Drag coefficient and settling velocity for particles of cylindrical shape

Solid particles of cylindrical shape play a significant role in many separations processes. Explicit equations for the drag coefficient and the terminal velocity of free-falling cylindrical particles have been developed in this work. The developed equations are based on available experimental data for falling cylindrical particles in all flow regimes. The aspect ratio (i.e., length-over-diameter ratio) has been used to account for the particle shape. Comparisons with correlations proposed by other researchers using different parameters to account for the geometry are presented. Good agreement is found for small aspect ratios, and increasing differences appear when the aspect ratio increases. The aspect ratio of cylindrical particles satisfactorily accounts for the geometrical influence on fluid flow of settling particles.     

Drag Correlation of Drop Motion on Fibers

The objective of this article is to correlate a drag coefficient to the Reynolds number for axial motion of barrel drops on fibers. This work includes effects of vibration-induced motion of droplets and coalescence. The study of motion of drops is important to understand the drainage behavior of droplets. Drainage of liquid helps to eliminate moisture from media samples before applying thermal energy and hence reducing the drying cost. A significant amount of literature describes the mechanisms of droplet capture, coalescence, and drainage from filter media and models are developed at a scale that accounts for the liquid held in the filter through averaged parameters such as saturation. Few papers discuss the motion of individual drops attached to fibers.

The study of drop motion on fibers is of scientific and economic interest for many possible applications like printing, coatings, drug delivery and release, and filters to remove or neutralize harmful chemicals or particulates from air streams. Gas convection-induced drop motion in fibrous materials occurs in coalescing filters, clothes dryers, textile manufacturing, convection ovens, and dewatering of filter cakes. Droplet removal can significantly reduce drying costs by reducing the free moisture contained in fibrous materials prior to applying thermal drying techniques.

In this article, the experimental drag coefficient versus Reynolds number data are compared for 1-D and 3-D cylindrical drop models. The results show that 1-D models are inadequate to predict the drag coefficient but do show the same general trends.     

Drag Correlation of Drop Motion on Fibers

The objective of this article is to correlate a drag coefficient to the Reynolds number for axial motion of barrel drops on fibers. This work includes effects of vibration-induced motion of droplets and coalescence. The study of motion of drops is important to understand the drainage behavior of droplets. Drainage of liquid helps to eliminate moisture from media samples before applying thermal energy and hence reducing the drying cost. A significant amount of literature describes the mechanisms of droplet capture, coalescence, and drainage from filter media and models are developed at a scale that accounts for the liquid held in the filter through averaged parameters such as saturation. Few papers discuss the motion of individual drops attached to fibers.

The study of drop motion on fibers is of scientific and economic interest for many possible applications like printing, coatings, drug delivery and release, and filters to remove or neutralize harmful chemicals or particulates from air streams. Gas convection–induced drop motion in fibrous materials occurs in coalescing filters, clothes dryers, textile manufacturing, convection ovens, and dewatering of filter cakes. Droplet removal can significantly reduce drying costs by reducing the free moisture contained in fibrous materials prior to applying thermal drying techniques.

In this article, the experimental drag coefficient versus Reynolds number data are compared for 1-D and 3-D cylindrical drop models. The results show that 1-D models are inadequate to predict the drag coefficient but do show the same general trends.     

Numerical evaluation of virtual mass force coefficient of single solid particles in acceleration

Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system.In this work the accelerating motion of a single solid particle is math-ematically formulated and solved using the vorticity-stream function formulation in an orthogonal curvi-linear coordinate system.The total drag coefficient was evaluated from the numerical simulation in a range of the Reynolds number (Re) from 10 to 200 and the dimensionless acceleration (A) between-2.0 to 2.0.The simulation demonstrates that the total drag is heavily correlated with A,and large decel-eration even drops the drag force to a negative value.It is found that the value of virtual mass force coef-ficient (Cv) of a spherical particle is a variable in a wide range and difficult to be correlated with A and Re.However,the total drag coefficient (Coy) is successfully correlated as a function of Re and A,and it increases as A is increased.The proposed correlation of total drag coefficient may be used for simulation of solid-liquid flow with better accuracy.     

Gas‐Solid Flow in an Airlift Loop Reactor: A Cluster Structure‐Dependent Drag Model

The hydrodynamic characteristics and heterogeneous structures in an airlift loop reactor (ALR) are analyzed by a computational fluid dynamics (CFD) approach. Based on the two‐fluid model, a modified cluster structure‐dependent (CSD) drag model under consideration of the cluster effects is applied to the prediction of the non‐uniform flow structure in the ALR. In comparison with experimental data and the traditional drag model, the present model enables a better prediction. The distributions of the local granular temperature in different regions of the ALR are indicated. The granular temperature in the particle diffluence region was found to be higher than that in the draft tube and annular zones.     

Influence of an Electric Field on the Burning Behavior of Solid Fuels and Propellants

An experimental study on the effects of an applied external electric field on the combustion behavior of solid fuels and solid propellants has been conducted. In an opposed flow burning configuration, application of an electric field was shown to extinguish a paraffin fuel and gaseous oxygen flame over a broad range of operating conditions. When subjected to the electric field, burning paraffin fuel strands were found to extinguish at various axial locations relative to the exit of the oxidizer gas jet. Extinguishment location was found to be a function of field strength as well as electrode surface area, while changes in polarity did not significantly alter the results. In addition, the combustion behaviors of two composite solid rocket propellants were studied while subjected to an external electric field. Both propellants were based on HTPB/AP combinations, with one propellant containing aluminum and the other being non‐aluminized. Application of an electric field to the composite solid rocket propellant strands demonstrated decreases in propellant burning rate under all operating conditions for both propellants including changes in polarity. The flame structure of the aluminized propellant was examined closely as the luminosity, flame length, and flame width varied significantly with field strength and burning location of the strand relative to the electrodes.     

New simple correlation formula for the drag coefficient of non-spherical particles

A simple correlation formula for the standard drag coefficient (i.e. a single stationary particle in a uniform flow) of arbitrary shaped particles is established using a large number of experimental data from the literature and a comprehensive numerical study [A. Hölzer, M. Sommerfeld, IUTAM Symposium on Computational Approaches to Multiphase Flow, Springer, 2006]. This new correlation formula accounts for the particle orientation over the entire range of Reynolds numbers up to the critical Reynolds number. Such a correlation may be easily used in the frame of Lagrangian computations where also the particle orientation along the trajectory is computed.     

Microkinetic Modeling of Nickel Oxidation in Solid Oxide Cells: Prediction of Safe Operating Conditions

Oxidation of the nickel electrode is a severe aging mechanism of solid oxide fuel cells (SOFC) and solid oxide electrolyzer cells (SOEC). This work presents a modeling study of safe operating conditions with respect to nickel oxide formation. Microkinetic reaction mechanisms for thermochemical and electrochemical nickel oxidation are integrated into a 2D multiphase model of an anode‐supported solid oxide cell. Local oxidation propensity can be separated into four regimes. Simulations show that the thermochemical pathway generally dominates the electrochemical pathway. As a consequence, as long as fuel utilization is low, cell operation considerably below electrochemical oxidation limit of 0.704 V is possible without the risk of reoxidation.     

Comparison of formulas for drag coefficient and settling velocity of spherical particles

Two formulas are proposed for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region. Comparisons with fourteen previously-developed formulas show that the present study gives the best representation of a complete set of historical data reported in the literature for Reynolds numbers up to 2 × 10⁵.     

Gas‐Solid Drag Coefficient for Ordered Arrays of Monodisperse Microspheres in Slip Flow Regime

Numerous analytical and numerical correlations for the drag force of particles in packed arrays are not applicable to microspheres because of the invalidity of the no‐slip assumption at a solid wall. The slip flow through assemblages of spheres is investigated by the lattice Boltzmann method (LBM). Three periodic arrays of static and monodisperse particles, i.e., a simple cubic, a body‐centered cubic, and a face‐centered cubic array, each with a relatively wide range of solid volume fraction, are considered. The LBM is validated for the slip flow over a single unbounded sphere and the continuum flow through spheres in a simple cubic array. The LBM results agree well with the experimental and numerical data in the literature. Simulations of slip flow through the three ordered arrays of spheres are performed. The effects of solid volume fraction and slip are both quantified within the developed drag laws.     

马来酸酐－醋酸异丙酯二元固液平衡的测定和关联

马来酸酐－醋酸异丙酯二元固液平衡的测定和关联陈新志侯虞钧（浙江大学化工系，杭州３１００２７）关键词固液平衡活度系数１引言相平衡数据在化工生产和研究中占有重要的地位。流体相平衡已得到了广泛的研究，并积累了大量的数据，与之相应的实验方法也较为完善，同时...     

Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems

Numerical simulation was made of transient mass transfer to a surfactant contaminated buoyancy-driven drop controlled by appreciable resistance in both liquid phases. For this purpose, the momentum equations were formulated and solved in a boundary-fitted orthogonal coordinate system. On the basis of resolved hydrodynamics of the contaminated drop, the transient mass transfer was formulated and solved in the same coordinate system. In order to check the applicability of the numerical scheme, single drop extraction experiments were conducted in a totally closed droplet file column with the terminal effect efficiently eliminated. The MIBK-acetic acid-water system was used with small quantities of SDS (sodium dodecyl sulphate), Triton X-100, or Tween 80 introduced into the continuous phase. For these experimental cases, the flow field and the drag coefficient of a contaminated drop were simulated first. The numerical prediction of the drag coefficient is found in good agreement with the corresponding experimental data. It illustrates that the behavior of a drop approaches that of a rigid sphere and that about 100 times higher bulk concentration of SDS than that of Triton X-100 is required for the same extent contamination of a MIBK drop of the same size. Then the information of the flow field of a contaminated MIBK drop was used in simulating the transient mass transfer of solute into the drop. The resulted extraction fraction and overall mass transfer coefficient are in reasonable coincidence with the experimental data. Both numerical results and experimental data show that overall mass transfer coefficient of a heavily contaminated drop is only about one third of that in the pure system. This can be explained well by the distribution of the local Sherwood number, which drops down abruptly along the rear stagnant surface. Also the interfacial resistance of adsorbed surfactant was incorporated in the mass transfer model and then estimated by the least square fitting the simulation with data. The numerical results also show that Tween 80 presents obvious interfacial resistance on the acetic acid diffusing across the interface, whereas SDS and Triton X-100 show no interfacial resistance. It is suggested that the numerical simulation can be resorted in some solvent extraction systems containing surfactants to conduct numerical experiments and parametric study.     

Performance and Evaluation of Cu‐based Nano‐composite Anodes for Direct Utilisation of Hydrocarbon Fuels in SOFCs

The anodes for direct utilisation of hydrocarbon fuels have been developed by using Cu/Ceria‐based nano‐composite powders. The CuO/GDC/YSZ–YSZ or CuO/GDC‐GDC nano‐composite powders were synthesised by coating nano‐sized CuO and CeO₂ particles on the YSZ or GDC core particles selectively by the Pechini process. Their microstructures and electrical properties have been investigated with long‐term stability in reactive gases of dry methane and air. The anodes fabricated using Cu‐based nano‐composite anodes showed almost no carbon deposition until 500 h in dry CH₄ atmosphere. The type of an electrolyte‐supported single cell in conjunction with the Cu/Ceria‐based anode must be selected together for the low melting temperature of Cu/CuO. The GDC electrolyte supported unit cell with the Cu/GDC–GDC anode showed the maximum power density of 0.1 Wcm^–2 and long‐term stability for more than 500 h under electronic load of 0.05 Acm^–2 at 650 °C in dry methane atmosphere.     

Numerical Simulations of Solid Circulation Characteristics in an Internally Circulating Elevated Fluidized Bed

A twin‐chamber internally circulating elevated fluidized bed (EFB) with one chamber elevated higher than the other within a single vessel is simulated using a two‐fluid model. Two EFB configurations termed as reaction chamber (RC)‐elevated and heat exchange chamber (HEC)‐elevated is evaluated. The effect of chamber elevation, variation of superficial velocities, and interchanging the two chambers are investigated and the results are quantified in terms of solid flux G_s. By increasing the RC gas velocity U_R at constant HEC velocity U_H, G_s is increased in both EFBs while an opposite behavior is observed by increasing U_H at constant U_R. Variation of the chamber elevation as well as interchanging the chambers also affects the performance of the two EFBs.     

固体推进剂燃烧波结构研究

设计了一套分析燃烧波结构的数值计算方法,可以利用热偶数据有效地分析均质推进剂固相反应的细节,为了解固体推进剂机理提拱了一种重要的手段;提出了均质推进剂也没有明显的固气界面的观点,因而也无表面温度可言;设计了固相反应热计算模型,提出了固相反应机理的观点,并指出压力不同固相反应机理基本相同,但固相放热程度不同;提出Π型热偶不宜测量非均质推进剂燃烧波结构的观点。     

固体硫化剂在工业中的应用（上）

探讨了固体硫化剂应用于裂硫汽油加氢装置二段催化剂预硫化新工艺,介绍了固体硫化剂的预硫化机理及工艺流程。     

Computational fluid dynamics (CFD) modeling of spouted bed: Assessment of drag coefficient correlations

In the computational fluid dynamics (CFD) modeling of gas-solids two-phase flows, drag force is the only accelerating force acting on particles and thus plays an important role in coupling two phases. To understand the influence of drag models on the CFD modeling of spouted beds, several widely used drag models available in literature were reviewed and the resulting hydrodynamics by incorporating some of them into the CFD simulations of spouted beds were compared. The results obtained by the different drag models were verified using experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72 (8), 561-568.] The quantitative analyses showed that the different drag models led to significant differences in dense phase simulations. Among the different drag models discussed, the Gidaspow (1994. Multiphase Flow and Fluidization, Academic Press, San Diego.) model gave the best agreement with experimental observation both qualitatively and quantitatively. The present investigation showed that drag models had critical and subtle impacts on the CFD predictions of dense gas-solids two-phase systems such as encountered in spouted beds.     

Drag on two coaxial rigid spheres moving along the axis of a cylinder filled with Carreau fluid

The boundary effect on the drag on two identical, rigid spheres moving along the axis of a long cylinder filled with a Carreau fluid for Reynolds number ranges from 0.1 to 40 is investigated. The influences of the key parameters of the problem under consideration, including the separation distance between two spheres, the relaxation time constant and the power-law index of a Carreau fluid, the Reynolds number, and the ratios (radius of sphere/radius of cylinder), on the drag acting on two spheres are investigated. We show that the boundary effect for the present case is more significant than that for the corresponding Newtonian fluid. The presence of the cylinder has the effect of enhancing the convective motion in the rear part of a sphere, thereby forming wakes and a reverse flow field, and this phenomenon is enhanced by the shear-thinning nature of a fluid. If the boundary effect is insignificant, the shear-thinning nature of a fluid has the effect of reducing the deviation of the ln(drag coefficient)-ln(Reynolds number) curve from a Stokes'-law-like relation. On the other hand, if it is significant, this deviation has a local minimum as the shear-thinning nature of a fluid varies.     

评估固体推进剂压强温度系数的方法

提出了目前评价压强温度系数所存在的问题,较系统地分析了压强温度系数的变化规律,建立了参比压强温度系数的计算方法。