Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

Low concentration sand transport in multiphase viscous horizontal pipes: An experimental study and modeling guideline

Low concentration particle transport in multiphase horizontal pipes in the presence of a viscous liquid is experimentally investigated. The experiments were conducted for a wide range of liquid and gas flow rates in both intermittent and stratified flows. Critical flow rates (velocity) is defined as the minimum required liquid and gas flow rates (velocities) to keep particles constantly moving in the pipe. The effects of physical parameters such as sand concentration, sand size, pipe size, and liquid viscosity are also experimentally investigated. It is observed that that critical velocity is a function of sand concentration and sand size and increases by increasing either within the ranges of particle concentrations and sizes examined. Regarding the effect of carrier liquid viscosity, the experimental data reveal that by increasing viscosity the minimum required flow rates to constantly move sand along the pipe increases within the range examined. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1821–1833, 2016     

On the use of approximate velocity profiles for modeling multiphase reactors

The use of an approximate axial gas velocity profile in a two-phase reactor model has been studied. The approximate velocity was assumed to vary linearly with conversion, which reduces the number of differential equations to be solved. The approximate model was studied in systems with one or two reactions. In most cases, the approximate and rigorous solutions were in good agreement. However, when mass transfer strongly influenced the velocity profile, errors in conversion became significant (～ 15%). Reactions with no change in the number of moles are also subject to errors if the rigorous velocity profile is not accounted for.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.     

Visualizing multiphase flow and trapped fluid configurations in a model three‐dimensional porous medium

We report an approach to fully visualize the flow of two immiscible fluids through a model three‐dimensional (3‐D) porous medium at pore‐scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the nonwetting oil and subsequent imbibition by the wetting fluid. During imbibition, the wetting fluid pinches off threads of oil in the narrow crevices of the medium, forming disconnected oil ganglia. Some of these ganglia remain trapped within the medium. By resolving the full 3‐D structure of the trapped ganglia, we show that the typical ganglion size, as well as the total amount of residual oil, decreases as the capillary number Ca increases; this behavior reflects the competition between the viscous pressure in the wetting fluid and the capillary pressure required to force oil through the pores of the medium. This work thus shows how pore‐scale fluid dynamics influence the trapped fluid configurations in multiphase flow through 3‐D porous media. © 2013 American Institute of Chemical Engineers AIChE J, 59:1022‐1029, 2013     

Detachment of rough particles with electrostatic attraction from surfaces in turbulent flows

The detachment of particles with coarse and fine roughnesses from surfaces in a turbulent boundary layer flow including electrostatic effects is studied. It is assumed that the real area of contact is determined by elastic deformation of asperities, and the effect of topographic properties of surfaces is included. The Johnson-Kendall-Roberts (JKR) adhesion model is used for analyzing the behavior of individual asperities. For an average Boltzmann charge distribution, the saturation charge condition as well as a fixed charge per unit mass, the Coulomb, the image, the dielectrophoretic, and the polarization forces acting on the particle in the presence of an imposed electric field are evaluated. The theories of rolling and sliding detachment are used to study the onset of removal of bumpy particles and those with fine roughness from plane surfaces. The hydrodynamic forces and torques acting on the particle attached to a wall, along with the adhesion force for the particle, are used in the model development. The minimum critical shear velocities needed to detach particles of different sizes from plane surfaces in the presence of an applied electric field are evaluated and discussed. The electric detachment of the particles is also studied and the field strength needed for particle removal is determined. It is shown that the surface charge distribution significantly affects the removal of particles from surfaces.     

The role of scale resolution versus inter-particle cohesive forces in two-fluid modeling of bubbling fluidization of Geldart A particles

Coarse grid simulations of Geldart A particles in bubbling fluidized beds using standard two-fluid (TF) models, where the constitutive laws are based on the homogeneity of sub-grid scale structures, have been demonstrated to be unsuccessful due to the existence of significant sub-grid scale heterogeneous structures. However, a definite consensus on the fundamental origin of the failure is still lacking. Some claim that the existence of significant inter-particle cohesive forces results in the sub-grid scale heterogeneous structures which takes the form of agglomerates or clusters; others claim that the inter-particle cohesive forces are not the dominant factor, and that the poor performance of TF models is primarily due to the fact that the grid sizes and the time step used in previous studies are too coarse to fully resolve the bubbling structure. To this end, a short overview is firstly presented to discuss the role of scale resolution and inter-particle cohesive force in two-fluid modeling of Geldart A particles; We then qualitatively explain, using a state-of-the-art discrete particle method, why the methods based on the existence of aggregates or clusters work quite well, although the sub-grid scale structure is not properly identified, that is, the sub-grid scale structure takes the form of a bubble-emulsion phase.     

On the effect of cluster resolution in riser flows on momentum and reaction kinetic interaction

Fine grid simulations of reactive gas-solid flows in a riser were carried out using an Eulerian multi-fluid kinetic theory of granular flow (KTGF) approach. A translationally periodic section of the riser was used to replicate experimental data collected in the fully developed region of a tall riser. The spatial and temporal resolution was varied in designed experiments to find an appropriate compromise between overall numerical accuracy and computational time. Results revealed that, when first order implicit timestepping is used, no timestep independence could be reached with timestep sizes that are practically feasible. Timestep independence could only be achieved by using second order implicit timestepping. Grid independence was studied in terms of cell width and cell aspect ratio. Solution independence could be reached at a cell width in the range of 10 particle diameters, but no complete grid aspect ratio independence could be achieved. Results suggested that grids with an aspect ratio smaller than one might be necessary to attain grid independent solutions. When sufficiently fine grids are used, however, the effect of a change in aspect ratio is sufficiently small to attain accurate solutions with an aspect ratio of two or lower. Certain important conversion measures were identified for scaling between simulation results collected in a 3D cylindrical domain and those predicted by a 2D planar simulation. System behavior predicted using these scaling rules agreed well with experimental results.     

概论多相反应系统的开发与设计

论述了气－液、气－液－固三相淤浆床及涡流床、气－固相固定床、气－固相流化床等多相反应系统的工业应用。并介绍了国内反应工程工业实践成果的参考索引。     

Effect of interparticle forces on the conical spouted bed behavior of wet particles with size distribution

This paper aims to analyze air-solid flow behavior in conical spouted beds composed of glass bead mixtures coated by glycerol. Four mixtures of glass beads are used as the solid phase. Although these mixtures have the same mean Sauter diameter, each one is characterized by a different size distribution function (mono-sized; flat, Gaussian or binary size distribution). When glycerol is added to the bed of these particles, which are spouted by air, the gas-solid flow characteristics are changed due to the growth of interparticle forces; however, the trends of these changes are affected by the glass bead mixture type as well as by the concentration of glycerol. For beds of mono-sized particles, the minimum spouting velocity is maintained almost unchanged as the glycerol concentration rises; while, for beds of inert particle mixtures, this velocity increases, becoming greater for flat and binary size distribution particles. Conversely, the minimum spouting pressure drop decreases as the glycerol concentration rises for all beds of particles used. Based on theoretical prediction of interparticle forces, it is shown that these changes in the minimum spouting conditions can be explained by the magnitude of these forces.     

Influence of the lift force closures on the numerical simulation of bubble plumes in a rectangular bubble column

Numerical Eulerian-Eulerian simulations of the unsteady gas-liquid flow in a centrally aerated two-dimensional bubble column were carried out in order to understand the effect of different formulations of the lift force coefficient (C_L) on the computational results. Three different values of the superficial gas velocity (U_G=2.4, 12.0 and 21.3 mm s⁻¹) that ensure the existence of different flow regimes were experimentally and computationally studied. The validation of the simulated results was based on visual observations and measurements of the global gas hold-up (ε_G) and the plume oscillation period (POP). The results presented reveal that, at U_G=12.0 and 21.3 mm s⁻¹, using C_L<0 results in under- and over-estimation of the ε_G and POP, respectively. On the other hand, taking C_L>0 does not affect the POP while it leads to increasingly higher ε_G values, which are different from those experimentally reported. At U_G=2.4 mm s⁻¹, the effect of the lift force is not so evident, although it slightly improves the prediction of experimental values. Particularly interesting is the case of C_L>0.4 at U_G=21.3 mm s⁻¹, producing a non-symmetric bubble plume oscillation. Since using Tomiyama's lift coefficient correlation does not improve the results, including the lift force into the simulation of bubble plumes is not recommended.     

On the mechanisms of secondary flows in a gas vortex unit

The hydrodynamics of secondary flow phenomena in a disc‐shaped gas vortex unit (GVU) is investigated using experimentally validated numerical simulations. The simulation using ANSYS FLUENT^® v.14a reveals the development of a backflow region along the core of the central gas exhaust, and of a counterflow multivortex region in the bulk of the disc part of the unit. Under the tested conditions, the GVU flow is found to be highly spiraling in nature. Secondary flow phenomena develop as swirl becomes stronger. The backflow region develops first via the swirl‐decay mechanism in the exhaust line. Near‐wall jet formation in the boundary layers near the GVU end‐walls eventually results in flow reversal in the bulk of the unit. When the jets grow stronger the counterflow becomes multivortex. The simulation results are validated with experimental data obtained from Stereoscopic Particle Image Velocimetry and surface oil visualization measurements. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1859–1873, 2018     

喷雾多相并存区温湿度测量方法及干燥特性

针对气液固并存区烟气温湿度测量问题,在对几种温湿度测量方法分析的基础上,设计了一种双回路抽气式温湿度测量装置,在喷雾干燥试验平台上,进行了对比和优化研究。在此基础上,分析了干燥塔内的温湿度分布特性。结果表明:内外层抽气速度均存在优化值,较外层抽气,内层抽气对测量值有更显著影响。内层抽气速度在12—24 m/s时,其测量值变化幅度仅为3.3℃;外层抽气速度在4—6 m/s时,其测量值变化幅度小于1℃。得出喷嘴雾化区域内干球温度呈径向双峰分布,湿度呈W型分布,且蒸发强度在距喷嘴200 mm处达到最大值。     

微/小通道内非牛顿流体多相流动与传热研究展望

概述了微/小尺度非牛顿流体多相流动与传热现象。在评述国内外已有文献的基础上,从实验研究与数值模拟二方面介绍了非牛顿流体管内多相流动与传热研究的现状、存在的问题。总结了微小通道内非牛顿流体多相流动与传热研究领域中若干值得探索的研究切入点,提出了若干值得探索的研究内容。讨论了非圆截面微通道试验器件的设计与加工、流动可视化与流型采集、流动参数测量、数值模拟等关键技术解决思路,给出了微/小通道内非牛顿流体的绝热气液二相流动可视化实验、流动沸腾传热及可视化实验设计方案,可为深入探索微/小尺度非牛顿流体管内多相流动与传热特性提供参考和借鉴。     

Analysis of the kinetics of agglomerate erosion in simple shear flows

A model for the erosion kinetics of particle agglomerates in simple shear flows has been developed. The erosion rate is taken to be proportional to the difference between hydrodynamic and cohesive forces and to the rotation velocity of the dispersing agglomerate. For dispersion under identical hydrodynamic conditions, the model predicts faster erosion for larger agglomerates. Moreover, at equivalent hydrodynamic stress, erosion is enhanced at higher shear rates. Dispersion experiments using silica agglomerates of various densities and liquid low molecular weight polymers (e.g., poly(dimethyl siloxane)) of different viscosities were conducted in an oscillatory shear flow device. The experimental results validate the erosion model; the general shape of the erosion kinetic curve, and the effect of viscosity, shear rate and agglomerate size on dispersion kinetics are well predicted. The model can also predict erosion for agglomerates with fractal structure.     

Surface Forces and the Adhesive Contact of Axisymmetric Elastic Bodies

A synthetic approach to the problem of the adhesive contact of axisymmetric elastic bodies is proposed. A convenient and general formulation is thus obtained, which is shown to yield directly most of the useful models. In particular, the roles of the shape of the indenter on the one hand, and of the nature of the attractive interactions on the other hand are clearly separated. By nature, this approach can also be used in the case where the bodies are in interaction but not in contact. This results in a consistent treatment of long-range interactions and contact properties.     

Surface Forces and the Adhesive Contact of Axisymmetric Elastic Bodies

A synthetic approach to the problem of the adhesive contact of axisymmetric elastic bodies is proposed. A convenient and general formulation is thus obtained, which is shown to yield directly most of the useful models. In particular, the roles of the shape of the indenter on the one hand, and of the nature of the attractive interactions on the other hand are clearly separated. By nature, this approach can also be used in the case where the bodies are in interaction but not in contact. This results in a consistent treatment of long-range interactions and contact properties.     

Polydisperse granular flows in a bladed mixer: Experiments and simulations of cohesionless spheres

The flow and segregation of polydisperse, spherical particle mixtures in a bladed mixer was investigated using experimental and computational techniques. Discrete element simulations were able to reproduce the qualitative segregation profiles and surface velocities observed experimentally. For a binary system with a 2:1 size ratio, segregation by size occurs due to a sieving mechanism. Segregation in the binary system is fast, with a fully segregated system observed after just 5 revolutions. However, the numerical simulations showed that the extent of segregation in the bladed mixer can be reduced by introducing intermediate particle sizes in between the smallest and the largest particles. Addition of intermediate particle sizes increases convective and diffusive particle motion promoting a mixing mechanism that reduces segregation via the sieving mechanism. Void fraction within the bladed mixer increases as the degree of polydispersity is increased allowing the particles to move more freely throughout the particle bed. Higher void fractions also increase the ability of large particles to penetrate deeper into the particle bed. Normal and shear stresses are also affected by particle size distributions, with lower average values obtained for the system with the largest number of particle species. Differences in the amount of stress generated by each particle species were observed. However, the difference in stresses is reduced as the number of particle species in the system is increased.     

Eigenvalue-eigenfunction analysis of infinitely fast reactions and micromixing regimes in regular and chaotic bounded flows

We analyze the dynamics of a single irreversible reaction A+B→ Products, occurring in a bounded incompressible flow. Within the limits of infinitely fast kinetics, the system is reduced to an advection-diffusion equation for the scalar φ, representing the difference between the reactant concentrations. By the linearity of the governing PDE, the system evolution is determined by the properties of the eigenvalue-eigenfunction spectrum associated with the advection-diffusion operator. In particular, the dependence of the dominant eigenvalue Λ—yielding the time-scale controlling the asymptotic reactant decay—as a function of the molecular diffusivity, , for different stirring protocols is analyzed. We find , where the exponent α∈[0,1] depends upon the kinematic features of the stirring flow. When the kinematics is regular within most of the flow domain (e.g. two-dimensional autonomous flows or time-periodic protocols possessing large quasiperiodic islands) a purely diffusive scaling, α=1 settles as . The singular scaling α=0 is found in the case of globally chaotic kinematics, whereas mixed regimes, 0<α<1, occur in flows that are characterized by the coexistence of quasiperiodic and chaotic behavior. The analysis of spectral properties of the advection-diffusion operator provides a new classification of micromixing regimes, and new mixing indices for quantifying homogenization performances in the presence of diffusion.