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.     

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.     

Particle motion and separation in a laminar tube flow with downstream enlargement

Particle classification becomes difficult when the difference in density between particle and fluid is low or negligible and the fluid is viscous. For such applications, a process capable of separating the particles according to their size is needed. Such applications are, e.g. found in biological systems for cell separation or in the removal of gel particles from polymer melts. Particle transport in laminar tube flows at low but non zero Reynolds numbers leads to accumulation of large particles near the tube center and forms a particle free zone near the wall. Small particles find their position on their equilibrium radius. Downstream widening of the flow enhances segregation between large and small particles. Large particles can be collected in a centered collector tube downstream, whereas small particles follow their streamlines around the collector tube and can be removed with the remaining flow. The said particle migration is observed when the ratio of particle to tube diameter is 0.2<d/D<0.51 and the tube Reynolds number is in between 0.2<Re<40. CFD simulations reveal the shape of the streamlines in the downstream enlargement with different tube Reynolds number. The efficiency of the classification process is characterized. Particles need a sufficient transportation length in the tube for proper demixing. This effect is analyzed by a laser sheet illuminated system within an acrylic glass tube.     

Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase flows

An analysis of the two-fluid model in the case of vertical fully developed laminar bubbly flows is conducted. Firstly the phase distribution in the central region of the pipe (where wall effects vanish) is considered. From the model equations an intrinsic length scale L is deduced such that the scaled system reduces to a single equation without parameters. With the aid of this equation some generic properties of the solutions of the model for pipes with diameter greater than about 20L (the usual case, since L is of the order of the bubble radius) are found. We prove that in all physically meaningful solutions an (almost) exact compensation of the applied pressure gradient with the hydrostatic force occurs (with ρ_eff the effective density and the gravity). This compensation implies flat void fraction and velocity profiles in the central region not affected by the wall, even when no turbulence effects are accounted for.We then turn to consider the complete problem with a numerical approach, with the effect of the wall dealt via wall forces. The previous mathematical results are confirmed and the near-wall phase distributions and velocity profiles are found. With the numerical code it is also possible to investigate the regime in which the pressure gradient is greater than the weight of the pure liquid, in which case a region of strictly zero void fraction develops surrounding the axis of the pipe (in upward flow of bubbles).Finally, the same code is used to study the effect of reducing the gravity. As decreases, so does the relative velocity between the phases, making the lift force increasingly dominant. This produces, in upward bubbly flows, narrower and sharper void fraction peaks that also appear closer to the wall.     

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.     

Centrifugal-force driven flow in cylindrical micro-channel

Micro-channel flow driven by the centrifugal force was studied by analytical and experimental methods. The analytical expression of flow rate as a function of angular revolution speed was applied to the flow under the condition that the increase in frictional loss due to Coriolis force could be neglected. The experimental verification was made by measuring the outlet volume of water through capillaries that were radially mounted. The experimental results show that cavitation can occur in micro-channel flow driven solely by centrifugal force.     

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.     

Liquid–gas flow patterns in a narrow electrochemical channel

The flow in a narrow (3 mm wide) vertical gap of an electrochemical cell with gas evolution at one electrode is modeled by means of the two-phase Euler–Euler model. The results indicate that at certain conditions an unsteady type of flow with vortices and recirculation regions can occur. Such flow pattern has been observed experimentally, but not reported in previous modeling studies. Further analysis establishes that the presence of a sufficient amount of small (∼10 μm) bubbles is the main factor causing this type of flow at high current densities.     

壁面润湿性对微通道内Taylor流动特性的影响

壁面润湿性不仅影响着Taylor气泡的形状,同时对通道内流体流动、相变换热等有着关键的作用。采用VOF模型对T型微通道内气液两相Taylor流动进行三维数值模拟,重点研究了接触角改变对Taylor气泡流体动力学特性的影响。模拟结果与他人实验数据对比基本吻合,验证了模型的有效性。结果表明：随着接触角增大,气泡周围液含量逐渐降低,相界面也由外凸形变为内凹形。壁面越接近润湿（或疏水）状态,气液接触面的曲率就越大;当120°≤θ≤150°时Taylor气泡稳定性变差。当θ≥150°时“拖曳流态”出现,分析指出在大接触角下气体更易贴附壁面导致接触区内流场发生变化,形成的涡流减弱了水对气相的水平剪切作用,进而引起流型转变。接触角对通道内压力有着重要影响,通道中心轴向压力曲线以θ=90°为过渡,润湿状态下呈凸函数递减且p _G>p _L,疏水状态下气液进口处的压力分配改变,曲线趋势相反。     

The effect of Al content on the wettability between liquid iron and MgOAl2O3 binary substrate

In the present study, the wettability between liquid iron with two different Al contents and MgOAl₂O₃ binary substrates was studied in reducing atmosphere. The contact angles between liquid iron with 18?ppm Al and MgO, MgO·Al₂O₃, Al₂O₃ were 133.5°, 113.7°, 126.9° respectively. With the variation of the substrate composition, the contact angles for the intermediate binary phases of the three components (MgO, MgO·Al₂O₃, Al₂O₃) obeyed the Cassie theory. In the experiment using iron with 370?ppm Al, all the contact angles were higher than that using low Al-containing iron. The surface of the iron drop was covered with an oxide layer, which mainly consisted of many small particles. With the variation of the substrate gradually from MgO to Al₂O₃, the composition of the oxide layer changed from MgO·Al₂O₃ to CaOAl₂O₃. The formation of the oxide layer prevented the spreading of liquid iron, leading to the increase of the contact angle.     

Modelling laminar pulsed flow in rectangular microchannels

Fully developed laminar pulsed flow of an incompressible Newtonian fluid through rectangular ducts has been modelled and analyzed using Green functions. Based on the solutions for the velocity profile presented previously [Fan, C., Chao, B.-T., 1965. Unsteady, laminar, incompressible flow through rectangular ducts. Zeitschrift für Angewandte Mathematik und Physik 16, 351-369], exact analytical solutions in series form for wall shear stress and volumetric flow rate have been obtained. Various flow effects in periodic pulsed flow through rectangular microchannels, including flow reversal, phase shift and wall shear stress enhancement were calculated indicating that a substantial increase in local wall shear stress can be achieved with a modest increase of average flow rate over a cycle. The analytical solutions and the calculated results will help optimize parameters in cleaning of microfluidic devices by pulsed flow.     

煤灰渣在Cr2O3-Al2O3-ZrO2砖表面润湿与渗入行为的研究

将灰分(w)为6.81%,挥发分(w)为32.68%的煤制成煤灰后,压成圆柱形的煤灰柱放在Cr2O3(w)含量约为90%的Cr2O3-Al2O3-ZrO2砖上,再推入管式加热炉中,在Ar气氛下,通过升温试验(升温至1200℃)和保温试验(升温至1165℃保温20min),考察了煤灰渣在Cr2O3-Al2O3-ZrO2砖表面的润湿与渗入行为。结果表明无论是升温试验还是保温试验,煤灰柱的变化过程完全一致,都经历了变形、熔融和润湿等一系列的变化。对升温试验过程中煤灰柱变化的观察和照片的处理结果均表明煤灰柱在1100℃时局部凹进去形成不规则形状;在1165℃时煤灰完全熔化,煤灰柱变成半球形;在1180℃时接触角<90°,煤灰渣开始在Cr2O3-Al2O3-ZrO2砖表面发生润湿。对升温试验后的Cr2O3-Al2O3-ZrO2砖表面和渣表面的化学组成分析表明有大量Fe堆积在煤灰渣与Cr2O3-Al2O3-ZrO2砖表面接触处,而邻近处几乎没有发现Fe,可能是由于Fe与Cr2O3-Al2O3-ZrO2砖中的一些组分形成了某种晶相,使得Fe很难进入Cr2O3-Al2O3-ZrO2砖;接近煤灰渣的Cr2O3-Al2O3-ZrO2砖表面组成中出现了Ca,说明熔融灰渣中的Ca渗入Cr2O3-Al2O3-ZrO2砖;同时,煤灰渣中出现了Cr,表明在熔融灰渣渗入Cr2O3-Al2O3-ZrO2砖的同时,砖中的Cr也熔入了熔渣中。     

Low Reynolds number flow in a channel with oscillating wavy-walls: An analytical study

An analytical study using perturbation methods has been investigated on the flow profiles and power requirements in an oscillating flow field with a wavy-walled boundary. The velocity field is found for a fluid in between two wavy-walled plates that oscillate in phase. The wavy-walled boundary causes the flow to produce regions of recirculations within the recesses of the boundary. Once the velocity profiles are identified, the power required to drive the oscillatory fluid motion is then calculated and compared to a flat plate geometry without recesses. As expected, the analytical results show that more power is needed to drive a wavy-walled system than a flat plate configuration.     

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.     

Investigating the effect of power/time in the wettability of Ar and O2 gas plasma-treated low-density polyethylene

Low-pressure glow discharges of Ar or O₂ gas plasmas were used to increase the wettability of low-density polyethylene (LDPE) films in order to improve their adhesion properties hence making them useful in technical applications. Surface free energies of such films were estimated by the aid of contact angle measurements at different exposure power/time combinations for a series of test liquids. Additionally, plasma-treated samples were subjected to several aging processes to determine the durability of different plasma treatments. Characterization of the surface changes due to plasma treatments were carried out by means of attenuated total reflectance, Fourier transform infrared spectroscopy (FTIR-ATR) to determine the presence of polar species such as hydroxyl, carbonyl, carboxyl, etc. groups. Furthermore, atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to evaluate changes in surface morphology and roughness. Considering the semi-crystalline nature of the LDPE film, XRD studies were also carried out to determine changes in the percentage of crystalinity. The results showed that all low-pressure Ar or O₂ gas plasmas improve the wettability properties of LDPE films. Contact angles decreased significantly depending on the discharge powers and exposure times. Surface morphology was also found to vary with plasma discharge powers, exposure times, and the type of gas being used. Ar gas plasmas comparatively produced superior results.     

Partial wetting in porous catalysts: wettability and wetting efficiency

Qualitative changes in the local (pore level) wetting efficiency of a porous catalyst as a function of catalyst wettability are proposed based on monitoring the 1-D motion of the solid-liquid-gas contact line. As catalyst wettability is increased, the resulting wetting efficiency is likely to show two distinct transitions viz., (1) a sudden decrease that is inspired by coalescence of neighboring rivulets and, (2) a sudden increase that is inspired by porous nature of the catalyst. As catalyst wettability decreases, the wetting efficiency is likely to decrease in the beginning but can then be held constant due to pinning or holding of the retracting contact line by liquid-filled pores. This will result in comparatively much higher wetting efficiencies. It is further proposed that under favorable circumstances this pinning can disappear and will, thus, allow the contact line to retract and wetting efficiency to decrease. In the end, the effect of catalyst geometry on the relation between wetting efficiency and wettability is presented.     

Experimental study of drag reduction by a polymeric additive in slug two-phase flow of crude oil and air in horizontal pipes

In this study the effect of the presence of a drag reducing agent (DRA) on the pressure drop in cocurrent horizontal pipes carrying slug two-phase flow of air and crude oil is investigated. An experimental set-up is erected. The test section of the experimental set-up is consisted of: a smooth pipe of polycarbonate with 10.3 m long and 2.54 cm ID, a rough pipe of galvanized iron with 8.8 m long and 2.54 cm ID and a rough pipe of galvanized iron with 8.8 m long and 1.27 cm ID. The employing DRA is a Polyalpha-olefin (Polyisobutylene). The percent drag reduction (%DR) is calculated using the obtained experimental data, in presence of the DRA. The results show that addition of DRA could be effective up to some doses of DRA after which the pressure drop is kept constant. A %DR of about 40 is obtained for some experimental conditions.     

Enhancement of laminar mixing by optimal control methods

Calculus of variations is applied to the problem of optimal mixing of two immiscible fluids in a laminar flow where stretching of the interface between the liquids is treated as an objective function. Under the action of an optimal control, the system behaves like that driven by a negative surface tension, i.e., an initially flat interface evolves in long tongues that are stretched and twisted by the flow. The method was tested for mixing by Stokes flow in lid-driven two-dimensional rectangular cavity.     

Laminar flow of power-law fluids in the entrance region of a pipe

The study is concerned with developing laminar flow of a power-law fluid in a circular tube. The analysis extends the filled-region concept, used previously to study Newtonian fluid flow, to the more general class of power-law fluids. Flow is analyzed in both the inlet and filled regions using an integral boundary layer method. Results obtained provide the lengths of the entrance, inlet and filled regions as a function of the generalized Reynolds number and the power-law fluid index. In addition, the variations of the local friction factor, the pressure drop and the centerline velocity along the axial coordinate are also provided. The available models are compared with the present one on the basis of experimental data. The present results are found to reach asymptotically the fully developed values, and also to be in good agreement with all available experimental data.     

Modeling pressure losses for Newtonian and non-Newtonian laminar and turbulent flow in long square edged orifices

A lack of experimental data and predictive models prompted the determination of loss characteristics of four sharp square-edged orifices for laminar to turbulent flow regime (1 ≤ Re ≤ 100,000). Novel experimental data for β ratios of 0.36, 0.4, 0.5 and 0.7 obtained with Newtonian and non-Newtonian fluids and an empirical correlation for predicting pressure losses through long square edged orifice plates is presented. For turbulent flow, new experimental results compared well with existing predictive models, thus validating the experimental results. Comparison of existing correlations as well as the new correlation shows that, although with some shortcomings, good progress is made toward a design correlation that spans a wide range of laminar to turbulent flow conditions for long orifices.