The Application of Mathematical Models to the Commercial High-Temperature Drying of Softwood Lumber

ABSTRACT

High temperature drying of softwood is used because it provides much faster drying rate than is possible at lower temperatures. However, the occurrence of some drying defects limits its use where the quality is critical. In order to understand the drying phenomena and to describe the drying processes, numcrous mathematical models have been developed in the past two decades. The diffusion model is the earliest attempt to describe wood drying processes and is relatively simple in form, so it is often used for stress analysis. However.further substantial work is still required before it is possible to apply the stress model to kiln control. Recently. transpon-based mathematical models have been receiving attention in modelling studies. This review discusses one of these models, a physiological-transport-based model, which has been further applied to the drying of mixed sap/heartwood boards and the drying of a kiln-wide stack. The mixed boards with a thin heanwood layer parallel to the flat surface are considered to have added difficulty in drying. In the analysis of the timber stack drying, a kiln-wide model is proposed in which the above physiological-transpon-based model is used to generate the characteristic drying curves. Airflow reversal is essential in kiln     

Some Considerations In Simulation Of Superheated Steam Drying Of Softwood Lumber

ABSTRACT

A mathematical model for high-temperature drying of softwood lumber with moist air has been modified and extended to simulate wood drying with superheated steam. In the simulation, differences between the two types of drying are considered, these include: external heat and mass transfer processes and calculation of equilibrium moisture content. The external mass transfer coefficient in the perheated steam drying was found to be much higher than that in the moist air drying, however, the heat ransfer coefficients for these two cases were of the same order. The predicted drying curves and wood temperatures from the superheated steam drying model were compared with experimental data and there was close agreement. Further studies will apply the model to development of commercial drying schedules for wood drying with superheated steam.     

喷雾干燥的数学模型和技术进展

介绍了国外在计算机模型基础上发展起来的喷雾干燥技术的最新进展,由于数字模型回答了喷雾干燥过程中的许多问题,新的喷雾干燥设备（它们更多的是喷雾干燥塔,流化床一体化装置）可以提供较好的品质控制,耗能少,细粉少而效率更高。     

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.     

Bibliography on Mathematical Models of Drying and Dryers

Mathematical modelling of drying processes as well as dryers has become an active and challenging area of research internationally. Despite the volume of literature published and continuing to appear on this subject, much remains to be accomplished in view of the intrinsic complexities associated with coupled heat, mass and momentum transfer with or without phase change occurring in porous media which are often deformable as well. Characterization of the solid media is still a major obstacle to modelling of drying. Since industrial drying is increasingly carried out using several modes of heat transfer (e.g. convection coupled wih conduction or microwave or infrared heating modelling of drying or dryers will remain an important research area in the years to come.

We hope that this bibliography will serve as a useful tool for both the novice as well as the experienced researcher in the subject area in locating appropriate literature for a critical evaluation.     

Comparative Analysis of the Kinetics of Drying of Disperse Polymers Using Mathematical Models

A comparative analysis of the kinetics showed that the duration of drying anid from beginning to acceptable moisture content is less than for polycaproamide; for example, in conditions of drying in a nitrogen current with a temperature of 140°C and rate of movement of 0.3 m/sec, the drying time for anid is approximately 28% less. As a consequence, for the same efficiency, the dryer for anid can have smaller geometric dimensions than the dryer for polycaproamide with all other conditions being equal.     

Experimental Investigation and Practical Application of Superheated Steam Drying Technology for Softwood Timber

Due to several advantages, superheated steam drying of timber has attracted great attention. However, the technology is still restricted to some special cases, partly due to the lack of fully understanding of the drying process. In this work, experiments were conducted to dry radiata pine timber using superheated steam under vacuum and at pressure. In the first part of the experiments, softwood timber was dried in a superheated steam kiln with drying rates, steam temperature across the stack and wood temperature being measured during drying. In the second part of the work, experimental studies were performed to investigate potential applications of the superheated steam drying at ultra-high temperatures (UHT) and pressurized steam conditioning of kiln dried timber. Compared to normal drying temperatures, the UHT drying can reduce the drying time by a factor of 5 to 10 and it is also more energy efficient. The pressurized steam conditioning has been proven to be a promising technology to relieve drying stresses and to reduce twist of the dried timer.     

Experimental Investigation and Practical Application of Superheated Steam Drying Technology for Softwood Timber

Abstract

Due to several advantages, superheated steam drying of timber has attracted great attention. However, the technology is still restricted to some special cases, partly due to the lack of fully understanding of the drying process. In this work, experiments were conducted to dry radiata pine timber using superheated steam under vacuum and at pressure. In the first part of the experiments, softwood timber was dried in a superheated steam kiln with drying rates, steam temperature across the stack and wood temperature being measured during drying. In the second part of the work, experimental studies were performed to investigate potential applications of the superheated steam drying at ultra-high temperatures (UHT) and pressurized steam conditioning of kiln dried timber. Compared to normal drying temperatures, the UHT drying can reduce the drying time by a factor of 5 to 10 and it is also more energy efficient. The pressurized steam conditioning has been proven to be a promising technology to relieve drying stresses and to reduce twist of the dried timer.

     

A Simulation of Wet Pocket Lumber Drying

In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.

A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D_eff) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D_eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.

Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments.     

A Simulation Tool for the Optimization of Lumber Drying Schedules

Abstract

A two-dimensional wood drying model based on the water potential concept is used to simulate the convection batch drying of lumber at conventional temperature. The model computes the average drying curve, the internal temperature and moisture content profiles, and the maximum effective moisture content gradient through board thickness. Various scenarios of conventional kiln-drying schedules are tested and their effects on drying time, maximum effective moisture content gradient, final moisture content distribution within and between boards, and energy consumption are analyzed. Simulations are performed for two softwood species, black spruce (Picea mariana (Mill.) B.S.P.) and balsam fir (Abies balsamea (L.) Mill.). The simulation results indicate that the predictive model can be a very useful tool to optimize kiln schedules in terms of drying time, energy consumption, and wood quality. Such a model could be readily combined with intelligent adaptive kiln controllers for on-line optimization of the drying schedules.     

A Simulation Tool for the Optimization of Lumber Drying Schedules

A two-dimensional wood drying model based on the water potential concept is used to simulate the convection batch drying of lumber at conventional temperature. The model computes the average drying curve, the internal temperature and moisture content profiles, and the maximum effective moisture content gradient through board thickness. Various scenarios of conventional kiln-drying schedules are tested and their effects on drying time, maximum effective moisture content gradient, final moisture content distribution within and between boards, and energy consumption are analyzed. Simulations are performed for two softwood species, black spruce (Picea mariana (Mill.) B.S.P.) and balsam fir (Abies balsamea (L.) Mill.). The simulation results indicate that the predictive model can be a very useful tool to optimize kiln schedules in terms of drying time, energy consumption, and wood quality. Such a model could be readily combined with intelligent adaptive kiln controllers for on-line optimization of the drying schedules.     

Comparative Analysis of Three Methods for Stochastic Lumber Drying Simulation

Abstract:

This article describes a novel stochastic model designed to simulate systems that cannot be analyzed as a unit, but as a collection of a large number of similar components. In order to state advantages and disadvantages, the proposed method is compared with two other published models. The first is a symbolic mathematical relationship designed to predict average moisture content and standard deviation after conventional drying of lumber. Since this model is exact, it was used as reference to evaluate the accuracy of the other approximate numerical methods. The second model is entirely random, and it emulates a real system behavior in which the parameters and conditions randomly change from one component to the other. The proposed method is based on numerical integration of the parameter's frequency distribution curves, which always produce the same and most probable result for the same parameters and conditions. The three methods were applied for simulation of conventional lumber drying, and the results were compared both qualitatively and numerically.     

A Study of the Boundary Layer Flow Through a Lumber Drying Stack

Experiments were performed to investigate the boundary layer flow over rough surfaces of sawn boards in a lumber drying stack. The measurements were conducted with hot-wire anemometry in a range of free-stream velocities of from 0.6 to 7.0 m/ over the rough surface of sawn boards. Boundary layer properties were calculated to demonstrate the development and structure of the flow for various free-stream velocities. The effect of the boundary layer flaw on the drying of lumber was discussed.     

A Study of the Boundary Layer Flow Through a Lumber Drying Stack

ABSTRACT

Experiments were performed to investigate the boundary layer flow over rough surfaces of sawn boards in a lumber drying stack. The measurements were conducted with hot-wire anemometry in a range of free-stream velocities of from 0.6 to 7.0 m/ over the rough surface of sawn boards. Boundary layer properties were calculated to demonstrate the development and structure of the flow for various free-stream velocities. The effect of the boundary layer flaw on the drying of lumber was discussed.     

混凝控制中的数学模型及其应用

水处理中混凝剂加注量的自动控制是一个既重要又难于解决的问题。本文系统介绍了三种典型的数学模型,探讨了它们对于混凝控制技术的促进作用,分析了基于不同数学模型的控制问题间的差异。     

Evaluation of Parameter Values For a High-Temperature Drying Simulation Model Using Direct Drying Experiments

ABSTRACT

An existing drying simulation model for softwood heartwood is revised lrom a theoretical point of view and is completed by extracting all the essential material parameters from moisture and temperature profiles measured in direct drying experiments. Some additional experimental results are presented to validate the qualitative characteristics of the model. The resulting computational model shows good agreement with experiments in the drying temperature range 45-120°C. Special attention is paid to the evolution of moisture gradient during drying, as the next step of the simulation project will be using the result as an input data for a computational stress model.     

Mathematical Model of Synthetic Leather Drying

A mathematical model of synthetic leather drying for removing the organic solvent is proposed. Analytical solutions are obtained for a number of problems of heat transfer in a plate, including the problem of a moving evaporation front. The model proposed adequately describes the real processes.     

Mathematical Modelling of Shrinkage During Drying

Main aim of this paper is to present a mathematical model describing the shrinkage phenomenon of materials undergoing drying processes. The model was constructed using the methods of continuum mechanics and the principles of thermodynamics of irreversible processes.it considers the similtaneous deformation of the dried body accompanying the heat and moisture changes and the drying induced stresses     

冷冻干燥过程的数学模型

本文以物料衡算和热量衡算为基础，作适当的简化，导出了所需参数较少，但能准确地预测冷冻干燥全过程时间的数学模型，通过对胡萝卜和土豆的实验研究，检验了模型的适用性和准确性。     

Optimization of the Drying Process: An Application to the Drying of Garlic

The response surface methodology (RSM) was used to derive an optimum drying condition for garlic drying. The responses analyzed were L* value and Optical Index (OI) as a measure of color and rehydration ratio (RR) as well as final moisture content (Mf) which are important quality attributes of dehydrated products. L*, OI, RR and Mf varied from 70.6 to 85.0, 72.0 to 191.1, 2.2 to 3.2 and 5.4 to 10.2 % MC, respectively. An analysis of variance (ANOVA) revealed that drying temperature and slice thickness significantly (90% confidence level) affected L*, OI and RR while no effect was observed for airflow rate and relative humidity (RH). An optimum drying temperature of 70°C for drying 2 mm garlic slices is recommended.