粘弹性流体的入口收敛流动

本文以聚合物流体为研究对象,对其在入口收敛流动中产生的粘弹效应及机理进行了初步的讨论和分析,并就近10年来国内外有关粘弹性流体入口流动研究及进展作了简要的评述。      

粘弹流体轴对称流动的格子Boltzmann方法

基于BGK碰撞模型，通过在迁移方程中引入作用力项，建立了粘弹流体的轴对称格子Boltzmann模型．通过Chapman-Enskog展开，获得了准确的柱坐标下轴对称宏观流动方程．采用双分布函数对运动方程和本构方程进行迭代求解，模拟分析了粘弹流体管道流动，获得了流场中的速度和构型张量的分布，通过与解析解进行比较，验证了模型的准确性．研究了作为粘弹流体流动基准问题的收敛流动，对涡旋位置进行了定量分析，将回转长度的计算结果与有限体积法进行了比较，两种数值结果十分吻合．研究结果表明，模型能够准确表征粘弹流体的轴对称流动，具有较广阔的应用前景．     

黏弹流体流动的数值模拟研究进展

综述了黏弹流体流动数值模拟的研究进展,突出介绍近十年来有限元法在黏弹流体流动数值模拟研究中取得的成果,通过动量方程的适当变形和本构方程离散权函数的合理选择,可以显著增强数值计算的稳定性。得到较高Weissenberg数下的解,同时文中对黏弹流体流动数值模拟中本构方程的应用、非等温情况和三维空间下的研究进行了介绍。     

配置点谱方法-人工压缩法(SCM-ACM)求解同心圆筒内流体流动

发展了配置点谱方法SCM(Spectral collocation method)和人工压缩法ACM(Artificial compressibility method)相结合的SCM-ACM数值方法,计算了柱坐标系下稳态不可压缩流动N-S方程组。选取典型的同心圆筒间旋转流动Taylor-Couette流作为测试对象,首先,采用人工压缩法获得人工压缩格式的非稳态可压缩流动控制方程;再将控制方程中的空间偏微分项用配置点谱方法进行离散,得到矩阵形式的代数方程;编写了SCM-ACM求解不可压缩流动问题的程序;最后,通过与公开发表的Taylor-Couette流的计算结果对比,验证了求解程序的有效性。结果证明,本文发展的SCM-ACM数值方法能够用于求解圆筒内不可压缩流体流动问题,该方法既保留了谱方法指数收敛的特性,也具有ACM形式简单和易于实施的特点。本文发展的SCM-ACM数值方法为求解柱坐标下不可压缩流体流动问题提供了一种新的选择。     

具有壁面射流激励的圆管内气相流动大涡模拟

采用大涡模拟方法和单方程亚格子模式对小尺度量进行模拟。研究了不同强度壁面射流激励对圆管内气相流动的影响,模拟结果给出了射流对瞬态拟序结构发展、时平均流向速度分布的影响。随着射流强度的增加,射流入口附近流体的回流现象增强。射流强度足够大时可以减小管壁处的切应力值,同时会减小壁面附近流动速度,这种速度分布会导致气体夹带颗粒的能力下降,从而在实际两相流动中容易造成壁面附近的气粒返混现象。     

微纳米结构壁面对流场及动压润滑的影响研究

固体边界具有的微纳米结构将影响流体在近壁面处的流动行为,进而由于尺度效应改变流体在整个微间隙的流动或润滑规律.将壁面可渗透微纳米结构等效为多孔介质薄膜,采用Brinkman方程来描述流体在近壁面边界渗透层内的流动,并将其与自由流动区域的不可压缩流体Navier-Stokes控制方程耦合,在界面处的连续边界条件下求解和分析了速度分布规律和压力变化规律.针对恒定法向承载力的油膜润滑条件,进一步讨论了静止表面或运动表面的微纳米结构对近壁面流动行为的影响;并揭示了考虑壁面微纳米结构的流体动压润滑的油膜厚度和摩擦系数的变化规律.论文结果为具有可渗透微结构表面的微间隙流动与润滑提供了理论参考.     

广义Maxwell黏弹性流体在两平板间的非定常流动

将分数阶微积分运算引入Maxwell黏弹性流体的本构方程，研究了黏弹性流体在两平板问的非定常流动．对于广义Maxwell黏弹性流体的分数阶导数模型，导出了对时间具有分数阶导数的特殊运动方程，利用分数阶微积分的Laplace变换理论，得到了流动的解析解．     

可记录光盘染料旋涂工艺的流动机制研究

染料旋涂是可记录光盘复制中的核心工艺，依据实验给出旋涂工艺的简化模型，并运用旋转圆盘理论分析流体流动，考虑基片上的预刻槽对流动的影响，考虑基片表面和流体间的滑移效应，导出运动方程、边界方程和连续方程，最终导出染料旋涂的控制方程。     

基于格子Boltzmann两相模型的粘弹流体挤出胀大分析

挤出胀大的数值模拟是非牛顿流体研究中具有挑战性的问题．本文运用格子Boltzmann方法(LBM)分析Oldroyd-B和多阶松弛谱PTT粘弹流体的挤出胀大现象，采用颜色模型模拟出口处粘弹流体和空气的两相流动，通过重新标色获得两种流体的界面，并最终获得胀大的形状．Navier-Stokes方程和本构方程的求解采用双分布函数模型．将胀大的结果与解析解、实验解和单相自由面LBM结果进行了比较，发现格子Boltzmann两相模型结果与解析解和实验结果相吻合，相比于单相模型，收敛速度更快，解的稳定性更高．研究了流道尺寸对胀大率的影响，并对挤出胀大的内在机理进行了分析．     

两相混合流体的非线性本构理论

本文从连续介质力学的基本原理出发,建立了微极流体与经典流体两相流动的非线性扩散理论。给出了混合流体本构方程的一般形式。对单相流体、单相微极流体及稀悬浮体三种特殊情形,得到了具体形式的二阶非线性本构方程,并同已有的理论进行了比较。     

Two-dimensional viscoelastic flows: experimentation and modeling

Extensive experimental data on the birefringence in converging and diverging flows of a polymeric melt have been obtained. The birefringence and pressure drop measurements were carried out in working cells of planar geometry having different contraction angles and contraction ratios. For investigation of diverging or abrupt expansion flow, the direction of flow in the cells was reversed. The theoretical predictions are based upon the Leonov constitutive equation and a finite element scheme with streamwise integration.In contrast to Newtonian and second-order fluids, viscoelastic fluids at high shear rates show significant differences in pressure drop and birefringence (i.e. stresses) in converging and diverging flows. For a constant flow rate, the pressure drop is higher and the birefringence smaller in diverging flows than in converging flows. This difference increases with increasing flow rate. Further, for the same contraction ratio but different contraction angles, the birefringence maximum increases considerably with contraction angle. In addition, an increase in contraction ratio has the same effect.The viscoelastic constitutive equation of Leonov has been shown to describe all the above viscoelastic effects observed in the experiments. In general, a reasonable agreement between theory and experiment has been obtained, which shows the usefulness of the Leonov model in describing actual flows.     

A boundary integral equation method for Navier-Stokes equations—application to flow in annulus of eccentric cylinders

A novel Navier-Stokes solver based on the boundary integral equation method is presented. The solver can be used to obtain flow solutions in arbitrary 2D geometries with modest computational effort. The vorticity transport equation is modelled as a modified Helmholtz equation with the wave number dependent on the flow Reynolds number. The non-linear inertial terms partly manifest themselves as volume vorticity sources which are computed iteratively by tracking flow trajectories. The integral equation representations of the Helmholtz equation for vorticity and Poisson equation for streamfunction are solved directly for the unknown vorticity boundary conditions. Rapid computation of the flow and vorticity field in the volume at each iteration level is achieved by precomputing the influence coefficient matrices. The pressure field can be extracted from the converged streamfunction and vorticity fields. The solver is validated by considering flow in a converging channel (Hamel flow). The solver is then applied to flow in the annulus of eccentric cylinders. Results are presented for various Reynolds numbers and compared with the literature.     

磁流体压缩管道热电磁流动特性研究

利用磁流体五波模型对低磁雷诺数下压缩管道中磁流体流动进行数值模拟。该模型由带有电磁作用强制项的Navier-Stokes方程组与电势Poisson方程组成,数值格式分别采用严格保证熵条件的熵条件格式和中心差分格式。数值模拟对不同磁作用数下的不同几何外形管道进行数值模拟研究,结果表明在磁流体压缩管道中,由于发生器模式提取...     

Solution of the Chaplygin equation in plane-parallel transonic flow with a normal shock

In [1], for the case in which the exact Chaplygin equation of motion is replaced by the Tricomi equation, Frankl constructed an example of plane-parallel transonic flow with a normal shock terminating within the flow (later this example was extended by Biibosunov to obtain a curved shock [2]). This flow is an analog of the point vortex flow and has concentric circles as streamlines, and a unique dependence of the velocity vector on the Cartesian coordinates is provided everywhere. In the present paper this example is extended to the case of the Chaplygin equation, and the shock is considered to be normal.The author wishes to thank S. V. Fal'kovich for discussion of the study results and helpful advice.     

An exact analytical solution of the unsteady magnetohydrodynamics nonlinear dynamics of laminar boundary layer due to an impulsively linear stretching sheet

In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.     

Ethanol–CO2 two-phase flow in diverging and converging microchannels

The present study investigates experimentally two-phase flow patterns and pressure drop of ethanol and CO₂ in a converging or diverging rectangular microchannel. The two-phase flow pattern visualization is made possible using a high speed video camera. The increased superficial gas velocity due to the acceleration effect and the large pressure drop in a converging channel may result in the elongation of bubbles in slug flow, while the decreased superficial velocity owing to the deceleration effect and the possible pressure rise in the diverging channel may cause shortening of bubbles in slug flow significantly. For both types of channel, the collision and merger of two consecutive bubbles may take place and result in necking of bubbles. Two-phase flow pressure drop in the converging microchannel increases approximately linearly with the increasing liquid or gas flow rate with the frictional pressure drop being the major contributor to the channel pressure drop. In the diverging microchannel, the deceleration effect results in the pressure rise and counteracts the frictional pressure drop. Consequently, for low liquid flow rates the channel pressure drop increases only slightly with the gas flow rate while it is low and a reversed trend appears while it is high. For high liquid flow rates the effect of increasing gas flow rate on channel pressure drop is much more significant; a more significant reverse trend of the effect of gas flow rate is present in the region of high gas flow rates. The two-phase frictional multiplier in the converging or diverging microchannel is quite insensitive to the liquid flow rate and can be fitted very well within ±15% based on the Lockhart–Martinelli equation with a modified Chisholm parameter for the diverging microchannel and together with a modified coefficient for the X⁻² term for the converging microchannel.     

Experimental and numerical study of entry flow of low-density polyethylene melts

The present work deals with experimental and numerical features of entry flows of two polyethylene melts, namely a linear low-density polyethylene (LLDPE) and a low-density polyethylene (LDPE) in an axisymmetric converging geometry. The study also involves rheological characterization of the polymers and determination of flow parameters, at 160°C. For both fluids, the data are fed into a viscoelastic integral Wagner constitutive equation. The numerical flow simulations are performed by using a stream-tube mapping analysis. Consideration of a sub-domain of the total flow domain, the peripheral stream tube, close to the wall of the converging duct permits to relate the results of the numerical simulation to experimental flow characteristics as total and entrance pressure drops. The agreement is good for the total pressure losses, but, concerning LDPE, a lack of consistency remains for the entrance pressure drop.     

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悬浮液中纤维的运动和旋转行为在许多现代工业领域都非常重要. Jeffery解析得到 了牛顿流中椭球型纤维的动力学演化方程,但方程只有在平面简单剪切和拉伸流的条 件下才有解析解. 采用数值求解时,由于方程中$\cot \theta $的存在会出现奇异性. 采用随体坐标的方法,消除了方程的奇异性,算法的有效性通过与解析解的比较得到了 验证,并为复杂流场下纤维的动力学数值计算提供了一个可行的方法.     

On the case when steady converging/diverging flow of a non-Newtonian fluid in a round cone permits an exact solution

This communication considers the steady converging/diverging flow of a non-Newtonian viscous power-law fluid in a round cone. The motion is driven by a sink/source of mass at the origin. It is shown that the problem permits exact similarity solution for a particular value (n=4/3) of the fluid index. In this case a complete set of governing equations can be reduced to an ordinary differential equation, which is solved numerically for different values of the main non-dimensional parameters (the cone angle and the dimensionless sink/source intensity).     

Remarks on the numerical solution of the adjoint quasi‐one‐dimensional Euler equations

We examine the numerical solution of the adjoint quasi‐one‐dimensional Euler equations with a central‐difference finite volume scheme with Jameson‐Schmidt‐Turkel (JST) dissipation, for both the continuous and discrete approaches. First, the complete formulations and discretization of the quasi‐one‐dimensional Euler equations and the continuous adjoint equation and its counterpart, the discrete adjoint equation, are reviewed. The differences between the continuous and discrete boundary conditions are also explored. Second, numerical testing is carried out on a symmetric converging–diverging duct under subsonic flow conditions. This analysis reveals that the discrete adjoint scheme, while being manifestly less accurate than the continuous approach, gives nevertheless more accurate flow sensitivities. Copyright © 2011 John Wiley & Sons, Ltd.