七方程可压缩多相流模型的HLLC格式及应用

针对Saurel和Abgrall提出的两速度两压力的七方程可压缩多相流模型,改进了其数值解法并应用于模拟可压缩多介质流动问题.在Saurel等的算子分裂法基础上,根据Abgrall的多相流系统应满足速度和压力的均匀性不随时间改变的思想,推导了与HLLC格式一致的非守恒项离散格式以及体积分数发展方程的迎风格式.进一步,通过改变分裂步顺序,构造了稳健的结合算子分裂的三阶TVD龙格-库塔方法.最后通过几个一维和二维高密度比高压力比气液两相流算例,显示了该方法在计算精度和稳健性上的改进效果.      

单组分多相系统驱替过程的格子Boltzmann模拟

结合格子Boltzmann方法中的Shan-Chen单组分多相模型,引入流体相间的内聚力和流体与 固体壁面间的黏附力,对二维孔隙网格中非浸润气相驱替完全浸润液相的过程进行模拟,流 体相间的交界面自然形成,整个驱替过程属于毛细指进. 随着毛细数的增加,黏性力的主导 作用增强,使得气相入侵的孔隙尺度减小,因此驱替形态随毛细数的不同有很大差别. 在微 重力的作用下,整个驱替过程受毛细力、重力和黏性力的共同作用,重力起到了稳定交界面 避免窜流的作用.     

Pressure calculations in disperse and continuous multiphase flows

In many models for disperse two-phase flows, the pressure of the disperse phase is often assumed to be the same as that of the continuous phase, or differ only by an amount caused by the surface tension. This type of model is referred to as an equilibrium pressure model. Recent research indicates that the stress difference between the phases caused by dynamics of the motion can be significantly important in the modeling of disperse two-phase flows. Although this difference is still ignored in most calculations of disperse multiphase flows for various reasons, when an equilibrium pressure model is applied to continuous multiphase flows, a conceptual difficulty arises. For instance, the equilibrium pressure model cannot be used to study the tensile break of a sponge with interconnected pores, because the air in the pores can never go into tension while the sponge material does not break without tension.     

Recent advances in studies on multiphase and reacting flows in China

The recent developments and advances of studies on multiphase and reacting flows, including gas-solid, gas-liquid, liquid-solid and reacting flows, in China are reviewed. Special emphasis is laid on the fundamental studies and numerical models. Some important experimental results are also reported. But measurement techniques are not covered.     

A two-phase elastoplastic model for unidirectionally-reinforced materials

A complete analytical formulation for the elastoplastic behaviour of a composite material comprising one single array of reinforcing inclusions perfectly bonded to the matrix is developed in this paper. Fundamental relationships establish the link between the total stress and strain variables, and those pertaining to the individual constituents (matrix and reinforcement) regarded as superposed continuous phases. Assuming that each constituent behaves as an elastic perfectly plastic material, the constitutive equations governing the evolution of the reinforced material as a whole are derived. They reveal a hardening phenomenon arising from the non-compatibility between matrix and reinforcement plastic strains. It is shown in particular that the obtained constitutive law falls within the formalism of generalized standard plasticity: the reinforcement residual stress plays the role of a hardening parameter which controls the evolution of the yield surface, while the associated kinematic variable is the plastic strain discrepancy between matrix and reinforcement phases.Owing to its inherent simplicity, the model is easily amenable to a numerical treatment for structural analysis. It is shown in particular how the classical iterative algorithm can be modified accordingly, and an illustrative application is finally presented in the field of civil engineering.     

A Brief Summary of L. van Wijngaarden's Work Up Till His Retirement

This paper attempts to provide an overview of Professor Leen van Wijngaarden's scientific work by briefly summarizing a number of his papers. The review is organized by topic and covers his work on pressure waves in bubbly liquids, bubble dynamics, two-phase flow, standing waves in resonant systems, and flow cavitation noise. A list of publications up till his retirement in March 1997 is provided in the Appendix.     

液体燃料空气炸药形成过程的数值模拟

对液体燃料的爆炸抛撒形成的云雾运动作了数值模拟。建立了多相流模型与算法，给出了云雾区的速度场与燃料浓度分布。云雾的外形变化与实验结果符合较好。     

Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media

This study is concerned with developing a two-dimensional multiphase model that simulates the movement of NAPL in heterogeneous aquifers. Heterogeneity is dealt with in a probabilistic sense by modeling the intrinsic permeability of the porous medium as a stochastic process. The deterministic finite element method is used to spatially discretize the multiphase flow equations. The intrinsic permeability is represented in the model via its Karhunen–Loeve expansion. This is a computationally expedient representation of stochastic processes by means of a discrete set of random variables. Further, the nodal unknowns, water phase saturations and water phase pressures, are represented by their stochastic spectral expansions. This representation involves an orthogonal basis in the space of random variables. The basis consists of orthogonal polynomial chaoses of consecutive orders. The relative permeabilities of water and oil phases, and the capillary pressure are expanded in the same manner, as well. For these variables, the set of deterministic coefficients multiplying the basis in their expansions is evaluated based on constitutive relationships expressing the relative permeabilities and the capillary pressure as functions of the water phase saturations. The implementation of the various expansions into the multiphase flow equations results in the formulation of discretized stochastic differential equations that can be solved for the deterministic coefficients appearing in the expansions representing the unknowns. This method allows the computation of the probability distribution functions of the unknowns for any point in the spatial domain of the problem at any instant in time. The spectral formulation of the stochastic finite element method used herein has received wide acceptance as a comprehensive framework for problems involving random media. This paper provides the application of this formalism to the problem of two-phase flow in a random porous medium.     

Predictive Pore-Scale Modeling of Single and Multiphase Flow

We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. The pore space is represented by a topologically disordered lattice of pores connected by throats that have angular cross-sections. We successfully predict single-phase non-Newtonian rheology, and two and three-phase relative permeability for water-wet media. The pore size distribution of the network can be tuned to match capillary pressure data when a network representation of the system of interest is unavailable. The aim of this work is not simply to match experiments, but to use easily acquired data to estimate difficult to measure properties and to predict trends in data for different rock types or displacement sequences.     

多相流局部混合型质点网格法

提出模拟多相流的局部混合型质点网格法，该方法能稳定地模拟高浓度流体颗粒两相 流. 在每一个颗粒团尺度的欧拉网格下(本文称之为欧拉微元)，基于Lagrangian 追踪原理，可直接估计体积内颗粒的总量，从而准确求出欧拉微元和控制容积内颗粒的 浓度(即颗粒在容积内的体积含量). 同时，假设在新的时间步下，颗粒在欧拉微元里充分 混合，形成新颗粒团. 作者对竖直和倾斜容器中单粒径颗粒沉降和竖直容器中双粒径颗粒双 峰悬浮液沉降过程进行了计算，结果与实测数据相符.     

明渠效应在多相计量中的应用研究

在多相流体力学和多相流测量方面大量的基础理论研究和实验研究的基础上,提出了全新的明渠流模型等多个流量计测模型用于多相流量计量。通过自主开发的智能型多相流量计测系统在室内多相流测试环道上,对模型的运用效果做了大量的实验研究。并且利用基于神经网络技术和模糊模式识别技术开发的计测软件对实验数据进行处理,结果表明:液相计测数据中 80%以上误差位于±5%的范围以内,除个别小流量外,所有误差位于±10%的范围以内;气相计测结果中 90%以上误差位于±10%的范围以内, 97%的误差位于±15%的范围以内。实验数据表明:该计测模型可以适用于多相流中不同粘度的液相流量计量;可适用于较宽的气、液相流量变化范围,模型计测误差稳定在可接受的水平。     

The development of the structure of water – air bubble grid turbulence

The development of the turbulent flow field generated due to the interaction of grid turbulence with a swarm of bubbles is investigated experimentally, in a vertical channel of rectangular cross section. Void fraction and streamwise mean and rms velocity distributions have been measured at several distances from the grid, with an optical probe and Laser Doppler Velocimetry, in relation to the air flow rate ratio. The obtained results indicate that close to the grid the void fraction and velocity distributions are dictated by the bubble injectors’ location on the grid. Downstream the void fraction distribution changes to a double peak pattern. The velocity distribution is characterized by a shear layer between the wall area and the central area of the channel. The extend of this shear layer is increasing as the distance from the grid and the gas flow rate ratio are increasing, and is associated with a corresponding increase of the turbulence fluctuations. Autocorrelation and spectra measurements at the centre of the channel show a reduction of the flow scales for low void fraction. Consistently, power spectra distributions indicate that bubbles cause a redistribution of energy manifested by the relative enhancement of the intermediate scales’ energy content and a consequent reduction in the larger scales. These trends are gradually alleviated and reversed at large distances from the grid, as the air flow rate is increased.     

Macroscopic capillary pressure

The macroscopic pressure difference between two immiscible, incompressible fluid phases flowing through homogeneous porous media is considered. Starting with the quasi-static motions of two compressible fluids, with zero surface tension, it is possible to construct a complete system of equations in which all parameters are clearly defined by physical experiments. The effect of surface tension is then formally included in the definition of the specific process under consideration. Incorporating these effects into the pressure equations and taking the limit as compressibilities go to zero, the independent pressure equations are shown to yield indeterminate forms. However, the difference of the two pressure equations is found to yield a new process-dependent dynamical equation.List of Symbols J LeverettJ function - K _i bulk modulus of fluidi (i=1, 2) - K _s bulk modulus of solid - K permeability - P fractional porosity of the wetting phase (in LeverettJ function) - p _i macroscopic pressure of fluidi (i=1, 2) - Q _ij Mobilities (i, j=1, 2) (cf. de la Cruz and Spanos, 1983) - V _i macroscopic velocity vector of fluidi (i=1, 2) Greek Letters surface tension - _i compliance factor for fluidi (i=1, 2) for incompressible flow defined in equations (29) and (30) (process-dependent) - compliance factor for the flow of two incompressible fluid (cf. eqns. (32) and (33) for relation to _i) - _i compliance factor for a compressible fluid (i=1, 2) (process-dependent) (cf. de la Cruzet al., 1989, 1993) - _i modification to static compliance factor for fluidi (i=1, 2) as a result of quasi-static flow - _i fraction of space occupied by fluidi (i=1, 2) measured dynamically - _i ^o fraction of space occupied by fluidi (i=1, 2) measured statically - _i shear viscosity of fluidi (i=1, 2) - _i bulk viscosity of fluidi (i=1, 2) - _i density of fluidi (i=1, 2)     

A perturbation solution for non-Newtonian fluid two-phase flow through Porous media

In this paper, the mathematical problem of weak non-Newtonian fluid two-phase flow through porous media, including the effect of capillary pressure, is solved by singular perturbation method in combination with regular perturbation method. The asymptotic analytical solutions of the fractional flow function and the wetting phase saturation are obtained. The results are verified by numerical calculations and by classical solutions for corresponding Newtonian case. The influences of the non-Newtonian exponent and capillary pressure are discussed.     

A theoretical research to effective viscosity of colloidal dispersions

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The Discontinuous Solutions of the Transport Equations for Compositional Flow in Porous Media

In the present paper we consider a multicomponent multiphase isothermal flow in porous media with mass exchange between phases. The system of equations of multiphase multicomponent flow has discontinuous solutions, but is not hyperbolic, except some particular cases. For this general, non-hyperbolic system, we propose a free energy condition to select unique physically admissible discontinuous solutions. We also develop a geometrical procedure which provides a tool to analyze the free energy condition. For a two-component mixture, analytical formulae are obtained for the allowed discontinuities.     

气固多相反应流中的煤粉颗粒相能量方程

为了合理地预测燃烧装置内煤粉颗粒的燃烧行为,从多相反应流中一般形式的颗粒相能量方程出发,导出了煤粉颗粒相的能量方程,给出了方程中反映相变引起的气固相间相互作用的源相的具体表达式,与此同时还给出了气相能量方程中代表相间相互作用的颗粒源项的一种计算式．     

Chebyshev super spectral viscosity solution of a two‐dimensional fluidized‐bed model

The numerical solution of a model describing a two‐dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite‐difference method. The mixed SSV/finite‐difference method produces physically shaped bubbles, on a very coarse grid. Fine scale details, which were not present in previous finite‐difference solutions, are present in the solution. Copyright © 2003 John Wiley & Sons, Ltd.     

A simple method for compressible multiphase mixtures and interfaces

We develop a Godunov‐type scheme for a non‐conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial differential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and non‐equilibrium thermodynamics (two pressures, two temperatures, two densities, etc.).Its numerical resolution poses several difficulties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non‐conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions. Copyright © 2003 John Wiley & Sons, Ltd.