Two-phase laminar zero net flow in a circular inclined pipe

Steady countercurrent zero net flow of two immiscible fluids in an inclined circular tube has been studied under laminar flow conditions. Using appropriate dimensionalization, the interface position and viscosity ratio become the only two parameters that govern the flow. Velocity profiles and shear stresses were determined from numerical solutions of the equations of motion and are compared with the analytical solutions for flow between parallel plates. Such zero net flows are encountered at shutdown of long inclined slurry pipelines. The results of the present investigation are suitable for modelling these flows.     

Reverse osmosis in laminar flow through curved tubes

A new design for reverse osmosis in a curved tube system takes advantage of the scouring-silting nature of the secondary flow pattern by utilizing a split membrane over the circumference of the tube. The wall concentration and concentration boundary layer thickness at the inside of the bend grow rapidly unless salt is allowed to escape there, whereas at the outside of the bend, the wall concentration and concentration boundary layer thickness remain small compared to straight tubes, thus indicating improved performance.     

Concentration distributions in laminar pipe flow with distorted velocity profiles

A laminar flow field in which the velocity profile may be distorted in a predictable manner was achieved in a 7-cm porous pipe with uniform wall injection over the ranges of variables: 0≤ λ ≤ 2, 200 ≤ N_Re ≤ 800 and 0.05 ≤ X ≤ 0.2. A mathematical model was then developed to describe the concentration distribution of a gaseous tracer discharged continuously from a finite source in this particular flow field. Experimental measurements taken over the same ranges of variables verified the validity of this model. The result from this study may be useful in the water desalination process using reverse osmosis.     

弯管体系内浆液流动分析

针对弯管系统中易在弯头处出现水合物堵塞的现象,以弯管系统中水合物浆液输送过程为研究对象,通过数值模拟对影响弯管系统中水合物颗粒最大体积分数的2个因素(颗粒直径、管径)进行了分析。结果表明:当水合物浆流速较小时,弯管系统中水合物最大体积分数受粒径的影响较大,即随着粒径的增大,水合物的最大体积分数趋近迅速增大的状态,而当浆液流速较快时,水合物最大体积分数受流速影响较大;管径的增大可以减小水合物颗粒直径对弯管系统中水合物最大体积分数的影响,到管道直径达到200 mm时,水合物颗粒直径的变化几乎不会影响水合物最大体积分数。研究结果为水合物浆液混输领域的发展提供理论依据。     

Steady pressure driven two-phase stratified laminar flow through a pipe

The two phase pressure driven flow in a circular pipe in which the interface occupies an arbitrary horizontal position has, as shown by earlier authors, an explicit analytical solution in which the velocities are expressed as Fourier integrals. Here this is used to express the volumetric fluxes of each fluid as one-variable integrals whose values can be easily computed. The results agree with those obtained by Gemmell and Epstein by numerical integration of the differential equations.     

Non-isothermal laminar pipe flow — II. Experimental

In a previous article [1] theoretical predictions of velocity distributions, pressure drops and mean Nusselt-numbers are given for non-isothermal pipe flow of power-law fluids having a temperature dependent consistency-index. In the present investigation these solutions are checked for Newtonian fluids with extensive experimental data.A flow visualization technique was used for measuring the non-isothermal, laminar velocity profiles of glycerol in a round tube. Furthermore, accurate pressure drop measurements were carried out for non-isothermal tube flow of a viscous. Newtonian liquid. Finally logarithmic mean heat transfer coefficients were measured in laminar flow heat transfer.The experimental velocity profiles, pressure drops and heat transfer coefficients show a good agreement with those predicted theoretically.     

Non-isothermal laminar pipe flow — I. Theoretical

The Graetz-problem — heat transfer to a fluid flowing laminarly in a circular tube with constant temperature — has been extended to the case of a variable viscosity. Calculations are performed on the heat transfer to and the hydrodynamics of non-isothermal, rectilinear, laminar flow of incompressible, power-law fluids in round tubes. The consistency-index is assumed to vary exponentially with temperature.The results are presented as logarithmic mean Nusselt-numbers and dimensionless velocity distributions and pressure drops as a function of the dimensionless axial length in the tube and as function of a quantity Q which measures the deviation of “isoviscous” fluid behaviour. It turns out that the heat transfer rate is a unique function of the velocity gradient at the wall.All results are summarized in a few practical approximations.     

Motion and deposition of fibrous flexible particles in laminar gas flow through a pipe

The equation of motion of a flexible slender particle in a straight horizontal cylindrical pipe, under conditions of gas flow similar to those which occur in part of human airways, is presented. Particle orientation, deformation and limiting trajectory is computed. The deposition efficiency of particles due to sedimentation, inertia and interception for different gas velocities, particle mass and geometry is discussed.     

边界条件对圆管层流流动的影响分析

应用Fluent软件,分别就匀速度、抛物线形速度分布入口边界条件下模拟圆管层流流场,得到进出口截面的静压降,并与理论值进行比较。计算结果显示,匀速度入口条件下,进出口静压降的百分误差随雷诺数增加而急剧增大;而抛物线形速度入口条件下,进出口静压降与理论值基本吻合。     

Fluid flow through 180° curved pipe of radiant tube

The present study was carried out to investigate the flow characteristics through the curved section of a radiant tube which is used in the steel industry. The velocity profiles in the curved section were measured at a 1/2 scale water model apparatus by using 2D-LDV. The flow was also simulated numerically and a comparison was made with the experimental results. The flow characteristics in the curved section for various flow conditions of the burner was investigated. The secondary flow in the curved section and the flow stagnation phenomena at the end of the curved section were confirmed. It was found that the swirl velocity component imparted by the burner degrades the uniformity of flow and enlarges the stagnant region in the curved section. This flow pattern is supposed to cause non-uniform heat transfer and the local failure at the end of the curved section.     

Liquid wall friction in two-phase turbulent gas laminar liquid stratified pipe flow

The main result of the present work is an analytic expression for the mean liquid wall shear stress in two-phase turbulent gas/laminar liquid stratified pipe flow. The Navier-Stokes equations are solved assuming a flat fluid-fluid interface subject to a constant interfacial shear — approximating the interfacial drag exerted by the gas. The effect of a pipe inclination is accounted for, thereby retaining the interesting two-phase phenomenon of backflow in upwardly inclined pipes. The corresponding expression for the wall shear stress distribution is obtained by formal differentiation. Its limiting behaviour in the triple points, where the fluid-fluid interface meets the pipe wall, is determined by residue calculus. The expression for the mean wall shear stress is given by integration. It is found to be a linear combination of two terms. The first term accounts for the free surface liquid flow in the absence of the gas. The corresponding approximate hydraulic diameter model is found to be in surprisingly good agreement with this term. The second term represents the shear flow associated with the interfacial drag exerted by the gas (not accounted for by the hydraulic diameter approximation). The shear flow increases the flow rate near the interface on behalf of the flow rate near the pipe wall, thus reducing the wall shear stress below the free surface flow value. Expedient evaluation of the expression for the mean wall shear stress, suitable for use in a 1-D multiphase pipe flow simulator, is facilitated by replacing certain one-parameter integrals with highly accurate rational approximations.     

随机分布纤维束间纵向层流流动数值模拟

按层流流动理论,采用数值方法模拟了随机分布纤维束间纵向流动时的量纲1速度分布,讨论了中空膜组件中纤维的装填率对流动阻力系数fRe和纤维束间流量分布的影响,并得到了0.1≤≤0.7范围内的fRe与的关系式。模拟结果表明,对于随机分布的纤维束,纵向流动速度分布不均匀,存在明显的偏流现象;由Voronoi划分所得的子单元通道面积分布与流量分布存在一定的关系,装填率对此关系影响较小。流动阻力系数fRe明显小于相同装填率下纤维按正三角形排列时的数值,它的模拟值与Sullivant和Costello等的实验值基本一致,随装填率增大而增大。     

Axial mixing in laminar pipe flows

A computational model has been developed to simulate the axial dispersion phenomena in laminar pipe flows. Peclet number (Pe=au₀/D_m) and dimensionless time (τ=D_mt/a²) have been covered over a wide range of 1-10⁵ and 10⁻⁸ to 10², respectively. An extensive comparison of predicted mean concentration profiles with the experimental data has been presented. The proposed computational model for concentration profiles was found to give an excellent agreement with the experimental measurements. Further, the results compare well with other analytical and experimental studies. The solution has been shown to be valid at both the short and long times and for all values of the Peclet number.     

Unified entry length for newtonian and power–law fluids in laminar pipe flow

A numerical method based on finite differencing is used for investigating the steady–state entrance region laminar flow of incompressible Newtonian and power–law fluids in a circular pipe. The Solution method is validated by comparing the results for Newtonian fluids with those reported in the literature. For power–law fluids, the entry length results are compared with other approximate solutions in the literature. On the basis of the calculated results, a generalized entry length ξ99 = 0.056 is shown to be valid for the laminar flow at Re > 200 of both Newtonian and power–law fluids with 0.75 < n < 1.5.     

Numerical study of laminar core‐annular flow in a torus and in a 90° pipe bend

A numerical study has been made of laminar core‐annular through a torus. It is a follow‐up of the study by Picardo and Pushpavanam, AIChE J. 2013;59(12):4871–4886, who obtained an analytical solution for the case that the core is concentric and circular. In our study, we investigated the possibility of eccentric core‐annular flow and the deformation of the core‐annular interface. We found that a stable eccentric core position is possible, which is shifted in the direction of the inner or outer side of the torus depending on the balance of the normal stresses at the core‐annular interface. When these stresses are too far off from those for concentric and circular core‐annular flow, fouling of the wall occurs. We compared the results of core‐annular flow in a torus with those for a 90° pipe bend and found that the flow pattern in the torus is representative for the flow pattern in the bend. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2319–2328, 2015