Effects of Navier slip on unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions

A study on the effects of Navier slip, in conjunction with other flow parameters, on unsteady flow of reactive variable viscosity third-grade fluid through a porous saturated medium with asymmetric convective boundary conditions is presented. The channel walls are assumed to be subjected to asymmetric convective heat exchange with the ambient, and exothermic chemical reactions take place within the flow system. The heat exchange with the ambient obeys Newton's law of cooling. The coupled equations, arising from the law of conservation of momentum and the first law of thermodynamics, then the derived system are nondimensionalised and solved using a semi-implicit finite difference scheme. The lower wall slip parameter is observed to increase the fluid velocity profiles, whereas the upper wall slip parameter retards them because of backflow at the upper channel wall. Heat production in the fluid is seen to increase with the slip parameters. The wall shear stress increases with the slip parameters while the wall heat transfer rate is largely unaltered by the lower wall slip parameter but marginally increased by the upper wall slip parameter.     

Thermodynamic analysis for a third grade fluid through a vertical channel with internal heat generation

This paper makes the thermodynamic analysis in forced convective flow of a third grade fluid through a vertical channel. Due to the reactive nature of the fluid, the effect of internal heat generation is considered and assumed to be a linear function of temperature. The coupled nonlinear dimensionless ordinary differential equations governing the fluid flow are solved by using the Adomian decomposition method(ADM). The effects of various physical parameters such as third grade material parameter, buoyancy parameter and heat generation parameter on the thermal structure of flow are presented and discussed.     

Natural convective heat transfer and nanofluid flow in a cavity with top wavy wall and corner heater

A numerical analysis of natural convection of nanofluid in a wavy-walled enclosure with an isothermal corner heater has been carried out. The cavity is heated from the left bottom corner and cooled from the top wavy wall while the rest walls are adiabatic. Mathematical model has been formulated using the single-phase nanofluid approach. Main efforts have been focused on the effects of the dimensionless time, Rayleigh number, undulation number, nanoparticle volume fraction and length of corner heaters on the fluid flow and heat transfer inside the cavity. Numerical results have been presented in the form of streamlines, isotherms, velocity and temperature profiles, local and average Nusselt numbers. It has been found that nanoparticle volume fraction essentially affects both fluid flow and heat transfer while undulation number changes significantly only the heat transfer rate.     

3-D numerical investigation of the wall-bounded concentric annulus flow around a cylindrical body with a special array of cylinders

Concentric annulus flow around a combinational cylindrical body with a special array of cylinders at five high Reynolds numbers is investigated numerically using Fluent 6.3.26 in this paper. The numerical results show a good agreement with the experimental data in regard to the axial velocity of the flow. This study focuses on the flow structure and the hydrodynamic characteristics based on the velocity distribution, the pressure distribution, streamlines and vectors under 1-D, 2-D and 3-D conditions. Meanwhile, some global parameters including the pressure coefficient, the drag coefficient and the lift coefficient are analyzed. Numerical results show that the high velocity region and the reverse wake zone with low velocity exist in some spaces due to the disturbance of the cylindrical body. Negative pressures appear in some regions. Neither a wide area vortex nor the vortex shedding appears in the wall-bounded domain. The drag along the axial direction is the main force acting on the cylindrical body in the pipe domain. The annulus flow around the cylindrical body is analyzed to reveal the hydrodynamic characteristics of the complex turbulent concentric annulus flow field due to the multi-effects in the pipeline.     

高粘幂律非牛顿流体在管内流动和传热的计算

本文的数值研究考虑了变物性,自然对流和粘性耗散的影响,采用SIMPLE方法进行数值求解,计算结果与实验值吻合很好,流场和温度场耦合,使进口段大大延长,计算结果还显示了高粘物系加热时径向温差很大。     

粘弹性流体平面收缩流动的数值模拟

在石油、化工、轻纺和材料等工业中，有大量粘弹性液体的流动问题。如原油升举过程和管道输送中的流动；聚合物溶液和纸浆的流动等。由于粘弹性具有复杂的流变性，实验模拟和解析求解都较困难，随着计算机和计算流体力学的发展，粘弹性流体流动的数值研究日益活跃，成为非牛顿流体研究的一个重要方向。粘弹性流体运动数值模拟的主要困难在于：当Ｒｅｙｎｏｌｄｓ数和Ｗｅｉｓｓｅｎｂｅｒｇ数达到一定值以后，方程组在求解域内是混合型的，既有椭圆型区又有双曲型区［１］，已有数值计算方法只是得到小Ｒｅ数（Ｒｅ≤８）和小Ｗｅｉｓｓｅｎｂｅｒｓ数（Ｗｅ≤０．４）的结果［２］，因此，探讨这类问题的数值方法有重要的实用意义。本文在二维Ｍａｘｗｅｌｌ流体控制方程组类型分析基础上，采用类型相关格式求解原始变量方程，对粘弹性流体二维流动进行了数值模拟，得到收缩通道在Ｒｅ＝０～２０００和Ｗｅ＝０～０．８的流动结果。和已有算例比较，扩大了线性粘弹性流体的可计算范围，为进一步研究粘弹性流体三维流动的数值方法打下了基础。     

Electro-osmotic flow of a second-grade fluid in a porous microchannel subject to an AC electric field

Studies on electro-osmotic flows of various types of fluids in microchannel are of great importance owing to their multifold applications in the transport of liquids, particularly when the ionized liquid flows with respect to a charged surface in the presence of an external electric field. In the case of viscoelastic fluids, the volumetric flow rate differs significantly from that of Newtonian fluids, even when the flow takes place under the same pressure gradient and the same electric field. With this end in view, this paper is devoted to a study concerning the flow pattern of an electro-osmotic flow in a porous microchannel, which is under the action of an alternating electric field. The influence of various rheological and electro-osmotic parameters, e.g., the Reynolds number, Debye-Huckel parameter, shape factor and fluid viscoelasticity on the kinematics of the fluid, has been investigated for a secondgrade viscoelastic fluid. The problem is first treated by using analytical methods, but the quantitative estimates are obtained numerically with the help of the software MATHEMATICA. The results presented here are applicable to the cases where the channel height is much greater than the thickness of the electrical double layer comprising the Stern and diffuse layers. The study reveals that a larger value of the Debye-Huckel parameter creates sharper profile near the wall and also that the velocity of electro-osmotic flow increases as the permeability of the porous microchannel is enhanced. The study further shows that the electro-osmotic flow dominates at lower values of Reynolds number. The results presented here will be quite useful to validate the observations of experimental investigations on the characteristics of electro-osmotic flows and also the results of complex numerical models that are necessary to deal with more realistic situations, where electro-osmotic flows come into the picture, as in blood flow in the micro-circulatory system subject to an electric field.     

Irreversibility analysis of unsteady couette flow with variable viscosity

This paper investigates numerically the inherent irreversibility in unsteady generalized Couette flow between two parallel plates with variable viscosity. The nonlinear governing equations are derived from the Navier-Stokes equations and solved numerically using a semi-discretization finite difference method together with the Runge-Kutta-Fehlberg integration scheme. The profiles of velocity and the temperature obtained are used to compute the entropy generation number, Bejan number, skin friction and Nusselt number. The effects of embedded parameters on entire flow structure are presented graphically and discussed quantitatively.     

Stability of fluid flow in a Brinkman porous medium–A numerical study

The stability of fluid flow in a horizontal layer of Brinkman porous medium with fluid viscosity different from effective viscosity is investigated. A modified Orr-Sommerfeld equation is derived and solved numerically using the Chebyshev collocation method. The critical Reynolds number cRe, the critical wave number αc and the critical wave speed cc are computed for various values of porous parameter and ratio of viscosities. Based on these parameters, the stability characteristics of the system are discussed in detail. Streamlines are presented for selected values of parameters at their critical state.     

Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium

Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-point boundary value problem is reduced to a system of coupled, highly nonlinear ordinary differential equations, which are solved subject to robust surface and free stream boundary conditions with the MAPLE 17 numerical quadrature software. Validation with earlier non-rotating studies is included, and also further verification of rotating solutions is achieved with a variational finite element method(FEM). The rotational(spin) parameter emerges as an inverse function of the Grashof number. The influence of this parameter, primary Darcy number, secondary Darcy number and Prandtl number on tangential velocity and swirl velocity, temperature and heat transfer rate are studied in detail. It is found that the dimensionless tangential velocity increases whilst the dimensionless swirl velocity and temperature decrease with the swirl Darcy number, tangential Darcy number and the rotational parameters. The model finds applications in chemical engineering filtration processing, liquid coating and spinning cone distillation columns.     

治导建筑物绕流机理及其下游流场的探讨

本文分析了治导建筑物的统流机理,建立了二维流动模式。前人的研究及笔者的试验资料均表明,治导建筑物下游流速分布呈自相似性,根据相似原理,二维沿水深平均的Reynolds方程可转化为常微分方程,这样就得到治导建筑物下游流速分布式。宽浅明槽中的试验表明,该流速分布式的计算结果与实测值吻合。     

THREE-DIMENSIONAL NUMERICAL SIMULATION OF INTAKE MODEL WITH CROSS FLOW

The hydrodynamics of a pump sump consisting of a main channel,pump sump,and intake pipe is examined using Truchas,a three-dimensional Navier-Stokes solver,with a Large Eddy Simulation(LES) turbulence model.The numerical results of streamwise velocity profiles and flow patterns are discussed and compared with experimental data of Ansar and Nakato.Fairly good agreement is obtained.Furthermore,unlike Ansar et al.'s inviscid solution,the proposed numerical model includes the effect of fluid viscosity and consid...     

THE ANALYSIS OF THE TREE－DIMENSIONAL ELASTOHYDRODYNAMIC LUBRICATIONFOR HEAVILY－LOADED FINITE JOURNAL BEARINGS IN NON－NEWTONIAN LUBRICANTS

ＴＨＥ　ＡＮＡＬＹＳＩＳ　ＯＦ　ＴＨＥ　ＴＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬ　ＥＬＡＳＴＯＨＹＤＲＯＤＹＮＡＭＩＣ　ＬＵＢＲＩＣＡＴＩＯＮＦＯＲ　ＨＥＡＶＩＬＹ－ＬＯＡＤＥＤ　ＦＩＮＩＴＥ　ＪＯＵＲＮＡＬ　ＢＥＡＲＩＮＧＳ　ＩＮ　ＮＯＮ－ＮＥＷＴＯＮＩＡ...     

VISCOSITY EFFECTS ON THE BEHAVIOR OF A RISING BUBBLE

In the incompressible fluid flow regime,without taking consideration of surface tension effects,the viscosity effects on the behavior of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by the Volume Of Fluid(VOF) method.The ratio of the gas density to the liquid density is taken as 0.001,and the gas viscosity to the liquid viscosity is 0.01,which is close to the case of an air bubble rising in water.It is found by numerical exp...     

Numerical analysis of flow separation zone in a confluent meander bend channel

The flow pattern in the confluent meander bend channel under the conditions of different discharge ratios and junction angles is numerically simulated by means of the large eddy simulation(LES), and the characteristics of the flow separation zone are analyzed. Numerical results are well validated by experimental data with a good agreement. Analysis of the vertical confinement shows that the turbulence within the separation zone can be characterized as quasi-2-D. Details of the separation zone characteristics are revealed as shown by mean velocity isolines. According to the analysis of numerical results, the length and the width of the separation zone generally increase with the increase of the discharge ratio and the junction angle. However, the width of the separation zone keeps substantially constant when the junction angle increases from 60 o to90o. The dimensionless shape of the separation zone is nearly the same for three discharge ratios and three junction angles. The formulas of the relative width and the relative length of the separation zone are obtained by means of the polynomial fit method.     

含植物明渠紊流流速分布无量纲化方法及流动分区

基于流速分布曲线的几何特点,提出一种新的无量纲化方法,结合水槽实验数据的回归分析,对含植物明渠紊流流速分布律及流动分区进行了研究。基于流速梯度变化率的特点,确定两个特征高度,采用特征高度、特征高度位置处的流速、水深、最大流速4个变量定义了新的无量纲流速和高度,对实验得到的流速数据进行无量纲化处理,进一步拟合得到流速分布律。结果表明,提出的无量纲流速在自由水面附近呈对数分布,对数分布律区域以下到床面的区域可用4段函数表示。根据分布律适用的区域明确流动分区边界,发现边界高度与特征高度并不重合,但和混合层的上下边界近似相等。与其他研究的对比表明,提出的无量纲化方法和流速分段函数分布律以及流动分区对速度描述有效,具有较好的适用性。     

SURFACE WAVE PATTERNS AND INSTABILITY IN A VERTICALLY OSCILLATING CIRCULAR CYLINDRICAL VESSEL

The natural frequency of surface wave, which has been derived from a vertically oscillating circular cylindrical vessel in inviseid fluid, was modified by considering the influence of surface tension and weak viscosity. Many flow patterns were found at different forced frequencies by numerical computation. In addition, the nonlinear amplitude equation derived in inviseid fluid was modified by adding viscous damping and the unstable regions were determined by stability analysis.     

NUMERICAL SIMULATION OF THE DISPERSION IN OSCILLATING FLOWS WITH REVERSIBLE AND IRREVERSIBLE WALL REACTIONS

This is a study on the mass transport of a solute or contaminant in oscillating flows through a circular tube with a reactive wall layer. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. The short-time dispersion characteristics are numerically investigated, incorporating the coupling effects between the flow oscillation, sorption kinetics, and retardation due to phase partitioning. The effects of various dimensionless parameters e.g., Da (the Damköhler number), α (phase partitioning number), Γ(dimensionless absorption number), and δ(dimensionless Stokes boundary layer number) on dispersion are discussed. In particular, it is found that there exist trinal peaks of the breakthrough curves in some cases.     

热泡数值研究

本文对二维热泡的演化过程进行数值研究，所采用的湍流封闭模式为双方程k-ε方程。数值结果表明：无量纲时间大于10后，流动与混合特性均符合自相似关系；热泡流场可分两区。混合区中示踪剂浓度场呈双峰肾形、湍流脉动强烈、旋流含一对涡眼，而外区示踪剂浓度为零、流动有势且符合偶极子模型；热泡流的附加等效质量系数近乎1，自相似阶段热泡的宽高比约为1.45。所得热泡扩展率和混合率亦与实验数据相符。     

Series solution of a natural convection flow for a Carreau fluid in a vertical channel with peristalsis

An analysis has been achieved to study the natural convection of a non-Newtonian fluid(namely a Carreau fluid) in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations are reduced to a system of nonlinear PDE by using the long wavelength approximation. The optimal homotopy analysis method(OHAM) is introduced to obtain the exact solutions for velocity and temperature fields. The convergence of the obtained OHAM solution is discussed explicitly. Numerical calculations are carried out for the pressure rise and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail.