固壁近旁Stokes流中粘性液滴的运动和变形

发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示,由于环境流动和浮力的作用,随着时间的推进,液滴在轴向压缩,在径向拉伸．当环境流动的作用弱于浮力作用时,随着时间的推移,液滴上升并向上弯,固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时,随着时间的推移,液滴变得越来越扁．在这种情形,当大初始间距时,壁面上的应力随液滴的演变而增大;当小初始间距时,由环境流动、浮力及壁面对流动的较强作用的联合影响,此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内,且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．     

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a “torpedo” shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour.     

Structure and rheological properties of polymers

The viscoelastic properties of linear flexible-chain polymers with a narrow distribution, for which M > 5M_c (M_c corresponds to the formation of a three-dimensional entanglement network), their mixtures, and concentrated solutions are examined. It is established that under the influence of deformation the polymer may undergo a transition to the rubbery state, which thus defines the limit of its flow state; this transition is also observed in mixtures and concentrated solutions of high-molecular-weight polymers with a narrow distribution. The relative simplicity of the rheological properties of linear high-molecular-weight polymers and their mixtures is determined by the sharpness of the transition to the rubbery state. It has been found that in mixtures of high-molecular-weight polymers the apparent viscosity mechanism associated with a decrease in dissipative losses on transition of the high-molecular-weight components to the rubbery state is dominant; on a broad range of molecular weights (M > M_c), and moreover for polymer solutions, the decrease in entanglement network density under the influence of deformation acquires considerable importance. It is established that the separate effect of the high-molecular-weight components on the viscoelastic properties of their mixtures contradicts the idea of a random network of macromolecular chains. Attention is drawn to the temperature dependence of the viscosity of polymers with a narrow distribution and the dynamic properties of their mixtures. Problems of theoretical and practical interest associated with the particular rheological properties of polymer systems at high deformation rates are defined.     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．     

Dynamic responses of shear flows over a deformable porous surface layer in a cylindrical tube

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy’s law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin’s algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.     

壁面效应对剪切稀化流体内气泡上浮特性的影响

数值研究了壁面效应对剪切稀化流体内气泡上浮运动特性的影响,气液两相的界面捕捉采用流体体积(VOF)法,剪切稀化流体流变特性和气液相间表面张力的计算分别采用Carreau模型和连续表面张力模型.详细研究了不同流变指数下,壁面效应对气泡形状、液相流场和气泡终端速度的影响.结果表明,强的壁面效应或弱的剪切稀化程度会限制气泡的变形和尾涡的形成,使气泡的终端速度减小;气泡终端速度最易受壁面效应的影响;强的壁面效应和强的剪切稀化程度会导致高剪切速率区域出现在壁面附近,引起壁面附近液相表观黏度大幅度的下降.     

Model Equations for Turbulent Shear Flow

A set of model equations for the calculation of turbulent shear flows is presented. It is shown how the equations can be modified to allow for the inclusion of viscosity, compressibility and density variations. Some results of numerical computations are given. The constant in the law of the wall is predicted to within 10% for flow over a perfectly smooth wall, and a dependence on wall roughness is obtained. The empirical law of the wall for compressible flow is also shown to be a consequence of the equations.     

The wall jet flow of a conducting gas over a permeable surface in the presence of a variable transverse magnetic field

The effects of the magnetic field, Mach number and the permeability parameter on the wall jet flow (radial or plane) of an electrically conducting gas spreading over a permeable surface have been investigated. Taking the Prandtl number of the fluid as unity and assuming a linear relationship between viscosity and temperature, it is found that similar solutions for the velocity distribution exist for a specified distribution of the normal velocity along the wall and the corresponding distribution of the transverse magnetic field. Previous non-magnetic flow results have been improved by adopting a new and simple transformation of variables.     

Transonic viscous inviscid interactions in narrow channels

Unsteady as well as steady transonic flows through channels which are so narrow that the classical boundary layer approach fails are considered. As a consequence the properties of the inviscid core and the viscosity dominated boundary layer region can no longer be determined in subsequent steps but have to be calculated simultaneously. The resulting interaction problem for laminar flows is formulated for both perfect and dense gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes one-dimensional in the leading order approximation. The latter allows an interpretation of the flow in the core region by means of the theory of one-dimensional transonic inviscid flow through a Laval nozzle while preserving the essential features of the interaction problem associated with the internal structure of pseudoshocks. The sensitivity of a separation bubble caused by a pseudoshock of sufficient strength to perturbations under the condition of choked flow will be demonstrated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local Interaction Theory for Laminar Transonic Flows in Slender Channels

Transonic flows through channels so narrow that the classical boundary layer approach fails are considered. As a consequence the properties of the inviscid core and the viscosity dominated boundary layer region can no longer be determined in subsequent steps but have to be calculated simultaneously. The resulting viscous inviscid interaction problem for weakly three dimensional laminar flows is formulated for perfect gases under the requirement that the channel is sufficiently narrow so that the flow outside the viscous wall layers becomes planar in the leading order approximation. Representative solutions for subsonic as well as for supersonic flows disturbed by three dimensional surface mounted obstacles will be presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force Using a Lattice Boltzmann Fictitious Domain Method

Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs, which motivates us to model the sedimentation of red blood cell (RBC) under strong external magnetic body force. To model the sedimentation of a RBC in a square duct and a circular pipe, a recently developed technique derived from the lattice Boltzmann and the distributed Lagrange multiplier/fictitious domain methods (LBM-DLM/FD) is extended to employ the mesoscopic network model for simulations of the sedimentation of a RBC in flow. The flow is simulated by the LBM with a strong magnetic body force, while the network model is used for modeling RBC deformation. The fluid-RBC interactions are enforced by the Lagrange multiplier. The sedimentation of RBC in a square duct and a circular pipe is simulated, which demonstrates the developed method's capability to model the sedimentation of RBCs in various flows. Numerical results illustrate that the terminal settling velocity increases incrementally with the exerted body force. The deformation of RBC has a significant effect on the terminal settling velocity due to the change in the frontal area. The larger the exerted force, the smaller the frontal area and the larger the RBC deformation become. Additionally, the wall effect on the motion and deformation of RBC is also investigated.     

Mathematical modelling of flows in recessed wall flame holder

A finite difference procedure has been employed to predict the flow situation in a recessed wall flame holder with and without combustion. Turbulence has been modelled by an ad hoc effective viscosity law. A single step chemical reaction has been assumed in dealing with the flows involving combustion. The predicted physical parameters have been compared with the experimental results. It has been argued that with the simplifying assumptions on turbulence and chemical kinetics the numerical procedure is adequately accurate to predict the important design parameters such as flame length and blow-off velocity. However, there are significant discrepancies between the predicted and measured distribution of velocity and temperature which could be attributed mainly to the inadequate turbulence modelling.     

Derivation of an adjoint high-Reynolds number model for thermally driven flows

This paper presents a high-Reynolds number (high-Re) approach to the adjoint Navier-Stokes-Fourier equations based upon modified high-Re boundary conditions for buoyancy-driven flows. For reasons of efficiency, the computational framework adheres to the continuous adjoint method using a frozen-turbulence assumption. Opposed to the state of the art, the present model uses a high-Re model for the primal equations and a high-Re model for the adjoint equations. The adjoint high-Re model can easily be implemented and be used for flow problems where wall functions are needed. The impact of this approach is an improved consistency of primal and adjoint equations which leads to stable and realistic shape optimisation results for industrial flows. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remarks on the solvability of transonic flow problems

The paper is devoted to the study of the viscosity method and upwinding in the transonic flow problems. We weaken the conditions from [6,7] under which we can obtain a nonviscous compressible transonic flow as a limit of viscous solutions, if the viscosity and heat conductivity tend to zero. Further, we give the justification of the density upwinding applied often in the calculation of transonic potential flows.     

First stages of drop impact on a dry surface: asymptotic model

After impact of a viscous liquid drop on a dry wall surrounded by a gas, the drop surface is highly deformed, leading to the formation of an axisymmetrical lateral lamella along the wall. A local asymptotic model for the potential flow and unsteady boundary layer flow is developed to describe the lamella dynamics at early stages after impact. The second-order potential flow displaced by the unsteady boundary layer is taken into account. The lamella shape, its velocity and pressure are calculated with this model in parametrical forms. The three model parameters are evaluated here by fitting with recent experimental findings.     

On Fully Developed Flows of Fluids with a Pressure Dependent Viscosity in a Pipe

Stokes recognized that the viscosity of a fluid can depend on the normal stress and that in certain flows such as flows in a pipe or in channels under normal conditions, this dependence can be neglected. However, there are many other flows, which have technological significance, where the dependence of the viscosity on the pressure cannot be neglected. Numerous experimental studies have unequivocally shown that the viscosity depends on the pressure, and that this dependence can be quite strong, depending on the flow conditions. However, there have been few analytical studies that address the flows of such fluids despite their relevance to technological applications such as elastohydrodynamics. Here, we study the flow of such fluids in a pipe under sufficiently high pressures wherein the viscosity depends on the pressure, and establish an explicit exact solution for the problem. Unlike the classical Navier-Stokes solution, we find the solutions can exhibit a structure that varies all the way from a plug-like flow to a sharp profile that is essentially two intersecting lines (like a rotated V). We also show that unlike in the case of a Navier-Stokes fluid, the pressure depends both on the radial and the axial coordinates of the pipe, logarithmically in the radial coordinate and exponentially in the axial coordinate. Exact solutions such as those established in this paper serve a dual purpose, not only do they offer solutions that are transparent and provide the solution to a specific but simple boundary value problems, but they can be used also to test complex numerical schemes used to study technologically significant problems.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel

The problem of fully-developed laminar free-convection flow in a vertical channel is studied analytically with one region filled with micropolar fluid and the other region with a viscous fluid. Using the boundary and interface conditions proposed by previous investigators, analytical expressions for linear velocity, micro-rotation velocity and temperature have been obtained. Numerical results are presented graphically for the distribution of velocity, micro-rotation velocity and temperature fields for varying physical parameters such as the ratio of Grashof number to Reynolds number, viscosity ratio, width ratio, conductivity ratio and micropolar fluid material parameter. It is found that the effect of the micropolar fluid material parameter suppress the velocity whereas it enhances the micro-rotation velocity. The effect of the ratio of Grashof number to Reynolds number is found to enhance both the linear velocity and the micro-rotation velocity. The effects of the width ratio and the conductivity ratio are found to enhance the temperature distribution.     

Surfactant-driven instability in two-fluid pipe and channel flows

Recent work on the stability of two-layer channel flow, with either smooth or corrugated walls, and core-annular flow is discussed with the emphasis on the potentially destabilising effect of an insoluble surfactant. Linearised normal mode analyses are conducted to identify unstable parametric conditions, and these are followed up by computer simulations which confirm the linear results and, furthermore, reveal a rich array of dynamical behaviour in the nonlinear regime. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)