聚合物流体渗流机理研究

聚合物流体在多孔介质中渗流的研究是近年来有重大进展的领域。本文介绍从力学与物理方法进行渗流机理研究的思路、主要结果和当前活跃的研究课题。流体的非牛顿性对复杂边界条件下均匀流体力学效应的影响已得到了较好的定量处理;揭示了拉伸流粘弹特性对渗流影响的机理,其定量描述则尚有待努力。进而讨论了石油工程中十分重要的非均一流体渗流的新进展,包括大分子效应与粘性指进效应及其分形描述。对于上述物理效应的综合考虑将使聚合物渗流力学研究进入新的阶段。      

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.      

Creeping flow through a model fibrous porous medium

Pressure losses and velocity distributions were measured for creeping flow through three model fibrous porous media. The three models consisted of square arrays of circular rods with solid volume fractions of 2.5, 5 and 10%. Measurements of flow resistances are in good agreement with theoretical predictions after wall effects are accounted for using Brinkman’s equation. Two-dimensional velocity vector maps were obtained in each array using particle image velocimetry. The velocity distributions are necessary for identifying non-Newtonian effects in flows with viscoelastic fluids.     

非饱和多孔介质有限元分析的基本控制方程与变分原理

本文在对问题研究现状进行阐述的基础上较系统地给出了骨架可变形非饱和多孔介质的全耦合分析模型，模型中考虑了孔隙气体，水（油）流动对介质力学性能的影响，多孔介质的饱和度，渗透系数与毛吸压力的关系，由实验给出，所导出的控制方程以固体骨架的位移与孔隙流体压力为基本未知量，由于问题的非自共轭特征，文中构造了非饱和介质动力问题的参数变分形式，并在此基础上给出有限元离散方程。     

Pore-scale modeling of viscoelastic flow in porous media using a Bautista–Manero fluid

This article examines the extensional flow and viscosity and the converging–diverging geometry as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista–Manero model, which successfully describes elasticity, thixotropic time dependency and shear-thinning, was used for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm, originally proposed by Philippe Tardy, that employs this model to simulate steady-state time-dependent flow was implemented in a non-Newtonian flow simulation code using pore-scale modeling. The simulation results using two topologically-complex networks confirmed the importance of the extensional flow and converging–diverging geometry on the behavior of non-Newtonian fluids in porous media. The analysis also identified a number of correct trends (qualitative and quantitative) and revealed the effect of various fluid and flow parameters on the flow process. The impact of some numerical parameters was also assessed and verified.     

Treatment of nonlinear terms in the numerical solution of partial differential equations for multiphase flow in porous media

Simultaneous flow of two or three immiscible fluids in porous media is modelled by a system of coupled, nonlinear partial differential equations. These equations are reduced to a system of nonlinear algebraic equations through the use of finite-difference approximations for derivatives. Several types of nonlinearities requiring careful analysis exist in this model. Here, we present a systematic study of all available, and some new, methods for the treatment of nonlinearitics in this model. It is believed that the solution techniques presented here may also prove useful for other strongly nonlinear partial differential equations.     

Numerical simulations of non-isothermal three-dimensional flows in an extruder by a finite-volume method

This study considers numerical applications of a finite-volume method to steady non-isothermal flows in geometries close to a single-screw extruder. Two geometrical configurations of the channel, with gap and zero gap, are investigated. The simulations concern incompressible fluids obeying different constitutive equations: Newtonian, generalized Newtonian with shear-thinning properties (Carreau–Yasuda law), and two viscoelastic differential models, the upper convected maxwell (UCM) and the Phan–Thien/Tanner (PTT). The temperature dependence is described by a Williams–Landel–Ferry (WLF) equation. For discretizing the equations and unknowns, we use a staggered grid with a QUICK scheme for the convective-type terms and solve the set of governing equations by a decoupled algorithm, stabilized by a pseudo-transient stress term and an elastic viscous stress splitting (EVSS) technique, in the viscoelastic case for the UCM model. The numerical results enable us to state the influence of temperature and rheological properties on the flow characteristics in the geometries investigated and underline the complex behaviour of the materials in such configurations.     

Evaluation of the Darcy's law performance for two-fluid flow hydrodynamics in a particle debris bed using a lattice-Boltzmann model

In the present paper, multiphase flow dynamics in a porous medium are analyzed by employing the lattice-Boltzmann modeling approach. A two-dimensional formulation of a lattice-Boltzmann model, using a D2Q9 scheme, is used. Results of the FlowLab code simulation for single phase flow in porous media and for two-phase flow in a channel are compared with analytical solutions. Excellent agreement is obtained. Additionally, fluid-fluid interaction and fluid-solid interaction (wettability) are modeled and examined. Calculations are performed to simulate two-fluid dynamics in porous media, in a wide range of physical parameters of porous media and flowing fluids. It is shown that the model is capable of determining the minimum body force needed for the nonwetting fluid to percolate through the porous medium. Dependence of the force on the pore size, and geometry, as well as on the saturation of the nonwetting fluid is predicted by the model. In these simulations, the results obtained for the relative permeability coefficients indicate the validity of the reciprocity for the two coupling terms in the modified Darcy's law equations. Implication of the simulation results on two-fluid flow hydrodynamics in a decay-heated particle debris bed is discussed. Received on 1 December 1999     

不可压饱和粘弹性多孔介质的变分原理及其无网格模拟

基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响.     

Flow of non-newtonian particulate suspension with a compressible particle phase

Continuum equations for a two-phase fluid-particle flow are developed and applied to the problem of steady, laminar flow over an infinite porous flat plate. Both phases are assumed to behave as non-Newtonian power-law fluids. The effects of particle-particle interaction and diffusion of particles are taken into account in the mathematical model. In addition, the particle phase is assumed to have a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate boundary conditions using an iterative, implicit finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to elucidate interesting features of the solutions.     

Pressure-driven and electroosmotic non-Newtonian flows through microporous media via lattice Boltzmann method

The lattice Boltzmann method is developed to simulate the pressure-driven flow and electroosmotic flow of non-Newtonian fluids in porous media based on the representative elementary volume scale. The flow through porous media was simulated by including the porosity into the equilibrium distribution function and adding a non-Newtonian force term to the evolution equation. The non-Newtonian behavior is considered based on the Herschel–Bulkley model. The velocity results for pressure-driven non-Newtonian flow agree well with the analytical solutions. For the electroosmotic flow, the influences of porosity, solid particle diameter, power law exponent, yield stress and electric parameters are investigated. The results demonstrate that the present lattice Boltzmann model is capable of modeling non-Newtonian flow through porous media.     

粘弹流体轴对称流动的格子Boltzmann方法

基于BGK碰撞模型，通过在迁移方程中引入作用力项，建立了粘弹流体的轴对称格子Boltzmann模型．通过Chapman-Enskog展开，获得了准确的柱坐标下轴对称宏观流动方程．采用双分布函数对运动方程和本构方程进行迭代求解，模拟分析了粘弹流体管道流动，获得了流场中的速度和构型张量的分布，通过与解析解进行比较，验证了模型的准确性．研究了作为粘弹流体流动基准问题的收敛流动，对涡旋位置进行了定量分析，将回转长度的计算结果与有限体积法进行了比较，两种数值结果十分吻合．研究结果表明，模型能够准确表征粘弹流体的轴对称流动，具有较广阔的应用前景．     

SPH-based numerical treatment of the interfacial interaction of flow with porous media

In this paper, the macroscopic equations of mass and momentum are developed and discretized based on the smoothed particle hydrodynamics (SPH) formulation for the interaction at an interface of flow with porous media. The theoretical background of flow through porous media is investigated to highlight the key constraints that should be satisfied, particularly at the interface between the porous media flow and the overlying free flow. The study aims to investigate the derivation of the porous flow equations, computation of the porosity, and treatment of the interfacial boundary layer. It addresses weak assumptions that are commonly adopted for interfacial flow simulation in particle-based methods. As support to the theoretical analysis, a two-dimensional weakly compressible SPH model is developed based on the proposed interfacial treatment. The equations in this model are written in terms of the intrinsic averages and in the Lagrangian form. The effect of particle volume change due to the spatial change of porosity is taken into account, and the extra stress terms in the momentum equation are approximated by using Ergun's equation and the subparticle scale model to represent the drag and turbulence effects, respectively. Four benchmark test cases covering a range of flow scenarios are simulated to examine the influence of the porous boundary on the internal, interface, and external flows. The capacity of the modified SPH model to predict velocity distributions and water surface behavior is fully examined with a focus on the flow conditions at the interfacial boundary between the overlying free flow and the underlying porous media.     

Effects of body shape and viscoelasticity on the slow flow around an obstacle

A study was made of the motion of axisymmetrical objects in viscous and viscoelastic fluids within a cylindrical tank with the assumption of negligible inertial effects. A numerical treatment based on the Stokes equations of motion and an optimization technique enabled the details of the velocity and rate-of-deformation fields for a Newtonian fluid to be predicted. The influence of the shape of various bodies, some even with concave surfaces, was examined. The corresponding experiments were carried out with viscous and viscoelastic fluids using a visualization technique. A correlation between the main flow characteristics and the rheological behaviour of the fluids was established.     

饱和-非饱和土壤中污染物运移过程的数值模拟

本文提出了一个模拟饱和 非饱和土壤中溶和污染物运移过程的数值模型．模拟的控制污染物运移的物理 化学现象包括：对流，机械逸散，分子弥散，吸附，蜕变，不动水效应．发展了一个修正的特征线Ｇａｌｅｒｋｉｎ方法以离散污染物运移过程的控制方程并导出了一个用于有限元方程求解的显式算法．数值例题结果表明所提出模型和算法的功能     

粘弹性流体的入口收敛流动

本文以聚合物流体为研究对象,对其在入口收敛流动中产生的粘弹效应及机理进行了初步的讨论和分析,并就近10年来国内外有关粘弹性流体入口流动研究及进展作了简要的评述。      

Steady-state countercurrent flow in one dimension

Two phase countercurrent steady-state flow through permeable media in one dimension is discussed. For steady-state countercurrent flow in water wet porous media, a saturation profile is predicted with the water saturation decreasing in the direction that the water phase is flowing. The de la Cruz and Spanos equations predict that the Muskat relative permeability curves for countercurrent flow will be less than the Muskat relative permeability curves for steady-state cocurrent flow. This result has immediate implications regarding the use of external drive techniques to determine relative permeabilities based on the Buckley-Leverett theory and Muskat's equations. These equations and current experimental evidence involving countercurrent flow indicate that Muskat's equations do not adequately describe the multiphase flow of immiscible fluids.     

Unsteady flow and heat transfer of porous media sandwiched between viscous fluids

The problem of unsteady oscillatory flow and heat transfer of porous medin sandwiched between viscous fluids has been considered through a horizontal channel with isothermal wall temperatures. The flow in the porous medium is modeled using the Brinkman equation. The governing partial differential equations are transformed to ordinary differential equations by collecting the non-periodic and periodic terms. Closed-form solutions for each region are found after applying the boundary and interface conditions. The influence of physical parameters, such as the porous parameter, the frequency parameter, the periodic frequency parameter, the viscosity ratios, the conductivity ratios, and the Prandtl number, on the velocity and temperature fields is computed numerically and presented graphically. In addition, the numerical values of the Nusselt number at the top and bottom walls are derived and tabulated.     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论，在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下，建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型，利用Laplace变换，求得了原初边值问题在变换空间中的解析解，并利用Laplace逆变换的Crump数值反演方法，得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应，分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明，与不可压流体饱和弹性多孔介质相同，不可压流体饱和粘弹性多孔介质中亦只存在一个纵波，并且固相骨架的粘性对动力行为有显著的影响。