PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

Two-Fluid,Two-Dimensional Model for Pneumatic Drying

Abstract

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

ABSTRACT

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

Two-Fluid, Two-Dimensional Model for Pneumatic Drying

Pneumatic drying is a widely used process in the chemical industries and includes simultaneous conveying and heat and mass transfer between the particles and the heat gas. The increase in the use of this unit operation requires reliable mathematical models to predict processes in the industrial facilities. In the present study a Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a two-dimensional steady-state condition and considering axial and radial profiles for the flow variables. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle is assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The numerical procedure includes discretization of calculation domain into torus-shaped final volumes, solving conservation equations by implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and controls over coupling of phases by IPSA (Interphase Slip Algorithm). The developed model was applied to simulate a drying process of wet PVC particles in a large-scale pneumatic dryer and to a drying process of wet sand in a laboratory-scale pneumatic dryer. The numerical solutions are compared successfully with the results of independent numerical and experimental investigations. Following the model validation, the two-dimensional distributions of the flow characteristics were examined.     

STEAM DRYING OF WOOD CHIPS IN PNEUMATIC CONVEYING DRYERS

ABSTRACT

A model for a pneumatic conveying dryer is presented. Although the main emphasis is put on superheated steam drying of wood chips, it can be used for other porous materials as well

The model includes a comprehensive two-dimensional model for the drying of single wood chips which accounts for the main physical mechanisms occurring in wood during drying. The external drying conditions in a pneumatic conveying dryer were calculated by applying the mass, heat and momentum equations for each incremental step in dryer length. A plug flow assumption was made for the dryer model and the single particle and dryer models were solved in an iterative manner. The non-spherical nature of wood chips were accounted for by measuring the drag and heat transfer coefficients

Model calculations illustrate the complex interactions between steam, particles and walls which occur in a flash dryer. The drying rate varies in a very complex manner through the dryer. The internal resistance to mass transfer becomes very important in The drying of less permeable wood species such as spruce. Two effects were observed as the particle size was increased: firstly the heat transfer rate decreased, and secondly the residence time increased. To some extent, these effects compensate for each other, however, the net result is that larger chips have a higher final moisture content.     

PNEUMATIC DRYING IN DILUTED PHASE: PARAMETRIC ANALYSIS OF TUBE DIAMETER AND MEAN PARTICLE DIAMETER

In previous work on pneumatic drying presented by the authors, a mathematical model based on the conservation equations of momentum, mass and energy was proposed. This model was developed taking into account axial and radial profiles for gas and solids velocities, pressure and porosity in the drying tube. These dynamic profiles influenced the behavior of temperature in the gas and particulate phases, gas humidity and solids moisture content. In this work, this model has been used to perform a parametric analysis of the tube and panicle diameters in the pneumatic drying process. These variables were analyzed here for fixed conditions of gas and solids flowrates and initial values of temperatures, humidity and moisture content. Factorial planning was applied to the numerical solution of the mathematical model. Experimental data obtained in a pilot scale pneumatic dryer were used as the initial conditions in the simulation to specify the levels of the variables analyzed. Results on the influence of tube diameter and particle diameter on the drying process were obtained by statistical analysis of the responses generated by the factorial planning.     

LASER-BASED FLOW MEASUREMENTS OF DILUTE VERTICAL PNEUMATIC TRANSPORT

Dilute vertical pneumatic transport in a vertical lifter was studied using the sophisticated measurement techniques of laser Doppler anemometry (LDA) and phase Doppler anemometry (PDA). The vertical lifter consisted of a lower fluidized silo, an upper receiving tank, and a connecting vertical transport pipe made of clear glass. The experimental study was performed in order to get detailed information of the complex gas-particle flow behavior in a dilute vertical conveying system. Particle diameter, axial particle, and tangential particle velocities, as well as root mean square velocities, were measured simultaneously for different flow conditions. In addition, overall solid mass fluxes were obtained using weighing cells. Smooth and spherical zirconium oxide (ZrO₂) solids were applied with two different particle size distributions. Measurements were performed using different flow rates of air. The air inlet condition was varied in order to study its effect on the flow behavior. The particle diameter measurements show that no axial or radial segregation by size occurs for this transport condition. The results show that the particle velocity is independent of the particle size as well. The axial velocity profiles at different heights are almost identical and flat, which indicates fully developed turbulent pipe flow. The turbulent velocity measurements show that turbulence is mainly caused by the velocity gradients, and not by particle-particle collisions in dilute flow. The solid mass flux measurements show the importance of optimum inlet condition and how this influences the mass flux.     

水平管加压密相煤粉气力输送数值模拟

针对加压密相气力输送,对现有的颗粒静摩擦力模型进行适当修正,并将其与颗粒动理学理论相结合,建立了可以描述加压密相气力输送的气固湍流流动状况的多相流模型。该模型充分考虑了颗粒间碰撞和摩擦力作用,以及气相和颗粒团湍流脉动之间的相互作用。采用该模型对水平管内加压密相气力输送进行了三维数值模拟研究,模拟得到了气相和固相的速度、浓度和湍流强度分布,以及压降梯度的变化规律,再现了颗粒沉积层的形成和运动的动态过程。并进行了加压密相煤粉气力输送试验研究,预测的压降梯度与试验测量结果相符合。     

Eulerian–Lagrangian Simulation and Experimental Validation of Pneumatic Conveying Dryer

This paper explores numerical and experimental studies on the performance of a pneumatic conveying dryer. The four-way coupling Eulerian–Lagrangian approach is utilized in the numerical study and the experimental study is carried out in a pilot-scale vertical pneumatic conveying dryer of diameter 8.1 cm and 4.5 m length. The effects of Reynolds number, particle size, solid mass flow rate, and inlet gas temperature on the dryer performance are investigated. It is found that the present model predictions agree well with the experimental data. Generally, it is concluded that the drying rate increases as the Reynolds number increases, while increasing the particle size or the solid mass flow rate decreases the drying rate.     

STEAM DRYING OF WOOD CHIPS IN PNEUMATIC CONVEYING DRYERS

A model for a pneumatic conveying dryer is presented. Although the main emphasis is put on superheated steam drying of wood chips, it can be used for other porous materials as well

The model includes a comprehensive two-dimensional model for the drying of single wood chips which accounts for the main physical mechanisms occurring in wood during drying. The external drying conditions in a pneumatic conveying dryer were calculated by applying the mass, heat and momentum equations for each incremental step in dryer length. A plug flow assumption was made for the dryer model and the single particle and dryer models were solved in an iterative manner. The non-spherical nature of wood chips were accounted for by measuring the drag and heat transfer coefficients

Model calculations illustrate the complex interactions between steam, particles and walls which occur in a flash dryer. The drying rate varies in a very complex manner through the dryer. The internal resistance to mass transfer becomes very important in The drying of less permeable wood species such as spruce. Two effects were observed as the particle size was increased: firstly the heat transfer rate decreased, and secondly the residence time increased. To some extent, these effects compensate for each other, however, the net result is that larger chips have a higher final moisture content.     

Cocurrent Downflow Fluidized Bed Dryer: Experimental Equipment and Modeling

ABSTRACT

Product damage, high energy consumption, and nonhomogeneous final properties are present in typical drying operations such as pneumatic drying, fluidized-bed dryers, and upward circulating fluidized-bed dryers. The downer bed has been shown to be a good technique for this processes. The objective of this work is to test an experimental downflow dryer and model its operation. The equipment consists of a 5-m-high stainless steel duct with 0.17 m i.d. Gas velocity was varied between 0.3 and 8 m/s in co-current solid flow varying between 0 and 50 kg/m²s. Drying rates, pressures, and total flux for solid and gas are determined. Temperature profiles for gas and solid along the radial and axial directions are determined and tested with model predictions. The solid particles were previously dried turnip (Brassica napus) seeds. The equipment shows good operational conditions and facilities for parameter determination, but must be complemented with better equipment for particle concentration determinations. The model's predictions of pressure, gas velocity, solid concentration, and temperature are compared with our experimental values or those reported in the literature.     

Three‐Dimensional Numerical Simulation of Dense Pneumatic Conveying of Pulverized Coal in a Vertical Pipe at High Pressure

A two‐fluid model based on the kinetic theory of granular flow was used to study three‐dimensional steady state flow behavior of dense phase pneumatic conveying of pulverized coal in a vertical pipe, where the average solid concentration ranges from 11 % to 30 %, and the transport pressure ranges from 2.6 Mpa to 3.3 Mpa. Since the solid concentration is rather high, a k–?–k_p–?_p model which considers the turbulence interaction between the gas and particle phase, was incorporated into the two‐fluid model. The simulation results including profiles of gas and particle phase axial velocity, profiles of solid concentration, profiles of the turbulence intensity of the particle phase, as well as the value of the pressure gradient were reported. Then, the influences of solid concentration and transport pressure on the flow behaviors were discussed. The experiment was also carried out to validate the accuracy of the simulation results which showed that the predictions of pressure gradient were in good agreement with the experimental data. Simulation results indicate that the location of maximal solid concentration deviates from the pipe center and the deviation becomes more obvious with the solid concentration increasing, which is analogous to the phenomenon in the liquid/solid flow. Besides, pressure gradient declines as the transport pressure decreases, which is validated by experiment described in the paper. Moreover, the analysis indicates that it is necessary to consider the turbulence of particles for the simulation of dense phase pneumatic conveying at high pressure.     

Pneumatic Drying of Iron Ore Particles in a Vertical Tube

Abstract

The drying and hydrodynamic characteristics of iron ore particles in a vertical pneumatic conveying dryer (0.078 m ID × 6.0 m high) have been determined. The pressure drop decreases along the height at the acceleration region, while it remains constant irrespective of the height in the fully developed region. The degree of particle drying in the dilute pneumatic region increases with increasing superficial inlet gas velocity at constant inlet gas temperature and solid injection rate. However, it decreases with increasing solid injection rates at identical superficial inlet gas velocity and inlet gas temperature. The degree of particle drying increases from 48.6 to 82.5% as the inlet gas temperature increases from 100 to 400 °C.     

LASER-BASED FLOW MEASUREMENTS OF DILUTE VERTICAL PNEUMATIC TRANSPORT

Dilute vertical pneumatic transport in a vertical lifter was studied using the sophisticated measurement techniques of laser Doppler anemometry (LDA) and phase Doppler anemometry (PDA). The vertical lifter consisted of a lower fluidized silo, an upper receiving tank, and a connecting vertical transport pipe made of clear glass. The experimental study was performed in order to get detailed information of the complex gas-particle flow behavior in a dilute vertical conveying system. Particle diameter, axial particle, and tangential particle velocities, as well as root mean square velocities, were measured simultaneously for different flow conditions. In addition, overall solid mass fluxes were obtained using weighing cells. Smooth and spherical zirconium oxide (ZrO₂) solids were applied with two different particle size distributions. Measurements were performed using different flow rates of air. The air inlet condition was varied in order to study its effect on the flow behavior. The particle diameter measurements show that no axial or radial segregation by size occurs for this transport condition. The results show that the particle velocity is independent of the particle size as well. The axial velocity profiles at different heights are almost identical and flat, which indicates fully developed turbulent pipe flow. The turbulent velocity measurements show that turbulence is mainly caused by the velocity gradients, and not by particle-particle collisions in dilute flow. The solid mass flux measurements show the importance of optimum inlet condition and how this influences the mass flux.     

高固气比状态下的粉煤气力输送

在自建的气力输送系统上,进行了高固气比状态下粉煤气力输送研究.分别在内径为15、20、32 mm的管道中进行了输送实验,考察了操作参数对粉煤质量流量、固气比、表观气速等气力输送特征参数的影响.结果表明,输送固气比达到200～580 kg•kg^-1;随气体流量增加,粉煤的质量流量增大,而固气比降低;与输送压力的影响相比,管径对粉煤质量流量的影响程度更为显著;给出了基于本系统描述各参数之间相互关系的经验方程,表明较小的气量和较大的输送管径更有利于实现高固气比状态下的粉煤气力输送.     

表观气速对密相气力输送流型影响的模拟研究

针对目前密相气力输送数值模拟关于流型演变方面所存在的问题,提出了一种基于颗粒所在局部空间的固相浓度及颗粒群运动特征来描述颗粒间相互作用的数学模型。该模型能够对气力输送,甚至是颗粒发生大量堆积情况下的密相输送进行数值模拟,使得长期以来缺乏有效模型对密相输送流型进行数值模拟研究的问题得到一定解决。利用该模型,对水平管中煤粉高压密相气力输送的颗粒流动过程进行了数值模拟,获得了输送过程中管道内所发生的气固两相之间的分离、沉积现象,展现了沙丘流及栓塞流等流型的演变特征,模拟结果与实验观察到的现象吻合较好,从而进一步验证了新数学模型的有效性。此外,通过对不同表观气速下固相流态分布的定量分析,揭示了输送流型变化的一些内在规律。     

Nonlinear model of pneumatic conveying dryer for economic process control

Abstract

This paper presents a nonlinear dynamic model, suitable for economic process control of pneumatic conveying dryer for drying of food grains. The dynamic model is developed by reshaping the process equations derived for the batch drying, dilute phase, and a negative-pressure conveying system. The dynamic model parameters are identified by numerically solving a nonlinear least squares optimization problem, subject to a set of differential and algebraic equality constraints that describe the system dynamics and bounds in the parameters. A detailed parametric uncertainty and sensitivity analysis are performed providing valuable insight into the influence of critical model parameters on observables, the interplay among various parameter-state-measured disturbances, and quantifying uncertainties in the model. Further, different process economic performance and product quality indicator of uncertain dryer model are studied. The model validation study as performed with the underlying process shows a very good agreement in understanding necessary dynamic characteristics and interplay between the various parameter of interest.     

Vertical pneumatic conveying: a flow regime diagram and a review of choking versus non-choking systems

For vertical pneumatic conveying of granular solids, a flow chart describing two different types of gas—solid systems, viz. the choking system and the non-choking system, is presented. Published equations for the prediction of whether a particular gas—solid tube system is of the choking type or non-choking type are reviewed. For the choking type system, a quantitative flow regime diagram for predicting demarcation between packed bed conveying and slugging dense phase conveying, and demarcation between slugging dense phase conveying and lean phase conveying, is developed in terms of the key parameters of loading ratio, gas and solid velocities. The usefulnes of the flow regime diagram in design is discussed. The shortcomings of an earlier flow regime diagram proposed by Leung [14] are overcome in the present diagram.     

粉煤灰中浓度气力输送管道压降研究

对于粉体气力输送流动区域划出中等浓度区，使浓相输送与稀相输送的区分变得清楚、分析了粉体气力输送管道压降的主要影响因素，在量纲分析基础上，对中浓度气力输送提出一个比较简洁的管道压降关联式，与文献的实验数据进行拟合，结果表明该式可以很好地描述粉煤灰中浓度气力输送管道的总压降。对于给定的一个相图，该式的系数k、有一固定的数值；此值与物料质量流率（或气体质量流率）、料气比无关。     

宁东灵武矿区煤粉密相输送管道压降研究

采用Barth气力输送理论,通过实验在质量流率1 550—1 700 kg/h的输送范围内,研究了宁东灵武矿区煤粉密相输送的压降和表观气速的关系。结果表明:随着表观气速的增加,水平管道和竖直管道的压降都是先降低后升高,但竖直段的压降变化速度比水平段变化快,水平段的经济气速(4 m/s)小于竖直段的经济气速(7 m/s)。通过计算值与实验值比较,发现理论计算值与实验值偏差在30%以内,说明基于Barth附加压降法对宁东灵武矿区煤粉密相气力输送管阻力特性的计算具有较好的适应性。