Contrôle passif d'écoulements incompressibles autour d'obstacles à l'aide de milieux poreux

Passive control of the flow behind a bluff-body is obtained by integrating porous area on the body. The penalisation method is used to modelize the flow in three different media. In fact each medium can be considered as a porous medium. The fluid is identified as a porous medium of infinite permeability and the solid is identified as a porous medium of zero permeability. This way, it is easy to compute the flow in each medium using the same parameter. Some benefical effects are due to the porous interface: the flow is smoothed, and the enstrophy and drag are significantly reduced.     

内源瞬态荷载作用下弹性介质与饱和多孔介质中衬砌隧道的动力响应对比分析

衬砌隧道周围介质不同,其内源瞬态荷载作用下的动力响应不同,该文对弹性介质与饱和多孔介质中作用有内源荷载的衬砌隧道的动力响应进行对比分析。首先,令饱和多孔介质孔隙率n=0,将衬砌周围饱和介质退化为弹性介质,动力响应解答相应退化为弹性介质中的解答,退化解与已有的隧道周围为弹性介质时的动力响应解答完全一致。其次,对不同孔隙率的饱和多孔介质和理想弹性介质中衬砌隧道的动力响应进行计算,结果表明：与弹性介质相比,饱和多孔介质中衬砌内表面的动力响应较大,轴向衰减速度较快;随着孔隙率的减小,饱和土中衬砌内表面的动力响应逐渐减小,位移和应力时程曲线均趋近于弹性介质。     

论“岩体结构控制论”

经过长期实践和研究,作者于1984年提出岩体结构控制论是岩体力学的基础理论,并全面、系统地以岩体结构控制论为指导研究了岩体变形、岩体破坏及岩体力学性质的基本规律;提出岩体变形系山岩体材料变彤和岩体结构变形共同贡献的,岩体破坏系受岩体材料破坏和岩体结构破坏控制的;岩体力学性质不仅决定于岩体材料力学的性质,而且受控于岩体结构力学效应及环境因素力学效应。在此基础上,作者提出了岩体可以划分为连续介质、碎裂介质,块裂介质及板裂介质四种岩体力学介质,从而建立了完整的岩体结构力学理论体系。     

Modeling the fluid dynamics and heat transfer in unsteady and periodic flow of a highly concentrated granular medium over an obstacle in a channel

The unsteady isothermal flow of a dense layer of a granular medium around an obstacle in a plane channel is modeled using the momentum transfer equations for an incompressible viscous liquid medium based on the slip of the medium at the walls. The validity of this approach is tested by comparing the calculated and experimental data for the flow of a highly concentrated granular medium with high flowability. The effect of periodic change in the flow rate of the granular medium over time in the inlet section of the plane channel on the unsteady distributions of the velocity and temperature fields is studied.     

Development of a high performance flexible porous burner(FPMB) with an adjustable cooling effect

A high performance flexible porous medium burner that can burn gaseous and liquid fuel with different type of flames(premixed and non-premixed) is proposed. The merit of the combustion within porous medium is that heat is recirculated from the combustion gas to porous medium at upstream wherein vaporization is taken place(in case of liquid fuel) or preheated(in case of gaseous fuel) before mixing with the combustion air followed by combustion within another porous medium at downstream. In a former version of the high performance flexible porous medium burner, the upstream porous medium is incorporated with a cooling system using the combustion air as a coolants to prevent thermal decomposition of fuels and thus the burner clogging caused by carbon deposit within the porous medium can be avoided. However, the cooling effect cannot be properly controlled such that the boiling point of the liquid fuel is maintained at suitable value irrespective of the volume flow rate of the combustion air,which is linearly varied with the firing rate of the burner. In particular at the lean burn condition, where high air flow rate is required with high cooling effect with porous medium. This can result in the porous medium temperature lower than the corresponding boiling point of the liquid fuel and thus evaporation of the fuel is failed and the combustion is ceased. Therefore, method of controlling the cooling air flow rate in the porous medium is proposed and studied in order to appropriately control the porous medium temperature and maintain it at above the boiling point irrespective of the combustion conditions. In this research, experimental and computation analysis are used to design the flexible porous burner(FPMB),with adjustable cooling effect. The result shows that, the new design of FPMB which has temperature in the upstream porous medium is higher than boiling point and lower than thermal decomposition temperature of fuel(kerosene) at all conditions and can be operated at a wide range of equivalence ratio without fuel decomposition and fuel non-vaporization problem.     

GENERALIZED RAY APPROXIMATE METHOD TO INVERSE MEDIUM PARAMETERS

In this paper,the inverse problem of the medium parameters in an inhomogeneousmedium is studied and a generalized ray approximate form of the total wave field is described.First,the acoustic wave equation derived from the elastic wave equation is studied,the referential variablesand perturbational variables are introduced,and the integral equation of the medium perturbational pa-rameters is obtained.Then from the point of view of the local principles of the wave function in an in-homogeneous medium,a generalized ray approximate form of the total wave field in an inhomoge-neous medium is described,and attention is focused on the Fredholm integral equation of the firstkind.Finally,the medium parameters in half-plane are inversed.Numerical examples show when theperturbations of the medium parameters are about 0.5,this method can effectively inverse its varia-tion.Apparently,this method is better than the conventional Born weak scattering approximation.     

Effects of Medium Permeability Anisotropy on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

This paper deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including medium anisotropic effects. Since a general anisotropic medium can be described as an orthotropic medium in the corresponding principal directions, a two-dimensional orthotropic porous medium is considered to derive the analytical solution for the critical condition, which is used to judge whether or not the chemical dissolution front can become unstable during its propagation. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved-mineral equilibrium concentration in the pore-fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid-saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when medium permeability anisotropic effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two-dimensional fluid-saturated porous media including medium anisotropic effects. The related theoretical and numerical results demonstrated that: (1) a decrease in the medium anisotropic permeability factor (or ratio), which is defined as the ratio of the principal permeability in the transversal direction to that in the longitudinal direction parallel to the pore-fluid inflow direction, can stabilize the chemical dissolution front so that it becomes more difficult for a planar chemical-dissolution front to evolve into different morphologies in the chemical dissolution system; (2) the medium anisotropic permeability ratio can have significant effects on the morphological evolution of the chemical dissolution front. When the Zhao number of the chemical dissolution system is greater than its critical value, the greater the medium anisotropic permeability ratio, the faster the irregular chemical-dissolution front grows.     

Velocity of sound in a multicomponent medium at rest

The Kuropatenko model is considered, as applied to a multicomponent medium where the number of the sought functions coincides with the number of equations. The velocities of sound in a multicomponent medium at rest are determined. A formula of a polynomial of power N whose positive roots are squared velocities of sound in a medium with N components is derived. For N = 2, the values of two velocities of sound are determined in explicit form. It is demonstrated that the thus-found maximum value of the velocity of sound in a two-component medium containing nitrogen and oxygen with volume concentrations corresponding to air differs (in dimensionless form) from the velocity of sound in air by less than 0.3%. Numerical calculations predict the existence of three velocities of sound in a three-component medium. If the velocity of sound in all N components is identical, it is proved that the maximum velocity of sound in such a medium equals this velocity, and there is only one more velocity of sound in the medium, which has a lower value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 35–44, May–June, 2008.     

双相介质半空间中圆孔对透射SH波的稳态分析

研究了平面SH波在半空间双相弹性介质中的传播。通过Green函数和积分方程方法,按照复变函数描述,对透射波被圆孔散射的情况进行稳态分析。将双相介质半空间沿界面剖分为1/4空间介质Ⅰ和含圆孔的1/4空间介质Ⅱ,分别构造了介质Ⅰ和介质Ⅱ中反平面点源荷载的Green函数,按双相介质中平面SH波的处理方法,给出介质Ⅰ和介质Ⅱ中的平面位移波,两种介质之间的相互作用力与对应Green函数的乘积沿界面的积分与平面位移波叠加得到介质Ⅰ和介质Ⅱ中的全部位移场。按照界面的位移连续条件,定解积分方程组,得到问题的稳态解,并给出圆孔位置和介质参数对散射的影响。     

Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium

Despite a large number of publications on bioconvection in suspensions of motile microorganisms, bioconvection in a fluid saturated porous medium is a relatively new area of research. This paper is motivated by experimental research by Kessler (1986) who established that a porous medium prevents the development of convection instability in algal suspensions. This suggests that there may exist a critical value of the permeability of a porous medium. If the permeability is smaller than critical, the system is stable and bioconvection does not develop. If the permeability is larger than critical, bioconvection may develop. This paper presents a model of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium. The focus of this research is the determination of the critical value of permeability of a porous medium by a linear stability analysis. A simple but elegant analytical solution for the critical Darcy number is obtained.     

粘性介质上的悬臂梁在冲击载荷作用下的刚塑性动力响应

本文考虑了一个放置在粘性介质上的刚-理想塑性悬臂梁在自由端受冲击载荷时的小变形动力响应。具体讨论了线性粘性介质时矩形脉冲,线性衰减脉冲及瞬时冲击等加载情况,并与无介质解进行了比较,讨论了介质对梁的运动变形模式、最终挠度、能量吸性的影响。     

Acoustic Waves in Channels with Porous and Permeable Walls

The propagation of acoustic disturbances in a porous medium crossed by numerous cracks (double porosity medium) is a complex problem that we here simplify by investigating the acoustics of a permeable channel. We consider a fluidfilled channel in two possible geometries, a slit or a cylindric pipe. The channel is surrounded by a porous medium (saturated with the same fluid) and is itself surrounded by an external medium. To simulate the average properties of the cracked rock, the external medium is either nonpermeable (few connections between cracks) or highly permeable (numerous connections). We present analytical and numerical results concerning acoustic disturbances of small amplitude generated in the channel, such as harmonic waves, step disturbanses and pulses.     

Fast Fourier homogenization for elastic wave propagation in complex media

In the context of acoustic or elastic wave propagation, the non-periodic asymptotic homogenization method allows one to determine a smooth effective medium and equations associated with the wave propagation in a given complex elastic or acoustic medium down to a given minimum wavelength. By smoothing all discontinuities and fine scales of the original medium, the homogenization technique considerably reduces meshing difficulties as well as the numerical cost associated with the wave equation solver, while producing the same waveform as for the original medium (up to the desired accuracy). Nevertheless, finding the effective medium requires one to solve the so-called “cell problem”, which corresponds to an elasto-static equation with a finite set of distinct loadings. For general elastic or acoustic media, the cell problem is a large problem that has to be solved on the whole domain and its resolution implies the use of a finite element solver and a mesh of the fine scale medium. Even if solving the cell problem is simpler than solving the wave equation in the original medium (because it is time and source independent, based on simple tetrahedral meshes and embarrassingly parallel) it is still a challenge. In this work, we present an alternative method to the finite element approach for solving the cell problem. It is based on a well-known method designed by H. Moulinec and P. Suquet in 1998 in structural mechanics. This iterative technique relies on Green functions of a simple reference medium and extensively uses Fast Fourier Transforms. It is easy to implement, very efficient and relies on a simple regular gridding of the medium. Through examples we show that the method gives excellent results, even, under some conditions, for discontinuous media.     

各向异性粘弹性多孔截止中平面波的传播

This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy considered is of general type, and the attenuating waves in the medium are treated as the inhomogeneous waves. The complex slowness vector is resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation, and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of the frame, and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.     

Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil,drainage is common.In this paper,the saturated porous soil with a two-phase saturated medium is simulated,and Lamb's integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot's equation and Betti's theorem(the reciprocal theorem).According to the basic solution to Biot's equation,Green's function Gij and three terms of Green's function G4i,Gi4,and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented.The displacement field with drainage,the magnitude of drainage,and the pore pressure of the center explosion source are obtained in computation.The results of the classical Sharpe's solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared.Good agreement is observed.     

Delay Model for a Cycling Transport Through Porous Medium

A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed.     

Similarity in stationary motions of gas and two-phase medium with incompressible component

In this paper we suggest the transformation between the equations for a perfect gas and the equations describing in one-velocity approach the two-phase medium with any volume occupied by the incompressible phase. It is proved that the motion of a two-phase medium in the transformed coordinate system is similar with certain accuracy to that of a perfect gas. It means that the solutions obtained for perfect gas can be used to solve wave problems for media with incompressible component. There is no necessity directly to solve the problem for medium with incompressible component, and it is only sufficient to transform the known solution of the similar problem for a homogeneous medium. Thus, the solutions of many hydrodynamic problems for multi-component media with incompressible phase can be obtained without solving the original set of equations. The scope for the suggested transformation is demonstrated by reference to the strong explosion in a two-phase medium.     

Extinction of elastic wave energy due to scattering in a viscoelastic medium

Forward scattering theorem for elastic longitudinal and shear wave scatterings by an arbitrary-shaped three-dimensional object embedded in a viscoelastic medium is derived. It is shown that the formulae for extinction cross-sections of an object in an energy-absorbing medium are formally the same with those of the object in the lossless elastic medium. Numerical calculations are executed for the longitudinal wave scattering in an epoxy matrix by a spherical inclusion with different material properties. The condition of negative extinction is examined with the causality constraint on the viscoelastic medium taken into account. It is found that the negative extinction occurs in the Rayleigh limit when the attenuation of the medium is sufficiently high and, more restrictedly, the wave speed in the object is larger than that in the medium, while it occurs less likely in the high frequency range considered in this paper (0<ka<100).     

Basic Equations of Kelvin's Medium and Analogy with Ferromagnets

A nonlinear elastic Cosserat continuum of special kind whose particles have dynamical spins (Kelvin's medium) is considered. The basic equations for this medium are obtained on the basis of fundamental mechanical laws. Various complete sets of strain tensors are discussed. The analogies between Kelvin's medium and other types of media are discussed. First, we show the analogy between constitutive equations for Kelvin's medium and for elastic shells. The main difference is caused by the dimensionality of the media. Then, for a special case of fast proper rotation we establish the analogy between the dynamic equations of Kelvin's medium and elastic ferromagnetic saturated insulators. The most general way to take into account the coupling between magnetic and elastic subsystems is presented. All results can be interpreted in terms of a mechanical medium as well as in terms of ferromagnets. This revised version was published online in July 2006 with corrections to the Cover Date.     

An elastodynamic reciprocity theorem for linear, viscoelastic media

Summary A reciprocity theorem for impulsive disturbances in a linear, viscoelastic medium is derived. Apart from the condition that the medium be linear and viscoelastic of the Boltzmann type, no restrictions as to the properties of the medium are imposed. Hence, the reciprocity theorem is applicable to disturbances in inhomogeneous and anisotropic media.As an illustration of its usefulness the reciprocity theorem is used to derive an integral representation of the Kirchhoff type for the displacement vector in a linear, viscoelastic medium.For reference, also the Laplace transform version of the obtained results is given.