Numerical models and theoretical analysis of supercritical bend flow

The flow pattern of supercritical flow in bend channels is complicated due to the shock wave phenomenon, which creates difficulties with regard to research and design of bend channels. Using the spillway of an actual project as an example, a three-dimensional numerical investigation was conducted to simulate the flow in a steep-slope bend based on the renormalization group(RNG) k-ε turbulence flow model and the volume of fluid(VOF) method. The validity of the numerical simulation was demonstrated by comparison between the results of numerical simulation and physical model tests. An optimal scheme of setting vertical vanes in the bend channel is presented. The results of numerical simulation and physical model tests are in agreement, which demonstrates the effectiveness of optimization of vertical vanes and the validity of the three-dimensional numerical simulation. Water depths along both bend walls were analyzed numerically and theoretically. The formula for calculating supercritical water depth along either bend wall was derived, and the critical condition of flow separation from the inner wall was determined.

EXPERIMENTAL STUDY OF 3-D TURBULENT BEND FLOWS IN OPEN CHANNEL

A generalized hend flow model, treating a 90° single bend and 60° continuous hends, was designed to quantitatively describe 3-D turhulenee mechanism of circulating notfully-developed flow in open channels with hends. The 3-D fluctuating veloeities of turbulent flow were measured and analyzed with a 3 D acoustic-Doppler velocimeter. Formula for 3 D turbulent intensity was derived using the dimension analysis approaeh. Expressions of vertical turbulent intensity distributions were obtained with the multivariant-rcgression theo ry, whieh agree with experiment data. Distrihutions of turbulent intensity and turbulent stress were characterized, and their relationships were concluded. In the bend-turbulent flow core region, longitudinal and lateral turbulent-intensity distri hutions are coincident with linear distribution, hut in nearwall region are coincident with the Gamma distribution. Verotical turbulent intensity distributions are coincident with the Rayleigh distribution. Herein, it is concluded that the bend turbulence is anisotropic.

Numerical Simulation of Turbulent Flow of Hydraulic Oil through 90° Circular-sectional Bend

Oil flow through pipe bends is found in many engineering applications. However, up to now, the studies of oil flow field in the pipe bend appear to be relatively sparse, although the oil flow field and the associated losses of pipe bend are very important in practice. In this paper, the relationships between the turbulent flow of hydraulic oil in a bend and the Reynolds number Re and the curvature ratio δare studied by using computational fluid dynamics （CFD）. A particular emphasis is put on hydraulic oil, which differs from air or water, flowing through 90° circular-sectional bend, with the purpose of determining the turbulent flow characteristics as well as losses. Three turbulence models, namely, RNG κ-ε model, realizable k-ε model, and Reynolds stress model （RSM）, are used respectively. The simulation results in the form of contour and vector plots for all the three turbulence models for pipe bends having curvature ratio of δ=0.5, and the detailed pressure fields and total pressure losses for different Re and δ for RSM are presented. The RSM can predict the stronger secondary flow in the bend better than other models. As Re increases, the pressure gradient changes rapidly, and the pressure magnitude increases at inner and outer wall of the bend. When δ decreases, two transition points or transition zones of pressure gradient arise at inner wall, meanwhile, the transition point moves towards the inlet at outer wall of the bend. Owing to secondary flow, the total pressure loss factor k increases as the bend tightens, on the contrary, as Re increases, factor k decreases due to higher velocity heads, and the rapid change of pressure gradient on the surface of the bend leads to increasing of friction and separation effects, and magnified swirl intensity of secondary flow. A new mathematical model is proposed for predicting pressure loss in terms of Re and δ in order to provide support to the one-dimensional simulation software. The proposed research provides reference for the analysis of oil flow with higher Re in the large bends.

Effects of bubbly flow on bending moment acting on the shaft of a gas sparged vessel stirred by a Rushton turbine

The bending moment acting on the overhung shaft of a gas-sparged vessel stirred by a Rushton turbine,as one of the results of fluid and structure interactions in stirred vessels,was measured using a moment sensor equipped with digital telemetry.An analysis of the shaft bending moment amplitude shows that the amplitude distribution of the bending moment,which indicates the elasticity nature of shaft material against bending deformation,follows the Weibull distribution.The trends of amplitude mean,standard deviation and peak deviation characteristics manifest an "S" shape versus gas flow.The "S" trend of the relative mean bending moment over gas flow rate,depending on the flow regime in gas-liquid stirred vessels,resulted from the competition among the nonuniformity of bubbly flow around the impeller,the formation of gas cavities behind the blades,and the gas direct impact on the impeller when gas is introduced.A further analysis of the bending moment power spectral density shows that the rather low frequency and speed frequency are evident.The low-frequency contribution to bending moment fluctuation peaks in the complete dispersion regime.

TWO-PHASE FLOW PATTERNS IN A 90° BEND AT MICROGRAVITY

Bends are widely used in pipelines carrying single-and two-phase fluids in both ground and space applications.In particular,they play more important role in space applications due to the extreme spatial constraints.In the present study,a set of experimental data of two-phase flow patterns and their transitions in a 90°bend with inner diameter of 12.7 mm and curvature radius of 76.5 mm at microgravity conditions are reported.Gas and liquid superficial velocities are found to range from (1.0～23.6)m/s for gas and(0.09～0.5)m/s for liquid,respectively.Three major flow patterns, namely slug,slug-annular transitional,and annular flows,are observed in this study.Focusing on the differences between flow patterns in bends and their counterparts in straight pipes,detailed analyses of their characteristics are made.The transitions between adjoining flow patterns are found to be more or less the same as those in straight pipes,and can be predicted using Weber number models satisfactorily. The reasons for such agreement are carefully examined.

Experimental and Numerical Study of Dilute Gas-Solid Flow inside a 90°Horizontal Square Pipe Bend

A pneumatic test rig is built to test a curved 90° square bend in an open-circuit horizontal-to-horizontal suction wind tunnel system. Sand particles are used to represent the solid phase with a wide range of particle diameters. Velocity profiles are constructed by measuring the gas velocity using a 3-hole probe. Flow patterns inside the bend duct are introduced using sparks caused by burning sticks of incense with the air flow inside the piping system for flow visualization purpose. Numerical calculations are performed by Lagrangian-particle tracking model for predicting particle trajectories of dispersed phase, and standard k-ε model for predicting the turbulent gas-solid flows in bends. Comparisons made between the theoretical results and experimental data for the velocity vectors and particle trajectories show good agreement.

The Effect of the Variation of the Downstream Region Distance and Butterfly Valve Angle on Flow Characteristics in a 90 Degree Bended Elbow

This study presents the numerical evaluation about the impact of flow disturbance near the intrados and extrados regions of the 90 degree bended elbow using CFX for several practical cases where the 90 degree bended upward elbow is located in a proximity to the butterfly valve and the butterfly valve open angle is changed. For the change of a butterfly valve open angle from 60% to 100% and the increase of the distance between a valve and a 90 degree bended elbow, the effect of FAC (Flow-Accelerated Corrosion) in the 90 degree bended elbow may be neglected because the value and distribution of the velocity and shear stress is rapidly decreased comparing with the present status installed in an industry, and the data of 100% valve open (Case 3) and L/D ≈ 5 (Case 4) are very good agreement comparing with the reference data, L/D ≈ 8 (Case 2). The reasons are that flow already maintains a fully developed condition and a steady state in spite of less distance than the reference case, L/D = 8. Therefore, smooth flow fields have approached at a 90 degree bended elbow. Then, the effect of shear stress and vortex is hardly investigated around the intrados area of 90 degree bended elbow.

Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

CVBEM and FVM Computational Model Comparison for Solving Ideal Fluid Flow in a 90-Degree Bend

While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boundary Element Method (CVBEM). However, to date, there has been no reporting of a comparison of computational results between the FVM and the CVBEM in the assessment of flow field characteristics. In this work, the CVBEM is used to develop a flow field vector outcome of ideal fluid flow in a 90-degree bend which is then compared to the computational results from a finite volume model of the same situation. The focus of the modelling comparison in the current work is flow field trajectory vectors of the fluid flow, with respect to vector magnitude and direction. Such a comparison is necessary to validate the development of flow field vectors from the CVBEM and is of interest to many engineering flow problems, specifically groundwater modelling. Comparison of the CVBEM and FVM flow field trajectory vectors for the target problem of ideal flow in a 90-degree bend shows good agreement between the considered methodologies.

基于Flow-3D的陡坡弯道水流三维数值模拟

弯道急流有其独特的冲击波现象,流态极其复杂,为研究弯道对急流的影响和提出改善措施增添了困难。采用RNG k-ε双方程紊流模型和VOF法,以某工程溢洪道为依托,利用Flow-3D软件,对陡坡弯道段的急流进行了三维数值模拟,通过物理模型试验数据的验证,显示数值模拟结果的正确性。通过计算结果,分析了陡坡弯道对急流流态的影响,提出了导流墙法的弯道急流优化方案,通过物理模型进一步证明,采用导流墙法可有效改善急流弯道水流流态,表明借助Flow-3D软件对弯道水流进行三维数值模拟是可行的。

Nanoparticle Transport and Coagulation in Bends of Circular Cross Section via a New Moment Method

Transport of nanoparticles and coagulation is simulated with the combination of CFD in a circular bend. The Taylor-expansion moment method(TEMOM)is employed to study dynamics of nanoparticles with Brownian motion,based on the flow field from numerical simulation.A fully developed flow pattern in the present simulation is compared with previous numerical results for validating the model and computational code.It is found that for the simulated particulate flow system,the particle mass concentration,number concentration,particle polydispersity, mean particle diameter and geometric standard deviation over cross-section increase with time.The distribution of particle mass concentration at different time is independent of the initial particle size.More particles are concen-trated at outer edge of the bend.Coagulation plays more important role at initial stage than that in the subsequent period.The increase of Reynolds number and initial particle size leads to the increase of particle number concentration.The particle polydispersity,mean particle diameter and geometric standard deviation increase with decreasing Reynolds number and initial particle size.

Effect of Liquid and Gas Velocities on Magnitude and Location of Maximum Erosion in U-Bend

Solid particle erosion is a micromechanical process that is influenced by flow geometry, material of the impacting surface, impact angle, particle size and shape, particle velocity, flow condition and fluid properties. Among the various factors, particle size and velocity have been considered to be the most important parameters that cause erosion. Particle size and velocity are influenced by surrounding flow velocities and carrying fluid properties. Higher erosion rates have been observed in gas-solid flow in geometries where the flow direction changes rapidly, such as elbows, tees, valves, etc, due to local turbulence and unsteady flow behaviors. This paper presents the results of a Computational fluid dynamic (CFD) simulation of dilute gas-solid flow through a U-Bend and the dynamics behavior of entrained solid particles in the flow. The effect of liquid and gas velocities on location of erosion were investigated for 50, 100, 150, 200, 250 and 300 microns sand particles. Three different fluid velocities of 15, 30.48 and 45 m/s were used in the CFD analysis. The magnitude and location of erosion presented in the paper can be used to determine the areas susceptible to maximum erosive wear in elbows and U-bends, along with corresponding rate of metal loss in these areas.

溢洪道弯道段流态改善试验研究和应用

溢洪道泄槽弯道泄流时,弯道段内易产生横向冲击波,水流紊乱,流态较差,会不同程度地影响溢洪道的正常运行。该文根据广东省部分水库陡槽溢洪道水力模型试验研究成果,介绍改善溢洪道泄槽弯道段流态的断面超高、斜向高低坎、纵向导流墙、阶梯跌坎、弯道前设置消力池等工程措施,并对各种工程措施的适用性进行分析,研究成果可供类似工程设计和运行参考。

Torque and bending moment acting on a flexible shaft agitated by disk turbines in a gas–liquid stirred vessel

The torque and bending moment acting on a flexible overhung shaft in a gas–liquid stirred vessel agitated by a Rushton turbine and three different curved-blade disk turbines(half circular blades disk turbine, half elliptical blades disk turbine, and parabolic blades disk turbine) were experimentally measured by a customized moment sensor. The results show that the amplitude distribution of torque can be fitted by a symmetric bimodal distribution for disk turbines, and generally the distribution is more dispersive as the blade curvature or the gas flow rate increases. The amplitude distribution of shaft bending moment can be fitted by an asymmetric Weibull distribution for disk turbines. The relative shaft bending moment manifests a "rising-falling-rising" trend over the gas flow number, which is a corporate contribution of the unstable gas–liquid flow around the impeller, the gas cavities behind the blades, and the direct impact of gas on the impeller. And the "falling" stage is greater and lasts wider over the gas flow number for Rushton turbine than for the curved-blade disk turbines.

侧式进/出水口偏流出流下的大涡模拟

实际工程中受地形地质条件影响,引水洞在水平上存在转角,导致出流工况来流不均,进/出水口内部紊流特性的复杂程度显著提升。利用大涡模拟对某带水平弯段抽水蓄能电站侧式进/出水口进行数值计算,其流速、概率密度分布与模型试验吻合较好。结果表明:偏流出流下进/出水口各流道分流比分别为0.64、0.81、1.26和1.29,水平方向流速分布极为不均;垂直方向主流靠近中下部,垂向雷诺切应力在扩散段内呈一正一负峰值分布,该现象主要由中上部的流动分离和底部的壁面剪切造成;两中间流道的回流区高度大于两边流道,导致中间流道的拦污栅更易受到反向流速影响;流动分离使拦污栅附近存在三轴漩滚,靠近过水断面中上部和底部产生2处能量集中的低频脉动,且各流道在偏流条件下的紊动强度相比均匀来流的紊动强度分别提高11%、25%、29%、3%,不利的水流流态和较高的紊动强度可能对拦污栅造成威胁。

铝合金型材挤压弯曲一体化成形技术研究进展

相比于直型材,铝合金弯曲型材更适用于日益复杂的部件形状并能更好地满足轻量化需求,具有提升部件结构强度和刚度、节约空间及增加工业设计自由度等优点,在汽车、高铁和航空航天等领域具有广泛用途。相较于传统冷弯成形技术,挤压弯曲一体化成形技术在生产弯曲型材方面具有流程短、精度高、缺陷少等优点,因而受到广泛关注。重点综述了基于外部弯曲装置和材料差速流动的挤压弯曲一体化成形技术的研究进展,分析并总结了不同挤压弯曲一体化成形技术的原理及发展现状,对比了不同挤压弯曲一体化成形技术的优缺点,最后展望未来发展趋势及其研究方向。

基于三维流动的弯管模型的建立及流场分析

排气歧管是发动机的必要零部件之一,对发动机的性能有很大的影响。文章对排气歧管的弯曲管进行了研究,建立了弯管内气体流动的理论模型,利用FLUENT软件对弯管内气体流动状况进行了仿真,然后对两种弯曲管道(90°-56°管和90°-90°管)中的气体进行了对比分析。结果表明,90°-90°管道内的气体速度分布、压力分布和流线分布更为均匀,流动分离面积和涡流相对较小,速度均匀系数更接近于1,对柴油机进气的影响较小,柴油机的动力性能得以充分发挥。

Study on Fluid Shear Flow on Osteoblast-like Cells in Their Tensile Loading Experiments

In vitro cell loading experiments are used to investigate stimulation of strain to cellular proliferation. As the flowing conditions of culture fluid in loading systems has been little known, strictly people can not detect the influence of strain to cellular proliferation exactly because shear flow can enhance cell proliferation either. Based on the working principle and cyclic loading parameters, we simplify Navier-Stokes equation to describe the flow of culture fluid on substrates of uniaxial and equi-biaxial flat tensile loading systems and four point bending system. With approximate solutions, the distributions of velocity field and wall shear flow to cells are gained. Results show: shear flows are zero in the middle (or fixed point or line) of substrate for all systems, and they get larger proportionally to distance from middle and substrate elongate; the shear flow on the substrate of four point bending system is much greater than those of others. This shear flow in four point bending system, confirmed by Owan, I., et al with OPN mRNA increase in their experiment, could cause more influence to osteoblast-like cells than that caused by strain. We estimate the average magnitude of shear stress in Owan’s device, the results are consistent with other experimental data about shear flow. In conclusion our study makes it possible to differentiate the influence of strain on cellular proliferation to that of shear flow in loading experiments with the devices mentioned above quantitatively.

小麦颗粒弯管流动特性数值模拟研究

目的为研究小麦颗粒在弯管处的气力输送的特性。方法以欧拉-欧拉双流体模型为基础,结合壁面碰撞摩擦模型、颗粒动理学的固体应力和Gidaspow曳力模型构建出小麦颗粒在弯管处的气力输送模型,采用FLUENT对弯管处小麦颗粒气力输送过程进行数值模拟,分析小麦颗粒在流经弯管过程中及弯管后直管中的小麦颗粒密度分布、气固两相速度、小麦颗粒与壁面剪切力和颗粒相湍动能。结果经过仿真分析和实验验证,小麦颗粒在流经弯管过程中,其颗粒相体积分数、气固两相速度、颗粒和壁面剪切力以及颗粒相湍动能4个方面随着流入弯管的角度变化而改变;由于颗粒-颗粒、颗粒-管壁之间的碰撞摩擦,小麦颗粒在流出弯管后随着输送距离的增大其各项参数逐渐减缓。结论采用FLUENT软件进行仿真得到了弯管内小麦颗粒的流动特性,并通过实验验证了仿真的可靠性。此次研究结合气固两相理论,为弯管气力输送设计的研发和优化提供了理论基础。

含错边焊缝缺陷弯管气固两相流冲蚀磨损研究

在天然气输送系统中,当考虑弯管焊接缺陷时,结构特征差异导致的流场变化会使弯管产生不同的冲蚀特性。采用Computational Fluid Dynamics-Discrete Phase Model(CFD-DPM)方法研究不同颗粒参数、弯管导向、缺陷高度及颗粒入射角度下无错边焊缝弯管、外错边焊缝弯管、内错边焊缝弯管的介质流态特征与冲蚀规律。研究结果表明:(1)气体在弯管部位出现二次流动现象,速度分布出现扭曲,其中外错边焊缝弯管速度分布曲线扭曲幅度大,二次流作用效应最明显;(2)流体速度对冲蚀速率的影响最大,两者呈幂指数函数关系,质量流量次之,与冲蚀速率呈线性函数关系,颗粒粒径的影响最小,与冲蚀速率近似呈线性函数关系;(3)外错边焊缝弯管会在弯头处形成第二冲蚀磨损严重区域,而内错边焊缝与无错边焊缝弯管冲蚀效果相似,均只有1个冲蚀严重区域;(4)当流体在竖直管流向一致时,“H-V”导向弯管最大冲蚀速率均大于“V-H”导向弯管,在不同弯管导向下外错边焊缝弯管冲蚀速率最大;(5)弯管最外侧最大磨损位置随着错边高度发生变化,在一定高度下会使弯头内壁形成第二冲蚀磨损严重区域,且错边高度越大,弯头最外侧所受冲蚀速率越大;(6)颗粒的入射角度会影响弯管的冲蚀效应,其影响程度需结合入口直管长度与颗粒运动状态分析。