CONVECTWE DRYING MODEL OF SOUTHERN PINE

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

Mathematical modelling of an industrial furnace for high‐temperature heat treatment of wood

There are various high‐temperature treatment methods for wood. In the “Bois Perdure” process, the thermal treatment of wood is carried out in a furnace by contacting it with hot combustion gases over 200°C without the addition of any chemicals in order to improve its dimensional stability and durability. The treatment eliminates free and bound water in the wood and modifies its molecular structure. In this study, a mathematical model describing the industrial furnace has been developed. The overall model consists of a 3‐D unsteady‐state sub‐model which solves for the flow, heat, and mass transfer in the gas coupled with a 1‐D unsteady‐state sub‐model which calculates the heat and mass transfer in the wood. The 3‐D gas sub‐model was developed using the commercial CFD code CFX. The 1‐D wood sub‐model is based on the solution of simultaneous heat and mass transfer equations (Luikov equations) using the implicit finite difference formulation. The model predicts the temperature and moisture distributions in the wood as well as the flow, heat, and moisture profiles in the gas. The model results are compared with the data obtained from the industrial furnace, and a good agreement was found between them.     

Vacuum Drying of Oak Wood

ABSTRACT

Vacuum drying, j,e drying under absolute gas pressure of about 10? Pa. is an efficient means of reducing the process period and of producing good quality wood. We will examine here continuous vacuum drying where the plank surfaces are kept at a constant temperature, which remains above the boiling point, and moisture flowing to the surface is extracted from the kiln.

We have carried out an experimental study of oak drying under such conditions. The drying rate and moisture content profile of the sample (40 mm thick) are recorded during the whole drying period.

A model of continuous drying is established from general conservation equations with the main approximation that the air is rapidly extracted. The two constitutive equations of the model which describe temperature and water content fields are of a diffusive type and coupled through coefficients. The adequate boundary equation is not a convective one, but expresses a hygroscopic equilibrium between the vapour in the chamber and the wood surface. The mass diffusive coefficient can be adjusted to the drying rates through capillary pressure and bound water diffusion functions. The wood heterogeneity (seasonal growth) is the main factor of discrepancy in these functions. The simulated drying rates correspond with the experimental ones.     

Vacuum Drying of Oak Wood

Vacuum drying, j,e drying under absolute gas pressure of about 10⊃ Pa. is an efficient means of reducing the process period and of producing good quality wood. We will examine here continuous vacuum drying where the plank surfaces are kept at a constant temperature, which remains above the boiling point, and moisture flowing to the surface is extracted from the kiln.

We have carried out an experimental study of oak drying under such conditions. The drying rate and moisture content profile of the sample (40 mm thick) are recorded during the whole drying period.

A model of continuous drying is established from general conservation equations with the main approximation that the air is rapidly extracted. The two constitutive equations of the model which describe temperature and water content fields are of a diffusive type and coupled through coefficients. The adequate boundary equation is not a convective one, but expresses a hygroscopic equilibrium between the vapour in the chamber and the wood surface. The mass diffusive coefficient can be adjusted to the drying rates through capillary pressure and bound water diffusion functions. The wood heterogeneity (seasonal growth) is the main factor of discrepancy in these functions. The simulated drying rates correspond with the experimental ones.     

流化床氛围下多孔物料干燥传热传质的数值模拟

用有限差分法数值求解一个热、质传递耦合模型,理论研究多孔物料流化床干燥过程。方程离散采用全隐格式的控制容积方法,三对角矩阵法（TDMA）用来求解线性方程组。选用球形的苹果丁作为多孔物料。在典型操作条件下,通过分析温度、饱和度和压力的分布侧形,讨论了物料内部的热、质传递机理。在对比条件下,考察了气体入口温度、气速和床面积因子对干燥过程的影响。结果表明：干燥过程受气、固相间的耦合传热传质的影响十分明显,干燥时间随气体入口温度和气速的提高而减少;随床面积因子的增大而增加。     

Modeling Superheated Steam Vacuum Drying of Wood

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^-1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

MEASURED GAS VELOCITY AND MOISTURE CONTENT DISTRIBUTION IN A CONVECTIVE VACUUM KILN

Transferring the necessary heat of evaporation to the stack is the bottleneck in convective vacuum drying of wood. Higher gas velocities are applied to compensate for the lower gas density and to obtain similar heat and mass transfer characteristics as under normal pressure. Like in conventional kiln drying the region with the most unfavorable drying conditions determines drying time and product quality. To use the full potential of the meanwhile established superheated steam vacuum drying technology, it is therefore necessary to work on an improved uniformity of process conditions in the kiln.

To evaluate the fluid dynamics and its influence on the final moisture content, experimenls in a laboratory convective vacuum kiln were carried out. For different total pressures the profiles of dynamic pressure in the stack entry section were measured in a dry atmosphere. At normal pressure the profiles were determined between the board layers throughout the whole stack. For the same slack configuration vacuum drying tests were used to assess the impact of the velocity distribution in the slack on the final moisture content distribution-Regions of low gas velocities coincided well with regions of high final moisture content.     

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE CONVECTIVE DRYING OF AUSTRALIAN PINUS RADIATA TIMBER

ABSTRACT

A series of experiments on the convective drying of Pinus radiata has been undertaken at the CSIRO Division of Forest Products in Australia. This paper uses the experimental results to compare predictions from both a comprehensive mathematical model, which includes wood temperature, moisture content and pressure distributions, and a simplified model (two versions) which assumes constant total pressure. From the- simulations, it is seen that both models adequately predict the overall kinetics of the wood drying process. For a complete understanding of the heat and mass transfer phenomena that occur in wood during drying the comprehensive model is necessary. However, it is computationally long and expensive, and as such, does not suit the practical drying needs of the timber industry in Australia. Consequently, the simplified model, which has acceptable computation time and sufficient accuracy for engineering purposes, enables die wood drying process to be optimised from both performance and economic perspectives.     

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE CONVECTIVE DRYING OF AUSTRALIAN PINUS RADIATA TIMBER

A series of experiments on the convective drying of Pinus radiata has been undertaken at the CSIRO Division of Forest Products in Australia. This paper uses the experimental results to compare predictions from both a comprehensive mathematical model, which includes wood temperature, moisture content and pressure distributions, and a simplified model (two versions) which assumes constant total pressure. From the- simulations, it is seen that both models adequately predict the overall kinetics of the wood drying process. For a complete understanding of the heat and mass transfer phenomena that occur in wood during drying the comprehensive model is necessary. However, it is computationally long and expensive, and as such, does not suit the practical drying needs of the timber industry in Australia. Consequently, the simplified model, which has acceptable computation time and sufficient accuracy for engineering purposes, enables die wood drying process to be optimised from both performance and economic perspectives.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

The Role of Nonuniformity in Convective Heat and Mass Transfer through Porous Media,Part 1

Through-air drying is commonly used in the drying of high-quality tissue and towel products. A representative elementary volume method was used to model the fluid flow and heat and mass transfer during through drying in heterogeneous porous biobased materials such as tissue and towel products. Results of flow both upstream and downstream of a modeled porous sheet allowed visualization of the effects of mixing at the top and bottom of the porous medium. The effect of initial nonuniformity on fluid flow and convective heat and mass transfer in heterogeneous porous media was studied. The effect of material nonhomogeneity and associated transport properties on moisture content of the porous material as a function of drying time was studied. Modeling results indicate that for the first time it is possible to simulate the effect of nonuniformity on fluid flow and convective heat and mass transfer in porous media during through-air drying of paper. Moisture and structural nonuniformity contributing to nonuniformity in air flow might contribute significantly to drying nonuniformity. Depending on the moisture regimes and degree of saturation of the convective medium, heat and mass transfer coefficients may have varying effects on the overall drying.     

Mass Transfer from Wooden Surfaces and Internal Moisture Non-Equilibrium

ABSTRACT

The transfer of moisture from a wooden surface and the corresponding mass transfer coefficient in relation to the heat transfer coefficient are considered. Experimental data are reviewed that show that the mass transfer coefficient often is one order of magnitude smaller than what could be expected from the analogy between heat and mass transfer. The nature of this deviation and its influence on wood drying models is discussed. It has been suggested by Wadsö.that moisture flow inside the wood exhibits non–Fickian behaviour and that this may be due to a slow desorptiodabsorption by the wood fibre. A model is thus developed where the normal assumption of internal local equilibrium between the vapour and bound phases is replaced by a mass transfer resistance. The model is applied to one–dimensional moisture flow in a body of finite thickness and solved analytically. Numerical values calculated with the model are analysed in order to establish whether “apparent” non–Fickian behaviour of the kind observed could be explained by such a model. It is also analysed whether the model could explain an apparent decreased mass transfer coefficient at the surface.     

A Study of the Power Density Distribution generated during the Combined Microwave and Convective Drying of Softwood

ABSTRACT

Investigations into new and innovative drying strategies can lead to the development of more efficient and effective drying processes. The commercialisation of these processes would prove invaluable to the drying industry as a whole and the associated technology would generate worldwide interest. Combined microwave and convective drying is one such process which offers great potential, with benefits that include : reduced drying times and increased drying rates; volumetric heating; higher fluxes of liquid to the drying surface; high temperature and internal pressure buildup within the material which enhances the overall moisture migration rate; and preferential heating of wetter areas. Numerical simulation can elucidate on the intricate details of the heat and mass transfer henomena that occur during the drying process, thus eliminating the need for performing numerous time consuming and expensive experiments. The simulations can predict the evolutionary behaviour of the moisture, temperature and pressure distributions, and can provide a detailed analysis of how microwaves interact with materials during drying and heating operations at a fundamental level. The research presented in this paper uses a comprehensive mathematical model to study the behaviour of the iniernal microwave power density distribution that is generated during the microwave enhanced convective drying of softwood. The configuration understudy concerns a plane wave microwave source irradiating the wood in the transverse direction.     

MEASURED GAS VELOCITY AND MOISTURE CONTENT DISTRIBUTION IN A CONVECTIVE VACUUM KILN

ABSTRACT

Transferring the necessary heat of evaporation to the stack is the bottleneck in convective vacuum drying of wood. Higher gas velocities are applied to compensate for the lower gas density and to obtain similar heat and mass transfer characteristics as under normal pressure. Like in conventional kiln drying the region with the most unfavorable drying conditions determines drying time and product quality. To use the full potential of the meanwhile established superheated steam vacuum drying technology, it is therefore necessary to work on an improved uniformity of process conditions in the kiln.

To evaluate the fluid dynamics and its influence on the final moisture content, experimenls in a laboratory convective vacuum kiln were carried out. For different total pressures the profiles of dynamic pressure in the stack entry section were measured in a dry atmosphere. At normal pressure the profiles were determined between the board layers throughout the whole stack. For the same slack configuration vacuum drying tests were used to assess the impact of the velocity distribution in the slack on the final moisture content distribution-Regions of low gas velocities coincided well with regions of high final moisture content.     

A MATHEMATICAL MODEL OF HIGH INTENSITY PAPER DRYING

High intensity drying occurs when one web surface is heated to the thermodynamic saturation temperature corresponding to the local hydraulic pressure. Rapid vapor generation causes the process to be driven by a total pressure gradient, so vapor leaves the web by a bulk flow mechanism rather than a slower diffusion mechanism. Vapor pressure build-up promotes rapid web heating and offers the opportunity for liquid removal by displacement. Lower energy usage can result if only a part of the moisture is evaporated.     

A MATHEMATICAL MODEL OF HIGH INTENSITY PAPER DRYING

High intensity drying occurs when one web surface is heated to the thermodynamic saturation temperature corresponding to the local hydraulic pressure. Rapid vapor generation causes the process to be driven by a total pressure gradient, so vapor leaves the web by a bulk flow mechanism rather than a slower diffusion mechanism. Vapor pressure build-up promotes rapid web heating and offers the opportunity for liquid removal by displacement. Lower energy usage can result if only a part of the moisture is evaporated.     

RADIATIVE DRYING MODEL OF POROUS MATERIALS

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

Investigation on Moisture Transfer Mechanism in Porous Media During Rapid Drying Process

In this work, moisture transfer mechanism in wet porous media during rapid drying process is investigated experimentally and analytically. By use of scanning electron microscopic device, the rapid drying processes for potato, carrot, and radish species were observed and recorded. The microscopic drying experiments show that during high intense and rapid drying process, the mechanism of moisture migration in materials is mainly considered as a displacement flow driven by pressure gradient along a capillary passage. A simplified displacement flow model during rapid drying process is proposed and the time needed for moisture transfer in porous media is calculated. To examine this drying mechanism, one-dimensional displacement flow test device is built up and a set of experiments under different pressure gradients and temperatures are conducted. Glass beads of 0.8 mm in diameter are used as the porous material. The experimental results show that when pressure gradient is getting greater at constant temperature, the moisture removal time is getting smaller. On the other hand, under the same pressure gradient, when liquid temperature increases, the time for moisture transfer from the internal to the external surface decreases. The calculated moisture removal times are well agreed with the experimental data.     

Investigation on Moisture Transfer Mechanism in Porous Media During Rapid Drying Process

Abstract

In this work, moisture transfer mechanism in wet porous media during rapid drying process is investigated experimentally and analytically. By use of scanning electron microscopic device, the rapid drying processes for potato, carrot, and radish species were observed and recorded. The microscopic drying experiments show that during high intense and rapid drying process, the mechanism of moisture migration in materials is mainly considered as a displacement flow driven by pressure gradient along a capillary passage. A simplified displacement flow model during rapid drying process is proposed and the time needed for moisture transfer in porous media is calculated. To examine this drying mechanism, one-dimensional displacement flow test device is built up and a set of experiments under different pressure gradients and temperatures are conducted. Glass beads of 0.8 mm in diameter are used as the porous material. The experimental results show that when pressure gradient is getting greater at constant temperature, the moisture removal time is getting smaller. On the other hand, under the same pressure gradient, when liquid temperature increases, the time for moisture transfer from the internal to the external surface decreases. The calculated moisture removal times are well agreed with the experimental data.