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.     

Generalized master curve for threshold superficial velocities in particle-fluid systems

This paper presents our previous analyses of pickup gas velocity from a layer of particles in pipes and big wind tunnels, pickup liquid velocity, boundary saltation and minimum pressure velocities, and a new analysis of the minimum fluidization velocity and the terminal velocity. All these threshold velocities are defined as simple relations between the Reynolds and Archimedes numbers as modified by various effects. The Reynolds number is modified by taking into account the pipe diameter while the Archimedes number is modified by taking into account various properties that affect each threshold mechanism. Since all threshold velocities could be defined successfully by the same non-dimensional groups it was possible, at the first time, to present a Generalized Master Curve, which provides an overview of all the threshold velocities. This overview enabled, for example, to find quantitatively the relationships between all the threshold velocities to the terminal velocity and to compare the pickup and saltation velocities.     

Phenomenological study of saltating motion of individual particles in horizontal particle–gas systems

A comprehensive use of particle–fluid conveying systems for a wide range of industries requires a deep understanding in all interactions of the particular conveying process. One of the most common particle motions occurring in conveying systems is the saltating motion of particles. Although the literature abounds with theoretical, empirical and numerical studies that investigate the saltation phenomenon, there remain many questions and misunderstandings. Some of the recently solved issues are: which non-dimensional groups are introducing the particle saltating motion, how the saltation length might be predicted, how the pipe diameter and the coefficient of restitution influence the saltation velocity and length.The present work investigates the motion of individual saltating particles and presents a wide range of experimental measurements of the conveying length for a variety of particulate solids, sizes and shapes. The total conveying length was divided into three lengths: the first flight, the rebound and the rolling/sliding and each one of them is theoretically and empirically analyzed and compared. This phenomenological study presents the theoretical evidence to previously empirical findings. The theoretical analysis is further used to define the border conditions between various mechanisms. The results show that for coarse particles the rebound and rolling/sliding motions might be presented by a simple relationship between the Reynolds and Archimedes numbers. Additionally we find that the preferred saltation mode of fine powders depends on the conveying system length and diameter. For example for large pipe diameters and short length the first flight mode is the dominant; however, for small pipe diameters and long systems length the rebound mode is the dominant.     

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.     

An experimental study of energy-saving pneumatic conveying system in a horizontal pipeline with dune model

In order to reduce power consumption and conveying velocity, a pneumatic conveying system where a dune model is mounted in a pipeline is proposed in this paper. The experimental study focuses on the effect of the mounted dune model in the horizontal pneumatic conveying system in terms of pressure drop, power consumption and conveying velocity. The test pipeline consisted of a horizontal smooth acrylic tube with an inside diameter of 80 mm and a length of about 5 m. Polyethylene spherical particles with a density of 952 kg/m³ and diameters of 2.3 and 3.3 mm are used as conveying materials. The mean air velocity is varied from 9 to 16 m/s, and the solid mass flow rate is from 0.25 to 0.45 kg/s. Firstly, the effect of the dune model location on pneumatic conveying is experimentally studied. It is found that in the lower air velocity range, the pressure drop of the pneumatic conveying with a mounted dune model is lower than that of a conventional pneumatic conveying system. A lower conveying velocity and energy-saving conveying can be realized by installing a dune model in the conveying pipe. Especially the case of fixing the dune model on the bottom of the pipe at the inlet of particle feed is more effective. The particle flow patterns also show that the dune model reduces the deposition of particles. Then, the effect of different surface materials of the dune model is examined. By using a surface material of the dune model with a large coefficient of restitution, the pressure drop of conveying large particles is the lowest. When conveying relatively small particles, however, the pressure drop becomes the lowest by a small coefficient of restitution. The maximum reduction rates of the minimum velocity and power consumption by the dune model are about 19% and 34%, respectively.     

Prediction of the choking velocity and voidage in vertical pneumatic conveying of coarse particles

A method for predicting the choking velocity and voidage in vertical pneumatic conveying of coarse particles is developed and verified using the data obtained in this study as well as the data of Capes and Nakamura [C.E. Capes, K. Nakamura, Vertical pneumatic conveying: an experimental study with particles in the intermediate and turbulent flow regimes, Can. J. Chem. Eng. 51 (1973) 31-38]. The method is based on momentum equation, variational expression for the fluid-particle interphase drag coefficient and empirical correlation for the slip velocity at choking. New experimental data for choking velocity and voidage in vertical pneumatic conveying of monosized glass spheres (1.2, 1.94 and 2.98 mm in diameter) in a 30 mm in diameter tube are presented. Different published methods for the prediction of the choking velocity and voidage are compared with available data for coarse particles. The average agreement for choking velocity between proposed method and experimental values is within ± 7.2%. It was found that the simplest method to measure regime transition points in vertical pneumatic conveying is to measure pressure fluctuations in the transport line.     

Application of high-speed PIV and image processing to measuring particle velocity and concentration in a horizontal pneumatic conveying with dune model

The purpose of this study focuses on analyzing the particle velocity and concentration characteristics in a horizontal pneumatic conveying with dune model, so as to reveal the mechanism of the low conveying velocity and saving-energy conveying. The test pipeline consisted of a horizontal smooth acrylic tube with an inside diameter of 80 mm and a length of about 5 m. The polyethylene particles of density 978 kg/m³ and 952 kg/m³ with diameters of 2.3 and 3.3 mm are used as conveying materials. High-speed PIV was first applied to measure the time-averaged particle velocity and was proven to be an efficient measurement technique in the pneumatic conveying. Then the particle velocity and concentration distributions of three locations were measured at mean air velocities of 12 m/s and 13 m/s and the solid mass flow rates of 0.45 kg/s and 0.43 kg/s. A comparison of the particle velocity and concentration profiles between dune model and non-dune model was performed. It is found that the particle concentration of using dune model becomes higher in the upper part of pipeline and becomes lower near the bottom of pipeline in the acceleration region. The particle velocities of using dune model are clearly higher than that of the conventional pneumatic conveying along pipeline and display a uniform profile at the downstream. It is also clear that the particles can be effectively accelerated by increasing air velocity and impacting the surface of dune model. The effect of dune model on the velocity profile of relatively small particles is larger than that of the larger particles and maintains to the downstream.     

Transport of solids by gas-liquid mixtures in horizontal pipes

Two sizes of particles of 500μ and 100μ mean diameter were conveyed as water slurries through 1 inch and 2 inch horizontal pipelines. Pressure drops and saltation velocities were measured over a range of slurry concentrations to 14% by volume with and without concurrently flowing air. In the former case, the principal flow patterns studied were in the bubble and plug flow regimes. Although small effects on saltation point were noted due to the induced turbulence from the air bubbles, these were not significant, and a reasonable estimate of saltation velocities could be made from Durand's correlation. Pressure drops were found to be correlated reasonably well by modified Lockhart-Martinelli parameters as used for turbulent-turbulent horizontal gas-liquid flow except at conditions near the saltation point. Pressure drops for slurry flow alone were predicted reasonably well by the modified Durand equation.     

Measurement and analysis of particle—particle interaction in a cocurrent flow of particles in a dilute gas—solid system

The experimental apparatus of Arastoopour et al.[3] was modified to measure pressure drop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle—particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle—particle interaction with relative velocity between the particles of 0.3–4.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.     

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。     

Influence of multiple gas inlet jets on fluidized bed hydrodynamics using Particle Image Velocimetry and Digital Image Analysis

A rectangular fluidized bed setup was developed to study the evolution of inlet gas jets located at the distributor. Experiments were conducted with varying distributor types and bed media to understand the motion of particles and jets in the grid-zone region of a fluidized bed. Particle Image Velocimetry and Digital Image Analysis were used to quantify the parameters that characterize these jets. A grid-zone phenomenological model was developed to compare these parameters with those available in the literature. It was determined from this study that jet penetration length behavior is consistently different for fluidization velocities below and above the minimum fluidization. For velocities above minimum fluidization, jet lengths were found to increase more rapidly with increase in orifice velocity than for operating conditions below minimum fluidization.     

Minimum transport boundaries for pneumatic conveying of powders

For the reliable design of pneumatic conveying systems, an accurate estimation of the minimum transport boundary is of significant importance. This paper presents results from an effort to establish a unified criterion for scaling-up the unstable boundary for the dense-phase pneumatic conveying of powders. An existing method of representing minimum transport criteria (based on superficial air velocity and solids loading) has been found inadequate for accurately predicting the unstable boundary, especially under diameter scale-up conditions. Using the experimental data from twelve different powders conveyed over a wide range of pipe lengths and diameters, a newly validated improved design procedure has been developed in this study using a Froude number based criterion at the entry to the pipe. The physical significance of Froude number in representing the minimum transport boundary is also discussed.     

Effects of passenger blockage on smoke flow properties in longitudinally ventilated tunnel fires

This paper investigates the effects of passenger blockage on smoke flow properties in longitudinally ventilated tunnel fires. A series of numerical simulations were conducted in a 1/5 small-scale tunnel with the different heat release rates (50-100 kW), longitudinal ventilation velocities (0.5-1 m/s), passenger blockage lengths (2-6 m), and ratios (0.17-0.267). The typical smoke flow properties in different tunnel fire scenarios are analyzed, and the results show that under the same heat release rate and longitudinal ventilation velocity, the smoke back-layering length, maximum smoke temperature, and downstream smoke layer height decrease with increasing passenger blockage length or ratio. The Li correlations can well predict the smoke back-layering length and maximum smoke temperature in tunnel fire scenarios without the passenger blockage. When the passenger blockage exists, the modified local ventilation velocity that takes the blockage length and ratio into account has been proposed to correct the Li correlations. The smoke back-layering length and maximum smoke temperature with the different blockage lengths and ratios can be predicted by the modified correlations, which are shown to well reproduce the simulation results.     

Influence of the Entrance Configuration on the Performance of a Non-Mechanical Solid Feeding Device for a Pneumatic Dryer

The solids feeder is an important component of a dryer, since it is responsible for introducing the moist material at controlled, specified rates. The purpose of this paper is to investigate the effects of solids feeding configuration on the fluid dynamic behavior of a 53-mm-diameter vertical pneumatic conveyor with a loop of 180°, aiming at further applications in drying granular materials. A non-mechanical solid feeding system constituted by a hopper connected to an inclined pipe was applied to feed type D particles in the conveying line. This simple feeding apparatus was modified through the insertion of different flow restriction devices at the air inlet, namely a reduction nozzle and a Venturi device. This was aimed at studying how the solids flow rates and the fluid dynamics of the whole conveying line are affected by the entrance configuration and inlet devices. The use of inlet devices combined with the non-mechanical inclined valve affected significantly the performance of the valve when operating with type D particles in a pneumatic conveying line. When using inlet devices, an increase in the conveyed solid flow rates at a given air velocity was observed. The reduction nozzle yielded a range of solids loading ratios similar to that of the inclined valve with no inlet device, and introduced some pressure instabilities at the entrance region. The Venturi device allowed operation at a wider range of solids loading ratios and no pressure instability was detected in the conveying line. For the conditions investigated, neither the gas velocity nor the loading ratio affected the extent of entrance length. The inlet devices may be successfully applied to modify and improve the performance of the inclined valve as a solids feeder in pneumatic dryers.     

单组分颗粒振动流化床的流体力学研究（2）──床层膨胀和起始流化速度

本文在振动流化床中研究床层膨胀和颗粒的起始流化速度,分别研究颗粒物性、振动特性（频率、振幅）和静止床层高度对它们的影响,根据不同的振动条件下Ｇｅｌｄａｒｔ’Ａ、Ｂ、Ｄ类１３种物料起始流化速度的实验结果,关联了实验条件下起始流化速度的计算式,此计算式对振动流化床的设计具有指导意义。     

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%.     

Bubbling fluidization of biomass and sand binary mixtures: Minimum fluidization velocity and particle segregation

Understanding the minimum fluidization velocity of biomass and sand mixtures is fundamental to ensuring the optimal performance of fluidized beds in a thermo-conversional process, such as fast pyrolysis. The present work aimed to determine the minimum fluidization velocity of binary mixtures using the characteristic diagram of pressure drop in the bed and to develop an experimental correlation for the minimum fluidization velocity of biomass and sand mixtures. Three types of biomass (sweet sorghum bagasse, waste tobacco and soybean hulls) and four sands with different sizes were investigated. The results showed that the fluid dynamic behavior of binary mixtures is directly related to the biomass size and shape. For sweet sorghum bagasse (more irregular particles), higher biomass percentages led to lower minimum fluidization velocities, which differed from the behaviors observed for waste tobacco and soybean hulls. The diameter ratio inert/biomass effectively influenced the segregation, with a higher ratio causing more pronounced bed segregation. A good fluidization regime (with little segregation) for biomass and sand mixtures was obtained using the smallest sand (d₅₀ = 0.35). Considering the studied operating conditions, the proposed correlation can be used satisfactorily to predict the minimum fluidization velocities for mixtures of biomass and sand in fluidized beds.     

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.     

New model to calculate the choking velocity of monosize and multisize solids in vertical pneumatic transport lines

The choking velocity is the minimum gas velocity required for the vertical dilute phase transport of a given solids flux. Experimental choking velocities obtained from the literature for both monosize and multisize particles were compared to choking velocities predicted with various published correlations. For monosize particles, Yang's correlation (1983) gave the most accurate predictions. For multisize particles, all the literature correlations gave rather poor predictions. Much more accurate predictions were obtained with a new simple physical model which assumes that an annulus forms along the pipe wall at low gas velocities. Choking then occurs when this annulus occupies approximately 25% of the total pipe cross-sectional area.     

Slug flow characterization in horizontal annulus

To characterize slug flows in annuli channels and highlight the effect of the eccentricity on the flow behaviors, experiments were conducted in two horizontal annuli setups (a) concentric and (b) fully eccentric using air and water as the testing fluids. The range of air and water superficial velocities investigated were 0.45–3.49 m/s and 0.15–2.77 m/s, respectively. Slug parameters measured using conductance probes designed for this study include slug length, translational velocity, slug frequency, and slug holdup. It is found that the slug translational velocity is unaffected by the annulus eccentricity; however, parameters including slug frequency, slug holdup, and slug lengths have a higher value in the fully eccentric annulus when compared with the concentric one. We introduced a new definition of hydraulic diameter, which reconciles the correlation between the dimensionless mean slug length and the mixture velocity of the horizontal annuli with different setups.