粘弹性流体的分数元模型及圆管起动流

分数元模型所描述的非牛顿流体属于复杂粘弹性流体,其应力与应变的分数阶时间导数成正比.本文提出一种用弹簧和油壶连接组成的分形网络结构来比拟分数元模型的应力-应变特性,利用Heaviside运算微积,证明了该分形网络结构对应的粘弹性流体为1/2阶导数的分数元.并证明了构成其他分数阶导数分数元模型需要引入弹簧和油壶的多重分形网络结构.本文还导出了分数元模型的圆管起动流的解析解,研究了分数元模型起动过程振荡特征与该模型导数阶β之间的关系;发现在β≠1的情况下,随时间的进程,圆管内分数元模型的运动最终均将趋于静止,只有β=1的情况是一个例外.     

三种分形和分数阶导数阻尼振动模型的比较研究

标准的整数阶导数方程不能准确描述粘弹性材料的记忆性参考文献[1]和阻尼的分数次幂频率依赖[2],因此分形导数、分数阶导数及正定分数阶导数被用于描述粘弹性介质中的阻尼振动.该文通过分析模型和数值模拟,比较了三种模型描述的振动过程.结果显示,当p小于约O.75或大于约1.9时(p为非整数阶导数的阶数),分形导数模型衰减最快;当P大于约0.75且小于约1.9时,正定分数阶导数模型衰减最快,衰减最慢的分别为分数阶导数模型(p<1)和分形导数模型(p>1).且正定分数阶导数模型衰减快于分数阶导数模型,当p接近2时,两种模型较为相近.     

膨胀性土壤中水分反常吸附的分形导数模型

本文基于物质坐标,构建了膨胀性土壤中水分吸附的时间分形导数模型,其中物质坐标建立了土壤含水率与空间坐标的联系,并推导了膨胀性土壤中水分的累积吸附量.分形导数模型对应水分的累积吸附量为时间分形导数的阶数和扩散系数的函数.分形导数的阶数能够用于吸附过程的分类,表征介质的非均质性.本文结合黑土和砂土中水分累积吸附,验证了该模...     

深埋圆柱形隧洞黏弹性衬砌-土系统稳态振动的解析解

衬砌和土体具有黏弹性性质.将土骨架和衬砌结构视为具有分数阶导数本构的黏弹性体,在频率域内研究了深埋圆柱形隧洞衬砌和土体系统的动力特性.基于黏弹性理论,根据界面连续性条件,分别得到了黏弹性土体和衬砌结构的径向位移、应力等的解析表达式.在此基础上,对比分析了经典弹性土和弹性衬砌系统、分数导数黏弹性衬砌和土体系统的动力特性.考察了土体和衬砌的模量比、衬砌厚度、分数导数阶数、材料参数比对系统动力响应的影响.结果表明:经典弹性土和弹性衬砌系统与分数导数黏弹性衬砌和土体系统的动力特性存在较大差异.随着分数导数阶数的增加,衬砌的径向位移和环向应力幅值明显减小;土体的黏性对系统动力特性的影响大于衬砌黏性的影响.     

非牛顿流体的广义Maxwell模型及其解

引进带分数阶导数的广义Ｍａｘｗｅｌｌ模型和Ｖｏｉｇｔ模型；用Ｌａｐｌａｃｅ变换正、反演算法，给出了非牛顿流体应力松弛和蠕变近似解析解。分数阶表征了其衰减或增长的变化特性，这是一种研究分数阶导数流变学的分析、计算方法．     

非牛顿重载滚滑工况有限长线接触热弹流研究

在流速主矢量方向使用Eyring流变模型,用多重网格法求出接触压力高达1.04 GPa的相交圆弧修形滚子的热弹流完全数值解.研究表明:随着Eyring流体非牛顿效应的增强,有限长线接触弹流二次压力峰的高度明显降低,每次工作循环中摩擦副受第二次高压的强度减小;热效应显著减弱,有助于防止由热效应导致的各种形式的失效;最小油膜厚度略有增加,有利于润滑膜的形成.因此,使用Eyring非牛顿流体有利于延长线接触副的寿命.与此同时,使用Eyring非牛顿流体时,非牛顿效应对滚子端部的压力分布影响很小,因此Eyring非牛顿效应对有限长摩擦副的凸度设计无明显影响.     

黏弹性土层中单桩纵向振动的对比分析

在频率域内研究了黏弹性土层中端承桩纵向振动的动力特性.将土骨架视为具有分数阶导数本构关系的黏弹性体,基于黏弹性理论,采用平面应变模型给出了分数阶导数黏弹性土层的动力阻抗.考虑桩纵向振动时的横向惯性效应,将桩等效为Rayleigh-Love杆,得到了桩头动力复刚度和导纳的解析表达式.通过数值计算,分析了不同模型土条件下桩头动刚度因子和阻尼随激励频率的动力响应.同时,研究了Rayleigh-Love和Euler-Bernoulli两种模型桩动力特性的差异.分析了桩-土界面连续性模型和相对滑移模型对黏弹性土层中桩纵向振动的影响.结果表明:1随着阶数和材料参数比的增加,桩头刚度因子和阻尼明显减小;2对于大直径桩,随着外荷载激励频率的增加,桩横向效应对刚度因子和阻尼有显著影响.3连续性模型条件下桩头的刚度因子和阻尼在共振时的振幅小于相对滑移模型条件.     

基于非局部理论的分数阶黏弹性场地地震放大效应分析

基于非局部理论和分数阶导数理论,研究上覆黏弹性场地土的地震放大效应。利用Eringen非局部理论考虑土体颗粒尺度等非局部效应的影响,通过分数阶黏弹性本构模型刻画场地土的应力应变本构关系,建立基于非局部理论的分数阶黏弹性场地土的振动微分方程;考虑分数阶导数的性质和黏弹性场地土的边界条件,得到了简谐地震波作用下黏弹性场地土的位移和剪切应力的解析解,并在频率域内给出了位移放大系数和应力放大系数的表达式;最后通过数值算例分析了非局部效应、分数阶导数的阶数和土体黏性参数等对黏弹性场地地震放大效应的影响。数值分析结果表明,在低频时位移放大系数和应力放大系数随频率变化曲线存在波动,高频时逐渐趋于稳定;非局部效应对场地土位移放大系数的影响与频率有关,对应力放大系数的影响较大,在研究场地土振动效应时有必要考虑土体非局部效应的影响;分数阶导数的阶数越小,位移放大系数和应力放大系数随频率变化曲线波动越大;场地土的力学性质对场地土的振动效应的影响较大;上覆场地土的黏性对位移放大系数的影响与频率有关,高频时,土体黏性越大,位移放大系数越大;越接近基岩,土体的应力放大系数越大,且土体深度对应力放大系数的影响越大。     

基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用

微生物是自然生态系统的重要组成部分,掌握微生物在复杂流体中的运动特性可以为微型器件的设计制造提供理论指导.壁面效应是微生物游动研究中的重要问题之一,已有研究表明微生物在壁面附近存在复杂的行为特征.然而已有研究大多集中于微生物在牛顿流体中的游动模拟,仅有少数涉及黏弹性流体等非牛顿流体.本文采用直接力虚拟区域法与乔列斯基分解相结合的数值方法,引入Squirmer微生物游动模型,研究了微生物在黏弹性流体中的游动问题.首先给出求解黏弹性流体本构方程的数值格式;并将该方法应用于研究微生物游动中的壁面效应.研究结果表明,游动方向是影响微生物颗粒壁面效应的重要因素.流体弹性应力会对微生物产生一个反向转矩,影响微生物的游动方向,从而阻碍微生物逃离壁面.微生物颗粒在黏弹性流体中与壁面作用时间较长,几乎达到牛顿流体的两倍以上.     

一个基于恢复时间的新剪稀模型及其对聚合油PAO 650流变特性的模拟

用球-杆比拟流体层上的分子,通过分析两流体层上球-杆的接触、通过和恢复的过程,基于球-杆恢复到原状态的时间,建立了一个新剪稀模型.该模型虽然在形式上与Carreau模型有相似之处,但其公式仅含有两个流变参数,且是经由严格的理论推导得到的.通过与Carreau模型得到的广义黏度曲线的比较,确定了新流变公式的待定参数.在点接触流变热弹流润滑的数学模型中使用新流变公式,数值模拟了大黏度聚合油PAO 650的流变特性,并与该油在文献中的试验曲线进行了比对.结果表明新流变模型能够较好地模拟大黏度聚合油的流变特性,从而证实了其正确性.进一步,使用新公式计算得到了更多工况下的流变特性曲线,光滑的、合理的曲线分布说明新流变模型具有广泛的适用性.     

Simulation of non-Newtonian ink transfer between two separating plates for gravure-offset printing

The inks used in gravure-offset printing are non-Newtonian fluids with higher viscosities and lower surface tensions compared to Newtonian fluids. This paper examines the transfer of a non-Newtonian ink between two parallel plates when the top plate is moved upward with a constant velocity while the bottom plate is held fixed. Numerical simulations were carried out using the Carreau model to explore the behavior of a non-Newtonian ink in gravure-offset printing. The volume of fluid (VOF) model was adopted to demonstrate the stretching and break-up behaviors of the ink. The results indicate that the ink transfer ratio is greatly influenced by the contact angle, especially the contact angle at the upper plate (α). For lower values of α, oscillatory or unstable behavior of the position of minimum thickness of the ink between the two parallel plates during the stretching period is observed. This oscillation gradually diminishes as the contact angle at the upper plate is increased. Moreover, the number of satellite droplets increases as the velocity of the upper plate is increased. The surface tension of the conductive ink shows a positive impact on the ink transfer ratio to the upper plate. Indeed, the velocity of the upper plate has a significant influence on the ink transfer in gravure-offset printing when the Capillary number (Ca) is greater than 1 and the surface tension dominates over the ink transfer process when Ca is less than 1.     

Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

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Attractors of non-Newtonian fluids

The existence of global attractors is demonstrated for the dynamical systems generated by motions of nonlinear bipolar and non-Newtonian viscous fluids and upper bounds are obtained for the Hausdorff and fractal dimensions of the attractors for the bipolar case.     

Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak. The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education     

Pulsatile pipe flow of pseudoplastic fluids

This note is concerned with a laminar pipe flow of a non-Newtonian fluid under the action of a small pulsating pressure gradient superposed to a steady one. The constitutive law describing the rheological behaviour of the fluid is the so-called power law (Ostwald–de Waele). An approximated analytical solution is found for the velocity, as power series of the amplitude of the periodic disturbance. The analytic solution is compared with a direct numerical solution and the perfect accord of the values obtained is underscored.     

Disappearance of criticality for reactive third-grade fluid with Reynold's model viscosity in a flat channel

In this paper, we consider how a model for the motion with exponential viscosity of a third-grade fluid flowing between parallel plates, under the action of externally imposed pressure gradient, affects the fully developed and laminar reactive flow. The non-dimensional form of the coupled equations are solved numerically. The temperature distribution is presented for various viscosity variational parameters and the number is related to the Frank-Kamenetskii parameter. The criticality and disappearance of criticality (transition) of physical parameters and the competing effects of viscous dissipation, viscosity variational number, heat generation and non-Newtonian are discussed.     

Flow of Robertson-Stiff fluids through an eccentric annulus

I.IntroductionInthepetroleumindustry,itisusuallythecasethatthedrillingstring(orcasingpipe)isnotlocatedinsidethecenteroftheflowgeometryduringdrillingandcompletillgpl'ocess,this,inturll,willaltertile'11owingbehaviorofdrillingmudandcementslurl.ieswhichtlowinginaneccentricallllulus.OilaccoUlltofviscousofnon-Newtoniantluid,flowillaneccentricannulusdifTeresmuchwiththatinacollcentricannulus.Mailyinvestigatorshaveconductedresearchworksonthisstlbject.Earlyin1935,TaoandDollovallrealizedthattheimpel.t…     

Effect of ion slip on the time-varying Hartmann flow of a non-Newtonian viscoelastic fluid with heat transfer

Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.     

Transient flows of a second grade fluid

Exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid are constructed. The flows are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient. Expressions for velocity, flux and skin friction are obtained for both large and small times. It is found that large and small times solutions are dependent on the coefficient of viscoelasticity. The solutions corresponding to Newtonian fluids can be easily obtained from those for fluids of second order by letting the viscoelastic parameter to be zero.     

An approximate solution for the Couette–Poiseuille flow of the Giesekus model between parallel plates

An approximate analytical solution is derived for the Couette–Poiseuille flow of a nonlinear viscoelastic fluid obeying the Giesekus constitutive equation between parallel plates for the case where the upper plate moves at constant velocity, and the lower one is at rest. Validity of this approximation is examined by comparison to the exact solution during a parametric study. The influence of Deborah number (De) and Giesekus model parameter (α) on the velocity profile, normal stress, and friction factor are investigated. Results show strong effects of viscoelastic parameters on velocity profile and normal stress. In addition, five velocity profile types were obtained for different values of α, De, and the dimensionless pressure gradient (G).