Incipient motion of individual particles in horizontal particle-fluid systems: A. Experimental analysis

This paper investigates the incipient motion velocity of individual particles in horizontal conveying systems. The first part presents a wide range of experimental measurements and an empirical analysis on incipient motion velocity (a type of pickup velocity) for a variety of particulate solids, sizes and shapes. Results from the literature for incipient motion of individual particles in gases and liquids are taken into account in the final empirical analysis. It was found that all the results for the single particle incipient motion velocity could be presented with a high accuracy by a simple relationship between the Reynolds and the Archimedes numbers. Furthermore, the friction coefficient should be taken into account for large particles by modifying the Archimedes number.The incipient motion velocity was added to a generalized master curve, which included various threshold velocities such as: pickup velocity from a layer of particle in gas and liquid, minimum pressure velocity, boundary saltation velocity, terminal velocity and minimum fluidization velocity. The different threshold velocities are presenting in this master curve through modified Reynolds and Archimedes numbers. The Reynolds number is modified by taking into account the effect of the pipe diameter and the Archimedes number is modified by taking into account various properties that affect each threshold mechanism. The incipient motion velocity was also compared to the boundary saltation velocity (saltation velocity of single particles) and some hysteresis was found. However, this hysteresis is larger for fine powders than for coarse particles.     

Boundary saltation and minimum pressure velocities in particle-gas systems

The saltation velocity is one of the key design parameters in pneumatic conveying systems. The aim of this work is to experimentally study the mechanism of saltation. Experiments were carried out with various spherical and non-spherical particles in a small wind tunnel with very dilute flow. For each velocity the distribution of halted particles along the tunnel bottom was measured. From this length distribution, the median length was determined and used for further analysis. It was found that the median conveying length approaches infinity at a certain threshold velocity. By testing many materials the boundary saltation velocity followed a simple correlation of the modified Reynolds number as a function of the modified Archimedes number. The conveying length was an accumulation of three lengths: the first flight length, the rebound length, which is affected by the coefficient of restitution, and the rolling/sliding length, which is affected by the coefficient of friction. By analyzing these lengths, the total conveying length and the boundary saltation velocity were easily defined. Furthermore, as the velocities at minimum pressure velocities (referred to in the paper as the minimum pressure velocities) have been found to follow the same trend as the boundary saltation velocity if the solid concentration is taken into account, our simple correlation can describe by ± 30% all the relevant experiments found in the literature.     

Analyzing threshold velocities for fluidization and pneumatic conveying

In previous works we have shown that by defining various threshold velocities in terms of the modified Reynolds number as a function of the modified Archimedes number a generalized master-curve can be plotted. Then, using this curve, the ratio between various threshold velocities can be easily determined. However, all the threshold velocities were defined for mono-sized particles. The purpose of this paper is to show how the threshold velocities can be used to design of particle-fluid systems for particle size distribution. The analysis provides practical guides for various engineering scenarios, such as selecting the appropriate fluidization velocity for maximum fluidization and minimum entrainment and determining the conveying velocity in pneumatic systems. In addition, the analysis provides a guide to determine whether the deposited layer of particles at the pipe bottom is stationary or moving, for cases where the superficial velocity is smaller than the saltation velocity.     

Pickup (critical) velocity of particles

This work presents experimental results on pickup velocity (critical velocity) measurements for a variety of particulate solids. The present experiments together with previously published experiments of a number of researchers encompass about 100 measurements of 24 materials for a wide range of particle sizes, shapes and densities. Based on the experimental results, three zones are defined by establishing simple relationships between the Reynolds and Archimedes numbers. The empirical relationships were further modified by taking into account the pipe diameter and particle shape (sphericity). The three-zone model was shown to reasonably correlate to Geldart's classification groups.     

Pickup, critical and wind threshold velocities of particles

This work presents experimental results on pickup velocity measurements for a variety of particulate solids in gases and in liquids. Based on our previously published experimental results for pickup in gas flow in pipes a three-zone master-curve is defined by establishing simple relationships between modified Reynolds and Archimedes numbers. The zones are distinguished by cohesive forces (van der Waals): Zone I represents negligible cohesion forces, Zone II represents considerable cohesion forces that increase the required pickup velocity of individual particles, and Zone III represents significant cohesion forces that cause pickup of agglomerates. Previously published experiments by others encompassing about 121 measurements for a wide range of particle sizes, shapes and densities picked up by liquids, were added to our master-curve with excellent agreement. The cohesive forces did not affect the critical velocity in case of liquid-particle systems. Therefore, these experiments extend the line fitting the pickup velocity of big dry particles. In most cases, the critical shear velocity (reported for liquid-particle systems) had to be converted to the average pickup velocity. Furthermore, additional 16 measurements of pickup velocities (in air) conducted in big wind tunnels were added to the master-curve with excellent agreement. We can conclude that our simple master-curve is appropriate for threshold velocities defined in three fluid-particle systems with a maximum error of only ± 30%.     

Effect of particle characteristics on particle pickup velocity

Particle entrainment is investigated by measuring the velocity required to pick up particles from rest, also known as pickup velocity. Pickup velocity is a function of individual particle characteristics and interparticle forces. Although 5-200 μm particles are investigated, the work presented here focuses on the pickup of particles in a pile in the size range of 5-35 μm. These smaller particle sizes are more typical for pharmaceutical and biomedical applications, such as dry powder inhalers (DPIs). Pickup velocities varied from 3.9 to 16.9 m/s for the range of particle sizes investigated.There is a strong correlation between particle size and the dominating forces that determine the magnitude of the pickup velocity. Preliminary data investigating pickup velocity as a function of particle size indicate the existence of a minimum pickup velocity. For larger particle sizes, the mass of the particle demands a greater fluid velocity for entrainment, and for smaller particle sizes, greater fluid velocities are required to overcome particle-particle interactions. Pickup velocity remains relatively constant at very small particle diameters, specifically, less than 10 μm for glass spheres and 20 μm for nonspherical alumina powder. This can be attributed to the negligible changes in London-van der Waals forces due to a hypothesized decrease in interparticle spacing. At intermediate particle diameters, electrostatic forces are dominant.     

Drag on Freely Falling Cones in Newtonian and in Power Law Fluids

New extensive data on the terminal falling velocities of conical shaped bodies in scores of Newtonian and power law fluids are reported. Altogether, 11 Newtonian and 11 non‐Newtonian test liquids together with 33 cones made from four different materials and 14 spheres of three different materials have been used to gather 486 individual data points covering wide ranges of conditions as follows: Reynolds number 0.0019 to 507; power law flow behaviour index 0.4 to 1, the value of sphericity 0.59 to 0.79; and the cone‐to‐fall tube diameter ratios up to 0.264 to assess the extent of wall effects. A simple expression is developed to estimate the terminal falling velocity of a cone from a knowledge of its dimensions, and the terminal velocity of an equivalent sphere. A generalized drag equation applicable to both Newtonian and power law liquids is also presented.     

EQUATIONS FOR CALCULATION OF THE TERMINAL VELOCITY AND DRAG COEFFICIENT OF SOLID SPHERES AND GAS BUBBLES

An analysis of the correlations proposed in the literature for calculation of the drag coefficient (C_D) and the terminal velocity of a falling rigid sphere has been made. Among the correlations describing C_D vs. Re, that of Turton and Levenspiel fits the experimental data almost perfectly. However, it is not explicit in the terminal velocity. The available explicit correlations do not fit the experimental data well. The present paper shows that a simple and precise explicit correlation can be developed if C_D is related to the Archimedes instead of the Reynolds number. The precision of the correlation proposed is similar to that of the Turton and Levenspiel (1986), while it is explicit in the terminal velocity. On the basis of this correlation, a model is proposed to calculate the drag coefficients and the terminal velocities of free falling or rising spherical particles in an infinite fluid as well as gas bubbles with any volume and shape rising in a contaminated liquid.     

稀疏气固两相湍流边界层拟序结构变动特性

应用PIV两相同时测量方法,对壁面Reynolds数为430的水平槽道稀疏气固两相湍流边界层拟序结构变动特性进行了研究。选取质量载荷为10^-4~10^-3的110 μm聚乙烯颗粒作为离散相。结果表明,低载荷颗粒仍能显著改变湍流拟序结构,进而影响宏观湍流属性。颗粒重力沉降形成的粗糙壁面增强了壁面附近湍流猝发行为,导致黏性底层中的气相法向脉动速度和雷诺剪切应力显著增大。颗粒与壁面的碰撞加强了低速流体上抛、削弱了高速流体下扫,同时增强了轨道交叉效应,从而抑制了湍流拟序结构发展,显著减小了黏性底层以上区域的法向脉动速度和雷诺剪切应力。此外,颗粒惯性还减小了黏性底层厚度、增大了流向速度梯度,导致气相流向脉动速度峰值增大,且其对应位置也更加靠近壁面。     

Minimum spouting velocity in multiple spouted beds

Studies have been carried out in multiple spouted beds having 2, 3 and 4 spout cells; different fluid inlet orifices and different solids have been used with air and water as spouting fluids. The minimum spouting velocities are measured for different bed depths. The experimental data for particle Reynolds number at minimum spouting have been correlated and the square root mean deviation between the calculated and experimental values is found to be 8.75 %.     

Mass transfer of a rising bubble in molten glass with instantaneous oxidation-reduction reaction

The mass transfer around a rising bubble has been studied within the field of glass melting processes. Due to the large value of liquid viscosity, creeping flow was used. The rising bubble is assumed to have a clean interface with a total mobility and the exact solution of Hadamard or Rybczynski was used to define the velocity field around the bubble. The mass transfer of oxygen in the soda-lime-silica glass melt where oxidation-reduction reactions of iron oxides occur is also described.The dimensionless mass transfer coefficient, Sherwood number, was determined as a function of the Péclet number based on the terminal rise velocity of the bubble. Two different techniques have been used: the first based on the boundary layer theory and the second using a finite element method.In order to take into account the oxidation-reduction reaction in a unified framework, a modified Péclet number has been defined as a function of two dimensionless numbers. The first is strongly linked to the equilibrium constant of the chemical reaction and the second is the glass saturation, defined as the ratio of oxygen concentration in the bulk to that at the bubble surface. The Sherwood number, taking into account the chemical reactions, increases with iron content as well as with glass reduction (i.e. small saturation level).From an application point of view, the determination of a modified Péclet number is important because it is possible to use a similar expression (determined without the reaction) by replacing the classical Péclet number by the modified one proposed herewithin.     

Brillouin Spectroscopy of Oriented Polymers

Abstract

We give a short overview of how to measure orientation-dependent velocities of hypersound by Brillouin spectroscopy, and what kind of data have been attained by this method. The observations in drawn segmented poly(urethane)-elastomers differ from all others: the sound velocity perpendicular to the chains runs through a minimum. At a draw ratio of ～3.8 a sudden step in the sound velocity indicates a strain-induced structural change.     

Threshold Energy: A Dimensional Extension of the Critical Energy for Jet Attack Application

The critical energy criterion (E_c) developed by Walker and Wasley is widely used to determine the response of explosive submitted to flyer plate impacts. As it has been shown previously to be limited in the pressure range over which it applies, in the number of explosive formulations which appear to obey it and in the range of projectiles covered by it, we have modified twice this criterion. The first modification, taking into account a trend toward lower minimum energy with increasing pressure (pressure fluence) enables it to be applied to explosives previously found to be outside the original criterion and to extend the pressure range. The second modification taking into account a trend toward higher minimum energy with decreasing impact surface area (impact surface dependence) is a bidimensional extension of the critical energy concept. The threshold energy per unit area thus defined allows to predict the shock initiation limits of bare explosives (PBX and cast formulations) impacted by shaped charge jets.     

Prediction of bubble terminal velocity in surfactant aqueous solutions

Bubble terminal velocity has a significant effect on gas holdup, residence time, and efficiency of the interface transfer. Surfactant is often required to generate small and stable bubbles in gas-liquid two-phase devices. In this paper, bubble terminal velocities were obtained for different surfactant aqueous solutions using high-speed CCD (charged couple device) system and digital image analysis technology. Experimental results showed that available correlations were not able to accurately predict terminal velocity of bubbles rising in surfactant aqueous solutions. Thus, a new correlation is proposed based on experimental data and it provides an accurate approximation of bubble terminal velocity. The average relative error for the proposed correlation is determined to be 7.2% in MIBC aqueous solutions, 4.5% in OP-10 aqueous solutions, and 4.6% in 2-octanol aqueous solutions. The proposed correlation agrees well with experiment data from literate within ranges of the Morton number, Mo, the bubble Reynolds number, Re, and the Eötvös number, Eo: 3.29 × 10⁻¹¹<Mo<4.29 , 0.08<Re<1062 , 0.04<Eo<91.16 .     

Averaged and time-resolved,full-field (three-dimensional), measurements of unsteady opposed jets

Full-field, time-resolved, velocity vector information was obtained for an opposing jet reactor. The velocities were measured by particle tracking velocimetry (PTV) over a range of jet Reynolds numbers (200–5000). The main results reported are for a Reynolds number of 200. Graphical representation of the extensive data fields cannot be conveniently reported here; however, examples are provided. A more thorough presentation is possible by using color and dynamic representations and these are provided at the URL (Uniform Resource Locator, i.e., the address for a location on the Internet) cited in Zhao and Brodkey (1998). It is important to emphasize that the velocity fields presented in this paper are experimental.     

Velocity histories of vaporizing fuel drops moving through stagnant gas

Newton's second law of motion has been applied here to a vaporizing drop being depleted according to the ‘d²-relation’ in order to determine the velocity histories of drops injected vertically into stagnant gas. In the evaluation of the drag forces, three possible values of drag coefficient, namely Stokes value based on instantaneous velocity and diameter, Stokes value based on average velocity and initial diameter, and a constant value of 1.0 independent of Reynolds number (for which there is experimental justification at Reynolds numbers not too small), have been employed. The second and third cases result in non-linear differential equations for the velocity histories, and have been solved using the Runge-Kutta-Nyström method. The effects on the histories of the initial velocity with which the drops are injected into the ambient gas, either vertically down or up, have been investigated for all three drag values. The results have been plotted in terms of normalized coordinates which (unlike others in the literature) are shown to have physical significance. The concept of a terminal velocity does not apply for a particle whose size is decreasing with time. The velocity histories for the two Stokes drag coefficients are quite similar, despite the considerably different manner in which the Reynolds number is defined in the two cases; this vindicates the common practice of calculating and correlating experimental values of (Re) and C_D on the basis of initial diameter and average velocity for the sake of convenience and practicality. For large downward injection velocities, the gravitational and buoyancy forces can be neglected, especially for the two cases of Stokes C_D; but the errors for all three cases of upward injection are too significant to be neglected.     

Minimum pickup velocity: The transition between nano‐scale and micro‐scale

The transport of nano‐scale particles has become increasingly important, but the knowledge base available is limited. This study aims to bridge the knowledge gap between the nano‐ and micro‐scales for pneumatic conveying. A key parameter is the minimum pickup velocity (U_pu), which is the minimum fluid velocity required to initiate motion in a particle originally at rest. The U_pu values of nine alumina particles with particle diameters (d_p) ranging from 5 to 110,000 nm were determined using the weight loss method, then compared against the established pickup Zones (analogous to the Geldart Groups). Results indicated that: (1) U_pu varied non‐monotonically with increasing d_p, thus revealing the missing link between the nano‐ and micro‐scales; (2) the intermediate particle diameters surprisingly did not agree with any pickup Zone; (3) Zone III (analogous to Geldart Group C) is inadequate for all the nano‐scale particles, so new boundaries and a new Zone are proposed. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1512–1519, 2017     

Effect of particle and fluid properties on the pickup velocity of fine particles

Systems involving fluid-particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids.In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems.     

Momentum transfer to Newtonian and non-Newtonian fluids flowing through packed and fluidized beds

This paper deals with the flow behaviour of Newtonian and non-Newtonian fluids flowing through packed and expanded beds. With the help of tube-bundle theory a generalized average shear-stress—shear-rate relationship is derived and found to predict the flow behaviour of power law as well as non-power law fluids. Polyvinyl alcohol solutions in water, a representative of power law fluids, and grease in kerosene, a representative of nonpower law fluids, are studied. The present investigation covers the range of Reynolds number from 10^?3 to 10³. An expression for average shear-stress at minimum fluidization velocity is derived and found to agree with that of our experiment. The generalized frictional Reynolds number is defined and a design chart is also presented for the evaluation of fluidizing velocities.     

Fall of drops in non-newtonian media

Terminal velocities of drops of organic liquids of diameter 0.0726 to 0.7256 cm in polymer solutions are determined. The Reynolds number range covered is 0.1 to 10³. Visual observations on the shapes and oscillations of drops are reported. A correlation for the terminal velocity data is presented.