SWIRLING FLOWS OF VISCOELASTIC FLUIDS OF THE INTEGRAL TYPE IN RHEOGONIOMETERS

Recent numerical methods for calculating the flow of fluids of the integral type have been extended to the case of swirling flows in geometries of revolution. Such flows are important in rheometry, as it was suggested in early experimental results by Savins and Metzner [1]. After having developed the necessary background for the numerical calculation, we apply the method to the flow in disk-and-plate and cone-and-plate rheogoniometers.     

ON NONISOTHERMAL FLOWS OF BINGHAM PLASTICS

A numerical scheme based on the Galerkin's finite element method is used to analyze nonisothermal flows of Bingham plastics. These fluids exhibit yield stresses, below which the material does not flow. This condition is enforced by introducing the bi-viscosity model in which the plug behaviour is approximated by a highly viscous fluid. The bi-viscosity model approaches the ideal Bingham plastic model if the pre-yield viscosity becomes large. This numerical method is applied to solve three problems namely the Graetz-Nusselt, recirculating flow, and sinusoidal channel flow problems for various values of the yield stress. The size of the plug as well as the velocity and temperature fields correspond closely with values available in literature.     

VELOCITY PROFILES OF NEWTONIAN AND NON-NEWTONIAN TOROIDAL FLOWS MEASURED BY A LDA TECHNIQUE

Laser Doppler Anemomeiry was used to measure the primary (axial) and secondary (recirculating) velocity profiles in laminar flows of Newtonian (ethylene glycol) and non-Newtonian (aqueous solutions of CMC and PAA) liquids in curved tubes. Rheological characteristics of these liquids were measured using standard viscometric techniques (Haake and Mechanical Spectrometer). The effect of the shear-thinning viscosity is to flatten the axial velocity profile while enhancing the circulating flow close to the walls. On the other hand, the viscoelasticity reduces the extent of the secondary flow for all Dean numbers. This fact explains the reduction of laminar friction reported in the literature.

The primary and secondary velocity profiles, which appear to be the first ones ever published for the toroidal flows, are compared with the predictions of numerical simulation. The agreement is good when comparing the profiles of the axial flow but it is unsatisfactory for the secondary flows.     

流道结构对膜分离性能的影响

基于CFD技术对不同流道结构的平板式纳滤膜分离器内的流动进行了数值模拟,以考察流道结构对膜分离性能的影响。分析了在平板膜器中加设螺旋形隔板和蛇形隔板后截面流体的次流状况。模拟结果表明在无绕流板流道中加设隔板后存在次流现象,螺旋形流道中流体流动存在二次流漩涡,蛇形流道拐角附近的流体也存在较强的二次流动,对减轻膜污染和浓差极化均有作用。     

NUMERICAL CALCULATIONS OF TUBE BUNDLES EROSION BY TURBULENT PARTICLE-LADEN GAS FLOWS

Erosion of tubes in tube bundles by particles suspended in gas flows is a major problem in the power industry. In this paper, a numerical study has been conducted for the flow of a dilute particle-laden gas moving past two row in-line tubes undergoing erosion. An orthogonal-curvilinear co-ordinate system was used to calculate turbulent flow around the tubes. The prediction of particle trajectories took into account the effect of the turbulence with a stochastic particle dispersion model. The results from this study included the distributions of particle collision frequency and erosion damage of tube surfaces.     

NUMERICAL CALCULATIONS OF TUBE BUNDLES EROSION BY TURBULENT PARTICLE-LADEN GAS FLOWS

Erosion of tubes in tube bundles by particles suspended in gas flows is a major problem in the power industry. In this paper, a numerical study has been conducted for the flow of a dilute particle-laden gas moving past two row in-line tubes undergoing erosion. An orthogonal-curvilinear co-ordinate system was used to calculate turbulent flow around the tubes. The prediction of particle trajectories took into account the effect of the turbulence with a stochastic particle dispersion model. The results from this study included the distributions of particle collision frequency and erosion damage of tube surfaces.     

A SIMULATION OF A MOTIONLESS MIXER

Continuous laminar mixing in segmented twisted-tape motionless mixers is considered. A solution to the steady isothermal creeping flow of a Newtonian fluid in a twisted-tape mixer has been obtained via two-dimensional numerical procedures. The developed flow within a section of the mixer has been solved in a helical coordinate system by an iterative scheme. The resulting solution is rigorously correct in the absence of entrance and exit flows at the junction between sections. An algorithm is presented for the modelling of these junction flows via two-dimensional procedures. Simulated cross-sectional mixing patterns have been generated for comparison with experimental results

The performance of twisted-tape mixers is simulated for various designs, beginning with the particular geometry of the Kcnics Static Mixer, and for different operating conditions Results suggest that the rate of mixing as a function of the total twist per section is optimized with respect to pressure drop when sections contain 80 degrees of twist. The capability for rational improvement in other design and operating parameters is illustrated. The mechanisms of laminar mixing are discussed and quantified; of primary importance is the tendency for interfacial area to assume an orientation within each section which is favorable to mixing in subsequent sections.     

Numerical prediction of three-dimensional fiber orientation in Hele-Shaw flows

A numerical technique is developed to determine the three-dimensional fiber orientation in complex flows. The fiber orientation state is specified in terms of orientation tensors, which are used in several constitutive models. This method is applied to quasi-steady state Hele-Shaw flows in order to predict the flow-induced fiber orientation during injection molding at zero volume fraction limit. At the inlet, a number of fibers are introduced at a specified rate into the flow and each fiber location is traced during the mold filling. Along these determined paths, the independent components of fourth order orientation tensors are solved, describing the orientation state. The numerical grid generation technique, which is suitable for complex mold shapes, is employed for the flow solution. Orientation ellipsoids are calculated from the second order tensors and are used to present the fiber orientation results. The numerical solutions are obtained for channel and converging flows. Planar, longitudinal, and transverse orientation results are generated from the orthogonal projections of the orientation ellipsoids.     

TWO-DIMENSIONAL TRANSIENT NUMERICAL SIMULATION OF SOLIDS AND GAS FLOW IN THE RISER SECTION OF A CIRCULATING FLUIDIZED BED

A computational fluid dynamics software (CFX) was modified for gas/particle flow systems and used to predict the flow parameters in the riser section of a circulating fluidized bed (CFB). Fluid Catalytic Cracking (FCC) particles and air were used as the solids and gas phases, respectively. Two-dimensional, transient, isothermal flows were simulated for the continuous phase (air) and the dispersed phase (solid particles). Conservation equations of mass and momentum for each phase were solved using the finite volume numerical technique. Two-dimensional gas and particle flow profiles were obtained for the velocity, volume fraction, and pressure drop for each phase. Calculations showed that the inlet and exit conditions play a significant role in the overall mixing of the gas and particulate phases and in the establishment of the flow regime. The flow behavior was analyzed based on the different frequency of oscillations in the riser. Comparison of the calculated solids mass flux, solids density and pressure drop with the measured pilot-scale PSRI data (reported in this paper) showed a good agreement.     

PREDICTION OF DENSE TURBULENT PARTICLE LADEN RISER FLOW WITH A EULERIAN AND LAGRANGIAN COMBINED MODEL

This paper formulates a new numerical model for the dense gas-solid flows, combining Eulcrian/Eulerian approach and Eulerian/Lagrangian approach together. The model takes account of inter-particle interactions in Eulerian coordinate using the kinetic theory of granular flow based on the Chapman-Enskog theory of dense gases. A stochastic particle dispersion model is incorporated in the model to calculate the turbulence diffusion of particles in Lagrangian coordinate. A comparison with published experimental results is made, and good agreement is shown.     

Simulation of thermophysical flow in axisymmetric nozzle with expansion chamber

Axisymmetric nozzle flows with a free‐jet expansion are simulated considering several substances and several flow conditions, and the thermophysical properties in the nozzle and the free‐jet region are predicted. The present numerical method is based on the preconditioning method developed by Yamamoto and the mathematical models of thermophysical properties of the substances. As numerical examples show, gas flows of carbon dioxide, water, and nitrogen under a subcritical pressure condition are first calculated. Calculated distances to the Mach disk are compared with the experimental results, and also the density distributions are compared among these three substances. Second, carbon dioxide flows while changing the pressure from subcritical to supercritical values are calculated and the effect of pressure on the flow field is investigated. Third, flows of water vapor with and without nonequilibrium condensation are calculated and the effect of condensation on the flow field is investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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.     

THE EFFECT OF DISTRIBUTORS ON TWO-PHASE AND THREE-PHASE FLOWS IN VERTICAL COLUMNS

Two-phase air-water and three-phase air-water-solids flows have been investigated in a 0.152 m internal diameter vertical column. Pressure drop across the distributor and average phase hold-up were measured for two-phase and three-phase flows over flow ranges of superficial gas velocity from 0 to 259 m/s and superficial liquid velocity from 0 to 0.0346 m/s. Gas hold-up/pressure-drop ratios were obtained as a function of superficial gas velocity and liquid flow rate. It was found that the bubble cap was better at gas distribution than that of the Koch static mixer in two-phase and three-phase vertical flows. Drift flux to gas hold-up and drift flux to gas flow rate correlations were obtained for two-phase and three-phase vertical flows. Three flow patterns, churn-turbulent, transition and ideal bubble flows, were observed for vertical upflow.     

EFFECT OF COMBINED SHEAR,SECONDARY AND AXIAL FLOW OF BLOOD ON OXYGEN UPTAKE

The oxygen uptake of red blood cells (RBC) has been investigated in a blood flowing model in which defined shear and secondary flows are produced with blood flow direction perpendicular to the shear plane. The model consists of a Couette flow realized by means of two coaxial cylinders with gas permeable walls. The “venous” blood flows in the axial direction. In the annual gap shear and secondary flows (Taylor-vortices) are produced by rotation of the inner cylinder which determine the amount of oxygen uptake. Different blood Row regions and conditions (Taylor-, Reynolds-number, and shear rates) in regard to non-Newtonian behaviour of blood have been reported. An increase of Taylor-number from 100 to 300 results in a greater than four-fold increase in oxygen uptake. For Taylor-numbers lower than 100 the oxygen uptake is not significantly enhanced due to flow instabilities. This can be explained by non-Newtonian flow behaviour of blood and appearance of different flow regions. The results for normal whole blood are compared to those for water and for artificially regidified red cell membranes.     

Capillary Filling Flows inside Patterned‐Surface Microchannels

Capillary flows inside microchannels with patterned‐surfaces are investigated theoretically and numerically. The surface energy method is used to derive an equivalent contact angle (ECA) model for small capillary number flows. The SIMPLE algorithm using a volume of fluid (VOF) method is adopted to investigate the flows in those microchannels. The flow characteristics such as the liquid front shapes and the evolution of the liquid lengths are obtained. The numerical results reveal that capillary flows in a patterned‐surface microchannel still follow the traditional capillary theories. The ECA model is confirmed by the numerical results. It indicates that the capillary flows inside the patterned‐surface microchannels can be estimated by means of the homogeneous‐surface microchannels with the equivalent contact angle. The ECA model provides a good criterion for the total wettability of a patterned‐surface microchannel, as well.     

The aspiration efficiency of a tube sampler operating in a slow moving air stream facing vertically upwards

The aspiration efficiency of a thin-walled, cylindrical aerosol sampler facing vertically upwards in a slow moving vertical air stream is numerically investigated using both a potential flow model and a viscous flow model. In order to predict the air flow around the sampler, for the potential flow model we use a boundary element method whereas for the viscous flow model we use a control volume method. The motion of the particles is then predicted by considering both the drag and gravitational forces. We have found that both numerical models produce similar predictions for the aspiration efficiency and the predictions reveal a more complex sampling behaviour when the sampler is operated in a slow moving air environment, where the air velocity is comparable with the magnitude of the particle settling velocity, than for faster moving air flows. The comparison of the numerical predictions with the only available experimental data indicates that the aspiration efficiency is in qualitative agreement but further investigations are required in order to fully reveal all the sampling characteristics in slow air flows.     

流体-固体两相流的数值模拟

鉴于流体 -固体两相流及其数值模拟在化学工程中愈来愈广泛的应用 ,本文综述了Euler坐标系下流体相湍流模型、颗粒轨道模型以及流体 -颗粒双流体模型的基本原理和数值模拟方法 ;对相间耦合和颗粒间的相互作用也进行了介绍 ,特别是对能详细描述多颗粒间相互作用的颗粒离散单元法在流体 -固体两相流中的应用进行了详细描述 ;在评述各模型的优缺点和分析目前存在的问题的基础上 ,提出了今后的发展方向     

CFD数值模拟技术在液滴微流控多相流特性研究的应用进展

高集成化的微流控系统具有界面面积大、传递距离短、混合速度快等优势,已被广泛应用于许多科学领域。然而,微通道内多相流间的相互作用及动力学行为受多方面的影响,仅依靠试验观测技术和理论预测方法难以全面了解多相流传质传热过程、获取流场特性参数、揭示多相流相互作用规律。当下CFD数值模拟技术的快速发展为预测和分析微流控通道内的多相流问题提供了更为直观、有效、准确的帮助。本文对数值模拟技术在液滴微流控多相流特性研究的应用进展进行全面综述,涵盖液滴微流控装置结构及演变、液滴微流控模拟方法及优化以及微通道内多相流作用过程及原理。