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,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.     

气流干燥含湿氧化铝颗粒传热传质数值模拟

基于二相流理论,提出了一个描述含湿氧化铝颗粒气流干燥过程的一维数学模型。模型考虑了干燥管内气固二相间的传热传质和动量传递、含水质量分数和气固二相温度的变化。根据B ird所提出的努赛尔数经验公式,利用标准四阶龙格-库塔法对由非线性常微分方程组成的气流干燥耦合模型进行计算,得到了含湿氧化铝颗粒在不同气流干燥条件的干燥曲线。整个干燥过程中数值计算结果与试验实测数据吻合得很好,可以用来预测含湿氧化铝颗粒的干燥含水质量分数。     

Modelling and simulation of heat and mass transfer in a packed bed of solid particles having high diffusion resistance

The heat and mass transfer processes between gas phase and solid particles are studied in a fixed bed throughflow dryer. The particles have a moderate size but high heat and mass transfer resistances. To describe the drying process, simple cell model approach is used. The transport resistances of the particles are taken into account by imbedding a Luikov-type distributed parameter model into each cell.

The relationships of this model to the cell model with lumped variables for the particles, as well as to the continuous two phase model are analysed. Numerical investigations show that moisture diffusion taking place inside the particles can control the drying process even at moderate Biot numbers.     

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.     

Simulation Study for Pneumatic Conveying Drying of Sawdust for Pellet Production

Pneumatic conveying drying (PCD) is a combination of heat and mass transfer and pneumatic handling technology. This technology has been extensively used in chemical, pharmaceutical, and food industries, as well as many others. The PCD technique is beneficial for agricultural products, because it can achieve high-quality drying with reduced heat damage in a very short time. In this study, one-dimensional and three-dimensional mathematical models for the drying of sawdust particles in a pneumatic dryer were developed and verified with experiments. The three-dimensional modeling was done with a computational fluid dynamics (CFD) package (ANSYS FLUENT, Ver. 13.0, Ansys, Inc.), in which the gas phase is modeled as a continuum using the Euler approach, and the droplet/particle phase is modeled by a discrete phase model with a Lagrange approach. One-dimensional analysis was performed in MATLAB (Ver. 7.0). The experiments were carried out to validate the model in a pneumatic dryer with a horizontal length of 1 m, vertical height of 1.1 m, and diameter of 0.14 m. Sawdust, a raw material used for producing pellets, was prepared from well-seasoned pinewood timber. The initial moisture content of the sawdust was 22% (wb). The hot air inlet temperature in the dryer was fixed at 100°C. The variations in air pressure, air velocity, air temperature, and particle moisture content were investigated along the length of the dryer. The final moisture contents of sawdust and air temperature were reduced by 2% (wb) and 5°C, respectively. The simulated values were in good agreement with the experimental values. The developed model was then employed for the design of a pilot-scale pneumatic dryer (length 7 m and diameter 0.14 m). The final moisture content of the sawdust particles was reduced to 14% (wb) when the dryer length was increased from 1 to 7 m. In addition, the modeling was performed using buffers in the pilot-scale dryers. The use of a buffer noticeably increased the drying efficiency.     

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.     

离心流化床干燥过程中传热传质的数值模拟

通过对典型的多孔湿物料在离心流化床中干燥过程的理论分析和实验研究 ,首次将含湿多孔介质传热传质过程和物料与气流之间的外部传递过程相耦合 ,导出了离心流化床的理论模型和控制方程组 ,对于离心流化床中湿物料的干燥过程引进了数值模拟 ,结果表明增加气体表观流速、控制入口气体的温度和相对湿度以及加大床体转速均对干燥有不同的影响     

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.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

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.     

Development and Thermal Modeling of a New Construction Biomass Dryer

A new dryer construction has been developed for drying biomass basic materials for energy purposes (straw, sawdust, and other light granular materials). As a result of its simple design, the machine is perfectly suitable for reducing moisture by heat transfer. Compared to the machine types applied thus far, this new construction provides a better ratio of dryer floor space and drying distance and, as a result, a longer drying time. A differential equation system for convection drying was applied for the thermal modeling of the equipment; the mathematical model produced on the basis there of is suitable for examining the heat and mass transfer processes within the dryer. In the course of experimental measurements performed in an industrial size apparatus, the temperature and moisture content of the drying gas were recorded with the initial and final moisture content and surface temperature of the product. The measured values were compared to the results of calculations using the mathematical model.     

Mathematical Modeling of Kiln Drying of Softwood Timber: Model Development, Validation, and Practical Application

Mathematical modeling of wood drying is a powerful tool to better understand and quantify the effects of wood properties as well as the effects of drying and post-drying treatment conditions on drying and thus the wood drying models can be used to improve drying quality. The models that have been developed can be divided into three categories: models for drying a single board, models for drying a kiln-wide stack, and models for drying stress and deformation. The single-board drying model employs comprehensive heat and moisture mass transfer equations and can be used to investigate the influence of wood variability. The kiln-wide drying model, which is based on the transfer processes between wood and the drying medium, is able to examine the influence of drying schedules and wood properties. The stress model can predict stress development in drying and stress relief in final steam conditioning and post-kiln treatment. An integrated model can be used to optimize drying schedules and develop strategies for high-quality dried timber.     

Towards a Complete Population Balance Model for Fluidized-Bed Spray Agglomeration

This article concerns the simultaneous processes of agglomeration and drying. In order to predict temperatures and moisture content in gas and particle phase, heat and mass transfer mechanism and particle size enlargement has been considered in one model. The model takes heat and mass transfer phenomena between particle phase, suspension gas, and bypass gas into account. The disperse phase is modeled by a three-dimensional population balance (PBE), which can be reduced to a set of three one-dimensional PBEs. The latter are coupled with heat and mass transfer balances of the gas phase. Furthermore, some simulation and experimental results are presented.     

MODELING AND SIMULATION OF DEEP-BED GRAIN DRYERS

This paper concerns with heterogeneous modeling of deep-bed grain dryers based on two-phase model by taking into account coupled heat and mass transfer within grains. This model also consider axial mass and heat dispersion in the fluid phase. The dynamic two-phase equations are solved numerically by finite difference with alternating direction implicit method algorithm, and then applied to simulate humidity and temperature profile of drying gas across dryers together with moisture content and temperature of grains. The capabilities of these models were compared with experimental data obtained from available literatures, under drying conditions such as temperature and absolute humidity of drying gas and moisture content of grains. The simulation results show that the dynamic of corn drying within the bed is well predicted by the two-phase model.     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

A SIMPLE DYNAMIC MODEL FOR SOLID TRANSPORT IN ROTARY DRYERS

ABSTRACT

The solid particle movement in a rotary drum plays an important role in drying processes. The solid distribution in the drum affects the amount of contact surface between the solid and the gas. The retention time of solids influences the time particles can stay in contact with the gas in order to transfer heat and mass. Any heat and mass transfer model for a solid particle dryer must be able to predict solid flowrate and solid hold-up. There have been several reports in the literature regarding the modelling aspects of solid transport in dryers. If the model is developed for model-based control, it must be simple and yet represent dynamics of the system accurately. This paper addresses solid motion modelling and the effects of different variables involved in solid transport phenomena. Sugar drying process is the case study in this work. A steady state semi-empirical model was modified to predict solid hold-up and flowrate in rotary dryers. This model was incorporated into a heat and mass transfer model ;o predict solid moisture and temperature for inferential and model-based control purposes. Results of several experiments that have been used to investigate dynamics of the system in terms of solid motion and to validate the model are also presented. The approach advocated in this paper is directly applicable to the transport of other solids in rotary drum equipment and can thus be regarded as a generalized model.     

MODEL DEVELOPMENT AND EXPERIMENTAL STUDIES OF VERTICAL PNEUMATIC CONVEYING DRYERS

A theoretical model is presented for particle motion, heat and mass transfer and drying rates in vertical tubular pneumatic conveying dryers. The model is one-dimensional and takes time increments along the tube; a computer program is required for its implementation. It is similar to previous models but incorporates several refinements, notably in wall friction, agglomeration and heat transfer. The predictions are compared with experimental results; agreement is good and clearly superior to that obtained by earlier models. The method may be used either for initial design or for scale-up from pilot plant data.