PROCESSES RELATED TO DRYING: PART II USE OF THE SAME MODEL TO SOLVE TRANSFERS BOTH IN SATURATED AND UNSATURATED POROUS MEDIA

From the mathematical formulation presented in part I, a numerical code is developed to simulate heat and: mass transfers in porous media. The aim of this· tool is to understand and to improve each process related to drying. The association of a comprehensive set of equations with a efficient 2-D computer code allows us to predict the comportment of several porous media even if submitted to severe drying conditions. A few runs have been selected with special attention paid to the effect of internal gaseous pressure:

Convective drying of softwood at high temperature illustrate the typical two-dimensional transfers that occur in an anisotropic medium.

Microwave drying of light concrete pinpoints liquid expulsion of water which is driven by the pressure due to internal heating.

Finally, appropriate physical behaviours of a bed of glass spheres allows one to deal with simple processes for which full saturation occurs.     

PROCESSES RELATED TO DRYING: PART I, THEORETICAL MODEL

The aim of this paper is to summarize ten years of work in order to model the drying of solids. Nowadays there is a general agreement amongst the various researchers worldwide. If the porous medium is viewed at the so-called “macroscopic” scale (that is to say when it is viewed as a continuous and homogeneous equivalent medium) a set of three partial derivative equations is derived, three state variables being necessary to thermodynamically describe the medium (temperature, moisture content and total pressure in the gaseous phase for example).

After a short historical survey of the modeling of drying, we want to obtain this set of equations drawing the readers attention to three particular points : the importance of the air mass balance, the right way to write the energy equation (and the associated boundary conditions) and the taking into account of the adsorbed water.

A second part of this article [I] will be devoted to the numerical solution of this problem and will illustrate these points.     

PROCESSES RELATED TO DRYING: PART I,THEORETICAL MODEL

The aim of this paper is to summarize ten years of work in order to model the drying of solids. Nowadays there is a general agreement amongst the various researchers worldwide. If the porous medium is viewed at the so-called “macroscopic” scale (that is to say when it is viewed as a continuous and homogeneous equivalent medium) a set of three partial derivative equations is derived, three state variables being necessary to thermodynamically describe the medium (temperature, moisture content and total pressure in the gaseous phase for example).

After a short historical survey of the modeling of drying, we want to obtain this set of equations drawing the readers attention to three particular points : the importance of the air mass balance, the right way to write the energy equation (and the associated boundary conditions) and the taking into account of the adsorbed water.

A second part of this article [I] will be devoted to the numerical solution of this problem and will illustrate these points.     

非饱和含湿多孔介质微波冷冻干燥过程传热传质分析

基于升华冷凝模型,对非饱和含湿多孔介质微波冷冻干燥过程作了数值计算．结果表明,干燥过程中不饱和含冰区内的冰饱和度有较大变化．通过与不考虑升华冷凝区相比较,表明升华冷凝区的存在不可忽略．     

A GENERAL MODEL FOR MOVING BOUNDARY PROBLEMS -APPLICATION TO DRYING OF POROUS MEDIA

ABSTRACT

This work presents a general model to describe momentum, heat and mass transfer for moving boundary problems. The equations are obtained supposing an instantaneous superposition of a moving volume with velocity V_s (Lagrangean reference frame) over a stationary volume in the stream velocity v (Eulerian reference frame)The set of equations for multicomponent single-phase systems is applied to porous media (multi-phase systems) using the volume-averaging method. Depending on the assumptions about the behaviour of the system, it is possible to obtain the different models proposed in the literature, showing the generality of the model proposed in this work. Numerical results were compared to experimental data of Kaolin drying during the shrinking stage. These results showed a good agreement.     

A GENERAL MODEL FOR MOVING BOUNDARY PROBLEMS -APPLICATION TO DRYING OF POROUS MEDIA

This work presents a general model to describe momentum, heat and mass transfer for moving boundary problems. The equations are obtained supposing an instantaneous superposition of a moving volume with velocity V_s (Lagrangean reference frame) over a stationary volume in the stream velocity v (Eulerian reference frame)The set of equations for multicomponent single-phase systems is applied to porous media (multi-phase systems) using the volume-averaging method. Depending on the assumptions about the behaviour of the system, it is possible to obtain the different models proposed in the literature, showing the generality of the model proposed in this work. Numerical results were compared to experimental data of Kaolin drying during the shrinking stage. These results showed a good agreement.     

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.     

DRYING GRANULAR POROUS MEDIA: GRAVITATIONAL EFFECTS IN THE ISENTHALPIC REGIME AND THE ROLE OF DIFFUSION MODELS

In this paper we have examined the influence of gravity on the moisture transport process during the isenthalpic drying period, and we have considered the use of diffusion models both to predict saturation pro- files and to extract apparent diffusivities from experi- mental data. For granular or unconsolidated porous media, the one-dimensional moisture transport process can be characterized by two dimensionless groups that account for capillary forces, gravitational forces and viscous forces. Detailed numerical solutions of the saturation transport equation indicate under what circumstances the diffusion model can be used with confidence, and under what circumstances the diffusion model can be used to predict saturation profiles even though it is an incorrect representation of the moisture transport process. In addition to exploring the predictive capabilities of the diffusion model, we have     

TRANSPORE : A GENERIC HEAT AND MASS TRANSFER COMPUTATIONAL MODEL FOR UNDERSTANDING AND VISUALISING THE DRYING OF POROUS MEDIA

ABSTRACT

In this work a sophisticated numerical model is presented that describes the drying of porous media. This model, which is known as TransPore, has evolved over the years through the direct inputs of both authors. Nowadays, TransPore can be used to analyse the drying of media that are of completely arbitrary shape and size, under a variety of drying conditions. The engine of the computational model uses a number of state-of-the-art numerical methods that ensure the simulation results describe the particular drying process accurately, whilst guaranteeing the most efficient and effective usage of computer resources. For example, the numerical discretisation method is based on a completely conservative hybrid finite element control volume technique that uses a finite element mesh for its background gradient interpolation. Furthermore, flux limiting is used to reduce numerical dispersion in the drying kinetics and the generated non-linear system is resolved using the full Newton method for the outer iteration coupled together with a preconditioned conjugate gradient technique for the inner iteration. A graphical interface has been linked to the model to enable online visualisation of the drying process. The mathematical model allows both homogeneous and heterogeneous porous media to be simulated. The resultant software is an extremely powerful and effective tool for investigating existing dryer designs and for proposing new and innovative drying schedules that provide optimal drying quality in minimal drying time.     

TRANSPORE : A GENERIC HEAT AND MASS TRANSFER COMPUTATIONAL MODEL FOR UNDERSTANDING AND VISUALISING THE DRYING OF POROUS MEDIA

In this work a sophisticated numerical model is presented that describes the drying of porous media. This model, which is known as TransPore, has evolved over the years through the direct inputs of both authors. Nowadays, TransPore can be used to analyse the drying of media that are of completely arbitrary shape and size, under a variety of drying conditions. The engine of the computational model uses a number of state-of-the-art numerical methods that ensure the simulation results describe the particular drying process accurately, whilst guaranteeing the most efficient and effective usage of computer resources. For example, the numerical discretisation method is based on a completely conservative hybrid finite element control volume technique that uses a finite element mesh for its background gradient interpolation. Furthermore, flux limiting is used to reduce numerical dispersion in the drying kinetics and the generated non-linear system is resolved using the full Newton method for the outer iteration coupled together with a preconditioned conjugate gradient technique for the inner iteration. A graphical interface has been linked to the model to enable online visualisation of the drying process. The mathematical model allows both homogeneous and heterogeneous porous media to be simulated. The resultant software is an extremely powerful and effective tool for investigating existing dryer designs and for proposing new and innovative drying schedules that provide optimal drying quality in minimal drying time.     

DRYING GRANULAR POROUS MEDIA: GRAVITATIONAL EFFECTS IN THE ISENTHALPIC REGIME AND THE ROLE OF DIFFUSION MODELS

In this paper we have examined the influence of gravity on the moisture transport process during the isenthalpic drying period, and we have considered the use of diffusion models both to predict saturation pro- files and to extract apparent diffusivities from experi- mental data. For granular or unconsolidated porous media, the one-dimensional moisture transport process can be characterized by two dimensionless groups that account for capillary forces, gravitational forces and viscous forces. Detailed numerical solutions of the saturation transport equation indicate under what circumstances the diffusion model can be used with confidence, and under what circumstances the diffusion model can be used to predict saturation profiles even though it is an incorrect representation of the moisture transport process. In addition to exploring the predictive capabilities of the diffusion model, we have     

多孔介质干燥机理在褐煤热力脱水中的应用

我国揭煤资源丰富,但是由于其水分高,导致了揭煤燃烧发电效率低下,不宜远距离运输.通过热力干燥可降低揭煤的水分含量,有利于揭煤运输和贮存,提高锅炉燃烧效率.从揭煤结构出发,提出其热力干燥过程的模型可将之视为多孔介质.分析了多孔介质的干燥过程特点,阐述了目前国内外的多孔介质干燥机理,总结了相关的多孔介质干燥模型,为多孔介质褐煤热力脱水模型化提供理论支持.     

CURING STUDY AND OPTIMIZATION OF A POLYURETHANE-BASED MODEL PAINT COATED ON SHEET MOLDING COMPOUND PART II: DRYING DEFECTS RELATED TO CURING CONDITIONS

ABSTRACT

This study deals with the bubbling phenomenon which appears in some drying conditions on paint films applied as thin layers on SMC substrates. The bubbles and craters origin can be due either to reactions which may occur at the interface paint / SMC either to inadequate drying conditions which affect the polymerization reaction (gelation, viscosity) and the solvent vaporization.

Firstly, we reported data describing the solvent interaction with the SMC substrate - namely the contact angle, the interfacial tension, the absorption kinetics and the sorption isotherms - and the relationship between the bubbling defects and the numerous process variable (operating conditions, paint formulation and support properties).

Then, we gathered experimental data concerning the influence of different parameters (state and type of substrate, temperature, heating mode, film thickness. paint formulation, etc.) on the bubbling phenomenon and we tried to establish some quantitative interpretation. It proved that this defect was mainly due to the SMC heterogeneity expressed by the porosity of this composite material.     

CURING STUDY AND OPTIMIZATION OF A POLYURETHANE-BASED MODEL PAINT COATED ON SHEET MOLDING COMPOUND PART II: DRYING DEFECTS RELATED TO CURING CONDITIONS

This study deals with the bubbling phenomenon which appears in some drying conditions on paint films applied as thin layers on SMC substrates. The bubbles and craters origin can be due either to reactions which may occur at the interface paint / SMC either to inadequate drying conditions which affect the polymerization reaction (gelation, viscosity) and the solvent vaporization.

Firstly, we reported data describing the solvent interaction with the SMC substrate - namely the contact angle, the interfacial tension, the absorption kinetics and the sorption isotherms - and the relationship between the bubbling defects and the numerous process variable (operating conditions, paint formulation and support properties).

Then, we gathered experimental data concerning the influence of different parameters (state and type of substrate, temperature, heating mode, film thickness. paint formulation, etc.) on the bubbling phenomenon and we tried to establish some quantitative interpretation. It proved that this defect was mainly due to the SMC heterogeneity expressed by the porosity of this composite material.     

EFFECT OF THE VARIABILITY OF HEAT AND MASS TRANSFER COEFFICIENTS ON CONVECTIVE AND CONVECTIVE-RADIATIVE DRYING OF POROUS MEDIA

A numerical investigation was conducted to study two-dimensional heat and mass transfer during convective drying of a clay brick. The established numerical code has allowed us to determine the effect of heat and mass transfer coefficients variability on state variables and on the drying kinetic.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS PART II: SOYBEAN DRYING

This is the second of two papers concerning conjugate transport in convective drying of multiparticle systems. In the first paper (part 1), a solution methodology for conjugate transport problems was porposed and successfully tested for assemblages of spheres. This paper deals with the application of the proposed methodology to a soybean drying problem. The analysis in this study allowed certain phenomena, that are usually not present in single-kernel and deep-bed drying analyses, to be captured by the drying rate curves. The results presented here reinforce the need to take into account particle interactions when studying the drying mechanisms of multiparticle systems.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF MULTIPARTICLE SYSTEMS PART II: SOYBEAN DRYING

Abstract

This is the second of two papers concerning conjugate transport in convective drying of multiparticle systems. In the first paper (part 1), a solution methodology for conjugate transport problems was porposed and successfully tested for assemblages of spheres. This paper deals with the application of the proposed methodology to a soybean drying problem. The analysis in this study allowed certain phenomena, that are usually not present in single-kernel and deep-bed drying analyses, to be captured by the drying rate curves. The results presented here reinforce the need to take into account particle interactions when studying the drying mechanisms of multiparticle systems.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING, PART I: MODEL DEVELOPMENT AND PREDICTIONS

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.     

THE EFFECT OF HETEROGENEITY ON WOOD DRYING,PART I: MODEL DEVELOPMENT AND PREDICTIONS

ABSTRACT

A two dimensional model which can predict the effects of the anisotropy and heterogeneity on the transport phenomena which occur in wood during drying is developed. It is shown that the appropriate driving potential for moisture transport is the ratio of the moisture content to the driving potential. In its one dimensional form, die model results compare favorably with experimental measurements for drying in the radial direction. In its two dimensional form the model is used to predict drying in a direction midway between the radial and the tangential. In this case free water moves in a diagonal direction because the low density earlywood dries faster than the latewood during the early stages of drying. The result is significant gradients in moisture content, not only in the drying direction, but also in the direction parallel to the drying surface.     

MICROWAVE VACUUM DRYING OF POROUS MEDIA: VERIFICATION OF A SEMI-EMPIRICAL FORMULATION OF THE TOTAL ABSORBED POWER

Vacuum drying experiments were performed on a laboratory scale dryer with two porous materials: a packing of initially saturated glass beads and of unsaturated pharmaceutical granules. Several incident powers and two vacuum pressure levels were tested in order to demonstrate different drying mechanisms. The drying kinetics, temperature of the product and the absorbed power are presented and the coupling between the drying rate and the absorbed power is shown. A semi-empirical formulation of the total absorbed power is proposed taking into account the water content, the temperature and the dielectric properties of each phase. This formulation is based on a quasi-static assumption which allows the local electric field inside the material to be expressed with an analytical equation.