Measurement of liquid film thickness and the determination of spin-up radius on a rotating disc using an electrical resistance technique

A method of rapid measurement of liquid film thickness on a spinning disc surface is presented. The concepts used are based on the analysis of the electrical resistance of the liquid film and its relationship to film thickness when high frequency voltages are applied. A comparison with the Nusselt model is made for a wide range of operating conditions. Experimental data are presented and calculations of mean radial flow velocity based on film thickness measurements are made and shown to compare well with a simplified two-dimensional model. An empirical model for the extent of the spin-up radius is developed to provide a guide to the zone at which the Nusselt model breaks down.     

Investigation of laminar flow in a stirred vessel at low Reynolds numbers

Many mixing applications involve viscous fluids and laminar flows where the detailed as well as overall flow structures are important. In order to understand the fluid dynamic characteristics of low Re laminar flows in mixing vessels, the flow induced by a Rushton impeller for three Re namely, 1, 10 and 28, was studied both experimentally and computationally. It was found that for the highest Re, the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re a reciprocating motion with negligible net pumping was observed. This behaviour has not been reported in the literature in the past and represents a highly undesirable flow pattern from the standpoint of effective mixing. The CFD results successfully reproduced this behaviour. In order to elucidate the physical mechanism responsible for the observed flow pattern, the forces acting on a fluid element in the radial direction were analysed. The analysis indicated that for the lowest Re, the material derivative of radial velocity near the blade tip is small thus a balance exists between pressure and viscous forces; the defining characteristic of creeping flow. The velocity and pressure forces are in phase because the velocity is driven by the pressure field generated by the rotation of the impeller. Based on these findings, a simplified analytic model of the flow was developed that gives a good qualitative as well as quantitative representation of the flow.     

Modelling laminar pulsed flow for the enhancement of cleaning

A Green function method is presented which enables computation of laminar flow of an incompressible Newtonian fluid in circular and annular pipes, subject to an arbitrary forcing periodic pressure gradient, in terms of Bessel functions. The response to a step change in pressure gradient in an annular pipe is presented. The method allows direct calculation of wall shear stress and flow rates generated by pulsed flows, which are of interest in fouling mitigation and cleaning-in-place systems.     

Microdynamic analysis of particle flow in a horizontal rotating drum

The flow of particles in a horizontal rotating drum is studied based on the results generated by Distinct Element Method (DEM). The simulation conditions are comparable to those measured by means of Positron Emission Particle Tracking (PEPT), with a drum being 100 mm in diameter, 35% filled by spheres of 3 mm diameter, and rotating at a speed from 10 to 65 rpm. The simulation method is validated from its good agreement with the PEPT measurement in terms of the dynamic angle of repose and spatial velocity fields. The dependence of flow behaviour on rotation speed is then analysed based on the DEM results, aiming to establish the spatial and statistical distributions of microdynamic variables related to flow structure such as porosity and coordination number, and force structure such as particle interaction forces, relative collision velocity and collision frequency. An attempt has also been made to explain the effect of rotation speed on agglomeration based on the present findings.     

An experimental study on the effect of liquid content and viscosity on particle segregation in a rotating drum

The segregation phenomenon of wet granular materials was experimentally studied in a quasi-2D rotating drum. The mono-disperse systems and binary-mixture systems (with 4 mm and 2 mm glass beads and 40% filled volume fraction) were used. All the experiments were controlled so the Froude number of the rolling regime was 2.79 × 10^− 4. The effects of the volume and the viscosity of the liquid added to the granular system on the segregation index and angle of repose in the rotating drum were investigated and are discussed in this paper.The experimental results indicate that the volume and viscosity of the added liquid have significant effects on the wet granular flow. The results demonstrate that the segregation index decreases with an increase of the repose angle of the wet granular materials, regardless of the volume or viscosity of the added liquid.     

Numerical simulation of particle dynamics in different flow regimes in a rotating drum

Flow regimes in a horizontal rotating drum are important to industrial applications but the underlying mechanisms are not clear. This paper investigated the granular flow dynamics in different regimes using the discrete element method. By varying the rotation speed and particle-wall sliding friction over a wide range, six flow regimes were produced. The macroscopic and microscopic behaviour of the particle flow were systematically analysed. The results showed that the angle of repose of the moving particle bed had a weak dependence on the rotation speed in the slumping and rolling regimes, and increased significantly as the flow transited to the cascading and cataracting regimes. The mean flow velocity increased with the rotation speed, but the normalised velocity against the drum speed in the continuous regimes collapsed into a single curve, which can be well described by a log-normal distribution. The particle bed at low rotation speed had a similar density to those of the random loose packing, and became more dilated with the increase of the rotation speed. Similarly, the mean coordination number showed linear dependence on the drum speed. Both the collision energy and collision frequency increased with the rotation speed. However, the normalised collision energy in different regimes can be fitted with a simple scaling law.     

倾斜波纹板上液膜流动的CFD研究

利用VOF法建立了液膜在倾斜波纹板上的气-液两相流CFD模型,并根据液膜流动特点提出了表面张力动量源项和气液界面作用力动量源项.模拟结果与文献实验值吻合较好,表明本文提出的CFD液膜流动模型具有一定的可靠性.通过模拟不同性质的液体在不同表面结构波纹板上的流动过程发现,波纹板表面微观结构以及液体性质尤其是液体的表面张力对连续液膜的形成有重要作用,表明通过改变波纹板面微观结构以及降低液体的表面张力可以促进连续液膜的形成,对提高气液之间的传质效率有重要意义.     

Experimental investigation of transition to laminar mixing of a homogeneous viscous liquid in a tilted-rotating tank

A tilted and partially filled rotating tank is investigated experimentally at O(1) Reynolds and small (?1) capillary numbers, to study the mixing of a viscous homogeneous fluid. Of particular interest is the transition from a previously studied low Reynolds number flow regime [Ward, T., Metchik, A., 2007. Viscous fluid mixing in a titled tank by periodic shear. Chemical Engineering Science 62, 6274-6284], that exhibited two large vortices, to the laminar flow regime which results in additional vortex generation. In the laminar Reynolds number limit O(1) the two primary vortices generated by the liquid rotation axis can interact with the bottom wall, generating two secondary counter-rotating vortices, via a cascade that is qualitatively similar to the well known Moffatt [1964. Viscous and resistive eddies near a sharp corner. Journal of Fluid Mechanics 18, 1-18] vortices in Stokes flow. While the secondary vortices aid in transporting material from the walls to the bulk, they also intensify in magnitude with increasing rotation rate leading to finite sized unmixed regions via the appearance of KAM-like surfaces [Alvarez-Hernández, M.M., Shinbrot, T., Zalc, J., Muzzio, F.J., 2002. Practical chaotic mixing. Chemical Engineering Science 57, 3749-3753]. This suggests that there may be an optimal tilt angle, for a given speed, with which to achieve the maximum mixed cross sectional area within a minimum amount of elapsed time. Experiments are performed using a 90% glycerol, 10% water mixture at two volume portions with angles ranging between 25^° and 65^° measured from the horizontal. Laser fluorescence is used to illuminate the vortices via experimental Poincaré mapping [Fountain, G.O., Khakhar, D.V., Ottino, J.M., 1998. Visualization of three dimensional chaos. Science 281, 683-686], and the resulting images are analyzed to determine the mixed cross sectional area versus elapsed time.     

The experimental observation and modelling of microdroplet formation within a plastic microcapillary array

This paper reports an experimental study of the formation of a two-phase liquid mixture in a circular capillary tube of 0.74 mm diameter. Organic liquid, the continuous phase, flowed through the capillary. Aqueous liquid, the dispersed phase, was injected through a hypodermic entering the side of the capillary and a stream of aqueous droplets was formed in the flowing organic liquid. The observed droplet diameters depended strongly on the ratio of the flow-rates between the dispersed and continuous phases: droplet diameters ranged between 480 and 64 μm. A simple model gave good predictions, matching the data and showing how the droplet diameter is dependant on the flow rates of the two phases. The flow geometry was similar to the T-junction configuration used for emulsion formation in microfluidic devices and was fabricated from an extruded plastic capillary array termed a microcapillary film (MCF).     

Axial dispersion of particles in a slugging column—the role of the laminar wake of the bubbles

Axial solid dispersion promoted by Taylor bubbles in a batch liquid column was studied. A mechanistic model was developed to predict the axial solid dispersion. The model is based on the upward transport of particles inside closed wakes of non-interacting Taylor bubbles. The model predictions are compared with experimental data. The experimental data were obtained in a test tube of internal diameter. The particle volumetric distribution was measured by several differential pressure transducers placed along the column. Two classes of glass beads, mean diameter 180 and , were suspended in aqueous glycerol solutions, with glycerol percentage ranging from 40% (v/v) to 100% (v/v). The amount of particles in the column was such that the volumetric particle fractions were 0.1, 0.2 and 0.3, supposing homogeneous liquid-solid suspension. The air flow rate ranged from 90×10⁻⁶ to at PTN conditions. The obtained experimental data are in good agreement with the model predictions for laminar wakes, i.e., closed wakes with internal recirculation and without vortex shedding. The experimental data show a higher upward particle transport for wakes in the transition laminar-turbulent regime; closed wakes with internal recirculation and vortex shedding. The upward particle transport is higher for increasing air flow rate, decreasing particle diameter and increasing amount of particles in the column.     

Integral methods for flow in a conical centrifuge

A set of through-thickness averaged equations for momentum and strain rate are derived for the problem of axi-symmetric free-surface flow within a spinning cone. The expressions are independent of the choice of constitutive law and can therefore be used for modeling the flow of a variety of materials within an industrial conical centrifuge. By assuming a through-thickness velocity profile the distribution of flow thickness and average velocity over the internal surface of the cone can be obtained. The approach has been validated for thin Newtonian viscous flow by comparison with full three-dimensional solutions of the Navier–Stokes equations obtained with a commercial CFD package. The averaged equations provide an accurate prediction of the flow thickness, velocity and the length of the zones of influence of inlet and outlet boundary conditions.     

The measurement and characterisation of residence time distributions for laminar liquid flow in plastic microcapillary arrays

Residence time distributions (RTDs) for a thermoplastic microreactor system were experimentally measured using fibre optic probes and step change concentration inputs. The distributions were then compared to models assuming plug flow superimposed by axial dispersion. The disc-shaped plastic microreactors contained microcapillary arrays of up to 19 parallel channels with diameters around 230 μm and lengths of 10 m. Two different systems were investigated, with either 1 or 19 active capillaries. The magnitude of axial dispersion in those two systems was characterised using Peclet numbers, which were in the range of 15-221 depending on flow rate, demonstrating that molecular dispersion along a single 10 m capillary can provide near plug flow characteristics. The multiple-capillary array showed small perturbations of this plug flow like RTD behaviour as the 19 microcapillaries displayed slight variations in diameter. These results confirm that the flow inside the presented plastic multiple capillary device provides a near plug flow behaviour for the use in continuous microreactors.     

水平管段塞流气弹区液膜特性研究

为了研究气液段塞流相界面的结构特征,采用了双平行电导探针技术对水平管内段塞流气弹区的液膜特性进行了实验测量,并基于一维双流体模型导出液膜厚度的控制方程,该方程对液膜厚度的预测结果与实验结果吻合良好。结合液膜厚度计算模型提出了计算段塞流的机理模型,该段塞流机理模型的计算结果表明对于液相表观速度较高而气相表观速度较低的段塞流,机理模型中忽略液膜非平衡性时得到的平均液膜厚度和气弹区长度明显偏低。     

Experimental analysis of the dynamic properties of wet granular matter in a rotating drum

We performed experiments to measure the dynamic properties of wet granular matter in a rotating drum device. Four different amounts of liquid and rotation speeds were used in the experiments. The purpose was to quantify the effect of the cohesive force in the granular system. The results show that when only very small amounts of liquid were added, no liquid bridges formed. This is because the liquid was first trapped on the surface of the particles due to the particle roughness. When the volume fraction of the fluid became larger, liquid bridges formed on almost every particle. The results showed that the addition of liquid contents, and changing the rotation speed, both had a significant effect on the dynamic properties of granular matter. This was due to the hysteretic formation and rupturing of liquid bridges and the introduction of inertial force to the device. After the liquid bridges formed between all particles the average energy dissipation due to the hysteretic formation and rupturing of the liquid bridges increased with an increase in the liquid content.     

A study of film thickness and hydrodynamic entrance length in liquid laminar film flow along a vertical tube

The liquid film thickness and hydrodynamic entrance length in a vertical tube was studied experimentally and numerically. Measurements using distilled water, 30 wt % MEA and 40 wt % sugar solutions were carried out to investigate the effects of liquid flow rate on the formation of the liquid film. The experimental results validate the new Navier‐Stokes based equation in cylindrical coordinates (Eq. 16) and the volume of fluid (VOF) model giving a competitively high prediction of the liquid film thickness especially in the low Reynolds number region. In addition, a new empirical model and an improved minimal surface model have been first proposed for calculation of the hydrodynamic entrance length, with a relatively reasonable average absolute relative deviation (AARD) of 3.03% and 6.83%, respectively. Furthermore, the effects of the hydrodynamic entry length on the gas–liquid interfacial area calculated by the improved minimal surface model were comprehensively studied, and can be ignored if the ratio of the liquid film length (y) and the hydrodynamic entrance length (λ_E) is lower than 10. However, it should be noted that the hydrodynamic entrance length cannot be ignored in packed columns in which the liquid flow is very complex due to the packings with different structures and materials. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2078–2088, 2018     

Forces on the surface of small ellipsoidal particles immersed in a linear flow field

Knowledge of the forces which a fluid motion exerts on the surface of suspended material is important for many processes in which the particles are broken apart by the hydrodynamic forces. In this paper, we examine the stresses on a small ellipsoidal particle which is immersed in either a constant, simple shear, two-dimensional straining or axisymmetric straining flow. Calculations have been performed using Oberbeck's and Jeffery's models and have been appropriately visualized. Furthermore, the motion and orientation of the ellipsoid have been examined and the extreme values of stresses have been analyzed. A simple criterion for the break-up of particles is proposed. The analysis shows that the straining flows are particular important for the load on particles. In contrast, simple shear flows are less crucial as the presence of vorticity leads to a rotation of the particles.     

规整填料表面液膜流动特性的数值模拟

精馏过程气液两相流运动分布特征对分离效率具有重要影响。为研究规整填料表面液膜流体动力学特性建立了基于VOF方法的CFD分析模型,并基于文献试验结果进行了验证。对液膜随时间和空间的演化分布特征、速度场分布和液相流量影响进行了模拟分析。液膜在波纹顶部下沿聚集形成凸起状波峰,在波纹底部波峰消失,而到达下节波纹上沿时,波峰重新形成;瞬态液膜厚度随时间波动,且沿填料表面液膜平均厚度先减小后保持稳定;发现液相聚集及形成液滴坠落容易导致出现干板区。不同位置液膜速度分布存在明显差异,沿填料表面液膜平均速度先增后减或保持稳定;液膜绕过波纹顶部时会加速,在波纹底部和上沿处会减速。液相流量增大,液膜平均厚度和速度均有所增大。     

管柱式气液旋流分离器液膜厚度的空间分布特性

管柱式气液旋流分离器(GLCC)是一种耦合离心力与重力的分离设备,其上部筒体内旋流液膜的分布特征显著影响其分离性能。液膜厚度作为该旋流液膜的关键参数,掌握其分布规律可为理解液膜的流动机制奠定基础。利用纽扣式电导传感器测量了GLCC上部筒体内的液膜厚度,通过改变入口气液相流量、入口喷嘴尺寸,系统地研究了其空间分布特性。结果表明,操作参数一定时,液膜厚度沿轴向向上趋于减小;在某一轴向位置,液膜厚度随入口气量的增大呈现"S"形分布,随入口液量的增大而近线性增大;此外,入口喷嘴尺寸对液膜厚度的分布影响显著:在不同的轴向位置,不同尺寸喷嘴对应的液膜厚度间的大小存在差异。液膜厚度随气液量的变化规律证明液膜逃逸是GLCC液相分离效率降低的直接原因,而喷嘴尺寸对液膜厚度沿轴向分布的影响则反映了GLCC旋流效应与重力效应间的相互作用。     

Flow visualization of the liquid emptying process in scaled-up gravure grooves and cells

The liquid-emptying process in scaled-up gravure grooves and cells is studied using flow visualization in order to better understand gravure coating and printing processes. Water and two different glycerin/water mixtures serve as the test liquids, and the emptying process is initiated by moving over the groove or cell a rotating roller or a glass top with a curved surface. For the scaled-up groove, a region of recirculating flow is observed to attach to the moving glass top. When the glass top is used to drive flow in the scaled-up cell, an air bubble may appear inside the cell when the gap between the bottom of the curved surface and the top of the cell is zero. When this gap is positive, a liquid bridge is formed, dragged across the cell, and then broken, leaving some liquid inside the cell. The amount of liquid remaining in the cell, V_r, is measured for different liquids, surface speeds, and gap distances for both the glass top and the rotating roller. The effect of using a soft elastomeric covering on the glass top and roller is also explored. For each liquid, V_r increases as the speed of the glass top or roller increases. The data are correlated by multiplying V_r by a liquid-dependent shift factor, which leads to a power-law relationship between the shifted V_r and the capillary number. These experimental observations and measurements can be used to benchmark theoretical calculations, which can then be applied to design gravure grooves and cells that empty in a controlled way.