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.     

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.     

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.     

Axial and Radial Pressure Drops of Dense Phase Plugs

An experimental technique to measure various characteristics of plug flow in dense phase pneumatic conveying systems based on the unique characteristics of plug flow, i.e., the fluctuation of axial pressure drop along a pipeline and pressure difference in the radial direction at the back of a plug, was developed by Li et al. (2002). Based on this work, a further experimental study combined with numerical modeling was carried out to describe the structure of plugs through the analysis of the measurements of pressure difference in both axial and radial directions. A theoretical explanation of these pressure differences was proposed and agrees very well with the recorded signals of pressure difference from differential transducers. This explanation will prove useful in understanding plug structures in industrial applications.     

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.     

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.     

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.     

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.     

Particle dynamics analysis in bend in a horizontal-vertical pneumatic conveying system with oscillatory flow

The pneumatic system is frequently operated in the high air velocity region, which aggravates the power consumption and erosion of bend, and the intensive study of the particles motion characteristic on a horizontal-vertical pneumatic conveying in various curved 90° bends is necessary. This experimental study focuses on the particles motion characteristic of bend on the horizontal-vertical pneumatic conveying with oscillatory flow (generated by installing the oscillator) in terms of on pressure drop, powder consumption, the evolution of particle velocity and particle fluctuating intensity during flowing through bends. The results indicate that powder consumption can be reduced by using oscillatory flow, which is more obvious with a larger radius ratios bend. Meanwhile, the pressure drop proportion of bend is higher than average pressure drop of the system within the same distance. Otherwise, the total reduction particles velocity through bend is less while using oscillatory flow, which is more obvious using larger radius ratios bend. The particle velocity using oscillatory flow is higher than that of the conventional pneumatic conveying for the cases of larger radius ratios bend, and this effect is less evident while through a smaller radius bend.     

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.     

The effect of oscillating flow on a horizontal dilute-phase pneumatic conveying

ABSTRACT

A horizontal dilute-phase pneumatic conveying system using vertically oscillating soft fins at the inlet of the gas–particle mixture was studied to reduce the power consumption and conveying velocity in the conveying process. The effect of different fin lengths on horizontal pneumatic conveying was studied in terms of the pressure drop, conveying velocity, power consumption, particle velocity, and intensity of particle fluctuation velocity for the case of a low solid mass flow rate. The conveying pipeline consisted of a horizontal smooth acrylic tube with an inner diameter of 80 mm and a length of approximately 5 m. Two types of polyethylene particles with diameters of 2.3 and 3.3 mm were used as conveying materials. The superficial air velocity was varied from 10 to 17 m/s, and the solid mass flow rates were 0.25 and 0.20 kg/s. Compared with conventional pneumatic conveying, the pressure drop, MPD (minimum pressure drop), critical velocities, and power consumption can be reduced by using soft fins in a lower air velocity range, and the efficiency of fins becomes more evident when increasing the length of fins or touching particles stream by the long fins. The maximum reduction rates of the MPD velocity and power consumption when using soft fins are approximately 15% and 26%, respectively. The magnitude of the vertical particle velocity for different lengths of fins is clearly lower than that of the vertical particle velocity for a non-fin conveying system near the bottom of the pipeline, indicating that the particles are easily suspended. The intensities of particle fluctuation velocity of using fins are larger than that of non-fin. The high particle fluctuation energy implies that particles are easily suspended and are easily conveyed and accelerated.     

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.     

Dynamic analysis of particles in vertical curved 90° bends of a horizontal-vertical pneumatic conveying system based on POD and wavelet transform

The pneumatic system is frequently operated in the high air velocity region, which aggravates the power consumption and erosion of bend, and the dynamic analysis of particles in bends with different radius of curvature in a horizontal-vertical pneumatic conveying system is necessary. This experimental study focuses on the particle motion characteristic of bend on the horizontal-vertical pneumatic conveying in terms of on pressure drop, particle velocity, power spectral characteristics of particle fluctuation velocity, the energy distribution of the proper orthogonal decomposition (POD) modes, time coefficients of POD, and spatial mode of POD mode during flowing through bends. The results indicate that the particle rope is the large-scale motion of particles containing high energy, which dominates the motion of particles in the bend, and the suppression of small-scale motion leads to the low pressure drop in a large radius ratio of the bend.     

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%.     

Industrial Multi-Plug Conveying Analysis

Single-plug conveying systems have the advantage of being easy to handle and highly controllable. In industry, however, multi-plug conveying systems are the most common choice due to their high transporting capacity. In order to study a multi-plug industrial conveying system, the system parameters were varied along with the materials being conveyed. The responses obtained were compared to the single-plug laboratory system, noting differences and similarities. The pneumatic conveying system at an industrial facility consisted of a 0.01 m Schedule 10 aluminum pipe, approximately 100 m long. To measure the pressure at different points along the system, a total of seven transducers were installed, four air transducers and three flush transducers. This study also used a high-speed video camera to view the plugs as they passed through the transparent viewing port, providing more detailed information on the multi-plug conveying process. Three materials were tested at different superficial air velocities and solid mass flows. In each experiment all transducers took data with a sample rate of 1,000 Hz, giving a highly detailed overview of the conveying process. The analysis included plug velocity and plug size with respect to the superficial air velocity. The Mi model for plug-flow pressure drops was found to yield agreement with the data within ±25%. For this type of industrial operation, this agreement is considered acceptable. The visual observations recorded with the camera showed that there were conditions of stable plug formation as well as varying degrees of plug stability and integrity depending on the operational conditions.     

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.     

Effect of particle size distribution on hydrodynamics of pneumatic conveying system based on CPFD simulation

The effect of particle size distribution on the hydrodynamics of dilute-phase pneumatic conveying system was analyzed using computational particle fluid dynamics (CPFD) simulation. The influence of a simulation parameter, i.e., correction factor of drag coefficient (k), on the hydrodynamics of pneumatic conveying system was determined via CPFD simulation. When results of simulation were compared with experimental data of previous studies, the average error of pressure drop per length predicted by the CPFD approach with the correction factor was below 4.4%. Saltation velocity and the pressure drop per unit length declined as the drag force coefficient increased. Simulation results also revealed that the pressure drop per length and the saltation velocity were decreased when the fine powder fraction in the particle size distribution was increased, although the width of particle size distribution was widened, and the standard deviation was increased. Finally, the Relative Standard Deviation (RSD) of pressure drop per length was measured and compared with median diameter (d₅₀), Sauter mean diameter, geometric mean diameter, and arithmetic mean diameter. The RSD of the Sauter mean diameter was 5.8%, approximately twice less than the RSD value of d₅₀ commonly used in pneumatic conveying.     

Industrial Multi-Plug Conveying Analysis

Single-plug conveying systems have the advantage of being easy to handle and highly controllable. In industry, however, multi-plug conveying systems are the most common choice due to their high transporting capacity. In order to study a multi-plug industrial conveying system, the system parameters were varied along with the materials being conveyed. The responses obtained were compared to the single-plug laboratory system, noting differences and similarities. The pneumatic conveying system at an industrial facility consisted of a 0.01 m Schedule 10 aluminum pipe, approximately 100 m long. To measure the pressure at different points along the system, a total of seven transducers were installed, four air transducers and three flush transducers. This study also used a high-speed video camera to view the plugs as they passed through the transparent viewing port, providing more detailed information on the multi-plug conveying process. Three materials were tested at different superficial air velocities and solid mass flows. In each experiment all transducers took data with a sample rate of 1,000 Hz, giving a highly detailed overview of the conveying process. The analysis included plug velocity and plug size with respect to the superficial air velocity. The Mi model for plug-flow pressure drops was found to yield agreement with the data within ±25%. For this type of industrial operation, this agreement is considered acceptable. The visual observations recorded with the camera showed that there were conditions of stable plug formation as well as varying degrees of plug stability and integrity depending on the operational conditions.     

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.     

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%.