Velocity of isolated particles along a pipe in stratified gas–liquid flow

The average velocity of isolated grains of sand was experimentally measured in smooth stratified flow in slightly declined pipes. Isolated particles in smooth stratified flow behave similarly to isolated particles propelled by both hydraulic conveying and intermittent gas/liquid flow. In all three cases, particle velocity is linear with respect to the average liquid velocity of the flow (or the average fluid velocity in the slug body for intermittent flow) and has a gradient of approximately one. The data in stratified flow are successfully correlated dimensionlessly (Eq. 7). The correlation is extrapolated to zero particle velocity to estimate the conditions required to ensure sand transport in a flowline in smooth stratified flow. The experimental results suggest that particle velocity is strongly governed by the size of a particle relative to the depth of the viscous sublayer at the pipe wall. If a particle is larger than the viscous sublayer, it is exposed to more coherent turbulent structures and therefore experiences a greater drag.     

Characterization of liquid‐liquid flows in horizontal pipes

Diverse flow regimes have been encountered in liquid‐liquid flows. Some degree of consistency in the observed flow patterns is shown in reported studies, while inconsistency exits when physical properties of the two phases concerned are wide enough. An attempt was made in this study to investigate the mechanisms behind flow patterns of liquid‐liquid flows in horizontal pipes. A literature review on flow patterns of liquid‐liquid flows in horizontal pipes was conducted. The ratio of the gravitational force to viscous force was proposed to characterize liquid‐liquid flows in horizontal pipes into gravitational force dominant, viscous force dominant, and gravitational force and viscous force comparable flow featured with different basic flow regimes. Comparisons of the proposed characterization criterion with the literature data show good agreement. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1132–1143, 2017     

Incipient motion of a bed of particles resting on a submerged oscillating plate

A model for the incipient motion of a particle resting on a bed of like particles carried by a submerged oscillating plate is presented. The model is developed by extending the theory of Stevenson et al. (Chem. Eng. Sci. 57, (2002) 4505) who gave a force balance for limiting equilibrium of a particle within the viscous sublayer at a pipe wall to the present case by including a d'Alembert type force due to the oscillatory motion of the plate. Simultaneous equations are presented that can estimate the phase and frequency of first motion as a function of system parameters. The new model is compared with the data of Bagnold (Proceedings of the Royal Society, London A 187, (1946) 1-15) and is shown to be in excellent agreement.     

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018     

Lift force in bubbly flow systems

From the significance of three-dimensional simulation of dispersed flow systems in many engineering fields, extensive study was conducted for lift force in a single particle system as well as a multiparticle system. In this study, the lift force in a single particle system was modeled by considering the effect of bubble deformation on the lift force. The model was finalized based on existing data obtained in the range of particle Reynolds number from 3.68 to 78.8, viscous number from 0.0435 to 0.203 and Eötvös number from 1.40 to 5.83. The viscous number is defined by where μ_f, ρ_f, σ, g and Δρ are, respectively, fluid viscosity, fluid density, surface tension, gravitational acceleration and density difference between phases. The applicability of the model to higher particle Reynolds number system such as an air-water system was qualitatively examined. The lift force model developed in a single particle system was extended to a multiparticle system. The applicability of the extended lift force model was qualitatively examined. The similarity between drag and lift forces were also discussed.     

垂直立管中颗粒移动床蠕动流动特性的实验研究

在无负压差的环境下,采用PV6D型颗粒速度测量仪,考察了垂直立管中FCC催化剂颗粒移动床的蠕动流动特性. 结果表明,颗粒质量流率较小时立管中颗粒流动具有明显的蠕动流动特性,可划分为两种流态,拟气固雷诺数Re<500时为间歇式蠕动流动,5004000时颗粒的蠕动流动转变为密相流化流动. 立管中颗粒的蠕动流动主要是出口区颗粒成拱与崩塌交替进行产生的,其次为颗粒与器壁滑动摩擦力的不稳定性变化起作用. 微观上颗粒流动的蠕动行为是颗粒之间力链作用变化的结果.     

应用热阻分析缩放管强化传热机理

应用分析求解和数值模拟方法对光滑圆管与缩放管内的湍流对流传热的热阻分布进行了计算,计算结果表明,光滑圆管的热阻主要位于粘性底层,缩放管通过壁面缩放,减小了粘性底层的热阻,湍流区成为热阻分布主要区域。在流动粘性底层,缩放管的热阻降低归功于该层厚度的降低,在流动粘性底层以外的传热粘性底层,则是边界层厚度的降低、速度矢量与温度梯度的协同影响。随Re数增大,圆管与缩放管各层热阻均减小,流动粘性底层以外的传热粘性底层的降幅最大。     

MASS TRANSFER IN TURBULENT PULSATING FLOWS

The effect of flow oscillation to the mass transfer between turbulent fluid and solid wall was investigatedby measuring the mass transfer rate between fluid and pipe wall with imposed oscillating flow usingelectrochemical method.The velocity and concentration field in the viscous sublayer which controls the mass trans-fer in such a process was simulated by a simple wave model of single harmonics.Experimental results confirmthat the flow oscillation has no influene on time averaged mass transfer rate,but the phase difference betweenphase averaged velocity field and concentration field shifts with the frequency of imposed oscillating flow.Numeri-cal analysis reveals that the concentration boundarylayer which is responsible for the mass transfer is muchthinner than the viscous sublayer which greatly weakens the influence of imposed oscillating flow on mass transfer.     

Prediction of Particle Deposition Using a Simplified Particle Model in Fully Developed Channel Flow

In this study the Eulerian particle model was modified to predict the particle deposition rate in fully developed channel flow. The modified model is less complicated and has much lower computation time. The performance of the simplified model was examined by comparing the particle deposition rate in a vertical channel with the experimental data for fully developed channel flow available in the literature. The effects of turbophoretic force, thermophoretic force, electrostatic force, gravitational force, Brownian/turbulent diffusion, and the wall roughness on the particle deposition rate were examined. The predictions of the modified particle model were in agreement with the experimental data.     

Incipient motion of a small particle in the viscous boundary layer at a pipe wall

A force balance is derived for a hemispherical particle in the viscous boundary layer at the wall of a horizontal pipe conveying Newtonian fluid; the hemisphere, of radius much less than that of the pipe, rests on the bottom with its flat face against the wall. The drag on the hemisphere is calculated from the creeping flow field of Price (Q. J. Mech. Appl. Math. Pt. 1 (1993)). This yields a prediction of the maximum velocity gradient at the wall for equilibrium, with limiting friction between the hemisphere and the wall. It is shown that the flow field of Price predicts a zero lift force but the validity of this, for actual flows, is questioned. Use of a hemisphere formulates a relevant well-posed problem, capable of mathematical solution. However, the flow field around real particles, e.g. sand, is complex, because of their irregular shapes, but the hemisphere work gives a qualitative indication of the behaviour of irregular particles. For turbulent flow in a pipe it is pertinent to consider a particle wholly within the viscous sub-layer, because it is isolated from significant turbulence and therefore hard to move; for such flow, the theory gives Eq. (21) to predict the critical pipe velocity, v_C, for incipient motion of the hemisphere. For laminar flow, the wall shear rate is readily obtained from the parabolic velocity profile leading to Eq. (26) for v_C. The flow field of Price (and therefore the force acting on the hemisphere) is valid only for creeping flow (i.e. very low particle Reynolds number). Modifications to the force balance are tentatively suggested to account for inertial components to the drag force. The predictions of critical velocity are tested against our data for the incipient motion of small hemispheres at pipe walls in hydraulic conveying as well as new and previously published data for both hydraulic and pneumatic conveying. The new method of predicting incipient motion works well for both the pneumatic and hydraulic conveying of hemispheres and sand shaped particles but it overpredicts the critical velocity for more rounded particles. The dependency of critical velocity on particle shape is under-researched.     

方形微通道内流动凝结时气液相界面演进过程的数值模拟

基于VOF模型,模拟了R32在水力直径为50 μm的方形微通道内流动凝结时的气液两相流型演进过程,模拟涉及的流型包括环状流、喷射流、泡状流和收缩泡状流。模拟结果显示,由于沿通道周向气液界面存在曲率差异,凝结液内部存在表面张力导致的横向压力梯度,驱使凝结液流向通道壁面拐角处,减薄通道壁面中部液膜厚度。基于势能最小原理,解释了表面张力与界面黏性力主导的喷射流形成机理。小质量流率时,喷射流诱发环状流上游气液界面波动,界面波动在界面黏性力的作用下逐渐生长。这与大质量流率时,流向下游并逐渐生长的界面波动导致流型转换的机理不同。     

Application of a modified Eulerian model to study the particle deposition on a vertical surface in turbulent flow

In this study the v2-f model was used with the two-phase Eulerian approach to predict the particle deposition rate on a vertical surface in a turbulent flow. The standard Eulerian particle model was adopted from the literature and modified, considering the majority of particle transport mechanisms in the particle deposition rate. The performance of the modified model was examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The model took into account the effects of drag force, lift force, turbophoretic force, electrostatic force, inertia force and Brownian/turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and charged particles under the influence of an electric field were considered. The predictions of the modified particle model were in good agreement with the experimental data. It was observed that when both electrostatic forces are present they are the dominant factor in the deposition rate in a wider range of particle sizes.     

Modeling of Particle Removal using Non-contact Brush Scrubbing in Post-CMP Cleaning Processes

Particle removal using non-contact brush scrubbing for post-CMP (Chemical Mechanical Planarization) cleaning is investigated analytically. The removal of Si O ₂ and A l ₂ O ₃ particles adhered onto Si O ₂ film coated on the wafer surface are considered. The cleaning fluid (H ₂ O/N H ₄ OH = 1:25 and 1:200) flowing between the brush and wafer surface is treated as a thin-film fluid flow. The flow field details and its effect on the drag force acting on the adhered particles are discussed. In addition to the drag force, the electrical double layer (EDL) and thermophoretic force effects on particle removal are also considered. It was found that the dominant force in achieving particle removal using a rolling mechanism is the drag force. The EDL and thermophoretic forces have an insignificant effect on particle removal. Based on the results from this study, particles of submicron size can be removed from a wafer surface using higher brush rotation speed and pure deionized (DI) water as the cleaning fluid.     

Effect of particle deposition on the reduction of water flux in reverse osmosis

The phenomenon of particle deposition from a liquid stream flowing inside a membrane duct was studied. The rate of particle deposition is determined by trajectory calculation. Deposition occurs if a particle trajectory intersects the membrane surface.The forces considered include the gravitational force, the drag force and the surface forces. The major contribution to particle deposition is due to radial flow. At low water flux, both Brownian and surface forces are important. Furthermore, with a repulsive double layer force, a barrier may be present near the membrane surface, which would limit particle deposition significantly. Comparison with experimental data on water flux reduction indicates that the analysis given in this work provides a useful framework which can be applied for the assessment of water flux reduction due to particle deposition.     

A Stochastic Model for Particle Deposition and Bounceoff

A new model for particle deposition and bounceoff that combines current knowledge of turbulent bursts with the stochastic properties of turbulent fluctuations is presented. The model predictions for deposition velocities agree with experimental results in the literature for dimensionless particle relaxation time τ_p ⁺ > 2. For τ_p ⁺ > 10, most of the particles delivered to the edge of the viscous sublayer are able to deposit onto the surface due to their inertia; the deposition velocity approaches an asymptotic value because the process becomes limited by the rate of turbulent delivery to the viscous sublayer. Because of the penetration of turbulent fluctuations into the viscous sublayer, the minimum values of vertical velocities needed for particles to deposit onto the surface are smaller than those predicted by the free flight model. Most of the deposition occurs from those turbulent fluctuations at the upper tail of the distribution of the vertical component of air velocity.

In addition to the deposition velocity, the model is able to provide the distribution of particle velocities on reaching the surface which is used to compute the fraction of particle bounceoff. The model predictions for the fractions of rebound agree reasonably with the measured results from a wind tunnel experiment for τ_p ⁺ > 2. However, both the deposition velocity and the fraction of rebound are underestimated by the model for τ_p ⁺ < 2. Other mechanisms such as Brownian diffusion must be included in further revisions to this model in order to obtain satisfactory predictions for smaller values of τ_p ⁺.     

Quasi-direct numerical simulation of lift force-induced particle separation in a curved microchannel by use of a macroscopic particle model

The macroscopic particle model (MPM) based on the finite volume method is employed to validate a mechanism of lift force-induced particle separation in a curved microchannel. According to the particle velocity at each time step in the unsteady simulation, the MPM gives momentum to those fluid cells touching the particle physical boundary. The summation of the given momentum with the reversed sign is divided by the time step to obtain the hydrodynamic force acting on the particle. Namely, the existence and motion of the particle causes fluid flow around the particle, while the flow field caused by the particle determines the particle motion by means of the hydrodynamic force. Therefore, the MPM can be regarded as implementing a quasi-direct numerical simulation over the static computational cells. The lift force acting on a spherical particle in a shear flow is a purely hydrodynamic force caused by the flow field around the particle. It is expected, therefore, that the MPM could predict the lift force effect without any additional model. At first, it is shown that the MPM is capable of predicting particle migration away from the wall of a straight microchannel due to the lift force. In a curved microchannel, subsequently, the particle trajectories from representative release points predicted by the MPM are compared to those predicted by a common particle tracking method without any lift force model. The MPM predicted that the particle trajectories are confined in the outer region of the channel cross-section. On the other hand, the circulating trajectories predicted by the tracking method tend to expand due to centrifugal force caused by the Dean vortices. It is concluded, therefore, that the lift force due to the steep shear rate is a significant factor to cause particle separation in a curved microchannel.     

Classification of Fine Particles Using the Hydrodynamic Forces in the Boundary Layer of a Membrane

The wet classification of particles < 10 μm is a complex process that has been researched for many years. In this study, the usage of a modified cross‐flow filtration process as a classification process was investigated. With this process, particles in a fine micrometer range can be separated from suspensions. The upper particle size is dependent on hydrodynamic forces. The experimental results were compared with different hydrodynamic force models to predict upper size. The influence of the permeate flux and the particle concentration in the feed on the upper particle size is studied.     

Dependence of shear and concentration on fouling in a membrane bioreactor with rotating membrane discs

Rotating ceramic membrane discs were fouled with lab‐scale membrane bioreactors (MBR) sludge. Sludge filtrations were performed at varying rotation speeds and in different concentric rings of the membranes on different sludge concentrations. Data showed that the back transport expressed by limiting flux increased with rotation speed and distance from membrane center as an effect of shear. Further, the limiting flux decreased with increasing sludge concentration. A model was developed to link the sludge concentration and shear stress to the limiting flux. The model was able to simulate the effect of shear stress and sludge concentration on the limiting flux. The model was developed by calculating the shear rate at laminar flow regime at different rotation speeds and radii on the membrane. Furthermore, through the shear rate and shear stress, the non‐Newtonian behavior of MBR sludge was addressed. © 2013 American Institute of Chemical Engineers AIChE J 60: 706–715, 2014     

Influence of the mass flow rate of secondary air on the gas/particle flow characteristics in the near-burner region of a double swirl flow burner

The influence of the mass flow rate of secondary air on the gas/particle flow characteristics of a double swirl flow burner, in the near-burner region, was measured by a three-component particle-dynamics anemometer, in conjunction with a gas/particle two-phase test facility. Velocities, particle volume flux profiles, and normalized particle number concentrations were obtained. The relationship between the gas/particle flows and the combustion characteristics of the burners was discussed. For different mass flow rates of secondary air, annular recirculation zones formed only in the region of r/d=0.3–0.6 at x/d=0.1–0.3. With an increasing mass flow rate of secondary air, the peaks of the root mean square (RMS) axial fluctuating velocities, radial mean velocities, RMS radial fluctuating velocities, and tangential velocities all increased, while the recirculation increased slightly. There was a low particle volume flux in the central zone of the burner. At x/d=0.1–0.7, the profiles of particle volume flux had two peaks in the secondary air flow zone near the wall. With an increasing mass flow rate of secondary air, the peak of particle volume flux in the secondary air flow zone decreased, but the peak of particle volume flux near the wall increased. In section x/d=0.1–0.5, the particle diameter in the central zone of the burner was always less than the particle diameter at other locations.