A Simple Technique for Scaling Up Pneumatic Conveying Systems

A brief survey has shown that although scaling-up techniques in pneumatic conveying systems have generally been based on laboratory-scale test data, there still exists a divergence of opinions about the right choice of certain basic parameters such as solids friction factor and air friction factor. In this article, a simple model for pressure drop calculation has been proposed based on the classical Darcy's equation with some modifications. A parameter K, called pressure drop coefficient, has been shown to be independent of pipe diameter and hence suitable for scaling up to pipe sizes different from those used in laboratory-scale tests. For each of the bulk material and pipe size combinations used in this study, we calculated the standard deviation of predicted pressure values from the experimental values along the central 45° line passing through the origin; it varied from±165 mbar to a maximum±285 mbar. It has been shown that the model can be used for both horizontal and vertical pneumatic conveying.     

Solids Friction Factors for Fluidized Dense-Phase Conveying

There have been numerous correlations proposed for determining a solids friction factor ( λs ) for fully suspended (dilute phase) pneumatic conveying. Currently, there are no equivalent correlations that predict λs in nonsuspension dense-phase flows. In dense-phase conveying there are two basic modes of flow: plug/slug flow, which is predominantly based on granular products, and fluidized dense-phase flow, which is more suited to fine powders exhibiting good air retention capabilities. In plug/slug type flow, the stresses between the moving plug of material and the pipe wall dominate the solid-phase frictional losses. In fluidized dense-phase flow the frictional losses are characterized as a mixture of particle-wall and particle-particle losses but are heavily influenced by the gas-solid interactions. In this paper, a series of calculations were performed on experimental data in order to estimate λs for four types of material conveyed in the fluidized dense-phase flow regime. The solids frictional factors were found to be relatively independent of particle properties for varying air and solid mass flow rates and pressure drops. The resultant pressure drop from the empirical model showed good agreement with the experimental data.     

Measurement of the Stress Transmission Coefficient of Material Slugs in an Aerated Radial Stress Chamber

In dense-phase pneumatic conveying, particles are transported along a pipeline at relatively low conveying speeds. Due to the relatively gentle handling characteristics of this mode of flow, it is suitable for conveying fragile and brittle bulk materials used in the food and chemical industries. The simulation of the stress field within a slug aims at developing an accurate prediction model for the pressure drop along a pneumatic conveying line. A reliable prediction of the pressure drop strongly depends on an accurate assessment of the particle properties, the pipeline dimensions, and the operating conditions. In past decades, a few models have been developed to serve this purpose, most of them including the mean particle diameter as a crucial parameter. This generally limits the selection of materials to those of nearly spherical particle shape, as it is extremely difficult to obtain a representative diameter for irregularly shaped particles or bulk commodities comprising differently sized and/or shaped particles. Another previously conflicting parameter is the so-called stress transmission coefficient k w , which relates the lateral wall stress within a slug of material to the axial stress. Previously, this parameter could not be measured directly in a test rig and had to be estimated; therefore, inaccuracies within the prediction were unavoidable. Consequently, a new test chamber was developed to measure the lateral and axial stresses within a slug, which leads directly to the stress transmission coefficient. The design of the test apparatus is outlined and the initial tests undertaken are reported. A strong dependence of the radial stress measurements on temperature changes of the test rig induced by the airflow was discovered. Possible solutions to compensate for this influence are addressed and further discussed.     

Effect of Close-Coupled Bends in Pneumatic Conveying

Pressure drop in a close-coupled double bend in pneumatic conveying of fly ash is studied. Tests are carried out with a 6.35 cm (2.5 in) diameter 169.8 m (557 ft) long pipeline with various combinations of airflow, ash flow, phase density, and conveying velocity. The pressure drop across two close-coupled 90-degree bends is compared to the pressure drop in an isolated single 90-degree bend. Six ash samples of different physical and chemical compositions are used in the tests. Resulting bend pressure drops are correlated to the corresponding phase density and superficial air velocity at the bend inlet. The correlation pattern represented by the relationship {\Delta P_{solids} \over {SLR}} = Y1 \cdot V^{Y2} is established and found to vary with ash properties. For both single and close-coupled double bends and operating test conditions with \Delta {\rm P}_{\rm solids} / {\rm SLR} 0.15 at the bend entry, 86% of the measured test points fall within the range of - 20% of the \Delta {\rm P}_{\rm solids} / SLR calculated point. Below this threshold, the test results show that the pressure drops due to solids flow through a close-coupled double bend and single bends are often indistinguishable. Consequently, the loss through a close-coupled double bend cannot be considered as the cumulative effect of two isolated single bends.     

A Pressure Drop Model for Positive Pneumatic Conveying of Flour Through a Vertical Pipeline

A differential equation of motion for gas-flour two-phase flow in a vertical pipe was first derived based on the momentum conservation and by adopting two empirical expressions for the velocity ratio of flour to gas and frictional coefficient between flour and pipe wall, and then a pressure drop model for dilute positive pneumatic conveying of flour through a vertical pipeline was developed by employing the continuity and state equations for gas. The conveying tests were conducted on a positive pneumatic conveying system of flour in a flour mill. Under each of the six different flow conditions, the conveying parameters, such as the flour and gas mass flow rates and the pressure drop between two selected cross sections on the vertical pipeline were measured. The pressure drop between the two selected cross sections was evaluated using the pressure drop model for each of the six flow conditions. The calculated values of pressure drop agree well with the measured data, and it is demonstrated that the model is applicable to vertical positive pneumatic conveying systems of flour.     

An Experimental Technique for the Analysis of Slug Flows in Pneumatic Pipelines Using Pressure Measurements

An experimental technique has been developed to measure the flow characteristics of slugs in dense phase pneumatic conveying using pressure measurements. This method is based on the unique characteristics of slug flows in pipes, i.e., an axial pressure fluctuation along the pipeline and a pressure difference in the radial direction at the back of a slug. Standard differential pressure transducers were used in this study and the influence of the finite response time of these transducers was considered. Experiments were conducted over a range of gas-solids flow conditions and experimental data were analyzed to describe the behavior of solids slugs through pipes. The calculated slug velocity and length using axial pressure measurements were confirmed by video recordings, and the synthesis between axial and radial pressure signals showed reasonable agreement in flow pattern analysis. This relatively simple measuring technique has been found effective in detecting solids slugs traveling through horizontal pipes and will distinguish various flow regimes. It provides a useful and easily applied tool for system optimizing and benchmarking in industrial applications.     

An Experimental Technique for the Analysis of Slug Flows in Pneumatic Pipelines Using Pressure Measurements

An experimental technique has been developed to measure the flow characteristics of slugs in dense phase pneumatic conveying using pressure measurements. This method is based on the unique characteristics of slug flows in pipes, i.e., an axial pressure fluctuation along the pipeline and a pressure difference in the radial direction at the back of a slug. Standard differential pressure transducers were used in this study and the influence of the finite response time of these transducers was considered. Experiments were conducted over a range of gas-solids flow conditions and experimental data were analyzed to describe the behavior of solids slugs through pipes. The calculated slug velocity and length using axial pressure measurements were confirmed by video recordings, and the synthesis between axial and radial pressure signals showed reasonable agreement in flow pattern analysis. This relatively simple measuring technique has been found effective in detecting solids slugs traveling through horizontal pipes and will distinguish various flow regimes. It provides a useful and easily applied tool for system optimizing and benchmarking in industrial applications.     

A Unified Scaling-Up Technique for Pneumatic Conveying Systems

A major challenge facing the designers of pneumatic transportation systems is how to scale up reliably based on the results from pilot-scale test facilities. Further, even if dense phase flow condition prevails at the start of the conveying system, it may be a dilute phase flow condition at the end of the pipeline. Hence, any scaling-up technique should be able to address the dynamic change of flow condition along the pipeline. The scaling-up technique presented here using the pressure drop prediction models based on modified Darcy-Weisbach equation successfully addresses these dynamic changes. It has been shown that the pressure drop coefficient ‘K,’ as defined by the models, is independent of the pipe diameter. Further, in the case of vertical conveying, ‘K’ has been shown to be independent of particle size distribution for a given material. The predicted pressure values were found to be in reasonably good agreement with the experimental results varying from 3.5% to 19.9%.     

A Unified Scaling-Up Technique for Pneumatic Conveying Systems

A major challenge facing the designers of pneumatic transportation systems is how to scale up reliably based on the results from pilot-scale test facilities. Further, even if dense phase flow condition prevails at the start of the conveying system, it may be a dilute phase flow condition at the end of the pipeline. Hence, any scaling-up technique should be able to address the dynamic change of flow condition along the pipeline. The scaling-up technique presented here using the pressure drop prediction models based on modified Darcy-Weisbach equation successfully addresses these dynamic changes. It has been shown that the pressure drop coefficient 'K,' as defined by the models, is independent of the pipe diameter. Further, in the case of vertical conveying, 'K' has been shown to be independent of particle size distribution for a given material. The predicted pressure values were found to be in reasonably good agreement with the experimental results varying from 3.5% to 19.9%.     

An Investigation into Pressure Fluctuations and Improved Modeling of Solids Friction for Dense-Phase Pneumatic Conveying of Powders

The aim of this paper is to investigate into flow mechanism with the help of pressure signal fluctuations analysis and modeling solids friction in case of solids–gas flows for fluidized-dense-phase pneumatic conveying of fine powders. Materials conveyed include fly ash (median particle diameter 30 µm; particle density 2300 kg m^?3; loose-poured bulk density 700 kg m^?3) and white powder (median particle diameter 55 µm; particle density 1600 kg m^?3; loose-poured bulk density 620 kg m^?3). These were conveyed in different flow regimes varying from fluidized-dense-to-dilute phase. To obtain information on the nature of flow inside pipeline, static pressure signals were studied using technique of Shannon entropy. Increase in the values of Shannon entropy along the flow direction through the straight-pipe sections were found for both the powders. However, drop occurred in the Shannon entropy values after the flow through bend(s). Change in slope of straight-pipe pneumatic conveying characteristics along the flow direction is another factor which provided indication regarding change in flow mechanisms along the flow. A new technique for modeling solids friction factor has been developed using a solids volumetric concentration and ratio of particle terminal settling velocity to superficial air velocity by replacing the conventional use of solids loading ratio and Froude number, respectively. The new model format has shown promise for predictions under diameter scale-up conditions.     

Experimental analysis on particle fluctuation velocity in a horizontal air–solid two-phase pipe flow having a dune model

To further elucidate the mechanism of energy-conserving conveying in horizontal pneumatic conveying with the dune model, the high-speed particle image velocimetry is applied to measure particle fluctuation velocity near the minimum conveying velocity of the conventional pneumatic conveying. This study focuses on the effect of mounting dune models on the horizontal pneumatic conveying in terms of power spectrum, autocorrelation coefficients, two-point correlation coefficients, fluctuation intensity of particle velocity, skewness factor, and probability density function. It is found that the power spectrum peaks with the dune model are larger than those of the nondune system, suggesting the acceleration and suspending efficiency of the dune model, especially dune models mounted at the bottom of the pipe. Meanwhile, the profiles of particle fluctuation velocity intensity indicate that the large particle fluctuating energy is generated due to mounting the dune model so that the particles are more easily accelerated and suspended. This is one of the important reasons why the mounted dune model results in a low pressure drop and low minimum conveying velocity. Based on the distribution of skewness factor and probability density function, it is found that the particle fluctuation velocities of all cases follow the Gaussian distribution in the lower and middle parts of the pipe. The particle fluctuation velocities in the case of the dune models mounted at the bottom of the pipe obey the Gaussian-type fluctuation more.     

Analysis of Forced Flow of Granular Materials in Vertical Pipes without and with Air Permeation

The problems associated with grain elevation and conveying under forced flow in vertical pipes are discussed. Based on experimental results, a theory is presented to describe forced flow with varying degrees of air permeation up to and just beyond the fluidization point. The theory takes into account the boundary and internal frictional properties, the degree of consolidation of the bulk granular material, and the stress fields that occur during forced flow. The force to elevate grain in a vertical tube is shown to be composed of two components, one to overcome Coulomb friction and initiate motion, and the other a time-dependent component that depends on the stiffness and damping characteristics of the granular material. The Coulomb friction component increases approximately exponentially with column height due to the positive feedback effect of the shear stresses at the pipe wall opposing the motion. Air permeation is shown to significantly reduce this component of the conveying force by reducing both the internal friction and the apparent bulk specific weight, the latter being the actual bulk specific weight less the air pressure gradient. Air permeation has a very significant effect on reducing both the bulk stiffness and, particularly, the damping characteristics, thereby reducing the time-dependent component of the conveying force.     

An experimental study on a horizontal-vertical pneumatic conveying system using oscillatory flow

To reduce the power consumption of a horizontal-vertical pneumatic conveying system, an oscillator is mounted with a 45° oblique plane through the pipe axis in this study. This experimental study focuses on the effect of oscillatory flow using the oscillator on the horizontal-vertical pneumatic conveying system in terms of the overall pressure drop of the system, power consumption, local pressure drop, and particle velocity. Compared with conventional pneumatic conveying (axial-flow), the pressure drop and power consumption can be reduced using the oscillatory flow in a lower air velocity range. Meanwhile, the particle axial velocity of the oscillatory flow is higher than that of the axial-flow near the bottom of pipe. This outcome indicates that the accelerating effect of oscillatory flow is obvious near the bottom of the pipe, and the particle vertical velocity of the oscillatory flow is positive, whereas the particle vertical velocity of the axial-flow is almost negative. This result shows that the particles of the oscillatory flow are suspended sufficiently, but the particles of the axial-flow have a tendency of deposition. Furthermore, the fluctuation intensity of the particle velocity of the oscillatory flow is higher than that of the axial-flow, especially near the bottom of the pipe.     

Modeling Solids Friction for Dense-Phase Pneumatic Conveying of Powders

This article results from an ongoing investigation aimed at developing a new validated test-design procedure for the accurate prediction of pressure drop for dense-phase pneumatic conveying of powders. Models for combined pressure drop coefficient (“K”) for solids-gas mixture were derived using the concept of “suspension density” by using the steady-state “straight pipe” pressure drop data between two different tapping locations of the same pipe and also for two different diameter pipes. It was observed that the derived models were different depending on the location of tapping points (for the same pipe) and selected pipe diameters. The derived models were then evaluated by predicting the pressure drop for pipelines with various diameters or lengths (69 mm I.D. × 168 m, 105 mm I.D. × 168 m, 69 mm I.D. × 554 m) for the conveying of power station fly ash. A comparison between the predicted pneumatic conveying characteristics (PCC) and the experimental plots showed that the models resulted in significant over-predictions. In the second part of the article, the “system” approach of scaleup was evaluated. “Total” pipeline pressure drop characteristics for test-rig pipelines were scaled up to predict the PCC for larger/longer pipes. It was found that the “system” approach generally resulted in grossly inaccurate predictions. It was concluded that further studies are needed for a better understanding of the solids-gas flow mechanism under dense-phase conditions.     

Simulation of Gas-Solid Flow in Vertical Pipe by Hard-Sphere Model

ABSTRACT

This article presents a two-dimensional study of the gas-solid flow in a vertical pneumatic conveying pipe by means of a hard-sphere model where the motion of individual particles can be traced. Simulations were performed for a pipe of height 0.9 m and width 0.06 m, with air as gas phase and particles of density 900 kg/m³ and diameter 0.003 m as solid phase. Periodic boundary conditions were applied to the solid phase in the axial direction. Different cases were simulated to examine the effects of the number of particles used, superficial gas velocity, and restitution coefficient. The results show that the main features of plug flow can be reasonably captured by the proposed simulation technique. That is, increasing the number of particles in a simulation will increase the length of plugs but does not change the velocity of plugs; the solid fraction of a plug is relatively low if the number of particles is small. In particular, it is shown that increasing superficial gas velocity will increase the velocity of plugs and the frequency of plugs, and the pressure drop through a rising plug increases linearly with the plug length, suggesting that the total pressure of a conveying system with a given length can be quantified from the information of plug length and plug frequency. Increasing the restitution coefficient can promote the momentum transfer between particles and hence the raining down of particles from the back of a plug in vertical pneumatic conveying. The simulation offers a useful technique to understand the fundamentals governing the gas-solid flow under pneumatic conveying conditions.     

Modeling and experimental validation of pressure drop for pneumatic plug conveying

This paper indicates that a variety of models exist to calculate the pressure drop of pneumatic plug conveying. Unfortunately these models are limited in their flexibility and calculate pressure drop only for two extremes, the active and passive case of bulk solid. Until now the stress state within the plug cannot be determined. Therefore a sensor was built to detect wall shear stress, normal stress and the stress state along a moving plug. Beginning with vertical pneumatic plug conveying, the previous models were verified and modified to get new perceptions about formation, stability and pressure drop of plugs.The DFG (German Research Community) is gratefully appreciated for the financial support to this work.Received October 2003     

A Possible Scaling-up Technique for Dense Phase Pneumatic Conveying

In this article experimental findings have been presented to show that the pressure drop coefficient (K) for vertical and horizontal pneumatic conveying for a given bulk material follows a certain pattern. The pressure drop coefficient for vertical pneumatic conveying for a given material has been found to be independent of any variation of particle size distribution, within experimental limits. The pressure drop prediction technique proposed by the authors previously has been validated with the test results of alumina and bentonite.     

Simulation of Gas-Solid Flow in Vertical Pipe by Hard-Sphere Model

This article presents a two-dimensional study of the gas-solid flow in a vertical pneumatic conveying pipe by means of a hard-sphere model where the motion of individual particles can be traced. Simulations were performed for a pipe of height 0.9 m and width 0.06 m, with air as gas phase and particles of density 900 kg/m³ and diameter 0.003 m as solid phase. Periodic boundary conditions were applied to the solid phase in the axial direction. Different cases were simulated to examine the effects of the number of particles used, superficial gas velocity, and restitution coefficient. The results show that the main features of plug flow can be reasonably captured by the proposed simulation technique. That is, increasing the number of particles in a simulation will increase the length of plugs but does not change the velocity of plugs; the solid fraction of a plug is relatively low if the number of particles is small. In particular, it is shown that increasing superficial gas velocity will increase the velocity of plugs and the frequency of plugs, and the pressure drop through a rising plug increases linearly with the plug length, suggesting that the total pressure of a conveying system with a given length can be quantified from the information of plug length and plug frequency. Increasing the restitution coefficient can promote the momentum transfer between particles and hence the raining down of particles from the back of a plug in vertical pneumatic conveying. The simulation offers a useful technique to understand the fundamentals governing the gas-solid flow under pneumatic conveying conditions.     

Application of an Eulerian granular numerical model to an industrial scale pneumatic conveying pipeline

In this paper, an Eulerian granular numerical model is applied in the modelling of an industrial scale pneumatic-based cement conveying system. Steady-state simulation results are found to match pressure and outlet flowrate values with actual system data. By modifying the inlet pressure and material feed rate, data that predicts the performance of the conveying system have been obtained within the present study. Transient simulations have also been conducted and the results reveal intricate details of the cement flows along the pneumatic pipes and pipe bends. In particular, particle roping behaviour is observed to follow the sides of the wall before, during and after the pipe bends. A sloshing-like cement flow motion is also observed after the cement exits the bend. The concentration distribution of the cement particles is found not only to be partly due to gravitational effects but also the pneumatic pipe configuration. Lastly, close inspection of the secondary flows within the pneumatic pipe shows that their directional changes lead to a corresponding change in the particle roping direction, indicating that particle roping is closely associated with the secondary flow structures induced by the exact pipe configuration.     

Modeling Dense-Phase Pneumatic Conveying of Powders Using Suspension Density

This article presents results of an investigation into the modeling of pressure drop in horizontal straight pipe section for fluidized dense-phase pneumatic conveying of powders. Suspension density and superficial air velocity have been used to model pressure drop for two-phase solids-gas flow. Two applicable models formats (developed by other researchers using two different definitions of suspension density) were used to represent the pressure drop due to solids-gas flow through straight pipe sections. Models were generated based on the test data of conveying power-station fly ash and electrostatic precipitator (ESP) dust (median particle diameter: 30 and 7 µm; particle density: 2300 and 3637 kg m^?3; loose-poured bulk density: 700 and 610 kg m^?3, respectively) through a relatively short length of a smaller diameter pipeline. The developed models were evaluated for their scale-up accuracy and stability by using them to predict the total pipeline pressure drop (with appropriate bend model) for 69 mm I.D. × 168 m; 105 mm I.D. × 168 m and 69 mm I.D. × 554 m pipes and comparing the predicted versus with experimental data. Results show that both the models with suspension density and air velocity generally provide relatively better prediction compared to the conventional use of solids loading ratio and Froude number. For fly ash, the two formats result in considerable different predictions, whereas they provide relatively similar results for ESP dust.