Modeling Indoor Air Pollution

Modeling Indoor Air Pollution

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Modeling Indoor Air Pollution Darrell W Pepper University of Nevada, Las Vegas, USA David Carrington Los Alamos National Laboratory, USA ICP Imperial College Press

Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. MODELING INDOOR AIR POLLUTION Copyright 2009 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-1-84816-324-9 ISBN-10 1-84816-324-X Printed in Singapore.

To our families, friends, and colleagues

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Acknowledgments This book is the result of many years of developing and applying various models to simulate the dispersion of contaminants. Some of the information presented stems from numerous interactions and collaborations with students and colleagues. Much of the material presented in this book can be found in other texts. Some of these texts briefly describe a few of the more simple numerical techniques, but generally don t provide source codes or describe the latest numerical techniques. We have attempted to integrate fundamental information and the basic formulations regarding indoor air quality and ventilation from the more popular textbooks and monographs. We wish to especially acknowledge Dr. Xiuling Wang, who diligently converted many of our old FORTRAN codes into MATLAB files, and also developed the COMSOL example files. Also we thank Ms. Kathryn Nelson who developed the website for the book and indoor air quality computer codes. We are grateful to Mrs. Jeannie Pepper, who typed the manuscript and made sure that we followed proper procedures and format. Her professionalism and patience in typing and proofreading the chapters are greatly appreciated. Finally, we wish to acknowledge the assistance and support of Miss Elizabeth Bennett, our Editor with ICP. This book was written using Microsoft Word and MathType, with conversion to Adobe pdf. The figures were made using TECPLOT, Microsoft Vizio, and PhotoShop. vii

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Preface Indoor air pollution is becoming a serious problem. This is especially pertinent in situations where sick building syndrome, under design air flow, and contaminant dispersion occur. Recent interest in homeland security and the aftermath of terrorist activities have created a desire among many governmental agencies to more fully understand interior pollutant dispersion and risk assessment. It is the intention of this book to acquaint the reader with enough information to begin using various modeling tools for assessing indoor air pollution. There are many levels of models, ranging in sophistication from simple analytical expressions to elegant, 3-D schemes for solving the Navier Stokes equations for fluid flow and species transport. The level of modeling effort resides ultimately with the user, and the desired level of accuracy. While 3-D numerical schemes based on finite difference, finite volume, or finite element techniques provide elegant solutions, they also require a great deal of understanding, patience, and computational resources. Analytical solutions, while fast and simple, may be orders of magnitude off in comparison to actual values. This book presents these most common of numerical and analytical tools that can be used for modeling indoor air pollution and the types of problems where a particular model is best suited. Chapter 1 presents an overview of indoor air pollution, types of ventilation systems, exposure, and general modeling techniques. Chapter 2 discusses the governing mathematical equations that serve as the basis for modeling air pollutant and flow patterns. In Chapter 3 a general discussion of contaminant sources routinely associated with indoor air quality assessment studies is given, with a presentation on particulates and evaporation of droplets. Assessment criteria are described in Chapter 4, including what to consider in exposure levels as well as economical issues associated with design. Chapter 5 introduces the fundamental analytical tools, along with advection and the classic box model approach, for performing simple model simulation, including their ix

x Modeling Indoor Air Pollution limitations. The dynamics of particle motion, including particle drag and flow in inlets and flanges, are given in Chapter 6. Chapter 7 describes the fundamental numerical approaches commonly used in CFD-type simulations, which are based on finite difference, finite volume, and finite element techniques. Additional discussions are given in Chapter 8 on more advanced methods that include boundary element, particle-incell, and meshless methods, which is relatively new. Several modeling examples are included. In Chapter 9, an extensive description of turbulence modeling is presented with consideration to both finite volume and finite element techniques. A time-dependent, two-equation closure model is presented in detail using the finite element method with adaptive meshing; results are shown for example problems. Issues regarding homeland security and the potential threats attributed to terrorist activities are discussed in Chapter 10, including an example scenario. The examples and computer techniques discussed in the book are available on the web. The website is: www.iaqcodes.com. We have elected to write the majority of the codes in MATLAB. The website lists locations where you can also find FORTRAN and C/C++ versions of some of the example codes. We have found that most engineering graduates today as well as science and engineering students are familiar with MATLAB, and prefer using it as their primary coding environment. We have also used COMSOL to run the example problems. COMSOL, with headquarters in Sweden, is a very versatile multiphysics finite element package used throughout the world; the package permits easy interface and flexibility in setting up problems, along with MATLAB scripting. Many universities and companies are now using COMSOL. In addition, an adaptive finite-element based model that can be used for indoor air pollution is also available from the authors. This model utilizes h-adaptation (mesh refinement) to accurately simulate the dispersion of contaminant within any shaped interior. Darrell W. Pepper David B. Carrington 2008

Contents Acknowledgements Preface vii ix 1. Introduction 1 1.1 What is Indoor Air Pollution... 2 1.2 Ventilation Systems... 2 1.3 Exposure Risks... 3 1.4 Numerical Modeling of Indoor Air Flow... 5 1.5 Comments... 7 2. Fluid Flow Fundamentals 9 2.1 Conservation Equations... 9 2.2 Ideal Fluids... 11 2.2.1 Conformal mapping... 16 2.2.2 Schwarz Christoffel transform... 19 2.2.3 Numerical mapping... 23 2.2.4 Superposition for stream functions... 24 2.3 Turbulence... 26 2.4 Species Transport... 30 2.5 Comments... 32 3. Contaminant Sources 33 3.1 Types of Contaminants... 33 3.2 Units... 35 3.3 Materials... 36 3.4 Typical Operations... 38 3.5 The Diffusion Equation... 39 3.6 Diffusion in Air... 41 3.7 Evaporation of Droplets... 43 3.8 Resuspension of Particulate... 46 3.9 Coagulation of Particulate... 48 3.10 Comments... 49 4. Assessment Criteria 51 4.1 Exposure... 51 4.2 Economics... 54 4.3 Comments... 56 xi

xii Modeling Indoor Air Pollution 5. Simple Modeling Techniques 57 5.1 Analytical Tools... 57 5.2 Advection Model... 65 5.3 Box Model... 67 5.4 Comments... 75 6. Dynamics of Particles, Gases and Vapors 77 6.1 Drag, Shape, and Size of Particles... 77 6.2 Particle Motion... 80 6.2.1 Deposition of particulate with aerodynamic diameters > 1μ by settling... 84 6.2.2 Particle motion in electrostatic field... 86 6.2.3 Particle motion induced by temperature gradients... 87 6.2.4 Thermophoretic motion for gases and particles with diameter less than the molecular mean free path... 87 6.2.5 Thermophoretic transport for particles with diameter greater than the molecular mean free path... 87 6.3 Particle Flow in Inlets and Flanges... 88 6.4 Comments... 91 7. Numerical Modeling Conventional Techniques 93 7.1 Finite Difference Method... 94 7.1.1 Explicit... 97 7.1.2 Implicit... 97 7.1.3 Upwinding... 98 7.2 Finite Volume Method... 104 7.2.1 FDM... 109 7.2.2 FVM... 109 7.3 The Finite Element Method... 112 7.3.1 One-dimensional elements... 115 7.3.1.1 Linear element... 115 7.3.1.2 Quadratic and higher order elements... 116 7.3.2 Two-dimensional elements... 122 7.3.2.1 Triangular elements... 122 7.3.2.2 Quadrilateral elements... 124 7.3.2.3 Isoparametric elements... 125 7.3.3 Three-dimensional elements... 128 7.3.4 Quadrature... 130 7.3.5 Time dependence... 132 7.3.6 Petrov Galerkin method... 133 7.3.7 Mesh generation... 135 7.3.8 Bandwidth... 140 7.3.9 Adaptation... 141

Contents xiii 7.3.9.1 Element subdivision... 145 7.4 Further CFD Examples... 150 7.5 Model Verification and Validation... 153 7.6 Comments... 156 8. Numerical Modeling Advanced Techniques 159 8.1 Boundary Element Method... 160 8.2 Lagrangian Particle Technique... 171 8.3 Particle-in-cell... 175 8.4 Meshless Method... 182 8.4.1 Application of meshless methods... 187 8.4.1.1 Smoothed particle hydrodynamics (SPH) techniques including Kernel Particle Methods (RKPM), and general kernel reproduction methods (GKR)... 187 8.4.1.2 Meshless Petrov Galerkin (MLPG) methods including moving least squares (MLS), point interpolation methods (PIM), and hp-clouds... 188 8.4.1.3 Local radial point interpolation methods (LRPIM) using finite difference representations... 189 8.4.1.4 Radial basis functions (RBFs)... 189 8.4.2 Example cases Heat Transfer... 196 8.4.2.1 Heat transfer in a 2-D plate... 196 8.4.2.2 Singular point in a 2-D domain... 197 8.4.2.3 Heat transfer within an irregular domain... 199 8.4.2.4 Natural Convection... 201 8.5 Molecular Modeling... 208 8.6 Boundary Conditions for Mass Transport Analysis... 212 8.7 Comments... 215 9. Turbulence Modeling 217 9.1 Brief History of Turbulence Formulation... 217 9.2 Physical Model... 221 9.2.1 Turbulent flow... 222 9.2.2 Two-equation turbulence closure models... 224 9.2.2.1 Two-equation k-ε... 225 9.2.2.2 Two-equation k-w... 226 9.2.3 Large Eddy Simulation (LES)... 227 9.2.4 Direct Numerical Simulation (DNS)... 229 9.2.5 Turbulent transport of energy or enthalpy... 230 9.2.6 Derivation of enthalpy transport... 231 9.2.7 Turbulent energy transport... 236 9.2.8 Turbulent transport species... 237 9.2.9 Coupled fluid-thermal flow... 237

xiv Modeling Indoor Air Pollution 9.3 Numerical Modeling... 239 9.3.1 Projection algorithm... 240 9.3.2 Finite volume approach... 243 9.3.3 Finite element approach... 245 9.3.3.1 Weak forms of the governing equations... 246 9.3.3.2 Matrix equations... 250 9.3.3.3 Time advancement of the explicit/implicit matrix equations... 252 9.3.3.4 Mass lumping... 253 9.3.3.5 General numerical solution... 254 9.4 Stability and Time Dependent Solution... 255 9.5 Boundary Conditions... 256 9.5.1 Boundary conditions for velocity under decomposition... 257 9.5.1.1 Viscous boundary condition for velocity... 258 9.5.2 Boundary conditions for pressure and velocity correction... 258 9.5.3 Boundary conditions for turbulent kinetic energy and specific dissipation rate... 259 9.5.4 Boundary conditions for thermal and species transport... 262 9.5.5 Thermal and species flux calculation in the presence of Dirichlet boundaries... 263 9.6 Validation of Turbulence Models... 264 9.7 Comments... 274 10. Homeland Security Issues 277 10.1 Introduction... 277 10.2 Potential Hazards... 278 10.2.1 Prevention and protection... 283 10.3 A Simple Model... 286 10.4 Other Indoor Air Quality Models... 296 10.4.1 CONTAM 2.4 (NIST)... 296 10.4.2 I-BEAM (EPA)... 298 10.4.3 COMIS-MIAQ (APTG-LBNL)... 299 10.4.4 FLOVENT (Flomerics, Inc.)... 300 10.5 Comments... 301 Appendix A Diffusion Coefficients in Gas 303 Appendix B 2-D Office Simulations: COMSOL and ANSWER Software 309 Bibliography 323 Index 341