Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

Vibration analysis of conveying fluid pipe via He’s variational iteration method

In this paper, a recently new semi-analytical method, i.e., He’s variational iteration method is developed to apply to free vibration analysis of conveying fluid pipe. The critical flow velocity and frequency of pipe conveying fluid are obtained with considering the various boundary conditions. The results are compared with the ones of different transform method, and prove VIM that has the same precision and efficient with DTM. The mode shapes of cantilevered pipe and both ends with elastic support pipe are shown under different flow velocity.     

The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: An analytical solution

An analytical solution for the flow of a third grade fluid in a pipe is obtained using homotopy analysis method (HAM). The fluid considered is with variable space dependence viscosity. The temperature of the pipe is taken to be higher than the temperature of the fluid. Expressions for velocity and temperature profiles are constructed analytically and explained with the help of graphs.     

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.     

弹性地基输流管道的耦合模态颤振分析

推导出了弹性地基输流管道的固-液耦合振动微分方程,用幂级数法计算了Winkler模型地基和双参数模型地基输流管道的临界流速和复频率,分析了弹性地基对输流管道静力稳定性与动力稳定性的影响.结果表明,与不考虑弹性地基的情况相比较,弹性地基的作用可使管道发生静力失稳和动力失稳的临界流速增大,并且增大弹性地基参数可提高静力失稳和动力失稳的临界流速,从而推迟发散与颤振的发生.当质量比β较大时,管道会在某个地基参数组合下,在发生静力失稳后,会在较高流速下出现再稳定和再发散现象,然后发生耦合模态颤振.     

Hall effect on the pipe flow of a Burgers’ fluid: An exact solution

An analysis is made to see the influences of Hall current on the flow of a Burgers’ fluid. The velocity field corresponding to the flow in a pipe is determined. The closed form analytical solutions for several Newtonian and non-Newtonian fluid models can be obtained from the present analysis as the limiting cases.     

Stability analysis of shear-thinning flow between rotating cylinders

Stability of the shear thinning Taylor–Couette flow is carried out and complete bifurcation diagram is drawn. The fluid is assumed to follow the Carreau–Bird model and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed, that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear thinning effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.     

广义二阶流体管内轴向流动

在流体的本构关系中引入分数阶导数运算，对于介于粘性与弹性之间的流体的描述更具有合理性。本文将这种关系引入二阶流体，研究其管内轴向流动。我们先求出了１／２阶导数的解析解，用以验证Ｌａｐｌａｃｅ数值反演的ＣＲＵＭＰ方法的有效性。然后用ＣＲＵＭＰ法分析二阶流体管内轴向流动的特征。分析表明粘弹性特征越明显的流体，其速度与应力对分数导数的阶数越具有敏感性。     

直圆管突扩通道内宾汉流体湍流流场的数值研究

本文依据牛顿流体中建立的标准ｋ＿ε湍流模型这一基本思想，考虑宾汉流体的本构方程，建立了适用于求解宾汉流体湍流流动的控制方程·采用压力修正算法，实现了宾汉流体速度场与压力场的关联·在理论研究基础上，对直圆管突扩通道内宾汉流体湍流流动进行了数值研究，并探讨了直圆管突扩通道内宾汉流体湍流流动机理·     

Landau-Hopf scenario of passage to turbulence in some problems of elastic stability theory

We consider a boundary value problem for a nonlinear integro-differential equation modeling the vibrations of a pipe transporting a fluid and the vibrations of a thin cylinder in an axisymmetric flow. For the boundary conditions we take the hinge support conditions. We show that the Landau-Hopf scenario of passage to turbulence can be realized in such a problem, whereby stable invariant tori of increasing dimensions are generated as the main bifurcation parameter increases.     

Secondary flow of a conducting fluid in a rotating straight annular pipe

A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight annular pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. The secondary flow pattern has been studied in detail for small values of angular velocity and Hartman number.     

二阶非牛顿流体环管流动解析解

本文采用积分变换的方法,找到了一类非牛顿流体在环形管道中不定常流动的解析解,并进行了数值计算,详尽分析了非牛顿性系数和其他各参数对二阶流体不定常流动的影响.指出当二阶流体非牛顿系数相同时,环管流与一般管流相比达到稳定的特征时间较短,并且相应的速度分布、平均速度分布的数值均较小,在外半径相同时,环管流内壁的剪应力较之一般管流,其大小随内半径的大小而变,环管流的外壁剪应力总相应地小于内壁剪应力.     

环空管内粘弹性流体不定常旋转流的解及流动特性分析

本文用Hankel积分变换法分别求得二阶流体和Maxwell流体在环管内不定常旋转流运动方程的解析解,据此可以分析环管内旋转速度和切应力的分布与变化特征;流体物性参数、管道环隙大小等参量在解析公式中有明确反映,便于定性分析和讨论,本解可以为钻探工程和高分子加工工艺的设计提供理论依据,另外还可用来分析双筒粘度计的流动状态和应力特征,拟合曲线,确定材料的粘弹性参数,在对这种流体进行特性分析时,我们发现,Maxwell流体的旋转流动在起动初期表现为方波振荡,振动的幅度和周期随Ha(物质常数)的增大而增大,此种现象还是首次发现,可能对实际应用有一定的意义。     

Spatial decay bounds for time dependent magnetohydrodynamic geophysical flow

This article is concerned with spatial decay bounds for the time dependent magnetohydrodynamic geophysical flow in an infinite pipe when homogeneous lateral surface boundary conditions are applied. Assuming that the entrance velocity and magnetic field data are small enough and the fluid flow converges to laminar flow as the distance down the pipe tends to infinity, we derive a second order differential inequality that leads to an exponential decay estimate for the “energy” associated with the velocity and magnetic field represented by the difference between the entrance flow and fully developed laminar flow. We also show how to establish the explicit decay bounds for the total energy.     

纵向磁场激励下简支输流微梁的动力学行为研究

受磁场驱动的微机电系统在工作中存在着力、磁、流-固耦合等非线性特征，其力学行为非常复杂，并将影响系统运行的安全性与可靠性.该文采用非局部Euler梁模型研究磁场激励下简支输流微梁（一种微机电系统）的动力学行为，通过动力系统分支理论和谐波平衡法来考察系统的稳定性和幅频特性曲线.结果表明，可以采用改变磁场强度、流速和阻尼的三重方式调节微机电系统的频率.研究中还发现，小尺度效应和磁场强度可以影响临界流速，阻尼的存在可以改变临界流速的个数和系统的分岔类型.     

输送流体管道的固——液耦合动力学研究

根据Ｈａｍｉｌｔｏｎ原理推导输送流体管道固—液耦合振动方程，得到反对称的固—液耦合阻尼矩阵和对称的固—液耦合刚度矩阵；用ＱＲ法计算管道固有频率，给出了管道前４阶固有频率—流速曲线；讨论了流体的流速、压强变化以及固—液耦合阻尼和固—液耦合刚度对管道固有频率的影响；用Ｎｅｗｍａｒｋ法计算不同流速时管道对阶跃载荷的动力响应；发现了各阶固有频率都有随流速的提高而降低、再提高、再降低的周而复始现象·     

流体诱发水平悬臂输液管的内共振和模态转换(Ⅰ)

运用牛顿法导出水平悬臂刚性输液管的非线性动力学数学模型．为了对该模型进行理论分析,通过对各个相关实际物理量的量级定性分析,给出了模型中各个物理参数的量级．在此基础上,应用多尺度法首先得到输液管自由振动模态的特征函数,利用悬臂管的边界条件给出了特征值满足的特征方程, 发现管内流体速度可以诱发第一阶模态和第二阶模态3种形式的内共振分别是3∶1、2∶1和1∶1内共振, 从理论上解释了流速诱发水平悬臂输液管系统内共振的机理．由于3∶1内共振所对应的流速最小,因此这种形式的内共振是最先出现的,也是最重要的．     

Investigation of micropolar fluid flow in a helical pipe via asymptotic analysis

In this paper we study the flow of incompressible micropolar fluid through a pipe with helical shape. Pipe’s thickness and the helix step are considered as the small parameter ε. Using asymptotic analysis with respect to ε, the asymptotic approximation is built showing explicitly the effects of fluid microstructure and pipe’s distortion on the velocity distribution. The error estimate for the approximation is proved rigorously justifying the obtained model.     

The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions

This article examines the magnetohydrodynamic (MHD) flow of non-Newtonian nanofluid in a pipe. The temperature of the pipe is assumed to be higher than the temperature of the fluid. In particular two temperature dependent viscosity models, have been considered. The nonlinear partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by homotopy analysis method (HAM). Explicit analytical expressions for the velocity field, the temperature distribution and nano concentration have been derived analytically. The effects of various physical parameters on velocity, temperature and nano concentration are discussed by using graphical approach.     

输流粘弹性曲管的稳定性分析

根据变质量弹性系统Hamilton原理,用变分法建立了输流粘弹性曲管的运动微分方程,并用归一化幂级数法导出了输流粘弹性曲管的复特征方程组．以两端固支Kelvin-Voigt模型粘弹性输流圆管为例,分析了无量纲延滞时间和质量比对输流管道无量纲复频率和无量纲流速之间的变化关系的影响．在无量纲延滞时间较大时,粘弹性输流圆管的特点是它的第1、2、3阶模态不再耦合,而是在第1、第2阶上先发散失稳,然后在1阶模态上再发生单一模态颤振．