狭窄血管内偶应力流体流动分析

本文考察了血管狭窄对血液流动的影响,血液以偶应力流体表示,并在求解过程中采用了在管壁上流体质点无相对涡量的边界条件,结果表明,和Young的经典工作相比流动阻抗和壁切应力大于同样程度狭窄下牛顿流体的相应值,偶应力流体对狭窄的敏感性大于牛顿流体;在狭窄发展过程中,偶应力流体的流量要小于牛顿流体的流量,和牛顿流体相比,这些结果更符合生理实际。     

非牛顿流体入口收敛流动分析

本文讨论了非牛顿流体的入口收敛流动问题,考虑到粘弹性流体在流动中的粘滑行为,应用最小能原理,导出了扩展的入口收敛流边界流线方程和流体自然收敛锥角方程,并与前人的工作进行了比较和分析。     

基于分形导数对非牛顿流体层流的数值研究

非牛顿流体具有复杂的流变特性,揭示该流变特性可以更加合理地指导非牛顿流体在工农业生产中的应用.经典的非牛顿流体本构模型往往形式复杂,仅能应用于某些特定的情况.分数阶导数模型具有参数少和形式简单的特点,己成功地应用于描述非牛顿流体的运动.Hausdorff分形导数作为一个备选的建模方法,相比分数阶导数具有更简单的形式以及更高的计算效率.本文基于Hausdorff分形导数改进现有牛顿黏性模型,提出分形黏壶模型.通过研究分形黏壶在常应变率下表观黏度的变化情况,以及在加、卸载条件下的蠕变及恢复特性,发现分形黏壶模型适合于描述具有黏弹性的非牛顿流体(本文称之为分形流体).结合连续性方程及运动微分方程,推导出分形流体在平行板间层流的基本方程.按是否拖动上板和是否存在水平的压力梯度分为3种工况,分别用数值方法计算这3种工况下流速在板间的分布及其随时间变化的情况.通过分析不同工况下的流速分布,发现水平的压力梯度会改变流速随时间变化的形状,且会推迟流速到达稳定的时间.在水平压力梯度不存在的情况下,不同阶数的分形流体具有相同的流速分布或是演变过程.另外,在水平压力梯度存在的情况下,上板速度不影响不同阶数分形流体间稳定速度的差值.     

工程湍流模式理论综述及展望

本文讨论了国内外湍流模拟的现状和发展趋势．指出湍流模式的建立除了应遵循理性力学原则外,还必须密切结合工程流体的复杂流动现象,如对具有浮力的回流、分离流及强旋流的模拟,对逆梯度的输运模拟,对单相流、多相流,单流体、多流体的湍流牛顿流体及湍流的非牛顿流体的模拟．应加深对湍流机理的认识,改进湍流模拟手段,结合工程实际,提出较为通用的工程湍流模式．      

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.     

二阶流体薄膜润滑研究

针对二阶流体薄膜润滑在润滑方程中引入二阶流体和弹性变形，在考虑薄膜润滑状态下的非牛顿性和类固体性的基础上，建立了薄膜润滑的粘变数学模型，并针对线接触弹流薄膜润滑进行了数值计算．结果表明，在相同载荷下基于粘变模型计算得到的膜厚同牛顿流体相应的膜厚相比大得多，而粘变薄膜厚度同速度的相关性比牛顿流体的小得多，且粘变薄膜能够承受更大的载荷；所建立的粘变模型适用于薄膜润滑的理论计算．     

二阶非牛顿流体蠕流精确解

二阶流体是工业界常见的非牛顿流体,因为其本构关系简单而被广泛采用和研究.逆方法预先假定流场满足某类特定的物理的或几何的特性,从而求出流体运动方程的精确解.本文通过假定平面定常二阶非牛顿流体的涡量场与受到扰动的流函数相等这一特定形式,采用求解非线性微分方程常用的逆方法,推导并获得了平面二阶蠕流流场的精确解,由此容易进一步获得流场的压力.所获得的精确解包含了Poiseuille,简单Couette平行流动以及两相向流体的相互作用等流动.这些精确解为实验,数值以及渐进解的检验提供了借鉴和参考.     

填隙二阶流体下圆球平行于壁平移的粘性阻力

离散元法是分析散体力学行为的数值方法。存在填隙流体时，颗粒之间或颗粒与壁之间产生的法向挤压力和切向阻力、阻力矩，是湿颗粒离散元法的理论基础。二阶流体是以微小偏离牛顿流体本构而考虑时间影响的一种流体。它具有常粘度，并且第一和第二法向应力差正比于剪切率的平方。根据Reynolds润滑理论，采用小参数法，导出了存在填隙二阶流体时，圆球沿平行于平壁缓慢移动时流体的速度场和压力方程，进而求出切向阻力和阻力矩的解析解。有趣的是在推导时所得的速度场和压力方程形式比牛顿流体要复杂得多，但最终结果表明圆球沿平行于平壁移动时因填隙二阶流体引起的切向阻力和阻力矩与牛顿流体时的结果相同。     

基于舌/上颚微间隙下流体流动行为研究

为探讨口腔环境下流体的流动行为，采用数值方法与流变试验深入研究舌/上颚微间隙下流体流量的影响因素. 建立舌/上颚微间隙的简化模型及Reynolds方程，通过数值方法获取微间隙下流量变化；在DHR-2流变仪上研究非牛顿流体的黏度与剪切率的变化，探讨牛顿流体和非牛顿流体的流量影响. 结果表明:牛顿流体流量平方的倒数同载荷和黏度比值和时间均呈线性函数关系；所制备的非牛顿流体近似为幂律流体，其黏度随脂肪含量的增加而增大，而非牛顿流体流量率先高于后低于等效牛顿流体，其研究结果将为特定人群功能产品的研发提供技术支持.      

纤维悬浮液搅拌流动的数值模拟

由于缺乏适当的本构方程，对纤维悬浮液流动的研究一直局限于纤维的牛顿流体悬浮液。本文采用ＭＵＣＭ模型对作者最近提出的纤维Ｏｌｄｒｏｙｄ－Ｂ流体悬浮液的本构方程作了改进，并对锚式桨搅拌槽的二维Ｏｌｄｒｏｙｄ－Ｂ流体和牛顿流体纤维悬浮液搅拌流动作了数值模拟。模拟的结果表明，本文所用的模型和方法能有效地抑制过大局部应力的影响并合理地处理流体的记忆效应。     

A remark on similarity analysis of boundary layer equations of a class of non-Newtonian fluids

A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluid in which the stress, an arbitrary function of rates of strain, is studied. It is shown that under any group of transformation, for an arbitrary stress function, not all non-Newtonian fluids possess a similarity solution for the flow past a wedge inclined at arbitrary angle except Ostwald-de-Waele power-law fluid. Further it is observed, for non-Newtonian fluids of any model only $90°$ of wedge flow leads to similarity solutions. Our results contain a correction to some flaws in Pakdemirli׳s [14] (1994) paper on similarity analysis of boundary layer equations of a class of non-Newtonian fluids.     

Moving wedge and flat plate in a power-law fluid

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a moving wedge in a moving fluid is studied in this paper. The transformed boundary-layer equation is solved numerically for some values of the involved parameters. The effects of these parameters on the skin friction coefficient are analyzed and discussed. It is found that multiple solutions exist when the wedge and the fluid move in the opposite directions, near the region of separation. It is also found that the drag force is reduced for dilatant fluids compared to pseudo-plastic fluids.     

GPU accelerated simulations of three-dimensional flow of power-law fluids in a driven cube

Newtonian fluid flow in two- and three-dimensional cavities with a moving wall has been studied extensively in a number of previous works. However, relatively a fewer number of studies have considered the motion of non-Newtonian fluids such as shear thinning and shear thickening power law fluids. In this paper, we have simulated the three-dimensional, non-Newtonian flow of a power law fluid in a cubic cavity driven by shear from the top wall. We have used an in-house developed fractional step code, implemented on a Graphics Processor Unit. Three Reynolds numbers have been studied with power law index set to 0.5, 1.0 and 1.5. The flow patterns, viscosity distributions and velocity profiles are presented for Reynolds numbers of 100, 400 and 1000. All three Reynolds numbers are found to yield steady state flows. Tabulated values of velocity are given for the nine cases studied, including the Newtonian cases.     

Evaluation of unsteadiness in effervescent sprays by analysis of droplet arrival statistics - The influence of fluids properties and atomizer internal design

The ideal spray theory of Edwards and Marx was used to investigate the dependence of effervescent spray unsteadiness on fluid properties and atomizer internal design. Results demonstrate that fluid properties and internal design of atomizer directly affect the two-phase flow pattern inside the atomizer which consequently affects the spray unsteadiness of the atomizer. Water sprays are more unsteady when the air to liquid ratio (ALR) increases, whereas, more unsteady is observed for using glycerol/water mixture (high-viscosity Newtonian fluid) or glycerol/water/xanthan (non-Newtonian fluid) mixture as ALR reduces. In addition, sprays using low-viscosity or strong non-Newtonian fluids usually are more unsteady, regardless of ALR.A short mixing chamber results in less unsteady for water but has no effect on spray unsteadiness for high-viscosity or non-Newtonian fluids at ALR of 0.15. Otherwise, the influence of mixing chamber distance on the spray quality is weak at ALR of 0.15. Large diameter of inclined aeration holes shows the low spray unsteadiness and good spray quality for water but causes more unsteady for glycerol/water/xanthan mixture at ALR of 0.15. Furthermore, the diameter of the inclined aeration holes has little influence on spray unsteadiness for glycerol/water mixture. Spray unsteadiness and quality are not affected by the angle of aeration holes for three fluids at ALR of 0.15.     

Extended thermodynamics of a non-Newtonian fluid

Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.     

Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media

Numerical analysis of the free convection coupled heat and mass transfer is presented for non-Newtonian power-law fluids with the yield stress flowing over a two-dimensional or axisymmetric body of an arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by the similarity transformation. The resulting system of equations is solved by a finite difference method. The parameters studied are the rheological constants, the buoyancy ratio, and the Lewis number. Representative velocity, temperature, and concentration profiles are presented and discussed. It is found that the results depend strongly on the values of the yield stress parameter and the power-law index of the non-Newtonian fluid.     

Natural convection of non-Newtonian power-law fluid over axisymmetric and two-dimensional bodies of arbitrary shape in fluid-saturated porous media

Numerical analysis of the free convection coupled heat and mass transfer is presented for non-Newtonian power-law fluids with the yield stress flowing over a two-dimensional or axisymmetric body of an arbitrary shape in a fluid-saturated porous medium. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by the similarity transformation. The resulting system of equations is solved by a finite difference method. The parameters studied are the rheological constants, the buoyancy ratio, and the Lewis number. Representative velocity, temperature, and concentration profiles are presented and discussed. It is found that the results depend strongly on the values of the yield stress parameter and the power-law index of the non-Newtonian fluid.     

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.     

A study on non-steady flow of upper-convected maxwell fluid in tube

The transient response of an upper-convected Maxwell fluid flow in a circular tube is analysed by variational approach of Kantorovich and the method of finite difference. The solution of the variational method is in agreement with the numerical results by the difference schemes. The results show that the method of Kantorovich is suitable for the study of non-steady flow of non-Newtonian fluids and the effect of elasticity of the fluid has an influence on the non-steady flow. project supported by National Natural Science Foundation of China