高浓度固-液两相流紊流的动理学模型

采用分子动理学方法,基于固-液两相流液相分子或颗粒相颗粒的Boltzmann方程,对Boltzmann方程分别取零矩和一次矩,则得到高浓度固-液两相流紊流的连续方程和动量方程,再和较成熟的低浓度两相流连续方程和动量方程比较,取低浓度两相流控制方程中较成熟合理的有关项和高浓度时由动理学方法推导出的颗粒间碰撞项,则得到高浓度固-液两相流紊流的最终控制方程:连续方程和动量方程.     

Fokker-Planck operator for free-molecular,nonspherical, thermally nonequilibrium Brownian particles

The Fokker-Planck collision operator entering into the kinetic equation for the velocity distribution function of convex nonspherical rigid homogeneous Brownian particles in a traveling inhomogeneous monatomic gas is derived. The regime of flow past the particles is free-molecular, i.e., the characteristic particle dimensions are much smaller than the average free path of the gas molecules, the interaction between the particles and their effect on the gas phase can be neglected, and a specular-diffuse law of interaction between the molecules and the particle surface holds. The particle temperatures T _p are the same and differ from the local gas temperature T. Thermal nonequilibrium (T _p ≠ T) leads to violation of the well-known relations between the diffusion coefficients in the spaces of the translational and angular velocities and the coefficients of forces and moments exerted on a particle. The coefficients in the unknown operator are calculated for the particles in the form of bodies of revolution with longitudinal symmetry. Data characterizing the effect of the nonsphericity of the particles, i.e., spheroids and sphere-cylinders, on the degree of violation are given.     

认识稀薄气体动力学

以通俗易懂的方式介绍了空气动力学当气体间断分子效应显著时发展起来的特殊分文——稀薄气体动力学、讨论了非平衡现象与稀薄气体动力学的关系．通过与8速度气体模型的间断Boltzmann方程的对比，解释了Boltzmann方程碰撞项的物理意义和数学困难，简要综述了其一般解法、讨论了分子在物体表面的反射和问题的边界条件，着重介绍了直接模拟Monte Carlo(DSMC)方法和为克服低速稀薄流动(如MEMS中流动)中模拟困难的信息保存(IP)方法。     

Kinetic Fokker-Planck equation for free-molecular,thermally nonequilibrium Brownian particles in an inhomogeneous gas

A kinetic equation for the translational and angular velocity distribution function of spherical rigid Brownian particles in an inhomogeneous monatomic gas is derived. The particle diameters are much smaller than the average free path of the gas molecules and the interaction between the particles and their effect on the carrier (gas) phase are neglected. The particle temperatures T _p are the same and differ from the local gas temperature T. The molecular velocity distribution function is specified by the first approximation of the Chapman-Enskog method. The difference between the characteristic phase velocities is small as compared with the mean thermal molecular velocity. The dependences of the diffusion coefficients in velocity space on the ratio T _p/T, which characterize the effect of thermal nonequilibrium, i.e., violation of the thermodynamic equilibrium between the phases of the disperse system, are found using a specular-diffuse law of reflection of the molecules from the particle surface.     

湍流两相流的脉动速度联合PDF输运方程

概率密度函数（PDF）的方法是构造两相湍流模型的一种重要的方法.构建气体-颗粒速度联合PDF输运方程的关键是颗粒所见气体微团速度的Langevin方程.首先由N-S方程出发,精确推导出颗粒所见气体微团脉动速度的Langevin方程,进而通过理论分析表明,对比通常采用的颗粒所见气体微团瞬时速度的Langevin方程而言,采用前者能有效地减少关联量的统计偏差.最后,给出了颗粒-气体脉动速度的联合PDF输运方程.     

Wave propagation in a non-ideal dusty gas

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in a non-ideal gas with dust particles. In the absence of non-ideal effect the gas satisfies an equation of state of Mie–Gruneisen type. An expansion wave resulting from the action of receding piston is considered and the solutions to this problem showing effects of dust particles and non-idealness are obtained. The propagation of weak waves is considered and the flow variables in the region bounded by the piston and the characteristic wave front are found out. The expansive action of a receding piston undergoing an abrupt change in velocity is discussed. Cases of central expansion fan and shock fronts are studied and the solutions up to first order in the physical plane are obtained. The effects of non-idealness and dust particles are discussed in each case.     

高阶多维半离散中心迎风格式及其应用

提出了求解多维对流-扩散方程的四阶半离散中心迎风格式。该格式以中心加权基本无振荡(CWENO)重构为基础,同时考虑到在Riemann扇内波传播的局部速度,从而更加准确地估计出了局部Riemann扇的宽度,最终既回避了网格的交错,又降低了格式的数值粘性,建立了介于迎风格式和中心格式之间的半离散中心迎风格式。本文还将该四阶半离散中心迎风格式与涡度-流函数方法相结合,有效地求解了二维不可压Euler方程组和Navier-Stokes方程组。     

Propagation of shock and detonation waves in dust-laden gases

This article examines the flows of a two-phase mixture of a gas with solid particles arising as a result of the propagation of shock waves or detonation waves through a homogeneous medium at rest. It is assumed that the basic assumptions of the mechanics of mutually penetrating continua hold [1], whereby it is possible to describe the flow of each phase of the mixture within the framework of the mechanics of a continuous medium. We assume that the solid phase consists of identical, incompressible, and nondeformable particles of spherical shape. It is assumed that the temperature inside the particles is homogeneous. Collisions between particles and their Brownian motion are ignored. It is assumed that the carrier phase is an ideal gas (the viscosity is only allowed for in the interaction forces between phases). The contribution of the volume of the particles is not considered. On the basis of these assumptions, the following problems are considered: the propagation of a detonation wave in a mixture of a detonating gas and chemically inert particles and the motion of a dust-gas mixture in a shock tube in the presence of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 93–99, November–December, 1984.     

Magnetic field assisted fluidization： A modified Richardson-Zaki equation

Magnetic particles can be uniformly fluidized by coupling the gas flow with an externally imposed magnetic field. Interparticle forces generated by the magnetic field cause aggregation of the particles in chain-like structures preferentially oriented along the magnetic field lines. In the present paper, we study the implications of the formation of these special types of aggregates on the empirical Richardson-Zaki （RZ） equation, originally proposed to describe the expansion of fluidized beds of non-aggregated particles. We have addressed two important issues, namely the flow regime, which is a function of the size of the aggregates, and the effect of shape and orientation of the chain-like aggregates with respect to gas flow on fluid drag. We propose a modified RZ equation （MRZE） in which the velocity scale, given by the terminal settling velocity of the individual aggregates, and the RZ exponent are predetermined as a function of the chain length. The chain length depends on the ratio of the magnetic energy to gravitational energy, and is estimated from the magnetic field intensity, and particle magnetization, size and density. Predictions of the MRZE are successfully compared with published results in the literature on the expansion of magnetic particles in the presence of externally applied magnetic fields.     

Kinetic description of Brownian movement of heated particles in rarefied gas

Translational and rotational Brownian movement of a spherical particle in a rarefied gas is considered. It is assumed that the particle radius is much less than the free path of the molecules in the gas. The collision integral of the considered particles and the gas molecules is generalized to the case of an arbitrary law of interaction between the molecules and the particle surface, this making it possible to consider the situation when there is no thermodynamic equilibrium between the particles and the gas, in particular, the particle temperature differs from the gas temperature. By expansion with respect to the small parameter — the ratio of the molecule and particle masses — the kinetic equation of the Boltzmann type reduces to the Fokker-Planck equation for the particle distribution function. The coefficients of the equation are calculated in an explicit form for the case of diffuse interaction between the molecules and the particle surface. A dependence of the diffusion coefficients on the ratio of the particle and gas temperatures is obtained.     

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

On the Formation of Discontinuities of Wave Fronts in a Saturated Granular Body

The paper deals with propagation of plane wave fronts in a solid with a non-linear relation between stress and deformation. The objective is to calculate the distance that a wave front covers before it loses continuity. The formulae derived for a general quasi-linear system of two equations are applied to the propagation of plane compression waves in dry and partially saturated granular bodies. In the case of a saturated body with gas bubbles, the influence of gas and capillary pressure on the stiffness of the body is taken into account. Numerical calculations relevant to soil mechanics are presented. For the numerical calculations a constitutive equation of the hypoplasticity theory for granular materials has been used. Received November 1, 1997     

Finite-amplitude acoustic pulses in a waveguide layer with longitudinal inhomogeneity

This paper considers the propagation of a weakly nonlinear acoustic pulse in a slightly curved waveguide layer which is strongly inhomogeneous in the transverse direction and weakly inhomogeneous in the longitudinal direction. The basic system of hydrodynamic equations reduces to a nonlinear wave equation, whose coefficients are determined using the equations of state of the medium. It is established that as the adiabatic exponent passes through the value γ = 3/2, the nature of the pulse propagation changes: for large values of γ, the medium is focusing, and for smaller values, it is defocusing. It is shown that the pulse propagation process is characterized by three scales: the high-frequency filling is modulated by the envelope, whose evolution, in turn, is determined by the moderate-rate evolution of the envelope phase and slow amplitude variation. A generalized nonlinear Schrödinger equation with the coefficients dependent on the longitudinal coordinate is derived for the pulse envelope. An explicit soliton solution of this equation is constructed for some types of longitudinal inhomogeneity.     

Heat exchange between a gas bubble and a liquid

The nonlinear problem of thermal and dynamic interaction between a single gas bubble and surrounding liquid is considered. This problem is met in studies of gas-liquid mixture flows, in particular, in Shockwave propagation in such media. A numerical solution is presented for various modes of bubble surface radial motion. The modes correspond to bubble behavior directly beyond a shock-wave front, where the latter enters the bubble screen, and to the behavior of a bubble located in the depths of the bubble curtain, where the wave becomes diffuse. Analytic solutions of the linearized problem of thermal conductivity for free and constrained small harmonic oscillations of a gas bubble in a liquid were obtained in [1, 2]. Cooling of a hot gas bubble was considered in [3], that study, however, contains inaccuracies. In particular, it was assumed in the solution that the gas density in the bubble was homogeneous. The equation for heat flux in dimensionless variables was written inaccurately. However, in the examples considered in [3] these inaccuracies do not lead to significant errors in the numerical results.     

Modified incompressible SPH method for simulating free surface problems

An incompressible smoothed particle hydrodynamics (I-SPH) formulation is presented to simulate free surface incompressible fluid problems. The governing equations are mass and momentum conservation that are solved in a Lagrangian form using a two-step fractional method. In the first step, velocity field is computed without enforcing incompressibility. In the second step, a Poisson equation of pressure is used to satisfy incompressibility condition. The source term in the Poisson equation for the pressure is approximated, based on the SPH continuity equation, by an interpolation summation involving the relative velocities between a reference particle and its neighboring particles. A new form of source term for the Poisson equation is proposed and also a modified Poisson equation of pressure is used to satisfy incompressibility condition of free surface particles. By employing these corrections, the stability and accuracy of SPH method are improved. In order to show the ability of SPH method to simulate fluid mechanical problems, this method is used to simulate four test problems such as 2-D dam-break and wave propagation.     

Temperature force of interaction between spherical particles

The force of interaction between small particles in a gas induced by a temperature difference between the particle surface and the gas far away from the particle is considered. The particle dimensions correspond to the free-molecular, transitional, and continuum heat transfer regimes. A Monte-Carlo numerical method of direct statistical simulation of the solution of the nonlinear Boltzmann equation and the results of asymptotic solutions are used. The force of interaction between two hot or cold spherical particles is investigated. The dependence of the temperature force on the particle size, i.e. on the flow regime (Knudsen number), and the distance between the particles is examined. Approximations for these dependences are constructed.     

基于气液相界面捕捉的统一气体动理学格式

气液相界面运动的研究无论是在科学还是工程领域都是非常重要的. 其中, 非平衡流动的计算尤其受到关注. 基于此, 我们构造了捕捉气液相界面的统一气体动理学格式. 由于统一气体动理学格式将自由输运和粒子碰撞耦合起来更新宏观物理量和微观分布函数, 故而可以求解非平衡流动. 具体思路是, 通过将范德瓦尔斯状态方程所表达的非理想气体效应引入统一气体动理学格式之中来捕捉气液相界面, 两相的分离与共存通过范德瓦尔斯状态方程描述. 由于流体在椭圆区域是不稳定的, 因此气液相界面可以通过蒸发和凝结过程自动捕捉. 如此, 一个锋锐的相界面便可以通过数值耗散和相变而得到. 利用该方法得到麦克斯韦等面积律(Maxwell construction)对应的数值解, 并与其相应的理论解相比较, 二者符合良好. 而后, 通过对范德瓦尔斯状态方程所描述的液滴表面张力进行数值计算, 验证了Laplace定理. 此外, 通过模拟两个液滴的碰撞融合过程, 进一步证明了该格式的有效性. 但是, 由于范德瓦尔斯状态方程的特性, 其所构造的格式仅适用于液/气两相密度比小于5的情况.      

Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer

This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. Dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs.