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.     

Modeling Microwave Heating and Moisture Redistribution in Wood

A finite element model was developed to describe and explain microwave heating of wood and the following moisture redistribution in wood. Dielectric and thermal properties are of great importance, since they are continuously affected during the process by moisture content, density, grain direction, temperature, and more. Computer tomography was used to detect wood density and moisture content. Heat distribution was verified by fiber-optic temperature sensors. The tests were performed in a designed microwave dryer based on 1-kW generators, 2.45 GHz. The results show that finite element modeling is a powerful tool to simulate heat and mass transfer in wood, providing the material is well described.     

Modeling Microwave Heating and Moisture Redistribution in Wood

A finite element model was developed to describe and explain microwave heating of wood and the following moisture redistribution in wood. Dielectric and thermal properties are of great importance, since they are continuously affected during the process by moisture content, density, grain direction, temperature, and more. Computer tomography was used to detect wood density and moisture content. Heat distribution was verified by fiber-optic temperature sensors. The tests were performed in a designed microwave dryer based on 1-kW generators, 2.45 GHz. The results show that finite element modeling is a powerful tool to simulate heat and mass transfer in wood, providing the material is well described.     

Discrete and Continuous Modeling of Heat and Mass Transport in Drying of a Bed of Iron Ore Pellets

Drying of a porous bed of iron ore pellets is here considered by modeling a discrete two-dimensional system of round pellets. As a complement to the two-dimensional model, a continuous one-dimensional model enabling fast calculations is developed. Results from the discrete model show that the temperature front advances faster in areas with large distances between the pellets. In areas with low flow speed, the temperature of the pellets increases with a relatively slow rate. The water inside these pellets will therefore remain for a long time. The continuous model fits the discrete model very well for a regular distribution of equal-sized particles. A discrete model with irregular packing will, compared to the continuous model, show a larger variation in the distribution of temperature and moisture content in the final phase of drying.     

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.     

Experimental study of the evaporation of a falling film in a closed cavity

This article concerns the experimental study of heat and mass transfer in a distillation cell. This latter is a parallelepiped, of large form factor, whose active walls are vertical. The cell is fed with salt water, and pure water is evaporated from a thin film that falls along a heated wall while the opposite wall is maintained at a lower temperature and is used as a condensation surface. The experimental results show that the heat transfer in the distillation cell is dominated by the latent heat transfer associated with evaporation. A parametric study of the behavior of the distillation cell has been performed. A convenient choice of the operating parameters is suggested to optimize the distillation yield.     

Modeling of Moisture Diffusion in Microwave Drying of Hardwood

A one-dimensional mathematical model was developed to predict temperature and moisture content profiles in red maple (Acer rubrum L.) and white oak (Quercus alba) during microwave drying. The model was solved using the finite element analysis with MATLAB software. The predictions for temperature and moisture content agreed favorably well with the experimental data. The diffusion coefficients of the red maple and the white oak in microwave drying conditions were calculated and analyzed. Equations of the diffusion coefficient in longitudinal and transverse directions based on input microwave power level are presented in this article. In microwave drying of hardwood, the red maple was heated more efficiently than the white oak because of higher absorbing efficiency of the microwave power.     

Modeling of Moisture Diffusion in Microwave Drying of Hardwood

A one-dimensional mathematical model was developed to predict temperature and moisture content profiles in red maple (Acer rubrum L.) and white oak (Quercus alba) during microwave drying. The model was solved using the finite element analysis with MATLAB software. The predictions for temperature and moisture content agreed favorably well with the experimental data. The diffusion coefficients of the red maple and the white oak in microwave drying conditions were calculated and analyzed. Equations of the diffusion coefficient in longitudinal and transverse directions based on input microwave power level are presented in this article. In microwave drying of hardwood, the red maple was heated more efficiently than the white oak because of higher absorbing efficiency of the microwave power.     

Modeling of vaporization and cracking of liquid oil injected in a gas-solid riser

Vaporization and cracking of liquid oil injected in a gas-solid riser (fluid catalytic cracking riser reactor) was computationally studied in this work. Evaporation of a single drop injected in a stream of gas-solid mixture was analyzed first. A model for simulating evaporation of a drop considering heat transfer from the gas phase as well as from the solid particles was developed. The model relates the evaporation rate of droplet with rate of collisions of solid particles, specific heat capacities of solid and liquid, latent heat of vaporization, relative velocity of gas and liquid and temperatures of three phases. The understanding gained from such a model was then extended to simulate evaporation of liquid drops injected in FCC risers. The Eulerian-Lagrangian approach was used to simulate simultaneous evaporation and cracking reactions occurring in FCC riser reactors. A commercial CFD code, FLUENT (of Fluent Inc., USA) was used. Four and ten lump models were used for simulating cracking reactions. Appropriate user defined functions were developed to implement heterogeneous kinetics and heat transfer models in FLUENT. A special algorithm was developed to calculate accumulated coke on catalyst particles. A boiling point range was considered for simulating realistic oil feedstock. The model was first evaluated by comparing predicted results with published industrial data. The simulations were then carried out to understand influence of key design and operating parameters on performance of FCC riser reactors. The parameters studied included; initial oil droplet distribution, catalyst inlet temperature, catalyst to oil ratio and thermal cracking. The approach, model and results presented here would be useful for optimization of FCC operation, cost to benefit analysis of new FCC nozzles and related decision-making.     

Numerical Modeling of Moisture and Temperature Distribution within a Rectangular Bagasse Layer Undergoing Drying

In this work, a numerical two-dimensional model using the finite volume method, which predicts the temperature and moisture distribution of the moist rectangular bagasse layer undergoing drying, is developed. During the drying process, variable heat and mass transfer coefficients are considered. The flow fields are numerically predicted using a commercial CFD package, Fluent. The temperature and moisture distributions under transient conditions are obtained, which determine both heat and moisture transport inside the material. The validation of the model is carried out by comparing the predicted mean moisture content values with those obtained experimentally. The comparison of the numerical and experimental result shows good agreement up to 8%.     

Spray Dryer Modeling in Theory and Practice

This article considers the modeling of spray dryers at various levels and the selection of the most appropriate level of detail for practical situations. The following model levels are described: (1) Heat and mass balances; (2) Equilibrium based models; (3) Rate based models; (4) Computational fluid dynamic (CFD) models. The value of each is discussed in relation to some typical problem scenarios. These include preliminary process design; process improvement; and troubleshooting operational and product quality problems. One particular focus of this article is finding realistic models of the performance characteristics of spray dryers which can be included in process flow sheet simulations while not imposing excessive run times and complexity.     

Mathematical Modeling of the Fluidized Bed Drying of Cubic Materials

The unsteady‐state simultaneous heat and mass transfer between gas and potato cubes during the drying process in a batch fluidized bed was described by a mathematical model. Mass transfer was considered to occur in three dimensions whereas heat transfer between the gas and dried material was assumed to be lumped. It was found that the model could describe the drying process with acceptable accuracy. The moisture profile inside the material at any cross‐section and at any time can be predicted by the model.     

The Proper Use of Mass Diffusion Equations in Drying Modeling: Introducing the Drying Intensity Number

This article intends to clearly define the possibilities and limitations offered by a simple diffusion approach of drying. Actually, many works use a simple diffusion equation to model mass transfer during drying, probably because a simple analytical solution of this equation does exist in the case of simple boundary conditions. However, one has to be aware of the limitations of this approach. Using a comprehensive formulation and a relevant computational solution, the most frequent assumptions of the diffusion approach were rigorously tested. It is concluded that analytical solutions must be discarded for several reasons: analytical solutions, either using Dirichlet or third kind boundary conditions, are often misleading and should be avoided; in the drying process, the coupling between heat and mass transfer is mandatory; nonlinearity (variation of diffusivity with moisture content) can hardly be avoided for mass transfer. In order to reach a verdict, a dimensionless number, the Drying Intensity Number (N_DI), is introduced. It allows the level of coupling between heat and mass transfer to be easily assessed. Thanks to this number, a guide is proposed for choosing the right level of modeling, depending on the drying configuration.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

ABSTRACT

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.     

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.     

Modeling the Heat Transfer during Log Heating

As one of the most commonly planted species in China, Masson pine (Pinus massoniana) logs are potentially used for structural poles and piles. Because phytosanitary regulations require that logs be heat-treated before delivery to customers (log core temperature of 56°C for 30 min), interest has recently arisen in the determination of the time required to reach this criterion. In this study, 12 logs were heat-treated in a laboratory drying kiln with two types of schedules. Using partial differential energy and mass conservation equations with gradient boundary conditions, the temperature increase in a log during heating was simulated. The boundary value problem of heat and mass transfer was solved using a numerical method, namely, a control volume approach. Results from the comparison between the observed and calculated temperatures indicated that the heat transfer performance during log heating can be described with this heating model. This model might therefore serve as a guideline for estimating the log heating times, assisting mill personnel in production planning. In addition, based on the experimental and calculated findings, it was well established that the log diameter, initial moisture content, wood density, and wet bulb temperature depression played significant roles in the heating rate during the heat treatment of logs.     

气泡在热液相介质中上升时的传热与传质

本文对气泡在热液相介质中上升时的传热与传质进行了分析,建立了数学模型,并进行了数值解,其结果可以说明气液相界面蒸发的特征。本文还通过实验对理论模型进行了验证。     

HIGH-TEMPERATURE SPRAY DRYING

This paper summarizes the results of long-term studies on high-temperature spray drying performed at the Institute of Engineering Thermophysics in Kiev. Two-stage processing involving evaporation followed by drying is proposed to dewater very dilute and temperature-sensitive materials. A new calculation procedure, which accounts for the gas-particle flow pattern and process kinetics, is given along with the performance data for selected drying plants designed according to the procedure developed.