Phenomenology of inertia effects in a dispersed solid-fluid mixture

Combining single particle results, average equations and thermodynamic considerations, we propose a way to build the equations describing a suspension of rigid spherical particles in a carrier fluid, with emphasis on inertia effects including virtual mass. The spatial fluctuations of the fluid velocity field are depicted by two phenomenological functions $\text{?(α}{}_{\mathrm{s}}\text{)}\text{and}\text{g(α}{}_{\mathrm{s}}\text{)}$ of the particle volume fraction, and a third function h(α_s) is necessary to describe the intensity of the particles internal stress. It is shown that all inertia effects occurring in the relative translational motion can be derived from the two functions $\text{?}\text{and}\text{g–h}$ only. The conditions under which the above system of equations is hyperbolic are determined and comparison is made with what is presently known about $\text{?, g}\text{and}\text{h}$ in the dilute limit.     

Constitutive equations for a nondilute dispersed fiber suspension

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 71–76, November–December, 1989.     

Thermal instability of a porous medium with relaxation and inertia in the presence of Hall effects

Summary  The thermal instability of a Rivlin–Ericksen fluid in a porous medium is considered in the presence of a uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the magnetic field has a stabilizing effect on the system, whereas the Hall current has a destabilizing effect on the system. The medium permeability has both stabilizing and destabilizing effects, depending on the Hall parameter M. The kinematic viscoelasticity has no effect on stationary convection. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The magnetic field (and corresponding Hall currents) introduces oscillatory modes in the system, which would be nonexistent in their absence. The sufficient conditions for the nonexistence of overstability are also obtained. Received 20 May 1999; accepted for publication 8 March 2000     

Kinetic equations for a finely dispersed rarefied gas suspension

Starting from the Liouville equation, the kinetic equations for a finely dispersed rarefied gas-particle medium are derived. The size of the suspension particles is assumed to be much less than the free path of the gas molecules, while their density is so small that interaction between the particles can be neglected. It is shown that in general the dynamics of this gas suspension can be described by a system of two kinetic equations, which differ radically from the Boltzmann equations. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 165–171, March–April, 1994.     

Multi-fluid model of suspension filtration in a porous medium

In the framework of a three-fluid approach, a new model of suspension filtration in a porous medium is constructed with account for the formation of a dense packing of trapped particles with finite permeability and porosity. The following three continua are considered: the carrier fluid, the suspended particles, and the deposited particles. For a one-dimensional transient flow of suspension, a system of equations for the concentrations of the suspended and deposited particles, the suspension velocity, and the pressure is constructed. Two cases of the flow in a porous medium are considered: plane and radial. Numerical solution is found using a finite-difference method. Numerical calculations are shown to be in agreement with an analytical solution for the simplest case of filtration with a constant velocity and constant porosity and permeability. A comparison is performed with the classic filtration models for five sets of experimental data on the contamination of a porous sample. It is shown that near the inlet boundary, where an intense deposition of particles takes place, the new model describes the concentration profile of the deposited particles more accurately than the classical model.     

冲击下混凝土试样应变率效应和惯性效应探讨

结合混凝土试件的真三轴静载冲击实验结果,分别运用考虑应变率效应的Holmquist-Johnson-Cook (HJC)模型和考虑静水压效应的Drucker-Prager (DP)模型进行数值分析,以探讨研究混凝土试样应变率效应和惯性效应的方法。在探究混凝土的应变率效应和横向惯性效应的关系时,使用HJC模型的数值模拟结果来拟合DP准则的各个参数。结果表明:随着应变率的升高,混凝土的强度会提高,并且这种强度的提高,也有一部分原因是第一应力不变量I₁的增大所导致的。因此,混凝土试件的应变率效应和横向惯性约束具有较强的耦合作用。理论和数值分析了冲击下试样内部的横向应力分布特征与应变率、静水压和试样尺寸的关系,结果发现:试样内部横向应力的幅值随着应变率、静水压的升高而增大,但随着试样尺寸的增大而减小。为了探讨横向惯性带来的强度提升效果,提出了一个有关冲击方向最大应力σ_x和等效应力σ_e的参数ξ,且ξ=(σ_x?σ_e)/σ_x。此参数具有尺寸效应、应变率效应和静水压效应,但是此参数与应力三轴度的关系表现出应变率无关特性,可为应变率效应的研究提供新的思路。     

Turbulent diffusion in a medium subjected to uniform deformation

Turbulent diffusion in media subjected to uniform deformation caused by the presence of average-velocity gradients which are constant throughout the space is an idealization of real processes, in particular, of processes such as diffusion in channels of variable cross-sectional area [1], in the lowest layers of the atmosphere [2], etc. In this article we formulate the problem of the connection between the statistical characteristics of the transfer of a passive substance in turbulent diffusion in deformed media with the statistical characteristics of the turbulence. The statistical transfer characteristics generally used are the first two moments of the vector of random displacement of a liquid particle under the action of turbulent pulsations in velocity: the average displacement and the components of the dispersion tensor of the displacement of a liquid particle. We obtain connecting relations for the dispersion tensor of a liquid particle in turbulent diffusion of a passive substance in a uniform turbulent medium subjected to uniform deformation caused by average-velocity gradients which are constant throughout the space. These relations are a generalization of known expressions for undeformed media [2, 3]. We investigate the case of rapid deformation when the turbulent characteristics of the medium vary in accordance with the linear theory [4].     

Fluid inertia effects in squeeze films

Summary Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.     

Energy method for problems of diffusion in a moving medium

Conclusions  For problems of admixture diffusion in a moving medium, diffusion problems in a gyrotropic medium at rest that have the same solutions have been formulated. This has allowed us to use the previously developed technique of symmetrization. The principle of minimum quadratic functional has been justified. Thermodynamically, this principle is interpreted as the principle of minimum fluctuations. The entropy produced by fluctuations is a measure of their intensity. Minimization is conditional in the space of admixture-concentrations distributions and unconditional in the space of the potentials introduced. A method for obtaining estimates of the integral characteristic of diffusion in the streamline-bounded domain has been proposed. Owing to symmetrization, new boundary-value problems have been formulated, which, in contrast to the original problems, have symmetric positive-definite operators. This makes it possible to use the most effective methods of approximate and numerical solutions. Computing Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 38, No. 2, pp. 32–39, March–April, 1997.     

Energy method for problems of diffusion in a moving medium

Conclusions For problems of admixture diffusion in a moving medium, diffusion problems in a gyrotropic medium at rest that have the same solutions have been formulated. This has allowed us to use the previously developed technique of symmetrization. The principle of minimum quadratic functional has been justified. Thermodynamically, this principle is interpreted as the principle of minimum fluctuations. The entropy produced by fluctuations is a measure of their intensity. Minimization is conditional in the space of admixture-concentrations distributions and unconditional in the space of the potentials introduced. A method for obtaining estimates of the integral characteristic of diffusion in the streamline-bounded domain has been proposed. Owing to symmetrization, new boundary-value problems have been formulated, which, in contrast to the original problems, have symmetric positive-definite operators. This makes it possible to use the most effective methods of approximate and numerical solutions. Computing Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 38, No. 2, pp. 32–39, March–April, 1997.     

Physical approach to averaging theorems on phase interfaces in a dispersed multiphase medium

Within the framework of a procedure for scale-changing by averaging a representative elementary volume, theorems are developed to relate the averages of derivatives to the derivatives of averages over a surface, using elementary differential calculus. These theorems form the basis of a general macroscopic balance equation for a given quantity over interfaces of a dispersed multiphase medium. The equations of phase interfaces complement equations related to bulk phases describing transport in dispersed multiphase media.     

Determining the moments of inertia of large bodies from vibrations in elastic suspension

To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should know the moments of inertia of their massive parts. But since the structure of some elements such as power units is very complicated, it is impossible to determine their moments of inertia analytically. Thus the problem of measuring the moments of inertia of massive large bodies arises. To this end, a measuring bench was designed in N. E. Zhukovskii Central Institute for Aerohydrodynamics (TsAGI) on the basis of a new method for determining the body moments of inertia from vibrations in the elastic suspension [1]. In this connection, it is necessary to develop the corresponding mathematical algorithms for determining the moments of inertia.In this paper, we develop mathematical algorithms for determining the body moments of inertia by using methods for identification of linear systems in the state space [2–5]. We present three versions of solving the problem of determining the body moments of inertia depending on the information about the method for exciting the vibrations or about the body parameters and the rigidity of the bench springs. We study the influence of damping on the accuracy of determining the moments of inertia. Numerical results are given for a specific system.     

Equivalent diffusion coefficient and equivalent diffusion accessible porosity of a stratified porous medium

Diffusion is an important transport process in low permeability media, which play an important role in contamination and remediation of natural environments. The calculation of equivalent diffusion parameters has however not been extensively explored. In this paper, expressions of the equivalent diffusion coefficient and the equivalent diffusion accessible porosity normal to the layering in a layered porous medium are derived based on analytical solutions of the diffusion equation. The expressions show that the equivalent diffusion coefficient changes with time. It is equal to the power average with p = −0.5 for small times and converges to the harmonic average for large times. The equivalent diffusion accessible porosity is the harmonic average of the porosities of the individual layers for all times. The expressions are verified numerically for several test cases.     

Anomalous diffusion in fractal porous medium

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Hydrodynamics and diffusion of an impurity in a cell of a two-phase medium

This study was made with financial support from the Russian Fund for Basic Research (Grant No. 95-01-99879a).     

Mathematical model of deep-bed filtration of a two-component suspension through a porous medium

A model of deep-bed filtration of a two-component suspension through a porous medium with formation of two types of the deposit which have different structures and properties is constructed. The influence of the parameters of fluid and particle flux densities which determine mass transfer between different components of the suspension and deposits on the filtration characteristics and properties of the resulting deposits is estimated on the basis of numerical experiments for the suspensions with contrast particle fractions.