Drying Of Softwood Research Articles

Improvement of the design and heat supply system of a convective dehumidification chamber based on the heat engineering method

Long-term operation of wood-drying plants manufactured by the China in the Siberian region made it possible to establish that the basic design of chambers offered by manufacturers often does not ensure the high quality of dry sawn timber and the estimated drying cycle time, especially in winter. Among the measures aimed at improving the quality of drying, the productivity of drying plants while reducing energy consumption, we can single out the direction associated with improving the design of chambers and their heat supply systems. Thus, the relevant areas of improving the energy efficiency of drying lumber is the use of the heat engineering method to improve the functional characteristics of the heat supply systems of the chambers. The analysis of various types of heat supply schemes of chambers with water coolant was made. The advantage of using a heat supply scheme with high-quality control of the coolant flow in the chamber is substantiated. The results of the introduction of design and technological solutions of the heat engineering method are presented, which made it possible to technically re-equip existing and new drying chambers of the China. The thermal power of the calorifier installations of chambers with various types of heat supply schemes was experimentally determined. Additional requirements are formulated for fences, the technological equipment of the chambers for their operation in difficult climatic conditions of the Siberian region with the provision of high-quality drying of softwood and hardwood lumber. On the example of the existing production, the positive experience of commissioning cameras with additional technological equipment is shown. The operational parameters and dynamics of reducing the humidity of control samples in technically re-equipped chambers are given.

Evaluation strategy of softwood drying stresses during conventional drying: a “mechano-sorptive creep gradient” concept

The detection and analysis of drying-induced stresses in wood are of fundamental importance for quality evaluation and grading of kiln-dried lumber, and thus, various such procedures have been developed commercially. In this paper, a softwood drying-induced stress evaluation concept was proposed that is based on the drying rheology and wood mechano-sorptive mechanism. The evaluation variables for the drying-induced stresses included moisture content gradient (MCG) and mechano-sorptive creep strain gradient (MSCG), both of which are calculated through the lumber thickness. The softwood species needle fir (Abies nephrolepis) was processed into flat-sawn lumber pieces of 40 mm × 120 mm in cross section and was further kiln-dried in conventional laboratory dryers. Width deformation changes along the thickness of lumbers were measured by a slicing method. Shrinkage and elastic and viscoelastic creep strains in the tangential direction were measured quantitatively. Based on the dynamic free shrinkage functions for this softwood species, determined according to small specimen tests, the mechano-sorptive creep strain variables were calculated theoretically. By comparing the mechano-sorptive creep strain differentials between wood surface and its center section, a conspicuous corresponding trend could be revealed between this difference and those of the shrinkage strain differences. A combined variable set, which includes the moisture content differences and mechano-sorptive creep differences between the wood surface and its core section, was proposed based on this research test. The mechano-sorptive creep gradient concept was defined to formulate the drying stress and strain development during conventional drying. After some further mathematical approximations, these newly proposed variables were recommended to estimate the magnitude of drying stress during the mid- and final stages of softwood drying. The effectiveness of this theoretical inference was further verified according to the experimental results of the needle fir drying test.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media: Application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock–Euler method, which is explicit in nature and requires a matrix–vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly “Jacobian-free” – the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton–Krylov strategy.

Krylov subspace approximations for the exponential Euler method: error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product $\varphi(tA)b$ where $\varphi(z) = [\exp(z)-1]/z$. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where $A$~is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to $\varphi(tA)b$, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error. References E. J. Carr, T. J. Moroney and I. W. Turner. Efficient simulation of unsaturated flow using exponential time integration. Appl. Math. Comput., 217(14):6587--6596, 2011. doi:10.1016/j.amc.2011.01.041 E. J. Carr, I. W. Turner and P. Perre. A Jacobian-free exponential integrator for simulating transport in heterogeneous porous media: application to the drying of softwood, submitted for publication. E. J. Carr, I. W. Turner and P. Perre. A new control-volume finite-element scheme for heterogeneous porous media:application to the drying of softwood. Chem. Eng. Technol., 34(7):1143--1150, 2011. doi:10.1002/ceat.201100060 E. Celledoni and I. Moret. A Krylov projection method for systems of ODEs. Appl. Numer. Math., 24(2--3):365--378, 1997. doi:10.1016/S0168-9274(97)00033-0 N. J. Higham. Functions of matrices: theory and computation. SIAM, Philadelphia, PA, USA, 2008. M. Hochbruck, M. E. Hochstenbach. Subspace extraction for matrix functions, submitted for publication. http://www.win.tue.nl/ hochsten/pdf/funext.pdf M. Hochbruck, C. Lubich and H. Selhofer. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput., 19(5):1552--1574, 1998. doi:10.1137/S1064827595295337 B. V. Minchev and W. M. Wright. A review of exponential integrators for first order semi-linear problems. Numerics No. 2/05, Norwegian University of Science and Technology, Trondheim, Norway, 2005. http://www.math.ntnu.no/preprint/numerics/2005/N2-2005.ps P. Perre and I. Turner. A heterogeneous wood drying computational model that accounts for material property variation across growth rings. Chem. Eng. J., 86(1--2):117--131, 2002. doi:10.1016/S1385-8947(01)00270-4

A New Control‐Volume Finite‐Element Scheme for Heterogeneous Porous Media: Application to the Drying of Softwood

AbstractAn improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass‐conservative scheme based on the Control‐Volume Finite‐Element (CV‐FE) method that partitions the moisture content field over the individual sub‐control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass‐conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Optimizing radiata pine drying schedules

In an era of increased energy costs and concern about profitability, using the best drying schedule is important for softwood drying. The first part of this study looked at the feasibility of finding the combination of dry bulb, wet bulb and air velocity that either minimizes overall drying cost or maximizes profit in a simple radiata pine drying schedule with fixed conditions. A full stack drying model simulation was used to predict drying time and energy costs. Drying parameter constraints were included but drying degrade was ignored. Typical structural and appearance grade set-ups were examined for given energy and fixed cost combinations. It was concluded that significant cost reductions or profit gains are possible by selecting the best schedule. The second part of the study allowed the parameters to vary during the schedule and used a Simplex optimizing algorithm to select the best parameters as the schedule proceeded. The resulting time-varying schedule should be optimal for the given combination of energy and fixed costs. While it was found that such an approach could result in further cost reduction (~10%), it was concluded that a more responsive full stack drying model simulation is required.

Energetic and Ecological Aspects of Softwood Drying with High-Temperature Heat Pumps

To provide short drying times, the Canadian softwood producers generally opt for drying at high temperatures (100–120°C). Industrial and laboratory-scale softwood dryers with high-temperature heat pumps have been developed and field-tested over the last few years in North America. Improvements in refrigeration circuits design, as well as in dehumidification speed and back-up heating controls, finally provided stable operating parameters of such advanced systems. This article shows that the energetic performances of softwood dryers with high-temperature heat pumps were as high as expected, and that a number of ecological impacts have to be considered.

Internal mass transfer coefficient during drying of softwood (Pinus elliottii Engelm.) boards

A drying experiment with 36 mm thick softwood boards having an average initial moisture content of approximately 1.2 (dry basis) was performed. Drying temperatures of 40, 60 and 80°C were used. Relative humidity and superficial air velocity were maintained at 40% and 3.0 m s−1, respectively. Internal moisture content was monitored along the process in the single direction of the internal flux of water. Loss in mass of the entire timber board was also determined. An effective coefficient of mass transfer was tuned to internal experimental profiles of moisture content by involving the Fick’s second law. An explicit finite difference method for the numerical solution of the mass balance represented by the Fick’s equation was combined with the simplex method of optimization to obtain a mass transport parameter in the magnitude of 1.5–3.5 × 10−9 m2 s−1. A positive and significant effect of temperature on the effective diffusion coefficient, which was well described by an Arrhenius type expression, was deduced from this investigation. Although a negative effect of the average moisture content on the internal resistance to mass transfer was also observed, it was much less evident; mainly above the wood fiber saturation point. A negligible influence of the local moisture content on the investigated transport parameter was noticed when either a linear or a nonlinear model correlating these variables was adopted.

Drying of timber in progressive kilns: Simulation, quality, energy consumption and drying cost considerations*

Progressive (semi-continuous) kilns for softwood drying are very common in Finland and Sweden and are used in some other countries too. A simulation program has been developed that covers all three types of this kiln. The program calculates the climate in the length direction of the kiln and moisture content, moisture profile, wood temperature, slicing test gap and stress development. Energy consumption and drying costs may also be determined. The temperature level is the most important parameter regarding kiln efficiency. Two-zone progressive kilns are found to be more efficient than single-zone kilns. Progressive kilns have lower energy consumption and drying costs than batch kilns. Experimental full-scale tests show that the timber quality from a progressive kiln is comparable to, or in some cases even better than, timber dried in batch kilns.

A heterogeneous three-dimensional computational model for wood drying

An accurate and efficient heterogenous three-dimensional computational model is developed for simulating the drying of wood. The complex macroscopic drying equations comprise a coupled and highly nonlinear system of partial differential equations. Due to the heterogeneous nature of wood, the physical model parameters strongly depend upon the local pore structure of the medium, the wood density variation within growth rings and the local variations in primary and secondary system variables. In order to provide a realistic representation of this behaviour, previously determined parameters derived using sophisticated image analysis methods and homogenisation techniques are used. Results are presented for a first generation virtual board description, where the board material properties vary along the section according to the pith position that defines the radial and tangential directions. These variations are assumed fixed throughout the longitudinal direction. The development of an accurate and efficient computational model requires the consideration of a number of significant numerical issues, including the virtual board description, the mesh design, the discretisation process, accurate flux approximations, and finally the solution of a large, nonlinear system. Each of these issues will be explored in this paper for the case of low temperature drying of softwood.

The release of Hydrocarbons from softwood drying: Measurement and modeling

The release of volatile organic compounds (VOC) during the drying of Norway spruce and Scots pine was experimentally studied. Heartwood and sapwood were separately dried at 60 oC. The Flame Ion Detector (FID) was used to measure the total amount of hydrocarbons (THC) released during the drying process. A large difference of the emissions course between heartwood and sapwood were found. For heartwood, a release maximum of hydrocarbons followed by a typical negative exponential course was found. When drying sapwood, the released amount of hydrocarbons was evidently more fluctuating before reducing to zero. A model describing the release of hydrocarbons during the drying with only diffusion as transport mechanism was applied. The aim was to obtain a suitable explanation of the characteristic release behavior from sapwood and develop a model describing the process.

The use of numerical simulation as a cognitive tool for studying the microwave drying of softwood in an over-sized waveguide

A previously developed mathematical model, which uses a comprehensive two-dimensional heat and mass transport code coupled with a three-dimensional code for resolving Maxwell's equations in the time domain, will be used to investigate numerous aspects of the microwave enhanced convective drying of softwood in an over-sized waveguide. At first, in order to highlight the predictive capabilities of the developed model, comparisons will be made between theory and experiment for spruce heartwood. It will be shown that the model is able to identify most of the important heat and mass transfer phenomena that arise throughout the drying process. After validation of the numerical simulation results, the work focuses on using the model as a cognitive tool for investigating important issues for closed microwave systems which include the effect of varying the sample dimensions and changing the location of the material within the applicator. Finally, a study will be presented that compares the overall drying kinetics generated within two different types of applicator designs. The first design uses a wave-trap located at the end of the waveguide to prevent reflected energy from back-propagating into the over-sized section of the guide, while the second design uses a short-circuit plane to ensure that this reflected energy is back – propagated towards the material. The advantages and disadvantages of these two designs will be deliberated.

Wet Line Extension Reduces VOCs from Softwood Drying

VOC emissions from drying softwood oriented strand board (OSB) furnish or particle increase with decreasing particle size and with increasing oven temperature and airflow rate. The surface area is related to particle size; hence, a decrease in size preferentially dries out the surface. Similarly, drying at high temperature or under high airflow depletes surface moisture. VOCs from dried particle increase sharply beyond 160 °C. The optimum drying strategy from the perspective of reducing VOCs should minimize temperature imbalances and moisture gradients within the flake in order to reduce dry spots. Since surface dry-out will impede the movement of water to the surface, its onset should be delayed. Hence, the wet line should be maintained at the surface for as long as possible to keep the furnish evenly wet during drying.

Microwave drying of softwood in an oversized waveguide: Theory and experiment

AbstractA comparison between experimental and theoretical results for the combined microwave and convective drying of softwood is presented. The microwave applicator used for the experiments was an oversized waveguide, and the results for both sapwood and heartwood were analyzed. To elucidate on the physics of the process at a fundamental level, a complete model is proposed, which considers the intricate link that transpires between the heat‐and mass‐transfer phenomena and the power distribution throughout the sample during drying. The resulting model, which uses a comprehensive 2‐D set of equations to describe the drying process, together with a complete 3‐D solution of the Maxwell equations within the waveguide in the time domain, can be used to investigate many aspects of dielectric drying. This research deals with the spatial variation of the power density within the material at various drying times and the effect of the anisotropy of the transfer properties on the shape and evolution of the power distribution. Most importantly, it focuses on the prediction of the location of hot spots and thermal runaway within the sample from the viewpoint of product quality. Strengths and weaknesses of the model are highlighted.

A Mathematical Model for Simulation of Sofiwood Drying in Temperatures above Boiling Point of Water with Special Attention to the Boundary Conditions

ABSTRACT A mathematical model for simulation of softwood drying also in temperatures exceeding the boiling point of water is presented. The equations are formulated in a conservative form based on the classical volume averaging technique with an addition of a pressure-driven moisture flux in the boundary condition. Numerical results using the control volume method are presented to show that this term missing in existing simulation models may account far the calculated build up of moisture at the very surface of a wood board. The possibility of neglecting the air- phase in the calculation of total gaseous pressure is investigated by means of an example. It shows that the effect of air pressure is only of very litde importance in the case of transversal flow in moderate tempertures.

An unstructured mesh cell-centered control volume method for simulating heat and mass transfer in porous media: Application to softwood drying, part I: The isotropic model

Drying is one of the most energy intensive industrial processes with applications in a wide variety of industries including the timber industry, the food industry, and the construction industry. In order to understand the physics of drying at a fundamental level it is necessary to analyze the motion of liquid and gas through a capillary porous medium. The governing transport equations are comprised of a set of tightly coupled, highly nonlinear partial differential equations for the dynamic system variables of moisture content, temperature, and internal gaseous pressure. Due to the complexity of this system of equations there is usually little alternative but to employ a numerical solution technique. In this work an innovative scheme known as the unstructured mesh cell-centered control volume method will be analyzed and subsequently applied to high temperature drying of softwood. The method will be tested for a wide range of meshes each having differently shaped polygonal control volumes or cells. This new method will lay the foundation for studying problems that concern heat and mass transfer in porous media defined on complex geometries, or more importantly, for drying problems that include a stress analysis implemented on a dynamically distorting mesh. The work consists of two parts: Part I is devoted to the study of isotropic porous materials using a two-node and a four-node formulation for the discretization of the equations on an unstructured mesh; in Part II the numerical discretization associated with the complex problem of an anisotropic porous material is presented.

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

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.

An optimal operational strategy for wood in batch drying system

AbstractA complete model based on the wood drying mechanism and incorporating a multi‐period operation was established for wood in batch drying systems. Both energy savings and improvement of wood quality were obtained by an optimal strategy proposed in this study. Energy saving was indicated by the numerical results to be roughly 22.5% for drying of soft wood under the conditions of a given drying time and final moisture content. The gradient of moisture content within the dried wood could be minimized for the sake of enhancing the quality of wood by applying the proposed operational model.

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

ABSTRACT 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.