection. Turbulent diffusion acts to decouple mean velocity and concentration fields, as demonstrated by the drop in concentration flux within the streamtube issued from the hole. Volume-averaged turbulent diffusivity is calculated using a mass–flux balance across the streamtube emanating from the jet hole, and it is found to vary slowly in the streamwise direction. The data are compared with Reynolds-Averaged Navier–Stokes simulations with standard k − ε closure and an optimal turbulent Schmidt number. The computations underestimate the strength of the counter-rotating vortex pair, due to an overestimated eddy viscosity. On the other hand the entrainment is increasingly underpredicted downstream of injection. To capture the correct macroscopic trends, eddy viscosity and eddy diffusivity should vary spatially in different ways. Therefore a constant turbulent Schmidt number formulation is inadequate for this flow.     

Steady vortex structures in inviscid flows in channels

The problem of inviscid incompressible flow through a rectangular channel is considered under the normal velocity component given at the chanel boundaries and the fluid vorticity at the entry. Nonconventional steady flows with recirculation zones and different functional dependences of the vorticity on the stream function are found by analytical and numerical methods. The stability of the steady regimes obtained is analyzed using the numerical solution of the time-dependent problem by the particle-in-cells method.     

Nonlinear waves in electromigration dispersion in a capillary

We construct exact solutions to an unusual nonlinear advection–diffusion equation arising in the study of Taylor–Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave ansatz. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approximations of the governing partial differential equation of electromigration dispersion.     

Oscillations of immiscible liquids in free space or in spherical containers in zero-gravity environment

Summary The natural coupled frequencies are determined for an arrangement of two immiscible incompressible and frictionless liquids with surface- and interfacial tension. The system is in the state of zerogravity and consists either of liquid globules or liquids in a spherical container.

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Schwingungen nichtmischbarer Flüssigkeiten im schwerelosen Raum

Übersicht Es werden die natürlichen gekoppelten Frequenzen zweier nichtmischbarer inkompressibler, reibungsfreier, aber mit Oberflächenspannung behafteter Flüssigkeiten im schwerelosen Raum bestimmt. Dabei werden sowohl flüssige Kugeltropfen als auch Flüssigkeiten im Kugeltank behandelt.

     

Particle transport in Poiseuille flow in narrow channels

Particle-tracking experiments were performed to validate a model [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 15, 1711–1733] for neutrally buoyant spherical particles convected by a Poiseuille flow in a thin microchannel for particles as large as d_p/H = 0.95, where d_p is the particle diameter and H is the channel width (narrow dimension). The measured and predicted velocities agree within experimental error and show that a particle’s velocity is more retarded when it is larger and/or closer to a channel wall. The particle distribution across the channel for a blunt entrance shows a focusing of small particles away from the walls and towards the center of the channel, whereas the particle distribution for an offset-angled entrance is slightly skewed towards the wall encountered first in the entrance region. As a result, the average particle velocities for the blunt entrance exceed those for the angled entrance. Moreover, due to the depletion of particles from the slow-moving region within one radius of the wall, the average particle velocity exceeds the average fluid velocity unless the particle diameter exceeds about 80% of the channel width.     

Ultrasonic field modeling in plates immersed in fluid

Distributed Point Source Method (DPSM) is a semi-analytical technique that can be used to calculate the ultrasonic field (pressure, velocity and displacement fields in a fluid, or stress and displacement fields in a solid) generated by ultrasonic transducers. So far the technique has been used to model ultrasonic fields in homogeneous and multilayered fluid structures, and near a fluid–solid interface when a solid half-space is immersed in a fluid. In this paper, the method is extended to model the ultrasonic field generated in a homogeneous isotropic solid plate immersed in a fluid. The objective of this study is to model the generation of guided waves in a solid plate when ultrasonic beams from transducers of finite dimension strike the plate at different critical angles. DPSM results for a solid half-space problem are compared with the finite element predictions to show the superiority of the DPSM technique. The predicted results are also compared with the experimental visualization of the mode patterns of Lamb waves propagating in a glass plate obtained from stroboscopic photoelastic method. Experimental and theoretical results show good qualitative agreement. The DPSM technique is then applied to study the mode patterns in aluminum plates immersed in water.