M O D E L L I N G RADIO F R E Q U E N C Y / V A C U U M D R Y I N G OF WOOD by ANASTASIOS K O U M O U T S A K O S B. Chem. Eng., Chemical Engineering, Aristotle University of Thessaloniki, 1994 M.A.Sc, Department of Chemical Engineering, University of British Columbia, 1996 A THESIS SUBMITTED IN PARTIAL F U L F I L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES FACULTY OF FORESTRY Department of Wood Science We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A October 2001 ® Anastasios Koumoutsakos, 2001 In presenting degree at the this thesis in University of partial fulfilment of of department this thesis for or by his or requirements British Columbia, I agree that the freely available for reference and study. I further copying the representatives. an advanced Library shall make it agree that permission for extensive scholarly purposes may be her for It is granted by the understood that head of copying my or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract The purpose of this study was to investigate the electromagnetic energy dissipation coupled with heat and moisture mechanisms in wood during radiofrequency/vacuum(RF/V) drying. This involved both numerical and experimental studies. Specifically, the objectives were to establish a continuous RF/V drying model, to examine first if a one-dimensional model is sufficient to capture the basic mechanisms of drying. Subsequently, this was extended to a two-dimensional model in order to study anisotropic effects. Experimental data required by the model were two parameters, namely, the bound moisture diffusion coefficient and the intrinsic permeability. In order to evaluate the predictability of the model developed, experimental information from a series of RF/V runs using a single specimen under different power densities and ambient pressures were performed. These data were used to evaluate the capabilities of the model. The mathematical model was derived by averaging the conservation equations over a representative differential volume. The final form of the model was developed after a detailed discussion of the controlling resistances and transport mechanisms during RF/V drying. Such a model may readily exclude liquid capillary transport, which is an important factor in convective drying. Comparison of the model prediction with the experimental data obtained revealed a good agreement for a variety of drying conditions, particularly with those predicting the total average moisture evolution and the total drying time. Extension to a twodimensional model was suggested to overcome its shortcomings in predicting accurately the temperature evolution and in describing in detail the internal heat and mass transfer phenomena during wood RF/V drying. ii Experiments were carried out to determine the permeability and the bound water diffusion coefficients of western hemlock and western red cedar for both heartwood and sapwood in the longitudinal, tangential and radial directions, respectively. The permeability data, though exhibited high variability, were found within the range reported in the literature. Diffusion coefficients were determined as a function of moisture content and temperature for all directions and wood types. The trends of the curves obtained are in agreement to theoretical ones. The fiber saturation point was determined for all the above cases. The sorption isotherms were calculated and the parameters of the Hailwood-Horrobin equation were calculated using a non-linear regression technique. All the results are discussed within the framework of developing a two-dimensional mathematical model for the RF/V drying of timbers. Finally, a small representative number of experiments was carried out by using "50 Ohm amplifier" technology. The improvement of the uniformity of the electric field was obvious through the temperature and final moisture measurements. The predictions of the two-dimensional form of the model were in good agreement for all cases examined. The agreement is considerably better compared to that found for the one-dimensional model. The value of using evolution strategies for the overall optimization of the process is also presented. iii Table of Contents Abstract Table of Contents List of Tables List of Figures Acknowledgements Dedication Preface Chapter 1: Introduction 1.1 Overview 1.2 Objectives 1.3 Practical application 1.4 Overview of the thesis Chapter 2: Literature Review 2.1 Introduction 2.2 Structure of wood 2.3 Permeability, bound water diffusion, equilibrium moisture content and sorption isotherms 2.4 Wood drying 2.5 Dielectric heating 2.6 Dielectric heating kinetics 2.7 Principles of vacuum drying 2.8 RF/V drying 2.9 Modeling of wood drying Chapter 3: Materials and Methods 3.1 Permeability experiments 3.2 Diffusion Coefficients and Sorption Isotherm experiments 3.3 RF/V drying experiments Chapter 4: Mathematical Formulation and Numerical Solution 4.1 Introduction 4.2 Controlling resistances and transport mechanisms during wood drying 4.3 Assumptions 4.4 Physical drying description 4.5 Continuum mechanics 4.6 Governing differential equations 4.6.1 Free water 4.6.2 Water vapor 4.6.3 Cell walls 4.7 Interfacial boundary conditions 4.8 Volume averaging 4.9 Macroscopic governing equations 4.9.1 Conservation of mass 4.9.2 Conservation of momentum 4.9.3 Conservation of energy 4.9.4 System of partial differential equations 4.9.5 Calculation of radio frequency source term ii iv vi vii ix x xi 1 3 4 5 8 9 15 17 19 26 27 29 33 36 38 40 49 49 51 52 52 54 54 56 57 58 60 61 62 62 64 66 68 iv 4.10 Capillary transport and RF/V drying 4.11 1-D model form 4.12 Numerical solution 4.13 Optimization methods 4.14 The concepts in ES 4.15 2-D model form Chapter 5: Results and Discussion 5.1 Calculations with the 1-D model 5.2.1 Comparison of RF/V experiments with 1-D calculations 5.2.2 Analysis of RF/V experiments with the oscillator 5.3 Permeability 5.4 Diffusion coefficients and sorption isotherms 5.5 Analysis of RF/V experiments with the amplifier 5.6 Calculations with the 2-D model and comparison with experiments Chapter 6: Conclusions and Recommendations 6.1 Conclusions 6.2 Future Research References Notation Appendix A Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 5.7 Table 5.8 Table 5.9 Table 5.10 List of Tables Master table of the experimental conditions for RF/V drying when using the oscillator. 103 Longitudinal intrinsic permeabilities of western hemlock and western red cedar, heartwood (FT) and sapwood (S). 108 Radial (R) and Tangential (T) intrinsic permeabilities of western hemlock heartwood (FT) and sapwood (S) and western red cedar heartwood (H). 110 Average diffusion coefficients and the respective average moisture contents at 70°C. The covariance is in parenthesis. (S^sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). 113 Average diffusion coefficients and the respective average moisture contents at 50°C. The covariance is in parenthesis. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). 114 Average diffusion coefficients and the respective average moisture contents at 30°C. The covariance is in parenthesis. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). 115 Fiber saturation points at different temperatures for western hemlock and western red cedar. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). 118 Parameters estimated for equation (5.4). (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). 120 Parameters estimated for Hailwood-Horrobin model for western hemlock and western red cedar. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). 120 Master table of the experimental conditions for RF/V drying when using the amplifier. 123 vi List of Figures Figure 2.1 Typical softwood structure showing three directional axes and cross section of wood (Rosen 1987). 11 Figure 2.2 Radial surfaces of earlywood and latewood tracheids (Siau, 1995). 12 Figure 2.3 Bordered pit with typical dimensions (Spolek, 1981). 13 Figure 2.4 Mechanistic models of softwood structure (a) tangential transport; (b) radial transport (Plumb et al., 1985). 14 Figure 2.5 Sorption isotherms of wood (Siau, 1995). 17 Figure 2.6 Electromagnetic spectrum. . 21 Figure 2.7 Relationship between saturated vapor pressure of water and temperature. 29 Figure 3.1 Schematic design of the permeability measuring apparatus. 37 Figure 3.2 A picture of the permeability apparatus in the U B C Wood Physics Lab. 39 Figure 3.3 A picture of the two conditioning chambers in the U B C Wood Physics Lab. 40 Figure 3.4 Schematic diagram of the laboratory RF/V dryer. 42 Figure 3.5 Picture of the front view of the RF/V dryer in the U B C Wood Drying Lab. 44 Figure 3.6 Picture of the side view of the RF/V dryer in the U B C Wood Drying Lab. 45 Figure 3.7 Picture of the matching network box, vacuum pump and heat exchanger in the U B C Wood Drying Lab. 46 Figure 3.8 Picture of the back view of the RF/V dryer in the U B C Wood Drying Lab. 47 Figure 3.9 Location of temperature and pressure probes. 48 Figure 4.1 Physical configuration of drying model, E = aluminum electrodes, P = polyethylene plates, W = wood specimens. 53 Figure 4.2 Schematic of averaging volume. 60 Figure 4.3 Equivalent circuit of real capacitor. 69 Figure 4.4 Phase diagram of a real capacitor. 69 Figure 5.1 The effect of wood permeability on the moisture and temperature evolution for three different permeabilities, case 1: K = 10" m , case 2: K = 5*10" m , case 3:K = 10" m . Other parameters of the model include miNi = 0.7, FSP = 0.3, O=5,000W/m , P |„= 7,500 W/m . The permeability is K = 5*10" m and m , FSP, Piai„„ X i t , and length of 3,000 Pa, X | = 9.2735, electrode plate length=2m. 85 Figure 5.2 The effect of power density on the moisture and temperature evolution for three different power densities, case 1: cp = 2,500 W/m , case 2: <D = 5,000 W/m , case 3: O = electrode plates is the same as in Figure 5.1. 87 Figure 5.3 The effect of voltage on the moisture and temperature evolution for three different voltages, case 1: V = 200 Volt, case 2: V = 250 Volt, case 3: V = 300Volt. The distance between the electrode plates is 250 mm and K, miNi, FSP, Pkiin,, X i , and length of electrode plates is the same as in Figure 5.2. 88 Figure 5.4 The effect of plates length on the moisture and temperature evolution for three plate lengths, 1 m, 1.5 m, and 2 m. The voltage is 200 Volt and the distance between the plates, K, miNi, FSP, Pidin,, Xi t are the same as in Figure 5.3. 89 Figure 5.5 Experimental temperature and pressure evolutions at quarter length, core and 13 12 2 13 2 2 3 3 13 2 ki m sat sa 3 3 sat sa ambient kiln points for Western Hemlock #11. Figure 5.6 Experimental temperature and pressure evolutions at quarter length, core and ambient kiln points for Western Red Cedar #1. 90 91 vii Figure 5.7 Experimental temperature and pressure evolutions at quarter length, core and ambient kiln points for Western Red Cedar #5. 92 Figure 5.8 Calculated and experimental total average moisture and temperature changes with time at quarter length and core points for Western Hemlock #11. 96 Figure 5 9 Calculated and experimental total average moisture and temperature changes with time evolution at quarter length and core points for Western Red Cedar #1. 98 Figure 5.10 Calculated and experimental total average moisture and temperature changes with time at quarter length and core points for Western Red Cedar #5. 99 Figure 5.11 Calculated longitudinal temperature changes with time for Western Hemlock #11. 100 Figure 5.12 Calculated longitudinal moisture changes with time and experimental final moisture profile for Western Hemlock #11. 100 Figure 5.13 Specific permeability as a function of reciprocal average pressure for the case of hemlock sapwood longitudinal #4. 107 Figure 5.14 Diffusion coefficient versus moisture content of hemlock (HSL) and cedar (CSL) sapwood at longitudinal direction and temperatures of 30, 50 and 70°C. 117 Figure 5.15 Diffusion coefficient versus moisture content of hemlock (HSR) and cedar (CSR) sapwood at radial direction and temperatures of 30, 50 and 70°C. 117 Figure 5.16 Drying curves of Western Hemlock at different power densities and ambient pressures. 126 Figure 5.17 Drying curves of Western Red Cedar at different power densities and ambient pressures. 126 Figure 5.18 Slices of cross sections of Western Hemlock #2 at different points longitudinally. 128 Figure 5.19 Slices of cross sections of Western Red Cedar #1 at different points longitudinally. 128 Figure 5.20 Slices of cross sections of Western Hemlock #4 at different points longitudinally. 129 Figure 5.21 Slices of cross sections of Western Red Cedar #3 at different points longitudinally. 129 Figure 5.22 Front end cross section of Western Hemlock #4 at the end of the experiment. 130 Figure 5.23 IDC for the case of Western Red Cedar #3. 135 Figure 5.24 IDC for the case of Western Hemlock #2. 136 Figure 5.25 Calculated and experimental total average moisture and temperature changes with time at quarter length, quarter width and core points for Western Hemlock #1. 140 Figure 5.26 Calculated and experimental total average moisture and temperature changes with time at quarter length, quarter width and core points for Western Hemlock #2. 140 Figure 5.27 Calculated and experimental total average moisture and temperature changes with time at quarter length, quarter width and core points for Western Hemlock #2. 141 viii Acknowledgements I would like to acknowledge several individuals whose help and cooperation throughout the years have made this research possible: to Dr. Stavros Avramidis, my advisor, and to Dr. Sawas G. Hatzikiriakos, my co-advisor, for their continuous guidance and support throughout my graduate studies and research at U.B.C.; to Drs. J.D. Barrett and F. Lam for their helpful suggestions and critical review of the thesis material. I owe a lot of gratitude and thanks to a number of friends and research colleagues. Dr. Liping Cai, Fang Fang, Pablo Garcia, Dr. Terry Enegren, Diana Hastings, Avtar Sidhu, Bob Myronyuk, Dayna Furst. I owe a special thank you to my brother for his continuous guidance in developing very useful tools such as the Evolution Strategies. I would also like to mention a number of friends that were very supportive all these years: Manolis Sarantidis, Eugene Rosenbaum, Igor Kazatchkov, Maria Arvanitakis, Dennis Trigilidas, Paul Jones, Greg Kaldis, Kostis Sakelaris, Zoran Miladinovic, Petros Gaganis, George Aliphtiras and Petros Lappas. An NSERC Strategic grant for two years and a SCBC GREAT award for another two years supported my studies at UBC. I am very grateful for thefinancialassistance provided by Mr. Robert Zwick, President and CEO of Heatwave Drying Systems Ltd. Finally I am indebted to my family for their support and encouragement during my university years. Especially, to my parents, thank you. ix Dedication the memory of Petros Preface Some of the materials contained in the thesis are from the following articles: 1. M O D E L I N G WOOD RADIO F R E Q U E N C Y V A C U U M D R Y I N G PART I. THEORETICAL M O D E L (by Koumoutsakos, A., Avramidis, S., and S. G. Hatzikiriakos, 2001, Drying Technology, 19(l):65-84) 2. M O D E L I N G WOOD RADIO F R E Q U E N C Y V A C U U M D R Y I N G PART II. E X P E R I M E N T A L M O D E L E V A L U A T I O N (by Koumoutsakos, A., Avramidis, S., and S. G. Hatzikiriakos, 2001, Drying Technology, 19(l):85-98) XI C h a p t e r 1: I n t r o d u c t i o n 1.1 Overview Wood as a raw material is one of the most vital natural resources that may be used for a variety of purposes in a number of different industrial sectors. Common to many wood product-manufacturing processes is the need to drive the natural moisture from wood. Drying is one of the most energy intensive stages of lumber and composite wood products manufacturing. As the demand for wood increases, while at the same time the volume and sometimes quality of natural resource decreases, more effective drying methods, which maximize yields, are necessary. However, practical experience has shown that this process is still quite far from what may be called optimal. This motivates the need for extensive research into state of the art heating and drying processes such as combined high frequency and vacuum drying, combined high frequency and convective drying, and high temperature (which may include superheated steam) convective drying. The two essential ingredients that are necessary in the development of these new drying technologies consist of both experimentation and mathematical modeling. The strategy of modeling followed by experimental validation appears to be a cost effective method of advancing and understanding technology in drying process. Dielectric heating is a term, which covers both radio frequency (RF) and microwave systems. It has been used in a number of different industrial operations other than for communication purposes for many years, and in many cases has replaced less efficient and economic conventional methods. One of these applications is the heating during drying of materials that contain large quantities of water. These products include among others, agricultural grains, ceramics, foodstuffs, textiles, paper products and wood (Chen and Schmidt 1990, Lyons et al. 1972, Tong and Lund 1993.) Vacuum drying is essentially "high 1 temperature" drying at low temperature. For the last ten years, many types of vacuum dryers have appeared on the market and are used in the wood industry (Chen 1997). Most of these dryers utilize air or steam circulated for convective heat transfer. The combined use of R F heating with vacuum drying may not only greatly enhance the drying of wood and improve its quality, but it may also reduce the total costs involved in the process. This, together with the gloomy outlook of a worldwide energy crisis, has paved the way for extensive research into new and innovative heating and drying processes. While capital and operating costs certainly still represent the criteria for greater acceptance of R F / V in industrial drying, an equally important constraint is the lack of the fundamental knowledge of how the RF field interacts with wood during heating and drying under vacuum because a considerable amount of applied research has been carried out over the last few years on the RF/V process development by the " trial-and error" approach. To fully comprehend the heat and mass transfer phenomena occurring within the material during R F / V drying, the moisture, temperature and pressure distributions within wood throughout the process need to be studied and understood. The complexities and time involved in measuring the distribution of such quantities during a drying experiment highlight the need for mathematical modeling as an essential ingredient in the research of the topic. Numerical simulations can aid in the design and understanding of dryers and can indicate the effectiveness of the RF released energy during the drying process. The dryer designer can employ the model to predict times and rates of drying for the product under various R F / V scenarios. The difficulties involved in the modeling of wood drying are highlighted by the fact that wood is heterogeneous, hygroscopic, anisotropic material, and that it shrinks during 2 drying so that dimensional changes cause internal stresses. Furthermore, in the case of coupled heat and mass transfer in wood, the formulation of the model is quite complex and a complete physical description of the medium requires an in-depth knowledge of numerous parameters, together with several correlating functions such as: capillary pressure, permeabilities, thermal conductivities, vapor flow characteristics as the bound water diffusivities, sorption isotherm curves and dielectric wood properties. It is also important that any modeling work must be verified by experiment. Unfortunately, at this stage it is difficult to experimentally differentiate all the relevant correlating functions in the longitudinal, tangential and radial directions of wood, and therefore, some quantitative approximations were adopted. Any modeling or coefficient correlation effort that does not adequately address the structure, transport, thermodynamic, and dielectric characteristics of wood is likely to misrepresent what actually occurs during the drying process. On the other hand, the simpler the model, the easier it can be utilized by non-experts on the field of drying and also be utilized readily by industry. 1.2 Objectives The objective of this study is to investigate and understand the electromagnetic energy dissipation coupled with heat and moisture mechanisms in wood during RF/V drying. This includes both numerical and experimental studies. A list of tasks required to achieve the objective are as follows. I. Model development a. Establishment of a continuous R F / V drying model. 3 b. Solution for the simple 1-D model case and examine if the longitudinal transfers can give reasonable predictions. c. Extension of the program to a 2-D case in order to study both the heterogeneous and anisotropic effects that persists in wood drying due to the anisotropic structure of wood. II. Experimental study a. To determine the effect of moisture content and temperature on the moisture diffusion coefficient of wood under the unsteady-state conditions. b. To evaluate the permeability of wood by using a specific flow measurement apparatus. c. To study the drying kinetics of an RF/V drying environment. d. To collect the experimental information from a series of RF/V runs for single specimen situations under different power densities and ambient pressures. III. Model evaluation a. To evaluate the predictability of the model developed under task I by the corresponding experimental results obtained under task II. 1.3 Practical application Most conventional kiln drying practices are carried out according to drying schedules which are designed to minimize the drying time while at the same time avoiding excessive moisture content gradients. This will help to reduce product loss resulting from stress related defects. The drying schedules have been developed and modified gradually over the years through practice without invoking detailed knowledge of the heat and mass transfer process involved. Nevertheless, there are only some initial RF/V drying schedules developed for few 4 species. The results obtained from this study will provide detailed knowledge of heat and mass transfer behavior in wood during R F / V drying. This knowledge could be used to develop new drying schedules and optimize the process. The computer models developed could be used to predict moisture movement and temperature distribution in wood under RF/V drying conditions. The computer program for the 1-D drying is designed to predict the longitudinal drying case. The 2-D model is a more general model that can be applied to longitudinal and transverse drying directions. However, when a drying process is simplified as for example by considering only drying in the longitudinal direction, the 1-D model becomes advantageous because of simplicity and reduced computational time. These models provide a far less expensive way to explore the RF/V drying process under various conditions. Moreover, they help in order to gain a better understanding of the thermophysical phenomena, to predict the drying history and to reduce experimentation required in process optimization. This will also help to obtain the best methods of controlling the drying parameters such as ambient pressure, voltage of the RF field, total power density, improve energy efficiency, wood quality, and the productivity of drying systems. 1.4 Overview of the thesis The thesis is organized as follows. The physical characteristics of wood are first described. The experimental systems and the methods are discussed next. The theoretical model is derived and the numerical solution of the 1-D model is also presented. Finally, all the experimental and computational results are presented and compared. 5 The main contents of the thesis are presented in Chapters 2 to 6 and brief overviews of these chapters are given below. In Chapter 2 a literature review of the basic theory related to R F / V wood drying and its modeling is presented. In particular, the structure of softwood is described at first, followed by the basic physics of wood drying. A brief description of vacuum drying, dielectric heating, the modeling of such processes and the basics on permeability and the bound water diffusion coefficient are discussed. Chapter 3 describes the experimental study, both for the transport properties and the RF/V drying experiments. Particularly, the investigation to determine the effect of moisture content and temperature on the bound water diffusion coefficient of wood and the experiments to evaluate the permeability of wood are depicted in detail. The experimental procedure for the R F / V drying experiments is also included. A description of the permeability test apparatus and the laboratory RF/V dryer are presented as well. Chapter 4 illustrates the mathematical formulation of the transport processes. A theoretical model for moisture and energy transport in wood under R F / V drying conditions is derived based on the conservation laws of mass, energy and momentum. The model development starts from the point equations and then utilizes the volume averaging theory to obtain a single set of governing equations, which also contain an extra component to account for the rate of dielectric energy adsorbed per unit volume of wood. The 1-D and the 2-D forms of the model along with the initial and boundary conditions are given. A brief description of the solution is discussed at the end of this chapter. 6 Chapter 5 presents the experimental results for permeability, bound water diffusion coefficient and the various RF/V drying cases. Calculations for the 1-D and 2-D modeling are also found in this chapter. The results are provided in the order that they were obtained. Finally, Chapter 6 presents the conclusions and recommendations for future research in both the experimental and the mathematical modeling areas. 7 C h a p t e r 2: L i t e r a t u r e R e v i e w 2.1 Introduction Wood is cellular in structure, anisotropic and a highly heterogeneous porous material. Large amounts of water have to be removed for freshly cut wood to produce commercial lumber. It is well known that dried wood has a number of distinct and important advantages: (1) Dried wood has good dimensional stability. (2) Many important wood properties such as mechanical strength, hardness, specific heat and thermal resistance increase as water is removed from wood. (3) Drying reduces the likelihood of mold, strain, insect attack or decay. (4) Wood must be relatively dry before gluing or finishing. (5) Drying reduces weight, and thus shipping and handling costs. (6) Controlled drying reduces splitting, checking and warp, which can occur as a result of uncontrolled drying. Drying is one of the most time- and energy-consuming steps in wood products processing. In Canada, the industry of wood and wood products has a key role in the country's economy and uses a substantial amount of the total energy consumed in the industrial sector. Drying can consume 40-70% percent of the total energy usage in manufacturing most wood products. ' Currently, there are two major technological approaches to dry wood. The first is conventional drying methods, such as low- and high-temperature kiln drying and dehumidification kiln drying. With these methods, rows of lumber separated by stickers are placed in a kiln where air temperature, relative humidity and velocity are controlled. 8 Considerable amounts of energy are required because of the relative humidity control, and the lumber degrade can be highly affected due to the variable properties of wood. The second is what is considered as the non-conventional group of drying technologies such as, vacuum, superheated steam/vacuum (SS/V), and RF/V drying. The conventional group will continue to play a dominant role, but the latter has recently created significant interest. This work is related to one of the relatively new methods of enhancing drying rates that improves product quality, namely, R F heating coupled with drying under vacuum. The anatomical structure of wood limits how rapidly water can move through and out of wood products. Variability of wood properties such as, diffusivity, permeability, capillary pressure, and thermal conductivity further complicates drying. The difficulty in improving the drying of wood also arises from the complex interactions of wood, water, heat and stress during drying. The purpose of this chapter is to provide the basic terms of wood drying, the general principles of dielectric heating and vacuum drying and a review of the limited literature on timber R F / V drying. Modeling efforts on convective, dielectric and vacuum drying are also included briefly. Finally, the primary heat and mass transfer mechanisms are discussed to support the model development following in later chapters. 2.2 Structure of wood In order to discuss the wood structure, a few basic terms concerning the classifications of materials must be defined, such as capillary porous and hygroscopic material. Wood can be treated as a capillary porous material as far as its structure is concerned. A capillary porous material is defined as being any collection of organic material that 9 contains an internal void structure, consisting of a series of interconnected channels of capillary size. Under the influence of an external force it is possible that fluids can migrate through that porous material by capillarity (capillary forces). Organic materials can be divided into non-hygroscopic, partially hygroscopic and hygroscopic which exhibit an affinity towards polar molecules. Complex cellular materials such as wood and foodstuffs are hygroscopic. These types of biological materials have a complicated internal structure, which often is dimensionally unstable during the removal of water. The primary concern in this section is to consider the wood anatomical features relating to drying. In this study the focus is on softwoods (gymnosperms), which have a much greater anatomical uniformity than those of hardwoods (angiosperms). A typical softwood structure is shown in Figure 2.1. There are two distinct regions in a log cross section. The outer region with a higher moisture content is called the sapwood, and the inner region with a lower moisture content is called the heartwood. The sapwood of softwood species is usually richer in moisture content than heartwood and the permeability is higher for sapwood than heartwood such that water evaporates from the sapwood quite rapidly. Where sapwood and heartwood appear in the same timber, the difference in the speed of drying can result in uneven shrinkage creating defects like splitting. Each growing season the tree forms a new increment, which separates the bark from the increment formed in the previous season. The growth that results in the spring is termed earlywood or springwood while that produced later on in the season is known as latewood or summerwood. Like sapwood and heartwood, the properties of earlywood are different than those of latewood due to differences in geometric structure and extractive content. 10 Figure 2.1 Typical softwood structure showing three directional axes and cross section o f wood (Rosen 1987). If we look at wood from the microscopic point of view, we can see that it is a highly porous and an extremely non-homogeneous material. A schematic of softwood morphology is shown in Figure 2.1 (b). Two types of cells are present in all softwoods: longitudinal tracheids, which constitute 90 ~ 94 % of the volume of softwoods, and ray parenchyma cells. The typical tracheid dimensions for species are 3 ~ 5 mm in length and 35 -40 Lim in width, while some western Canadian softwoods have tracheids half as long. Tracheids have overlapping ends, which communicate with each other through small apertures known as 11 bordered pits (Figure 2.2). It is clear from Figure 2.2 that the latewood tracheids have much thicker cell walls, along with fewer and smaller pit pairs. Although these pits are distributed along the entire length of the tracheids, they are more frequent at the ends. Figure 2.2 Radial surfaces o f earlywood and latewood tracheids (Siau 1995). A bordered pit typically found in most species is diagrammed in Figure 2.3, along with representative dimensions (Spolek 1981). As can be seen, a pit aperture opensfromthe tracheid cavity on each side of the pit. Centrally, the pit membrane has a thickened, impermeable center called torus spans the pit chamber. The membrane (marco) consists of many cellulose strands that project radially from the torus to the cell wall. The openings between these strands are typically between 0.02 ~ 4 u.m (Siau 1995). Furthermore during drying, as air takes the place of free water, a large percentage of the pit membranes are aspirated and become an obstacle to gaseous movement. Sapwood is almost always more 12 permeable than heartwood because of the effect of pit aspiration or encrustation with extractives in the latter. Also, latewood is more permeable than earlywood because of the more rigid structure of the pit membranes, which renders them more resistant to the capillary forces causing aspiration during drying. Pit Chamber Pit Aperature Torus Pit Membrane Figure 2.3 Bordered pit with typical dimensions (Spolek 1981). The mechanistic models of sapwood structure developed by Plumb et al. (1985) are illustrated in Figure 2.4. In there, the longitudinal cells are assumed to have an approximately square cross section. Since nearly all of the pits are on radial surfaces, most of the fluid transport between tracheids is in the tangential direction. Ray cells are not included in the model because they occupy a relatively small fraction of the volume of softwoods. Their contribution to the overall flow of fluids is of secondary importance and therefore can be neglected. The radial model also incorporates square longitudinal cells tapered at the end, but 13 includes arrays of smaller, square ray cells. On the other hand, the longitudinal permeability of softwoods is much greater than the transverse permeability. This is because in the longitudinal direction there are many fewer pitted cross walls of high resistance as compared to the transverse per unit length. The tangential permeability is close to the radial permeability. An adequate model would take into account all three directions of transfer. (a) (b) Figure 2.4 Mechanistic models of softwood structure: (a) tangential transport; (b) radial transport (Plumb etal. 1985). 14 2.3 Permeability, bound water diffusion, equilibrium moisture content and sorption isotherms The two major modes for the transport of fluids through wood are diffusion and bulk flow (Siau 1995). The latter occurs through the interconnected voids of the wood structure under the influence of a capillary or static pressure gradient. There are two kinds of diffusion, namely, bound water diffusion which occurs within the cell walls of wood,, and intergas diffusion consisting of the transfer of gases or water vapor through the lumens and interconnected pit openings. The magnitude of bulk flow through wood is determined by its permeability. Permeability is a measure of the ease with which fluids move through a porous solid under the influence of a pressure gradient. Permeability can only exist if the void spaces are interconnected by openings such as an open pit structure between the tracheid lumens of a softwood. If these pit openings are occluded or encrusted, or if the pit membranes are in the aspirated position, the wood will have a very low permeability. The permeability level depends on the structure of the porous medium and the viscosity of the fluid that is transported. The product of the permeability and the viscosity gives the specific permeability, which is only dependent on the porous structure of the medium. Diffusion is a molecular mass flow resulting from a gradient of concentration of the diffusing substance. Below the fiber saturation point (FSP) bound water diffusion is considered the predominant mechanism for transport of moisture. The coefficient describing this molecular bound water motion in wood depends highly on the direction of flow and the conditions of temperature and moisture concentration. Literature about theoretical and 15 experimental values for different species on both the bound water diffusion coefficient and the permeability can be found in Siau (1995). Equilibrium moisture content (EMC or M ) is the moisture at which wood neither e gains nor loses moisture when surrounded by air at a given temperature and relative humidity. The E M C is the minimum moisture content to which the wood can be dried for the specified air humidity and temperature. During drying, the moisture content slowly decreases until it reaches the equilibrium value and then it remains constant at this value. The most important factor affecting the E M C of wood is the relative humidity (H) or relative vapor pressure (h) to which the wood is exposed (Skaar 1972). The graphical representation of the moisture content as a function of relative humidity at a constant temperature is called a sorption isotherm. Kadita (1960), Stamm (1964), Skaar (1988) and Siau (1995) have reviewed sorption from the molecular standpoint and concluded that the sigmoid shape of the type II sorption isotherm characterizes all woods. Depending on whether moisture is absorbed or desorbed, this isotherm may be called an adsorption or desorption, respectively, as shown in Figure 2.5. Since there are many paths along which moisture can migrate, either as evaporation along a desorption path or as condensation along a sorption path, the phenomenon of hysteresis is often apparent during the drying process. In drying operations, desorption isotherms are more often used. Usually, the vapor pressure in the cell is assumed to be saturated as long as free water is present in the cell. When the moisture content is below the FSP and the cell walls are not saturated with the bound water, the partial vapor pressure p (Pa) in the cell becomes v unsaturated. To model the sorption isotherm, a functional correlation dependent on moisture content or saturation and temperature is often used. The relative humidity is given by 16 h=p / v (2.1) pv S where p is the saturated vapor pressure (Pa). sv 32 24 M % 16 100 H,% Figure 2.5 Sorption isotherms of wood, IN.DES = initial desorption, SEC.DES = secondary desorption, ADS = adsorption (Siau 1995). 2.4 Wood drying Wood is a hygroscopic material. Water transport among its cells is a basic requirement for the growth of a living tree, as it is for all living organisms. The moisture of wood in living trees varies from 30 to 300%, depending mainly on species (Tsoumis 1991). In relation to the conditions of the surrounding air, wood loses or gains moisture to reach* a. state of equilibrium. Nearly all the physical properties of wood are influenced by its moisture 17 content. Therefore, some knowledge of wood-moisture relations is helpful in understanding what happens to wood during drying. Wood has a cellular structure and the cells of various shapes, sizes and arrangements are composed mainly of cellulose, hemicellulose, and lignin. The moisture in wood may be present in three principal forms: free water, which is situated in the voids in liquid form within the wood; bound water, which is dissolved or adsorbed in the hygroscopic cell wall, and water vapor, which, together with air, occupies that part of the cell lumen not occupied by free water. Free water is held primarily by capillary forces and is relatively easy to move. Bound water is attached to the cellulose and hemicellulose molecules with much stronger molecular forces, termed hydrogen bonds, and requires more energy to move (activation) or evaporate (vaporization). The gas phase is defined as being a binary mixture of air and water vapor. Some authors in the past (Quintard and Puiggali 1986) have ignored the amount of water vapor present in the solid matrix during drying, assuming it to be negligible in comparison to the liquid. However, a more accurate criterion induces the terms involving the water vapor throughout the entire analysis (Turner 1991). This can be achieved by assuming that the vapor density can be related to the vapor pressure via the ideal gas law. The FSP is defined as the moisture content corresponding to saturation of the cell wall with no free water in the voids. At this point the wood usually has a moisture content of about 30%, although it can vary from 24% to over 30%, depending on the species (Siau 1995). The FSP is a very significant point in the drying of wood because more energy is required to evaporate water from a cell wall than from the cell cavity and large changes in physical properties of wood begin to take place below this moisture content level. 18 The simplest method of drying wood is air-drying. The main advantage of this method is the low investment. One major disadvantage is the deterioration that can occur because the temperature, the air velocity and the relative humidity are not controlled. Other disadvantages are drying times are dependent upon the weather and the inability to dry lumber for certain uses. Shed-fan air-drying gives better quality lumber and shorter drying times that offset the additional cost for the shed and the electricity to drive the fans. Most of the literature on wood drying deals with the conventional kiln drying which is the most widely used method when the temperature, the relative humidity and the air velocity are controlled. This is because the final product has less degrade compared to the previously mentioned methods. Another reason is that although the energy demands are high, the steam generated with wood waste can be cheaper than electricity. Dehumidifier kilns are another option for wood drying. They require lower initial investment, they have lower energy requirements and they are easier to operate. The drawbacks of this method are the slower drying, especially below 12%, the difficulty to condition the lumber since steam is not available, and the cost of the electricity, which can be higher than steam. Superheated steam vacuum drying is another method that has gained some respect recently. The main principles of heat and mass transfer are similar to those in conventional kiln drying. 2.5 Dielectric heating The ability of high frequency electric fields to heat electrically non-conducting materials, usually referred to as dielectric heating, has been known for many years (Biryukov 1968). High frequency energy has two unique and valuable aspects, namely selective heating 19 of water, volumetric heat transfer which can be regarded as another method of heat transfer in additional to the three understood techniques of conduction, convection and radiation. In general the term "dielectric heating" can be applied to all electromagnetic frequencies up to and including at least the infrared spectrum. However, it appears that most references to dielectric drying in the literature are confined to radio and microwave frequencies. The locations of the two bands are shown in Figure 2.6, with microwaves having higher frequencies than radio frequencies, though the distinction between the two frequency bands is often blurred (Stmmillo and Kudra, 1986). Nevertheless, RF and microwave dielectric heating can be distinguished by the technology that is utilized to produce the required high frequency electric fields. RF heating systems use high power electrical valves, transmission lines and applicators in the form of capacitors, whereas microwave systems are based on magnetrons, waveguides and resonant (or non-resonant) cavities (Jones 1992, Jones and Rowley 1996). All materials are conventionally divided in three electric groups: conductors, dielectrics, and semiconductors. The dielectrics differ from the conductors by their low specific conductivity (Torgovnikov 1993). Dielectrics like wood are heated in the electric field of a capacitor. A critical factor is that the high frequency waves and their energy are not forms of softwood heat, but rather forms of energy that are manifested as heat through their interactions with materials. It is as if they cause materials to heat themselves. The following are the four main types of polarization, which take place in moist heterogeneous dielectrics that might be summarized as the polarization of wood. Firstly, electronic polarization arises as a result of the shift of the electron orbits relative to the positively charged nucleus under the influence of an external electric field. Secondly, 20 induced dipole moment known as ionic (atomic) polarization, which arises as a result of an elastic displacement of atoms in the molecules as well as because of mutual displacement of charged ions of opposite signs in substances with ionic bonds. Thirdly, dipole (orientation) polarization that consists of rotation of dipolar molecules in the direction of external electric field. Finally, a type of polarization that affects the material as a whole at a macroscopic scale and is due to the few free-charge carriers, which can migrate to the electrodes when an electric field is applied. If the field is alternating, then the backward and forward migration is continuous. This process, called interfacial (structural) polarization also gives rise to a heating effect. 10" 10" 11 10~ 9 10" 7 5 10" 10"' 3 10 10 3 W a v e l e n g t h (cm) [ j Radio 10* (Microwave] W (infrared;] (Vsibfa] 1 10 4 [Ultraviolet] 10* [ /ray) iO 4 (Gamma Ray] Iff* 1Qf tt ® anilcimis Figure 2.6 Humans Honey Hoc Withead Praoroans Atotecufe* Atoms - Atomic Nuclei Electromagnetic spectrum. Not all kinds of polarization contribute equally to the general polarization of wood. Since wood is characterized by the presence of relatively few charge carriers (ions), but a 21 large number of permanent dipoles (water, sorption sites), dipole and interfacial types of polarization play the main role in the polarization of wood. Thus, the application of a voltage gradient will result in only a very small current. However, when wood is placed between the electrodes of a plane capacitor to which an oscillating potential difference is applied, an electric field permeates the whole volume causing the ions and dipoles present to oscillate around their equilibrium positions. The energy absorbed in carrying out these displacements, is dissipated as heat and if this energy is large, the technique is viable for industrial heating processes. The dielectric properties of wood are critical parameters when analyzing the effectiveness of dielectric heating. During the last fifty years, scientists from various countries made considerable effort and progress in the understanding of the dielectric properties of different materials and their behavior in an electric field. The relative dielectric constant or relative permittivity s' of a medium is defined as r the ratio of the absolute permittivity s ' of the medium to the permittivity of free space, e e ;=e'/e o o (2.2) where 8 =8.85*10" F/m, is the permittivity offreespace. o The relative dielectric constant of wood is a measure of the extent to which the electric charge distribution in wood can be distorted or polarized by the application of an electric field. When wood is placed within an electric field (E), the existing electric charges such as water molecules and hydroxyl ions shift within their range of movement. Within wood, the shift does not create any net electrical charge, but at the boundaries this displacement current creates a net surface charge. The surface charge generates an electric field E ' proportional to E, which opposes the applied voltage and reduces the electric field 22 within wood by a factor of to E/s' . This factor e' , also called relative permittivity or r t relative dielectric constant, typically ranges between 1 and 10, but can be as high as 80, such in the case of water. The loss factor is introduced via such a concept as the complex dielectric constant 8 * defined as: e* = e ; - j e " (2.3) or complex dielectric constant, 8 * r 8 / = 8 * / 8 = e; -j o = eKi-jtanS) (2.4) Such components of Eq. 2.4 as the relative dielectric constant, s' , and loss tangent or r dissipation factor, tan 5, are the principal dielectric parameters of wood. In some cases it is convenient to use the loss factor, s " = e' tan 8 . r The loss tangent tan 6 is the ratio of energy loss to the total energy used to establish polarization. The value of the loss factor determines the amount of power absorbed within the wood. In general, the dielectric properties can be affected by several parameters. A brief discussion on some of the more important parameters such as moisture content, temperature, frequency, grain orientation, sapwood/heartwood and tree species is presented here. For a more complete discussion, the reader is referred to Torgovnikov (1993). Dependence on moisture content The most important parameter affecting the dielectric properties is the moisture content. Water is highly dipolar molecule with a dielectric constant of about 80, which is 20 23 times larger than that of dry cell wall of the wood in the same direction. The dielectric constant and loss factor of wood generally increases as the moisture content increases. The values for the dielectric constant of wood start under 5 for dry wood (less than 10% moisture content) rising up to 20 or higher for wet wood. The energy absorption is low when the moisture content is below the FSP and dielectric properties have values fairly close to those of the dry cell wall of wood. Above the FSP, the dielectric properties are much higher and have values that tend towards that of the free water. Hence the dielectric loss will decrease as the wood dries and consequently the effectiveness of dielectric heating or drying diminishes as the product dries out. The large increase in the loss factor with moisture content can however be used with great effect to produce a moisture leveling phenomenon during drying. This effect arises because the electromagnetic energy will selectively or preferentially dry the wettest regions of wood with greater intensity. Dependence on temperature There is a strong correlation between temperature and complex dielectric of wood at high moisture contents. At low moisture contents, the temperature has a relatively small impact on wood dielectric properties. However, the dielectric loss factor of wood may still increase with temperature at low moisture contents. This may lead to thermal runaway, which in turn causes the wood to burn internally if heating continues once the wood is dried. 24 Dependence on frequency The loss tangent does not change significantly for high frequency power input between the range of 1 MHz and 1 GHz, which implies that the ability of wood to absorb high frequency power is not significantly affected by frequency in the range of interest for dielectric heating (Torgovnikov 1993). Also, since this work is restricted to a small bandwidth of the radio frequency, this effect will not be analyzed. Dependence of grain orientation, sapwood/heartwood and tree species The dielectric properties of wood vary for different orientations of the wood grain. Wood anisotropy can be characterized by cylindrical coordinates, namely: longitudinal L, tangential T and radial R, as shown in Figure 2.1. For all wood species, the relative dielectric constant, e', is higher in the longitudinal direction than that in the radial or tangential direction. Between the radial and tangential directions there is practically no difference. If the electric field is along the grain, the water molecules are easily oriented in the longitudinal direction because this is also the natural orientation of the molecular structure of wood. Water molecules and hydroxyl groups possess more freedom in the direction along the grain rather than across it. The degree of polarization is higher and so the corresponding dielectric constant is also higher. The loss tangent has a different behavior for the longitudinal direction in comparison with the radial and tangential directions; especially between the initial (high) and the mid-range of moisture contents. The loss tangent for the longitudinal direction shows a maximum at mid-range moisture contents and drops at higher moisture contents. Torgovnikov (1993) explained this phenomenon as a result of an increase in freedom of rotation of polar molecules from the cell wall, thus having an important contribution to the 25 dielectric properties above the FSP. All species measured at complete saturation show a higher loss factor in the longitudinal versus the radial direction. Experimental information on the dielectric properties of the sapwood and heartwood regions for different species reveals inconsistent behavior (Zwick 1995). For some species (e.g., western hemlock) there is little difference in the loss factor between the sapwood and heartwood. Other species (e.g., Douglas-Fir, sitka spruce) exhibit a higher loss factor for the sapwood zone than heartwood zone, especially at lower frequencies and higher temperatures. One explanation for the above could be the higher ion content of water in the sapwood region. Generally, it could be stated that there is a difference between the dielectric properties of different wood species, which with higher moisture contents become more pronounced. Different wood density implies that there is different wood cell structure and wood permeability. However, the difference between the dielectric constants of different species is almost negligible. 2.6 Dielectric heating kinetics Kudra et al. (1990) reviewed the literature and concluded that the principal mechanisms of moisture removal for dielectric heating are basically similar to the ones governing the conventional methods. Nevertheless, the intensity of dielectric heating environment may evoke some special phenomena. Due to the internal heat caused by the absorption of the high frequencies, it is possible to raise the temperature of the material up to the boiling point of water. Intensive water evaporation takes place inside the wood, which in turn results in high internal pressure. This becomes the main driving force for transfer. It 26 causes moisture movement to the wood surface where the lower temperature and lower vapor pressure exist. Therefore, dielectric heating may completely change the moisture distribution in wood because of the complex dependence of dielectric properties and physical-chemical parameters such as diffusivity on temperature and moisture content. In conjunction with the increase in temperature and pressure, the conventional moisture profiles may become leveled, something that was observed by Avramidis and Liu (1994). Kudra et al. (1990) identified the following four periods during the dielectric heating process: (1) The period of preliminary heating in which the temperature of wood increases to the boiling point of water. (2) The external flow resistance and the input power determine the period of vapor pressure evolution inside the wood. (3) The internal vapor flow resistance and the power absorption determine the period of the constant drying rate. (4) The period of falling drying rate is because of the reduction of moisture content. However, the above stated idealized drying kinetics is only suitable for dielectric heating or combined dielectric heating with hot air. 2.7 Principles of vacuum drying Vacuum drying of lumber is not a new idea. It has been considered since the turn of the century (Chen 1997). During the early 1970's, the economic outlook for vacuum drying became more favorable; largely because of the increased costs of holding large lumber inventories during long drying processes. This is particularly true in the drying of thick, 27 refractory, high value species, which can be safely dried in a vacuum kiln in a small fraction of the time required in a conventional kiln. In conventional kiln drying, wood is exposed to warm and dry air, thus the moisture inside the wood will have the tendency to diffuse to the surface and evaporate. The driving potential for this moisture movement is generally considered to be the vapor pressure difference between the surface and the drying air. In order to reduce the drying time without decreasing the quality of the dried wood, the drying conditions must be such that the temperature of the wood is above the boiling point of water. Such conditions ensure that an overpressure exists within the wood, which implies that a pressure gradient drives the moisture (liquid and/or vapor) towards the exchange surfaces. This is exactly the aim of convective drying at high temperature (moist air or superheated steam), a possible aim of contact drying or drying with high frequency field, and vacuum drying. The principal attraction of vacuum drying is that the lowered boiling temperature of water in a partial vacuum allows free water to be vaporized and removed at temperatures below 100 °C almost as fast as it can at high-temperature drying at above 100 °C at atmospheric pressure. Drying rate is therefore increased without the dangers of defects that would surely develop in some species during drying above 100 °C. Vacuum drying is analogous to high-temperature drying at low temperature. It allows faster drying and provides a good quality of specific high valued timber species (the most representative being oak), which are known to be difficult to dry. A graph of the saturation vapor pressure versus the temperature is presented in Figure 2.7. Most of the literature on vacuum drying is for continuous contact (hot plates) drying. Very limited amount exist for either superheated vacuum drying in cycles or dielectric 28 vacuum drying. A very recent thesis by Chen (1997) provides a very good literature reference for contact vacuum continuous drying and in cycles drying. 110 0 10 20 30 40 50 60 70 80 90 100 T(C) Figure 2.7 Relationship between saturated vapor pressure of water and temperature. 2.8 RF/V drying The demand for drying very thick lumber has been clearly expressed by the wood industries. A number of advantages with RF/V drying of wood have already been reported (Avramidis and Liu 1994, Avramidis et al. 1996, Avramidis et al. 1994). Energy is transferred directly to the water molecules distributed throughout the wood so that the heating becomes volumetric and moisture leveling can be achieved because the loss factor of wood increases with its moisture content. The internal stresses and the relevant degrade are reduced due to these lower moisture gradients. The rate of drying is significantly increased since the driving forces of drying, namely, pressure and temperature gradients are pointing in the same direction (from inside towards outside), thus resulting in shorter drying times. The influence of vacuum is also significant since high temperatures are not required for vaporization and moisture removal. As a result, lower internal stresses develop and much lower degradation of wood is being observed. No stickers are required in R F / V drying reducing the handling cost. Low energy consumptions and drying costs are two additional advantages compared to conventional kiln drying, as are product quality and the lack of surface discoloration due to the absence of oxygen. Moreover, the R F / V technology is environmentally friendly since the effluent is recovered in a closed-loop system. Finally, R F / V drying allows for batch drying due to the greater depth of field penetration and the absence of standing waves, which could result in "cold spots" as has frequently been observed in microwave drying. The number of publications on RF/V drying of wood is very limited. They basically focus on the quality of the dried specimen and analyze the economic viability of the method. Kanagawa (1989) studied the resin distribution in Douglas fir dried by R F / V drying. He concludes that the resin portion on the surface is much lower compared to conventional kiln drying methods. Rozsa and Avramidis (1996) dried eucalypt timbers that are usually dried slowly with conventional methods, minimum 8-12 weeks, and are prone to collapse. Drying with RF/V reduced the drying time to less than 200 hours and in the final run the drying defects were significantly less than those which would have been expected in conventional drying. 30 Hayashi et al. (1995) reported on the experimental evidence of the importance of the permeability in RF/V drying. They concluded that regardless of the initial moisture content, pretreated specimen with local steam explosion dried faster with RF/V drying. On the contrary this does not happen with conventional kiln drying for low initial moisture content specimen. Smith et al. (1994) analyzed energy, quality and value issues for the RF/V drying of red oak. They dried 200 mm by 100 mm squares from 85% to 8% average moisture content in less than 60 hours with little moisture variation and residual stress comparable to conventional dried wood. They finally concluded that higher-grade logs could be more profitably processed than lower grade logs using RF/V drying. Havener (1990) examined moisture content variability and stress development drying red oak in two different industrial size RF/V kilns. Insignificant differences were found for the stress levels between RF/V and conventional dried squares. Also the difference in the final moisture content never exceeded 2%. Trofatter et al. (1986) published previously similar results. Lee et al. (1995) investigated the drying defects and shrinkages of walnut during RF/V drying and RF/V-to-press drying. They suggest that it is desirable to dry in RF/V dryer with mechanical pressure system to get tree disks without heart checks and also V-cracks. Avramidis and Zwick (1992) explored the RF/V drying of three British Columbia coastal softwoods, namely, western hemlock, western red cedar and Douglas-fir. They found that the drying is fast and economical particularly with lumber thickness over 80 mm. Avramidis and Liu (1994) dried thick (254 mm) western hemlock and western red cedar using RF/V. The quality of the dried specimen was exceptional with no drying stresses, 31 internal or external checks and surface discoloration. The drying lasted less than 33 hours in all cases. Raising the voltages with time resulted in shorter drying times and higher drying rates. Avramidis et al. (1994) and Liu et al. (1994) reported similar results. Avramidis et al. (1996) examined the spatial moisture distributions in the longitudinal and transverse directions as a function of time for different dimensions of hemlock and cedar. They concluded that both longitudinal and transverse moisture transfer contribute to the overall flow within wood since the shorter pieces dried faster than the longer ones. They also did not observe any discontinuities and abrupt drying front changes. Zhang et al. (1997) reported similar results. Finally Avramidis (1999) discussed the basics of RF/V drying, and the recent developments on the latest generation of RF/V dryer technology. The 4 generation systems th with sophisticated loading and pressure systems; efficient RF generators and intelligent matching networks are capable of monitoring the charge's moisture content for accurate drying. The result is application of kiln schedules that can dry thick timbers within two to three days (versus months with conventional drying techniques), with limited degrade and very low energy consumption (1.4kWh/kg of water removed). Furthermore, this technology has allowed the industry to access fibre, such as trim-ends and shorts which before were converted to low value chips, so it can dry and use to produce high quality lumber by finger joining. 32 2.9 Modeling of wood drying Modeling of wood drying is a challenging problem due to its complex structure that gives rise to a highly anisotropic behavior. The first model on drying of solids appeared in 1929 (Sherwood, 1929) that accounted only for the diffusion transfer mechanism. The inability of a simple diffusion model to give adequate predictions in many cases led to the development of empirical models that could give a better fit to the data. Their main disadvantage was the lack of theoretical background, so that their applicability to ranges out of those covered by the experimental data led to prediction failure in most cases. The most recently developed models are highly sophisticated and they include all possible mechanisms of heat and mass transfer that could occur during drying. This is considered to be the proper approach to follow in order to develop a model for a complicated process such as RF/V drying. A more extensive review on models of wood drying developed through the years can be found in Rosen (1987), Simpson (1983, 1984), and Kamke and Vanek(1992). The ultimate purpose in any modeling procedure is not just a good description of the experimental data, but the equations under consideration should be capable of describing all participating physical phenomena and of quantifying their magnitude for different drying scenarios properly so that extensions to different operating conditions could be realistic. A classification of drying models for porous solids and a very good description of all possible transfer mechanisms can be found in a review paper (Waananen et al. 1993). The very important topic of controlling process resistances is also discussed and all possible internal and external transfer mechanisms and driving forces are analyzed. 33 A problem related to wood drying simulations is usually the approximations made to the complete models and the question of their validity. Data for the heat and mass transfer coefficients are not always available and therefore, additional assumptions are required for proper evaluation of all simplifications. Experiments are always useful to uncouple the complicated phenomena and usually provide the correct order of magnitude of the properties under investigation. The problem of wood drying simulations is too complicated and we still cannot determine fast and in detail important information such as the initial moisture profile with non-destructive methods. Even the FSP is almost always considered to be 30% and cannot be definitely measured individually (Siau 1995). Furthermore, liquid or vapor transfer cannot be distinguished in a real drying situation since there is no available technology to do so. Though the problem of scaling is solved by definition through simulations, it is not the same in experiments, where many factors may play an important role and could lead to misleading conclusions. The determination of the z" with the Q-method, where edge effects contribute to errors on the results due to the small size samples, can be considered as a representative example of experimentally derived parameters that deviate from the true values (Zhou and Avramidis 1999). In a recent paper by Perre (1999), a good description on how to develop a relevant model for wood drying is presented. The question of the proper number of independent variables and space dimensions is addressed. Addition of spatial dimensions and parameters provides more detailed information about the drying procedure and adds flexibility in the calculated results according to the assumptions. On the other hand, these detailed models lose part of their simplicity and become more time consuming. Thanks to the continuous increase of computing speed, this will not be a limiting factor in the future. 34 Another question usually posed when developing a drying model is related to whether or not a one-dimensional (1-D) model is justified over a two-dimensional (2-D) or even a three-dimensional (3-D) one. When modeling a new process for the first time, it always seems prudent to start with a simple I-D model. Its capabilities and limitations have to be judged well before its extension to more dimensions is attempted. Though the development of a general 3-D code is always thefinalgoal, each specific case has to be handled with its own assumptions and simplifications before any validation through experimental work is completed in detail. A limited number of papers exist in modeling vacuum drying and/or dielectric drying (Defo et al. 1999, Turner and Jolly 1991, Chen 1997). These cases are different from RF/V drying, either because the heat is transferred externally through hot plates in vacuum drying, or in the case of dielectric heating, it is combined with convective drying. Dielectric drying without external hot air supply is much closer in heat and mass transfer concepts with RF/V drying, though coupling with vacuum still imposes some important differences. Models for such a case already exist in the literature (Chen and Schmidt 1990, Constant et al. 1996). All the above information could serve as a basis in developing a new model for the process of RF/V drying of wood. The conceptual background exists, but the proper justification of any assumptions and further refinement of a model is a task that has to be tackled very carefully. 35 Chapter 3: Materials and Methods 3.1 Permeability experiments The cylindrical permeability specimens were cut serially from all-sapwood and allheartwood western hemlock (Tsuga helerophylla) and western red cedar (Thuja plicata) timbers. A number of specimens were prepared to examine individually the longitudinal, the tangential and the radial direction. They were 1 2 0 mm, 3 0 mm and 3 0 mm, in the longitudinal, radial and tangential direction, respectively, and 2 5 mm in diameter. They were cut from green, straight-grained and detect-free wood and were conditioned at constant temperature and relative humidity ( 2 0 ° C ) approximately 1 0 % . ( 5 0 % ) to an equilibrium moisture content Then, they were slowly dried in a vacuum oven at 6 0 ° C ( M s ) of for one week to approximately 0 % M e . Subsequently, the cylindrical surfaces of the specimens were coated with epoxy resin to ensure one-directional flow through the ends. They were then stored in a desiccator containing drierite to ensure that no moisture was re-adsorbed. Permeability measurements were carried out with a steady-state flow method apparatus, the schematic diagram of which is illustrated in Figure 3 . 1 . The air is drawn through a flow-meter, the specimen, and two needle valves by a vacuum pump. The pressure differential (AP) is monitored by the center differential mercury manometer and the flow rate (Q) is controlled by a volumetric valve. The closed manometer on the vacuum side (Pi) is used to simplify the measurement by not only providing the barometric pressure (P tm) before a flow measurements, but also by eliminating the need to use the barometric pressure for the determination of the average pressure (P) within each specimen. In this case, Pcan be calculated by the sum of direct readings from the closed manometer (AP,) and the half value 36 AP of the pressure differential (AP= P2 - Pi); i.e. P = AP, + — . An open mercury manometer on the high pressure side (or air side), P2, is included to be used only for the examination of possible air leaks between the stainless cylinder and rubber tubing, that is, the pressure on the air side, P2, which can be obtained from the reading (AP ) of the open mercury manometer 2 (P = P 2 atm - AP ), should be equal to the sum of the direct reading from the closed 2 manometer on the vacuum side and the pressure differential ( AP, + AP). D V VM M V A SH f S t 2 SH MM M VP R D: Drierite; F: Flowmeter; MM: Differential Mercury Manometer; Mi: Closed Mercury Manometer; M : Open Mercury Manometer; R: Vacuum Reservoir; S: Specimen; SH: Specimen holder; V: NeedleValves; W : Volumetric Valve; VP: Vacuum Pump 2 Figure 3.1 Schematic design of the permeability measuring apparatus. 37 The specimen holder consists of two stainless steel cylinders covered by high vacuum thick-walled rubber tubing and a set of hose clamps. The end surfaces of each specimen were trimmed with a razor blade to obtain a smooth surface free of wood dust and foreign matter. Then, it was inserted in the center of the tubing and three clamps were used to prevent air leaks between the tubing wall and the specimen. Trial measurements were often conducted on dummy (epoxy end-coated) specimens to assure that no leaks existed in the permeability assembly. A total of thirty-two longitudinal direction specimens were measured, eight for each case of hemlock and cedar, both sapwood and heartwood and a total of thirty were measured for the transverse directions. A picture of the permeability apparatus is given in Figure 3.2. 3.2 Diffusion coefficients and sorption isotherm experiments Desorption curves were determined by clear and defect-free all-sapwood and allheartwood hemlock and cedar specimens. They were prepared for longitudinal, radial, and tangential moisture movement studies and were crosscut serially. Their dimensions were 50x50x10 mm for longitudinal and 100x50x5 mm for both tangential and radial directions, respectively. A thickness of 10 mm for the longitudinal axis was chosen since the longitudinal diffusion is fast, whereas a thickness of 5 mm for the radial and the tangential axes was chosen, since the diffusion in these two directions is much slower. Diffusion coefficient and sorption isotherm measurements were carried out on six specimen replicas of every type of wood at three temperatures, namely, 30, 50 and 70°C. All specimens were side-coated with epoxy to eliminate side desorption and they were initially oven-dried at 103±2°C. 38 Figure 3.2 A picture of the permeability apparatus in the UBC Wood Physics Lab. The specimens were firstly exposed to a 95% relative humidity. When their weight did not show any change after successive measurements of four to seven days, equilibrium was assumed. Later, the specimens were exposed to successive relative humidity levels in desorption mode in two conditioning chambers (Parameter Generation & Control 4-PC and 9-PC, Figure 3.3). The temperature was controlled to within ±0.2°C, the relative humidity to within ±0.5% and the air velocity was 2.5 m/s, approximately. Successive weightings were made after the initial exposure to the test conditions on a Sartorius type A200s electronic 39 balance with an accuracy of 0.0 lmg. When the specimens reached a weight where no change was observed for one to three weeks, they were assumed to be at equilibrium. Consequently, M e of these two wood species were obtained thus, allowing the derivation of the sorption isotherms. Once a desorption step was completed, the humidity of the chamber was changed to the next level and the same process was repeated. Figure 3.3 A picture of the two conditioning chambers in the U B C Wood Physics Lab. 3.3 RF/V drying experiments The drying experiments were carried out in an approximately 0.28 m lumber holding 3 capacity laboratory RF/V dryer. The drying chamber consists of a 2.75 m long and 0.76 m 40 diameter carbon steel cylinder that had removable bolted caps on both ends to facilitate loading and unloading of the specimens. Both caps were fitted with o-rings, which were coated with silicon grease for the elimination of possible air leaks. One cap was also fitted with observation windows. The internal surfaces of the cylinder were coated with epoxy paint. Two 2.24 m by 0.3 m by 0.0127 m in thickness aluminum electrode plates, are located horizontally in the center of the cylinder. The lower electrode was also used to support the lumber load. Polyethylene bolts support the top electrode, whereas the bottom one is supported by polyethylene bolts when an oscillator was the RF generator, and by metal bolts when an amplifier was the RF generator. Raising or lowering the upper electrode plate could adjust the vertical space between the plates in order to accommodate lumber loads of different height. The maximum lumber load height can be 0.4 m. A small air gap could be maintained between the top surface of the lumber load and the upper electrode for electrical load stabilization. The same stability resulted when polyethylene plates were introduced between the metal plates and the specimen. The ambient pressure in the cylinder was initially controlled by a liquid ring vacuum pump with an air injector attached to the main input line. A rotary vane pump replaced this pump recently. The pressure could be lowered with either of the pumps to an absolute value of 2.7kPa. The vapor produced during drying is condensed by passing over cold copper coils of a heat exchanger located between the cylinder and the vacuum pump. Cooling of the coils and sealing of the vacuum pump was achieved by circulating regular tap water. The condensed water was collected in a steel tank under vacuum, where the height and therefore the volume of the accumulated water are monitored with a differential pressure transducer. At the same time, any condensation accumulating at the bottom of the drying chamber is also 41 transferred to the collection tank by a pump located underneath the main cylinder. This way, the amount of water extracted from the lumber load, can be monitored with time, and therefore, the drying curve of each run can be determined. A complete schematic design of the RF/V dryer is given in Figure 3.4. Figure 3.4. Schematic diagram of the laboratory RF/V dryer. An oscillator or an amplifier provided the electromagnetic radiation responsible for the thermal energy generated within the lumber load. The oscillator is an air-cooled, lOkW, radio-frequency generator, which was operating at a fixed frequency of 13.56 MHz. It can provide a maximum electrode voltage of 5kV at 2 amperes. This generator was connected to both electrode plates by a set of copper leads. Adjustments of the electrode voltage were done manually. The electrode assembly provided a homogeneously distributed electric field 42 through the wood. The amplifier is an air-cooled, lkW, RF generator, which was operating at a fixed frequency of 6.78 MHz. This generator was connected only to the upper electrode plate by a set of copper leads. The upper plate was also connected with a system that was providing additional pressure to it so that the plate is always in contact with the upper face of the specimen. The lower plate in this case was serving as the grounded electrode. Adjustments of the electrode voltage or the RF power, in the cases of oscillator and amplifier respectively, were done manually. Instrumentation on the RF/V dryer is connected to a personal computer (PC) through a data acquisition system. The variables that can be recorder in a run are: moisture content change of the lumber load, temperature and pressure at various locations within the lumber load, ambient temperature and pressure within the cylinder, RF electrode voltage and current intensity, ambient pressure in the condensation unit, inlet and outlet temperature of cooling water (condensation unit), and total electrical energy. Figure 3.5 shows the front view of the RF/V dryer. On the left side is the PC for collection of the data. In the middle of the picture, the cylindrical tube is the drying chamber. On the right side of the kiln is the oscillator. On the top of the dryer, the small box on the left is the Luxtron control unit for monitoring the temperatures and the big box on the right is a transformer for the oscillator. On top of the dryer (to the back) is the vacuum pump and above it is the heat exchange unit. The small box on the left of the vacuum pump is the power control for the heat exchange unit. The larger box right below is the power control for the amplifier and right above it there is a very small unit that measures the power input. The metal box right above the center of the kiln contains all the circuits for the matching network. On the very left o ffigure3.6 the amplifier can be seen. In the center o f the side o f the kiln, 43 the point where all the temperature and pressure probes exit the kiln can also be seen in this figure. Figure 3.5 Picture of the front view of the RF/V dryer in the UBC Wood Drying Lab. In figure 3.7 the matching network box is at the bottom on the right side. On its left there is a long tube where vapor is transferred from the RF kiln to the heat exchange unit. Closer views of the vacuum pump and the heat exchanger may also be seen in the same figure. Figure 3.8 is the back view of the RF kiln. The water collection tank can be seen to be right on the left side of the drying kiln. Specimens of green western hemlock (Tsuga heterophylla), and western red cedar {Thuja plicata), 0.25 m by 0.25 m by 2 m in length were dried in a series of experimental runs. Each piece of green timber came at about 5 meters in length from the sawmill and 44 provided end initial moisture content samples, each 30 mm long, and two kiln specimens, each 2 m long. Only one specimen could be placed in the dryer for each run. Figure 3.6 Picture of the side view of the RF/V dryer in the UBC Wood Drying Lab. The specimens were dried to about the same final moisture content of 17% under different voltage levels (oscillator), or maximum core temperature or power density (amplifier) and different ambient pressure levels. Four fiber optic temperature sensors, Luxtron MIA/04 (4m long), each 1.4 mm in diameter were attached to a multichannel Flurotropic thermometer, model # 755. They monitored the temperature rise inside the heated specimens and in the surrounding partial pressure environment (Fig. 3.9). The readings were tested, with ice water and boiling water, before and after the experiments and no drifting was observed. The temperature resolution is 0.1°C on the instrument and 0.2°C on the computer. The range is -200°C to +200°C. The absolute accuracy of the instrument is ± 0.1 °C at the 45 calibration point and ±0.5°C within 50°C of the calibration point. The stability is ±0.3°C per four hours. The temperature displayed on the instrument is an average of 20 consecutive readings and the precision is 0.1°C. The actual accuracy of the temperature measurements is within ±1.0°C. Figure 3.7 Picture of the matching network box, the vacuum pump and the heat exchanger in the UBC Wood Drying Lab. Vapor pressures were measured by teflon fittings tightly attached to the specimens, and connected with 2.5 mm diameter teflon tubes to pressure transducers located outside the dryer. All four probes were tested before, after and between the experiments. No drifting was observed and the accuracy was +2 mmHg. Three different locations inside each specimen were chosen for temperature and pressure monitoring. The first was in the center of the specimen, the second on the central 4 6 longitudinal line at a distance one quarter of the total length from one end of the specimen. The third was close to the center at a distance one quarter of the total width from the lateral surface of the specimen. This way temperature and pressure data could be obtained for both longitudinal and transverse directions. In order to achieve maximum absorbed energy by the specimen, in most cases, no air gap was left between them and the upper electrode plate. Figure 3.8 Picture o f the back view o f the R F / V dryer in the U B C W o o d Drying Lab. Three positions were also selected to measure the shrinking in the direction between the plates and the direction along the width of the plates. The positions were in the center and 200 mm away from the ends of the pieces. The points were initially marked and then measured with Mitutoyo calipers. The accuracy of the measurements was within ± 0.01mm. 47 At the end of each run, the measurements were repeated. Also, the moisture distribution within each specimen was measured by slicing and oven drying sections at various locations along its length. The moisture content was further calculated in the beginning and the end of the tests through weight measurements and dimensions of the samples. The required adjustments were always less than ±0.5%. T T c a a c Figure 3.9 A qw Location of temperature and pressure probes. 48 Chapter 4: Mathematical Formulation and Numerical Solution 4.1 Introduction This chapter presents the derivation of the mathematical model used to predict the heat and mass transfer in wood during RF/V drying. Since green wood contains free water, water vapor, bound water, and the wood matrix itself, wood drying is a multiphase heat and mass transport process. Due to the fact that the moisture transport in different phases is dominated by different mechanisms, the fundamental thermodynamic and fluid mechanic relationships will be used to derive the transport equations. The model accounts for the heterogeneous and anisotropic nature of wood. The local transport properties presented in the model vary with the moisture content and temperature. The model development begins with the governing equations for each phase along with the specific boundary conditions on the interfacial areas. Since a macroscopic, heterogeneous, anisotropic model is more interesting in terms of practical applications, the governing equations will be volume averaged over a representative elementary volume and a single set of governing equations for wood RF/V drying can be obtained. An extra component is also included in the energy equation to account for the rate of dielectric energy absorbed per unit volume of wood. 4.2 Controlling resistances and transport mechanisms during wood drying Before presenting the model, it is necessary to explain the controlling process resistances as well as the external and internal mechanisms of heat and mass transfer in the case of wood RF/V drying. A comparison with convective drying will also be discussed, since this is the most popular drying method today. 49 In convective drying above FSP the controlling resistance is the energy transfer, whereas below FSP is the mass transfer as concluded by Waananen et al. (1993). The drying time required for a slab of thickness "x" to reach a given moisture content is proportional to "x" for external mass control and proportional to "x " for internal diffusion control. In RF/V 2 drying, the energy is generated throughout the volume of the specimen thus, the energy transfer resistance does not apply. This is one of the reasons why RF/V is considered superior to convective drying from the point of view of drying times, especially for thick lumber. Also, due to the presence of vacuum in RF/V drying, the internal mass transfer is highly enhanced due to pressure differences that are created by internal water evaporation. Furthermore, external mass transfer due to vacuum does not apply. As a consequence, the main resistance in RF/V drying is always the internal mass transfer. The intrinsic and relative permeability of each of the different phases therein for different conditions are among the most important factors under consideration in a RF/V drying modeling problem above FSP. Among the several mechanisms of internal mass transfer that have been proposed in the literature, only capillary and bulk flow may be considered imperative above FSP. The continuous internal water evaporation and the external vacuum cause the vapor bulkflowdue to pressure gradients as the most obvious internal mass transport mechanism above FSP. It can then be assumed that vapor or liquid molar diffusion, internal or external, can be excluded from any mathematical modeling due to their low magnitude compared to the bulk flow. Below FSP the moisture is considered bound to the cell wall and therefore bound water diffusion is the dominant mass transfer mechanism. Heat, generated in wood through the RF applicator, is removed through conduction and is consumed for evaporation. 50 4.3 Assumptions We consider the general case of 3-D RF wood drying under vacuum. The main assumptions used to formulate the model follow. Additional assumptions will be discussed into some detail later in the text, in order to justify further simplifications of the model. 1) The solid, the liquid and the gas are considered to be continuous phases above FSP. 2) The wood matrix is rigid and the total volume of the sample is constant during the drying period. 3) Moisture transport is dominated by bound water diffusion and vapor bulk flow (pressure driven) below FSP and by capillary and vapor bulk flow above FSP. 4) The gas phase is water vapor, which behaves as an ideal gas. 5) Darcy's law holds for the vapor and free water phases. 6) The bound water has physical properties similar to those of free water. 7) The driving force of bound water transport is its concentration gradient. 8) Local thermal equilibrium is maintained between vapor, free liquid water, and bound water within the wood cell-walls. 9) The kinetic energies of the various phases, the fluid viscous dissipation and the work done by body forces (gravity) are assumed to be negligible. 10) Convective accelerations are small and the assumption of creeping or Stokes's flow is assumed valid. 11) The latent heat of evaporation varies only with temperature. 12) The diffusivity is taken as a function of temperature and pressure. 13) The viscosities of the liquid and vapor phases depend on temperature. 51 14) The permeabilities of water vapor and liquid water can be expressed in terms of relative permeabilities. 15) No chemical reaction occurs during wood drying. 4.4 Physical drying description The theory and modeling of wood drying has gone from very general ideas and basic equations to highly complex analyses based on wood ultrastructure geometry and multiphase flow. In this work, wood is defined as being a rigid, heterogeneous, and hygroscopic capillary porous material, which has some portion of its void space occupied by liquid water. The drying configuration is illustrated in Figure 4.1. Transport phenomena in the longitudinal and transverse directions of the wood are considered in the construction of the mathematical model. For wood, the relevant anisotropic material properties are known to be in mutually perpendicular directions of the longitudinal and radial axes and therefore, an orthotropic mathematical description is sufficient if it is assumed that the lumber is cut from a perfect cylinder far away from the main centerline axis of the tree. 4.5 Continuum mechanics In order to investigate the heat and mass transfer that occurs within wood during drying, each phase must be identified and analyzed. This can be done by assuming that every portion of each phase constitutes a continuum within the local boundaries that separate it from the neighboring phases. Within this domain, the continuum conservation laws must be satisfied in addition to certain boundary conditions that must be met at the phase interfaces. First we analyze the balance of conserved properties within a continuum control volume. 52 Then, we allow the control volume to shrink in size to include only a differential volume. The result is a set of governing differential equations that describe the behavior of the anisotropic, porous matter. Figure 4.1 Physical configuration of drying model, E = aluminum electrodes, P = polyethylene plates, W = wood specimen. Using the assumptions discussed above, the following equations result: Conservation of mass (continuity equation) Dp (4.1) Conservation of momentum (Navier-Stokes equation) Dv p — = -VP + uV v Dt 2 (4.2) Conservation of energy (first law of thermodynamics) p c ^ = V ( k V T ) + cD p (4.3) We distinguish between the physical quantities by the following notation: 53 s = scalar (lightface) v = vector (boldface italic) x = tensor (boldface) where p = density (kg/m ); v =velocity (m/s); t is the time (s); P - pressure (Pa); u. = dynamic 3 viscosity (Pas); c =heat capacity at constant pressure (J/kg-K); T = temperature (K); p k = thermal conductivity ( W/m- K); O = internal heat generation source term (W/m ). 3 D The term —refers to the substantial derivative (Bird et al. 1960) and includes the partial time derivative with respect tofixedposition as well as the convective acceleration, DB dB dB =— + — Dt dt ' dx (4.4) t 4.6 Governing differential equations In this section we examine Equations (4.1), (4.2), and (4.3) and list the forms that these take in the three separate phases. We use 1, v, and b as subscripts to denote the free liquid, vapor an bound water phases respectively, while s and c denotes solid cell walls matrix of wood and cell walls (including bound water) respectively. 4.6.1 Free water Continuity equation for the free water By assuming the presence of only one component in the liquid phase, the continuity equation for thefreewater can be written according to Equation (4.1) as 54 ^ - + V-(p,v,) = 0 (4.5) Momentum equation for the free water An expression for the fluid velocities can be derived by solving the momentum equation for each phase. Equation (4.2) can be simplified for free water as in homogeneous porous media. The volume-averaged value of the convective acceleration term (v, • v)v, is equal to zero for uniform rectilinear macroscopic flow. This is because the average velocity is unchanged in both magnitude and direction. Usually, the velocity of thefluidin the porous dv, . medium is relatively small, and thus, —r- is also very small. For heterogeneous porous media eft and non-uniform rectilinear flow, the assumption of neglecting both local and convective acceleration terms in the momentum equation is generally acceptable. Thus, Equation (4.2) can rewritten for the motion of the free water in wood as, VP, = u,V v, (4.6) 2 Based upon dimensional analysis, the solution to momentum equation for the various phases must be of the form -K v = H (VP-ps) (4.7) where K = intrinsic permeability of wood, m . 2 The relationship is known as Darcy' law and assumes not only that the flow is laminar, but also that viscous forces are much greater than interfacial ones. The above equation is mainly for single-phase flow at fully saturated conditions. Nevertheless, during drying, the porous media include two phases which are unsaturated. Namely, a gaseous and a liquid phase are present. The conductance value of the wood varies from the intrinsic one. 55 Under such conditions, the conductance is referred to as effective permeability K and e Darcy's law is applied individually to each mobile phase -K. -(VPi-ptf) (4.8) Hi where the subscript i refers to fluid i. Since the effective permeability of wood for a given fluid varies directly with the saturation state of the fluid, it is more convenient to express it as a relative permeability K (=—-). For free water phase, Darcy's law is therefore extended as (the r gravitational effect can be neglected) v, = K .lK ^rl (4.9) VP, where K, = intrinsic permeability for free water in wood (m ); and K = relative permeability for 2 rl free water in wood. Energy equation for the free water The energy equation for the free water can be written as p,c I PI V ST. ir '- < +v VT = V-(k,VT ) + O 1 l (4.10) 4.6.2 Water vapor Continuity equation for the water vapor The gas phase consists of water vapor and air. However, the effect of air pressure is of minor importance and therefore its effects can be neglected in the calculation of the total 56 pressure. Therefore, we may assume that the gas phase consists only of water vapor that behaves as an ideal gas. The mass conservation law for the vapor phase leads to dt (4.11) + V-(p v ) = 0 v v Momentum equation for the water vapor Applying Darcy's equation for the vapor phase results into (4.12) where K = intrinsic permeability for water vapor in wood (m ); K 2 v n = relative permeability for water vapor in wood. Energy Equation for the Water Vapor pv "<5T - + v -VT„ = v .(A. .VT )+<I\ dt W v (4.13) 4.6.3 Cell walls Continuity The cell walls consists of the wood matrix itself and the bound water at sorption sites when it is in the moisture state. Since the wood matrix is rigid, the only mass exchange with the surroundings is due to the bound water diffusion under the influence of the concentration gradient of bound water. As the continuity becomes ^ +' V ' -( V K bv' b ) = 0 Pb b (4.14) We consider the solid phase to be arigidmatrixfixed.Therefore, the velocity in the s phase is zero. 57 ^ =0 (4.15) Momentum Due to the fact that the bound water movement in the cell walls is a pure diffusion process, there is no bulk movement of water. The momentum equation for cell walls then is reduced to Energy The overall energy equation for the bound water and the wood matrix are as follows: Pc ^ s +P c ^ ps b pb + v • VT = V • (XJ ) + <D b b C C (4.17) 4.7 Interfacial boundary conditions Since each phase is in contact with other phases, proper boundary conditions must be specified at all interfaces. As shown in Fig. 4.2, the interfacial areas between different phases are defined as follows: A lv =freewater - vapor phase interfacial area ( m ); A lc =freewater - cell walls interfacial area (m ); A v c 2 2 = vapor phase - cell walls interfacial area ( m ). 2 Note that A =A , l v and "phasei-phasea = v l A =A , l c c l A =A v c c v (418) outwardly directed unit normalfromphase 1 to phase 2, thus 58 For the phase equations, the interfacial conditions on the three interfaces may be represented as: Liquid-vapor interface A lv Mass flux: Pi P, (V, - w) • n + p (v - w) • « = 0 Heat flux: <7i Surface temperature: T, = T Mechanical forces: P JFigure 4.2 w v v vl (20a) (20b) V v (20c) (20d) Schematic of averaging volume. 59 Liquid-cell walls interface A : l c Mass flux: v, = v = w = 0 (21a) Heat flux: X., VT, • n + X VT • « = 0 b ic Surface temperature: T,=T C C (21b) cl (21c) C Vapor-cell walls interface A : v c Mass flux: p (v - w) • n Heat flux: q =q v v Surface temperature: y vc c b b w (22a) (22b) c T =T + p (v - w) • « = 0 v (22c) where w = interfacial velocity ( m /s). 2 4.8 Volume averaging At this stage, a complete set of governing differential equations for each phase, as well as interfacial boundary conditions, have been derived. If the wood structure is known, the boundaries of each phase can be identified so that for the given initial conditions a solution to the equations can be theoretically generated. However, the complicated, albeit regular geometry of wood, makes it all but impossible to keep track of surfaces at all times during the drying process. For example, analysis of moisture movement in a single direction, say, tangential, would require solution of the 3-D transport equations in each phase since the phase point equations are valid only if the point in question lies within the boundaries of the appropriate phase. A more desirable set of governing equations would be one that is valid everywhere within the wood structure regardless of position. This can be accomplished by volume averaging the governing equations. 60 The basic concept of volume averaging applied to the drying problem was developed by Whitaker (1977). This method provides an effective tool for obtaining volume-averaged quantities, which are very important for developing useful relationships for engineering applications. There are three types of averages that are useful in the analysis of transport phenomena in porous media. Thefirstof these is the spatial average of some function (e.g., T) defined everywhere in space. This average is represented by F and is defined by < >=vE F <-> Fdv 42 3 More often, we are interested in the average of some quantity associated solely with a single phase, and we have defined the phase average of the quantity, (FJ ), as ( >=vE F i <-> F dv 42 4 i i where V is the volume occupied by V in the I phase. th ( Another type of average, intrinsic phase average, is more representative of the overall value of a given variable in that it takes into account the volume fractions occupied by each phase. This average is represented by ((F;)) and defined as: 4.9 Macroscopic governing equations Based on the above definitions, a set of governing equations specifically applicable to both moisture and energy transport in wood during RF/V drying can be derived. 61 4.9.1 Conservation of mass For the liquid phase (4.26) |(4>,((p ))) + V.(p v ) = -(rh) 1 1 1 For the gaseous phase (water vapor only) |(*v((Pv») + V.(p v ) = < > v v m (4.27) (m ) + b For the bound water (4.28) | ( * ( ( p ) » + V-(p v ) = -(rh ) b b b b b The phase average of the product density by velocity is used for the bound water flux: (4.29) We notice that above the fiber saturation point, v and (rh ) are null and below this b b point v, = 0 . In the above equations m is the evaporation rate per unit volume of medium (kg/m s). 3 4.9.2 Conservation of momentum As already shown, although Darcy's law was first discovered by experiment, several researchers have derived it from the general Navier-Stokes equations for viscous flow. Darcy's law is extended by using relative permeabilities. For wood, the gravitational effect can be neglected. Darcy's law gives expressions for the free liquid and gas phase velocities as follows: K,K Vi = - ri V ( P . ) (4.30) 62 v =-^-v(P ) v (4.31) v rv Here it is assumed that the gas phase is only water vapor and it behaves like an ideal gas. where R = universal gas constant (8.314J/mol-K); M = molecular weight of water vapor v (0.018kg/mol). The liquid pressure is connected to the gaseous pressure by capillarity: P,=P -P and the capillary pressure (P ) is further defined by V C (4.33) c P o[ 1 +1 ] (4.34) = where P = capillary pressure (Pa); a = surface tension (N/m); r, = principal radius of curvature of c the interface in liquid phase (m); r = principal radius of curvature of the interface in vapor 2 phase (m) By assuming that the capillaries are cylindrical in shape, then the capillary pressure may be written as r.-- r (4-35) where r = radius of capillary (m). 63 In general, the surface tension is a linear function of temperature and it is assumed that the Leverett "J" function can be used to represent the capillary radius effect in Eqn. (4.35). The correlating function for capillary pressure may be written in the following form: P (m, T) = P a(T)l(m)a(T) = °o - PT c (4.36) M where m is the fractional moisture content given by: m =£L±£L±£V_ P (4.37) s and P is a constant whose magnitude depends on the material being modeled, a , and Pare co 0 also constants. 4.9.3 Conservation of energy While there are many processes in which the vapor temperature ((T f} is different v from either the cell walls ( ( T ) ) C and((T ))or b liquid temperature ( ( T , ) ) , most drying processes are characterized by relatively low convective transport rates. Under these circumstances one is encouraged to assume that conductive transport is sufficient to eliminate significant temperature differences between the separate phases. Thus, the solid liquid-vapor system is considered to be in local equilibrium. A logical consequence of this assumption is that the intrinsic phase average temperatures are equal: ((T,» = ({T.)) = ((T )} = {<T ))=((T)> t s (4.38) Therefore, based on the definition, the spatial averaged temperature can be expressed as = (•. + * v + * ) « T » c (4.39) = «T» 64 Thus the energy equation becomes ( p ) C | ( T ) + [(p,c v,) + (p c v ) + (p c v )] • V(T> p pl + (<m> + (m ))Ah b vap v pv v b b b (4.40) = V • [(k^ )V(T)] + (O) where (4.41) <t>.((p.)) pl t > v ( ( p y ) ) c _ C + <t> ((p ))c +< pv c c (4.42) pc (p> <k-r > = (4.43) » + *v « k . » + * . « k „ » <0> = (0,) (4.44) (cP ) + ( 0 ) v + v (^Ah^^^p^^K-^.n.dA (4.45) JI PlC| lv ( ' ~ )' ' V (m >Ah =^[jj b vap W Avc n vdA P c (v - ).« dA v pv v W vc (4.46) jj A P c (v - w ) / i d A b b b w in which (p) = spatial average density (kg/m ); C =mass fraction weighted average specific heat (J 3 p / kg K); k ^ = effective thermal conductivity ( W / m K); Ah vap = latent heat of vaporization (J/kg)- 65 4.9.4 System of partial differential equations Among the several choices of two independent variables, the temperature T and the moisture content m are retained. Similar equations can be found in the literature for conventional drying (Turner and Jolly, 1991; Chen and Scmidt, 1990; Couture et al., 1995). Further description on how to combine all these equations in order to arrive into a system of two partial differential equations can also be found therein. However, we can summarize the following steps for the sake of completeness. The vapor pressure in Eq. (4.31) can be replaced by Eq. (4.33). The liquid and the vapor velocities, vi and v , can be introduced into Eqs. (4.26) and (4.27) by means of Eqs. v (4.30) and (4.31). In addition, the evaporation term in the energy balance (Eq. 4.40) can be replaced by the relative term in the water vapor mass balance (Eq. 4.27). Adding Eqs. (4.26), (4.27) and (4.28) and using Eq. (4.37), we can finally derive the total moisture mass balance. For the energy equation simple replacement of the evaporation rate by Eq. (4.27) can easily be carried out. Some further mathematical manipulations of the total mass and energy balances may yield a coupled system of two diffusion-type partial differential equations relating the temperature and the moisture content (the averaging symbols have been dropped, but are still implied), having the following form: p , ^ = V ( D V p ) +V. b (KK b M "rv* v P„ v KK, (4.47) J p C ^ =V.(k VT) p d r + Ah , v fKK M W p V ? }V P y v - ^ y . + <D 5t (4.48) 66 dp In Equation (4.48), the last term - ~ , called accumulation term, is negligible in at comparison to the others. The energy is generated through the RF generator (third term on the right hand side), it is transferred by conduction (described by the effective thermal conductivity and the first term on the right hand side), and it is consumed for the phase change of liquid or bound water to vapor (second term on the right hand side). Equations (4.47) and (4.48) can be expressed as follows: | p V . ( D V m + D VT) M (4.49) T < P P L T£ = C •( V k M V m + k VT)+ O (4.50) T where the D ' s and k's are complex diffusion-type terms in the total mass and the total heat balance, respectively. The M and T subscripts denote the type of the partial derivative, i.e., T for temperature partial derivative and M for moisture partial derivative. Above FSP: PsM-i _ KK„M D ( RUvPs V d P m w ( KK ,p r HlPs T dP (T) w d k =0 T = k KK rl PsHl r3P c OT (4.53) M k T g e f f + A h V A P ^ M . ^ ^ - (4.54) and below the FSP: DM = D b + K K M , P., dP. ™"^z±zzz. Rp.M-v T (4.55) dm 67 KK^M Rp,u v k„=Ah k =k T e ( r V p ap T ST v KK^M vap Ru + A h vap (4.56) v V P SP v (4.57) V T 5m v KK„M Ru v V P T V S P V S T (4.58) In order to simplify the system of equations even further, an order of magnitude analysis of the various terms can be carried out. As can easily be calculated, the terms D M and k j are about two orders of magnitude higher than the D T and kM respectively (Fohr et al. 1995). In a RF/V drying case the VT term is about two orders of magnitude higher than the term Vm. Thus, further simplification can be made in the above model by assuming that the first term on the right hand side of the energy balance is negligible. 4.9.5 Calculation of radio frequency source term Dielectric heating can be regarded as being due to the power loss in the dielectric of a real capacitor in an alternating current circuit. For an ideal capacitor, the phase angle <{> between the current passing through it and the voltage across it is %I2. In a real capacitor the phase angle differs from nil by the loss angle 5 due to energy losses in the dielectric. The tangent of this angle is called the loss tangent. At any frequency a real capacitor C can be represented by an ideal capacitor C in parallel with a pure resistance R, where e/ determines e the capacitance of a capacitor containing a dielectric of complex permittivity e/, ande" represents the energy loss, i.e., the resistance in the equivalent circuit in Figure 4.3. 68 Figure 4.4 Phase diagram of a real capacitor The phase diagram of the equivalent circuit shows the current I through the capacitor to be e nil out of phase with the current I through the pure resistance (Figure 4.4). r If for the real capacitor C , the cross sectional area of the dielectric is A and the thickness is b, then the magnitude of the ideal capacitance is given by: e c o rA e c="^- ( 4 5 9 > and the resistance by: = ; ^ b R ( 4 - 6 0 ) whereC =equivalent capacitance (F); e = permittivity of free space (8.85.x IO"' F/m); 2 e 0 e" = loss factor; A = cross section area (m ); d= thickness (m); R= resistance (H); 2 co = 27rf, angular frequency (Hz) Referring to the equivalent circuit and phase diagram: I = ^ = oV6 6:^ K d (4.61) I =coC V = coV6 e; A d (4.62) 0 r c e 0 where Ic = current through a capacitor (A); I = current through a resistor (A); V=voltage (V); r From Figure 4.4 it follows that: 1 tan5 = — — (4.63) substituting forC and RfromEquations (4.59) and (4.60) gives: e e" tan 5 = - 7 or e;' = e;tan6 (4.64) where 70 8 = loss angle (rad); $ = phase angle (rad); e' = relative dielectric constant; The power loss in an alternating current circuit is given by: P = v i =coV — s s' d 2 r 0 t (4.65) where P - power (W). V Since the electric field strength E = — and the volume is Ad, then, the power per unit volume d or power density O is: <D = 27rfE s;'e (4.66) 2 0 where <t> = power density (W/m ); f = frequency (Hz); E = electricfield( V/m). 3 Equation (4.66) is the key dielectric heating equation. It is the power dissipated within the dielectric in which thefieldstrength, E, is constant. The rate of heating of the material under the action of an electromagnetic field is determined through the following formula: dT dt <D pC 27tfE E s" 2 0 pC p (4.67) p From the theory developed above, it can be seen that the loss factor is the most important variable in dielectric heating. To achieve a given amount of energy transfer, the higher the loss factor the lower the electricfieldis needed at any given frequency. In the case of an amplifier, the power density (G>) is an externally controllable variable through a matching network. In Eq. (12) knowledge of the function of the dielectric loss factor with the temperature and the moisture content for each species is required. Data for western hemlock and western red cedar are availablefromZhou (1997). The form of the equation for e" is: e" = a + p m + ym + 5 T + C m T 2 (4.68) 71 where a, (3, y, 6 and C, are coefficients characteristic for each species and these are different for heartwood or sapwood. 4.10 Capillary transport and RF/V drying Capillary pressure is the driving force in convective wood drying at mild conditions, (Perre and Turner 1997). The temperature is higher outside than inside. The moisture gradient during convective drying is in the opposite direction with the drier part being towards the exposed surface of wood. These competing patterns of moisture and temperature profiles lead to the concept of the wet front that separates the outer area, where the water is bound to the cell wall, from the inner area, where free water exists in liquid and vapor form. A wet front that moves slowly from the surface towards the center of a board during convective drying leads to subsequent enhancement of capillary transportation. Capillary transportation can then be justified due to the moisture gradients developed around that area. When drying conditions are mild, the drying period is longer so that the relative portion of the total moisture removal, due to the capillary phenomena, is high and it seems that this is the most important mass transfer mechanism. An important difference between the RF/V and conventional drying is that in the former, the temperature and moisture gradients are not competing and yet a wet front has not been identified experimentally (Avramidis and Liu 1994; Kanagawa 1989). By assuming uniform initial moisture profile in a wood specimen that is to be dried with RF/V, after the initial heating period, the temperature profile is practically uniform. This is because dielectric heating is a strong function of the moisture content. Also, the vacuum outside significantly reduces the conductive heat losses from the surfaces. Wood compared to 72 others is a material that exhibits high specific heat and low thermal conductivity (Siau 1995). All the above suggest that a longitudinal temperature profile would exhibit slightly higher temperature levels inside than outside. Thus, the area that first reaches the boiling temperature is expected to be closer to the centerline. As a result, water vaporization starts and moisture is transferred to outer parts. If the total moisture content is not very high, then a large percentage of the pore space is empty and the relative vapor permeability becomes high. This enables most of the vapor to reach the surface of the wood specimen and be removed effectively. Due to the lower temperatures outside, a percentage of the vapor leaving the central part might turn to liquid closer to the surface; however, this can be assumed low if the total vapor permeability is high. In such a case, the dominant mass transport mechanism is considered to be vapor flow. The moisturefluctuationsare very low as is the capillary mass transport, compared to the vapor flow. An assumption of negligible capillary transport seems reasonable in this case. If the initial moisture content is high or the vapor permeability is low, a large part of the vapor leaving the center of wood will condense due to lower temperatures. The moisture profile will no longer be uniform with the moisture content increasing from inside towards outside. Capillary transport is expected with moisture movement towards inside. However, such a movement has to overcome the high pressure built inside due to moisture evaporation and the low permeability. The volume of the pores is limited, and since an increase in pressure at a specific temperature leads to vapor saturation and condensation to liquid, it is clear that the amount of evaporation is restricted. Thus, a non-uniform pressure profile develops with the higher pressures nearest the core. This pressure gradient opposes the capillary transport. The external vacuum reduces the required temperature for evaporation. 73 The higher moisture content at the outer areas, initiate further increases of the temperature towards the surface due to dielectric heating so that boilingfinallyoccurs closer to the surface. The effective vapor transport increases with decreasing distance from the surface. It can then be concluded that moisture is mainly removed by vapor transport, and thus, capillary transportation can be assumed to be negligible. The assumption for negligible capillary liquid transport eliminates the only term of the right hand side of the mass balance (Eq. 4.51) above FSP. It also eliminates the liquid transport part, the second term and the last term of the right hand side of Eq 4.52. At this point it can be summarized that the main differences between RF/V and convective drying models are: a) the source term in the energy balance accounting for the RF generation, b) the assumption that air mass is negligible due to continuous vacuum in the RF/V drying and c) liquid transportation due to capillary effects is negligible in RF/V drying. 4.11 1-D model form The selection of a simple 1-D will now be justified on physical grounds rather than for the sake of simplicity. The plates of a dielectric dryer should be in contact with the specimen since this way transfer of energy is more efficient (Biryukov 1968), and moisture leveling is highly enhanced (Jones and Rowley 1996). Thus, mass and heat transfers are limited in the direction parallel to the plates. Literature also indicates that most of the mass transfer in RF/V drying occurs in the longitudinal direction, that is the direction parallel to the length of the plates (Avramidis and Liu 1994). The high anisotropy of permeability is another factor that explains why a 1-D model is adequate to yield reasonable results. A great advantage of the RF/V technology for drying wood is the ability to dry thick timbers. Since 74 the ratio of longitudinal to transverse direction increases up to five times, from 50 mm to 250 mm, the respective percentage of the longitudinal to the total transfers is expected to increase by five times compared to the conventional drying. Therefore, selecting the numerical solution of a 1-D model in the longitudinal direction seems a good choice. Since the longitudinal direction is used as the direction of transfer, the following corrections can be applied, since the transfer in the transverse direction (which is possible) is neglected. It is well known that the effective thermal conductivity in the longitudinal is 2.5 times higher than that in the transverse direction (Siau 1995). The usual wood drying problems include ratios of longitudinal to transverse directions of 2.5 and higher. This implies that a correction has to be introduced in such a 1-D longitudinal model accounting for the higher total conductive heat transfer in the transverse direction. The same should be taken into account for the bound water diffusion coefficient below FSP (Siau 1995). Since the drying occurs under vacuum, it can be assumed that below FSP the cell walls and gross wood have similar bound water diffusion coefficients. It should be noted here that a similar assumption for the wood bound water diffusion coefficient that can be found in some convective wood drying models is not accurate, since it does not account for the interdiffusion of water vapor in bulk air (Siau 1995). Since the permeability plays an important role in the model, some discussion is relevant here, i.e., Knudsen diffusion and slip flow (Perre et al. 1995). The mean free path (K) increases as the pressure decreases and when X is comparable to the pore size then free molecular diffusion and slip flow occur. The fiber length for softwoods is about 3,500 urn (Siau 1995) and according to Perre et al. (1995), X of water at a low pressure of P = 3000 Pa is about 3.5 um. Since the difference of these two length scales is high, it can be assumed 75 that Knudsen diffusion and slip flow do not occur in the longitudinal direction. Such an assumption is not valid in the transverse direction, where the fiber diameter and the pore size in softwoods are about 35 u.m and can be considered comparable to an X of 3.5 (im. At the pressure P= 3000 Pa, the evaporation temperature is less than 25°C (Siau 1995). Due to the volumetric heating in RF/V drying, temperatures over 25°C are achieved rapidly all over the volume of the specimen. This leads to significant tendency for evaporation and increase of the local internal pressure that renders the phenomena of Knudsen and slip flow negligible. 4.12 Numerical solution The 1-D form of Eqs. (4.49) and (4.50), if x is the direction of transport, are: Mass balance Energy balance dm dt dm n dx (pr) v d ( ^ oT^ = —-I D — + D — p A o t M — =— / k dt T dx dx \ M —+ k dx (4.69) dx J T T — dxj (4.70) In order to solve Eqs. (4.69) and (4.70), one initial condition (I.C.) and two boundary conditions (B.C.) are required for each equation. These are: 1. I.C: At t = 0 for all x's, m and T were set equal to the known initial moisture content and initial temperature of the green wood as it enters the kiln, (experimental determination). The moisture content, even if it is different at the two ends, it is assumed to be uniform at the mean experimental value. The initial temperature is also assumed uniform throughout the specimen. 76 2. B.C. 1: dm For all t's at x = 0, — = 0 and — = 0 due to symmetry. dx. 8K 3. B.C. 2: For all t's at x = L / 2, m = 0 due to vacuum and T = Treasured where L is the total length of the sample. In moderate drying conditions the end temperature is slightly higher than the kiln temperature. Under extremely rapid drying conditions (high voltages or power densities) the end temperature deviates significantly from the kiln temperature. In such cases, significant undesirable internal degrade is obtained. Such cases are not considered here. The equations are discretized by using the finite volume method (Patankar, 1980). The finite difference scheme was constructed by nodal discretization of the scalar functions and cell-centered discretization of the vector functions. The error contribution of the space and the time discretization was kept to be approximately the same. An implicit method was selected for time and space integrations so that the truncation error to be of second order. In order to reduce the error introduced from the coupling effect through the diffusion coefficients, and since these coefficients are always calculated from the temperature and moisture profiles of the previous time steps, the time step was kept very small. The resulting linear system of equations was solved by using the Gauss-Seidel method. The convergence criterion for the Gauss-Seidel was kept strict so that the relative error introduced after convergence was kept low, less than 10". Numerical expressions for the parameters that were 6 used in the 1-D calculations can be found in the Appendix A. Some of them were taken from 77 the literature and some were taken from experiments in our laboratory. A summary of the solution algorithm is given right below. Solution Algorithm 1. Input data from experiments, e.g. voltages, temperatures, pressures, etc. 2. Input constant quantities, e.g. density, intrinsic permeability, frequency, etc. 3. Choose implicit or explicit scheme for the time integration. 4. Set coordinates for grid points. 5. Compute geometrical quantities, which do not depend on time. 6. Set initial conditions for both the temperature and moisture contents. 7. Begin time integration. a) Set boundary conditions for both PDE's. b) Compute the diffusive type coefficients of the original equations in cells. c) Calculate properties common for heat and mass transfer by means of subroutines that are part of the algorithm, e.g. relative permeabilities, viscosities, etc. d) Calculate parts of diffusive type equations and finally the diffusion coefficients for mass transfer. e) Calculate parts of diffusive type equations andfinallythe diffusion coefficients for heat transfer. f) Compute the right hand side of the Differential Equations in all nodes, i.e. the source terms. g) Compute the coefficients for the elliptic part of the equations. 78 h) Compute the coefficients and the right hand side of the finite difference equations for the case of implicit schemes. i) Solve thefinitedifference equations by the Gauss-Seidel method. External iteration required to keep coupled thefinaltemperature and moisture results. j) Record computed results. k) If total time is less than the maximum time set, then increase total time by the set increment and go back to step 6. 4.13 Optimization methods Wood drying is one of the complicated cases to develop an efficient mathematical model. This is basically due to the variability, the high anisotropy and the hygroscopicity that characterizes wood. Many different models for the various types of wood drying exist already in the literature. In the most recent cases the transport mechanisms have been well identified. The same is not true when it comes to the coefficients of the models. Optimization methods have recently been used as a tool to either improve existing schedules (Carlsson and Arfvidsson 2000, Pordage and Langrish 2000), assuming that the models describe effectively the heat and mass transport phenomena, or to identify coefficients that are either unknown to most species or they are hard to be measured (Weres et al. 2000). The latter approach seems more appropriate since the physical properties of wood depend on a large number of factors and in most of the cases it is extremely hard to design and conduct experiments that will include all of the possible effects on the particular property to be identified. Finally, even if such experiments are conducted, further 79 assumptions have to be included in order to compensate for the effect of coupling of the different parameters affecting this property in a real drying situation. The choice of optimization method is a crucial step. One of the most important aspects to be considered is the complexity of the mathematical model describing the heat and mass transfer phenomena. When the model is empirical or semi-empirical, it can be fairly simple. If derivatives with respect to the optimization parameters can be easily calculated, then hill climbing strategies are the best option due to their rapid convergence in an optimum value, usually local. Mathematical models for wood drying that describe adequately the physical phenomena can be derived through general conservation equations. Though many approximations and assumptions are always incorporated to simplify the solution, the final result is usually a set of two to three partial differential equations (PDE's) well coupled through their coefficients. In such cases it is extremely difficult to find the derivatives with respect to the optimization parameters. The only choice then is random strategies for numerical optimization. Evolution strategies (ES) were selected as a method that can solve effectively an optimization problem, involving all the difficulties that can arise when combining them with a system of PDE's. One of the main advantages of ES is that they can handle constraints. This is usually the case in physical systems. They can also avoid local minima in a good extension and give a well-improved solution. Also instabilities in the solution of the PDE's that may arise from extreme values in the optimization parameters can be handled exactly the same way as the constraints are managed. The main disadvantage of such methods is that they are time consuming. One more difficulty arises in the choice of the steps of the 80 parameters initially. Small steps might lead to a local optimum and very high steps might lead to missing an optimum that is very close to the initial guess. The above disadvantages are more pronounced as the number of parameters to be optimized increases. Finally another disadvantage in the use of the ES is that the solution method has to be stable. To avoid any instability additional constraints or penalty functions can be introduced. The choice of the objective function can be defined arbitrarily giving a incredibly good flexibility. As an example the objective function can be the evolution of the total moisture content or it can also be the summation of the evolution of the total moisture content and the evolution of some local temperatures that can be measured experimentally. In a case when the objective function to be optimized is mixed, the relative accuracy of each of the measured parameters might lead to completely different results for the optimization parameters, mostly if these parameters are of very different order of magnitude. The choice of optimization parameters can also be flexible. One case can be that when a single multiplier is applied to each one of the complex diffusion-type terms or some subparts of them. Any deviation from a value of one means that this specific term, if given properly, is underestimated or overestimated. Such a result should lead to proper improvement of the model so thatfinallyall the optimization terms get eliminated i.e. equal one in a case of multiplication factors or zero in case of addition factors. This could sufficiently simplify a model from unnecessary terms. Another case of optimization parameters could be model parameters that exhibit a high variability, as is the permeability. Optimization parameters could also be those for which experimental results do not exist. Such an example is the effect of pressure on the bound water diffusion coefficient. The possibilities of introducing and testing new concepts are unlimited with the ES. Efficient 81 stochastic modeling can also be incorporated very easily. The usefulness of the ES will become clear in the results and discussion section. 4.14 The concepts in ES Rechenberg (1994) proposed the hypothesis "that the method of organic evolution represents an optimal strategy for the adaptation of living things to their environment" and he concludes "it should therefore be worthwhile to take over the principles of biological evolution for the optimization of technical systems". In the language of biology the rules are: 1. Initialization, where a given population consists of u. individuals. Each is characterized by its genotype, which has n genes that determine the fitness of survival. 2. Mutation, where each parent has a XI u, offspring on average that differ only slightly from the parent. The number of genes remains the same. 3. Selection, where only the u, best of the X. offspring become parent of the following generation. Other important issues to be resolved are: the step length control, the convergence criterion and the type of recombination to be chosen (Rechenberg, 1989). The KORR algorithm was utilized given in Schewfel (1995). Almost all of the cases were exarnined with the 10,100 with intermediate recombination of all parents in pairs. The mutation hyperellipsoid, the locus of equal probability density, can extend and rotate. The convergence criterion is taken 82 as the change of the mean of all the parental objective function values to be less than one absolute and one relative value. The search can also be terminated after a specified period. 4.15 2-D model form A more complete description of the phenomena can be achieved when the model is in its 2-D form. The accuracy that is expected to be obtained will be on expense of the loss of simplicity and the additional computational time required when solving the 2-D case. The 2D forms of the Equations (4.49) and (4.50), if x is the longitudinal and y is the transverse direction of transport, are: Mass balance: + DTL ar +ax. ay D MT am + D ar TT a7 (4.71) Energy balance: / \ ar a (. am , ar^ a (. am , ar") _ where the D's and k's are complex diffusion-type terms in the total mass and heat balance, respectively. The M and T initial subscripts denote the type of the partial derivative, i.e., T for temperature partial derivative and M for moisture partial derivative. The second subscripts, L and T denote the direction offlow,longitudinal and transverse respectively. Additional assumptions and combination with optimization routines will be described later in the results and discussion section. 83 Chapter 5: Results and Discussion In this chapter the results will be presented as were obtained chronologically starting from the single case of 1-D model and building towards the more complicated case of 2-D. 5.1 Calculations with the 1-D model The total drying times and the maximum internal temperatures are important parameters in industrial drying. In particular, the former has to do with the efficiency of drying and the latter with the quality of the final product. The effect of different model parameters on both the drying curve and local temperature evolution curves will be examined in this section. The parameters of interest will be the core temperature, Tco, and the temperature calculated at a quarter length from the end of the specimen, T i. q The parameters affecting RP/V drying can be separated in two categories. The first category includes the independent variables such as the voltage of the oscillator, the power density of the amplifier, and the kiln pressure. The second includes all the parameters that characterize the material to be dried. Namely these are, the initial moisture content, the oven dry density, the FSP, the intrinsic permeability and the length of the specimen. The effect of changing each of these parameters on the total drying time and the temperature evolution will be calculated for the 1-D case. Figure 5.1 depicts calculated drying and temperature evolution curves at two points (x = L / 4, x = L / 2) for three different intrinsic wood permeabilities. The temperature decreases with increasing permeability due to quicker removal of water vapor. However, the effect of wood permeability on the drying time is more complicated. Increase of permeability reduces the temperature gradients, but increases the diffusive coefficients. The relative change of 84 temperature gradients at high temperatures is small so that the effect of decreasing the permeability on the diffusive coefficient prevails and drying rates are reduced. At lower temperatures the relative change of the temperature gradients becomes higher and this counterbalances the increase of the diffusive coefficients. The temperature curves are not smooth and this can be explained by the functions utilized for the calculations that exhibit discontinuities at the FSP. Also possible moisture discontinuities and non-uniformities could causefluctuationsin the temperatures introduced via s" and the heat source term. r Figure 5.1 The effect of wood permeability on the moisture and temperature evolution for three different permeabilities, case 1: K = 10 m , case 2: K = 5*10 m , case 3: K = 10 m . Other parameters of the model include man - 0.7, FSP = 0.3, <D = 5,000W/m , Pkih = 3,000 Pa, Xtat = 9.2735, electrode plate length = 2 m. ,3 2 l3 2 12 2 3 85 Figure 5.2 plots the drying and temperature evolution curves at two points (same as in Fig. 5.1) for different power densities. Increase of the power obviously causes an increase in the temperature everywhere. The temperature gradients are also higher so that the drying times are significantly reduced. It is interesting to note that the local temperature evolution curves exhibit an increase, resembling experiments on microwave drying for polymer pellets and alumina beads as reported by Chen and Schmidt (1997). It is prudent to mention here that while by using an amplifier the total power density can be kept constant, in practice, for a material like wood, it is by no means constant due to differences in local temperatures and moisture contents. These differences suggest that e" and the power density vary locally. r Figure 5.3 depicts the drying and temperature evolution curves at two points (same as in Fig. 5.1) for different voltages. The distance between the plates is assumed to be 250 mm and all other parameters are the same as those defined in Figure 5.2. It can be seen that the drying time decreases, while the maximum temperature increases with increase of the voltage. In particular, the temperature curves reach almost a plateau and do not increase sharply, when the moisture content is below FSP. This is important in practice, since temperatures must be kept low in order to keep wood drying defects to a minimum. Figure 5.4 shows drying and temperatures evolution curves at two points (same as in Fig. 5.1) for different sample lengths. It can be seen that the drying time and the maximum temperature increase with an increase in the specimen length. Keeping all the parameters the same as in case 1 of Figure 5.3, and increasing the oven dry density from 350 kg/m to 400 3 kg/m , an increase in both drying time (t=95h) and maximum temperature (T=95°C) is 3 observed. Lowering the FSP value to 0.25 and keeping the density to 350 kg/m , the total 3 drying time increases to only 89 h and the maximum temperature to 94°C. Keeping FSP 86 equal to 0.3 and increasing the initial moisture content to 1.3, the drying time increases to 110 h and the maximum temperature to 96°C. Finally, a change of the external pressure from 3 to 10 kPa with m=0.7, increases the total drying time to 153 h and changes the maximum temperature to 93°C. 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (hrs) Figure 5.2 The effect of power density on the moisture and temperature evolution for three different power densities, case 1: O = 2,500 W/m , case 2: O = 5,000 W/m , case 3: <D = 7,500 W/m . The permeability is K = 5*10' m and m™, FSP, Pidi„„ X ^ , and length of electrode plates is the same as in Figure 5.1. 3 3 13 3 2 87 All the above results could serve as a first estimate of drying times and maximum temperatures in RF/V wood drying. A comparison with experimental data could reveal deficiencies of the model. Based on these deficiencies, a more elaborate model can be developed in a sense that, new mechanisms for moisture and energy transport can be envisioned in RF/V wood drying. Time (hrs) Figure 5.3 The effect of voltage on the moisture and temperature evolution for three different voltages, case 1: V = 200 Volt, case 2: V = 250 Volt, case 3: V = 300Volt. The distance between the electrode plates is 250 mm and K, m , FSP, Pub,, X ^ , and length of electrode plates is the same as in Figure 5.2. m 88 T i m e (hrs) Figure 5.4 The effect of plates length on the moisture and temperature evolution for three plate lengths, 1 m, 1.5 m, and 2 m. The voltage is 200 Volt and the distance between the plates, K, miNi, FSP, Pkiin,, Xu«t are the same as in Figure 5.3. 5.2.1 Comparison of RF/V experiments with 1-D calculations A series of runs were carried out with western hemlock and western red cedar. Experimental data were compared with the predicted results from the 1-D model as reported by Koumoutsakos et al. (2001a) and as presented here. The selection for presentation was made so that the moisture range is as high as possible and the experimental conditions as much as possibly different. At least one experiment is presented for constant core temperature or power density or voltage. These experiments are for two different species and 89 at two different ambient kiln pressures. The conclusions presented here are in compliance with all other experimental and calculated results obtained. Figures 5.5, 5.6 and 5.7 show the temperature and pressure trends of western hemlock run #11 (WH11), of western red cedar run #1 (WRC1), and western red cedar run #5 (WRC5), respectively. The dryer operating conditions in these experiments are: core temperature T = 60°C and kiln pressure P = 3.33 kPa for the WH11; Voltage = 0.44 kV and c a kiln pressure P = 3.33 kPa for WRC1 and power density PD = 4.8 kW/m and kiln pressure 3 a P = 10kPaforWRC5. a 0 5 10 15 20 25 30 35 40 45 50 55 Time (hrs) Figure 5.5 Experimental temperature and pressure evolutions at quarter length, core and ambient kiln points for Western Hemlock #11. 90 The pressure evolution in these experiments along with explanation about this behavior will also follow. When the vacuum pump and the power generator start at the same time, an internal pressure reduction is observed due to the introduction of vacuum (during the first 2 hours in Figure 5.5). When vacuum is introduced before the power generator is turned on, the pressure exhibits an initial drop similar in magnitude to that of the ambient kiln pressure, (initial values in Figure 5.6). However, due to the volumetric heating and the water evaporation, an increase of the internal pressure is observed after this initial reduction. If the vacuum is introduced much later in the drying run, this initial pressure reduction step is not observed (Figure 5.7). Figure 5.6 Experimental temperature and pressure evolutions at quarter length, core and ambient kiln points for WRC1. 91 It is also apparent that the increase in pressure is accompanied by a slower increase in temperature. As the internal pressure increases, local internal moisturefluctuationsalso increase. Initial liquid and vapor discontinuities are eliminated resulting in a more balanced moisture profile. When most of the vapor discontinuities disappear, the vapor has an avenue of escape and subsequently, the internal pressures begin to decrease. This decrease can be more abrupt for higher power densities and lower ambient pressures. It must be noted here that the cell wall could crack under extreme conditions (P and T), which should be avoided for better product quality. Finally, when the local moisture content is below the FSP, the internal pressure is very close to the ambient pressure of the dryer, as expected (Figure 5.5). Figure 5.7 Experimental temperature and pressure evolutions at quarter length, core and ambient kiln points for WRC5. 92 The temperature evolution follows similar patterns with an initial rise. Fluctuations in temperature measurements during the initial heating period can be explained by local internal moisture variations within the sample. Since the local temperature is strongly affected by the selection of the drying method, i.e., constant maximum (core) temperature or power density, by using an oscillator, or voltage by using an amplifier, the temperature patterns can be different. In WH11 (Figure 5.5), after an initial rise and fall, the core temperature is kept about constant, but the quarter length temperature, T i, shows a reduction with time after the q initial heating period. When the voltage is kept constant as in WRC1 (Figure 5.6), the temperatures, after reaching a maximum, begin to decrease. This can be explained by the local reduction of moisture content, which affects (reduces) the dielectric loss factor ( 6 / ' ) and subsequently reduces the local power density and heat generation. When the total power density is kept constant as in WRC5 (Figure 5.7), after a rapid initial increase of temperature, a reduction of the rate of change of temperature (dT/dt) is observed due to the reduced moisture content within the specimen. Some more interesting points on the temperature and pressure evolution curves as obtained by the experiments need to be further elaborated here. Hemlock is one of few wood species that contain wet pockets, namely, areas of very high moisture content accompanied by bacterial activity. The procedure for drying hemlock with conventional methods is complicated since highly non-uniform moisture content distribution might be observed in the dry product. In addition, there is no means to identify the distribution of these wet pockets before drying. A possible explanation for the increase in temperature (case W H 1 1 ) first at T i q compared to T could be the fact that a wet pocket might have been existed close or even at c the point of the T i measurement (Figure 5.5). This also explains the much higher P i that was q q 93 observed compared to P . Another possible explanation for the higher temperatures and c pressures observed initially in the quarter length point of measurement compared to the core one (Figures 5.5 and 5.6), could be minor non-uniformities of the voltage throughout the length of the plates. Since the power source, in the case of the oscillator, is connected at the quarter length of the plates at the opposite side (back side) from the quarter length point of measurement (front side), solution of the Maxwell equations can prove that the temperature and pressure at the front end can have a voltage of at least 10% higher than those at the point where the plates are connected to the RF source. Higher local voltage means higher local power density and therefore faster initial temperature increase. Figures 5.8, 5.9 and 5.10 present the total moisture and the local temperature evolutions as were measured experimentally and calculated by the model derived in the last chapter for the cases presented in Figures 5.5 to 5.7. The RF/V wood drying is characterized by an initial heating period, the length of which increases as the applied constant total power density or the constant voltage decreases or the ambient pressure is kept high. Almost constant moisture content and elevated internal temperatures and pressures characterize this heating period. When the internal temperatures and pressures reach values high enough to eliminate the vapor discontinuities, the pressure drops, drying rate increases and the rate of temperature rise decreases. This is because most of the heat generated within wood is not consumed for heating, but for evaporation so that water vapor can easily escape from the ends of the specimen. When FSP is reached, the drying rate decreases due to the difference of the nature of water removed, i.e., free vs. bound water. The differential heat of vaporization kicks in (Siau 1995) and Zt"decreases due to the reduced mobility of the adsorbed water molecules (Torgovnikov 1993). This explains why the rate of mass transfer decreases, though 94 the temperatures might stay constant or even slowly increase depending on the drying schedule. Figures 5.8, 5.9 and 5.10 describe the evolution of moisture content and local temperatures at the core and quarter length of the specimen, as were measured experimentally, (WH11, WRC1 and WRC5, respectively), and calculated from the 1-D model. At Figures 5.8 and 5.9, where the ambient pressure is 3.33 kPa the water boiling temperature is about 25°C. This temperature is exceeded rapidly and as evaporation occurs, the moisture content decreases since the vapor is rapidly removed due to the low external pressure. In Figure 5.10 where the ambient pressure is about 10 kPa and the corresponding water boiling temperature is about 47°C, a minor removal of vapor moisture is observed when the vacuum is introduced at 2 hours onto the schedule. The sharper reduction of the moisture content starts after both measured temperatures exceed the boiling point. This is an important indication that moisture transport and removal occurs mainly in the vapor form. As the total moisture reaches FSP, an expected reduction of the drying rate can be identified (Figures 5.8 and 5.9). The parameters for the model calculations were taken from Siau (1995), Avramidis and Dubois (1992) and experiments in our laboratory as described in appendix A of this thesis. It is apparentfromFigures 5.8, 5.9 and 5.10 that the drying times and the evolution of moisture content can be well quantified by the theory. The qualitative agreement for the temperatures calculated is also acceptable. The calculated temperatures are higher than the experimental ones. This is due to the nature of the heat transfer that in this case is definitely 2-D. Assumptions were made to cover for probable inaccuracies when solving the 1-D case through the thermal conductivity, but they do not seem sufficient enough to give acceptable 95 quantitative predictions for the temperature profiles. Possible mass transfer in the transverse direction could diminish these experimental and calculated discrepancies. It should be noted here that the transverse mass transfer that was assumed negligible in the 1-D case should cover possible declines of the drying rates due to lower temperatures. Time (hrs) Figure 5.8 Calculated and experimental total average moisture and temperature changes with time at quarter length and core points for WH11. Figures 5.11 and 5.12 present the calculated evolution of the temperature and moisture distribution, respectively, for WH11. The total length of the samples in each of the experiments was 2m. The location x = 0 denotes the plane of symmetry. This particular 96 experiment is presented because here the initial moisture content was the highest. Figure 5.11 shows the need for non-uniform grid spacing at the ends of the specimen where large temperature gradients exist. Since the temperature and the moisture are highly coupled, and the calculated temperature difference between the core and the quarter length is small compared to the measured ones, the assumption of equality between capillary transportation towards the center and the opposing pressure induced mass transfer must be re-examined and quantified properly. Quantification of the internal pressure due to vaporization and capillary pressures could give higher mass internal fluctuations and higher internal temperature differences. In other words, the effect of the internal pressure on mass transfer is expected to be higher than the opposing capillary transportation and the higher internal mass fluctuations will yield higher internal temperature gradients. Figure 5.12 also reveals that at the edges of the specimen, minor capillary transportation is possible due to the very low surface area normal to the longitudinal direction. Since similar behavior must be exhibited in the transverse direction and because of the higher surface area normal to this direction, the overall capillary transportation in the transverse direction cannot be neglected, as is the case for the longitudinal direction, especially when modeling very wet pieces. This is another reason why extension to 2-D is a necessity. The "wavy" pattern that the longitudinal moisture profiles exhibit is similar to the ones obtained by more extensive theories found in literature for microwave heating (Constant et al. 1996). A great similarity can also be observed by comparing the experimental moisture profiles found in the literature for R F / V drying (Avramidis et al. 1994, Liu et al. 1994, Hayashi et al. 1995) with the calculated moisture profile evolution (Figure 5.12). This is 97 another direct evidence that the most important phenomena are described by the theory developed. Refinements can also be made for the end points of both moisture and temperature profiles. Introducing, above FSP, heat and mass exchange coefficients under vacuum at the outer boundaries should also eliminate end inconsistencies that can be observed in Figure 5.12 for the longitudinal moisture profile. Below FSP, since all the water is in the form of bound water and the pores are empty of free water, moving boundary conditions can be imposed. 4 5 6 10 Time (hrs) Figure 5.9 Calculated and experimental total average moisture temperature changes with time evolution at quarter length and core points for WRC1. 98 Finally, further extension of the model could yield a quantitative agreement for the predicted and measured evolution of the pressure distribution. Elimination of the assumption that the vapor pressure is always equal to the saturated vapor pressure above FSP can be carried out by the solution of a partial differential equation for pressure that can be derived by an air mass balance. Figure 5.10 Calculated and experimental total average moisture and temperature changes with time at quarter length and core points for WRC5. 99 Figure 5.11 Calculated longitudinal temperature changes with time for WH11. 1.2 — t = 0 hrs 1 = 11 hrs - - -t = 22 hrs 1 = 33 hrs 1 = 44 hrs 1 = 55 hrs / 1 • Final Exp M 0.8 E 0.6 J 0.4 V 0.2 -t -1 0 Length Figure 5.12 Calculated longitudinal moisture changes with time and experimental final moisture profile for WH11. 100 The step-by-step construction of the model was based on calculations in conjunction with the ES. In the next paragraphs the use of the ES will be described briefly through a chronological description of this modeling attempt. Initially the model was oversimplified by not accounting for the temperature effects in the mass transfer. The results obtained were unacceptable by failing to predict the magnitude of the relevant temperatures and total mass. The time scale of the predictions was also completely different than the experimental results. Addition of the temperature effects in the mass transfer yield a great improvement of the time scale predictions though the quantitative disagreement was still considerable for both local temperatures and the total moisture content. The form of the model derived initially included a term to account for the transfer by capillarity in the longitudinal direction similar to the one usually found in a number of models for convective drying. Applying once again ES to assess the effect of capillary flow, the optimization parameter reached zero. This is another indication that in the longitudinal direction the capillary transport is negligible. Perre and Turner (1997) give a function to describe the capillary transport in the longitudinal direction when modeling convective drying. This function gives similar results so that the overall transfer due to capillarity in the longitudinal direction is negligible. No explanation is given therein of experimental verification by capillary experiments. The calculations that were presented above for each different experiment included optimization parameters. The values of all of them were calculated to be very close to one thus validating our experimental findings. The inability for a large number of experiments to have exactly the same values reveals the variation between the pieces that were dried. 101 5.2.2 Analysis of RF/V experiments with the oscillator A view of Table 5.1 reveals that the drying time in some cases does not exhibit normal behavior. As an example, a comparison between runs #3 and #4 for W H gives drying time higher for #3, although the initial moisture content is lower and the drying conditions are the same in both experiments. This is an indication that the variability between pieces is very important and can give results very different. Another important aspect is the duration of the timing of the applied voltage. The voltage was extremely difficult to control and there was a trend for it to decrease in the heating period and to increase dramatically in the end of the runs. The idea of controlling the central temperature as the maximum one and control the degrade arising from high pressures and temperatures in this way, rather was not successful. This was due to the longitudinal anisotropy of the field that has been described before that many times led to maximum temperatures away from the core. It was also due to the factor that a local temperature is a factor of the heat absorbed locally. This is highly connected with the local moisture mass, which was not a priory known. WRC exhibits lower drying times for several reasons. The initial moisture content was low. Also in all WRC cases there was not any air gap or polyethylene plate because stability could be obtained without them. Since all the pieces, W H and WRC, had the same thickness, an air gap or introduction of a polyethylene plate increases the distance between the plates. Equation 4.66 revealed that any difference in the distance is significant because the total power density absorbed by the specimen is a second order function of the electric field. 102 Table 5.1 Master table of the experimental conditions for R F / V drying when using the oscillator. RUN # 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Time Hrs 24 26 15 82 59 24 42 19 27 78 22 55 25 18 32 30 41 35 32 Mi % 65.2 49.8 42.6 49.2 73.9 73.2 35.1 35.6 45.2 60.5 46.5 117 61.7 59.2 56.2 71.4 74.3 37.3 39.3 1 2 3 4 11 11 10 10 47.88 42.2 36.9 34.2 HEMLOC]EC M TMAX PA Torr % C 97 32 11.94 33 100 16.07 34 14.63 104 33 12.11 96 32 13.43 95 90 25 15.68 66 32 11.95 80 31 12.73 68 35 15.41 29 12.95 99 29 6.48 85 30 13.22 70 95 29 14.40 30 14.25 110 35 95 13.91 57 20.58 85 115 57 17.36 116 12.37 112 116 17.72 118 CEDAR 25 9.57 80 21 13.55 75 21 16.77 84 96 21 19.32 F Target Voltage V 0.35 - 0.83 0.30-0.33 0.28 - 0.32 0.20 - 0.27 0.20 - 0.26 0.14 - 0.37 0.16-0.43 0.20 - 0.57 0.16-0.29 0.22 - 0.26 0.20- 1.40 0.14-0.69 0.15 - 0.45 0.20-0.36 0.15 - 0.25 0.12 - 0.47 0.1 - 0.35 0.15-0.37 0.18-0.52 Practice V = 0.3 V = 0.3 V = 0.2 V = 0.2 T = 80 T = 60 T-80 T = 60 V = 0.22 T = 80 T = 60 T = 80 V = 0.3 V = 0.22 T = 80 T = 60 T.= 80 T = 60 0.24-0.8 0.25-0.42 0.3-0.32 0.22-0.23 T = 80 T = 60 V = 0.3 V = 0.22 A comparison of runs #7 and #17 reveals that there is a trend for faster drying at lower pressures when all the other conditions are kept constant even though the temperatures are higher in the case of higher ambient pressure. This is a sign that the most of the mass transport will occur in the vapor phase, which appears at higher local temperatures for higher local internal pressures. 103 The total energy requirements of the RF/V dryer for WH were: 109 kWh for run #12, 120 kWh for run # 14, 131kWh for run #17 and 110 kWh for run #18. Comparison of runs #12 and #14 shows that variable voltage is preferable, within an energy requirement point of view, to remove the same amount of moisture. It is also more energy expensive to operate in higher ambient pressures as is revealed by a comparison of runs #12 and # 17. Also it seems that difference in temperatures has no effect in the total energy requirements. Comparison of runs # 17 and #18 would be expected to yield similar results if run #18 was ending at lower final moisture content. The total energy requirements of the RF/V dryer for WRC were: 77 kWh for run #1, 45 kWh for run # 2, 38 kWh for run #3 and 38 kWh for run #4. Comparison of runs #2 and #4 shows similar trend as in WH that variable voltage is preferable in order to make less energy use. Comparison of runs #1 and #2 reveals the same trend as in WH that a difference in core temperature does not affect significantly the total energy requirement. It also seems slightly favorable to operate in higher voltages in order to utilize less energy. This becomes evident, when comparing the moisture range and the energy requirements for runs #3 and #4. An analysis of the final moisture profile data, in the longitudinal direction for WH, reveals that in 7 5 % of the cases, the minimum moisture content was towards thefrontend. In another 19% of the cases, the minimum was found to be exactly at the center of the piece. This behavior of longitudinal heating preference was expected since the coils connecting the RF plates with the heating source were at a quarter length of the plates from the back end. This means that the plate voltage towards the front door was higher inducing higher local power transfer and subsequently higher mass transfer rates. The final moisture content maximum in 8 7 % of the cases was towards the back side. It is important to say that in none 104 of the cases the maximum was in the center of the pieces. The remaining 13% can be explained by relatively high initial moisture content at the back side. Analysis of the final moisture profile data in the horizontal direction yields minimum moisture content always in the center. This is a serious indication that there is a considerable moisture flow in the horizontal direction, at least below FSP because in all the experiments the final moisture content was well below it. Experiments with final moisture content well above the FSP could reveal if such a trend exists in this regime too. Similar results were obtained when comparing the moisture profile of pieces that were cut in three sections, a core, a middle and an outer section. In more than 90% of the cases the maximum moisture content was found in the outer sections. A clear result for the behavior of flow in the direction of the plates could not be established since the minimum moisture content along the plates was distributed almost equally among the WH experiments. The above-described trends for the WH experiments were verified in the WRC experiments too, though in the latter case the number of experiments was much smaller to draw generalizations. When higher maximum temperatures were obtained for the same ambient pressure, more degrade was observed, though in all cases it was considered minimal compared to the average degrade during a convective kiln drying of thinner pieces at mild conditions. No temperature gradient was observed in the direction of the plates in all of the above runs. Finally, the average shrinking for all the pieces in Table 5.9 was 1.66% horizontally and was 1.65% vertically. The ranges of shrinking were 0.49-2.98% vertically and 0.24-3.44% horizontally. 105 5.3 Permeability Assuming that Darcy's law for gases is valid (Siau 1995) and based on the flow apparatus measurements described above, the superficial gas permeability can be calculated by QLP v g ~ A f atm 0.760 AP^1.013xl0 5 P U where k is the superficial gas permeability (m (gas)/m-Pa-s); Qis the volumetric flow rate 3 g ( m / s ) ; L i s the length in flow direction (m); A is the cross-sectional area of specimen 3 ( m ) ; APis the pressure differential across specimen (Pa); P tm is the barometric pressure 2 a (Pa); and AP i is the open manometer reading on the vacuum side (Pa). The superficial gas permeability calculated from equation (5.1) can be converted to the specific permeability. This then becomes the same for all fluids used. It can be done by multiplying the superficial gas permeability by the corresponding gas viscosity. The specific permeability as a function of the reciprocal average pressure is shown in Figure 5.13. The intercept permeability, assuming no nonlinear or slip flow, which is called intrinsic permeability, K, can be obtained by linear regression through the Klinkenberg's equation (KJinkenberg 1941): K . = K ( I + =) (5.2) ,. _ AP where Ks is the specific permeability (m /m); b is the slip flow constant; P = AP, + — , is the average pressure (Pa). 106 4 ~ . 5 E - 1 4 5 E - 1 4 4 E - 1 4 i 3 . 5 E - 1 4 CM < E 2 . 3 E - 1 4 5 E - 1 4 E - 1 4 y = 7E-12x + 3E-14 2 R2 = 0.981 1 . 5 E - 1 4 1 E - 1 4 0 0 . 0 0 0 5 0 . 0 0 1 0 . 0 0 1 5 0 . 0 0 2 0 . 0 0 2 5 0 . 0 0 3 1/Pave(1/Pa) Figure 5.13 Specific permeability as a function o f reciprocal average pressure for the case o f hemlock sapwood longitudinal #4. The results of the longitudinal K values are listed in Table 5.2. Due to the high variation, the median value is also presented along with the range of the measurements (highest and lowest values). In the longitudinal direction the resistance to flow is almost entirely in the pitmembrane pores. Krahmer and Cote (1963) examined the membranes of both hemlock and cedar using electron microscopy. The membrane in hemlock has torus extensions in addition to fine strands radiating from a torus. In cedar, the membrane does not posses a torus, but consists of numerous, closely packed strands. The largest openings between the strands in 107 cedar are about one tenth of those in hemlock and this is why the latter exhibits average K values. Table 5.2 Longitudinal intrinsic permeabilities of western hemlock and western red cedar, heartwood (H) and sapwood (S). Sample # Hemlock-H Hemlock-S (um ) (um ) 0.31408 0.018441 0.028411 0.19651 0.136816 0.0030568 0.02146 0.27579 0.055326 0.113908 0.013226 0.147531 0.0075415 0.278611 0.019281 0.152611 2 1 2 3 4 5 6 7 8 Median Mean SD Covariance Highest Lowest 0.018861 0.0208429 0.0160634 77.069093 0.055326 0.0030568 2 0.174561 0.201982 0.076832 38.03877 0.31408 0.113908 Cedar-H Cedar-S (Um ) (um ) 0.0073081 0.13102 0.0011152 0.07429 0.0040388 0.1050129 0.23298 0.033298 0.0062125 0.09826 0.53533 0.013533 0.11235 0.039235 0.0084346 0.078917 2 0.0097932 0.0154015 0.0132959 86.328552 0.039235 0.0040388 2 0.1016365 0.1107954 0.0549792 49.622262 0.23298 0.053533 The ratio of heartwood to sapwood average K values was found to be about 10 in both hemlock and cedar - very similar to the 10 and 6.5 reported by Krahmer and Cote (1963). Pit aspiration is considered as the major reason for heartwood low K as compared to sapwood. The number of aspirated pits increases from sapwood to heartwood with a sharp increase in the intermediate zone, just prior to the apparent heartwood zone. In species like cedar, deposition of extractives in the heartwood evidently plays a part in partially blocking the fine microstructure of wood thus, affecting fluid flow. 108 Comparing Tables 5.2 and 5.3, it can be seen that all species always exhibit much lower transverse K values when compared to the longitudinal ones. This is due to the relatively lower total area for fluid transport in the transverse direction (size and number of rays), compared to the longitudinal direction (size and number of lumens). A comparison of the longitudinal with the transverse values reveals the high anisotropic behavior in K for both hemlock and cedar. The longitudinal K is two to three orders of magnitude higher than that in the tangential or the radial direction. This is especially important in timber drying since K is one of the major factors affecting moisture loss rates. The specimen ratio of longitudinal to transverse length does never exceed two orders of magnitude. All these are strong indications that the majority of bulk water flow above FSP should occur in the longitudinal direction - a phenomenon that has visually been observed in the past (Zhang et al. 1997). An average K value for the transverse fluid flow can be easily obtained and used in modeling since in most cases the exposed timber surfaces perpendicular to the longitudinal direction are almost always between the radial and the tangential ones. The smaller number of specimens measured for the transverse K was due to the longer time periods necessary to achieve constant flow rates. For hemlock, the sapwoodheartwood ratio of 2:1 remained for both the radial and tangential directions. The tangential K, in all cases, appeared to be slightly higher than the radial in both sapwood and heartwood for hemlock and in the cedar heartwood. A possible explanation could be that the number of rays and the total effective flow path was so small that the variability of the K values in the radial case could have a higher effect and thus provide such unexpected results. Furthermore, the number of specimens measured was also very low so that we cannot statistically assign a high certainty to a mean value for either radial or tangential permeability values. In a large 109 number of specimens it is expected that the average radial K would be higher than the tangential one. Finally, in two out of the three cases we studied heartwood where extractives and other substances could block some of the rays, the difference between radial and tangential K values could become more trivial. Table 5.3 Radial (R) and Tangential (T) intrinsic permeabilities of western hemlock heartwood (H) and sapwood (S) and western red cedar heartwood (H). 1 2 3 4 5 Hemlock H-R (um ) xlO 0.1417 0.2449 0.1013 0.6563 0.3231 Hemlock S-R (um ) xlO 0.5322 0.4828 0.4535 0.4131 0.8911 Hemlock H-T (um ) xlO 0.2537 0.3243 0.1907 0.5339 0.591 Hemlock S-T (um ) xlO 0.4633 0.8366 0.9148 0.7214 0.5107 Cedar H-R (um ) xlO 0.3868 0.5266 0.2248 0.1534 0.0698 Cedar H-T (um ) xlO 0.6395 0.2355 0.464 0.4211 0.4088 Median Mean SD Covariance Highest Lowest 0.2449 0.29346 0.220707 75.20849 0.6563 0.1013 0.4828 0.55454 0.193089 34.81958 0.8911 0.4131 0.3243 0.37872 0.1754186 46.318801 0.591 0.1907 0.7214 0.68936 0.197833 28.6981 0.9148 0.4633 0.2248 0.27228 0.183833 67.5162 0.5266 0.0698 0.4211 0.43378 0.144338 33.27445 0.6395 0.2355 Sample # 2 4 2 4 2 4 2 4 2 4 2 4 The results obtained for cedar are in the range of the ones given in Siau (1995). The longitudinal cedar values seem to be somewhat smaller than the ones given by Krahmer and Cote (1963). This can be attributed to a number of possible reasons, such as, the moisture content which in that study was about 14% compared to 0-1% in this one, and the temperatures that were used to remove the moisture which in their study were lower than those in our one. Higher percentage of pit aspiration is thus expected in this study and 110 therefore, lower K values. Another important issue pertains to the data analysis. In this study, the Klinkenberg equation (Figure 5.13) was used to calculate the average K, possibly resulting in lower values than the calculated K ones. Higher differences have already been s reported in the literature when the experimental procedures and data analysis are different between researchers. In an exactly similar comparison between a study similar to ours by Beall and Wang (1974) and a study similar to Krahmer and Cote (1963) by Comstock (1965), more than one order of magnitude difference was reported for eastern hemlock when comparing K and K values. Another possible source of difference is the very short s specimens (10 mm) used in the study by Krahmer and Cote (1963). Studies in the past have also revealed that when the specimen length is below a critical value, K drastically increases with decreasing specimen length (Lu 1997). Krahmer and Cote (1963), also measured the longitudinal K for hemlock. Their values are slightly higher than those in the present study. s The reasons are suspected to be the same as in the case of cedar. Finally, another important issue that is obvious through a quick examination of the K statistics is that, modeling that does not account for the high variability of K will probably not describe accurately the phenomena therein. A possible solution for consideration of this high variability is the stochastic modeling of the RF/V drying procedure. 5.4 Diffusion coefficients and sorption isotherms For the determination of the diffusion coefficient, the fractional change in moisture content at time t ( E ) was plotted against the square root of time ( Vt). The slope of the linear portion was determined and the moisture diffusion coefficient, D , can be calculated as (Siau b 1995): 111 5.10t b 5.10 ' v where D is the diffusion coefficient (m /s), E is thefractionalchange in moisture content 2 b E at time t (as defined in Siau 1995), d is the thickness (m); t is the time (s) and A = -j= is the slope. The final results collected for D can be given as a function of moisture content b [M = Mj + 2/3 (Mf - Mj)] and absolute temperature (T). The subscripts f and i indicate final and initial respectively. This can be obtained by nonlinear regression using the form of the following relationship: 1 (fa } a ^ D =— exp[[-^r + a J M - y - a ^ p. " M A T b 2 (5.4) where a,, a , a , and a are regression parameters. 2 3 4 The Hailwood-Horrobin (1946) model: 18. k.k,h k,h w l + k,k h l-k,k h m =—(—L_2— + 2 . 1 ) , _ ,.. (5.5) 2 where m is thefractionalmoisture content, h is thefractionalrelative humidity, ki and k are 2 equilibrium constants, and w is the molecular weight of the dry cell-wall per sorption site (Skaar 1988), was fitted to the sorption data using a nonlinear regression technique, (conjugate gradients with central derivatives and quadratic estimates), for the calculation of its parameters. The calculated Db values at temperatures 70, 50 and 30°C are listed in Tables 5.4, 5.5 and 5.6, respectively. These results are the average values of the sue replicas for each case. The variation is higher for the longitudinal specimens, as can be seen by the coefficient of 112 variation value inside the parenthesis, but it is generally much lower than the ones obtained from the permeability measurements. Though the variability is very high when we examine specific flow parameters, like the intrinsic permeability, less variability is observed when the transport phenomena are described by more general parameters, such as the Db. When modeling RF/V drying the above could be taken into account, i.e., to allow for a higher degree of variability in the most refined terms. Table 5.4 Average diffusion coefficients and the respective average moisture contents at 70 °C. The covariance is in parenthesis. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). D (m /s) *10 2 b 10 M D (nv7s) (%) *10 b 10 M (%) Hemlock 45-25% 65-45% 85-65% 95-85% Humid. D (m'/s) *10 (%) b 10 M D (m /s) *10 M (%) 2 b 10 S-L 5.7 (8.9) 14.73 6.41 (9.3) 11.72 7.83 (13) 8.09 8.79(16) 5.81 S-T 1.8(4.6) 14.91 1.32(5.3) 11.35 1.04 (5.1) 8.36 0.89 (5.8) 6.01 S-R 3.81 (12.7) 16.22 1.92 (12.6) 12.59 0.88(13.4) 9.47 0.56 (8.4) 7.07 H-L 2.85(11.4) 15.39 3.43 (12.8) 12.49 3.88 (17.9) 9.59 6.25 (13.3) 6.44 H-T 2.49 (3.9) 14.19 1.82 (5.1) 11.7 1.25 (6.5) 8.88 0.90 (7.7) 6.03 H-R 2.39 (6.7) 15.48 1.87 (7.1) 12.9 1.44 (5.8) 8.75 1.28 (5.2) 6.25 Cedar H-L 4.79(12.3) 13.47 5.63 (14.4) 10.93 6.19(18.3) 8.25 8.48 (12.7) 5.32 H-T 4.97 (8.7) 15.01 2.09 (5.2) 10.98 1.41 (6.9) 8.37 0.97 (5.6) 5.55 H-R 2.24 (7.2) 12.55 2.12(6.8) 9.18 1.81 (5.3) 6.33 1.47(9.7) 5.35 S-L 7.56 (8.6) 11.28 8.77 (14) 8.96 11.96(11.2) 5.97 14.95 (9.7) 3.91 S-R 1.99 (9.8) 11.68 1.69 (8.6) 9.22 1.22(6.7) 7.05 0.96 (6.5) 5.44 113 Table 5.5 Average diffusion coefficients and the respective average moisture contents at 50 °C. The covariance is in parenthesis. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). M (%) D (m7s) * io 8.55 7.17(10.8) 6.01 0.73 (6.9) 8.86 0.48 (4.2) 6.2 14.02 0.47 (8.8) 10.01 0.38(8.1) 7.31 3.03 (14) 13.57 3.44 (16.2) 9.62 5.23 (13.9) 7.01 16.98 0.82 (5.8) 13.15 0.52 (6.3) 9.67 0.32 (6.7) 6.67 16.77 1.04(9.4) 13.24 0.73 (6.2) 9.26 0.40 (6.7) 6.63 D (m'/s) *10 D (m'/s) *10 M (%) D (mVs) *10 S-L 3.51 (8.4) 15.54 4.46 (9.1) (%) Hemloc c 6.30(12) 12.15 S-T 1.20 (3.9) 15.79 0.76 (7.8) 12.5 S-R 1.11 (12) 17.83 0.67 (10) H-L 2.13 (12) 17.64 H-T 1.17(5.2) H-R 1.69 (5.3) b 10 45-25% 65-45% 85-65% 95-85% Humid. b 10 M b 10 b 10 M (%) Cedar H-L 3.19(8.8) 15.08 3.81 (7.6) 12.22 4.78(15.3) 8.72 5.98(11.8) 5.81 H-T 1.35 (5.3) 16.07 1.23 (8.8) 12.26 1.81 (9.2) 8.96 0.36(6.1) 6.21 H-R 1.60 (6.1) 13.12 1.30(5.2) 9.8 1.02 (6.9) 7.51 0.46 (7.8) 5.64 S-L 5.52(16) 12.72 6.69(15) 9.73 7.85 (15.7) 6.86 10.01 (18.6) 4.18 S-R 0.90 (6.6) 13.28 0.73 (8.7) 10.31 0.60(11.8) 7.75 0.45 (14.5) 5.62 In all cases examined, the cedar exhibits higher Db than hemlock when comparing the means at the same temperature, wood type and direction. This is according to the theory that an increase in specific gravity, in our case 0.31 to 0.42, results in significant reductions in Db due to the increased resistance of the cell wall paths for diffusion (Siau 1995). A comparison of heartwood and sapwood at the longitudinal direction for both species, when the temperature and the wood type are the same, reveals that sapwood has higher diffusion coefficient by 30-100% for hemlock and by 25-80% for cedar .The sapwood-heartwood comparison for the tangential and radial directions does not yield a clear trend. This is because other factors become dominant, such as, the moisture content that has a higher effect 114 on the Db than do structural differences of heartwood and sapwood. The longitudinal Db is always higher than the tangential or the radial one when comparing the same species at the same temperatures, wood types and moisture contents. The different configuration of the flow path in each direction explains well this behavior. In most cases, when the effect of the moisture is not more significant than the one of anisotropy, the radial Db is higher than the tangential one. Similar results have been published in other studies (Siau 1995). This phenomenon was explained therein by the additional ray flow paths in the radial direction. Table 5.6 Average diffusion coefficients and the respective average moisture contents at 30 °C. The covariance is in parenthesis. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). D (m /s) *10 2 b 10 M (%) 65-45% 85-65% 95-85% Humidity D (m /s) *10 2 b 10 (%) D (m7s) *10 M (%) M b 10 Hemlock S-L 1.32(4.5) 24.34 2.75 (6.8) 13.96 4.01 (8.1) 10.48 S-T 0.86 (6.6) 21.18 0.59(8.7) 14.64 0.29 (4.3) 11.17 S-R 1.11 (4.8) 20.35 0.56 (6.7) 14.19 0.33 (5.3) 10.82 H-L 1.09 (8.7) 21.84 1.83 (9.2) 15.46 2.58 (6.8) 11.64 H-T 1.47 (4.2) 21.85 0.67 (4.1) 15.04 0.42 (5.4) 11.5 H-R 0.98 (4.8) 18.91 0.79 (7.8) 13.56 0.53 (4.3) 10.17 Cedar H-L 1.82 (8.1) 19.65 2.68 (5.3) 14.14 3.22 (8.6) 10.46 H-T 0.82 (5.2) 13.98 0.60(6.1) 10.67 0.36 (9.2) 8.69 H-R 1.18 (6.1) 19.17 0.95 (5.8) 13.92 0.72 (5.6) 10.58 S-L 3.22(12.9) 16.81 4.78 (17.8) 11.54 5.48(13.3) 8.82 S-R 0.98 (7.9) 14.56 0.51 (5.4) 11.03 0.31 (3.7) 8.97 115 Figures 5.14 and 5.15 present the Db data versus moisture content at different temperatures, for the longitudinal and radial cases of hemlock and cedar sapwood. Similar curves can be obtained for the tangential direction and for all heartwood data for both specimens. The curves follow the same trend as the theory predicts (Siau 1995). The higher values at low moisture contents for the tangential and radial direction are a consequence of the greater bonding energy at the sorption sites. In the longitudinal direction the overall diffusion coefficient is dominated by the water-vapor diffusion coefficient of air in the lumens because of the overriding effect of the conductance of the lumen (Siau 1995). Increase in diffusion rates is also observed in all cases with an increase in temperature. Higher temperatures mean higher percentage of water molecules with energies sufficient enough to overcome the energy barrier for adsorption or desorption depending on the initial and thefinalconditions. This, in turn, means higher diffusion coefficients. A difference in the FSP between species and among directions is also obtained through the diffusion coefficient data. Table 5.7 lists the FSP values for each case. The FSP decreases with an increase in temperature according to the literature (Stamm and Nelson 1961). For the longitudinal direction the FSP seems to be at about 21.5%, which is very close to the 21% given in Siau (1995) for room temperature. The FSP seems to decrease 0.2% with each 10°C rise in temperature for cedar, which is double to the one reported by Stamm and Nelson (1961). Also, in most cases the decrease observed is not linear. The effect of the specification of the FSP though has not been presented along with the current model of RF/V drying. This can be obviously considered as very important since the transfer mechanisms and the relevant equations describing the phenomena change considerably. 116 100 HSL T30 HSL T50 HSL T70 C S L T30 C S L T50 o < C S L T70 5f 10 CM < E 15 10 25 20 M(%) Figure 5.14 Diffusion coefficient versus moisture content of hemlock (HSL) and cedar (CSL) sapwood at longitudinal direction and temperatures of 30, 50 and 70°C. 10 o < o « 5r 1 < E H S R T 3 0 H S R T 5 0 H S R T70 C S R T30 C S R T50 C S R T70 0.1 5 —i— 15 10 20 25 M(%) Figure 5.15 Diffusion coefficient versus moisture content of hemlock (HSR) and cedar (CSR) sapwood at radial direction and temperatures of30,50 and 70°C. 117 Table 5.7 Fiber saturation points at different temperatures for western hemlock and western red cedar. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). Hemlock T(°C) S-L S-T S-R H-L H-T H-R 30 26.77 23.30 22.39 24.02 24.04 20.80 50 17.09 17.37 19.61 19.40 18.68 18.45 70 16.20 16.40 17.84 16.93 15.61 17.03 Cedar T(°C) S-L S-R H-L H-T H-R 30 18.49 16.02 21.62 17. 68 21.09 50 13.99 14.61 16.59 16.51 14.43 70 12.41 12.85 14.82 15.38 13.81 Table 5.8 was compiled by using equation (5.4). Such equations can be very useful when modeling RF/V drying although a correction should be added to compensate for the vacuum. While linear approximations already appear in the literature (Fohr et al. 1995), an exponential type of approach for the pressure similar to the temperature term seems physically more appropriate. Table 5.9 includes the parameters as were estimated using the Hailwood-Horrobin model to describe the sorption isotherms. There are several interesting points to observe in these data. First, there is considerable variation among the examined cases with respect to the values of the constants obtained. This indicates substantial difference in hygroscopicity among these cases. Higher value of w means that there are fewer sites available for sorption. In all cases the value of w for cedar is higher than the respective one for hemlock, except for the cases of heartwood in the radial direction for both thicknesses at T=30°C. The w is higher for 118 sapwood compared to the respective heartwood ones except for the thin radial hemlock at all temperatures, the thick radial hemlock at T=30°C and the thin radial cedar at T=50 and 70°C. For hemlock, the longitudinal values of w are higher than the tangential and the radial respective ones. The opposite is observed for the thick sapwood radial hemlock case at T=50°C and T=70°C and for the hemlock heartwood where all the directions exhibit higher w value than the longitudinal one at all temperatures. For cedar sapwood, the longitudinal w is always higher than both radial cases. For cedar heartwood at T=70°C, the longitudinal value of w is lower than all the other directions. At T=50°C, the tangential value is lower than the longitudinal and at T=30°C the trend becomes completely opposite for all directions. It seems like there exists a mechanism that with increase of the temperature activates more sites for sorption in the longitudinal direction. There is no clear trend in the results when comparing the values of w for the tangential versus the radial corresponding cases. For cedar sapwood the thicker pieces exhibit higher w values. However, for heartwood, w is higher for the thinner radial pieces at all temperatures. The same is observed for hemlock sapwood and heartwood at T=30°C, although this trend completely reverses at higher temperatures. Finally, w increases in all cases with a temperature increase. This was expected since it is known that increasing the temperature reduces the hygroscopicity of wood. 119 Table 5.8 Parameters estimated for equation (5.4). (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). Hemlock ai a2 a 3 &4 S-L S-T S-R H-L H-T H-R -104.86 0.2540 383.8 -2.702 -40.75 0.2053 2471.8 -5.62 -219.4 0.8374 2482.4 -4.470 -0.752 -0.089 794.17 -3.826 -131.2 0.5217 1825. 7 -3.3281 -295.8 0.9827 -1492 6.1631 H-T H-R -545.49 1.78354 -1477.4 6.79107 59.246 -0.116 3710.5 -9.801 Cedar H-L S-R -101.9 31.197 0.4121 -0.163 2474.2 1814.1 -5.379 -6.611 S-L ai a2 a 3 &4 115.82 -0.4335 2461.8 -9.102 Table 5.9 Parameters estimated for Hailwood-Horrobin model for western hemlock and western red cedar. (S=sapwood, H=heartwood, L=Longitudinal, T=Tangential and R=Radial). T = 70°C T = 50°C T = 30°C w k, k 0.776 378.8 1635.7 0.772 1632.3 0.770 370.4 1631.4 0.765 302.8 1619.5 0.761 313.4 1616.3 0.740 0.781 319.7 3381.3 0.772 325.2 3374.2 0.740 3388.2 0.788 326.7 3356.1 0.768 346.8 3352.2 0.736 3344.7 0.777 332.4 3353.9 0.771 344.9 3335.9 0.762 0.769 389.4 3380.1 0.756 w w ki K S-L 340.9 1641.7 0.856 365.5 1635.8 S-T 288.4 3386.0 0.787 351.2 S-R 295.6 3383.5 0.783 H-L 272.6 3359.8 H-T 280.9 H-R 309.2 2 k, Hemloc c k 2 2 H-L 301.0 3389.9 0.781 Cedar 364.0 3386.5 H-T 333.1 3322.1 0.705 354.5 3340.2 0.775 396.3 3378.8 0.785 H-R 293.0 3295.2 0.765 400.0 3375.7 0.747 451.5 3377.9 0.769 S-L 367.1 3346.8 0.790 501.1 3347.8 0.808 545.4 3374.4 0.800 S-R 324.8 3380.9 0.710 391.6 3386.8 0.748 405.4 3336.1 0.716 120 5.5 Analysis of R F / V experiments with the amplifier A small number of experiments were conducted using a 50-Ohm technology amplifier. This is the first time to obtain results of RF/V drying, where the power absorbed by the material can be controlled and quantified very accurately. That the heating characteristics of an oven are intimately dependent on the dielectric properties of the workload to the conditions subjected, and that small changes may totally change the heating pattern is a fact which few realize (Meredith 1996). The "50 ohm systems" have been characterized as the next step forward (Jones 1996). These are based on afixedfrequency where a crystal oscillator amplifies the required power in several stages. Typically the first stage, up to a few kilowatts, is done by solid-state devices and thereafter by a thermionic valve circuit. Such an arrangement allows much better control of generation, transmission and application. It brings to RF the opportunities offered by the separation of the generators from the process environment, which up to now have only been possible with microwave. Because of the fixed frequency of the signal it is very simple to ensure that the equilibrium moisture content regulations on stability are met at the more tightly controlled frequencies of 13.56 and 40.68 MHz., which sometimes has process advantages over the more usual 27.12 MHz option. Furthermore, since the output is controlled from the crystal driver and every section of the system is made to look like 50 ohms, it is not necessary to use variable inductors or moving electrodes as a means of energy transfer control. Once this is fixed, it becomes possible to set up a truly uniform electric field over the whole area of a large electrode. This will result into a much more uniform temperature distribution within the product. 121 The species were the same as in the previous experiments, namely western hemlock and western red cedar. Two experiments were conducted with hemlock that had average moisture content in the so-called hygroscopic region. Another eight experiments covered both regions above and below the FSP, where four pieces were western red cedar and another four were western hemlock. Details about the experimental conditions can be found in Table 5.10. The frequencies during the last two runs of western hemlock were 8.4 and 8.5 MHz, respectively and the rest of the experiments were carried out with a frequency of 6.78 MHz. All the specimens were 2 m long. The cross section dimensions of each of the pieces were 200 by 200 mm except for the last two western hemlock runs, where the specimens were 250 by 250 mm in cross section. Another unique aspect of these experiments is that they were conducted in low power densities (PD) in order to ensure that no internal checking will occur. Modeling with a constant permeability factor throughout the piece might not be totally true. Internal checking can increase the local permeability locally by many orders of magnitude. Since permeability has such a central role in modeling drying behavior of porous materials, acceptable comparison of experimental and modeling results can only be obtained if such inaccuracies are avoided. This type of degrade can be monitored at the end of an experiment. Modeling involving the increase of permeability due to internal cracks, is possible with the use of ES. A direct consequence of the above choice was an increase of the drying times. The complexity to locate the proper time for a number of internal checks increases considerably with the number of these checks. Thus, the increase in the drying duration is well justified. It has to be reminded here that there are two possible ways by which internal checks may appear. One is due to a non-uniform shrinking below the F S P . The other is due to extremely 122 rapid local heating and vaporization. Since wood has low permeability, the internal pressures that evolve inside the material can cause fracture of the cell wall. Since the local moisture content during a drying run is not measured, there is no means by which to clarify the mechanism responsible for each specific case. Table 5.10 Master table of the experimental conditions for RF/V drying when using the amplifier. HEMLOCK kPa Voltage V Target PD (kW/m ) 3.3 0.04-0.18 1.1 61 3.3 0.03-0.16 2.2 13.3 0.04-0.13 1.1 13.3 0.05-0.2 2.2 Mi % M % TMAX PA # Time Hrs C 1 201.16 63.32 10.39 62 2 97.33 68.11 10.64 RUN F 3 500 51.22 14.17 57 4 88.33 42.40 15.43 65 J 5. 57.75 32.93 10.56 50 3.3 0.08-0.35 2.4 6 68.94 29.84 12.79 69 13.3 0.09-0.42 2.4 CEDAR 1 155 51.78 14.95 88 3.3 0.05-0.15 2.2 2 220 54.98 14.88 70 3.3 0.04-0.17 1.1 3 195 55.44 14.76 98 13.3 0.05-0.26 2.2 340 66.24 15.12 91 13.3 0.04-0.20 1.1 4 It can be observed that there is a trend in the maximum temperature for the same power density conditions, when the initial moisture content is higher. This is expected since the power absorbed is proportional to the moisture content. For similar initial average moisture contents (runs # 5 and # 6 of western hemlock), the maximum temperature is obtained when the ambient pressure is higher. This is a strong indication that moisture transport occurs mainly in the vapor state. Lower ambient pressure means lower boundary temperatures which facilitate vaporization. Assuming similar temperature and pressure gradients (same internal mass transfer), the maximum temperature usually appears in the center when the ambient pressure is lower. It has to be noted here that sometimes the 123 maximum temperature may not be obtained in the center, i.e., if the initial moisture profile is extremely non-uniform with high local moisture gradients and at the same time the heating is very rapid using high power densities. Comparing the drying times for both species, we observe that the WH pieces dry faster though their moisture ranges are higher than those of the WRC pieces. The WRC pieces were almost pure heartwood but the WH pieces were mostly sapwood. A reasonable explanation can then be found if the relevant properties of these species are examined. For example, the permeability of WH sapwood is higher than that of WRC heartwood. The ranges of voltage between the plates, as these are presented in table 5.10, can provide some additional information. The lower voltage values are not the initial ones but they are obtained during the heating period. During this period the total moisture can be assumed constant. The same is true for the power density, the frequency and the distance between the plates. Examination of relation 4.66 yields that the loss factor of the dielectric should increase to counterbalance this decrease in voltage during the heating stage. In other words, the temperature increase yields an amplification of the loss factor, which is consistent with those reported in the literature (Torgovnikov 1993, Zhou and Avramidis 1999). The maximum voltage values are obtained at the end of the experiments, when the total moisture content is the lowest. Thefrequencyin runs #5 and #6 of WH was higher than the rest of the experiments, by a significant amount of 25%. However, the dimensions of the pieces and therefore the distance between the plates were 25 % higher. The effect of the plate distance change is of second order and the effect of frequency change is of first order, as is evident by the relation 4.66. This is why runs #5 and #6 exhibit higher maximum voltage values 124 compared to those of thefirstfour WH runs. The effect of temperature through the loss factor is very little because of the low loss factor value in the end of the drying runs. Figures 5.16 and 5.17 display the drying curves of WH and WRC at different ambient pressures and different power densities. Details for these runs can be found in Table 5.10. Assuming that the M is 42%, the FSP is 25% and the M is 15% for WH, we observe r F that the drying time increased 3 and 6 times, above and below the FSP respectively, when the PD decreased in half at ambient P = 13.3 kPa. At ambient P = 3.3 kPa the drying time increased 3 times in both areas above and below the FSP. Above and below the FSP an increase in the drying time by 2 and 2.5 respectively is observed, when the ambient pressure increases 4 times and the PD = 2.2 kW/m . At PD = 2.2 kW/m the drying increases by 2.5 3 3 and 5 times above and below the FSP respectively when the ambient pressure increases 4 times. At the moisture range of 25-15% another interesting comparison can be done between #5 and #2 and between #6 and #4 pieces. It has to be reminded here that pieces #5 and #6 had larger dimensions, 25% larger thickness and width, and were dried at 10% higher PD. At P = 3.3 kPa a 50% increase in drying time was obtained, when the piece was thicker though the PD was higher. At P = 13.3 kPa, the drying time increased by 10% for the piece dried under lower PD though this piece was thinner. Assuming Mi = 52%, FSP = 25% and M = 15% for WRC, the drying time increased F by 100% and 30% above and below the FSP, respectively, when the PD decreased in half at P = 13.3 kPa. At P = 3.3 kPa the respective increases were only 20% and 30%. Comparing the experiments with same PDs, in all cases below the FSP we obtain an increase in the drying time by 20%, when the ambient pressure increases 4 times. Similarly, above the FSP the drying time increases by 10% and 50% at the high and the low PDs, respectively. 125 0 50 100 150 200 250 300 350 400 450 500 Time (hrs) Figure 5.16 Drying curves of WH at different power densities and ambient pressures. —%ced1 —B— % ced2 -%ced3 — * - % ced4 Figure 5.17 350 400 300 200 250 Time (hrs) Drying curves of WRC at different power densities and ambient pressures. 126 All the above results are indications of the general rules that a drying run exhibits. More specifically, it was indicated that the effect of change of PD on the drying time is stronger than the effect of changing the ambient pressure. There is a limit of increasing the power density due to internal checking and significant quality degrade of the product. There is also a limit of reducing the ambient pressure. This is related to the ability to achieve and maintain low ambient pressures and energy requirements in industrial level. The above preliminary results can suggest directions to set the levels of PD and ambient pressure for future investigations. The results discussed above certainly cannot be generalized due to lack of repetitions and due to the short range of investigated parameters. The total power per mass of water removed can also be an important parameter to optimize future RF/V drying schedules utilizing the 50-ohm technology. Figures 5.18-5.21 display cross sections taken along the pieces that were dried under the highest PD of 2.2 kW/m . Thefirstpiece in all cases is taken 200 mm from the front end. 3 Each next piece is taken 400mm after the previous one. There was no case where internal checking was obtained. Distinct lines in these pictures are either due to uneven surface due to chainsaw cutting or due to moisture unevenness. On the other hand,figure5.22 shows end checks radially and tangentially at the front cross section of WH4. Though the picture was taken at the end of the experiment, these end checks were observed to develop during and not at the end of the experimental run. In all cases these were developed at the very early stages of the drying when the total moisture content was well above the FSP. Similar observations were obtained for all experimental WH runs. In none of these experiments, side checks were obtained. This is an indication that the drying conditions were mild. Therefore, assumption that the permeability was not significantly altered during the runs is considered valid. 127 Figure 5.18 Slices o f cross sections of Western Hemlock #2 at different points longitudinally. • Figure 5.19 z'}..:. v .....L..,. sm^mmm Slices o f cross sections o f Western Red Cedar #1 at different points longitudinally. 128 Figure 5.21 Slices of cross sections of Western Red Cedar #3 at different points longitudinally. 129 Figure 5.22 Front end cross section of Western Hemlock #4 at the end of the experiment. A possible explanation for the appearance of end checks will be described. Lowering the ambient pressure and heating the pieces volumetrically leads to the development of local internal pressure gradients. The stresses that are thus developed are isotropic. The strength of the cell wall is higher in the longitudinal direction so cracks appear in the weaker directions i.e., the radial and the tangential. These are obvious at the surface that is perpendicular to the longitudinal direction, which is the end surface. The reason that only end checks and no internal checking is observed, is that the magnitude of the pressure gradient is much greater at the ends in the case of vacuum drying. Also, due to the mild drying conditions (due to lower power densities), any internal pressure gradients that could develop (possibly to unevenness in the moisture profile), are low. This might be due to extended time for internal moisture transport and redistribution. 130 Another possible explanation can be that the small layers at the ends reach MC's below the FSP rapidly due to vacuum. These layers being in a dry environment on the side of the vacuum start shrinking below the FSP. Shrinking is a highly anisotropic phenomenon for wood and strong stresses can be developed leading in cracks. The concept of the Transition Layer under vacuum drying has already been proposed in the literature (Sebastian et al. 1996) that completely agrees with the explanation provided above. An additional important observation during the experiments is that due to the configuration of the dryer with the lower plate grounded, gives rise to a temperature gradient between the plates. This was never the case with the oscillator, where none of the plates was grounded. The temperature gradient is usually mild of about 5°C. However, in some cases it can reach as high as 20°C, as in WRC#3 run. In such a case, an extreme moisture difference is observed in the direction of the plates. Specifically in this run, the moisture content was measured to be at about 7% close to the top phase and above 40% close to the bottom phase. Though all the temperature and pressure probes during the experiments were in the middle of the distance between the plates, future modeling and experimentation should account for such observations. Such a phenomenon should be of primary interest in industrial level, where the quality of the product is a strong function of the final moisture distribution. In order to avoid such non-uniformities, a low thermal conducting material could be introduced between the lower plate and the specimen, such as a polyethylene plate that was utilized previously to stabilize the electricfieldin the case of an oscillator. Some additional information was obtained from the initial and final moisture profiles. Moisture uniformity is considered an important quality factor of wood products. The initial profiles were assumed to be linear interpolation of the end profiles that were measured. The 131 final profiles were measured and no assumptions are necessary. A total of six pieces will be compared. These are all the WH pieces and the last two WRC ones. The selection was done so that the initial average moisture contents are the highest and so that all possible comparison cases can be covered adequately. WH #1 had an average initial moisture content of 53% on the front end, 39% on the left side and 63% on the right side. On the back side the moisture content ranged from 64% on the left to 91% on the right. Thefinalmoisture profile horizontally was extremely uniform with 9-12% moisture content in all pieces. The final longitudinal moisture content was 1011% all over the piece. As it will be shown later this is the greatest uniformity and was achieved at the lowest ambient pressure and low power density. The results are even more significant if we consider the high initial variation that was recorded. The initial longitudinal moisture profile for WH #2 can be considered very uniform since the moisture content was 72% and 69 % on the back and the front side respectively. Large initial non-uniformity was obtained for the initial horizontal profiles. In both ends the center was drier than the edges. On the front a range of moisture contents of 45 to 40 and to 143% was recorded from the left to the right as the piece can be seen from the front side when it is in the dryer. Similarly for the back side, a range of 45 to 40 and to 124% was recorded initially. The longitudinal profile in the end was uniform at 12% moisture content. The local moisture in the horizontal direction was in the range of 11-15%. The final horizontal profile resembled the initial one, where the pieces in the center were drier. WH #3 exhibited initially an even longitudinal moisture profile of 44 and 46 % for the front and the back part respectively. This was a major factor to obtain a very uniform longitudinal final profile in the range of 10 to 13%, where the end parts were dryer than the 132 inner ones. The horizontal initial moisture profile on the front was almost linear ranging from 50% on the left to 40% on the right side. The back side exhibited initially a wavy pattern with minimums and maximums of 53, 41, 51 and 41% moisture contentfromleft to the right. Though in previous WH cases the initial non-uniformity in the horizontal direction was higher, the larger final moisture content range of 8-15% was measured in this experiment. This is an important indication that in order to achieve maximum uniformity, the ambient pressure must be kept as low as possible. The patterns of the final moisture profiles in the horizontal were opposite to what were described for the previous run. Similar to the longitudinal direction, the inner parts were wetter than the end ones. The initial longitudinal moisture content patterns for WH #4 can be considered as rather uniform, since the front and back moisture contents were 49 and 41 % respectively. This is the major factor to obtain final longitudinal moisture uniformity in the range of 1517%. The initial moisture content recorded horizontally was for the front side, 40 to 74%, from the left to the right. Similarly on the back side 38 and 45% was measured. All the final moisture content measurements for the horizontal profile were in the range of 14-19%. It was the first time that no trend was exhibited so that the inner or outer parts to be always either wetter or dryer. The initial horizontal moisture profile at the front and the back end of WRC #3 had dryer edges. It was respectively 34 to 56 to 31% and 45 to 63 to 39% from left to right. Though the total moisture range of the pieces for the final horizontal profile ranged between 13 and 18%, extreme horizontal uniformity was observed for each individual piece measured along the length. The maximum difference was always within 1%. The average initial moisture at the ends was 43 and 50% at the front and the back correspondingly. The final 133 moisture longitudinal range was narrow at 13 to 16% with the ends been dryer, following the initial horizontal trend. WRC #4 exhibits a rather non-uniform initial longitudinal moisture profile, where the moisture content is 79 and 53% at the front and the back end respectively. The range of final longitudinal moisture profile is 11-16% and the ends are drier. Similar "memory" trend that was observed for WH #2 was observed in this WRC run, for the horizontal profile. Initially the front was wetter inside in both ends. On the front the moisture initially was, from left to right, 61, 103 and 47%. Similarly on the back we measured moisture content of 40 67 and 32%. Thefinalhorizontal moisture profile gave a range of 8-18%, the highest so far. Both factors, the initial non-uniformity and the high ambient pressure, can explain this observation. The outer parts were in all cases dryer than the inner ones. Comparing WH #1 and WRC #4, we see that for similar drying conditions, the final moisture content is more uniform in the case of WH. A possible explanation is that the WH piece was mostly sapwood and the WRC piece was mostly heartwood. The transport properties are enhanced in the sapwood so a condition of "equilibrium" and uniformity is more probable. In all cases compared when only the power density was changing, no clear trend could be obtained on if a lower or higher power density enhances uniformity. Finally the shrinking was minimal in all directions similar to what was obtained with an oscillator. The pressure system introduced had an effect on the shrinking but it is considered not significant. At an average the shrinking was about 1.55% for the width, and 2.02% for the thickness. 134 In the next paragraphs the concept of the Identity Drying Card (IDC) as was developed by Perre (1995) will be applied to RF/V drying experiments in order to obtain useful information related to the drying mechanisms and the relevant phase transitions. Figures 5.23 and 5.24 are pressure-temperature diagrams for the cases of WRC #3 and WH #2. The saturated vapor pressure lines, which separate the liquid phase areas from the vapor phase areas, are denoted as Psat- Above the line is the liquid phase and below the line is the vapor phase. The three points of comparison are: the core which is right at the geometric center of the piece, the quarter length which is a quarter lengthfromthe front face and at the center of this face, and the quarter width which is a quarter width awayfromthe left side at half length and height. 550 500 H 450 400 350 •p 300 o l— ST 250 200 150 100 50 270 280 Figure 5.23 290 300 310 320 330 T(K) 340 350 360 370 380 IDC for the case of WRC #3. 135 Initially a pressure drop is observed in all cases due to the externally induced vacuum, until a local minimum of pressure is obtained. This local minimum is a factor of the local parameters of permeability, power density, porosity and moisture content. At this stage the vapor generated inside the material at the position of measurement and the vapor removed from this position towards neighbor areas of lower pressure are equal. 350 • Psat -B-Pc 300 -Ar-Pql -*-Pqw 250 — 200 o °- 150 -\ 100 50 280 290 300 310 320 330 340 T(K) Figure 5.24 IDC for the case of WH #2. As the heating stage proceeds, more liquid turns into vapor because of the continuous dielectric heating. The creation of these new vapor molecules is faster than the removal of water from the neighbor areas. This is enhanced in areas, where there is a temperature gradient as for example at the outer layers. There due to lower outer temperatures the vapor can turn into liquid and more energy and time will be required for further transfer of this water mass. At some point, there is not more void space in the neighborhood for water to be 136 removed. As a consequence local heat removal is reduced and the temperature increases. Increase in temperature means a new local equilibrium between liquid and vapor, favoring more vapor generation. More vapor generation results in higher pressures. This is the loop leading in higher temperatures and pressures as is observed in all cases in both figures. The difference in the rate of increase of these both parameters is now clear that is a function of the local power density, permeability, moisture content and porosity. The existence of the dynamic equilibrium between the liquid and vapor is apparent from the shape of the Pressure-Temperature (PT) curve that is obtained experimentally. When the majority of water is removed from the area of measurement, the PT line crosses the saturation vapor pressure line and the conditions describing the area of measurement are characteristic of a mixture rich in vapor phase. A pressure drop follows in this state, which is more obvious in Fig 5.22. This is probably due to the higher ambient pressure in this run. It can be noted here that in both Figures 5.22 and 5.23, for runs of same power densities and dimensions, the core pressures reached a high, which is about four times higher than the ambient pressure before crossing the saturation vapor pressure curve. In both cases above the core curve crosses the saturation curve at about 40 hours. For WRC the quarter length crosses at about 35 hours and the quarter width at about 45 hours. For WH 50 and 55 hours were required to cross the saturation line respectively. In all cases, the longer time was required for the quarter length position. This is a serious indication that during the experiment water migrates in the outer layers and due to lower temperatures at the boundaries, liquid transformation of the vapor arriving from the interior occurs, requiring further heat absorption for evaporation. The fact that only in one of the cases, conditions characterizing vapor phase, appeared faster in the core compared to the quarter length, can be 137 explained by the longitudinal moisture non-uniformity in wood. If the core and the neighbor areas are dryer, they are expected to cross the saturation curve faster than other points of the geometric center line across the length, as is here the quarter length point of measurement. On this basis, non-destructive methods for moisture measurement could be very useful in the future, giving a clearer picture of the phenomena inside wood during RF/V drying. Measurements of more points, mainly closer to the boundaries could also enlighten the subject of existence or not of an evaporating front during RF/V drying and its possible behavior and extent. 5.6 Calculations with the 2-D model and comparison with experiments In this chapter the 2-D calculation details will be given. Comparison with the last experiments obtained with the amplifier will follow. Initially some key points on the optimization procedure (ES) and changes as can be considered in comparison with the 1-D case will be disclosed. The minimization function is a summation of the absolute experimental and calculated differences of the local temperatures, the total moisture content and the final moisture profile. Optimization parameters were involved to allow parameters such as the permeabilities that exhibit variability to take a mean value in the ranges that can be found in section 5.3. The pressure above the FSP was corrected in cases where it exceeds considerably the assumed saturated pressure, as can be seen in Figure 5.23. In cases where no noteworthy difference was observed as in the case shown in Figure 5.24, no pressure enhancement was introduced. The relative permeability though could be taken, as an optimization parameter at each direction, in the form given in Perre and Turner (1997). 138 The temperatures and moisture contents calculated were allowed to vary only within certain ranges due to instabilities that could arise during the optimization procedure. Temperatures calculated were always in the range of 0-100°C and m was always positive and not higher than the maximum moisture content introduced by the initial conditions. When local temperatures or moisture contents calculated were out of ranges, the concept of a penalty function was introduced. The barrier method was followed where a very high value is given to the function to be minimized when the calculated parameters of interest were out of range. This technique eliminated instabilities that occurred during the optimization procedure. The experiments that were selected for presentation here cover all the cases of different ambient pressures and power densities for western hemlock. Similar results were obtained for western red cedar. The higher range of moisture content was also an important factor in the choice for presentation of the cases below. The temperature predictions of the 2-D form of the model are better than the ones of the 1-D form mainly due to additional flexibility that is allowed by the range of permeabilities in both the longitudinal and transverse directions. Another important factor that allowed better temperature predictions is the uniformity of the heating in the cases of the 50-ohm amplifier as compared to the cases of the oscillator. The total average moisture content is predicted extremely well in all situations. Since the 2-D form of the model is a simple extension of the 1-D form, the evolutions of the moisture and the temperature profiles are similar in both directions to the ones presented previously in Figures 5.11 and 5.12. 139 Figure 5.26 Calculated and experimental total average moisture and temperature changes with time at quarter length, quarter width and core points for WH2. 140 Figure 5.27 Calculated and experimental total average moisture and temperature changes with time at quarter length, quarter width and core points for WH3. 141 Chapter 6: Conclusions and Recommendations 6.1 Conclusions The objective of this thesis was the development of a model that describes the heat and mass transfer phenomena during RF/V drying. Initially a 1-D model was constructed and its predictions were compared with experimental results. This comparison has led us to improve and extend the 1-D model to a 2-D one. For more accurate predictions, the most important parameters, namely the permeability and the bound water diffusion coefficient were measured for two different species, different wood parts (sapwood and heartwood) and different directions (longitudinal, tangential and radial). The data obtained were utilized in the 2-D form of the model to predict the drying times, the total moisture evolution and the local temperature evolution at different points. From this investigation, the following conclusions can be drawn: 1. 1-D modeling of RF/V drying is not enough to describe completely and accurately the phenomena of heat and mass transfer. Success in many cases to predict reasonable behavior is basically due to the high anisotropy in the permeability that favors the mass transfer to occur mostly in the longitudinal direction above the FSP. 2. It is impossible to obtain reasonable results in cases where the temperature and pressure effects are omitted. These seem to be dominant in the case of RF/V drying of thick lumber. Moisture gradients are not enough to describe completely the phenomena occurring during RF/V drying. 3. Capillary phenomena are less important in the longitudinal direction compared to the transverse direction due to the high ratio of longitudinal to transverse dimensions common to commercial RF/V wood drying. 142 4. Evolution strategies can be a very effective tool in developing mathematical models even for very complicated situations. The ability to examine many possible practical situations is ideal. 5. Extension in two dimensions yields more realistic and improved predictions, i.e. temperature profile. 6.2 Future Research In the light of this investigation, certain conclusions have been drawn and it has been realized that further research is needed. The extension of the model in a three-dimensional form is a priority. The usefulness of such an extension can only be justified in a case where a greater number of temperature and pressure points can be measured internally so that such profiles can be provided in detail. Comparison of calculated and experimental results can provide a realistic error analysis of the model. Another challenging problem is the measurement of the evolution of the moisture profile. Non-destructive methods (i.e., CT-scanning) appeared recently in the literature could be investigated and the feasibility for the combination of these methods with RF/V wood drying should be definitively explored. A method to deal with the extremely complicated nature of products like wood that are highly anisotropic and hygroscopic is to make basic research at different situations like RF/V drying of species only below the FSP or only above the FSP. The heat and mass transfer phenomena can be much better quantified in such a way. The scale of such experiments can be much smaller than the one in this study. This will enable the investigation 143 of the pure effects of each wood part (sapwood and heartwood) and each direction offlowon the drying behavior. The effect of the external pressure below the FSP has to be examined and quantified properly. This could be easily done as long as well-designed experiments exist and the results are compared with the predictions of a proper three-dimensional model and an evolution strategy optimization code. The model can be improved with the addition of solving the Maxwell equations together with the flow model. Stress analysis can also be implemented so that proper set values for the power density and pressure could be identified. The latter is expected to be a matter of high industrial interest. The total effect on the heat and mass transfer in different directions can also be studied by simply comparing drying experiments at different scales of length, width and thickness. Finally, an investigation and improvement of the evolution strategies optimization codes in order to achieve faster results for real life problems is a future challenge. 144 References Avramidis, S. and R.L. Zwick. 1992. Exploratory radio frequency/vacuum drying of three B.C. coastal softwoods, Forest Prod. J., 42 (7/8): 17-24. Avramidis, S. and J. Dubois. 1992. Holzforschung, 46(2): 177-179. Sorption energies of some Canadian species. Avramidis, S. and F. Liu. 1994. Drying characteristics of thick lumber in a laboratory radiofrequency/vacuum dryer. Drying Technol. 12(8): 1963-1981. Avramidis, S., F. Liu and B.J. Nelson. 1994. Radio-frequency/vacuum drying of softwood: drying of thick western red cedar with constant electrode voltage. Forest Prod. J., 44 (1): 41-47. Avramidis, S., R.L. Zwick and. B.J. Nelson. 1996. Commercial-scale R F / V drying of softwood lumber. Parti. Basic kiln design considerations. Forest Prod. J., 46 (5): 4451. Avramidis, S , L . Zhang and S. Hatzikiriakos. 1996. Moisture transfer characteristics in wood during Radio Frequency/Vacuum drying. In Proceedings of 5 IUFRO Wood Drying Conference, 125-133. th Avramidis, S. 1999. Radio Frequency Vacuum Drying of Wood, in Proceedings of International Conference of COST Action E l 5 Wood Drying, Edinburgh, Scotland, United Kingdom, October 13-14, 1-14. Beall, F.C. and J-H. Wang. 1974. Longitudinal diffusion and permeability of nonpolar gases in Eastern Hemlock. Wood and Fiber, 5(4): 289-298. Biryukov, V . A . 1968. Dielectric heating and drying of wood, ppl 17. Bonneau, P. and J-R. Puiggali 1993. Influence of heartwood-sapwood properties on the drying kinetics of a board. Wood Sci. and Technol., 28: 67-85 Carlsson, P. and J. Arfvidsson. 2000. Optimized wood drying. Drying Technol., 18(8): 17791796. Chen, Z. 1997. Primary Driving Force in Wood Vacuum Drying. Ph.D. dissertation, Department of Wood Science and Forest Products, Virginia Polytechnic Institute and State University, 172 p. Chen, P. and P.S. Schmidt, 1997. Chapter 12: Mathematical modeling of dielectricallyenhanced drying. Mathematical Modeling and Numerical techniques in drying technology: edited by Turner, I., and Mujumdar, A.S., Marcel Dekker, Inc., 83-156, ISBN 0 8247 9818 X 145 Chen, P. and P S . Schmidt, 1990. An integral model for drying of hygroscopic and nonhygroscopic materials with dielectric heating. Drying Technol., 8(5): 907-930. Comstock, G. L . 1965. Longitudinal permeability of Green Eastern Hemlock. Forest Prod. J., 15(5): 441-449. Constant, T., Moyne, C. and P. Perre. 1996. Drying with internal heat generation: theoretical aspects and application to microwave heating. AIChE Journal, 42(2): 359-368. Coulson, J.M., Richardson, J.F., and R K Sinnott. 1989. Chemical Engineering Design, vol.6, Pergamon Press, pp.838. Couture, F., Fabrie, P. and J.-R. Puiggali. 1995. An alternative choice for the drying variables leading to a mathematically and physically well described problem. Drying Technol., 13(3): 519-550. Defo, M , Fortin, Y . , and A. Cloutier. 1999. Determination of the effective water conductivity of sugar maple sapwood and white spruce heartwood under vacuum. Wood and Fiber Sci., 31(4): 343-359. Fohr, J-P., Chakir, A., Arnaud, G. and M A . du Peuty, 1995. Vacuum drying of oak wood. Drying Technol., 13 (8 & 9), 1675-1693. Hailwood, A.J. and S. Horrobin. 1946. Adsorption of water by polymers: Analysis in terms of a simple model. Trans. Faraday Soc, 42B: 84-102. Hanever, W.P. 1990. Drying Northern Red Oak dimension squares with industrial sized radio-frequency/vacuum dry kilns. M.Sc. Thesis. College of Environmental Science and Forestry, Syracuse, New York. 91 p. Hayashi, K., Y . Nagase, and Y Kanagawa. 1995. Experimental evidence of an importance of permeability in the RF/Vacuum drying. In Proceedings Vacuum Drying of Wood '95: 261-269. Jones, P L . and A T . Rowley, 1996. Dielectric drying. Drying Technol., 14(5): 1063-1098. Jones, P L . 1996. RF Heating, an old technology with a future. Proceedings of Microwave and High Frequency Heating. L I . 1-L1.9. Kadita, S. 1960. Studies on water sorption of wood. Wood Res. 23:1-61. Kamke, F.A., and M . Vanek, 1992. Critical review of wood drying models: plan of study. Holzforschung und Holzverlung, 6: 81-83. Klinkenberg, L.J., 1941. The permeability of porous media to liquids and gases. Drilling and Production Practice. The American Petroleum institute, New York, pp: 200-213. 146 Knagawa, Y . 1989. Resin distribution in lumber dried by vacuum drying combined with radio frequency. In Proceedings of 1 IUFRO Wood Drying Conference, 158-164. st Koumoutsakos, A., Avramidis, S., and S. G. Hatzikiriakos. 2001 (a). Modeling radio frequency vacuum drying of wood, Part I: Theoretical model. Drying Technol., 19(1): 65-84. Koumoutsakos, A., Avramidis, S., and S. G. Hatzikiriakos. 2001 (b). Modeling radio frequency vacuum drying of wood, Part II: Experimental model evaluation. Drying Technol., 19(1): 85-98. Krahmer, R.L., and W.A. Cote Jr. 1963. Changes in coniferous wood cells associated with heartwood formation. Tappi, 46(l):42-49. Kudra, T., U.S. Shivhare, and G.S.V. Raghavan. 1990. Dielectric heating - a bibliography. Drying Technol., 8(5): 1147-1160. Lee, N - H , Hayashi, K . and H-S Jung. 1995. Possibility of drying of walnut disk for wooden arts in Radio-Frequency/Vacuum dryer with mechanical pressure system. In Proceedings of Vacuum Drying of Wood '95, Zvolen, Slovak Republic, 270-279. Liu, F., Avramidis, S. and R. L. Zwick. 1994. Drying thick western hemlock in a laboratory radio-frequency/vacuum dryer with constant and variable electrode voltage. Forest Prod. J., 44 (6): 71-75. Lu, J. 1997. Non-darcian air flow in wood. Ph.D. Thesis, Department of Wood Science, The University of British Columbia, Vancouver, BC. 126 p. Lyons, D.W., Hatcher, J.D., Sunderland, J.E. 1972 Int. J. Heat Mass Transfer, 1: 897-905. Meredith R. J. 1996. Industrial Microwaves, the Foundation for the Future. Proceedings of Microwave and High Frequency Heating. K A 1 - K A 6 . Patankar, S, 1980. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, McGraw Hill Perre, P. 1995. Drying with internal vaporization: introducing the concept of identity drying card (IDC). Drying Technol., 13(5-7): 1077-1097. Perre P. 1999. How to get a relevant material model for wood drying simulation, in Proceedings of the 1 Wood Drying Workshop, Scotland, U K , 58-84. st Perre, P., Joyet, P., and D. Aleon. 1995. Vacuum drying: physical requirements and practical solutions. In Proceedings of Vacuum Drying of Wood '95, Zvolen, Slovak Republic, 7-34. Perre, P. and I. Turner. 1997. Chapter 2: The use of macroscopic equations to simulate heat and mass transfer in porous media: Some possibilities illustrated by a wide range of 147 configurations that emphasize the role of internal pressure, Mathematical Modeling and Numerical techniques in drying technology: edited by Turner, I., and Mujumdar, A.S., Marcel Dekker, Inc., 83-156, ISBN 0 8247 9818 X Pordage, L.J. and T.A.G. Langrish. 2000. Optimization of hardwood drying schedules allowing for biological variability. Drying Technol., 18(8): 1797-1815. Quintard, M . and J.R. Puiggali. 1986. Numerical modeling of transport processes during the drying of granular porous medium. Heat and Technol., 4(2):37-57. Rechenberg, I. 1989. Evolution strategy-nature's way of optimization, in: Bergmann, 1989, pp.106-126. Rechenberg, I. 1994. Evolutionsstrategie '94. Frommann-Holzboog, Stuttgart. Rosen, N . H . 1987. Recent advances in the drying of solid wood. Advances in Drying, vol 4, edited by Mujumdar, A S . , Hemisphere Publishing Corp., Washington, D C , 99-146. Rozsa, A . N . and S. Avramidis. 1996. Radio Frequency Drying of Eucalypt Timbers. In Proceedings of 6 IUFRO Wood Drying Conference, 135-138. th Schewfel, H-P. 1995. Evolution and optimum seeking, Wiley-Interscience publication, pp. 444, ISBN 0 471 57148 2 Sebastian, P., Jomaa, W. and I.W. Turner. 1996. A New Model for the Vacuum Drying of Wood based on the Concept of the Transition Layer. In Proceedings of 6 IUFRO Wood Drying Conference, 135-138. th Sherwood, T.K. 1929. The drying of solids -I. Ind. & Engr. Chemistry, 21(1): 12-16. Siau, J.F. 1995. Wood: Influence of moisture on physical properties, Department of Wood Science and Forest Products, Virginia Polytechnic Institute and State University Press, pp. 126. Simpson, W.T. 1983. Drying Wood: A review. Drying Technol., 2(2): 235-264. Simpson, W.T. 1984. Drying Wood: A review. Drying Technol., 2(3): 353-368. Skaar, C. 1972. Water in Wood. Syracuse Univ. Press, Syracuse. 218 pp. Skaar, C. 1988. Wood-Water Relationship. Springer. New York. 283 pp. Smith W.B., Smith A. and E.F. Neauhauser. 1994. Radio-Frequency/Vacuum drying of Red Oak: Energy, quality, value. In Proceedings of 4 IUFRO Wood Drying Conference, 158-164 th Stamm, A.J. 1964. Wood and cellulose science. Ronald, New York. 549 pp. 148 Stamm, A.J. and R . M . Nelson. 1961. Comparison between measured and theoretical drying diffusion coefficients for southern pine. Forest Prod. J., 11: 536-543. Strumillo, C. and T. Kudra 1986. Drying: Principles, Applications, and Design. Gordon and Breach Science Publishers, New York. Tong, C H . and D.B. Lund. 1993. Microwave heating of backed dough products with simultaneous heat and moisture transfer. J Food Eng., vol. 19: 319-339. Torgovnikov, G.I., 1993. Dielectric Properties of Wood and Wood-Based Materials. Springer-Verlag, Berlin, Germany, pp. 196 Trofatter, G., Harris, R.A., Schroeder, J. and M . A . Taras. 1986. Comparison of moisture content variation in red oak lumber dried by radio-frequency/vacuum process and a conventional kiln. Forest Prod. J., Vol: 36(5): 25-28. Tsoumis, G. 1991. Science and Technology of wood; structure, properties, utilization. Van Nostrand Reinhold, New York. 494pp. Turner, I. 1991. A two dimensional orthotropic model for simulating wood drying processes. J. App. Math. Modeling, Vol. 20, January, pp. 60-81. Turner, I.W. and W. J. Ferguson. 1995. A study of the power density distribution generated during the combined microwave and convective drying of softwood. Drying Technol. 13(5-7):1411-1430. Turner, I.W., and P.G. Jolly 1991. Combined microwave and convective drying of a porous material. Drying Technol., 9(5): 1209-1269. Waananen, K.W., J.B. Lirchfield and M.R. Okos. 1993. Classification of drying models for porous solids. Drying Technol., 11(1): 1-40. Weres, J., Olek, W. and R. Guzenda. 2000. Identification of mathematical model coefficients in the analysis of the heat and mass transport in wood. Drying Technol., 18(8): 16971708. Whitaker , S. 1977. Simultaneous heat, mass, and momentum transfer in porous media: a theory of drying, In: Advances in Heat Transfer, Vol. 13, Academic Press, New York, pp. 119-203. Whitaker, S. 1980. Heat and mass transfer in granular porous media. In: Mujumdar, A.S. (Ed.). Advances in Drying, Vol. 1, pp.23-61. Hemisphere Publishing Corp., New York. Zhang, L . , S. Avramidis and S.D. Hatzikiriakos. 1997. Moisture flow characteristics during radio frequency vacuum drying of thick lumber. Wood Sci. Technol., 31: 265-277. 149 Zhou, B. and S. Avramidis, 1999. On the loss factor of wood during radio frequency heating. Wood Sci. and Technol., 33: 299-310. Zhou, B. 1997. Dielectric characteristics of two B C coastal species during Radio Frequency heating. M.Sc. Thesis, Department of Wood Science, The University of British Columbia, Vancouver, BC. 115 p. Zwick, R L . 1995. The COFI Radio Frequency/Vacuum Kiln Project, Council of Forest Industry, Vancouver, B.C., Canada. 121 pp. Zwick R . L . and S. Avramidis 2000. Commercial R F V kiln drying recent successes. In Proceedings of the Western Dry Kiln Association annual meeting, Reno, N Y , 36-44. 150 NOTATION AntB, AntC Coefficients in the Antoine equation bi, b2, b , b Curve fitting coefficients for vapor pressure Cp Heat capacity at constant pressure D Diffusion coefficient E Field strength F Frequency G Specific Gravity of Wood K Intrinsic Permeability K Thermal conductivity m Evaporation / Condensation Rate m Fractional Moisture Content M Molecular weight of water vapor (=0.018) P Pressure R Universal gas constant (=8.314) T Temperature V Velocity Z Compressibility constant Greek Symbols a, P, y, 8, C Curve fitting coefficients for dielectric loss factor Ahvap Latent heat of vaporization e" Dielectric loss factor |j. Viscosity p Density $ Internal heat generation source term. (j> Porosity or fractional void volume of wood Subscripts Subscripts A Ambient OD B Bound r C Critical red eff Effective S fsp Fiber saturation point sv L Longitudinal direction Tran L Liquid phase v M Moisture Vap max Maximum 3 v 4 J/kgK m /s V/m Hz 2 m W/mK kg/m s 2 3 kg/mol Pa J/mol K K m/s m/s J/kg kg/ms=Pa s kg/m W/m 3 3 Wood ovendry relative reduced Solid Saturated vapor Transverse direction vapor phase vaporization 151 APPENDIX A The equations selected for the model must be carefully considered. Although there are several suggested expressions in the literature, we adopted the ones that are the more appropriate for Western red cedar and Western hemlock. The specific heat are calculated according by (Siau 1995): Cp = ( 1260 + 4185 m ) / ( 1 +m) Cp = ( 1176 + 5859 m ) / ( 1 +m) Cp = ( 1678 + 4185 m ) / ( 1+m) 0.05 > m 0.05 < m < 0.3 m > 0.3 Temperature correction for the specific heat of the dry cell wall is given by: Cp,cw = 1260 * ( 1 + 0.004 * ( T - 303)) The effective thermal conductivity is calculated by: kefr=G(0.2 + 0.0038 m ) +0.024 for m< 0.4, transverse direction keff = G (0.2 + 0.0052 m ) + 0.024 for m > 0.4, transverse direction keff,L 2.5 = * keff/Trans Pressure corrections for P < 1 atm are not taken into account. Since the above equations refer to T=303 K, temperature correction is given by: kdr = kdpo3 *( 1 +0.004 ( T - 3 0 3 )) Psv = exp (53.421 -6513.6/T-4.125 In T ) u = 3.01 IO ( T - 273 ) ( -13.91 + 0.05533 T ) -5 v Above the FSP the latent heat of vaporization of water can be estimated by the equation suggested by Haggenmacher and is derived by the Antoine vapor pressure equation (Coulson et al, 1989): Ahvap = (8.32/0.018) * AntB * T * A z / ( T + AntC) 2 where AntB = 3816.44, AntC = - 46.13 for water and Az = z - zi is calculated by v Az = ( 1 - P ^ / T,,,, ) °3 5 and T = 647.3 K and P = 220.5 * 10 Pa for water. 5 c c 152 Below the FSP an equation calculating average Ah vap derived for western red cedar and western hemlock of the form like the one given by Siau (1995) will be utilized. Data were takenfromAvramidis and Dubois (1992). Ahvap = 303513*exp(-12.62*m) Krv =1 m < mfp S Kn, = 1 + ( 4 m* - 5 ) m* where m* = mi / m>m 4 6p (from Perre and Turner 1997) and mi = m - mf sp The maximum liquid saturation misat can be calculated by 4W = 1-G*0.653 misat = ( C J W / (1- (from <> | m a x ) ) * ( P H 2 C ) / p O D ) " Hlf Siau 1995) sp The bound water diffusion coefficient Db at lower pressures is not available experimentally. Since an increase in temperature, increases Db, it can be assumed that an enhancement at lower pressures occurs similar to the one assumed by Fohr et al (1995). Thefinalexpression for the bound water diffusion coefficient is D = (P b P =P v sv / P )*7.*10- *exp(-(38500.-2.9*m)/(R*T)) 6 atm (T) i|/ ( m, T ) (by sorption measurements in our lab) \|/ (m, T ) = 1 - exp (bi T (100 m ) b 2 b3T * ) 4 153
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Modelling radio frequency/vacuum drying of wood Koumoutsakos, Anastasios 2001
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Title | Modelling radio frequency/vacuum drying of wood |
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Koumoutsakos, Anastasios |
Date Issued | 2001 |
Description | The purpose of this study was to investigate the electromagnetic energy dissipation coupled with heat and moisture mechanisms in wood during radio frequency/vacuum (RF/V) drying. This involved both numerical and experimental studies. Specifically, the objectives were to establish a continuous RF/V drying model, to examine first if a one-dimensional model is sufficient to capture the basic mechanisms of drying. Subsequently, this was extended to a two-dimensional model in order to study anisotropic effects. Experimental data required by the model were two parameters, namely, the bound moisture diffusion coefficient and the intrinsic permeability. In order to evaluate the predictability of the model developed, experimental information from a series of RF/V runs using a single specimen under different power densities and ambient pressures were performed. These data were used to evaluate the capabilities of the model. The mathematical model was derived by averaging the conservation equations over a representative differential volume. The final form of the model was developed after a detailed discussion of the controlling resistances and transport mechanisms during RF/V drying. Such a model may readily exclude liquid capillary transport, which is an important factor in convective drying. Comparison of the model prediction with the experimental data obtained revealed a good agreement for a variety of drying conditions, particularly with those predicting the total average moisture evolution and the total drying time. Extension to a two-dimensional model was suggested to overcome its shortcomings in predicting accurately the temperature evolution and in describing in detail the internal heat and mass transfer phenomena during wood RF/V drying. Experiments were carried out to determine the permeability and the bound water diffusion coefficients of western hemlock and western red cedar for both heartwood and sapwood in the longitudinal, tangential and radial directions, respectively. The permeability data, though exhibited high variability, were found within the range reported in the literature. Diffusion coefficients were determined as a function of moisture content and temperature for all directions and wood types. The trends of the curves obtained are in agreement to theoretical ones. The fiber saturation point was determined for all the above cases. The sorption isotherms were calculated and the parameters of the Hailwood-Horrobin equation were calculated using a non-linear regression technique. All the results are discussed within the framework of developing a two-dimensional mathematical model for the RF/V drying of timbers. Finally, a small representative number of experiments was carried out by using "50 Ohm amplifier" technology. The improvement of the uniformity of the electric field was obvious through the temperature and final moisture measurements. The predictions of the two-dimensional form of the model were in good agreement for all cases examined. The agreement is considerably better compared to that found for the one-dimensional model. The value of using evolution strategies for the overall optimization of the process is also presented. |
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Thesis/Dissertation |
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File Format | application/pdf |
Language | eng |
Date Available | 2009-10-07 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0090722 |
URI | http://hdl.handle.net/2429/13724 |
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Doctor of Philosophy - PhD |
Program |
Forestry |
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Forestry, Faculty of |
Degree Grantor | University of British Columbia |
Graduation Date | 2001-11 |
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UBCV |
Scholarly Level | Graduate |
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async >
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