Modeling of Diffusion in Capillary Porous Materials During the Drying Process

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.     

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.     

DRYING OF CLAY. II RHEOLOGICAL MODELISATION AND SIMULATION OF PHYSICAL PHENOMENA

ABSTRACT

The present study proposes the development of a complete mathematical modelling transfer phenomena involving at the same time heat, mass and momentum transfer during the drying process of clay. Clay is a generic example of colloid materials forming particulate gels. That can be considered as bi-constituent, homogeneous, isotropic, and highly deformable. The model was numerically solved by the finite difference method and validated by comparison of the numerical results with a previous set of experiments data. The simulation has allowed the determination of spatio-temporal evolution within the solid of different variables: temperature fields, moisture contents, displacement, deformation and stresses. The parametric sensibility has been analyzed in the case of thermophysical properties and the external heat transfer coefficient. Various values of external conditions have been analyzed.     

ELECTRICAL-RESISTANCE ELEMENT ARRAYS OPERATING AT HIGH VOLTAGES FOR HEATING AND DRYING IN INDUSTRIAL APPLICATIONS

Abstract

Drying using ambient subzero temperatures is of potential interest for thermosensitive products. Existing theoretical drying models have been used to predict the response of the system to different aeration systems. The model is based on enthalpy balances and includes water freezing and deposition of water on the surface of the commodity. It uses thermophysical properties of the commodity (i.e., maize in this study) and ambient weather data collected from northeastern China. Water within the grain is modelled as bound, free or frozen. The physical state of water under subzero temperatures has been investigated using a differential scanning calorimeter and nuclear magnetic resonance spectrometry. It has been established that the quantity of bound water was around 17%. Thermophysical properties characterizing the drying behavior of maize kernels cv. Huangmo 417, the most common variety grown in northeastern China, were determined under a wide range of moisture contents and drying temperatures. Those were: particle and bulk density, porosity, thermal conductivity, specific heat, thin layer drying, and sorption isotherms. It could be established that the thermal conductivity and specific heat were strongly dependent on temperature and relative humidity and that the sorption isotherms followed the 5-term Guggenheim-Anderson-de-Boer model. The industrial-scale in-store drying experiments in northeastern China have demonstrated the feasibility of in-store drying under subzero conditions. Advantages in terms of reduced susceptibility of maize to mould formation have been established, resulting in improved quality and financial returns to the processor.     

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.     

THE DEVELOPMENT AND VALIDATION OF A SYSTEM MODEL FOR A COUNTERCURRENT CASCADING ROTARY DRYER

ABSTRACT

An overall system model for a countercurrent rotary dryer has been developed with the ullimale aim of assessing controller pairings in these dryers. This model is based on heat and mass balances within dryer regions combined with two subsidiary models, one describing the equipment (which determines particle transport and heat transfer)and the other describing the behaviour of the material (the drying kinetics). Six partial differential equations have been set up to evaluate six state variables: solids moisture content, solids temperature, gas humidity, gas temperature, solids holdup and gas holdup as functions of time and rotary dryer length. A control-volume method has been used to reduce the six partial differential equations with respect to time and the length of the rotary dryer to six ordinary differential equations in time.

The drying model has been implemented in the SPEEDUP flowsheeting package (with FORTRAN subroutines) The model has been validated by fifteen experiments-in a pilot scale countercurrent-flow rotary dryer (0.2m in diameter and 2m in length)     

A Simulation Model for Heat Pump Dryer Plants for Fruits and Roots.

ABSTRACT

Dryer design requires food properties, drying rate and mass-heat transfer coefficients. These values change continuously during drying due to changes in food fractions, particularly the water fraction. The high energy demand and costs allied to inefficient devices, creates a great need for new processing equipment. Along these guide-lines, several heat pump drying research projects were established at the Norwegian University of Science and Technology. The heat pump dryer provides high quality final product as its drying conditions can be controlled. Its efficiency and non-polluting operation come from closed air-refrigerant circuits and from its ability to fully recover the latent heat of moist air as it exits the drying chamber. Most of the above features are quite the opposite of the conventional dryer characteristics. Several experiments were made on heat pump drying of fruits and roots at temperatures from -22.5 to 40°C to obtain data and correlations on thermophysical properties, specific enthalpy and rehydration. Also, tests were done on drying rate, moisture content, drying constant, effective mass diffusivity and heat and mass transfer equations. The next important phase is the development of a simulation model to predict the performance and characteristics of the heat pump dryer plant. The objectives of the present work are to develop and lo test a heat pump dryer simulation model. The simulation provides results on the characteristics of both plant and components which are integrated by heat and mass transfer equations. The program has menus with click-on icons, input and output pop-up dialogue boxes. The usual commands such as, file-open, file-save, edit-delete are available in this program simply called Hpdryer. The model contains moist air psychrometric. natural and conventional refrigerant property libraries. Ammonia is a time-tested, self-alarming and natural refrigerant. It has been used extensively in the past, and it has better thermodynamic and transport properties than halocarbons. Safety is easily attained by design and its restrictive standards have helped increase its use in several countries. There are 36 ammonia installations in Norway and in the United Kingdom, including a drying plant. Ammonia has zero Odp, zero Gwp and the recent R&D has led to viable small-sale heat pump plants. Ammonia and dichlarodifluoromethane refrigerants were used in the test cases simulated by Hpdryer madel.     

A comprehensive review on modeling of pneumatic and flash drying

Pneumatic conveying drying (PCD) is a widely used process in the industries and is a combination of heat and mass transfer and pneumatic handling technology. Drying processes consume large amounts of energy and, therefore, reduction in operating cost will be extremely beneficial for the industry. Many studies have been conducted to model and optimize the pneumatic drying. This review article focuses on the different strategies used in the literature to model pneumatic drying processes. An analysis is provided for the different mathematical modeling and its components such as balance and complementary equations and modeling assumptions. Two-fluid theory, Eulerian granular, and the discrete element method are reviewed as well as gas–solid flow modeling methods. In addition, the numerical methods and the main studied parameters in the field of pneumatic drying are investigated. To this end, heat and mass transfer coefficients, gas and dispersed phase properties are reviewed.     

A COMPREHENSIVE MATHEMATICAL AND NUMERICAL MODELING OF DEEP-BED GRAIN DRYING

ABSTRACT

This paper deals with comprehensive mathematical and numerical modeling of deep-bed grain drying. In order to build the process model, it is necessary to analyze the transport in both grain and gas phases. Experimental works were carried out for a layer of grain bed in order to validate the models. The models consider momentum, energy, and mass conservation within grain and drying air phase. The two-dimensional dynamic equations of energy and mass conservation are solved numerically by finite-difference method (FDM) and utilizing alternating direction implicit algorithm within grain and drying air phase, while momentum conservation are solved by finite difference method by utilizing Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. Furthermore, the models will be applied in consideration with developing and designing dryer in order to simulate humidity and temperature profiles of the drying gas together with moisture content and temperature of grain across dryer in term of the dryer performance. The simulations show that the models can be used to predict the dynamic drying characteristic profiles as well as the superficial velocity of drying air phase across dryer.     

多孔介质对流干燥机理及其模型

在对现有的多孔介质对流干燥传热、传质模型归类分析的基础上,从介质内部热湿迁移机制出发,建立了能较完善、较准确地描述多孔介质在恒速段及降速段热质传递规律的“三耦合-六场量”混合理论模型.同时针对干燥问题数值模拟中的移动边界问题,提出了一种迭代修正的思想,并发展了相应的数值计算方法.对砖的干燥模拟计算结果表明,本文的模型较其他模型具有更好的精确性.     

ANALYSIS OF TRANSPORT PHENOMENA DURING THE CONVECTIVE DRYING IN SUPERHEATED STEAM

Abstract

This work focused on high-temperature convective drying (superheated steam drying). The process has been investigated both experimentally and numerically. The experimental analysis was carried out in an aerodynamic return-flow wind-tunnel, with very small cylinders of cellular concrete. For the local analysis, the samples were fitted with thermocouples and pressure sensors. The mean moisture content of the cylinders was measured by simple weighing while the temperature and pressure readings were being taken. Global and. local analysis of heat and mass transfer in small cylinders in superheated steam were carried out. The systematical study for several sizes and aerothermal conditions show a similar behavior for moisture content, pressure and temperature values. A numerical model for high temperature drying, using the finite elements method, in a 2-D configuration, was implemented and validated.     

A Thermo-Hydro-Mechanics Bidirectional Coupling Mathematical Model for Drying of Biological Porous Medium

Based on Fickian diffusion theory, Fourier's law of heat conduction and thermoelasticity mechanics, a thermo-hydro-mechanics bidirectional coupling mathematical model has been developed to simulate the hot air convective drying of biological porous media. The transient model, composed of a system of partial differential equations, was solved by finite difference methods. The numerical results were compared with available experimental data obtained during the drying of potatoes. The numerical results obtained using the mathematical model were in good agreement with the experimental data. Numerical simulations of the drying curve variations and the spatio-temporal distributions of moisture, temperature, and drying stresses and strains were evaluated.     

STUDY OF HEAT AND MASS TRANSFER DURING IR DRYING OF PAPER

ABSTRACT

A mathematical model has been developed to study the drying of paper using a gas-fired IR dryer. The model accounts for various phenomena : water and vapour mass transfer, conduction, convection and radiation heat transfer. The phenomenological equations are solved with a finite difference scheme, including a modified upwind differencing scheme to account for water migration within the paper sheet. The simulation results illustrate the basic underlying phenomena involved in IR paper drying and can be instrumental to the engineer to make the detailed analyses of such a drying process. A sensitivity analysis has shown that the drying rate is most sensitive to parameters governing the IR beat transfer process whereas the paper sheet temperature is most sensitive to parameters governing the mass transfer process with the surroundings.     

INVESTIGATION ON THE INCIPIENT FLUIDIZATION AND HEAT TRANSFER IN A CENTRIFUGAL FLUIDIZED BED DRYER

Abstract

Based on the continuum theory, a physical model of gas-solid two phase flow in a centrifugal fluidized bed has been proposed. A set of governing equations to describe the fluidization state are obtained and solved numerically after some simplifying. The quantitative experimental study on the characteristics of the incipient fluidization in the centrifugal fluidized bed is performed to examine the proposed model. Gas-solid two phase heat transfer in CFB during a drying process is also conducted. The influences of bed thickness, particle diameter, physical properties of particle, rotating speed of the bed and the gas superficial velocity on heat transfer characteristics are examined. A correlation that can be used to calculate the heat transfer coefficients in the drying process in CFB is obtained.     

DRYING OF CLAY. II RHEOLOGICAL MODELISATION AND SIMULATION OF PHYSICAL PHENOMENA

The present study proposes the development of a complete mathematical modelling transfer phenomena involving at the same time heat, mass and momentum transfer during the drying process of clay. Clay is a generic example of colloid materials forming particulate gels. That can be considered as bi-constituent, homogeneous, isotropic, and highly deformable. The model was numerically solved by the finite difference method and validated by comparison of the numerical results with a previous set of experiments data. The simulation has allowed the determination of spatio-temporal evolution within the solid of different variables: temperature fields, moisture contents, displacement, deformation and stresses. The parametric sensibility has been analyzed in the case of thermophysical properties and the external heat transfer coefficient. Various values of external conditions have been analyzed.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

ABSTRACT

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

NUMERICAL SIMULATION OF DRYING IN A CYCLONE

ABSTRACT

This work presents a complete improved mathematical model of drying in cyclone. The slip condition of the particles on the wall, the heat transfer wall-panicle and the shrinkage of the panicles during the drying process were considered. The mathematical model considers a two-dimensional turbulent gas-particle flow where the panicle phase is treated as a continuum. The momentum equations of both particle and gas phases were written in cylindrical coordinates. The discretized equations were solved by the SIMPLE algorithm. Considering the slip condition to the panicle phase and the shrinkage of the material during the drying process it was revealed a better fitness between numerical and experimental results than the previous model.     

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     

Drying at Sub-zero Temperatures: Case Study on In-store Drying of Grains

Drying using ambient subzero temperatures is of potential interest for thermosensitive products. Existing theoretical drying models have been used to predict the response of the system to different aeration systems. The model is based on enthalpy balances and includes water freezing and deposition of water on the surface of the commodity. It uses thermophysical properties of the commodity (i.e., maize in this study) and ambient weather data collected from northeastern China. Water within the grain is modelled as bound, free or frozen. The physical state of water under subzero temperatures has been investigated using a differential scanning calorimeter and nuclear magnetic resonance spectrometry. It has been established that the quantity of bound water was around 17%. Thermophysical properties characterizing the drying behavior of maize kernels cv. Huangmo 417, the most common variety grown in northeastern China, were determined under a wide range of moisture contents and drying temperatures. Those were: particle and bulk density, porosity, thermal conductivity, specific heat, thin layer drying, and sorption isotherms. It could be established that the thermal conductivity and specific heat were strongly dependent on temperature and relative humidity and that the sorption isotherms followed the 5-term Guggenheim-Anderson-de-Boer model. The industrial-scale in-store drying experiments in northeastern China have demonstrated the feasibility of in-store drying under subzero conditions. Advantages in terms of reduced susceptibility of maize to mould formation have been established, resulting in improved quality and financial returns to the processor.     

HYGROTHERMAL AND MECHANICAL BEHAVIOUR OF ABRASIVE AGGLOMERATE. APPLICATION TO RECTIFICATION WHEELS DRYING.

ABSTRACT

The distribution of the water content and temperature have been modelised and numerically investigated within the body of unbaked rectification wheels during convective drying. The obtained profiles have been applied to mechanical stress distribution simulations, fitting process parameters in order to avoid crack formation. The thermophysical, cinetical and mechanical properties of the abrasive agglomerate were determined experimentally.

The transport phenomena within the medium have been described by a classical water vapour diffusion and thermal conduction model with convective boundary conditions. The water vapour diffusivity and thermal conductivity were obtained respectively by water content profile analysis during 1-D isothermal diffusional water vapor transfer and by the flash method. The heat and mass transfer coefficients at the boundaries were calculated on the basis of [itterature correlations. The set of coupled non-linear differential equations was discretized in the space domain by the finite-volume method and integrated in the time domain by Runge-Kutta-Fehlberg procedure widi ACSL package.

A finite-element variational formulation with elasto-plastic behaviour laws has been used to assess the mechanical strain and stress distribution resulting from the pre-calculated water content and temperature profiles. The simulations were carried out with the industrial Abaqus package. The shrinkage coefficient was measured by means of a laser beam displacement detector on samples dried by micro-wave radiation. The elasticity modulus, tangential plastic modulus, compression and tension failure stress were determined by compression and bending tests on hygro thermally conditioned samples.