Motion of large gas bubbles ascending in a liquid

An equation is derived for the ascent velocity of large gas bubbles in a liquid. This velocity is assumed to be governed by the propagation of a wavelike perturbation caused by the bubble in the liquid.Notation w bubble (or drop) velocity - specific gravity - dynamic viscosity - kinematic viscosity - r bubble (or drop) radius - surface tension - coefficient of friction - g gravitational acceleration - D bubble (or drop) diameter - p pressure - c propagation velocity of the wavelike perturbation - wavelength     

Laminar flow development and heat transfer in converging plane-walled channels

The characteristics of flow development and heat transfer in converging plane-walled channels are studied by the finite difference method. The velocity and temperature profiles in both angular and radial directions, the average Nusselt number and the pressure drop are calculated for three different taper angles. The results show that the transport process is governed by three parameters: the inlet Reynolds number, the Péclet number and the taper angle. The increase of the taper angle yields an increase of the Nusselt number and a decrease of the pressure drop.     

Microscopic mechanism of periodical electroosmosis in reservoir rocks

Based on the electric double layer (EDL) theory and the momentum equation governing the electroosmosis flow, this paper presents an analytical solution to the periodical electroosmosis with a parallel straight capillary bundle model of reservoir rocks to reveal the microscopic mechanism of the electroosmotic flows in rocks. The theory shows that both the frequency dispersion characteristics of the macroscopic electroosmotic Darcy velocity in unsealed rocks and the electroosmotic pressure coefficient in sealed rocks depend on the porosity and electrochemical properties of reservoir rocks. The mathematical simulation indicates that the distribution of the periodical electroosmotic velocity is wavelike in the rock pore. The greater the porosity is, the greater electroosmotic the Darcy velocity and the smaller electroosmotic pressure coefficient are generated. The module values of the electroosmotic Darcy velocity and the electroosmotic pressure coefficient increase with the decreasing solution concentration or the increasing cation exchange capacity without affecting the phase of the electroosmotic Darcy velocity.     

旋风分离器减阻杆结构及减阻前后流场的测定与分析

报告了在旋风分离器内安装不同断面形状及尺寸的细杆（简称减阻杆）后对流动阻力降低及安装减阻杆前后旋风分离器内流场变化的测定结果，得出了减阻幅度与减阻杆插入长度和迎风面积及背风面曲率半径成正比、减阻杆使切向速度及轴向速度梯度减小、径向上静压梯度减小和轴向上逆压梯度减小等结论．本文同时对减阻杆的减阻机理及减阻时保证分离效率或提高分离效率的原因进行了分析．     

Investigation of pressure drop in horizontal pipes with different diameters

The pressure drop has a significant importance in multiphase flow systems. In this paper, the effect of the volumetric quality and mixture velocity on pressure drop of gas-liquid flow in horizontal pipes of different diameters are investigated experimentally and numerically. The experimental facility was designed and built to measure the pressure drop in three pipes of 12.70, 19.05 and 25.40 mm. The water and air flow rates can be adjusted to control the mixture velocity and void fraction. The measurements are performed under constant water flow rate (CWF) by adding air to the water and constant total flow rate (CTF) in which the flow rates for both phases are changed to give same CTF. The drift-flux model is also used to predict the pressure drop for same cases. The present data is also compared with a number of empirical models from the literature. The results show that: i) the pressure drop increases with higher volumetric qualities for the cases of constant water flow rate but decreases for higher volumetric qualities of constant total flow rate due to the change in flow pattern. ii) The drift-flux model and homogenous model are the most suitable models for pressure drop prediction.     

Zur Kondensation an der Wand dampfdurchströmter Kanäle mit veränderlichem Querschnitt

The flow of pure vapor in channels with variable cross section and cooled walls is considered. The balances for mass, energy and momentum and the transport of heat across the film of condensate are dealt by a finite difference method. Selected examples show that convergent channels improve condensation compared with channels of constant cross section. Excessive temperature drop by acceleration, however, must be avoided. Adversed pressure gradient may cause separation of the condensate film. The influence of the following parameters is discussed: gravity, increased friction, entrainment of condensat, cocurrent and countercurrent flow of the cooling medium and finite resistance of heat of channel wall. The shape of velocity profiles of the condensate is shown as a function of the pressure gradient.     

Criteria of High-Pressure Shockless Drop Breakup by Soliton-Type Gasdynamic Impulses

A specific regime of liquid-drop breakup in the absence of pressure disturbances is considered. In contrast to the regimes studied earlier, this regime, realized when a drop crosses a sheet (a layer or jet) of gas moving in isobaric space, is called shockless drop breakup. Fragmentation occurs near a velocity contact discontinuity in the medium under the action of a gasdynamic impulse, whose duration is determined by the drop velocity and the dimensions of the discontinuity. When the impulse duration is close to the drop deformation time or the intrinsic-oscillation period, the drop response to the action of the external forces is not quasistatic. On the range of initial-pressure variation between 0.1 and 8 MPa, the criteria of onset of shockless breakup of ethanol and liquid-oxygen drops are established in the form of empirical relations for the critical Weber numbers. The coincidence of the critical conditions of realization of shockless drop breakup and the conditions of breakup induced by pressure disturbances is noted.     

Experimental investigation of ice slurry flow pressure drop in horizontal tubes

Pressure drop behaviour of ice slurry based on ethanol–water mixture in circular horizontal tubes has been experimentally investigated. The secondary fluid was prepared by mixing ethyl alcohol and water to obtain initial alcohol concentration of 10.3% (initial freezing temperature ?4.4 °C). The pressure drop tests were conducted to cover laminar and slightly turbulent flow with ice mass fraction varying from 0% to 30% depending on test conditions. Results from flow tests reveal much higher pressure drop for higher ice concentrations and higher velocities in comparison to the single phase flow. However for ice concentrations of 15% and higher, certain velocity exists at which ice slurry pressure drop is same or even lower than for single phase flow. It seems that higher ice concentration delay flow pattern transition moment (from laminar to turbulent) toward higher velocities. In addition experimental results for pressure drop were compared to the analytical results, based on Poiseulle and Buckingham–Reiner models for laminar flow, Blasius, Darby and Melson, Dodge and Metzner, Steffe and Tomita for turbulent region and general correlation of Kitanovski which is valid for both flow regimes. For laminar flow and low buoyancy numbers Buckingham–Reiner method gives good agreement with experimental results while for turbulent flow best fit is provided with Dodge–Metzner and Tomita methods.Furthermore, for transport purposes it has been shown that ice mass fraction of 20% offers best ratio of ice slurry transport capability and required pumping power.     

The prediction of stratified two-phase flow with a two-equation model of turbulence

A two-equation model is applied to a stratified two-phase flow system to predict turbulent transport mechanisms in both phases.In the present analysis, the effects of interfacial waves on the flow field are formulated in terms of boundary conditions for the gas-liquid interface. For the gas phase, the wavy interface has such flow separation effects as a rough surface in a single-phase flow. While for the liquid phase, the waves generate turbulant energy which is transported progressively toward a lower wall region. The analytical results are in good agreement with available data regarding pressure drop, holdup and velocity profiles.     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

Ceramic foam substrates for automotive catalyst applications: fluid mechanic analysis

Several properties of ceramic foams render them promising substrates for various industrial processes. For automotive applications, the foam properties that need to be further studied include the substrate impact on the exhaust gas flow, in terms of pressure drop and flow uniformity. In this paper, pressure drop measurements are performed with different honeycomb and ceramic foam substrates, and pressure drop correlations are discussed. The flow uniformity upstream and downstream of the substrates is evaluated using particle image velocimetry. The results show that ceramic foam substrates induce higher pressure drop, while increasing the uniformity of the flow. In contrast to honeycomb monoliths, the flow uniformity downstream of ceramic foams does not decrease with increasing flow velocity. The higher flow uniformity of ceramic foams is not only caused by their higher pressure drop, but also by flow homogenization that occurs inside the ceramic foam structure, as a result of the momentum exchange perpendicular to the main flow direction.     

A unified theory of turbulent flow

Summary A general theory of turbulent flow is applied to incompressible flow in a circular pipe. The theoretical mean velocity distribution is found to be in good agreement with experiment, but there is some discrepancy in the normal stress distribution. The available pressure drop data are used to estimate the value of the apparent wall velocity as a function of Reynolds number and roughness. It is found that the results can be represented by simple expressions which in turn imply simple expressions for the pressure drop as a function of Reynolds number and roughness. However, it has not been possible to derive these results from fundamental considerations. The basis of Reynolds analogy and the application of the theory to channel flow are also discussed.     

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxelbased simulator V-FLOW VOF3 D, where the vessel geometry is expressed by using volume of fluid(VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model.     

Velocity profile characterization in sub-millimeter diameter tubes using molecular tagging velocimetry

Fluid flow through microtubes is of interest to many industries and there exists a need for detailed measurements of the velocity field. Velocity profile data are critical for momentum, mass, and heat transport analysis, and thus the design of devices utilizing microgeometries. This paper outlines a measurement technique that has led to time-resolved measurements of velocity profiles in microtubes (less than 1,000 μm). The research program was experimental in nature and consisted of an extension of molecular tagging velocimetry to the microscale. Average velocity and rms profile data in the fully developed region, in addition to mass flow rate and pressure drop data, are presented for numerous Reynolds numbers ranging from 600 to 5,000 in a tube of diameter 705 μm. Received: 20 December 1999 / Accepted: 20 March 2001     

微型管中液滴流动的三维数值模拟

对于微型设备中的低雷诺数流动，毛细力和黏性力起主导作用. 应用相场方法，引 入自由能泛函，研究了二相流体在微型管中流动问题及表面浸润现象，并给出了微型管中二 相流体的无量纲输运方程. 针对方形微管道，利用差分法给出了输运方程的数值求解方法. 最后，模拟了方形直管中的液滴流动和变形的过程，并给出了液滴前后压力差与其它主要物 理参数之间的变化关系. 结果表明，压力差随液滴半径增大而增加，而随毛细管系数的增大 而减小.     

The pressure drop characteristics of air–water bubbling flow for evaporative heat transfer

This paper presents a study on a novel water bubbling layer pressure drop and heat transfer experiment that was conducted to investigate the characteristics of pressure drop of air flow across the water bubbling layer. The attempt was to reduce the pressure drop while maintaining a higher value of the heat transfer coefficient. This type of heat transfer between water and merged tubes has potential application in evaporative cooling. To achieve the goal the pressure drop should be reduced by decreasing the bubble layer thickness through the water pump circulation. Pressure drops of air passing through the perforated plate and the water bubbling layer were measured for different heights of water bubbling layer, hole-plate area ratio of the perforated plate and the air velocity through the holes. Experimental data show that the increase of water bubbling layer height and air velocity both increase the pressure drop while the effect of the hole-plate area ratio of the perforated plate on the heat transfer coefficient is relatively complex. The measurements showed that even at a considerably lower height of water bubbling layer the heat transfer coefficient can exceed 5,000 W/m²-K. The heat transfer coefficients of 30 mm high water bubbling layer are higher than that of other higher water bubbling layers tested in the experiments     

3D CFD modeling of acetone hydrogenation in fixed bed reactor with spherical particles

Acetone hydrogenation in a fixed bed reactor packed with spherical catalyst particles was simulated to study the effects of inlet gas velocity and particle diameter on hydrogenation reaction. Computational results show that the catalyst particles in the reactor are almost isothermal, and the high isopropanol concentration appears at the lee of the particles. With the increase of inlet velocity, the outlet isopropanol mole fraction decreases, and the total pressure drop increases drastically. Small diameter catalyst particles are favorable for acetone hydrogenation, but result in large pressure drop.     

Modelling the flow of power law fluids in a packed bed using a volume-averaged equation of motion

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous microstructure model based on a cell model is used. Numerical solution of the resulting equation is effected using a penalty Galerkin finite element method. Experimental pressure drop values for dilute solutions of carboxymethylcellulose flowing in narrow tubes packed with uniformly sized spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model through the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the bed pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.     

倾斜非均匀磁场下导电方管磁流体管流的数值模拟研究

热核聚变反应堆液态金属包层应用中的一个重要问题是液态金属在导电管中流动和强磁场相互作用产生的额外的磁流体动力学压降.这种磁流体动力学压降远远大于普通水力学压降.美国阿贡国家实验室ALEX研究小组,对非均匀磁场下导电管中液态金属磁流体动力学效应进行了实验研究,其实验结果成为液态金属包层数值验证的标准模型之一.液态金属包层在应用中会受到不同方向的磁场作用,本文以ALEX的非均匀磁场下导电方管中液态金属管流实验中的一组参数为基础,保持哈特曼数、雷诺数和壁面电导率不变,采用三维直接数值模拟的方法,研究了外加磁场与侧壁之间的倾角对导电方管内液态金属流动的速度、电流和压降分布的影响.研究结果表明:沿流向相同横截面上的速度、电流以及压力分布均随磁场的倾斜而同向旋转.倾斜磁场均匀段,横截面上的高速区位于平行磁场方向的哈特曼层和平行层交叉位置,压力梯度随磁场倾角的增大先增大后减小.倾斜磁场递减段,在三维磁流体动力学效应作用下,横截面上的高速射流位置向垂直磁场方向偏移.磁场递减段的三维磁流体动力学压降随磁场倾角的增大而增大.随磁场倾斜,截面上的射流峰值逐渐减小,二次流增强,引发层流向湍流的转捩.      

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semiempirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.