Experimental study of “laminar” bubbly flows in a vertical pipe

Measurement of bubbly two-phase flow parameters in a vertical pipe were performed. To keep the pipe Reynolds number below that for single-phase turbulent transition, a water-glycerin solution was used as the test liquid. Local void fraction and liquid velocity profiles along with the wall shear stress were measured by an electrochemical method. Experiments were made with bubbles of two different sizes. As the gas flow rate was increased, a gradual development of the liquid velocity profile from the parabolic Poiseuille flow to a flattened two-phase profile was observed. The evolution of the wall shear stress and of the velocity fluctuations were also quantified.Centre National de la Recherche Scientifique. Université Joseph Fourier, Institut National Polytechnique de Grenoble.     

Local characteristics of upward gas-liquid flows

The results of two-phase flow structure measurements in an upward gas-liquid flow in a 86.4 mm i.d. tube by the electrochemical and conductivity techniques are presented. Measurements were made in bubble and slug flow regimes at liquid flow rates ranging from 0.2 to 2 m/s.The flow instability and ambiguity in a bubble regime at low velocities is shown to exist. Great discrepancy between measured wall shear stress values and those predicted by the Lockhart-Martinelli model are due to the nonuniform distribution of gas over the tube cross section. Measurements of intensity of wall shear stress and liquid velocity fluctuations in a two-phase flow are presented.     

刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。     

Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180‐degree turn by algebraic Reynolds stress model

Turbulent flow in a rectangular duct with a sharp 180‐degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure‐driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large‐scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180‐degree turn using the algebraic Reynolds stress model. A boundary‐fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser‐Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log‐law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180‐degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log‐law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied. Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid. An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress. Finite difference method is employed to solve the momentum equation for the core region. The numerical solutions for velocity, flow rate and flow resistance are computed. The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated. It is observed that the velocity increases with the increase of plasma layer thickness. An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t. An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number. The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature.     

一种确定均匀动脉壁面切应力的非线性方法

从Ling和Atabek提出的``局部流'理论出发，提出一种利用测量血液黏度、管轴上 的血流速度、压力和管径波形计算均匀动脉管壁切应力的非线性方法. 将这种方法与柳兆荣 等提出的利用测量血液黏度、管轴上的血流速度和平均管径计算切应力的线性方法比较，结 果表明，当管壁脉动幅度较小时，两种方法计算的压力梯度、流速剖面和管壁切应力差别较 小；而当管壁脉动幅度增大时，两种方法计算的压力梯度、流速剖面和管壁切应力差别增大. 对于小幅脉动均匀动脉，用线性方法计算管壁切应力有较高的精度；而对于大变形 均匀动脉，则需要考虑非线性因素对管壁切应力的影响. 由于作为输入量的血液黏度、轴心 血流速度、压力波形和管径波形可在活体上通过无损伤或微损伤的检测方法得到， 所提出的计算切应力的方法为在体或离体研究切应力与动脉重建的关系提供了方法学基础.     

A method for estimating wall friction in turbulent wall-bounded flows

We describe a simple method for estimating turbulent boundary layer wall friction using the fit of measured velocity data to a boundary layer model profile that extends the logarithmic profile all the way to the wall. Two models for the boundary layer profile are examined, the power-series interpolation scheme of Spalding and the Musker profile which is based on the eddy viscosity concept. The performance of the method is quantified using recent experimental data in zero pressure gradient flat-plate turbulent boundary layers, and favorable pressure gradient turbulent boundary layers in a pipe, for which independent measurements of wall shear are also available. Between the two model profiles tested, the Musker profile performs much better than the Spalding profile. Results show that the new procedure can provide highly accurate estimates of wall shear with a mean error of about 0.5% in friction velocity, or 1% in shear stress, an accuracy that is comparable to that from independent direct measurements of wall shear stress. An important advantage of the method is its ability to provide accurate estimates of wall shear not only based on many data points in a velocity profile but also very sparse data points in the velocity profile, including only a single data point such as that originating from a near-wall probe.     

A critical re-appraisal of the jet-thrust technique for normal stresses,with particular reference to axial velocity and stress rearrangement at the exit plane

It is shown that the thrust, T, exerted by a jet on the tube from which it flows, and the corresponding die-swell ratio, D, are closely related and dependent on the axial velocity and stress profiles at the exit plane. Velocity-profile data, calculated by Tanner using a finite element method, have been used to demonstrate that for a Newtonian liquid the reduction in measured thrust from the expected value arises from a re-arranged, non-parabolic axial velocity profile and the related re-arranged non-zero axial stress profile at the exit plane. The axial stress re-arrangement is the major effect.Using the correction-curve thus derived to determine the normal stresses, ν₁ + $\text{1}\text{2}$ν₂ aqueous and non-aqueous polymer solutions gives values that are higher than the “correct” results by a significant, substantial amount. The difference is not due to neglect of the second normal stress difference, ν₂, nor to the neglect of the wall pressure at the exit plane, which is shown experimentally to be very small. It is suggested that the difference, which is a function only of the shear stress (or rate of shear) at the wall, may arise from a difference in the stress profile associated with the velocity re-arrangement at the exit between Newtonian liquids and elasticoviscous liquids for which the extensional viscosity may be high.     

In situ flow visualization of capillary flow of concentrated alumina suspensions

A new approach was taken to understand the flow behavior of concentrated particle suspensions in pressure-driven capillary flow. The flow of concentrated alumina suspensions in a slit channel was visualized and quantitatively analyzed with modified capillary rheometer. The suspensions showed complex flow behaviors; unique solid–liquid transition and shear banding. At low flow rates, 55 vol% alumina suspension showed a unique transient flow behavior; there was no flow at first and continuous change of flow profile was observed with time. At low shear rates in particular, the suspensions exhibited shear-banded flow profile which could be divided into three regions: the region with low flow rate near the wall, the region with rapid increase of flow velocity to maximum, and the region of velocity plateau. Based on both flow visualization and measurement of shear stress, it was found that the shear-banded flow profile in pressure-driven slit channel flow was strongly correlated with shear stress. The banding in pressure-driven flow was different from that in Couette flow. The banding of concentrated alumina suspensions was unique in that sluggish velocity profile was pronounced and two inflection points in velocity profile was exhibited. In this study, shear banding of concentrated alumina suspensions in slit channel flow was visualized and quantitatively analyzed. We expect that this approach can be an effective method to understand the flow behavior of particulate suspensions in the pressure-driven flow which is typical in industrial processing.     

局部扩张动脉管血液振荡流的切应力分布

本文求解局部缓慢扩张动脉管中血液振荡流的基本方程，得到血管内血液的流速与压力梯度的关系。通过导出压力梯度沿局部扩张管轴向的变化特性。建立利用扩张段上游血管均匀段中心流速波形确定局部扩张管中血液流的速度和切应力分布的方法，文章以人体颈动脉余弦扩张为例进行分析。详细讨论了局部扩张对血管壁切应力及其梯度分布的影响。数值结果表明，在与刚性均匀管中管壁切应力沿轴向保持不变不同，在局部扩张段，管壁切应力将随着血管半径的增大而减小，因而管壁切应力梯度一般不为零，甚至在某些位置达到相当大的数值。另外，随着血管扩张程度的增加，管壁切应力还将进一步减小，而且管壁切应力梯度也将进一步增大，血管扩张导致管壁切应力的这些变化将直接影响血管壁的结构和功能，使其产生适应性的变化。     

Numerical analysis of developing turbulent flow in a 180° bend tube by an algebraic Reynolds stress model

A numerical analysis has been performed for three‐dimensional developing turbulent flow in a 180° bend tube with straight inlet and outlet section used by an algebraic Reynolds stress model. To our knowledge, numerical investigations, which show the detailed comparison between calculated results and experimental data including distributions of Reynolds stresses, are few and far between. From this point of view, an algebraic Reynolds stress model in conjunction with boundary‐fitted co‐ordinate system is applied to a 180° bend tube in order to predict the anisotropic turbulent structure precisely. Calculated results are compared with the experimental data including distributions of Reynolds stresses. As a result of this analysis, it has been found that the calculated results show a comparatively good agreement with the experimental data of the time‐averaged velocity and the secondary vectors in both the bent tube and straight outlet sections. For example, the location of the maximum streamwise velocity, which appears near the top or bottom wall in the bent tube, is predicted correctly by the present method. As for the comparison of Reynolds stresses, the present method has been found to simulate many characteristic features of streamwise normal stress and shear stresses in the bent tube qualitatively and has a tendency to under‐predict its value quantitatively. Judging from the comparison between the calculated and the experimental results, the algebraic Reynolds stress model is applicable to the developing turbulent flow in a bent tube that is known as a flow with a strong convective effect. Copyright © 2005 John Wiley & Sons, Ltd.     

Hydrodynamics study in a plane ultrafiltration module using an electrochemical method and particle image velocimetry visualization

 The wall shear stress is determined at the surface of a plane sheet of Plexiglas, taking the place of a membrane, using an electrochemical method. Several microelectrodes are mounted flush to this plane plate, and maps of shear stress are determined for two inlet and outlet configurations and three channel heights. The heterogeneity of the wall shear stress is observed for both configurations. Furthermore, the study of the turbulence features of the flow shows a decreasing fluctuating rate of velocity gradient when the channel height is decreased. The wall velocity gradients and turbulent intensity rates analysis are confirmed by a flow visualization using the particle image velocimetry method. Received: 25 September 2000 / Accepted: 23 April 2001     

用管轴流速确定动脉中血液振荡流的速度剖面

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的速度与压力梯度之间的关系式，文章提出一种利用管轴外流速计算管内压力梯度，进而确定血液振荡流动速度分布的方法，该方法用于检测活体血管内血液振荡流的速度剖面，具有操作简单，精度较高的优点，最后，以人体颈动脉为例，讨论血液周期振荡流的速度分布特征，发现在任意时刻，除了邻近管壁速度迅速降为零之外，沿管截面速度分布相当均匀，呈现出与定常流不同的速度分布特征。     

Wall shear stress prediction in three-dimensional turbulent boundary layers

A method is developed to infer the wall shear stress for three-dimensional turbulent boundary layers based on the assumption that the resultant surface shear stress and the effective velocity based on Prahlad's model correlates the velocity profile into its two-dimensional form. Existence of the near wall region similarity has been demonstrated for three-dimensional turbulent boundary layers.     

输气管道壁面涂料减阻机理的实验研究

用IFA-300热线风速仪以高于对应最小湍流时间尺度的分辨率精细测量了风洞中不同壁面涂料的管道湍流边界层不同法向位置流向速度分量的时间序列信号,利用湍流边界层近壁区域对数律平均速度剖面与壁面摩擦速度、流体黏性系数等内尺度物理量的关系和壁面摩擦速度与壁面摩擦切应力的关系,在准确测量湍流边界层近壁区域对数律平均速度剖面的基础上,间接测量湍流边界层的壁面摩擦阻力．对不同壁面涂料的壁湍流脉动速度信号用子波分析进行多尺度分解,用子波系数的瞬时强度因子和平坦因子检测管道湍流边界层中的多尺度相干结构,提取不同尺度相干结构的条件相位平均波形,对比研究输气管道壁面涂料的减阻机理．     

An experimental study of nonrheometric flows of visco-elastic fluids: I. flow into a re-entrant tube

A laser anemometer has been used to study the developing flow both upstream and downstream from the entry plane in a re-entrant tube geometry. A 0.75% polyacrylamide/water solution was used and Reynolds numbers (based on wall conditions in the fully developed downstream flow) in the range 100–500 were obtained in 1.82-cm and 2.40-cm-diameter tubes.The shear stress-shear rate relationship for the fluid was measured using a cone and plate geometry in conjunction with a Weissenberg rheogoniometer. Theoretical fully developed velocity profiles were calculated numerically from these measurements. The measured fully developed velocity profiles were found to be in excellent agreement with those calculated.Velocity profiles measured at the tube entry plane showed the pronounced wall region distortion typically predicted by recent numerical solutions of the flow of purely-viscous fluids through an abrupt tube contraction.It was found that the major velocity rearrangements were achieved within only a few diameters (both upstream and downstream) of the entry plane. In particular, the velocity distribution near the tube wall varied negligibly over the relatively longer distance (many diameters) that it took for the centreline velocity to achieve its fully developed value. Entry lengths were found to be only about half those for purely-viscous fluids.Calculation of the time of flight along the central streamline confirmed that the major rearrangements of velocity suffered by the fluid occurred over a relatively short time period. This indicates that hereditary integral constitutive equations may have to be used in theoretical analyses of this type of flow situation.     

Wall shear stress characterization of a 3D bluff-body separated flow

Efficient flow control strategies aimed at reducing the aerodynamic drag of road vehicles require a detailed knowledge of the reference flow. In this work, the flow around the rear slanted window of a generic car model was experimentally studied through wall shear stress measurements using an electrochemical method. The mean and fluctuating wall shear stress within the wall impact regions of the recirculation bubble and the main longitudinal vortex structures which develop above the rear window are presented. Correlations allow a more detailed characterization of the recirculation phenomenon within the separation bubble. In the model symmetry plane the recirculation structure compares well with simpler 2D configurations; specific lengths, flapping motion and shedding of large-scale vortices are observed, these similarities diminish when leaving the middle plane due to the strong three-dimensionality of the flow. A specific attention is paid to the convection processes occurring within the recirculation: a downstream convection velocity is observed, in accordance with 2D recirculations from the literature, and an upstream convection is highlighted along the entire bubble length which has not been underlined in some previous canonical configurations.     

适用于浸入边界法的大涡模拟紊流壁面模型

基于近壁定常剪切应力假设,提出了一种新的适用于浸入边界法的大涡模拟紊流壁面模型。通过引入壁面滑移速度,修正了线性速度剖面计算得到的壁面剪切应力,使之满足Werner-Wengle模型。将其应用于平板紊流和高Re数圆管紊流的数值模拟,对比采用和不采用壁面模型的结果得知,采用此模型的速度剖面与实验值吻合良好,验证了此模型的有效性。研究了不同欧拉/拉格朗日网格相对位置对结果的影响,证明了此模型具有较好的鲁棒性,以及可根据局部流动状态和网格精度自动开闭的特点。     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

Mathematical modeling and parametric investigation of blood flow through a stenosis artery

In this study, a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel. The stenosis disease is caused because of the abnormal narrowing of flow in the body. This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel. Mathematical modeling helps us analyze such issues. A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method. The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid. A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem. Moreover, the flow characteristics such as the impedance, the wall shear stress in the stenotic region, the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed. The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel, which has a direct impact on the wall shear stress. It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.