基于水平集方法的毛管上升特征研究

毛管上升现象与许多行业密切相关,系统地对此现象进行研究具有重大意义。与传统理论研究方法不同,本文使用N-S方程耦合水平集方法模拟毛管气液上升行为。通过与简化条件的解析解对比,验证了模拟方法的可靠性。此外,详细地研究了毛管振荡现象,并分析了影响毛管振荡行为的主要因素。结果表明,水平集方法能够精确地表征毛管振荡现象,与数值解相比具有更高的精度。毛管长度的增加能够减弱液柱振荡,主要归结于非湿相气体的粘滞力作用;湿相密度和湿相粘度同样对毛管振荡现象影响显著。湿相密度越大,惯性力越大,促进了毛管振荡;而湿相粘度变大,会增大粘滞力作用,因此减弱了毛管振荡现象。毛管振荡是由多种影响因素共同控制的,流体的惯性力是造成毛管振荡的主要原因,而粘滞力是减弱毛管振荡行为的主要因素,使液柱振荡逐渐衰减,并稳定至平衡高度。     

非牛顿流体两相渗流问题的摄动解

本文用奇异摄动法结合正则摄动法求解了考虑毛管力因素时多孔介质中弱非牛顿流体的两相驱替问题,得到了分流函数和湿相饱和度的渐近解析解。所得结果同数值解和经典的牛顿流体两相渗流结果进行了比较,并着重讨论了非牛顿因素的影响。     

基于场力的驾驶员影响因素交通流动力学模型

为研究驾驶员行为对道路交通的定量影响,针对驾驶员行为特点,综合考虑了驾驶员受到的直接物理影响和间接心理影响、相对速度以及车辆自身特性等因素,结合场力、图论等方法,提出了一种用于模拟考虑驾驶员影响因素的元胞自动机交通流动力学模型(简称IDCA模型).通过计算机数值模拟,研究了考虑驾驶员影响因素下车流演化机理及不同驾驶员类型对道路交通流的影响.结果表明:与NaSch模型相比,本文建立的IDCA模型能够模拟得到丰富的交通行为,再现了同步流等交通现象,从速度波动和车头间距波动分析得出IDCA模型下道路交通流具有更强的稳定性,堵塞消融效率更高.此外得到了由不同驾驶员类型按不同比例组成的混合交通流的密度-速度图和密度-流量图,发现在道路相同中高密度下,激进型驾驶员所占的比例越大,车辆速度与交通流量越大,交通流量随着保守型驾驶员比例的增加而降低.最后模拟实现了车辆高速跟驰现象,得到小间距高速跟驰率超过7%的结果与实测结果相符合.     

基于场力的驾驶员影响因素交通流动力学模型

为研究驾驶员行为对道路交通的定量影响, 针对驾驶员行为特点, 综合考虑了驾驶员受到的直接物理影响和间接心理影响、相对速度以及车辆自身特性等因素, 结合场力、图论等方法, 提出了一种用于模拟考虑驾驶员影响因素的元胞自动机交通流动力学模型(简称IDCA模型). 通过计算机数值模拟, 研究了考虑驾驶员影响因素下车流演化机理及不同驾驶员类型对道路交通流的影响. 结果表明: 与NaSch模型相比, 本文建立的IDCA模型能够模拟得到丰富的交通行为, 再现了同步流等交通现象, 从速度波动和车头间距波动分析得出IDCA模型下道路交通流具有更强的稳定性, 堵塞消融效率更高. 此外得到了由不同驾驶员类型按不同比例组成的混合交通流的密度-速度图和密度-流量图, 发现在道路相同中高密度下, 激进型驾驶员所占的比例越大, 车辆速度与交通流量越大, 交通流量随着保守型驾驶员比例的增加而降低. 最后模拟实现了车辆高速跟驰现象, 得到小间距高速跟驰率超过7%的结果与实测结果相符合.      

注塑成型喷射现象数值模拟及机理分析

喷射是熔体充填过程中一种特殊流动形态,也是注塑成型的不良现象,为了预测射流长度、形态演化,揭示喷射的产生机理,建立了粘性、非等温的熔体三维流动模型,构造了熔体流动前沿演化的输运方程。用有限体积法离散控制方程,提出了压强与速度及速度与温度的两重解耦合方案,开发了模拟程序,分析了模拟成型过程中粘性力、惯性力、速度、温度、压力等物理量的大小及变化规律。基于模拟结果分析了粘性力、惯性力的大小对喷射的影响,发现:当惯性力大于粘性力时产生喷射现象,随着粘性力增大,射流变为蛇形流;射流长度依赖于注射速度,速度越大,射流越长,熔体温度对射流长度基本没有影响。此外,实验结果表明,注塑成型喷射现象数值模拟及机理分析方法可以较好地预测射流长度、蛇形流的形态以及蛇形流中、后端摆动幅度。     

燃爆压裂中压挡液柱运动规律的动力学模型

针对燃爆压裂过程中压挡液柱受冲击运动机理的复杂性,假设火药燃气与压挡液柱存在完全气液 接触界面,采用拉格朗日的微元分析方法,建立了由连续性方程、动量守恒方程、能量守恒方程组成的压挡液 柱运动规律动力学模型,并给出了该模型与火药燃爆模型的耦合数值解法。经程序编制和实例计算表明,在 综合考虑火药燃气对液柱的宏观推动作用、冲击压缩作用、液柱自身的动能分布及管壁对其摩擦阻力的影响 后,火药燃烧过程中气液界面上升高度有限(实例计算不足0.1m),可起到很好的持压作用;但全过程中最高 液柱位移较大(18.9m),水力振荡增效作用明显。研究成果对提高燃爆压裂的数值模拟精度具有一定促进 作用。     

幂律流体在单根弯曲毛细管中的毛细上升

基于分形理论和数值模拟的方法, 给出了幂律流体在单根弯曲毛细管的上升高 度和上升累积质量随时间的变化关系曲线. 研究结果表明: 在上升初期阶段, 重力因素可以 忽略; 但随着时间增加, 重力因素的影响越来越大; 幂律流体上升的最大高度只与毛细管直 径$\lambda$、幂律流体密度$\rho $有关, 与毛细管弯曲程度$\tau _0 $和幂指数$n$无关; 幂指数$n$越小, 上升初期上升速度越快; 迂曲度分形维数$D_T $越大, 平衡时吸入的幂律流体质量也越大.     

冲击载荷作用下柱壳链中的弹性波传播简化模型及其解析解

柱壳链能引起波形的弥散,具备操控波形的潜力。建立了柱壳链结构的等效连续介质模型和细观有限元模型,研究了质量块冲击作用下柱壳链中的弹性应力波传播过程及其几何弥散特性。基于考虑横向惯性修正的Rayleigh-Love波动方程,建立了柱壳链在质量块冲击下的控制方程,采用Laplace变换及其逆变换获得了位移场、速度场和应变场的解析解,所得结果与细观有限元模拟结果较好吻合。结果表明,在冲击过程中应变和速度峰值均逐渐减小,应变峰值、振荡幅度和波形前沿宽度与泊松比和惯性半径相关,泊松比和惯性半径越大,应变峰值越小,应变分布振荡越剧烈,波形前沿宽度越宽。     

气流作用下同轴带电射流的不稳定性研究

通过对气体驱动同轴电流动聚焦的实验模型进行简化,开展了电场力和惯性力共同作用下同轴带电射流的不稳定性理论研究.在流动为无黏、不可压缩、无旋的假设下,建立了三层流体带电射流物理模型并得到了扰动在时间域内发展演化的解析形式色散关系,利用正则模方法求解色散方程发现了流动的不稳定模态,进而分析了主要控制参数对不稳定模态的影响.结果表明,在参考状态下轴对称模态的最不稳定增长率最大,因此轴对称扰动控制整个流场.外层气流速度越高,气体惯性力越大,射流的界面越容易失稳.内外层液-液同轴射流之间的速度差越大,射流越不稳定.表面张力对射流不稳定性起到促进作用.轴向电场对射流不稳定性具有双重影响:当加载电场强度较小时,射流不稳定性被抑制;当施加电压大于某一临界值时,轴向电场会促进射流失稳.临界电压的大小与界面上自由电荷密度和射流表面扰动发展关系密切.这些结果与已有的实验现象吻合,能够对实验的过程控制提供理论指导.     

两相流中密度波现象的研究及进展

密度波（又称连续波、空隙度波、运动学波）是两相流中的特殊现象，本文评述两相流密度波理论的主要研究进展，这些理论不仅研究了线性密度波和非线性密度波的特性，还研究了气液两相流的流型转变与密度波的关系，流化床中气塞的形成和床层的塌陷现象与密度波的关系等．同时介绍试验和理论研究在密度波的波速、频率、稳定性和色散性等方面取得的主要结论．最后指出密度波的理论和试验研究尚需进一步解决的问题．     

Elliptic Regions and Stable Solutions for Three-Phase flow in Porous Media

In the limit of zero capillary pressure, solutions to the equations governing three-phase flow, obtained using common empirical relative permeability models, exhibit complex wavespeeds for certain saturation values (elliptic regions) that result in unstable and non-unique solutions. We analyze a simple but physically realizable pore-scale model: a bundle of cylindrical capillary tubes, to investigate whether the presence of these elliptic regions is an artifact of using unphysical relative permeabilities. Without gravity, the model does not yield elliptic regions unless the most non-wetting phase is the most viscous and the most wetting phase is the least viscous. With gravity, the model yields elliptic regions for any combination of viscosities, and these regions occupy a significant fraction of the saturation space. We then present converged, stable numerical solutions for one-dimensional flow, which include capillary pressure. These demonstrate that, even when capillary forces are small relative to viscous forces, they have a significant effect on solutions which cross or enter the elliptic region. We conclude that elliptic regions can occur for a physically realizable model of a porous medium, and that capillary pressure should be included explicitly in three-phase numerical simulators to obtain stable, physically meaningful solutions which reproduce the correct sequence of saturation changes.     

A new method to determine viscosity of liquids using vibration principles

A new method for determining viscosity of liquids is examined. The method employs the principles of vibration and measures the viscous damping due to the motion of a liquid placed in a cylindrical tube. The apparatus and the test liquid are treated as a dynamic system and the measured mechanical impedances are used to calculate energy dissipation due to the viscous damping. The newly designed apparatus is able to generate shear deformations in the liquid without using moving solid surfaces. A harmonic varying force with a frequency close to the resonance frequency of the system is applied through a piston and the resulting velocities of the oscillations generated in the system are measured. Liquids with higher viscosities result in lower velocities due to the higher damping. Analytical equations are provided to relate the viscous damping of the dynamic system to the viscosity of the liquids. The viscosities obtained from the proposed method are in good agreement with the ones obtained from standard rotational viscometry using a cone and plate geometry.     

Gas displacement of viscoplastic liquids in capillary tubes

The displacement of viscoplastic liquids in capillary tubes by gas injection is examined. The viscoplasticity alters the flow kinematics and changes dramatically the amount of mass left attached at the tube wall as compared to the Newtonian case, studied experimentally by G.I. Taylor in 1961 [G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, J. Fluid Mech. 10 (1961) 161–165]. Experiments with Carbopol aqueous solutions were performed for different flow rates. A recently proposed viscosity function for viscoplastic liquids was fitted to the rheological data of the Carbopol solutions. A new dimensionless rheological property – the jump number – arises in the dimensionless version of this viscosity function. The results show the effect of the viscoplastic character of the liquid on the free surface shape and on the thickness of the film of liquid left attached to the wall. This thickness decreases with the jump number and increases with the flow rate. It is also observed that there is a critical dimensionless flow rate below which the displacement is apparently perfect, i.e. there is no observable liquid left attached to the wall. This behavior is shown to be directly related to the fully developed flow far ahead the air–liquid interface.     

Viscous coupling in two-phase flow in porous media and its effect on relative permeabilities

An idealized model of a porous rock consisting of a bundle of capillary tubes whose cross-sections are regular polygons is used to assess the importance of viscous coupling or lubrication during simultaneous oil-water flow. Fluids are nonuniformly distributed over tubes of different characteristic dimension because of the requirements of capillary equilibrium and the effect of interfacial viscosity at oil-water interfaces is considered. With these assumptions, we find that the importance of viscous coupling depends on the rheology of the oil-water interface. Where the interfacial shear viscosity is zero, viscous coupling leading to a dependence of oil relative permeability on oil-water viscosity ratio for viscosity ratios greater than one is important for a range of pore cross-section shapes and pore size distributions. For nonzero interfacial shear viscosity, viscous coupling is reduced. Using values reported in the literature for crude oil-brine systems, we find no viscous coupling.     

微重力下成一定夹角平板间的表面张力驱动流动的研究

空间微重力环境中,由于重力基本消失,表面张力等次级力发挥主要作用,流体行为与地面迥异,因此有必要深入探究微重力环境中的流体行为规律和特征.板式贮箱利用板式组件在微重力环境中对流体进行管理,从而为推力器提供不夹气的推进剂,这对航天器精确进行姿态控制、轨道调整具有重要意义.板式组件中常包含成一定夹角的平板结构,比如蓄液叶片...     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Oscillations of a gas bubble in a non-Newtonian liquid under the action of an acoustic field

The evolution of the radius of a spherical cavitation bubble in an incompressible non-Newtonian liquid under the action of an external acoustic field is investigated. Non-Newtonian liquids having relaxation properties and also pseudoplastic and dilatant liquids with powerlaw equation of state are studied. The equations for the oscillation of the gas bubble are derived, the stability of its radial oscillation and its spherical form are investigated, and formulas are given for the characteristic frequency of oscillations of the cavitation hollow in a relaxing liquid. The equations are integrated numerically. It is shown that in a relaxing non-Newtonian liquid the viscosity may lead to the instability of the radial oscillations and the spherical form of the bubble. The results obtained here are compared with the behavior of a gas bubble in a Newtonian liquid.     

A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media

Infiltration of water and non-aqueous phase liquids (NAPLs) in the vadose zone gives rise to complex two- and three-phase immiscible displacement processes. Physical and numerical experiments have shown that ever-present small-scale heterogeneities will cause a lateral broadening of the descending liquid plumes. This behavior of liquid plumes infiltrating in the vadose zone may be similar to the familiar transversal dispersion of solute plumes in single-phase flow. Noting this analogy we introduce a mathematical model for ‘phase dispersion’ in multiphase flow as a Fickian diffusion process. It is shown that the driving force for phase dispersion is the gradient of relative permeability, and that addition of a phase-dispersive term to the governing equations for multiphase flow is equivalent to an effective capillary pressure which is proportional to the logarithm of the relative permeability of the infiltrating liquid phase. The relationship between heterogeneity-induced phase dispersion and capillary and numerical dispersion effects is established. High-resolution numerical simulation experiments in heterogeneous media show that plume spreading tends to be diffusive, supporting the proposed convection-dispersion model. Finite difference discretization of the phase-dispersive flux is discussed, and an illustrative application to NAPL infiltration from a localized source is presented. It is found that a small amount of phase dispersion can completely alter the behavior of an infiltrating NAPL plume, and that neglect of phase-dispersive processes may lead to unrealistic predictions of NAPL behavior in the vadose zone.     

Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.     

Dynamic stabilization of Rayleigh capillary instability

The effect of high-frequency vibrations on the stability of a cylindrical liquid interface is studied. In the absence of external disturbances the interface will be unstable if the length of the liquid cylinder exceeds the length of the normal boundary section. It is shown that vibrations circularly polarized in the plane of the normal section can suppress the development of instability however great the length of the liquid cylinder. The effect of the density ratio of the liquids and the dimensions of the rigid outer shell on the stability of the system is investigated. It is shown that vibrations can stabilize the cylindrical interface only if the radius of the shell is not too great as compared with the radius of the liquid cylinder. The critical value of the radius ratio is approximately equal to 1.58 and does not depend on the density ratio of the liquids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–7, November–December, 1991.