精确计算Bingham流体圆管层流压降及速度分布规律的新方法

Bingham(宾汉)模型情况下,多采用通用公式进行圆管层流压降的解析计算,即将Bingham模型本构方程代入粘性流体圆管层流流动通用公式进行计算,仅能得到压降的解析解.新方法结合Bingham流体本构方程与运动方程,建立有关力学平衡方程,并运用代数方程的根式解理论对圆管层流流动时的非线性方程进行求解,可直接求得Bingham流体圆管层流压降及速度流核区半径的解析解,进一步可求得圆管层流速度解析解;Bingham流体圆管层流速度的直接影响因素为流量、塑性粘度和屈服值,研究发现速度流核宽度与屈服值成正比,与流量及塑性粘度成反比,且流核的宽度越大,流核区的速度越小.     

宾汉流体稠密两相湍流流动中的二阶矩模型

建立的Bingham流体稠密两相流动的二阶矩-颗粒动力论湍流模型（USM-theta模型）既体现了两相的作用,又体现了屈服应力所引起的附加项,并提出了USM-theta模型下考虑浓度修正值影响的两相湍流流动的算法．利用该模型对圆管内Bingham流体的单相湍流流动、稠密液固两相的湍流流动进行了计算,并和五方程湍流模型进行了比较,结果表明该模型的预测效果更好．利用USM-theta模型对含颗粒的Bingham流体的两相湍流流动进行了模拟,随着屈服应力的增加,Bingham流体相与颗粒相在管道中心附近的主流速度减小．液固两相湍流和Bingham流体两相湍流的计算结果表明屈服应力引起的附加项对流动有很重要的影响．     

非牛顿流体偏心环空螺旋流的解析解

石油和化工中许多问题需要求解非牛顿流体偏心环空螺旋流。本文全面地研究了幂律流体和宾汉流体在偏心环空中层流螺旋流的流动规律与流动状态的判别。在理论上,根据流体力学原理,运用数学方法,在作者同心环空螺旋流的理论基础上,通过对偏心环空螺旋流流场的无限细分法,给出了该流场的视粘度分布、速度分布、流量和压降方程,进而建立了判别流态的稳定性参数。     

微通道内电渗压力混合驱动幂律流体流动模拟

为了研究微通道内电渗压力混合驱动幂律流体的流动特性,建立了微通道内电渗压力混合驱动幂律流体的计算模型,其双电层电势、流体的流场分布分别由Poisson-Boltzmann(P-B)方程和Navier-Stokes(N-S)方程描述.讨论了无量纲Debye(德拜)参数K、壁面ζ*电势和幂律指数n对流体流动特性和Poiseuille数的影响.结果表明,当压力梯度与外加电场方向一致(Γ0)时,剪切变稀流体的速度大于剪切变稠流体;压力梯度与外加电场方向相反(Γ0)时,结果相反.Poiseuille数是无量纲Debye常数K、壁面ζ*电势和幂律指数n的增函数.     

激波在异种气体中传播及诱导的剪切混合研究

利用二阶迎风TVD格式求解多组分,层流全N－S方程,针对直通道和突扩直通道,研究了马赫数为2和4的激波在H2和空气界面上的传播及诱导的燃料剪切混合,计算结果表明：（1）直通道中,剪切层中的激波阵面要发生畸变,存在对混合起主要作用的卷吸涡,激波马赫数不同,卷吸涡结构和横向混合的尺寸也不同,激波马赫数低,剪切混合效果好,（2）在突扩直通道中,马赫数为2和4的激波在H2中产生不同强度激波,在剪切层中都能产生顺时针,尺度较大的卷吸涡,后台阶增强了剪切层的混合。     

针对壁面旋转变径管内螺旋流的压力应变项研究

通过壁面旋转变径圆管内螺旋湍流流动特征的分析，确定其切向速度场内涡流区为微团旋转主导的椭圆形流动，外涡流区为微团变形主导且受壁面旋转影响的双曲形流动.进而利用张量的不变量理论，引入旋转率张量与应变率张量的综合不变量作为模型系数，将适用于微团旋转主导的旋转湍流Reynolds应力压力应变项修正模型拓展到了非旋转效应主导的双曲形流动中.将修正压力应变项应用于壁面旋转变径圆管流场的模拟，并将结果与实测结果进行了对比，验证了修正模型的改进效果.     

微小通道内空气流动特性实验研究

研究了空气在不同压比条件下,在内径分别为0.4 mm和0.5 mm的微圆直管内的流动特性.研究表明空气流过微圆管的阻力系数是常规管道的4至5倍,且存在层流状态提前过渡到湍流状态的提前转捩现象.微圆管管径越小,管内流动压力损失越大.     

两相流中柱状固粒对流体湍动特性影响的研究

对含柱状固粒的两相流场,建立了包含柱状固粒对流场影响的流体脉动速度方程,在求解脉动速度方程的基础上,经平均得到流体的湍流强度和雷诺应力.将该方法用于槽流湍流场的求解,并与单相流实验结果进行了比较.计算中变化柱状固粒的参数,给出了固粒的体积分数、长径比、松驰时间对流场湍动特性的影响,说明粒子对流场的湍动特性起着抑制作用,其抑制的程度与粒子的体积分数、长径比成正比,与粒子的松弛时间成反比.     

粉末注射成形填充过程的数值模拟

本文将粉末注射成形喂料在薄壁模腔中的流动视为二维流动，以流变学的基本方程为基础，建立了从动量方程、连续方程和热传递方程得到的描述PIM喂料充模二维流动的数学模型。在无滑移边界的条件下，推导了喂料熔体流导率的计算公式和压力场的控制方程，得到的压力场控制方程是一非线性椭圆偏微分方程．从而可用Galerkin方法进行数值求解，使模型的数值求解成为可能，为进一步对粉末注射成形进行计算机模拟和数值分析奠定了数学基础。     

空间分数阶非Newton流体本构及圆管流动规律研究

对非Newton流体的本构及流动规律进行研究是分析、预测和控制非Newton流体在管道中流动的关键.实验表明非Newton流体在流动过程中具有历史记忆性,基于空间分数阶微积分方法,建立了分数阶非Newton流体本构模型;并推导了该模型在圆管中的流速分布、流量、平均流速、压降、平均Reynolds数等管道流动参数;提出了分数阶非Newton流体圆管流态判别准则.研究表明非Newton流体的圆管流层间的切应力可以通过流速的轴向分布大小来描述.对于不含屈服切应力的分数阶非Newton流体,分数阶的阶数越大,断面流速分布越均匀,记忆能力越强.分数阶的阶数大小反映了流体对全域空间的记忆性强弱;而对于含有屈服切应力的分数阶非Newton流体,分数阶的阶数越大,速梯区流速分布越均匀,流核区速度越小.分数阶的阶数大小反映了局部空间记忆性强弱.该研究为非Newton流体的记忆特征提供了一种新的建模方法.     

Elasto-viscoplastic fluid flow in tubes of arbitrary cross-section

Elasto-viscoplastic fluid flow in tubes of arbitrary cross-section is explored. A constitutive equation superposing elasticity on the viscoplastic behavior through a linear combination of the non-linear simplified Phan–Thien–Tanner constitutive model of viscoelasticity and the non-linear Bingham constitutive equation of viscoplasticity is developed. The equation of motion is solved analytically for the longitudinal field for steady flow in tubes of non-circular cross-section. The evolution of the plug and stagnant zones, hallmarks of viscoplastic behavior, is studied when elasticity is present, and the rate of flow is determined in terms of the Weissenberg and Bingham numbers. Elasticity tends to enhance the rate of flow for given viscoplastic conditions, and stagnant and plug zone configurations are substantially altered.     

Helical flow of a Bingham fluid arising from axial Poiseuille flow between coaxial cylinders

The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.     

Bingham流体数值模拟的双罚函数—正交投影的隐式求解方法

本文对Bingham流体给出了双罚函数逼近和正交投影的隐式求解方法.这个方法把Bingham流体处理为承受不等式应力约束的Newton流体的逼近解.有效地模拟了可以出现流动或不流动的“刚性核”的Bingham流体的流动问题.     

On contact instabilities of viscoplastic fluids in two-dimensional setting

The Richtmyer–Meshkov and Rayleigh–Taylor instabilities in viscoplastic (Bingham) fluids are studied in two-dimensional setting. The evolution of the Richtmyer–Meshkov instability in a Bingham fluid is analyzed as compared with its evolution in a Newtonian fluid. The critical amplitude of the initial perturbation in the velocity field is estimated. Numerical results obtained for Richtmyer–Meshkov and Rayleigh–Taylor instabilities in a Bingham fluid are presented and compared with those obtained for a Newtonian fluid.     

Steady flows of Cosserat–Bingham fluids

The equations describing the steady flow of Cosserat–Bingham fluids are considered, and existence of weak solution is proved for the three‐dimensional boundary‐value problem with the use of the Lipschitz truncation argument. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro‐rotations and two types of plug zones. Our approach is based on an approximation of the constitutive relation by a generalized Newtonian constitutive relation and a subsequent limiting process. Copyright © 2016 John Wiley & Sons, Ltd.     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Regularity results for the quasi–static Bingham variational inequality in dimensions two and three

We consider the variational inequality describing the stationary flow of a Bingham type fluid in bounded domains. Differentiability properties of weak solutions in suitable energy spaces providing existence theorems are studied. We suppose that the volume forces belong to classes of Morrey type and generalize our previous regularity results concerning slow, steady–state flow of Bingham fluids. Received: 12 February 1996; in final form 16 July 1996