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M A T H E M A T I C A L M O D E L I N G and N U M E R I C A L T E C H N I Q U E S in D R Y I N G T E C H N O L O G Y This Page Intentionally Left Blank M A T H E M A T I C A L M O D E L I N G and N U M E R I C A L T E C H N I Q U E S in D R Y 1 N G T E C H N O L O G Y edited by IAN TURNER Queensland University of Technology Brisbane, Australia ARUN S . MUJUMDAR Mc Gill University Montreal, Quebec, Canada MarDcee lk kINne rYce ,. wo r k.Basel*HoKno gn g Library of Congress Cataloging-in-Publication Data Mathematical modeling and numerical techniques in drying technolog/y edited by Ian Turner, Arun S. Mujumdar. pc m. . Includes index. ISBN 0-8247-9818-X (alk. paper) 1. Drying-Mathematical models. I.T urner, Ian. 11. Mujumdar, A. S. TP363.M3517 9 96 660'28426'01 5 1 184~20 96-1 8672 CIP The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Saleskofessional Marketing at the address below. This book is printed on acid-free paper. Copyright 0 1997 by MARCEL DEKKER, INC. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or bya ny information storage and retrieval system,w ithout permission in writing from the publisher. MARCEL DEKKER,I NC. 270 Madison Avenue, New York, New York 10016 Current printing (last digit): 1 0 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERI[CA Preface Drying is one of the most energy intensive industrial processes, with applica- tions in a wide variety of industries including the food, timber, paper,a nd con- struction sectors. In an attempt to minimize the energy consumption necessary for the day-to-day functioning of typical drying operations, a substantial amount of research has been focused on the identification of innovative heating and drying processes as well as the classification of state-of-the-art optimization strategies for existing dryer designs. Although experimentation is an essential ingredient in the advancement of drying technology, fundamental researchw ith the aid of mathematical modeling and numerical simulation provides an ex- tremely powerful and cognitive tool for investigating the complicated physics that evolve during the dryingo f wet porous materials. The resultso f the simula- tions can be used subsequently by drying engineers and practitioners to guide future experimental design and, perhaps most importantly, to provide a better understanding of the drying process as a whole. The strategy of modeling- which requires experimental input for the determination of key model parameters, followed by system optimization and overall experimental validation of the results-is a cost-effective and efficient method for furthering drying technology The study of drying is truly interdisciplinary with the literature being di- vided amongp ublications in heat and masst ransfer,t ransportp henomena, chemicale ngineering, mechanical engineering,a griculturale ngineering, soil science, wood science, food science, and mathematics. A survey of this litera- iii iv Preface ture over the last two decades unveils a numbero f key review-type articles that have gone a long way in identifying and improving the knowledge of mathematical modeling in drying. It is now well accepted that the key mechanisms for simulating heat and mass transport in capillary porous media have been clearly defined. The solution of the resulting set of governing equations, how- ever, has been hindered severely by the strongly coupled and highly nonlinear nature of that equation set. Typically, these models require the resolution of important drying variables such as moisture content, temperature, internal pres- sure, stress and, in the case of dielectrically assisted drying processes, the com- putation of the power density distribution. In the past, analytical solutions of this problem were confined to simple drying configurations and were valid only under a very stringent set of assump- tions. In general, numerical simulation was the only possible solution strategy. With increased computing facilities readily available worldwide, the possibili- ties for obtaining fasta nd accurate solutions to many of the previously intracta- ble drying problems are becoming a reality. In fact, not only are rigorous one- dimensional and two-dimensional models being published,b ut three-dimensional models for drying are now beginning to appear. It seems that the era of computational engineering has burst onto the scientific sceanned the difficulties associated with resolving the most challenging problems are becoming problems of the past. Furthermore, with the benefits that parallel computing technology can offer, it appears that the once impossible dreamo f on-line, real-time three- dimensional analyseso f real-world drying configurationsm ay soon be realized. Nevertheless,t he path of developing an efficient and effectives olution strategy for the drying equations ibsy no means straightforward. The numerical analyst must overcome numerous stumbling blocks before the implementation task is completed. For example, some of the more formidable tasks are: mesh generation, identification of the best discretization strategy to use, solution of the nonlinear equation set, solution of the linearized and often sparse algebraic system, convergence criteria,t ime step control, experimental validation, and,f i- nally, the best means of graphically visualizing the results. One of the main objectives of this book concerns the analysis of many of these issues and the identification of the most efficient and state-of-the-art numerical methods that can be used to assistw ith the implementationo f the above-mentioned tasks. Furthermore, mathematical modelso f drying could beu sed to evaluate new concepts, for example,t he use of opposing jets tod ry dispersed materials or the use of an intermittent heat supply in batch drying, without expensive experimentation at the outset. Once verified with carefully chosen experimental data, mathematical modelsc an be used to study the effects of various parameteris.e, ., for the optimizationo f the drying process subject to pertinent objective functions and for model-based control of degrees. While most models currently focus on the heat and mass transfer aspects together with, for example, stress-induced Preface V cracking, in many cases it also becomes necessary to simulate chemical or bio- chemical reactions to assess the quality parameters. Much further research and development work needs to be carried out in the area of modeling quality parameters since they are highly product-specific. It is hoped that this book and an earlier special issue of Drying Technology-An International Journal (Vol. 13, No. 9,1 996) will stimulatea dvances in the development and utilization of mathematical models for simulation, optimization, control, and innovation in drying operations. The relentless advances in computing power and numerical techniques will undoubtedly provide greater impetus to increased applicationo f modeling in practice. Theb ooki so rganizedi ntof ours ections: “Fundamentals,” “Drying of Wood,” “Drying of Granular and Particulate Solids,” and “Miscellaneous Ap- plications.” Note that this categorization is not very rigid and is not intended to be mutually exclusive. New fundamental concepts and computational schemes can also be found in chapters that aren ot in Section I, for example. The overall philosophy of the material presented in this book is to provide the reader with the detailed knowledge that is necessary to develop mathematical models and efficient numerical techniques for solving problems in drying. The material presented here covers a wide cross sectiono f drying research and, will benefit not only scientists just commencing work in this field but active drying practitioners. Furthermore, the information throughout thist ext will provide a useful foundation for future modelingw ork in drying. Finally, the editors would like to thank all the authors who contributed to this text. They have toiled hard to present a very interesting and highly readable book. In particular, special thanks must go to Patrick Perrt? for the extensive effort that he put into the development of the first two chapters. The many fruitful discussions, together with the number of suggestions that he offered for the final presentationo f these chapters,i s very much appreciated. Ian Turner Arun S. Mujumdar This Page Intentionally Left Blank Contents Preface iii Contributors xi Section I: Fundamentals 1. A Synopsis of the Strategies and Efficient Resolution 1 Techniques Used for Modellinga nd Numerically Simulating the Drying Process Ian Turner and Patrick Perrb 2. TheU se of Macroscopic Equations to SimulateH eat 83 and Mass Transfer in Porous Media Patrick Per& andI an Turner 3. Modelling and SimulatinSg im ultaneoLu siq uid and Vapour 157 Transport in Partially Saturated Porous Materials A. J. J. van der Zanden Section 11: Drying of Wood 4. High-Temperature Kiln Drying of SoftwoodT imber:T heR ole of 179 Mathematical Modelling S. Pang andA . N. Haslett vii