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.     

TWO-FLUID MODEL FOR PNEUMATIC DRYING OF PARTICULATE MATERIALS

The Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a one-dimensional steady-state condition and was applied to the drying process of wet PVC particles in a large-scale pneumatic dryer and to the drying process of wet sand in a laboratory-scale pneumatic dryer. 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 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 drying process is assumed to stop when the moisture content of a particle falls to a predefined value or when the particle riches the exit of the pneumatic dryer. Our developed model was solved numerically and two operating conditions, adiabatic and given pneumatic dryer wall temperature, were simulated. Comparison between the prediction of the numerical models of Rocha and DryPak, (Pakowski, 1996), which were presented by Silva and Correa (1998), with the prediction of our numerical simulation reviled better agreements with DryPak then with the models of Rocha. The results of the developed model were also compared with experimental results of Baeyens et al. (1995) and Rocha.     

TWO-FLUID MODEL FOR PNEUMATIC DRYING OF PARTICULATE MATERIALS

The Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a one-dimensional steady-state condition and was applied to the drying process of wet PVC particles in a large-scale pneumatic dryer and to the drying process of wet sand in a laboratory-scale pneumatic dryer. 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 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 drying process is assumed to stop when the moisture content of a particle falls to a predefined value or when the particle riches the exit of the pneumatic dryer. Our developed model was solved numerically and two operating conditions, adiabatic and given pneumatic dryer wall temperature, were simulated. Comparison between the prediction of the numerical models of Rocha and DryPak, (Pakowski, 1996), which were presented by Silva and Correa (1998), with the prediction of our numerical simulation reviled better agreements with DryPak then with the models of Rocha. The results of the developed model were also compared with experimental results of Baeyens et al. (1995) and Rocha.     

Three-dimensional modelling of pneumatic drying process

Steady-state three-dimensional calculations of heat and mass transfer in vertical pneumatic dryer were performed. The theoretical model of the drying process is based on two-phase Eulerian-Lagrangian approach for gas-particles flow and incorporates advanced drying kinetics for wet particles. The model was utilized for simulation of the drying process of wet PVC and silica particles in a large-scale vertical pneumatic dryer. The influence of wall thermal boundary conditions was investigated by assuming either known value of the wall temperature or adiabatic flow in the dryer. Analyzing the predicted particle drying kinetics, an uneven product quality was predicted due to non-uniform drying conditions in the central and peripheral zones of the pneumatic dryer. Moreover, for the case of non-insulated chamber walls such quality unevenness was estimated to be substantially greater than for the case with thermally insulated drying chamber. The examination of the predicted temperature profiles within the silica and PVC wet particles showed that the latter is subjected to higher temperature gradients potentially resulting in the greater rate of thermally-degraded final product.     

Modelling of batch fluidised bed drying of pharmaceutical granules

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control.     

Numerical Study of Two-Stage Horizontal Spray Dryers Using Computational Fluid Dynamics

This article presents the findings of a numerical simulation model of the spray-drying process in a two-stage horizontal chamber design with the aid of a computational fluid dynamic (CFD) model. The model describes heat, mass, and momentum transfer between two phases; namely, a continuous gas phase and a discrete phase of droplets (or particles), using the finite volume method. In this study, a new two-dimensional horizontal spray dryer (HSD) geometry is considered as a pilot study into the spray-drying process in this novel chamber configuration. The tested model is able to predict some important features of the spray-drying process, such as air flow patterns indicating recirculation zones and particle trajectory plots. Some performance parameters for spray drying, such as the rate of evaporation, average volumetric heat and mass transfer rates, etc., are calculated and discussed. This two-stage drying process especially applicable for the horizontal spray dryer (HSD) model is investigated and modeled. The bottom wall of the HSD is assumed to be a shallow fluid bed used for second stage drying. In this article, the fluid bed drying conditions are changed and compared. The drying within the fluid bed itself is not modeled in this study, however. It is shown that the particle residence time is higher when the fluid bed is included. The drying performance of this two-stage horizontal spray dryer is expected to be better than that of a single-stage dryer.     

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.     

Numerical Study of Two-Stage Horizontal Spray Dryers Using Computational Fluid Dynamics

This article presents the findings of a numerical simulation model of the spray-drying process in a two-stage horizontal chamber design with the aid of a computational fluid dynamic (CFD) model. The model describes heat, mass, and momentum transfer between two phases; namely, a continuous gas phase and a discrete phase of droplets (or particles), using the finite volume method. In this study, a new two-dimensional horizontal spray dryer (HSD) geometry is considered as a pilot study into the spray-drying process in this novel chamber configuration. The tested model is able to predict some important features of the spray-drying process, such as air flow patterns indicating recirculation zones and particle trajectory plots. Some performance parameters for spray drying, such as the rate of evaporation, average volumetric heat and mass transfer rates, etc., are calculated and discussed. This two-stage drying process especially applicable for the horizontal spray dryer (HSD) model is investigated and modeled. The bottom wall of the HSD is assumed to be a shallow fluid bed used for second stage drying. In this article, the fluid bed drying conditions are changed and compared. The drying within the fluid bed itself is not modeled in this study, however. It is shown that the particle residence time is higher when the fluid bed is included. The drying performance of this two-stage horizontal spray dryer is expected to be better than that of a single-stage dryer.     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

ABSTRACT

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

Mathematical Modeling of Drying of Liquid/Solid Slurries in Steady State One-Dimensional Flow

A mathematical model of simultaneous mass, heat and momentum transfer for two-phase flow of a gas and a solid/liquid slurry was developed. The model was applied to calculation of the drying process of coal-water slurry droplets in a gas medium in a steady one-dimensional flow. The model was based on the well-known two-stage drying process for slurry droplets. After the first period of drying, in which the evaporation rate is controlled by the gas phase resistance, the evaporating liquid diffuses through the porous shell (crust) and then, by convection, into the gas medium. Inside the dry external crust of the drop, a wet central core forms, which shrinks as evaporation proceeds. The temperature of the slurry droplet rises. The process ends when the temperature of the dry outer crust reaches the coal ignition temperature in the case of combustion or when the moisture of the particle reaches the final required moisture. The developed model was based on one-dimensional balance equations of mass, energy and momentum for the liquid/solid and gas phases. The system of governing equations was represented by first-order differential equations and solved simultaneously. The numerical solution of the governing equations was obtained using Gear's method. The model permitted calculation     

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.     

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.     

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.     

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.     

The Drying of Sludge in a Cyclone Dryer Using Computational Fluid Dynamics

A control volume-based technique implemented in FLUENT (ANSYS Inc., Canonsburg, PA) computational fluid dynamics (CFD) package was applied along with the kinetic theory of granular flow (KTGF) to simulate the flow pattern and heat and mass transfer processes for sludge material in a large-scale cyclone dryer. The drying characteristics of sludge at the dryer inlet were obtained from a previous study on the drying of sludge in a large-scale pneumatic dryer. User-defined subroutines were added to extend FLUENT's capability to account for mixture properties and to simulate the constant and falling rate drying periods. The convective heat and mass transfer coefficients were modeled using published correlations for Nusselt and Sherwood numbers. Sensitivity analysis was conducted to determine the effect of gas-phase velocity and temperature on the final product outcome. Numerical predictions for the multiphase flow hydrodynamics showed a highly diluted region in the dryer core and a higher concentration of particles close to the wall region, an indication of nonuniform distribution of particles at a cross-sectional area. The numerical predictions for the hydrodynamic profiles qualitatively depicted the flow behavior natural to these designs. The work demonstrated the successful application of CFD in the design stage of a combined pneumatic-cyclone dryer model.     

Pneumatic Drying of Iron Ore Particles in a Vertical Tube

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.     

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.     

气流干燥器分段设计的通用模型及计算方法

气流干燥器在工农业生产中有广泛的应用。目前,有关气流干燥器设计的方法有多种。本文在夏诚意法的基础上,利用气-固两相流动及传热的理论,建立了直管型气流干燥管设计的通用数学模型。模型针对干燥过程中物料恒速干燥与气力输送过程中颗粒加速运动之间的不同关系,将气流干燥过程分为四段:颗粒第一加速段(预热段)、颗粒第二加速段、颗粒第三运动段(分两种情况讨论)以及颗粒匀速段。模型综合考虑气固相对雷诺数Rer在过渡区、湍流区的情况,对一般气流干燥过程具有一定的普适性。利用本文数学模型编程设计,计算结果与实际吻合较好。     

A computational investigation of non-isothermal gas-solid flow in a U-bend

The non-isothermal gas-solid flow through a U-bend of a pneumatic conveying dryer system is calculated using the commercial CFD program Fluent 6.1. Steady-state, incompressible and non-isothermal gas-solid flows are employed to simulate the cases. Variables studied include: particle diameter, particle density, solid loading ratio, feed gas temperature, heat flux through the wall, gas velocity and bend radius ratio on heat transfer phenomena between gas and solid particles. Validation is done by comparing calculation results with the available experimental data provided by Baughn et al. [J.W. Baughn, H. Iacovides, D.C. Jackson, B.E. Launder, Local heat transfer measurements in turbulent flow around a 180° pipe bend, Journal of Heat Transfer 109 (1) (1987) 43-48] and Depew and Farbar [C.A. Depew, L. Farbar, Heat transfer to pneumatically conveyed glass particles of fixed size, Journal of Heat Transfer 85 (1963) 164-172].In general, data validations of both cases show good agreement. The gas temperature decreases and the solid temperature increases along the axial direction of the pipe due to transfer of heat from the gas phase to the solid phase. The gas temperature decreases significantly at the outer bend wall due to an accumulation of particles, which causes much more energy to be transferred from the gas to solid phases. At the inner bend wall, the gas temperature decreases slightly but the solid temperature increases significantly due to a low concentration of particles. A U-bend significantly increases the local and area average Nu numbers, but not the mass average Nu number. The slip velocity and particle distribution are the major factors influencing the value of the mass average Nu number.