An Introduction To Mathematical Fire Modeling

An Introduction to Mathematical Fire Modeling

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SECOND EDITION

An

Introduction to

Mathematical Fire Modeling

Marc L. Janssens, Ph.D. Southwest Research Institute

This eBook does not include ancillary media that was packaged with the printed version of the book.

An Introduction to Mathematical Fire Modeling a~~c~~0~1~9ublication Technomic Publishing Company, Inc. 851 New Holland Avenue, Box 3535 Lancaster, Pennsylvania 17604 U.S .A. Copyright O 2000 by Technornic Publishing Company, Inc. All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America l 0 9 8 7 6 5 4 3 2 1 Main entry under title: An Introduction to Mathematical Fire Modeling, Second Edition A Technomic Publishing Company book Bibliography: p. Includes index p. 257 Library of Congress Catalog Card No. 00-103008 ISBN NO. 1-56676-920-5

DEDICATION

This book is dedicated in memory of the late Professor Edward Zukoski (1927- 1997)' who developed the plume flow correlation that forms the core of the mathematical compartment fue models presented in this book. This correlation was just one of Professor Zukoski's numerous important and unique accomplishments in 30 years of pioneering work on fluid mechanics of fires.

CONTENTS

Preface lntroduction

xi

xv

...........1

Chapter 1. Basic Compartment Fire Theory 1. l Introduction 1 1.2 Approaches to Mathematical Fire Modeling 1.3 Computer Languages Used for Fire Modeling

4

8

Chapter 2. Introduction to Mathematical Compartment Fire Modeling 2.1 The Fire Compartment 11 12 2.2 The Fire Flame and Plume 2.3 The Hot and Cold Gas Layers 12 2.4 Heat Release Rate of the Fire 13 2.5 Heat Transfer in Enclosure Fires 14 2.6 A Generic Compartment Zone Fire Model 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . 11

. . . . . . . . 51

Chapter 3. ASET-QB: A Simple Room Fire Model 3.1 Introduction 51 3.2 Formulation of the ASET Equations 54 3.3 Solution of the Differential Equations 58 3.4 The ASET-QB Computer Program 59 3.5 Comparison between ASET-QB and ASET-B 61 63 3.6 Limitations of ASET-QB Chapter 4. Modifications to ASET-QB 4.1 Venting of the Hot Layer 69

. . . . . . . . . . . . . . 69

viii

Contents

4.2 4.3 4.4 4.5

Oxygen-Limited Burning 80 83 Heat Loss Fraction Calculation Heat Release Rate Predictions 87 The Prediction of Flashover 104

.

.

Chapter 5. The FIRM-QB Model . . . . . . 5.1 Introduction 111 11 2 5.2 Fire Problem Modeled by FIRM-QB 11 3 5.3 Technical Description of FIRM-QB 1 17 5.4 FIRM-QB Program Description 117 5.5 FIRM-QB Data Libraries 11 8 5.6 Predictive Capability of FIRM-QB

..

. . . . . . . . 111

. . . . . . . . . 119

Chapter 6. FIRM-QB User's Manual . .. 6.1 Introduction 1 19 6.2 Technical Documentation 11 9 6.3 Program Description 120 120 6.4 Installing and Operating FIRM-QB 6.5 Program Considerations 120 6.6 Input Data 122 6.7 External Data Files 124 125 6.8 System Control Requirements 6.9 Output Information 125 12 7 6.10 Personnel and Program Requirements 128 6.1 1 Sample Problems 144 6.12 Restrictions and Limitations 6.13 Error Messages 14 4

Chapter 7. Evaluation of the Predictive Capability of FIRM-QB . . . . . . . . . . 7.1 Introduction 147 148 7.2 Predictive Capability of Fire Models 153 7.3 Predictive Capability of FIRM-QB 7.4 Conclusions 174

.

Chapter 8. Conclusion

. .

.

. . . . . . . . 147

. . . . . . . . . . . . . . . . . . . . . 179

Appendix A: Conversion Factors and Constants Appendix B: Review of Fundamentals of Engineering for Fire Modeling

181 183

Contents

Appendix C: Installing and Running the Software Appendix D: QBASIC Programmer's Notes Appendix E: Visual Basic Programs References Index

257

25 1

247

23 7

227

PREFACE This is the second, completely revised edition of an introductory textbook on mathematical fire modeling. The first edition was written by David Bitk, and published by Technomic Publishing Co. in 1991. Because the book provided some unique material of interest to the ASTM Subcommittee E05.39 on Fire Modeling, which I chaired at that time, I obtained a copy of the book shortly after its release, and read it very carefully fiom cover to cover. In 1992 I shared the results of my review with the author, and made a number of suggestions for corrections and improvements to be included in a future edition of the book. In 1995 Technomic approached me, and asked me whether I would be interested in preparing a second edition. The book was almost out of print, the author of the first edition was too busy, and I qualified as an alternate for the job because of the suggestions for corrections and improvements that I had made in 1992. Once the scope of the project was more clearly defined, I decided to accept the challenge. Originally, the plan was to keep the text largely intact. I was only going to correct the errors that I had found in the fist edition, update the text where necessary to include the latest developments in the rapidly evolving field of fire science and technology, and convert the software fiom obsolete GW-BASIC to QBasic. The revision was estimated to take six months. Piece of cake! Unfortunately it did not work out that way. It is now nearly four years later, and what lies in fiont of you is almost a new book. Although the concept and structure of the book have largely remained the same, the details have changed significantly. Since 1991, ASTM published standard guides for documenting and evaluating the predictive capability of deterministic f i e models. The revision of the book provided a unique opportunity to apply the guides. To my knowledge, the FIRM model developed in this book, is the f i t fire model to be documented, validated, verified, and evaluated according to the ASTM guidelines. Compared to Birk's model, many changes have been made to the underlying physics of FIRM, and more accurate numerical techniques are used to solve the model equations. Since these changes slightly affect the sirnulations, all sample

xi i

Preface

problems and applications in the first edition had to be reworked. Some sample applications in the f ~ sedition t were replaced with problems that better illustrate the use and limitations of FIRM. In recent years, Microsoft has phased out DOS-based programs such as QBasic in favor of Windows software. This created the need to include a Visual Basic version of the QBasic software. The decision to include Visual Basic programs was made at the end of 1997, shortly after I delivered the final draft of the manuscript to the publisher. To save time, the text, which only refers to the QBasic programs, was kept more or less intact. An appendix was added to cover the V i s d Basic software. Unfortunately, the addition of the new s o h a r e delayed the project by nearly two more years. The main challenge was to ensure consistency and compatibility between the two versions of the software. I believe this fmally has been accomplished, and the reader should be able to reproduce the sample applications of FlRM in this book with either version. The introctuction and first chapter are largely unchanged fiom the fust edition of the book. The introduction describes the primary intent of the book, and the approach that is followed, Chapter 1 provides a qualitative description of enclosure fires, and summarizes different approaches to simulate such fires. Chapter 2 is a completely revised and expanded description of the quantitative aspects of two-zone compartment fire models. A simple room fire model is developed in Chapter 3 by simplifying the more general equations developed in Chapter 2. This model is named ASET, an acronym for Available Safe Egress Time. The QBasic version of the corresponding computer program is referred to as ASET-QB (ASET-VB is its Visual Basic counterpart). Five significant and useful modfications to ASET-QB are presented in Chapter 4. Similar modifications were described in the fust edition of the book, but the present material is more detailed, and quite different in many respects. For example, the main modification is that of the addition of routines to calculate mass flows of gases that enter or leave the compartment through an opening in one of the vertical walls of the compartment. The routines provided in the first edition only considered the main vent flow regime, while two additional regimes are considered in the present routines. A technical description of the modified ASET model, which is referred to as FIRM (Fire Investigation and Reconstruction Model), is provided in Chapter 5. The next chapter is a user's guide for the QBasic version of the model, called FIRM-QB. Chapter 5 and 6, together with some of the appendices comprise the documentation for FIRM-QB, which was

Preface

xiii

prepared according to the guidelines for documenting deterministic fire models in ASTM E 1472.A detailed evaluation of the predictive capability of FIRM-QB, according to the guidelines in ASTM E 1355, forms the subject of Chapter 7. Final conclusions and recommendations for further study are presented in Chapter 8. The second half of the main text, i.e., Chapters 5-8, is completely revised fiom the corresponding material in the first edition o f the book Useful unit conversions and physical constants are provided in Appendix A. To understand the technical sections of the book, the reader must have some basic knowledge of mechanical engineering. The necessary fundamentals are presented in Appendix B. Minimum system requirements, and instructions for installing and using the software can be found in Appendix C. In Appendix D, notes are provided for QBasic programmers who wish to customize the source code to suit specific needs. Appendix E covers the Visual Basic version of the software. The source code, executables programs, and input and output data fies for all applications and sample runs discussed in the book are on the accompanying CD-ROM. Some files are in a compressed format, and can only be installed as described in Appendix C. The reader should fust quickly browse through Appendix B, to determine whether he needs to look at this material in more detail. After a review of the fundamentals, it is recommended that the chapters of the main text be read in order, and the appendices be consulted as needed. Impatient readers and experienced fue model users, who want to immediately start exploring the FIRM software, may skip to Appendix C for instructions to install and run the software, and subsequently consult the FIRM-QB user's guide (Chapter 6). I hope it is clear £tom the above summary that the present edition of this book is very different fiom the first. Owners of the original edition of the book should find more than enough new material in the present volume to justify the purchase of a new copy. A sigtllficant amount of time was put in the preparation of this revision. My wife, Ingrid, and children, Jasmijn and Maarten, can testify to the extent of this effort. I would like to use this opportunity to thank them for their encouragement, sacrifice, and patience during the past four years while I was working on this book. Marc L. Janssens San Antonio, TX September 1999

INTRODUCTION The primary intent of this book is to introduce the reader to mathematical compartment fue modeling. The approach is through the development of a simple mathematical model that will provide an engineering approximation of the time-varying conditions created by a f r e in an enclosure that may be subject to hot-layer venting. The hot layer, as it is commonly referred to in fire modeling, is the collection of hot gases generated by a f r e that forms below the ceiling due to its buoyancy over the ambient-temperature air in the compartment. The hot-layer gases contain the products of combustion released by the fire, along with air entrained by the fire and its resultant plume. In the model, venting due to buoyancy forces is considered, while vent flows associated with forced ventilation are not. Also, venting through openings in vertical planes (walls) is considered, and openings in horizontal planes (floor and ceiling) are not. The development of the model includes the derivation of the governing equations, casting these equations into computer code, and the evaluation and application of the resulting model. It is also anticipated that the simplistic approach to the problem and the documentation provided herein will result in a model that proves to be an excellent instructional model for all students of mathematical fire modeling. There are two general approaches for the development of a simple compartment fire model. The first approach is to simplify an existing, but complex model, such as FIRST [l], or CFAST [2]. A second option is to take an existing simple model, such as ASET [3], and upgrade it to meet the requirements of the model and documentation sought. This second option, that of taking a simple model and upgrading it, appeared to be the more attractive procedure to follow. This method was also suggested by Kanury [4] who wrote: It seldom takes extraordinary skill to formulate an all-too-comprehensive mathematical model of a given phenomenon. Complete solution of such a model is usually unattainable. A gifted investigator skillfully sifis out all that is not relevant to arrive at a tractable but approximate model which contains all the essentials of his present vision of the phenomenon. One can obtain a

xvi

Introduction

satisfactory approximate model by either gradually simplifying a comprehensive model or by progressively complicating a simple model. The close relationship between simplification and approximation is thus evident. The approach of complicating a simple model, only to the extent necessary, almost always leads to the most clear results. Through the solution of a simplified model, the features of the phenomenon are more readily apparent. The simpler the model yielding reasonable results, the easier, more elegant and beautiful the explanation of the phenomenon.

This thought provided motivation for the procedure taken during the development of the model developed herein. Indeed, the initial approach followed during the development of the model presented was the upgrading of an existing model. That model was ASET. ASET is perhaps the most basic mathematical compartment fire model available today that accounts for time-varying conditions. However, the model developed here is not simply a modification of ASET, but a completely new model. Initial motivation for the simplicity and structure of the model was so that it could be used as a tool in the investigation and reconstruction of fires. With this in mind the model developed herein was titled FIRM, an acronym for Fire Investigation and Reconstruction Model. As with ASET, the model is certainly not limited to those uses suggested by its name. The ASET model did have an important role in the development of FIRM. As such, Chapter 3 will address the ASET model with primary emphasis on the development of the governing mathematical equations. The more complex models mentioned above also influenced the development of FIRM. It is beyond the scope of this book to present these models. However, the physical concepts that are at the basis of these complex models will be reviewed in Chapter 2. This will provide the reader with a good introduction to the discussion of the ASET and FIRM models in subsequent chapters. The numerous references listed should be consulted for a more complete discussion of the individual models and fire modeling in general. A comprehensive list of fire models, with a concise summary of and references to each model, can be found in the survey by Friedman 151.

CHAPTER 1

Basic Compartment Fire Theory I.l INTRODUCTION

The ability to adequately model the conditions within an enclosure resulting from a hostile fire requires an understanding of basic enclosure fire theory. A knowledge of the various modeling techniques is also a prerequisite. These topics will be covered in this chapter. To present a qualitative introduction to basic compartment f i e theory, consider an enclosure, such as a room, containing an object that has just been ignited. After ignition, the fire may self-extinguish or it may grow and become a great threat to life and property. Assuming the fire does not extinguish, it will grow as long as there is adequate fuel and oxygen and enough energy received at the fuel surface to release further flammable volatiles. Associated with the process of combustion is the presence of a flame and plume. As the fire progresses, air is entrained into the rising plume where it mixes with the fuel vapors released. The mixing of the oxygen, supplied ftom the entrained air, with the flammable vapors emitted by the pyrolizing fuel results in combustion that liberates heat. A large fiaction of this energy is absorbed by the gases within the combustion zone resulting in an increase in the temperature of these gases and airborne solid particulates. As the fire gases rise due to buoyancy, they continue to entrain air. This lateral entrainment of air, above that needed for combustion, results in the increase of the plume mass flow while the plume gas temperature decreases with respect to the height above the burning fuel surface. Thus the plume is composed of mass and energy contributed by combustion and the entrained air. Figure 1- 1 depicts the primary processes associated with a burning object. The plume gases will continue to rise vertically until they are impeded by a horizontal surface, which is usually the ceiling of the enclosure. At this time, the gases are forced to flow in a predominantly horizontal 1

2

BASIC COMPARTMENT FIRE THEORY

I 1 2 3 4 5 6

l FUEL

I

Conduction heat transfer through the fuel Radiative heat losses f r o m the fuel surface Convection a n d radiation from the flame Flow of combustible fuel volatiles Entrained a i r flow Plume mass flow

FIGURE 1-1. Primary processes associated with a burning object

direction that results in what is commonly referred to as a ceiling jet. Since the flow under the ceiling is turbulent, the flow is not strictly horizontal due to the vortices present. As time goes on, the products of combustion transported by the plume collect below the ceiling and form a hot smoky layer. The bottom of this hot layer may continue to descend as long as the fire progresses. The hot layer, made up of the products of combustion and entrained air, poses a severe threat to life due to irritation effects, toxic poisoning, and thermal burns. In addition to the human tissue damage, the thermal radiation emitted by the hot layer can result in flashover of the

Introduction

3

enclosure. Just prior to and afker flashover, the thermal radiation fkom the hot layer can also have a pronounced effect on the burning rate because the increased heat flux incident on the fuel surface will increase the pyrolysis rate and thus the burning and heat release rates. The concepts and importance of flashover and the effects of hot-layer radiation to fuel surfaces will be discussed in greater detail in Section 4.5. Not all of the heat energy released by the fire remains within the enclosure. At any given time, a portion of the energy released by the f r e is radiated away from the combustion region and rising plume. A major hction of this energy is received by the interior surfaces and is conducted away fiom the interior of the enclosure through the bounding surfaces of the enclosure 161. The energy not radiated away fiom the combustion region and plume is convected up through the plume into the forming hot layer. A fraction of this energy is lost fiom the hot layer to the bounding surfaces through convection and radiation. Once again, the energy imparted to the walls is conducted througb the walls from the hot interior surface towards the cool rear surface. The energy transferred to the bounding walls also results in the elevation of the temperature of the walls. The energy remaining in the hot layer is directly responsible for the increase in gas temperature of the smoky hot layer. As will be shown, the energy and mass of the hot layer are the unknowns that must be found in order to calculate the size and temperature of the hot layer within the enclosure. The other major source of energy loss from the hot layer is due to hot-layer venting. Hot-layer venting also accounts for mass loss from the hot layer. As a hot layer forms, it will descend. If a vent is present within an enclosure, the hot layer may eventually drop below the top (or soffit) of the vent. At this time, hot gas will flow out of the compartment due to the pressure differential created by the temperature differences of the interior and exterior (ambient) gases. Associated with this hot gas flow is the loss of mass and energy that is important in the calculation of the hot-layer size and temperature. The inflow of relatively cool, ambient-temperature air, through the lower portion of an opening (vent) in the enclosure boundaries, is partially responsible for providing the owgen required for combustion within the fire compartment. It is assumed that the ambient air supply is uncontaminated, at a constant temperature, and that the supply available is sufficient to provide the necessary volume needed throughout the course of the fire. If insufficient amounts of air enter the compartment, the fire

4

BASIC COMPARTMENT FIRE THEORY

may become oxygen starved. This condition results in reduced heat release rates and an increase in the products of incomplete combustion. Therefore, it is quite important to consider the flow of air into an enclosure and the oxygen needed for complete combustion. Figures 1-2(a)- (d) depict the typical stages of a developing compartment fire with respect to compartment venting. A more detailed explanation and discussion of the various venting regimes is presented in Section 2.6.2.2. Oxygen starvation is discussed in Section 4.2.

1.2 APPROACHES TO MATHEMATICAL FlRE MODELING Fire modeling can be accomplished through the use of experimental or mathematical techniques. Experimentalmethods include such methods as reduced and fUII-scale replicas of the situation or phenomenon being studied. Experimental methods need not actually use a f r e or other form of heat source for a particular study. For example, Steckler et al. [7] used saltwater modeling to study vent flows with much success; Prahl and Emmons [g] used reduced-scale kerosene/water analog experiments for the same purpose. Mathematical methods are commonly divided into two groups: stochastic and deterrninistic models [9].

1.2.1 Stochastic Models Stochastic models, also referred to as probabilistic models, treat fire growth as a sequence of events or steps. These events have a given probability of occurring, hence the term probabilistic model. The events, coupled with their probabilities, are used to predict the progress of a fire within a compartment or building. Since these models are based on a probabilistic approach to the fire problem, they typically fail to make use of the known physical and chemical equations that can mathematically describe the progress of fire development. One example of a stochastic or probabilistic model is the Building Fire Safety Model developed by Fitzgerald [l01; another is the Building Fire Simulation Model (BFSM) maintained by the National Fire Protection Association [l l].

(W FIGURE 1-2. Stages of the hot-layer formation in an enclosure fire

(4 FIGURE 1-2 (continued). Stages of the hot-layer formation in an enclosure fire

Approaches to Mathematical Fire Modeling

7

L2.2 Deterministic Models Deterministic models predict fire development based on the solution of mathematical equations that describe the physical and chemical behavior of fire. The probability of an event occurring is not an integral part of the approach. Most of the compartment f i e models available today are deterministic. There are two are types of deterministic compartment fire models: field models and zone models. 1.2.2.1 Field Models

Field models, as applied to compartment fire modeling, are those models that are based on an approach that divides an enclosure into a large number of elemental volumes. The model then solves the hdamental equations governing the transfer of mass, momentum, and energy between these small volumes to predict the progress of a fue within the enclosure. Field models are also referred to as Computational Fluid Dynamics (CFD) models, because they are extensions of computer codes that were originally developed to solve complex fluid flow problems. This type of modeling can be considered as a micro approach to the fue modeling problem. Field models are currently not considered for widespread use. This is primarily due to the extensive computer requirements that are not available to most computer users. Also, a more detailed understanding of the fundamental physical phenomena, such as turbulence, combustion kinetics arid chemistry, etc. are needed. As affordable personal computing power continues to increase, it is expected that field modeling will gradually become the preferred approach to simulate compartment fires. However, this will take some time, and zone models (see Section 1.2.2.2)will remain popular in the fire science and fire protection engineering community for many years to come. A detailed discussion of field modeling is beyond the scope of this book. Reference [l21 provides an excellent introduction to field modeling. 1.2.2.2 Zone Models

Zone models are the most common type of physical compartment fire models in use today. Zone models predict fxe development within an

8

BASIC COMPARTMENT FIRETHEORY

enclosure by solving the conservation of mass, momentum, and energy equations for a small number of zones (control volumes). Typically, the enclosure is divided into two distinct zones: an upper hot gas layer and a lower uncontaminated cold gas layer. This technique can be considered as a macro approach to the fire-modeling problem. Zone models have been widely accepted and applied due to their relatively simplified approach to the modeling problem, especially when compared to the overwhelming requirements of field models. When properly applied, zone models have proven to be a source of good engineering approximations of fire development within enclosures. Indeed, Emmons [l31 has stated, " ... the zone model provides all the accuracy required for engineering decision making." The Harvard Code, FIRST, CFAST, and ASET as well as most of the other compartment fire models available today are zone models. The model developed and presented in this book is also a zone fire model. 1.3 COMPUTER LANGUAGES USED FOR FlRE MODELING Historically, mathematical f ~ modelers e have written their programs in FORTRAN. This was primarily due to FORTRAN being a widely applied engineering language for computer programming. However, when W. D. Walton of the U.S. National Institute of Standards and Technology (formerly the National Bureau of Standards) released ASET-B in 1985, he opted to write the program in GW-BASIC. According to Walton [3], this decision was due to personal computers becoming commonplace in engineering offices, and GW-BASIC being "by far the most popular programming language." In addition, ASET-B being written in GW-BASIC would allow the program to be widely distributed and easily modified by its users. For the same reasons, the models presented in the first edition of this book were also written in GW-BASIC. One of the mainproblems with GW-BASIC is that it lacks the tools for developing well-structured programs. This problem has now been eliminated with new-generation BASIC interpreters, such as QBasic, which is shipped with the more recent versions of MS-DOS (5.0 and up) and Windows 95. Perhaps the most significant changes in this book fiom the first edition are the revised computer programs. The source code is provided in QBasic, which allows virtually anybody with access to an IBM-compatible PC to run the software with the QBasic interpreter. The

Computer Languages Usedfor Fire Modeling

9

source code is provided for every program, to allow the user to customize the software to suit his specific needs. Stand-alone executables are also provided for the programs described in this book. More recent versions of BASIC, such as Visual Basic, would have made it easier to include efficient and attractive user interfaces. To illustrate this point, the programs are also provided in Visual Basic. This version of the software is discussed in Appendix E. Thus, the user can examine, customize, and use the models that are developed in this book without any additional investment by using the QBasic programs. Alternatively, he can purchase a Visual Basic compiler, and use the Visual Basic code to develop a customized compartment fire simulator with a professional user interface.

CHAPTER 2

Introduction to Mathematical Compartment Fire Modeling

A qualitative description of the events that occur within an enclosure subject to a hostile fue was presented in Chapter 1. In this chapter, an introduction to the quantitative aspects of mathematical compartment fire modeling will be presented. The approach that will be applied is that of zone modeling of the fire development within an enclosure. To understand the material that will be presented in this and some subsequent chapters, it is assumed that the reader has a basic knowledge of fluid mechanics, thermodynamics, heat transfer, combustion, and numerical methods. A brief review of the pertinent fkdamentals of engineering is provided in Appendix B. 2.1 THE FIRE COMPARTMENT The problem to be studied is that of the time-varying conditions produced by a fue within an enclosure. For a general solution, it will be assumed that the compartment is a room that is basically rectangular in shape with equal and parallel floor and ceiling areas. For simplicity, it will be assumed that the room has a single vent that may or may not be open at any given time. A vent may be a door, window, leak, or other opening in a vertical boundary of the enclosure. It will also be assumed that there are no horizontal vents, i.e., no openings in the floor or ceiling. Also, throughout this book, the definition of terms such as compartment, enclosure, room, or other similar words are considered to be consistent unless otherwise noted.

12

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

2.2THE FlRE FLAME AND PLUME In a basic sense, a fxe is simply an object that releases heat into an enclosure. A small amount of mass in the form of fuel vapors is also released. The fuel vapors mix with the smounding air and react with the oxygen, releasing heat and forming products of combustion. The combustion reactions take place in a luminous gas volume that is referred to as the flame. The heat generated in the flame is released partly in the form of radiation, and partly by convection. The hot products of combustion rise fiom the flame, and form a thermal plume. Additional surrounding air is entrained in the plume, resulting in increasing plume mass flow and decreasing temperature as a function of height. Some zone models, e.g., FRST [l], approximate the flame as a grey gas volume of a particular shape, usually a cone or cylinder, with a uniform temperature. The radiation fkom the flame is calculated on the basis of simple engineering equations for emission of radiant heat fiom hot gas mixtures. The volume of the plume is lumped into that of the upper hot gas layer. Other models, such as CFAST [2], assume that the fire is a point source of mass and energy, and that flame and plume volumes can be neglected. In this case, the radiation fiom the flame is estimated as a constant fi-action, L, of the total heat release rate. The convective heat released by the fire, which is determined as the remaining fkaction of the total heat release rate, is directly injected into the upper layer.

2.3THE HOT AND COLD GAS LAYERS The rising plume gases collect below the ceiling and form a hot smoky layer. This layer may continue to grow while the f ~ exists. e The space between the floor and the hot layer consists of cool uncontaminated air. Numerous pre-flashover full-scale room f i e tests have shown that the interface between both layers is relatively sharp, while the composition and temperature of the layers are reasonably uniform. Consistent with these experimental observations, zone models are based on the assumption that the room gas volume comprises two distinct and uniform layers or zones: a lower layer of cold air and an upper layer of hot gases. The resulting idealized geometry of the gas volume inside the compartment is shown in Figure 2- 1.

Heat Release Rate of the Fire

FIGURE 2a1. Thermodynamic properties of upper and lower layer

In a thermodynamic sense, the gas layers inside the dashed lines in Figure 2-1 are neither "syktems" (because mass flows across the boundaries), nor "control volumes" (because some boundaries change with time). Strictly speaking they should be referred to as "open systems." The term "control volume" is most often used in practice. The state of each layer is uniquely defined by the values of the thermodynamic properties listed in Figure 2-1. 2.4 HEAT RELEASE RATE OF THE FIRE

Some zone fae models have the capability to predict heat release and mass loss rate fi-om the fire as a function of calculated conditions within the enclosure. However, this capability is available only for a few simple fuel geometries. For example, FIRST has a growing fire subroutine that predicts the size and heat release rate of a horizontal fuel slab such as a mattress [l]. FIRST also includes a subroutine to model flammable liquid pool fres. In general, the heat release and mass loss history must be supplied by the model user. It is a common misconception that zone models predict fire growth, while, apart from the few exceptions cited above, they only

14

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

determine the effects of a fire that is specified by the user. There are several methods and many data sources that can be used to estimate heat release and mass loss rates from burning objects. This topic is addressed in more detail in Section 4.4.

2.5 HEAT TRANSFER IN ENCLOSURE FIRES The radiation from the flame is transferred to the floor, wall, and ceiling surfaces, and is partly absorbed by the upper hot layer gases. In addition, the bounding surfaces of the enclosure exchange heat internally by radiation, and with the gas layers by radiation and convection. At each surface, there is a balance between the total radiative and convective heat flux that is received, and the heat flux that is transferred by conduction into the solid. It is clear, therefore, that it is not trivial to calculate the heat losses or gains of the gas layers. An enclosure-wide heat balance is needed that includes the three modes of heat transfer. An engineering approach will be used in Section 2.6.3.1 to arrive at an approximate, but reasonably accurate solution.

2.6 A GENERIC COMPARTMENT ZONE FIRE MODEL Zone models predict how the state of the upper and lower gas layers change with time by solving the conservation equations of mass and energy with the appropriate boundary conditions. To illustrate the technique of zone fire modeling, a generic set of equations will be developed, and a procedure for solving the equations will be presented below. However, since there are eight properties (four for each layer), and only four conservation equations, four additional equations are needed. These additional equations are derived first.

2.6.1 Primary and Secondary Variables The consemation equations that will be developed must be expressed in twms of four of the eight properties that are listed in Figure 2-1: two describing the lower layer and two describing the upper layer. There are thirty-six possible choices, but some combinations are better than others.

A Generic Compartment Zone Fire Model

15

A good choice will result in a concise set of conservation equations, in a form that makes it possible to easily obtain a numerical solution, avoiding instabilities or other mathematical problems. The four properties that will be selected are referred to as the primary variables. The remaining properties are defined as secondary variables. To facilitate the selection process, four additional equations that relate some of the properties will be developed fust. Because the total volume of the enclosure is fixed, the following relationship exists between the volumes of upper and lower layer: V, +

V'= V

= WLH

where V, V, V W L H

volume of the upper layer (m3) volume of the lower layer (m3) = total volume of the enclosure (m3) = width of the enclosure (m) = length of the enclosure (m) = height of the enclosure (m)

= =

The static pressure difference between floor and ceiling level is equal to the hydrostatic pressure at the bottom of an air column of room height. At ambient temperature this is approximately 12 Pa per meter of room height, or 35 Pa for a typical room height of 3 m. Because atmospheric pressure is close to 100,000 Pa, the pressure difference between the two layers can be neglected and

where

P,, = average pressure in the upper layer (Pa) P, = average pressure in the lower layer (Pa) P = characteristic room pressure, for example at floor level (Pa) A pressure difference of a few Pa is sufficient to cause significant air movement. Therefore, hydrostatic pressure differences will have to be

considered when calculating gas flows through openings (see Section 2.6.2.2). The question remains whether P is approximately equal to atmospheric pressure, or whether there is a significant overall pressure rise in the enclosure due to the f ~ eThe . following section is based on an important paper by Zukoski [14], that addressed this topic. When heat is added to a gas (air and smoke for the present problem) that is constrained to a specific fuced volume, the pressure must increase in response to the temperature increase of the gas. However, if some of the gas is allowed to escape fiom its enclosure, the pressure rise may be negligible. To gain an appreciation for the pressures that can develop in a sealed room, consider the following equation presented by Zukoski:

where P P, Q t

= = = =

p, = c, =

T,

=

pressure created by the fire (Pa) ambient pressure (Pa) heat added to the gas by the fire (kW) time (S) density of air (kg/m3) constant volume specific heat of air (W/kg=K) ambient temperature (K)

This analysis assumes that the process is adiabatic, the specific heat is constant, the gas behaves like an ideal gas, hydrostatic pressures are negligible, and the heat addition rate Q is constant. Zukoski presented an example using Equation (2.3) in his paper. The same example is repeated here. Consider a small fire that steadily releases 100 kW in a room that has a total volume of 28.5 m3. In ten seconds (t = 10), the pressure would rise approximately 0.07 bar (1 psi). This pressure increase would be sufficient to cause the breaking of a window that would effectively vent enough gas to prevent any W e r rise, thus limiting the pressure rise to a negligible amount. Other building construction materials would also fail at such pressure increases (see Reference [15], page 3-327). Table 2-1 lists damages to structures exposed to various overpressures.

A Generic Compartment Zone Fire Model

17

Table 2-1. Damages to Construction Assemblies due to Overpressures Damage

Overpressure (bar)

Shattering glass windows

0.03 to 0.07

Buckling or connection failure of steel or aluminurn paneling

0.07 to 0.13

Shearing and flexwe failure of 400-600 mm thick nonreinforced cinder block walls

0.13 to 0.20

For Wood Frame Dwellings: Minor Damage: similar to that caused by high wind

0.07

Slight Damage: doors, sashes, or frames removed; plaster or wallboard broken; shingles or siding off

0.13

Moderate Damage: walls bulged; roof cracked; studs or rafters broken Severe Damage: standing but substantially destroyed; some walls gone Demolished, not standing

1.00

0.20 to 0.27 Collapse of self-framing steel panel building Reprinted from the Handbook of Fire Protection Engineering [l 51 with permission 1 bar = 14.5 psi

Rooms typically have at least one door, especially in normal occupancies. Other openings such as windows, heat and ventilating registers connected to ducts, and other penetrations are also commonly present that would allow for added leakage paths. Klote and Fothergill [l 61 published some leakage areas for walls and floors in typical commercial buildings. Values for various occupancies, including residential occupancies, are also available [17,18]. Thus, leakage paths are commonly present in most normally constructed occupancies. Based on the data provided by the Zukoski example, it is apparent that pressure increases capable of causing structural damage can be generated by even small fires. However, the early pressure rises are likely to cause structural damages that would prevent any continued pressure increase within the enclosure. The leakage paths that are normally found in most buildings would also allow for the venting of gas from the enclosure, thus resulting in negligible pressure rises.

This brief analysis of the pressures developed by a fire in an enclosure, and the leakage normally associated with most buildings, suggests that a near-atmospheric pressure approximation is reasonable. This condition allows the use of Equation (2.2) in the development of the generic model. Since mixing between the layers is usually minimal and can be ignored, the lower layer consists of clean cool air. The pressure at floor level is near ambient. Atmospheric air contains small amounts of carbon dioxide and water vapor, but the radiation absorbed by these gases is negligible. The temperature of the air rises slightly due to convective heat transfer with the floor and lower wall sections, which are heated by radiation from the flame, upper layer, upper wall sections, and ceiling. Under such conditions of pressure and temperature, the lower layer air behaves as an ideal gas for which the following equation of state is valid:

where

m, = mass accumulated in the lower layer (kg) R, = gas constant for the mixture in the lower layer (Jkg-K) T, = temperature of the lower layer (K) For practical purposes, moisture may be ignored and the lower layer air considered dry. Based on the discussion above, pressure at ceiling level may also be considered equal to atmospheric pressure. The upper layer temperature seldom exceeds 1500 K. Therefore, the upper layer also behaves as an ideal gas so that

where

m, R, T,

mass accumulated in the upper layer (kg) = gas constant for the mixture in the upper layer (JkgK) = temperature of the upper layer (K) =

The main constituents of the upper layer are N,, 4,H20, CO2, and CO. Under some conditions appreciable amounts of other species such as HC1,

A Generic Compartment Zone Fire Model

19

HCN, and unburnt hydrocarbons may also be present. The ideal gas constant for the upper layer can be expressed as

all species

where Y,, = upper layer mass fi-actionof species i (kgkg)

ki= gas constant of species i (J/kg*K)

Note that as the composition of the upper layer varies with time, the value of 4 changes also. To determine Y,, it is necessary to solve additional mass conservation equations for the species that need to be tracked. To avoid this, the following approximation is often made [l91. Air entrained into the flame, up to the tip of the flame, is typically 10-20 times that required for complete combustion. Since the plume above the flame continues to entrain more air, it is clear that the plume is composed mostly of entrained air. (T~Isis particularly true forfree-burn fires, but is perhaps questionable for oxygen-limited fires.) Therefore, it can generally be assumed that the smoke produced by fies behaves like heated air. The conservation equations of mass and energy for the two layers will be developed in the next section. Equations (2. l), (2.2), (2.41, and (2.5) will be used to eliminate the secondary variables, and to express the equations in terms of the primary variables. The topic of selecting primary variables for zone model equations, and the consequences of choosing the wrong set are discussed in detail in Reference [20]. According to the guidelines in this reference, a suitable set of primary variables consists of T, and P, = P for the lower layer, and T, and V, for the upper layer. However, instead of the volume of the upper layer, the height of the interface between the two layers, Zi, will be used because it has direct relevance to fire hazard assessment. The two variables are related by

where Z

=

height of the layer interface above the floor (m)

20

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

Furthermore, the pressure difference at the height of the layer interface, AP(Zi), and the height of the neutral plane, Z,, will be used instead of the pressure at floor level, P,. The neutral plane is located at a height where there is zero pressure difference between the enclosure and the environment, and, consequently, no flow through the vent. Provided the neutral plane is located between the sill and soffit of the vent, hot smoke is flowing to the outside above the plane and fiesh air is flowing into the compartment below the plane. A relationship between AP(ZJ, Z, and P, is given in Section 2.6.2.2.

2.6.2 Conservation of Mass Conservation of mass of a layer can be expressed in general terms as

{rate of change of mass accumulated in layer

=

{ massflow in }

-

{ massflow out } (2.8)

The terms on the right hand side of Equation (2.8) account for all flows that add mass to or remove mass from the layer. They consist of the mass loss rate of the fuel and rate of entrainment into the flame and plume (see Figure 1-l), and mass flows through the vent (see Figures 1-2(a)- (d)). The mass loss rate of the fuel, riz, is small compared to the other mass flow terms and is often neglected. For the purpose of developing a generic zone model, it is assumed that m, is specified. The remaining terms on the right hand side of Equation (2.8) can be written as an algebraic function of the primary variables. These functional relationships will be developed fmt, before casting Equation (2.8) into mathematical form and applying it to the two gas layers. 2.6.2.1 Entrainment Rate

Air is entrained from the lower layer into the flre flame and plume over a height between the fuel surface and the hot layer interface. This provides a mechanism for transfer of mass from the lower layer to the upper layer. Hence, the mass conservation equations for upper and lower layer include an entrainment term that is of the same magnitude, but opposite in sign.

A Generic Compartment Zone Fire Model

21

Numerous empirical correlationshave been developed to predict plume mass flow. These correlations have the following general form

where

mp = A2 = Q = D =

plume mass flow (kg/s) height above the source (m) heat release rate of the fire (kW) characteristic fuel dimension (m)

For circular pool fires, D is the diameter of the fuel pan. For fres with a rectangular or square surface, D is usually the equivalent diameter, i.e., the diameter of a circle with the same area as the fuel surface. A commonly used plume model of the form of Equation (2.9) is the following correlation developed by Zukoski, Kubota, and Cetegen in 1980 12l]:

where K

=

a constant (kglk~"~-rn~'~*s)

L, = radiative loss fraction

The fuel mass flow rate has usually been ignored in the derivation of plume correlations. Therefore, Equation (2.9) can also be used to predict the entrainment rate over a particular height above the fuel surface (see Figure 2-2). Hence, the flow of lower layer air into the flame and plume can be expressed as follows

22

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

FIGURE 2-2. Plume entrainment below upper layer

where m, = air mass flow entrained in the flame and plume (kgls)

AZi = distance between the fuel surface and the layer interface (m) Equation (2.11) takes the following form, based on the plume model of Zukoski et al.

Equation (2.12) was used by Cooper in the development of ASET with K = 0.076. Other values of K can be found in Reference [19]. Breaking out the value of K allows the user some alternatives that were not readily available in the original ASET work. The energy used in the plume equations is the convective portion of the total heat release rate of the fie, not the total heat release rate. Therefore, the radiative losses must be accounted for before utilizing the plume equations, thus the presence of the (1 - L$" term in Equation (2.12). The l/3 power is required because Equation (2.12) is written with t)raised to the 1/3 power. The model of Zukoski et al. was based on previous work reported by Morton, Turner, and Taylor [22] combined with data reported by Yokoi [23]. The following assumptions were made in these plume models:

A Generic Compartment Zone Fire Model

23

The fire is considered to be a point source of heat, i.e., the burning fuel is considered to release its heat fiom a point and not fiom an area. Variations of density in the flow are considered small when compared to the ambient density. Air entrainment into the plume is considered to be proportional to the velocity of the plume at each location. The profiles of the vertical velocity and buoyancy force in horizontal sections are similar at all heights. Plume correlations are generally based on the assumption of a point source fire. However, unlike the model developed by Zukoski et al., most of the point source correlations indirectly account for the fact that the actual frre size is f ~ t (rather e than infinitesimal). This is accomplished by locating the point source at a distance below or above the actual fuel surface, so that entrainment characteristics for the point source plume are in agreement with those of real plumes. This approach is commonly referred to as the "virtual origin correction." Various expressions for calculating the virtual origin location, MO, are available in the literature. The height of the virtual origin, rather than the height of the actual he1 surface, serves as the reference for A.2in Equations (2.9) and (2.1O), and AZi in Equations (2.11) and (2.12) (see Figure 2-3). A fi-equently used expression for the virtual origin is reported by Heskestad in the SFPE Handbook (see Chapter 2-2 in Reference [15]):

where

AZ,

=

distance between the fuel surface and the virtual origin (m)

Negative values for calculated virtual origin corrections correspond to locations above the actual fuel surface and are associated with low heat release fies and./or large surface areas. Positive values correspond to locations below the actual fuel surface and are typically associated with high heat release frres.

FIGURE 2-3. Virtual origin correction

2.6.2.2 Mass Flows through ihe Vent Gas velocities inside the compartment averaged over a short time interval are negligible. At the vent, however, the horizontal component of the average velocities can be sigmficant. The gas flow into and out of the compartment are driven by hydrostatic pressure differences, which vary with height in a piecewise linear fashion. In a similar way as for the flow through an orifice, velocity v at height Z follows from Bernouilli's equation (see Section B. 1.3.4):

where v(2) = velocity at height Z (&S) Z = height above floor level (m)

A Generic Compartment Zone Fire Model

25

C = orifice coefficient PO&) = static pressure outside the compartment at height Z (Pa) P,(Z) = static pressure inside the compartment at height Z (Pa) p,@ = gas density in the vent at height Z (kg/m3) A reasonable estimate for the orifice coefficient C is 0.68, as found by Prahl and Emmom in salt water model experiments [g]. According to the sign convention introduced in Equation (2.M),velocities are positive when directed into the compartment. Immediately after ignition, combustion products start to accumulate beneath the ceiling. As the smoke layer descends, cold lower layer air is pushed out. This ccpiston"effect is illustrated in Figure 2-4a. The static pressure inside the compartment is higher than that outside the compartment over the full height of the vent (G < Z < &). The neutral plane, where P, = Pout,is located far below the sill of the vent. At some time the upper hot layer descends to the soffit of the vent. However, the upper layer still expands faster than the entrainment rate of air into the fire. As shown in Figure 2-4(b), the total flow exiting the compartment consists of lower layer air that is pushed out at the bottom of the vent due to the piston effect, and upper layer gas that spills under the sofit. Hydrostatic pressure inside the compartment still exceeds that outside the compartment over the full height of the vent, and the neutral plane remains below the sill of the vent.

FIGURE 2-4a. Piston flow (2,S Z,and Zi 2 2,)

26

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

Subsequently, the neutral plane rises above the sill and ambient air starts to flow into the compartment at the bottom of the vent. The neutral plane height continues to increase, and quickly exceeds the height of the interface between the gas layers (see Figure 2-4c). The resulting flow conditions prevail for almost the entire pre-flashover fire period, since the duration of the preceding piston flow regime is typically less than one minute.

FIGURE 2-4b. Piston flow (2, I Z,and Z,< & < ZJ

FIGURE 2-4c. Main pre-flashover fire flow regime

A Generic Compartment Zone Fire Model

27

If flashover conditions are reached, the inflow of air may no longer be controlled by the entrainment rate, but by the size of the vent. This "choking" effect or ventilation controued regime was first identified in 1958 by Kawagoe. For this regime, Kawagoe found that air flow is proportional to A@?, where A, and H, are area (in m') and height (in m) of the vent, respectively [24]. Eventually, when the fire dies down, a reverse piston regime develops. Equations to predict vent flows for the different regimes will now be developed. Vent flows are calculated by integration of velocities over the appropriate height. Integration intervals and the resulting equations are different depending on the location of the neutral plane. Furthermore, T, is initially equal to Ta.Some models, such as ASET, neglect the convective heat transfer between the lower layer and the floor and lower wall sections, so that T, is equal to Ta by default. This condition has to be considered separately to avoid problems in the numerical calculation of lower layer vent flows. In the derivation of the vent flow equations, use is made of the following relationship for dry air:

where p(T) = pRf = T, = T =

density of dry air at temperature T (kg/m3) density of dry air at temperature T, (kg/m3) reference temperature (K) temperature (K)

It is assumed that the composition of the upper layer is close enough to that of dry air, so that Equation (2.15) is applicable to both layers. 2, _c 2,and Zir 2, Typical pressure profiles for this case are shown in Figures 2-5(a) (T, = TJ and 2-5(b) (T, > TJ. Pressure difference as a function of height is given by

-

T, = Ta:A P (2) P X , 2 )- Pin(2) = constant and 2,-

-m

(2.16a)

28

INTRODUCTIONTO MATHEMATICALCOMPARTMENT FIRE MODELING

or

where

AP(2) = static pressure difference = acceleration of gravity ( ~ 9 .18m/sZ) g Consequently, vent flows are calculated fiom

FIGURE 2-5. Piston flow pressure profiles (2,

I Z,, and Zi 2 2,)

A Generic Compartment Zone Fire Model

29

and ni,=m,=O

(2.17b)

where vent flow of lower layer gas leaving the compartment (kg/s) W, = width of the vent (m) p, = density of lower layer gas (kg/m3) nia = vent flow of ambient air entering the compartment (kg/s) m, = vent flow of upper layer gas leaving the compartment (kg/s) m, =

Typical pressure profies for this case are shown 2, S-2and , 2'' Z, 4. in Figures 2-6(a) (T, = Td and 2-6(b) (T, TJ. The pressure difference below the interface (Z i ZJ can be calculated fiom Equation (2.16a) (T,= Th or Equation (2.16b) (T, > T,). Between the interface and the soffit of the vent, the pressure difference is given by

FIGURE 2-6. Piston flow pressure profiles (2,

S

Z, and Z,, < Z < ZJ

30

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

Vent flows are calculated fiom z,

~ , = W v l p , ~ ( Z ) d Z ~ 2 6 . 6 W v ~ C (2.19a) ~ ~ d Z Zb

Zb

and

The mass flow of ambient air into the compartment is still zero (ma = 0).

Zb c 2, S Ziand Zb < Zi< 2, Typical pressure profiles for this case are shown in Figures 2-7(a) (T, = TA and 2-7(b) (T, TJ. The pressure difference equations are the same as for the previous case, i.e., Equation (2.16a) (T,= TJ or Equation (2.16b) (T,> TJ below the interface (Z S 23, and Equation (2.18) above the interface. Note that the constant in Equation (2.16a) in this case is equal to zero, and that 2, is equal to Zi. Equation (2.19b) is still applicable for the upper layer flow, m,. However, ambient air flows into the compartment below the neutral plane, and lower layer gases leave the compartment between Z, and 3. The equations for ni, and m, are given below. Equation (2.19b) is still valid for calculating the upper layer flow, ni,.

and

A Generic Compartment Zone Fire Model

31

FIGURE 2-7. Pressures during transition to main flow regime (2,< 2, < Zi)

Zi< 2, < Z, and 2,< Zi< 2, Typical pressure profdes are shown in Figures 2-8(a) (T, = T h and 2-8(b) (T, > Td. The pressure difference is given by

and

Vent flows are calculated from 2,

1

7 \iar::z)..

f i a = W,, pJv(Z)ldZ=26.6Wy C zb

zb

32

INTRODUCTlON TO MATHEMATICAL COMPARTMENT FIRE MODELING

FIGURE 2-8. Pressure profiles during main flow regime (Zi IZ, ZJ

and

The flow of lower layer gases leaving the compartment is zero, m, = 0. 2.6.2.3 Mnss Consetvation Equations

Mass flows are shown in Figure 2-9. The conservation equation of mass for the lower layer is

Furthermore, to relate density to temperature for the lower and upper layer gases, the equation of state for dry air, Equation (2.15) is used. Consequently, the mass of the lower layer can be expressed as

A Generic Compartment Zone Fire Model

FIGURE 2-9. Mass flows

Substitution of Equation (2.24) in Equation (2.23) leads to

It is shown below that the temperature derivative on the right hand side of Equation (2.25) is a function of the primary variables. Hence, since m,, ni, (see Section 2.6.2.2), and m, (see Section 2.6.2.1) are also functions of the primary variables, the lower layer mass conservation equation is of the following form

Conservation of mass for the upper layer is expressed by

34

INTRODUCTIONTO MATHEMATICALCOMPARTMENT FIRE MODELING

where m, = mass loss rate of the fuel @/S)

Equation (2.27) can be transformed in an analogous way to

Substitution of Equation (2.25) into Equation (2.28), to eliminate the time derivative of Zi leads to

Hence, because the time derivative of pressure is neglected, upper layer mass conservation leads to an algebraic rather than a differential equation. 2.6.2.4 Species Conservation Equations Since layer mixing is ignored, composition of the lower layer is equal to that of the incoming air. Composition of the upper layer is determined from the solution of species conservation equations. Before deriving these equations, the following simplifying assumptions are made: 1 The moisture content of the incoming and lower layer air is neglected. (Typically, the moisture content of ambient air is of the order of 1% by mass.) With this assumption, the air consists of oxygen (23.2% by mass) and a balance of inert gases, primarily nitrogen. 2 Air is entrained below the interface into the flame and plume at a rate that exceeds the rate needed for complete combustion of the fuel volatiles. This condition is generally met in the early stages of a fie.

A Generic Compartment Zone Fire Model

35

It may not be valid if the distance between the fuel surface and the interface is too small, i.e., because the fuel is located far above floor level, or because the layer interface has descended too close to the fuel surface. Underventilated fires that occur in these cases are discussed in more detail in Section 4.2. 3 The flame can be modeled as a Simple Chemical& Reacting System (SCRS), in which 1 kg fuel reacts with s kg dry air to form 1 + S kg products of combustion (see Section B.4.1 S). The air to fuel ratio, S, is usually larger than the stoichiometric ratio, S,,,,. If the composition of the fuel volatiles vary during the course of the fire (as they do for realistic fuels), s may not be constant. If more lower layer air is entrained into the flame and plume than needed for stoichiometric combustion, only a fi-action (S,,, h ) is used. The remaining fraction of the entrained air (m, - S, liz,) is theoretically not needed for combustion, and is referred to as excess air. The excess air is not affected by the combustion reactions, and acts as a diluent of the products of combustion. The stoichiometric air to fuel ratio, S,,,,, is usually not known. However, the stoichiometric mass flow of air can be determined fi-om the heat release rate on the basis of the oxygen consumption principle. In 1917, Thomton showed that for a large number of organic liquids and gases, a nearly constant amount of heat is released by complete combustion per mass unit of oxygen consumed 1251. Huggett found this to be also true for organic solids [26], and determined an average value for this constant of Ah,,Jr,,, = 13,100 kT/kg of 0 , where Ah,,, is the net heat of combustion and rdCh is the stoichiometric oxygen to fuel ratio. This generic value may be used for most practical applications, and is accurate, with very few exceptions, to within &5%. Consequently, the stoichiometric air flow rate can be estimated fi-omthe heat release rate via

sstozch . mf =

where

36

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

sstoi, Ah,,

stoichiometric dry air to fuel ratio (kgkg) net heat of combustion of the fuel (kJ/kg) r,, = stoichiometric oxygen to fuel ratio (kgkg) Y , 0, = mass fiaction of oxygen in air (~0.232kg O2kg dry air) = =

If the stoichiometric ratio of species i generated per mass unit fuel burnt is denoted as y , the mass fraction of the various species comprising the plume flow entering the upper layer can be written as (see Figure 2-10):

where mass fraction of species i in the plume at the interface (kgkg) stoichiomebic ratio of species i generated per mass unit fuel b m t (Wkg) Y,, = mass fiaction of species i in the lower layer (kgkg)

Y, yi

=

=

The generation rate of oxygen is equal to zero. The generation rate of nitrogen is equal to sm, Y,., The generation rate of other species such as CO,, H20,etc. are either specified on the basis of experimental data, or are calculated fiom the stoichiometry of combustion if the elemental composition of the fire1is known. The upper layer mass balance for species i is given by

Subtracting Y, times the overall upper layer mass balance Equation (2.27), after rearrangmg, leads to

A Generic Compartment Zone Fire Model

37

FIGURE 2-10. Species generation in the flame

As a minimum, Equation (2.33) must be solved at every time step to determine the upper layer mass fraction of oxygen. As long as the flow of air supplied to the combustion system greatly exceeds the rate for stoichiometric combustion, the mass fractions of all other species are proportional to the oxygen depletion of the upper layer, provided the stoichiometry does not change with time. 2.6.3 Conservation of Energy

The remaining two primary variables, T, antiT,, are obtainec fiom the solution of the lower and upper layer energy conservation equations. Conservation of energy of a layer can be expressed in general terms as =

{ enthalpyfrow in } - { enthalpyflow out } +

{ heat transferred to the layer )

- { work done by the layer )

(2.34)

38

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

This is the first law of thermodynamics (see Section B.2.2.6), applied to a layer. Before these conservation equations can be developed and solved, it is necessary to determine the net heat gained or lost by each layer. As explained in Section 2.5, this can only be done on the basis of a compartment-wide heat transfer analysis, which forms the subject of the first sub-section below. The energy conservation equations are derived in the next sub-section. 2.6.3.1 Enclosure Heat Transfer

Radiative Heat Transfer.The inside surface of the enclosure is subdivided into N,usually rectangular, segments which are assumed to have a uniform temperature 1; (j = 1...N. The enclosure is partially fded with an absorbing-emitting gas at temperature T,. M segments are in contact with the upper layer. The remaining N-M segments are in contact with the transparent lower layer gas. The fire is approximated as a point source that emits, but does not absorb radiation. The location of the point source for the purpose of calculating radiation heat transfer may be different than for the thermal plume model (see Section 2.6.2.1). The fire releases a certain fraction, L, of its heat release rate, Q, in the form of thermal radiation. Figure 2-10 shows a schematic of the geometry used to obtain the following set of N transfer equations (k = 1...N.

where

N = number of segments or surfaces in enclosure 6,, = Kronecker delta, i.e., 6,, = 1 i f j = k, and 6,, = 0 i f j # k Fkj = configuration factor between surface k and surfacej X, = transmitted fi-actionof radiation from surfacej to k ej = emissivity of surfacej

A Generic CompartmentZone Fire Model

39

FIGURE 2-11. Network for radiative heat transfer

q ,

net radiative heat flux entering surfacej (kw/m2) elk = emissivity of gas volume between surfacej and surface k o,, = configuration factor between the fire and surface k z, = transmitted fraction of flame radiation to surface k A, = area of surface k (m2) =

The net radiative heat flux entering surface j is equal to the heat flux removed fiom surface j by means other than radiation to keep it at temperature I;. The set of radiation transfer equations is obtained by integrating similar equations for monochromatic radiation derived by Siege1and Howell [27] over all wavelengths, assuming that the gas and all surfaces are grey, and taking flame radiation into account. With grey surfaces and a grey gas, zjkand E,, may also be written as

where

k,,

L,

= =

extinction coefficient of the upper layer gas (llm) mean beam length in upper layer between surfacesj and k (m)

Equation (2.36) is also valid for radiation from the flame. Because the calculation of the mean beam length in Equation (2.36) is rather complex,

40

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

the following simplified engineering approach is ofien adopted. If both swrfacesj and k are in contact with the lower layer, then ej, = 0 and r,, = 1. Likewise, if the fire is located below the layer interface and the receiving segment k is in contact with the lower layer, then E, = 0 and .c,= 1. In all other cases, an average transmissivity and emissivity are determined on the basis of the overall mean beam length for the upper layer geometry:

where z, = average upper layer transmissivity E, = average upper layer emissivity L, = overall mean beam length for the upper layer (m)

The extinction coefficient, k,is a complex function of the concentration of absorbing/emitting gas species (CO,, H,O, etc.) and soot particles. Modak [28] developed a method to calculate R,, that is used in FIRST [l]. The mean beam length is a function of the geometry and size of the upper layer gas volume. It may be estimated fiom the following expression:

where

A,

=

enveloping area of the upper layer (m2)

Since the upper layer has the shape of a parallelepiped, V, and A, are given by

and

A Generic Compartment Zone Fire Model

41

Convective Heat Transfer.The convective heat flux to each wall surface, can be witten as

where

T,, = temperature of the gas layer in contact with surfacej (K) Because the gas layers are relatively quiescent, the convection coefficient, h, can be obtained fiom empirical correlations for natural convection over an isothermal flat plate. Such correlations have the following non-dimensional form:

where

Nu,

Nusselt number for convective heat transfer to surfacej = characteristic length of surfacej (m) = thermal conductivity of gas in contact with surfacej (W1m.K) = constant Gr, = Grashof number for convective heat transfer to surfacej Pr, = Prandtl number for convective heat transfer to surfacej n = constant =

Both C and n depend on the orientation of the plate, the flow regime (laminar or turbulent) and whether the plate is cooled or heated by the fluid. Appropriate values can be found in a textbook on heat transfer (e.g., Reference [29]). The Nusselt, Grashof, and Prandtl numbers in Equation (2.41) are calculated using properties of air evaluated at the film temperature, i.e., the average of fluid and surface temperature. The length

42

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

scale, I,, is equal to (LW)'" for horizontal surfaces, and to the height for vertical surfaces. If the momentum of the fire is sufficiently high when the plume hits the ceiling, a forced flow is generated, commonly referred to as the ceiling jet. Cooper developed an approach to account for the forced convection heat transfer fiom the ceiling jet to the ceiling and upper wall sections. Algorithms implementing this approach for a two-zone room fire environment are described in Reference [30]. Beller included a ceilingjet algorithm into the WPI fire code [3 l], which is an extended and modified version of FIRST, developed at Worcester Polytechnic Institute [32]. For the purpose of the generic model developed in this chapter, ceilingjet heat transfer is not considered. Additional discussion of the subject can be found in Section 4.3.

Heat Conduction.The net heat flux to a surfacej, q;,,, is the sum of the net radiative and convective heat fluxes, which are calculated as described above.

The heat that is supplied externally by radiation and convection is conducted into the solid. The assumption that surface temperature of every segment is uniform implies one-dimensional heat transfer (perpendicular to the surface). Assuming each wall segment has thermal conductivity $ density pj, and specific heat cj, all of which may be a function of temperature, the heat conduction equation takes the following form:

A Generic Compartment Zone Fire Model

43

where

4

thickness of segmentj (m) = heat loss from the unexposed side of segmentj (kw/m2)

=

The heat loss from the unexposed side, qy,,ms,may be a function of the unexposed surface temperature, or it may be a constant (zero for a wellinsulated segment, approximating adiabatic boundary conditions). Equations (2.43a) to (2.43d) are too complex for an analytic solution. Most often, finte difference techniques are used to solve the equations numerically [33]. Additional complexities, such as multilayered walls or temperature-dependent thermal properties, can also be addressed without too much difficulty if a finite-difference technique is used. Source Termsfor the Energy Conservation Equations. The source term for the energy conservation equations of a layer consists of the net amount of heat supplied to the layer by external sources, i.e., other than the sensible enthalpy of flows that add or remove mass from the layer. The source term can be positive, indicating a net heat gain, or negative if there is a net heat loss. Because the lower layer is assumed to be transparent, it can only gain or lose heat by convection with the floor and lower wall sections. Hence, the source term for the lower layer is given by

where Q~ = net heat transferred to the lower layer (kW)

In addition to convective heat gains or losses, the upper layer also absorbs and emits radiation. Because of conservation of radiant energy, the upper layer source term follows from

44

INTRODUCTIONTO MATHEMATICAL COMPARTMENT FIRE MODELING

where

i), = net heat transferred to the upper layer (kW) 2.6.3.2 Energy Conservation Equations Figure 2-12 shows the enthalpy flows pertinent to the energy conservation of the gas layers. Application of the fust law of thermodynamics to the lower layer results in the following equation

where U, = internal energy of the lower layer (kJ/kg) ha = enthalpy of the incoming air at temperature Ta (kJ/kg) h, = enthalpy of the lower layer gas at temperature T, (W/kg)

FIGURE 2-12. Enthalpy flows

A Generic Compartment Zone Fire Model

45

Because internal energy of the lower layer and enthalpy of the lower Iayer are related via m,h, = mlul + P,&, and because P, is assumed to be constant (see Equation 2.2), Equation (2.46) can be rewritten as

dm,h, dt = -

dm,

+

hzdt

dh, m,dt

=

maha - m,h,

-

fieh,

+

Q, (2.47)

Substitution of the lower layer mass balance Equation (2.23) to eliminate the time derivative of m, on the left hand side of Equation (2.47), after rearranging, leads to

Enthalpy of an ideal gas mixture can generally be written as

where enthalpy of the mixture at reference temperature To (kJ/kg) C = mean heat capacity between To and Tat constant P (kJ/kgK)

h"

=

Because ambient air and lower layer gases have identical composition, their reference enthalpies are identical. The energy balance of the lower layer, therefore, can be rewritten as

where =

=

mean heat capacity of dry air between To and T, (kJ/kg-K) heat capacity of lower layer gas between To and T, (kJ/kg*K)

Because the composition of the lower layer does not change, c; only varies with time due to lower layer temperature changes. Hence, the lower layer energy conservation equation can be written in the following final form:

The first law of thermodynamics applied to the upper layer yields the following equation, similar to Equation (2.46) for the lower layer:

or

where uu = internal energy of the upper layer (kJ/kg) h, = enthalpy of the fbel volatiles at temperature T, (kJ/kg) h, = enthalpy of the upper layer gas mixture at temperature Tu(kJkg) The reference enthalpies of fbel volatiles, entrained air, and plume gases at the layer interface are related by the following equation

where

A Generic Compartment Zone Fire Model

47

h; = reference enthalpy at Toof the fuel vapors (kJ/kg) h: = reference enthalpy at Toof the lower layer gases (kJ/kg) nip = plume mass flow at the layer interface height (kg/s) hi = reference enthalpy at Toof the plume gas mixture at Z = Zi (kJ/kg)

Since it is assumed that there is no combustion in the upper layer, the following equation is also valid:

Combination of Equations (2.56) and (2.57) leads to

Subtracting Equation (2.58) from Equation (2.55) gives

The upper layer mass balance Equation (2.27) can be used to eliminate the time derivative of m, on the left hand side of Equation (2.59). Therefore, if he1 mass flow is neglected, Equation (2.59) can be rewritten as

W, - h,") mu

dl

=

d,[(hl- hlo)- (h, - h a ] +

i) +

Q,

(2.60)

Using Equation (2.49) to express enthalpy differences as a function of temperature then leads to

48

INTRODUCTION TO MATHEMATICAL COMPARTMENT FIRE MODELING

or

where

c; = heat capacity of upper layer gas between Toand Tu(kJ/kgK) 2.6.4 Solution of the Model Equations Equations (2.26) for mass conservation of the lower layer, (2.33) for upper layer species conservation, (2.53) for lower layer and (2.62) for upper layer energy conservation form a set of ordinary differential equations (ODEs). Equation (2.29) for mass conservation of the upper layer, and auxiliary Equations (2.35), (2.40), (2.42), (2.43) (in a finite difference form), (2.44), and (2.45) form a set of, primarily non-linear, algebraic equations. The system of equations is very complex, so that an analytic solution cannot be obtained. Numerical techniques have to be used to estimate the values of the primary and auxiliary variables at discrete times At, 2At, etc. One approach to solve this complex combined system of ODEs and non-hear algebraic equations is by using a canned solver that can handle this type of problems. An example of such a solver is described in Reference [34]. An alternative approach consists of an iterative sequence by which groups of equations are solved in a predetermined order. If values are available for the primary and auxiliary variables at time t, the following steps are taken to obtain values at t + At: 1 Calculate radiative fluxes to surfaces j = 1 ... N at time t [Equation (2.35)]. 2 Calculate convective fluxes to the N surfaces at time t [Equation (2.40)]. 3 Estimate surface temperatures at t + At assuming that heat fluxes do not change between t and t + At [Equations (2.42) and (2.43)].

A Generic Compartment Zone Fire Model

49

Calculate total heat transfer to lower [Equation (2.44)] and upper [Equation (2.491 layer. Estimate values of the primary variables at t + At [Equations (2.26), (2.29), (2.53), and (2.62)], and determine updated mass flows in the process. Estimate radiative fluxes to the N surfaces at t + At pquation (2.35)]. Estimate convective fluxes to the N surfaces at t + At Pquation (2.40)]. Obtain improved estimates of surface temperatures at t + At, using heat flux averages between t and t + At [Equations (2.42) and (2.43)]. Calculate total heat transfer to lower [Equation (2.44)] and upper pquation (2.45)] layer. Obtain improved estimates of the values of the primary variables at t + At @%pations (2.26), (2.29), (2.53), and (2.62)l. Repeat steps 6-10 until the difference between successive approximations of the values of the primary variables at t + At is within a user-specified tolerance. Rehun to step 1 to advance to the next time step. If the time step At is small (e.g., of the order of 1 second) and the userspecified tolerances are reasonable (e.g., of the order of 0.1 K for temperatures), the solution usually converges rapidly and steps 6- 10 have to be repeated not more than two or three times.

ASET-QB: A Simple Room Fire Model

CHAPTER 3

3.1 INTRODUCTION

In 1980, Cooper presented the general methodology for computing the available safe egress time fiom an enclosure subject to a hostile fire [6]. In 1982, Cooper and Stroup presented a computer program and user's guide for the equations presented earlier by Cooper. The model was named ASET, an acronym for Available Safe Egress Time [35]. The ASET program is basically a smoke-fiing model based on the Zukoski et al. model for mass flow in a fue plume. In addition to calculating the hot-layer location and temperature, ASET is capable of providing estimates of the concentration of species within the hot layer. The user can define the onset of untenable conditions for humans based on the value or the rate of rise of the hot-layer temperature, location of the layer interface, as well as concentrations of toxic gas species. The user can also define the time at which the fire is detected. When the user-defmed hazardous conditions are reached during the simulation, the available safe egress time is then found by using

where t,, is the time into the simulation at which the user-defined hazardous conditions are reached, and t, is the time at which the userdefined conditions for fire detection are reached (i.e., the time that egress is initiated). The concept of estimating the available safe egress time according to Equation (3. l), which is at the basis of the ASET model, is discussed in detail in Reference [36]. The original ASET program by Cooper and Stroup was written in FORTRAN and contained over 1500 program lines. When it was released,

52

ASET-QB: A SIMPLE ROOM FIRE MODEL

personal computers were just becoming an available tool for practicing engineers. Thus the original ASET program was not written for personal computers. A more detailed description of the ASET model is provided through References [3,6,35,36,37,38,39,40]. In 1985, Walton introduced ASET-B [3,40]. ASET-B was a response to the desire to run the ASET model on personal computers that had become generally available to the public and practicing engineers. According to Walton, personal computers were not considered effective for running the ASET model in its original form. As mentioned, ASET consisted of over 1500 lines of FORTRAN source code. However, the most popular programming language on personal computers, according to Walton, was BASIC, not FORTRAN. Also, the size and run time of the program made it difticult to work with on personal computers. A different mathematical solution technique was used in the ASET-B model to reduce the average nm time on a typical 16-bit personal computer from 5 minutes for the original ASET model to 1 minute. When ASET-B was being developed, it was decided that some of the features of the original ASET model would be eliminated to produce a program that was effective for personal computer use. ASET can handle multiple runs, identifl user-defmed end points for the simulation, and calculate hot-layer species concentrations. These features were eliminated and the program was written in GW-BASIC. The result, ASET-B, was a program of approximately 100 program lines that solved the same basic equations used in the ASET model. As mentioned above, a different numerical solution routine was selected for ASET-B. ASET used a fourth-order Runge-Kutta method with a variable time step. ASET-B was written using an improved Euler predictor-corrector solution to the differential equations. Walton reported this to be a major difference between the two models that resulted in reduced run times; the mathematical agreement between the two methods was reported to be within a fkaction of a percent [3]. A M e r discussion of the numerical solution techniques will follow later in this chapter. Today, personal computers can easily handle the original ASET FORTRAN code. However, the ASET model is simple enough so that comparable accuracy and acceptable calculation speed can be obtained with BASIC, in particular if a compiler is used. The integrated environment of modern versions of BASIC, such as QuickBasic, QBasic, and Visual Basic greatly facilitate program development. It is easy to add an efficient and atb-active user interface, in particular in Visual Basic.

Introduction

53

Finally, users of BM-compatible personal computers don't need to make additional investments to run structured BASIC programs, because the QBasic interpreter comes with the operating system. The most recent version of ASET is included with FPETool[4 l], and is referred to as ASETBX. The program was developed in QuickBasic, and interacts with the enhanced FPETool user interface. However, the model equations in ASETBX are the same as in ASET and ASET-B. FPETool is a collection of fire protection engineering software tools for fire hazard estimation that were developed at the Building and Fire Research Laboratory (BFRL) of the National Institute of Standards and Technology (NIST). FPETool is in the public domain, and can be downloaded at no cost fiom the NIST BFRZ, web site (URL: http://f~e.nist.gov/). A qualitative and quantitative overview of mathematical fire modeling was presented in Chapters 1 and 2, respectively. With this background, a detailed description of the ASET model will now be presented. For reasons described in Chapter 2, it is known that a vent is a requirement of all enclosure fires. The ASET model assumes that the only vent in the enclosure is a leak at the floor level. Figure 3-1 shows a schematic of the problem addressed by the ASET model. The floor leak is a conservative approach when concerned with life safety because floor leaks (as opposed to other vents) will result in the most rapid development of the hot layer.

FIGURE 3-1. Schematic of the fue problem addressed by ASET

54

ASET-QB: A SIMPLE ROOM FIRE MODEL

3.2 FORMULATION OF THE ASET EQUATIONS The assumptions used in the derivation of ASET are as follows: Two-zone (layer) approximation is considered acceptable. The pressure within the compartment is constant and equal to atmospheric pressure (see Section 2.6.1). Heat transfer from the floor and lower wall sections to the lower gas layer is neglected, and the temperature of the lower gas layer is constant and equal to ambient air temperature. The specific heat at constant pressure is assumed to be constant for all gases, and is equal to the specific heat of dry air at 293 K, i.e., c,, = 1.OO4 kJ/kgK (a reasonable assumption since the specific heat of nitrogen increases only slightly with temperature, as shown in Section B.2.2.4, and the upper layer gases consist primarily of nitrogen). Zukoski's point source plume model is considered to yield acceptable results in the flaming, intermittent, and plume regions. Entrainment occurs between the surface of the fuel and the layer interface. Virtual source corrections are considered negligible and are not included. Stratification does not occur, i.e., all heat and mass from the plume reach the hot layer located below the ceiling. The transport time fiom the fire to the hot layer is negligible, i.e., quasi-steady state conditions are assumed. The plume occupies a negligible fraction of the lower layer. The heat release rate of the f i e is specified by the user. Compartment effects and oxygen starvation are ignored. A constant fkaction, L,, of the heat released by the fire consists of radiation (the balance is convection). In ASET, the radiative fiaction is set equal to 35% (L, = 0.35). The energy losses fiom the flame and plume, and the energy losses from the compartment through the bounding surfaces are described simply as a fraction, L , of the total heat release at any given time. Venting occurs only through a crack-like vent located at floor level. Due to assumptions 3 and 10, there are only two primary variables, Z and T,. Furthermore, assumption 9 greatly simplifies the heat transfer calculations, eliminating the need for any auxiliary variables. Consequently, the system of ASET model equations only consists of two conservation equations.

Formulation of the ASET Equations

55

Cooper expressed the equations in a non-dimensional form, to facilitate a systematic analysis of the development of hazardous conditions in enclosures with growing fies (e.g., Reference [42]). Here the equations are derived from the generic model equations presented in Chapter 2. The variables and parameters are purposely not converted to a non-dimensional form, so that the reader has a better feel for the magnitude of dimensions, temperatures, heat release rates, mass flows, etc. as they vary over the course of the fie. 3.2.1 Layer Interface Height As described in Section 2.6.2.3, the location of the interface, thus the hot layer, can be predicted by an equation describing the conservation of mass for the lower or upper layer. The latter is easier because it does not require calculating vent flows. The mass conservation for the upper layer is given by Equation (2.28). Because there are no upper-layer gases leaving the compartment and fuel flow can be neglected, the upper layer mass balance can be written as

where A = area of the floor of the compartment, equal to L

X

W (m2)

The time derivative of T, on the right hand side can be expressed as a fimction of the priqary variables, as will be shown in the next section. The entrainment rate, me,is calculated based on Zukoski's plume model, Equation (2.12), with K = 0.076. Zukoski expressed plume mass flow as a function of non-dimensional heat release rate, defined as follows:

56

ASET-QB: A SIMPLE ROOM FIRE MODEL

where

i)* = non-dimensional heat release rate

c,

=

specific heat of air at temperature Taand constant P (kJ/kgK)

Substitution of Equation (3.3) in Equation (2.12); with p, = 1.2 kg/m3, c, = 1.004 kJ/kg=K,and Ta = 293 K, leads to the following form of Zukoski's plume model equation:

This is the form that Cooper et al. used in the derivation of the ASET model equations [6,371. Equation (3.2) is valid as long as AZi > 0 (or Zi > Z,). When the interface drops below the fuel surface, the same equation can still be used with rir, equal to zero. However, when Zi S 2 , it is likely that the userspecified heat release rate will be affected by the reduced oxygen that is entrained into the flame and plume. Therefore, it is recommended to terminate the calculations when the interface drops below the fuel surface. 3.2.2 Hot-Layer Temperature

Assumption 9 implies that the heat transferred to the upper layer is given by

*

Therefore, Equation (2.61) for conservation of energy of the upper layer, with T,= T, = T, and constant specific heat, can be written as

Formulation of the ASET Equations

57

or in the following fmal form

Equation (3.7) is indeterminate at time t = 0. This mathematical problem can be eliminated by assuming that the layer interface is located slightly below the ceiling, e.g., Zi = H - 0.0 1 (in m) at t = 0. When the interface drops below the fbel surface, Equation (3.7) cim still be used with m, equal to zero. However, the question is again whlether the user-specified heat release rate will remain unaffected by the reduced oxygen that is entrained into the flame and plume.

3.2.3 Outnow of Lower Layer Gases An expression for the outflow of lower layer gases can be derived from the mass balance Equation (2.25), with T, =

;c:

Combination of Equations (3.2) and (3.7) leads to the following expression for the time derivative of 2,:

Substitution of Equation (3.9) into (3.8) then leads to

58

ASET-QB: A SIMPLE ROOM FIRE MODEL

3.3 SOLUTION OF THE DIFFERENTIAL EQUATIONS

To apply the equations shown above, they must be solved at each time step throughout the simulation. However, the equations cannot be solved explicitly, i.e., they are not simple algebraic equations. Therefore, numerical methods for providing solutions to the equations for dZJdt, and dTJdt, must be used. It was mentioned earlier that the original ASET model incorporated a fourth-order Runge-Kutta solution to the differential equations, while ASET-B (and subsequent versions of ASET) used the improved Euler method. The Euler method is one of the simplest stepwise methods for solving differential equations [43]. It is commonly referred to as the tangent line method. Given an equation, the slope of the tangent line at a given point can be found. With this, a tangent line can be constructed and used to estimate the solution to the equation at the next point. The improved Euler method, as the name implies, is a modified version of the standard Euler method. The modification, and added accuracy, lies in the method's use of an averaging scheme between the points of interest. This approach was used in the ASET-B programs to solve the differential equations at each time step. The Runge-Kutta method was used in the original ASET program. The fourth-order Runge-Kutta method is equivalent to a five-term Taylor formula. This method is the most complex of the three mentioned, but is also the most accurate. For a detailed discussion of the numerical solution methods mentioned, the reader is directed towards Section B.5.2, or any text on the subject (e.g., [43]). With regard to the ASET-B model, the program was written to consider the solution to the differential equations reached if the difference between the predicted and corrected values for Z and T, is less than 0.001 m and 0.3 K respectively. Note that the equations considered by Walton were the non-dimensional equations derived by Cooper, and that the corresponding limit for the transformed interface height and upper layer temperature is equal to 0.001. Also, to avoid possible i n f i t e loops by the solution subroutine, the program allows 30 iterations for a solution. If a solution is not reached within the limit, a warning is printed and the program uses the last corrected value to proceed to the next time step. If this occurs, the value used is an unconverged value and likely to introduce an unknown error into the solutions. The user could change the program source code to allow for greater solution tolerance and iteration limit values.

The ASET-QB Computer Program

59

In the first edition of this book, Birk simplified the ASET-B model by using the standard Euler method to solve the ODES. The corresponding computer program, ASETB-S, gave nearly identical results for three sample cases. On this basis, Birk recommended the simplified approach and used it in F'IRM, an extended version of the ASET model that includes algorithms for calculating the flow through a wall vent. 3.4 THE ASET-QB COMPUTER PROGRAM

A new version of the ASET computer program was written in QBasic to solve the equations that were derived in Section 3.2. In spite of Birk's findings and the fact that it is very easy to understand how the standard Euler method works, a different technique is used to obtain a numerical solution. The main reason is that textbooks on numerical methods generally recommend against using the standard Euler method for practical computing, because it has limited accuracy and is not very stable (e.g., see Reference [44], page 704). A fourth-order Runge-Kutta method with adaptive stepsize control was chosen. This method and the QBasic code that was developed to perform the calculations are described in Appendix B and D respectively. The new model program is referred to as ASET-QB. The program guides the user through a series of questions to obtain the necessary input data. The results of the calculations are displayed on the screen in tabular form, and are saved in a disk file. A hardcopy can be obtained if a printer is attached. The QBasic source code of ASET-QB is provided on the accompanying CD-ROM. Installation instruction can be found h Appendix C. The program should run without problems in the QBasic environment on any IBM compatible PC with 640 K of conventional memory. A faster executable version of the program is provided for users who do not need to modifjr the source code. It may prove beneficial to the reader to review the ASET-QB source code before proceeding. A printout of the source code can be obtained directly from the QBasic environment, or by importing the code as an ASCII (DOS) text file into any word processing sohare. Comments on the ASET-QB source code are provided in Appendix D. The input data required by ASET-QB are discussed in some detail below.

60

ASET-QB: A SIMPLE ROOM FIRE MODEL

3.4.1 Heat Release Rate ASET models, including ASET-QB, require that the heat release rate history of the fire be provided as input. The data is entered in two parts: the heat release rate and the time at which it occurs. ASET-QB, like the other ASET models, uses a linear interpolation routine to provide heat release data at times other than those given as input. Since the routine is based on the equation of a straight line, it is important for the user to provide enough data sets to adequately describe the heat release history of the fire. An example of this procedure can be found in Section 3.S.

3.4.2 Geometry of the Fire Compartment

In addition to the heat release rate history of the fire, ASET-QB requires input describing the geometry of the f ~ compartment, e in particular the room floor (or ceiling) area A, the height of the compartment H, and the height of the fire above the floor 2, 3.4.3 Radiative and Total Heat Loss Fractions

The values that are perhaps the most difficult to determine are those of the radiative and total heat loss fractions, i.e., L, and L, respectively. The values for L, and L, vary throughout the course of a fire as the characteristics of the radiating source (flame) change and the bounding surfaces of the compartment are heated. However, in the development of the ASET models, the simplifying assumption was made that L, and L, remain constant. Values for L, which generally fall between 0.15 and 0.40, are available in the literature (e.g., see Reference [lS], pages 3-78 to 3-8 1). A generally accepted average value was proposed by Cooper [6] such that

Other values can be found in Table 4-3. Based on Equation (3.1 l), approximately 35 percent of the heat released by a fire is radiated away fiom the combustion region. Unless the user changes the source code, the

Comparison between ASET-QB and ASET-B

61

radiative loss fiaction is preset in ASET-QB (as in other versions of ASET) to this value. The ASET model predictions are more sensitive to the amount of energy released by the f ~ that e remains within the compartment, and more specifically, within the hot layer. Obviously, this is simply the total heat release rate minus the rate of losses fiom the compartment. Without any venting, energy can leave the compartment only via conduction through the bounding walls. Heat (energy) is imparted to the bounding walls via radiation and convection from the fire and hot layer. In Appendix A of the original ASET report, Cooper estimated that values for the fiaction of energy lost through the walls, L, fall within the following range 161:

The derivation of these values will not be repeated here. There are currently no simple accurate means for estimating the value of Lc, beyond the simple rules offered by Cooper. A method to estimate L, will be developed in Section 4.3. 3.5 COMPARISON BETWEEN ASET-QB AND ASET-B

ASET-QB solves the same equations as ASET-B, albeit in a different form (dimensional vs. non-dimensional) and using a different numerical technique. In this section, a comparison is presented between the two model programs for the example provided by Walton in the ASET-B documentation [3]. The ASET-QB input data for Walton's example are given in Figure 3-2. The reader can substitute his or her own data path andor file names. If the output data file name exists, the user will be asked to c o d m that the fde may be overwritten. If the heat release rate data file name exists, the user will be asked whether he or she wants to use the data from that file. If not, the heat release rate data in the file will be replaced by new data that are entered by the user for this m. According to Walton, the example exercises most of the computer program, and should provide an indication of the accuracy of the new model.

PATH FOR OUTPUT FILE? c:\FIRM\DATA\ OUTPUT FILE NAME (WITHOUT PATH AND EXTENSION)? CH3-A01 DO YOU WANT TO PRINT THE RESULTS (Y/N)? Y S.1. ENGINEERING, OR MIXED UNITS (S, E, M) ? M RUN TITLE? ASET-QB SAMPLE RUN OF WALTON'S ASET-B EXAMPLE ROOM FLOOR AREA (ftA2)?225 ROOM CEILING HEIGHT (ft)? 9 FIRE BASE HEIGHT (ft)? 1 MAXIMUM TIME (sec)? 180 TOTAL HEAT LOSS FRACTION (DEFAULT=O.SOO)? 0.8 HEAT RELEASE FILE NAME (NO PATH OR EXTENSION)? CH3-A01 DESCRIPTION? -TON'S ASET-B EXAMPLE CASE FIRE HEAT OF COMBUSTION OF THE FUEL (DEFAULT IS 5159 Btu/lb)? ENTER HEAT RELEASE RATE (kW) AT TIME O? 0.1 INPUT TIMES AND HEAT RELEASE RATES (-9,-9 to end) TIME (sec), HEAT RELEASE RATE (kW)? 20'40 TIME (sec), HEAT RELEASE RATE (kW)? 100,200 TIME (sec), HEAT RELEASE RATE (kW)? 180,500 TIME (sec), HEAT RELEASE RATE (kW)? -9,-9

FIGURE 3-2. ASET-QB input data for Walton's sample run of ASET-B [3]

The results of the comparison runs are provided in Table 3-1. The ASET-QB results were obtained using mixed units for the input data, i.e., U.S. engineering units for all input data except heat release rate. The latter is specified in kW instead of Btds. The small differences between the upper layer temperature predictions from ASET-QB and ASET-B are primarily due to the fact that

1 ASET-B uses a different approach to resolve the singularity in (the equivalent of) Equation (3.7) at t = 0. 2 ASET-QB uses a slightly more accurate numerical technique to solve the system of ODES. In addition, due to the stepsize control algorithm in the ODE solver, the time step for this case in ASET-QB is 0.5 seconds (as opposed to 1 second in ASET-B). Note that the ASET-QB run terminates at 151 seconds, when the layer interface drops below the fuel surface.

Limitations of ASET-QB

63

Table 3-1. Comparison between ASET-B and ASET-QB HRR Time ASET-B ASET-QB ASET-B ASET-QB (S) T" (W T" (OC) 4(m) 4(m) (kW) 10

25

25

2.5

2.5

20.0

3.6 LIMITATIONS OF ASET-QB This section addresses the limitations of the ASET-QB model. All models have limitations. However, if the limitations are known and understood by those using the model, then a simple model can be a very powerful and helpful tool. Recommendations for users in establishing the limitations of a fire model for a specific application can be found in Reference [45]. The limitations of ASET-QB are identical to those of other versions of ASET, since they are all based on the same general approach. Many of the limitations regarding other versions of ASET have been reported in the literature [3,6,35 -391. Limitations in the scope and utility of ASET-QB, and limitations due to approximations and assumptions in the underlying theory of ASET-QB are discussed below.

3.6.1 The Plume Model The plume model was presented in Section 2.6.2.1. The plume model assumes a point source of heat release from the fuel surface. The model does not account for virtual origin corrections or varying fuel surface areas. A possible explanation for the lack of virtual source corrections in ASET is that virtual source correctionswere just beginning to be studied when the model was developed. Many of the plume experiments conducted were of areas and heat release rates that correspond to small virtual origin corrections, thus the corrections went unnoticed. When ASET-B was released, it was based on the physics present in the original ASET model, thus no virtual origin correction was included, although they were by then available in the literature. According to Heskestad [46], the application of the virtual origin correction to real fuels, such as upholstered fbmiture, is untested, because the derivation of the expressions are based on pool-type fires. Although the ASET models fail to account for virtual origin corrections, they have been shown to agree with actual fire data in many situations [37]. However, a virtual source correction may be important when modeling some fire scenarios, and this is a limitation that should be considered when applying and validating the models. Equation (3.4) predicts the mass flow in the plume only, i.e., above the flaming region. Several models that can be used to predict mass flow rates in the flaming and intermittent regions are available in the literature [19]. An implicit assumption when using only the plume equation, is that the model provides acceptable mass flow predictions in the flaming, intermittent, and plume regions, not just hthe plume region alone. Relying on a single plume equation, as in the ASET models, will ultimately introduce some error into the model predictions. Another assumption implicit in the derivation of the ASET models is that stratification of the plume gases does not occur; that is, all plume gases enter the hot layer that forms just below the ceiling. Stratification, which in the present sense is defined as the layering of fue gases at some distance below the ceiling due to aidgas density differences, occurs when the buoyancy of the plume at the layer interface is too weak to penetrate into the hot layer. Except for very low heat release rates in tall enclosures, stratification should not be a concern in most compartment fire-modeling problems. The convective heat release rate that results in stratification at a height AZ, above the fuel surface, based on an ambient temperature rise of AT,, over that height is given by (see Reference [l 51, page 4-255):

Limitations of ASET-QB

QC = 0.001 ~ ~ A z , Z . ~ A T ~ . ~

65

(3.13)

where

Q AZ, AT,

= = =

convective heat release rate (kW) height above he1 surface where stratification occurs (m) ambient temperature rise at height AZ, (K)

This equation can be used to determine if stratification is a concern. The entrainment of air into the plume goes from a maximum just below the interface to zero at the interface. As such, the model cannot provide estimates of entrainment within the hot layer. Finally, it should be pointed out that the mass flow predicted by Equation (3.4) does not account for any mass contribution from the fuel source, i.e., the fuel volatiles. However, this limitation does not introduce observable errors based on Zukoski's experimental verification of the mass flow model [2 l]. Other data also suggest that the mass contributed by the burning fuel can be considered negligible for many practical situations. For a series of upholstered furniture items, Babrauskas reported vent mass flow rates no less than 12 times greater than the mass contribution rate of the fire [48]. Similar results can also be found in other test data [49,50,5 l]. Beyler [l91 reported that "The entrainment of air into the flame up to the flame tip is 10-20 times that required for complete combustion." With the knowledge that the air-to-he1 mass ratio for fuels is generally much greater than 1, this M e r suggests that the fuel mass can be neglected in many cases without suffering unacceptable error.

3.6.2 Hot-Layer Venting The lack of hot-layer venting capabilities is a utility limitation of the model; it simply was not developed to handle hot-layer venting. ASET was designed to provide conservative estimates of the Available Safe Egress Time (ASET) from an enclosure. Venting from the hot layer would extend the time allowed for egress. Thus, hot-layer venting was not considered in the development of ASET. This factor is a major element to be incorporated into the desired model. The addition of hot-layer venting capabilities will be provided in Section 4.1.

66

ASET-QB: A SIMPLE ROOM FIRE MODEL

3.6.3 Hot-Layer Species Concentrations ASET-B was a simplification of the original ASET model that was capable of calculating hot-layer species concentrations. ASET-B and the models presented here are not capable of performing these calculations. The needed equations could be added with moderate difficulty, as discussed in Section 2.6.2.4. 3.6.4 Burning in the Hot Layer The ability to calculate combustion within the hot layer is a deficiency of most models, and this fact was mentioned earlier. Regardless, the ASET models, except for Cooper's initial version, cannot even calculate fuel gas concentrations within the hot layer. So, attempting to model burning of these vapors in the hot layer would be impossible. 3.6.5 Oxygen Starvation One of the most limiting features of the ASET model is their inability to account for oxygen starvation. The models assume there is enough oxygen present within the lower layer to allow fiee-burn conditions at all times. This is obviously a gross oversimplification. The models use the heat release given as input and do not consider if the heat release is even physically possible. The he1 surface can be submerged in the descending hot layer, but the model will continue to release fiee-bum heat into the enclosure. This limitation can result in temperature predictions that are physically impossible. None of the ASET model programs, including ASET-QB, warn the user when conditions occur that could result in predictions that are physically impossible. However, ASET-QB terminates automatically when the layer interface drops below the fuel surface, because the model equations are defmitely invalid at that point.

Limitations of ASET-QB

67

3.6.6 Heat Loss Fraction The limitations introduced by using a simple heat loss fiaction approach have been previously discussed. The main limitations lie in the inability to predict values for L, and L, beyond the basic recommendations provided by Cooper et al. [6,35] and Walton [3]. These values must be provided by the user, who may not have a sufficient understanding to select accurate values. The configuration of the enclosure can also affect the accuracy of the results. This is due to the complexity of the heat loss fraction in irregularly shaped enclosures. It has been reported that enclosures with length-to-width ratios greater than 10:l or ratios of height-to-minimum horizontal dimensions greater than 1 may not result in accurate calculations. Further discussion is provided in Section 4.3.

3.6.7 Burning Rates The burning rate, and, more accurately, the heat release rate history of a fire must be provided as input. The model cannot perform heat release rate predictions. According to Cooper and Stroup [35], the model is not considered accurate once the hot-layer temperature reaches approximately 350-440°C. This limit is due to the radiation augmentation of the hot layer on the fbel-burning behavior. At these temperatures, the radiation emitted by the hot, smoky layer that is incident on a burning fbel may substantially alter the fi-ee-burn rates provided as input by the user. The concern of compartment effects on burning rates will be discussed in greater detail in Section 4.5.

CHAPTER 4

Modifications to ASET-QB

Five significant and usell modifications to ASET-QB will be discussed in this chapter. The enhanced model that results fkorn implementation of these modifications will be referred to as FIRM-QB. FIRM is an acronym for Fire Investigation and Reconstruction Model. FIRM-QB is a revised QBasic version of the original FIRM model that was developed by David Bkk, and that was discussed in the fmt edition of this book. Further details pertaining to the use, limitations, and predictive capability of FIRM-QB will be presented in subsequent chapters.

4.1 VENTING OF THE HOT LAYER

4.1.1 Introduction Through the use of Zukoski's example of pressure rises resulting fkom hostile fires in enclosures presented in Section 2.6.1, it was shown that there must be a vent present in all enclosure fues or damaging pressures would result. It was also shown that the ASET models include a vent that is simply a crack-like leak at floor level. The mass flow leaving the enclosure at any given time was determined by using the mass balance of the lower layer, Equation (2.251, such that

The ASET models assume that the only vent in the compartment is a crack-like opening at floor level. Hot-layer venting does not occur in ASET-QB, because the program terminates when the layer interface drops below the fuel surface, i.e., before the interface descends to the floor. An important modification of the ASET-QB model will be the inclusion of the ability to model buoyant hot-layer venting. This modification will be based on the equations that were developed in Section 2.6.2.2, because simple vent flow equations developed by other investigators are not suitable. For example, the so-called slide-rule estimates for hot-layer venting reported by Lawson and Quintiere [S21 and the model presented by Nelson in the "FIREFORM" [53]are inappropriate for many situations, especially when modeling time-varying compartment conditions. The equation suggested by Lawson and Quintiere can be modified to present more accurate results for time-varying conditions. The equation used by Nelson in "FIREFORM" has severe limitations, and can be written as

where A, = area of the vent (m2) It can be noted from inspection of Equation (4.1) that the flow will approach zero when the layer approaches the midpoint of the vent. Quite obviously, an expression such as this cannot be used in time-varying enclosure f r e models.

4.1.2 Basic Theory of Vent Flow Modeling A gas within an enclosure will move only if forced to. Overall, smoke will move within buildings due to several forces, such as stack effect, buoyancy, expansion, wind, and HVAC systems. These are covered in detail by Klote and Fothergill [16]. Although stack effect is due to buoyancy, the two are frequently considered separate forces in the

Venting of the Hot Layer

71

literature regarding smoke movement within buildings. Smoke that has cooled loses its buoyancy but can stiIl move in buildings if caused to by the stack effect. Buoyancy typically refers to the movement of smoke due to the decreased density associated with its elevated temperature, thus the smoke moves by itself. With regard to enclosure fires, there are but two forces that account for non-forced vent flows. These are pressure (due to expansion) and gravity (buoyancy). Gravity acts only in the vertical direction but can cause horizontal vent flows due to pressure differences. Mathematical vent flow algorithms in zone fire models are based on hydraulic theory [54]. The equations developed via hydraulic methods are based on the assumption that the vent can be treated as an orifice. To simplifl the derivation of the vent flow equations, such effects as fluid viscosity, non-uniform velocities across the vent, and turbulence are not explicitly considered. The derivation of vent flow equations was discussed in detail in Section 2.6.2.2.

4.1.3 Vent Flow Regimes in Compartment Fires In the development of the Harvard Fire Code, Mitler identified the following vent flow regimes [55]:

1 Cold outjlow only. This occurs early on, when the expansion of the gases collecting below the ceiling acts like a piston pushing down and expelling cool air. 2 Both hot and coldflow out. In this regime, the piston effect is still present, but hot gases are also vented due to the hot layer dropping below the vent soffit. 3 Hot gases venting out and coldjlow in. 4 ChokedJlow. This regime is typically associated with post-flashover compartment fires that are oxygen-starved. The most important regime, according to Mitler is No. 3 above, that of hot flow out and cold (ambient) flow in. The f ~ s regime t always occurs, provided the soffit of the vent is located at some distance below the ceiling. The duration of the first regime is a firnction of this distance. The second regime usually passes quickly. The inflow during the fourth regime is proportional to the ventilation factor, A$H, [24]. The four regimes are accounted for in FIRM-QB. The flow equations for the first three regimes

72

MODIFICATIONSTO ASET-QB

were developed in Section 2.6.2.2.Implementation of these equations to enhance ASET-QB will be described in detail in this section. The vent inflow limit in the fourth regime, and its potential effect on the heat release rate fiom the f ~ eform , the subject of Section 4.2.1. 4.1.4 The Neutral Plane and Layer Interface The neutrl plane is a simple but important variable in the vent flow modeling process. Basically, the neutral plane height, by definition is the vertical location within a vent at which the pressure difference across the vent is zero. Thus, there is no flow at the neutral plane. Above the neutral plane, hot gases flow out of the compartment, and below, ambient air flows into the compartment. The hot-layer interface plane and neutral plane are not the same, although they may be numerically close. The layer interface height, Zi, is the vertical elevation within the compartment, away fiom any vents, at which the discontinuity between the hot and cold layer is located. The neutral plane height, 2, is the vertical location within the vent at which the pressure difference across the vent is zero. 4.1.5 The Vent Flow Equations

To simplify the notation in this section, four auxiliary parameters are defined as follows

Venting of the Hot Layer

73

4.1.5.1 Flow Regime l (Zi r Z&

This flow regime is modeled in ASET-QB. Typical pressure profiles inside and outside the room during this regime are shown in Figure 4-1(a). The inflow of ambient air, mayand the outflow of hot upper layer gases, h,, me equal to zero. The outflow of lower layer gases, m , can be calculated fiom Equation (3.10). 4.1.5.2 Flow Regime 2 (2,< Zi < Z, and 2, ZJ

Typical pressure profiles inside and outside the room during this regime are shown in Figure 4-l(b). The inflow of ambient air, ki,is still zero in this case. Equation (2.16a) indicates that the pressure difference across the vent is constant at and below the layer interface, and, for example, equal to the pressure difference at the interface height, AP(4). Substitution of this constant into Equation (2.19a), and using the auxiliary parameter defined by Equation (4.2), leads to the following expression for the lower layer vent flow:

A suitable value for the orifice coefficient, C, is 0.68 [8].

74

MODIFICATIONS TO ASET-QB

(a) Flow regime 1

(b) Flow regime 2

FIGURE 4-1. Pressure profiles for different vent flow regimes

An expression for the upper layer vent flow, m, is obtained by integrating Equation (2.19b), using the relationship between pressure difference and height in Equation (2.18). Using the auxiliary parameters defied by Equations (4.4) and (4.9, Equation (2. Hb), after substitution of Equation (2.181, can be written as

Integration of Equation (4.7) leads to the following expression for the upper layer vent flow:

4.1.5.3 Transition between Flow Regimes 2 and 3 (Zi < 2,and Z,, = Zi)

Typical pressure profdes inside and outside the room during this regime are shown in Figure 4-l(c). In this case, air inflow and lower gas layer outflow are both equal to zero. An expression for the upper layer

Venting of the Hot Layer

75

outflow can be obtained fiom that derived in the previous section, but with X, = 0:

4.1.5.4 Flow Regime 3 (2; 2,and 2,> Zi)

Typical pressure profdes inside and outside the room during this regime are shown in Figure 4-l(d). The integral in Equation (2.22a) has to be split into two parts, because the expressions for the pressure difference below and above the interface are different. Equation (2.22a), after substitution of Equations (2.21a) and (2.21b), and using the auxiliary parameters defined in Equations (4.2) and (4.3), can be written as

After integration, the following expression is obtained for the lower layer vent flow:

(c) Transition between regimes 2 and 3

(d) Flow regime 3

FIGURE 4-1 (continued). Pressure profiles for different vent flow regimes

76

MODIFICATIONS TO ASET-QB

The upper layer vent flow follows fiom Equation (2.22b). Using Equation (2.21a) for the pressure difference, and the auxiliary parameter X,defined by Equation (4.5), this can be written as

Integration of Equation (4.12) leads to the following expression for the upper layer vent flow:

4.1.6 Computer Solution of the Vent Flow Equations

The expression for the lower layer vent flow in regime 1 is identical to that in ASET-QB, i.e., Equation (3.10). This expression is valid as long as Z,2 G. Both rig and rid are equal to zero. Therefore, as far as the computer solution is concerned, regime 1 does not present a problem because there is a simple criterion for this regime (Zi 2 23, and it is clear which equations must be used to determine the vent flows. If the layer interface is located below the soffit, the situation is much more complex There are three possibilities, corresponding to flow regime 2, the transition between regimes 2 and 3, and flow regime 3. The first task of the vent flow routines is to determine which of the three cases is in effect. A procedure to accomplish this task is developed below. Equation (2.29), which is obtained by combining Equations (2.25) and (2.28) to eliminate dZi/dt, can be written as

Venting of the Hot Layer

77

It is useful to defie the following auxiliary variable:

In flow regime 2, m, is equal to zero and h, is greater than zero. Hence, it follows fiom Equations (4.14) and (4.15) that 4 is greater than iz,,in this regime. In flow regime 3, m, is greater than zero and m,is equal to zero, and, therefore, 4 is smaller than m,. In the transition between flow regimes 2 and 3, both m, and m,are equal to zero, and m: is (by defmition) equal to iz,. Another useful auxiliary variable is defined by

is smaller than m, in It follows fiom Equations (4.8) and (4.16) that flow regime 2. In flow regime 3, Z, is greater than Zi. Therefore, a comparison of Equations (4.13) and (4.16) shows that m : exceeds fiU. In the transition between flow regimes 2 and 3,Zn is equal to Zi, and m : is (again by definition) equal to mu. Based on the previous two paragraphs, it is easy to develop a method to determine which flow regime is in effect. The fust step consists of calculating and according to Equations (4.15) and (4.16) respectively. Then, if is larger than rhy ,flow regime 2 is in effect. If is smaller than %*, flow regime 3 is in effect. Finally, if 4 is equal to the transition between flow regimes 2 and 3 is in effect. After it has been determined which flow regime is in effect, the second task of the vent flow routines is to calculate the flows. In regime 2, rir, is equal to zero, and both rir, and riz, are hctions of IAP(ZJ [see Equations (4.6) and (4.8)]. Consequently, for given values of Z and T,, Equation (4.14) is a non-linear algebraic equation in (AP(Z>1that, with the aid of Equation (4.15), can be written as follows:

6

c,

78

MODIFICATIONS TO ASET-QB

The bisection method is a simple technique to solve this type of equation. The method is explained in detail in Section B.5.2. To start the iterative solution procedure, the bisection method requires that an interval be specified which brackets the root of the equation. The root is found by repeatedly halving the interval until the function value at the midpoint is equal to zero, within a specified tolerance. In the case of Equation (4. V), it is easy to find a lower limit of the interval because IAP(ZJ must be greater than zero. An upper limit for the interval is not as easy to find, but can be determined as described below. Equation (4.17) can be rearranged as follows

Replacing the lower layer vent flow on the left hand side of Equation (4.19) with the expression on the right hand side of Equation (4.6), and using the d e f ~ t i o nof X, fiom Equation (4.2), after rearranging, leads to

Finally, it is also important for the bisection method to know whether the slope of the fimction is positive or negative. At the lower limit, IAP(ZJ= 0, m, is equal to zero. Therefore,f,(O) = TU(~, - m3 is negative, and the slope of the function must be positive. In regime 3, rizl is equal to zero, and both maand m, are functions of AP(Z9 and Z, [see Equations (4.11) and (4.1311. In addition, according to Equation (2.2 la), 2,can also be written as a function of AP(ZJ:

Venting of the Hot Layer

79

Therefore, for given values of Zi and T,, Equation (4.14) is again a nonlinear algebraic equation in @(&) that, with the aid of Equation (4.15), can be written as follows:

This equation can also be solved with the bisection technique. In this case it is much easier to fmd the limits of an interval that brackets the root. dP(Z,) = 0 is again a suitable lower limit. An upper limit for the interval follows fkom Equation (4.21), and the fact that Z, cannot exceed 2,:

The reader can easily verify that the slope of the h c t i o n in this case is negative, becauseL(0) is positive. Finally, in the transition between flow regimes 2 and 3, completing the second task is straightforward because m, = = m:, and both m, and m, are equal to zero. A review of the vent flow routine will provide the reader with additional understanding of the vent flow equations and their solution. This can be found in the subroutine VentFlows of the QBasic source code of FIRM-QB on the accompanying CD-ROM. 4.1.7 Limitations of the Vent Flow Subroutine

The vent flow model assumes that the lower layer remains at ambient temperature, which affects the accuracy of the vent flow modeling technique. This simplification has been discussed by Steckler et al. [49]. In some cases, the lower layer can reach significant temperatures. However, the assumption of a f i e d lower layer temperature is acceptable to predict the growing stage of most fues with reasonable accuracy.

4.2 OXYGEN-LIMITED BURNING

A limitation of ASET-QB is that the model is unable to consider oxygen-limited burning. The inability of the model to consider the effects of oxygen starvation can result in the prediction of physically impossible burning rates and hot-layer temperatures. A simplified approach to predicting and compensating for oxygen starvation within enclosures will now be presented. Two conditions that lead to limited supply of air (and oxygen) must be considered. 4.2.1 Vent-Controlled Burning

The vent flow equations for regime 3 developed in Section 4.1 allow the interface height to descend to the bottom of the vent. In reality, when the layer interface drops to a certain height, typically between one half and one third of the vent height, the inflow of ambient air reaches a maximum that corresponds to ventilation-controlled burning conditions. Based on work by Kawagoe [24], Drysdale derived the following expression for the maximum flow 1571:

where

(mh-

=

maximum inflow of ambient air (kg/s)

A check is included in subroutine VentFlows of FIRMIQB, so that the inflow of air in flow regime 3 is not allowed to exceed the maximum value given by Equation (4.24). If the inflow is equal to the maximum,ventcontrolledburning conditions prevail. The interface height quickly adjusts until the flow of lower layer gases entrained into the flame and plume is equal to the same limiting value.

Oxygen-Limited Burning

81

4.2.2 Entrainment-Controlled Burning It was noted in Section 2.6.2.4 that a nearly constant amount of heat is released by complete combustion per mass unit of oxygen consumed, regardless of the type fbel burnt. The constant is equal to the ratio of the net heat of combustion of the fuel and the stoichiometric oxygen to fuel ratio, Ahc,dr&.$ch.Based on this observation, the maximum mount of heat that can be released in a flame that entrains a mass flow of (dry) air equal to m,, is given by:

Drysdale provided a listing of MC,&, and Ahc,JsStoiCh for various fuels, which is reproduced in Table 4-1. If the reactive fuels and carbon monoxide are removed f?om the table, an average of 3,030 (*2%) kJkg is found for Ahc,le&sa~ch. Thus Equation (4.25) can be written in a general form (if the specific value of A h C , A i c for h a fbel is unknown) as

Since i z e is a function of the heat release rate [see Equation (2.12)], an expression to find the rate of entrainment that corresponds to the maximum allowable heat release rate according to Equation (4.26), is required. Recalling Zukoski's plume flow model, and substituting Equation (4.26) above, results in

Solving for rir, and renaming the variable (li2,)maximum possible entrained air flow, yields

to indicate it is the

Table 4-1, Heats of Combustionaof Selected Fuels (@2S°C) &,M

kJ/g fuel

Carbon monoxide

CO

Methane

CH4

Ethane

c,&

&,ueJssbich

kJ/g air

&,neJrstoich

kW! 0

2

Ethene Ethyne

c2H2

Propane n-Butane

n-C4Hl0

n-~entane

n-C5H12

n-octane

n-C8H18

c-Hexane

c-C6H,

Benzene

C,&

Methanol

CH30H

Ethanol

C,H,OH

Acetone

(CH3)2C0

D-Glucose

C6H1206

Cellulose Polyethylene Polypropylene Polystyrene Polyvinylchloride Polymethylmethacrylate Polyacrylonitrile Polyoxyrnethylene Polyethyleneterephthalate

Polycarbonate

"

Nylon 6.6 29.6 Apart from the solids glucose and the polymeric materials) the initial state of the fuel and all the products are taken to be gaseous.

Heat Loss Fraction Calculation

83

The maximum possible heat release rate can be estimated fiom Equations (4.26) and (4.28) such that

The heat release rate to be used for the governing equations is the smallest value of that specified by the user, and that calculated fiom Equation (4.29). The subprograms in FIRM-QB that calculate the right hand side of the conservation equations (Derivatives), and the plume flow (PlumeFlow) were modified to account for entrainment-controlled burning. The reader is encouraged to review the source code of these subprograms. 4.3 HEAT LOSS FRACTION CALCULATION

The governing equations in ASET-QB require that an estimate of the heat loss fraction, L,, be provided by the user as input. Cooper has shown that L, can be estimated to lie between 0.6 and 0.9, and states The lower 0.6 value would relate to high aspect ratio spaces with smooth ceilings, and fires positioned far away from walls. The intermediate values and the high 0.9 value for L, would relate to low aspect ratio spaces, fire scenarios where the fire position is within a room height or so from walls and/or to spaces with highly irregular ceiling surfaces.

The derivation of these values is presented in Appendix A of the original ASET report [6] and will not be repeated here. It is obvious that the guidelines are not quantitative and leave the user with little assistance. It would be very helpful to the novice fue modeler, if the model were to suggest a value for Lc. The total heat loss could be determined on the basis of a detailed heat transfer analysis, as described in Section 2.6.3.1. A more pragmatic approach will be used here to develop an expression to estimate L,. 4.3.1 A Procedure for Estimating L,

According to Cooper, the heat losses consist primarily of radiation, and convective losses to the ceiling. Therefore, L, can be written as

84

MODIFICATIONSTO ASET-Q9

'c

=

Lr

+

'ceiling

+

'0th

where Lceiling= fiaction of heat losses in the form of ceiling convection L = fraction of heat losses not included in L, and L ,, To allow for a more precise estimate of the radiative losses, the user of FIRM-QB will be given the option to choose a value for L, that may be different from the default value of 0.35. This option was not available in the original ASET models without changing the source code. Some values for L, are provided in Table 4-3. More data can be found in the literature (e.g., see Reference [15], pages 3-78 to 3-81, where L, = hHrad/AHCh). Cooper calculated the heat losses to the ceiling on the basis of experimental ceiling jet data, and plotted the ratio of ceiling heat losses to convective fraction of the heat release rate as a h c t i o n of the ratio of radial distance fkom the plume centerline to distance between the ceiling and the fuel surface. Cooper's data are shown in Figure 4-2 as solid circles. The following expression provides a good fit to Cooper's data:

where

R

=

radial distance fiom the plume centerline (m)

The range of Rl(H - 23 values in Cooper's plot extended fkom 0 to 2. Cooper stated that Lmfid(l - Lr) approaches an asymptotic value of 0.4 for RI(H - ZJ 2 2 [it appears fiom Equation (4.31) that the asymptotic value is 0.47 instead of 0.41. The lower limit of L, values suggested by Cooper was obtained from Equation (4.30), with L, = 0.35 and L,,, = 0.4(1 - L,). Cooper cited f i e experiments with rough ceilings where heat loss fractions were measured as high as L, = 0.89. Therefore, Cooper recommended using a value for L, between 0.6 and 0.9, corresponding to a range of L, fiom 0 (for smooth ceilings and high aspect ratio rooms) to 0.3 (for rough ceilings or low aspect ratio rooms).

Heat Loss Fraction Calculation

0.4

0.3

0.2

0.1

Cooper

[6]

0.0

FIGURE 4-2. Ceiling heat loss fraction as a function of Rl(H - ZJ

The values recommended by Cooper are valid only if the ceiling span exceeds four times the distance between the ceiling and the fuel surface. In addition, heat transfer between the ceiling jet, after it hits a vertical wall and is deflected downward, and the walls of the enclosure is not accounted for. A new procedure will now be developed to address these two problems. Shortly after ignition, andjust before the upper layer starts to develop, the ceiling jet covers the entire ceiling. R can be estimated as the radius of a circle with the same area as the ceiling. In this early stage, the temperature of the ceiling is close to the initial temperature. Cooper's calculations of were based on the assumption that the ceiling temperature is equal to ambient, and, therefore, are most accurate in this stage. As time progresses, the upper layer volume increases, possibly until

86

MODIFICATIONSTO ASET-QB

the layer interface descends to approximately one-third of the vent height above the sill, corresponding to flow regime 4. During the transition between these two extremes, the wall area in contact with the deflected ceilingjet and upper layer gases increases. However, the ceiling and wall temperatures increase also, which compensates for the effect of the growing area on the convective heat transfer. To obtain an estimate for the average convective heat transfer, it is assumed that the losses to the walls can be included by increasing R in Equation (4.31) over the value that corresponds to the area of ceiling. In other words, the walls are treated as an extension of the ceiling for the purpose of calculating convective heat transfer. Using R with no increase would probably underestimate the convective losses because the area in contact with the ceiling jet is larger than the ceiling area for almost the entire duration of the fire. FIRM-QB terminates when the layer interface descends down to the fire base height. Consequently, the maximum possible value of R is given by

One would expect that L, values calculated from Equation (4.3l), with R = R,, would be excessive. However, the resulting heat loss fractions actually would turn out to be consistently slightly smaller than the values recommended by Cooper, and those used by Birk in the first edition of this book. The lower values are probably more realistic for vented enclosure fires that last more than a few minutes. Note that L, is equal to 0.05 for rough ceilings, or 0.10 for very rough ceilings, as suggested by Birk. 4.3.2 Limitations of the Calculation of L,

It is important the reader understands that the methodology presented for calculating values for L, is only a f ~ s attempt t at quantitatively describing the fiactional heat loss to the surroundings. This approach has not been extensively tested and is based on minimal data. Several simulations have been run using the computer-predictedvalue of L, with favorable results.

Heat Release Rate Predictions

87

The method includes no correction for the heat release of the fie. Obviously, the magnitude of the ceiling jet is proportional to the heat release rate of the fire [19]. Thus, high heat release fires in small compartments are likely to suffer fiom poor estimates. The primary purpose of introducing the expression for the heat loss fiaction is to provide novice users with a first guess of what L, should be. The FIRM-QB model displays the value, and the user may select the value or enter his~herown. This should not discourage those familiar with selecting values for L, fiom choosing their own. L, will have a profound effect on the results of the simulation, and, therefore, these values must be selected with an understanding of their importance. A discussion of the effects of L, and L, on the predictions of the FIRM-QB model is presented in Chapter 7. This discussion reinforces the need for careful selection of values for the heat loss fractions. 4.4 HEAT RELEASE RATE PREDICTIONS

The use of ASET, ASET-QB and the FIRM-QB model developed in this book requires that the user provide data describing the heat release rate history of the f i e being considered. This section will describe some of the simple methods that can be used to determine heat release rates. i l l also present a calculation procedure to predict heat This section w release histories for upholstered furniture. 4.4.1 The Time-Squared Heat Release Model

Perhaps the simplest mathematical expression that can be used to predict heat release rate is the time-squared model. This can be written as

88

MODIFICATIONS TO ASET-QB

where time past flaming ignition (S) = a constant for a particular fuel or fuel package (kW/s2) Q ~ W= maximum heat release rate (kW) t,, = time to reach maximum heat release rate (S) t

=

a

This method of predicting heat release rates has been widely reported and used in the literature to determine spacings of detectors and sprinkler heads. It is referenced in some of the National Fire Protection Association (NFPA) codes and standards that deal with these issues [58,59]. However, this simple approach has significant limitations when used for f i e hazard assessment. First, it requires that the user have knowledge of the growth factor, a, which is fuel-specific, and is typically found through curve fitting of full-scale fire test data of the particular fuel. Some examples of growth factor values for upholstered fhxiture are shown in Table 4-2. The expression cannot account for decay because heat release rate increases with the square of time. Also, the heat release is based on free-burn conditions. A more detailed discussion of the limitations of using fires can be found in Appendix A of Reference [601. The data in Table 4-2 were obtained by fitting the power law in Equation (4.33) to the results of 40 furniture calorimeter tests conducted at NIST 1611. The first column in the table contains the test numbers used in the original NIST reports. The second column is a brief description of the item that was tested. In NFPA 72, fires are classified as being either slow-, medium-, or fast-developing. A slow-developing f i e has a growth factor of 0.0066 kW/s2or less. A fast-developing fire has a growth factor greater than 0.0469 kw/s2.A mediumdeveloping fire has a growth factor greater than 0.0066 kW/s2,but less than or equal to 0.0469 kw/s2. The virtual time of origin, t,,, is the time at which the f ~ f ebegan to obey the power-law f i e growth model. Prior to t,, the he1 might have smoldered, but did not burn vigorously with an open flame. The last two columns contain the time to reach and the value of the maximum heat release rate.

Table 4-2. Furniture Heat Release Data E581 Test No.

42

Item Description Metal Wardrobe (4 1.4 kg total) Chair F33, Trial Loveseat (39.2 kg) Chair F21, Initial (28.2 kg) Chair F21, Later (28.2 kg) Metal Wardrobe, Initial (40.8 kg total) Metal Wardrobe, Average (40.8 kg total) Metal Wardrobe, Later (40.8 kg total) Chair F24 (28.3 kg) Chair F23 (3 1.2 kg) Chair F22 (3l .9 kg) Chair F26 (19.2 kg) Chair F27 (29.0 kg) Chair F29 (14.0 kg) Chair F28 (29.2 kg) Chair F25, Later (27.8 kg) Chair F25, Initial (27.8 kg) Chair F30 (25.2 kg) Chair F3 1, Loveseat (39.6 kg) Chair F3 1, Loveseat (40.4 kg) Chair F32, Sofa (5 1.5 kg) W in. Plywood Wardrobe with Fabrics (68.5 kg) ?4in. Plywood Wardrobe with Fabrics (68.3 kg) '/a in. Plywood Wardrobe with Fabrics (36.0 kg) 1 h in. Plywood Wardrobe with FR Interior Finish, Initial 1' 6 in. Plywood Wardrobe with FR Interior Finish, Later

a

tv

tm,

class* f

(kW/s2)

(S)

(S)

0.4220

10

42

-**

1.1722

100

65

Q(kW)

5000

Table 4-2 (continued). Furniture Heat Release Data [SS] Test No.

a (kW/s2)

tv

tmax

Qmaa

Item Description class' (S) (S) (kW) Repeat of % in. Plywood Wardrobe (67.6 kg) in. Plywood Wardrobe with F'R Latex Paint (37.3 kg) Chair F2 1 (28.3 kg) Chair F2 1 (28.3 kg) Chair, Adj. Back Metal Frame, Foam Cushions (20.8 kg) Easy Chair C07 (1 1.5 kg) Easy Chair F34 (15.7 kg) Chair, Metal Frame, Minimum Cushion (16.5 kg) Chair, Molded Fiberglass, No Cushion (5.3 kg) Molded Plastic Patient Chair ( l l .3 kg) Chair, Metal Frame with Padded Seat and Back (15.5 kg) Loveseat Metal Frame with Foam Cushions (27.3 kg) Chair, Wood Frame and Latex Foam Cushions (1 1.2 kg) Loveseat, Wood Frame and Foam Cushions (54.6 kg) Wardrobe, % in. Particleboard (120.3 kg) Bookcase, Plywood with Aluminurn Frame (30.4 kg) Easy Chair Molded Flexible Urethane Frame (16.0 kg) Easy Chair (23.0 kg) Mattress and Boxspring, Later (62.4 kg) Mattress and Boxspring, Initial (62.4 kg) S 0.0009 90 667 400 ***s = slow, m = medium, f = fast Fire growth exceeds design data Reprinted with permission from NFPA 72-1996, National Fire Alarm Code, Copyright Q 1996, National Fire Protection Association, Quincy, MA 02269. This reprinted material is not the complete and official position of the National Fire Protection Association on the referenced subject, which is represented only by the standard in its entirety.

91

Heat Release Rate Predictions

4.4.2 The Semi-Universal Fire When Cooper [6] introduced the original ASET report in 1980, he included an expression for a semi-universal fire based on the work of Friedman. The expression provides the heat release for a f i e spreading throw an imaginary fuel package consisting of a polyurethane mattress with sheets, fuels similar to wood cribs and polyurethane on pallets, and commodities in paper cartons stacked on pallets. The expression is designed to provide a broad range of heat release rates. The heat release rates plotted against time are shown in Figure 4-3. The expressions for the heat release rates as a h c t i o n of time are as follows:

Qo=10 k W 4 IMMEDIATELY AFTER IGNITION

I I 1 I I 100 200 300 400 500 TIME FROM 110 kW1 FIRE IGNlTlON (sec1

600

FIGURE 4-3. Free-burn heat release rate of a semi-universal fire 161

l 0 exp [O.O25 t ] 400 exp [0.01 ( t - 147.6)] 300 exp [O.OO5 ( t - 349)]

0I t I 147.6 147.6S t _c 349 (4.34) 349 2 t

4.4.3 Pool Fire Predictions

Mathematical predictions of a pool f ~ heat e release rate have also been widely reported in the literature [9,15,62,63]. A common expression for mass loss rates for pool fires has been presented as

where

h'' = mass loss rate per unit area (kg/m2*s) = mass loss rate per unit area for an infmite pool (kg/m2*s) k = extinction-absorptioncoefficient of the flame (l/@ p = mean beam length correction for the flame D = pool diameter (m) Equation (4.35) is valid for pools with a diameter greater than 0.2 meters that are burning in the open. Pool fires with a diameter greater than 0.2 meters are characterized by burning that is governed by radiative heating fkom the optically thick flame. This dependence is seen in the expression by the presence of the kp parameter. Equation (4.35) provides only the mass loss rate per unit area. The heat release rate is obtained fkom:

Unless the user changes the pool diameter with respect to time (or any other variable), the equation will yield a constant heat release rate. Values to use in Equations (4.35) and (4.36) are shown in Table 4-3. The expression can be applied to melting plastics, but data for these materials are, however, quite limited at the present time.

Material Cryogenics Liquid H2 LNG (mostly CH,) LPG (mostly c3&)

Table 4-3. Data for Large Pool Burning Rate Estimates [91 Density Ahg Ahqne* tjt: kP (kg/m3) (kJ/kg) J/kg) (kgfm2*s) (m)

L,"

70 415 585

442 619 426

120.0 50.0 46.0

0.017 (fO.001) 0.078 (k0.018) 0.099 (f0.009)

6.1 (k0.4) 1.1 (h0.8) 1.4 (k0.5)

0.25 0.16-0.23 0.26

Alcohols Methanol (CH,OH) Ethanol (C2H,0H)

796 794

1195 891

20.0 26.8

0,017 (fO.001) 0.015 (kO.001)

b b

0.17-0.20 0.20

Simple Organic Fuels Butane (c4H10) Benzene (c6b) Hexane (C&H1,) Hepme (c7H16) Xylenes (C&&O) Acetone (C3&O) Dioxane (C4H802) Diethyl Ether (C,H,,O)

573 874 650 675 870 79 1 1035 714

362 484 433 448 543 668 552 382

45.7 40.1 44.7 44.6 40.8 25.8 26.2 34.2

0.078 (h0.003) 0.085 (h0.002) 0.074 (*0.005) 0.101 (f0.009) 0.090 (f0.007) 0.041 (h0.003) 0.018" 0.085 (h0.018)

2.7 (h0.4) 2.7 (k0.4) 1.9 (h0.4) 1.1 (h0.4) 1.4 (-10.4) 1.9 (h0.4) 5.4" 0.7 (k0.3)

0.27-0.30 0.14-0.38 0.20-0.40

Table 4-3 (continued). Data for Large Pool Burning Rate Estimates [g] Density Ah, Mcget rit," kP Material (m) (km3) WJM) (kg/m2*s) Petroleum Products 740 44.7 0.048 (h0.002) 3.6 (h0.4) Benzene 740 330 43.7 0.055 (h0.002) 2.1 (k0.3) Gasoline 820 670 43.2 0.039 (h0.003) 3.5 (M.8) Kerosene 760 43.5 0.051 (kO.002) 3.6 (kO.1) JP-4 810 700 43.0 0.054 (hO.002) 1.6 (h0.3) JP-5 Transformer oil 760 46.4 0,039" 0.7" Heavy fuel oil 940- 1000 39.7 0.035 (hO.001) 1.7 (h0.6) 830-880 42.6 0.022-0.045 2.8 (h0.4) Crude oil Solids Polymethylmethacrylate (c5%02) Polyoxymethylene (CH20)n Polypropylene (C,&), Polystyrene (C8H8),

0.020 (h0.002)

3.3 (k0.8)

L," 0.18 0.35

0.18

1184

1611

24.9

0.40

1425

2430

15.7

0.15

905 1050

2030 1720

43.2 39.7

0.40 0.44

For diameters ca. 1 m. Decreases for small and for very large diameters Value independent of diameter in turbulent regime c Only two data points available Reprinted with permission from Fire Protection Handbook, 16th Edition, Copyright O 1986. National Fire Protection Association, Quincy. MA 02269

a

Heat Release Rate Predictions

95

4.4.4 The Furniture Calorimeter

In 1982, Babrauskas et al. released a report documenting the buming rates of upholstered fiuniture measured within a furniture calorimeter [64]. The fixnitwe calorimeter opened a new door for the fire test community. It allowed researchers to measure the buming and heat release rates of complex fuel packages such as upholstered furniture. A schematic diagram of the furniture calorimeter is shown in Figure 4-4. The specimen is located on a platform that rests on a load cell, to measure mass loss during the test. The products of combustion are collected in a hood, and extracted through an exhaust duct. Probes are located in the exhaust duct for measuring flow and gas composition. Heat release rate is determined fiom these measurements on the basis of the oxygen consumption technique (see Sections 2.6.Z.4 and 4.2.21, using equations developed by Parker [65] and Janssens [66]. These equations are rather complex, and will not be discussed here. Furnitwe calorimeter test standards have been developed in North America 1671, and in other countries [68]. Most f i e research and testing laboratories concerned with fimitwe flammability now have a furniture calorimeter. Since the initial studies by Babrauskas at MST, a tremendous amount of research has been done in this area. An extensive review is provided in Reference [69]. For the purpose of this book, two important results evolved fiom the fhniture calorimeter research. First, the test results provide a direct source of heat release data for f r e models, such as ASET-QB and FIRM-QB. To use these data for model input, the user simply selects an acceptable data set that describes the heat release curve of the fuel desired. The user then chooses enough data points (heat release rate vs. time) to adequately describe the heat release curve. Both ASET-QB and FIRM-QB allow the user to enter these data. HRR-QB is a separate QBasic program to create heat release rate data fdes, which are compatible with the MAKEFIRE fde format of FPETool[41], and can be read by ASET-QB and FIRM-QB. Second, the research has resulted in a number of calculation methods to predict the heat release rate of f'umiture items. The most accurate of these methods are based on correlations between fbmiture calorimeter data and small-scale heat release rate data of furniture composites measured in the Cone calorimeter 1701. These correlations are described in detal in Reference [69]. In the next section, a less accurate, but more generic calculation

method will be described. This method was developed by Babrauskas on the basis of test data for residential furniture [71,721. 4.4.4.1 Babrauskas ' Generic Heat Release Rate Model

Babrauskas observed that many upholstered fiuniture items have heat release rate vs. time graphs that are triangular in shape (see Figures 4-5, 4-6,4-9, and 4-10). He found that the area of the triangular part of the curve on average accounts for 63% of the total heat released by furniture items with a combustible fi-ame. This is because the triangular part of the

c THERMOCOUPLE

THERMCA^' '-'

'1 1 r mCi 1 1

'

PRESSURE PROBE U

PRESSURE

f

TRANSDUCER

EXHAUST BLOWER

GAS SAMPLE

SMOKE - .- .- - - METER -

PARTICULATE FILTER & COLD TRAP

CHEMICAL H20 TRAP

U

Ot ANALYZER

U U

CO, ANALYZER

CO ANALYZER

PRESSURE REGULATOR

fDuMp

LOAD PLATFORM

U DATA LOGGER

FIGURE 4-4. Furniture calorimeter schematic

97

Heat Release Rate Predictions

2000

-

1800

-

I

1

I

I

I

1

I

SPECIMEN F2 1

-

-

FIGURE 4-5. Example of triangular heat release approximation

curve does not include the "tail,"which is primarily the heat release rate of the frame. Indeed, Babrauskas also found that the triangular part accounted on average for 91%of the total heat released by furniture items with a non-combustible fiame. Babrauskas developed a simple model to predict peak heat release rate (top of the triangle) and burning time (triangle base width) on the basis of generic characteristics of the furniture item.

TIME IsL

FIGURE 4-6. Examples of fuels with triangular-shaped heat release curves

According to the model, peak heat release rate can be estimated fiom Qm=

210 [ F F ][ P F ][CM] [ S F ][ F C ]

(4.37)

where

FF

=

PF

=

CM SF

= =

fabric factor 1.O for thermoplastic fabrics (e.g., polyolefm) 0.4 for cellulosic fabrics (e.g., cotton) 0.25 for PVC or polyurethane film-type coverings padding factor 1.0 for polyurethane foam, latex foam, or mixed materials 0.4 for cotton batting or neoprene foam combustible mass (kg) style factor 1.5 for ornate convoluted shapes 1.2- 1.3 for intermediate shapes 1.0 for plain, primarily rectilinear construction

Heat Release Rate Predictions

99

FC = frame combustibility factor 1.66 for non-combustible frames 0.58 for melting plastic 0.30 for wood 0.18 for charring plastic The triangle base width (burn time) is estimated by

where burn time (S) FM fkame material factor 1.8 for metal or plastic frames 1.3 for wood fimes Ah,, = effective heat of combustion for the fuel item (kJ/kg) t,

= =

The values for the different factors required in the equations presented above were derived in Reference [71]. Babrauskas reported that this method should not be used when the product of the fabric factor FF and the padding factor PF is less than 0.225, because values this low are indicative of extensively low burning rates that will not yield the triangular-shaped heat release curve. Table 4-4 provides some descriptive information and data regarding 13 items of fbmiture that have been tested in the furniture calorimeter at NBS. Predicted [according to Equation (4.3 711 and measured peak heat release rates for the 13 specimens are given in Table 4-5. The predictions are within &15%of the measured values, except in two cases (F26 and F28). However, the predictions in those two cases greatly exceed the measured peak heat release rates, i.e., the error is on the conservative side. Table 4-6 provides a comparison between burning times calculated according to Equation (4.38), and the base width of triangles that were fit to the heat release rate curves. The Ah,, values are those recommended by Babrauskas et al. [64]. The calculated times are larger in most cases, which again indicates that the model is generally consetvative.

100

MODIFICATIONS TO ASET-QB

The selection of Babrauskas' calculation method for estimating heat release rate of upholstered fiuniture is based on the intended application of the FIRM-QB model. The model is intended primarily for, but is not limited to residential-type rooms. The fuels that are typically found in residential-type rooms are upholstered furniture items, such as beds, couches, chairs, etc. Thus, the Babrauskas model appeared to offer the widest utility. Again, this certainly does not preclude the use of more accurate calculation methods that predict heat release rate on the basis of bench-scale data measured in the Cone calorimeter. The Eurniture calorimeter has also been used to test non-funnitwe items such as television sets, Christmas trees, wardrobes and many other items (see Reference [15], Chapter 3-1). 4.4.5 The HRR-QB Program

A program was written in QBasic that allows users of ASET-QB and FIRM-QB to create heat release rate data files. The fie name extension (*.FIR) and file format are identical to those of the fire fies in FPETool [4 l]. Therefore, if the user already has a database of FPETool fue files, there is no need to re-enter the data to conduct simulations with ASETQB or FIRM-QB. The f i e files consist of numerical data in three parallel columns, followed by two lines of text. The fust column is the time in seconds, the second column is the heat release rate in kW at the corresponding time in the first column, and the third column is the mass loss rate in g/s. The latter is equal to the heat release rate divided by the heat of combustion, which is supplied by the user. The mass loss rate is not used by ASETQB and FIRM-QB, but it is needed for compatibility with FPETool. The values in the last row of the three columns are equal to -9, to designate the end of the numerical data. The first line of text contains the name of the file, and the date it was created. The second line is a description of the fue file entered by the user. HRR-QB allows the user to create fire files for fires as described in Section 4.4.1, a semi-universal fire as described in Section 4.4.2, pool fires as discussed in Section 4.4.3, and upholstered fiuniture fires based on Babrauskas' triangle model described in Section 4.4.4.1. The program also offers the user the option to enter a series of data points on a curve, which can also be done directly fi-om within ASET-QB and FIRM-QB.

Table 4-4. Descriptive Information and Data for 13 Furniture Calorimeter Tests [72] Mass specimen

(@)

CM (kg)

&m ,

Style traditional easy chair

Frame wood

Padding FR PU

Fabric (gls) olefin

traditional easy chair

wood

cotton

traditional easy chair

wood

traditional easy chair

wood

FR cotton FR cotton FR PU

cotton

traditional easy chair

wood

PU

olefin

thinner easy chair

wood

olefin

traditional easy chair

wood

FR PU mixed

cotton

traditional easy chair

wood

mixed

cotton

traditional easy chair

PP 1

PU

olefin

traditional easy chair

PU

PU

olefin

traditional loveseat

wood

olefin olefin cotton

traditional sofa

wood

FR PU FR PU

traditional loveseat

wood

mixed

Q(kW)

olefin

75.0

940

Table 4-5. Predictions of Peak Heat Release Rate with Triangular Model

omm

Actual Qmm (kw)

Specimen

FF

PF

CM (kg)

F2 1

1.o

1.o

28.3

1.o

0.30

1780

1970

F22

0.4

0.4

31.9

1.o

0.30

320

370

F23

1.o

0.4

31.2

1.0

0.30

790

700

F24

0.4

1.o

28.3

1.0

0.30

710

700

F25

1.o

1.o

27.8

1.o

0.30

1950

1990

F26

1.o

1.0

19.2

I .O

0.30

1210

810

F27

0.4

1.o

29.0

1.2

0.30

880

920

F28

0.4

1.o

29.2

1.2

0.30

880

730

F29

1.0

1.o

14.0

1.2

0.58

1820

1950

F30

1.o

1.o

25.2

1.2

0.18

950

1060

F3 1

1.o

1.0

40.0

1 .o

0.30

2520

2890

F32

1.o

1.o

51.1

1.o

0.30

3220

3 120

F33

0.4

1.0

39.2

1.0

0.30

990

940

SF

FC

Predicted (kw)

Table 4-6. Predictions of Burning Time with Triangular Model Ah, (kJ/kg)

Predicted Qma (kw)

Specimen

FM

CM (kg)

F2 1

1.3

28.3

18,000

1780

Predicted t,, (s) 372

Actual t,, (s)

F22

1.3

31.9

14,900

320

1931

a

F23

1.3

31.2

16,100

790

827

746

F24

1.3

28.3

14,600

710

756

490

F25

1.3

27.8

18,000

1950

334

234

F26

1.3

19.2

18,000

1210

371

388

F27

1.3

29.0

20,300

880

870

820

F28

1.3

29.2

13,900

880

600

600

F29

1.8

14.0

35,100

1820

486

381

F30

1.8

25.2

20,900

950

988

a

F31

1.3

40.0

18,000

2520

371

278

F32

1.3

51.1

18,000

3220

371

359

F33 a Poor fit

1.3

39.2

13,900

990

715

637

240

4.5 THE PREDICTION OF FLASHOVER 4.5.1 Introduction

Flashover is a term applied to the transition period in which conditions within an enclosure change fkom localized burning to full-room involvement of most of the available combustibles. Since the transition is usually quite rapid, flashover has been termed an event much like ignition, even though it is more a process than an event [57]. Figure 4-7 depicts the typical regimes associated with compartment fires that become fully developed. Obviously not all fires become fully developed nor follow the pattern suggested by the figure. The ability to predict flashover has enjoyed great attention in the fre research community. This is primarily due to the dramatic change in magnitude of the threat of a fire to life and property once flashover occurs.

0

300

600

900 Time

1200

1500

1800

(S)

FIGURE 4-7. Gas temperature vs. time for a typical compartment fire

The Prediction of Flashover

105

As flashover signifies a transition to full development of the fire, it can be considered to be the point at which those persons still trapped in the room are unlikely to survive, and at which time structural damage starts to occur. Flashover may also result in fire rapidly spreading fi-om the room of origin to other locations within the building. To predict flashover by mathematical methods requires a quantitative description of flashover. In 1982, Peacock and Breese presented a paper that explored predicting flashover using mathematical computer methods 1731. A review of the various definitions of flashover were offered in that paper. Numerous researchers do agree that good working definitions can be stated in terms of measurable physical parameters such as the following: 1 Upper Layer Gas Temperature 2 600°C. 2 Flux at Floor Level 2 20 kW/m2. The first defmition (T, 2 600°C) has been widely used as an indication of the onset of flashover, although many researchers prefer to consider a change in temperature of 600°C as an indicator of flashover. The present study will consider the onset of flashover to occur when the average upper layer gas temperature reaches 600°C. The FIRM-QB model developed here accounts for only a single fire plume. Because multiple fires mean multiple plumes, it is clear that this model is no longer valid once flashover is achieved. As such, the model has a temperature check that will flag the user if the upper layer gas temperature reaches 600°C. The user does have the option of continuing the simulation, because he may be using another definition of flashover.

4.5.2 Compartment Effects on Burning Rates and Flashover Babrauskas and Walton [71] wrote: The first and most important application of the heat release data is to predict room flashover. To make this determination, only the peak value of the heat release is needed, supplemented by physical data characterizing the fire room.

Thus, the burning rate has a direct influence on the prediction of flashover.

A valid and pertinent question is, "Does the enclosure affect the burning rate of the fuel to a point that ffee-burn data are no longer valid?" In other words, "Can fkee-burn data be used to predict flashover in compartments?" First consider a simple expression for the mass loss of a fuel that is burned in the open, i.e., subjected to fkee-bum conditions. This relationship [57] can be written as

where ml

=

q q Ah,

= = =

the mass burning rate per unit area (g/m2*s) heat flux from the flame above the fuel (kw/m2) heat losses fkom the fuel surface (kW/m2) heat required to produce volatiles (kJ/g)

Ahg Is the heat of gasification. For a liquid fuel it is equal to the sum of the enthalpy to raise the temperature of the he1 to its surface temperature (slightly below the boiling point) and the latent heat of vaporization. When a fuel is placed in an enclosure, Equation (4.39) changes to

where q: (in units of kW/m2)is the heat flux incident on the fuel surface from extemal sources [57]. In enclosures, these sources can be from the hot layer, heated walls, and other flames. It is clear that external heat fluxes can affect the burning rate of fuels. Hence, the heat release rate becomes

where A, is the surface area of the burning fuel in m2.

The Prediction of Flashover

107

TIME ttscl

FIGURE 4-8. Enclosure effects on the burning rate of a slab of PMMA

The question now becomes, ''Do enclosure effects significantly affect the burning rate?'For slab fbels with optically thin flames, the answer is certainly yes (see Figure 4-8) [57]. For many complex fuel configurations such as wood cribs, the answer is no. Wood cribs are known to burn the same in free-burn and enclosure situations. This is attributed to the shielding of the interior faces of the sticks by the exterior sticks, and at the same time, the interior sticks act like effective radiators that are continually heating each other. Thus enclosure effects for wood cribs are neghgible in most cases 1571. The FIRM-QB model was developed to be p r i m d y concerned with fuels that are found in residential settings. Babrauskas has reported on a comparison of burning rates for upholstered fi;lmiture in fiee-burn and room-frre scenarios 1561. Based on the results of this investigation, Babrauskas stated The validity of open-burning measurements for determining pre-flashover burning rates in room fires has been successfully verified for typical upholstered furniture specimens.

Babrauskas continued by saying that post-flashover rates are not significantly altered for fires that are fuel limited. It appears, therefore, that heat release data f?om the fimiture calorimeter c m be used to estimate flashover in compartment fires involving upholstered furniture. According to Babrauskas, the explanation lies in the radiative thick flames masking the fuel fiom much of the exterior fluxes. Figures 4-9 and 4-10 graphically compare heat release rates for free-burn and room-fke conditions. I

1

I

1

I

I

I

I

1

CHAIR F21

-Furniture calorimeter -S---

Room fire t e s t no. 5

r Flashover

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FIGURE 4-9. Free-burn vs. room-fire heat release rates for a chair

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FIGURE 4-10. Free-burn vs. room-fire heat release rates for a chair

1 10

MODIFICATIONS TO ASET-QB

It is clear from these two graphs that enclosure effects are in fact negligible, even just after flashover. Complex he1 configurations, such as wood cribs, can also explain, in part, the negligible difference between free-burn and compartment-fire burning rates. Some chairs and other similarly shaped fbmiture items may also have pronounced radiative exchanges between different surfaces such that they behave like wood cribs. The ability to use £tee-bum data of other fuels ($001 fires for example) to predict flashover is unclear. No general guideline can be offered, except that complex he1 configurations and optically thick flames tend to reduce enclosure effects. Users of f ~ models e are cautioned to determine the appropriateness of such data when predicting flashover. To summarize this section, it has been shown that an upper layer gas temperature at or above 600°C can be used to predict the onset of flashover. It has also been shown that the fiee-burn heat release data for most upholstered fiuniture items can be used to predict flashover.

The FIRM-Q6 Model

CHAPTER 5

5.1 INTRODUCTION The ASET-QB model described in Chapter 3 and the modifications and additions presented in Chapter 4 can now be combined into one fmal product, the FIRM-QB model. The FIRM-QB model is documented in detail in this and subsequent Chapters. The FIRM-QB documentation is structured according to ASTM E 1472, "Standard Guide for Documenting Computer Software for Fire Models." ASTM E 1472 [74] was developed by Committee E-5 on Fire Standards, Subcommittee E05.39 on Fire Modeling, and was first published in 1992. Subcommittee E05.33 on Fire Safety Engineering currently has the responsibility for maintaining the guide. ASTM E 1472 provides guidelines for the development of documentation for computer software for scientific and engineering computations in fire models and other areas of fxe protection engineering. According to ASTM E 1472, documentation of fire model s o h a r e shall consist of the following three parts:

1 Technical Documentation 2 User's Manual 3 Programmer's Guide The technical documentation describes the theoretical and mathematical foundations of the model. The technical documentation for FIRM-QB is presented in this Chapter. ASTM E 1472 recommends that the technical documentation include an assessment of the uncertainty and accuracy of the model. For detailed guidelines on how to perform this important task, reference is made to ASTM E 1355, "Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models" [75].

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An evaluation of the predictive capability of FIRM-QB according to ASTM E 1355 is presented in Chapter 7. The user's manual provides instructions for installing and operating the software. Sample runs are included to allow the user to verify correct operation of the program. The user's manual for FIRM-QB forms the subject of Chapter 6. The programmer's guide provides instructions for users who want to customize the program. Guidelines for QBasic programmers who want to change the FIRM-QB code are presented in Appendix D. The Visual Basic version, FIRM-VB, is described in Appendix E.

5.2FIRE PROBLEM MODELED BY FIRM-QB FIRM-QB predicts the consequences of a user-specified fire in a compartment with a single vent in a vertical wall. Figure 5-1 depicts the fire problem that is modeled. The main variables that are calculated as a function of time are upper layer temperature, layer interface height, and mass flows through the vent. These variables are pertinent to the f r e hazard, which is quantified by the time to reach untenable conditions inside the compartment, or by the time to reach flashover. The fire is located in the center of the compartment, at a sufficient distance fi-omthe walls so that air is entrained unifody over the entire perimeter of the flame and fire plume.

FIGURE 5-1. Fire problem modeled by FIRM-QB

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5.3 TECHNICAL DESCRIPTION OF FIRM-QB 5.3.1 Theoretical Foundation 5.3.1.1 Assumptions

The assumptions used in the derivation of FIRM-QB are as follows: Two-zone (layer) approximation is considered acceptable. The pressure within the compartment is constant and equal to atmospheric pressure. Heat transfer from the floor and lower wall sections to the lower gas layer is neglected, and the temperature of the lower gas layer is constant and equal to ambient air temperature. The specific heat at constant pressure is assumed to be constant for all gases, and is equal to the specific heat of dry air at 293 K, i.e., c, = 1.004 kJ/kgK. Zukoski's point source plume model is considered to yield acceptable results in the flaming, intermittent, and plume regions. Entrainment occurs between the surface of the fuel and the layer interface. Virtual source corrections are considered negligible and are not included. Stratification does not occur, i.e., all heat and mass from the plume reach the hot layer located below the ceiling. The transport time from the fire to the hot layer is negligible, i.e., quasi-steady state conditions are assumed. The plume occupies a negligible fkaction of the lower layer. The heat release rate of the fire is specified by the user. Compartment effects are ignored, but oxygen starvation due to vent or entrainment controlled burning are accounted for. A constant &action, L,, of the heat released by the f i e consists of radiation. The energy losses from the flame and plume, and the energy losses from the compartment through the bounding surfaces are described simply as a &action, L, of the total heat release at any given time. Venting occurs only through a rectangular opening in one of the vertical walls of tfie comartment.

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Since it was developed fiom ASET-QB, the assumptions in FIRM-QB are largely identical to those listed in Section 3.2. The main differences are: FIRM-QB accounts for oxygen starvation due to vent or entrainment controlled burning (assumption 7), the radiative heat loss fraction is not fixed at 35% but is specified by the user (assumption g), and FIRM-QB simulates hot layer venting through a door or window in a vertical wall of the enclosure (assumption 10). Both models assume that the heat losses through the compartment boundaries are a constant fraction of the energy released (assumption 9). FIRM-QB assists the user in the selection of a proper value by providing an estimate of the heat loss fraction. This feature is not available in ASET-QB. 5.3.1.2 Governing Equations

The main equations in FIRM-QB express the conservation of energy in the upper layer, and the conservation of mass in the lower layer. These equations were obtained by simplifying the generic set of conservation equationsdeveloped in Chapter 2 on the basis of the assumptions listed in Section 5.3.1.1. With a lower layer temperature that is constant and equal to ambient temperature (assumption 3), a constant specific heat (assumption 4), and upper layer heat losses equal to a fraction, L,, of the heat release rate fiom the fire (assumption 9), Equation (2.6 1) can be written as

Equation (5.1) is used in FIRM-QB to calculate the upper layer temperature, T,, as a function of time. This equation is identical to the upper layer conservation equation in ASET-QB [see Section 3.2.2, Equation (3.7)]. Q is supplied by the user, either interactively in the form of a series of time vs. heat release rate data pairs, or by specifying an existing fire file. The HRR-QB program is a convenient tool to create fire files that can be read by FIRM-QB.

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The heat loss fi-action, L , is also specified by the user. However, FIRM-QB uses an algorithm to estimate L, as a function of the height of the fuel, the geometry of the compartment, and the location of the vent soffit. This algorithm was developed in Section 4.3. The entrainment rate, riz, is calculated on the basis of Zukoski's plume model (see Sections 2.6.2.1 and 3.2.1). If the air entrained into the flame and plume is insufficient to support complete combustion of the fuel volatiles, Q is adjusted to account for the lack of oxygen. This, in turn, affects the entrainment rate, because me is a a c t i o n of Q. A detailed discussion of the approach in FIRM-QB to address oxygen starvation is provided in Section 4.2. Because the lower layer is assumed to remain at ambient temperature, Equation (2.25) can be simplified to

Equation (5.2) is the lower layer mass conservation equation in FIRM-QB. This equation is used to determine the layer interface height, Z,, as a function of time. The entrainment rate, rir, is calculated on the basis of Zukoski's plume model, as mentioned above. The rather complicated procedure to determine the vent flows, ma and k,,,is discussed in Section 4.1. Note that the two flows cannot be different from zero at the same time. If the layer interface is located above the vent soffit, ni, is equal to zero, and lower layer air is pushed outside the compartment at the following rate:

This equation is identical to that ASET-QB for calculating the flow through cracks at floor level [see Section 3.2.3, Equation (3.1011. If the layer interface is located below the vent soffit, Equation (2.29), which expresses the conservation of mass for the entire compartment, is used to determine the vent flows. In FIRM-QB, this equation takes the following form (see Section 4.1.6)

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The three vent flows can be expressed as a function of the static pressure difference at the layer interface height, AP(Zi). Hence, Equation (5.4) is a non-linear algebraic equation, which is solved for AP(Zi) at every time step. Once M(ZJ is known, the corresponding vent flows can be calculated, and substituted into Equation (5.2). FIRM-QB does not allow rir, to exceed Kawagoe's choked flow limit (see Section 2.6.2.2). The rate at which hot layer gases are vented, mu, is also calculated in this process, although it is not needed for the lower layer mass conservation equation. A more detailed discussion of the vent flow equations in FIRM-QB can be found in Section 4.1. 53.2 Mathematical Foundation

The conservation Equations (5.1) and (5.2) form a set of two ordinary differential equations (ODES). This set is solved at every time step to predict the upper layer temperature, T, and layer interface height, Zi, at the next time step. A fourth-order Runge-Kutta method with stepsize control is used for this purpose. The stepsize control algorithm reduces the time step so that the estimated error of the solution vector is within certain tolerances. The maximum errors permitted are 0.3 K and 1 mm for T, and Zi respectively. These values are comparable to the tolerances used by Walton in ASET-B [3]. The ODE solver and stepsize control algorithms are discussed in more detail in Section B.5.3. Equation (5.4) is a non-linear algebraic equation that is solved with the bisection technique. First, upper and lower limits are found of an interval that brackets the root of the equation. The root is then found by repeatedly halving the interval, until the function value, within a certain tolerance, is equal to zero. In FIRM-QB, this tolerance is set equal to 0.3, which corresponds to a mass flow of less than 1 g/s. Further details concerning the bisection method utilized in FIRM-QB can be found in section B.5.2. Note that two different approaches are used to implement the numerical techniques in FIRM-QB. The ODE solver was added to the

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FIRM-QB program in the form of a collection of subprograms, in a similar way as external software libraries would be linked with a program. The bisection method was implemented by inserting lines of code directly into the VentFlows subroutine of FIRM-QB. Both approaches are acceptable. 5.4 FIRM-QB PROGRAM DESCRIPTION

The FIRM-QB program is written in QBasic. Instructions for installation and use of the software can be found in Appendix C. The QBasic source code must be loaded into the QBasic environment before it can be run. The executable version of the program can be run directly from DOS or Windows. The two versions of the software are functionally identical. FIRM-QB first goes through an interactive session to obtain information concerning the case to be simulated. The user is asked to specify the data path and output file name; the geometry of the compartment, vent, and fuel; and the heat release rate fiom the fue. After the necessary input has been provided, the program calculates vent flows and solves the conservation equations at 1 second intervals (or smaller intervals if required to obtain the desired accuracy). The results are printed on the screen, and saved to disk every 5 seconds. A hardcopy of the results is also generated, if requested by the user. When flashover occurs (defmed as T, = 600°C), the user is given the option to terminate the run.At the end of the m, a message is displayed explaining what caused the program to terminate. The user then has the option to view a plot of the results (T,, 2, Q, and m3 on the screen.

5.5 FIRM-QB DATA LIBRARIES No data libraries are needed to run FIRM-QB. However, it is helpll to have a database of fire files for fuels of interest. Fire fdes that can be read by FIRM-QB can be easily created with HRR-QB (see Section 4.4.9, and are compatible with the files used by ASET-QB (see Chapter 3) and FPETool[4 l].

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5.6 PREDICTIVE CAPABILITY OF FIRM-QB

The predictive capability of FIRM-QB was evaluated according to the guidelines of ASTM E 1355 [75]. The results of this evaluation will be discussed in Chapter 7.

FIRM-QB User's Manual

CHAPTER 6

6.1 INTRODUCTION This chapter contains the user's manual for the Fire Investigation and Reconstructzon Model FIRM-QB. The information in this chapter is structured according to the guidelines in ASTM E 1472, "Standard Guide for Documenting Computer Software for Fire Models" [74f.

6.2 TECHNICAL DOCUMENTATION FIRM-QB is a two-zone computer model that predicts the consequences of a user-specified f i e in a compartment with a single vent in a vertical wall. FIRM-QB is based on the assumption that the volume inside the compartment consists of a uniform layer of hot gases beneath the ceiling, and a layer of cold air between the floor and the hot layer. The main variables that are calculated as a function of time are upper layer temperature, layer interface height, and mass flows through the vent. The first two variables are estimated at discrete time steps by numerically solving the conservation equations of upper layer energy and lower layer mass. The conservation equations are ordinary differential equations (ODES) that are solved with a fourth-order Runge-Kutta technique with stepsize control. The vent flows are determined sirnultaneouslyby solving the compartment-wide mass balance equation. The bisection technique is used to solve this non-linear algebraic equation. The technical documentation of FIRM-QB is discussed in more detail in Chapter 5.

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6.3 PROGRAM DESCRIPTION

The FIRM-QB program is written in Microsoft QBasic. The source code of the program is included on the accompanying CD-ROM. The program is also provided in the form of a stand-alone executable. Instructions for installing and operating the FIRM-QB software are given in Appendix C. FIRM-QB first goes through an interactive session to obtain information concerning the case to be simulated. After the necessary input has been provided, the program calculates vent flows and solves the conservation equations at 1 second intervals (or smaller if required to obtain the desired accuracy). The results are printed on the screen, and saved to disk every 5 seconds. A hardcopy of the results is also generated, if requested by the user. When flashover occurs (defied as Tu= 600°C), the user is given the option to terminate the run. At the end of the run, a message is displayed explaining what caused the program to terminate. The user then has the option to view a plot of the results (T,, &, i),and mJ on the screen. 6.4 INSTALLING AND OPERATING FIRM-QB

For minimum system requirements and installation instructions, the reader is referred to Appendix C. 6.5 PROGRAM CONSIDERATIONS

FIRM-QB first goes through an interactive sequence of questions, to obtain the necessary input information for the run. A typical example of the questions and answers (in bold print) is shown in Figure 6-1. For some of the questions, the program chooses one of several alternate paths depending on the user's response. Other questions allow the user to select certain optional features of the program. The remaining questions ask the user to supply data that describe the geometry of the compartment and characterize the intensity of the fne. The first two types of inputs are discussed in this section. The geometry and fire data form the subject of the next section.

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PATH FOR OUTPUT FILE? C:\FIRM\DATA\ OUTPUT FILE NAME (WITHOUT PATH AND EXTENSION)? DIPTANK DO YOU WANT TO PRINT THE RESULTS (Y/N)? N S.I., ENGINEERING, OR MIXED UNITS (S, E, M) ? M RUN TITLE? ACETONE DIP TANK ROOM FLOOR AREA (ftA2)?1500 ROOM CEILING HEIGHT (ft)? 15 WIDTH OF THE VENT (ft)? 12 VENT SILL HEIGHT (ft)? 0 VENT SOFFIT HEIGHT (ft)? 10 FIRE BASE HEIGHT (ft)? 4 RADIATIVE HEAT LOSS FRACTION (DEFAULT=0.35)? 0.25 DO YOU WANT TO PREDICT THE HEAT LOSS FRACTION (Y/N)? Y IS THE CEILING SMOOTH, MODERATE, OR ROUGH (S/M/R)? M ROOM LENGTH TO WIDTH ASPECT RATIO? 1.67 TOTAL HEAT LOSS FRACTION (DEFAULT=0.606)? 0.55 MAXIMUM TIME (sec)? 900 FIRE FILE NAME (WITHOUT PATH AND EXTENSION)? DIPTANK DESCRIPTION? ACETONE DIP TANK FIRE HEAT OF COMBUSTION (DEFAULT IS 5159 Btu/lb)? 11092 ENTER HEAT RELEASE RATE (kW) AT TIME o? 1457.8 INPUT TIMES AND HEAT RELEASE RATES (-9,-9 to end) TIME (sec), HEAT RELEASE RATE (kW)? 150,1457.8 TIME (sec), HEAT RELEASE RATE (kW)? -9,-9

FIGURE 6-1. Typical sequence of questions and answers for FIRM-QB run

1 Path to the directory where the data andfire files are located. It is assumed that the two types of files (output and fire are located in the same directory. After the path has been specified, it remains the same for all runs in a session. If the user wants to change the path, he must terminate and restart the program. 2 Output file name, without path and extension. This is a string of maximum eight characters. The name is not case-sensitive, and can contain only the letters A-Z, the numbers 0-9, and the special (, ), and '. The data fle characters ', -, !, @, #, S, %, ", &, (, ), -,, name is automatically given the extension ".FOF." FIRM-QB checks whether the f l e already exists, and verifies that the user wants to overwrite the file if this is the case.

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Option to print results during run. To generate a printout, a printer must be connected to the computer. A hardcopy of the results can be generated later by printing the output file. System of units. The user has the option to specifjr the input data in S.I., U.S. engineering, or mixed units. If mixed units are selected, all values are in U.S. engineering units, except energy values, which must be specified in kW. Note that FIRM-QB internally uses S.I. units. The data in fire files (.FIR extension) are also in S.I. units. R m title. This is a text string that describes the run. Although the user can supply up 256 characters (any characters, except commas), the string is truncated by FIRM-QB to a maximum of 60 characters. Fire file name. This is a string of maximum eight characters. The name is not case-sensitive, and can contain only the letters A-Z, the numbers 0-9, and the special characters ', -, !, @, #, $, %, ", &, (, ), -, {, f , and '. The fire file name is automatically given the extension ".FIR." FIRM-QB checks whether the file already exists. If the file exists, FIRM-QB determines whether the user indeed wants to use that file. If not, the user can specifl a different name. If the file does not exist, it is created and the user is asked to specify a heat release rate curve in the f o m of a set of time and heat release rate data pairs. The user is also asked to supply an average value for the heat of combustion of the fuel, so that the program can calculate the corresponding mass loss rate. FIRM-QB (and ASET-QB) does not use the mass loss rate column, but it is required for compatibility with FPETool fire f11es [4 11. Screen plot menu. At the end of a run, the user has the option to view screen plots of four output variables: layer interface height, upper layer temperature, heat release rate, and upper layer vent flow. The heat release rate curve might be different from that specified by the user, if the fire was oxygen-starved during part of the run.

6.6INPUT DATA 6.6.1 General Considerations

Since FIRM-QB is intended primarily as a usefid tool in fue investigation and reconstruction, the geometry of the compartment and the

Input Data

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vent, and the dimensions of the fuel are usually relatively well known. The main problem is to characterize the fire itself. This type of information can be found in handbooks, journals, reports of standard tests, reports of custom experiments, etc. For example, burning rates for a wide range of fuels can be found in Chapter 3-1 of Reference [15]. An extensive number of heat release rate curves are compiled in Reference [76]. The radative loss fraction, L,, is generally in the range of 25 to 35%, and values for a wide range of fuels are reported in the literature (e.g., see Reference [15], pages 3-78 to 3-81, where L, = AHradAHCh). FIRM-QB can assist the user in estimating the total heat loss fraction, L, (see Section 4.3.1). All input values, except heat release rate data, are typed on a single line in the appropriate format (numeric or text) followed by ENTER. Heat release rate data (except at time zero) are entered in pairs. Each data pair consists of the time and the corresponding heat release rate, separated by a comma. All variables, except the data and fire file path, are reset in between runs. AU text variables are reset to null strings, except that the default units are S.I. All numeric variables are reset to 0, except L,, which has a default value of 0.6. 6.6.2 Specific Considerations for Each Input Variable

The input variables that describe the geometry of the compartment, and that characterize the intensity of the fire, are listed below. Floor area, A. It is assumed that floor and ceiling area are identical, and that the floor plan is rectangular in shape. The model will provide reasonable predictions for compartments with irregular floor plans, but the estimate of L, might not be reliable. The units for this variable are m2(S.I.) and ft2 (U.S. engineering and mixed). Room height, H. This is the distance fiom the floor to the ceiling. Units are m (S.I.) or ft (U.S. engineering and mixed). Vent width, W,. This is the width of the vent. If multiple vents are present, use the sum of the widths. Units are m (S.I.) and ft (U.S. engineering and mixed). Vent sill height, 2,. This is the height of the bottom of the vent. If multiple vents with different sill heights are present, use the average height as a starting point, and check the effect of sdl height (within the

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range for the different openings) on the predictions. Units are m (S.I.) and ft (U.S. engineering and mixed). Vent sofit height, Zt. This is the height of the top of the vent. If multiple vents with different soffit heights are present, use the average height as a starting point, and check the effect of soffit height (within the range for the different openings) on the predictions. Units are m (S.I.) and ft (U.S. engineering and mixed). Fire base height, ZfThis is the height of the base of the flame. It is not trivial to specify this variable for irregular objects, such as chairs or sofas. If the height of the fuel surface is not very well defined (or if it varies with time), it is recommended to repeat the simulations for a range of he1 height values, and to retain the most conservative results. Units are m (S.I.) and ft (U.S. engineering and mixed). Radiative heat lossfiaction, L, This is the fraction of the heat released by the fire that is lost in the form of thermal radiation. This variable is dimensionless. Total heat lossfraction, L,. This is the fraction of the heat released by the fm that is lost to the room boundaries. FIRM-QB has an algorithm to estimate the value of L,. The algorithm requires the user to specify the length to width ratio of the floor, and whether the ceiling is smooth, moderate, or rough. This variable is dimensionless. Maximum simulation time, t,,. The simulated time will never exceed this value. However, the program will terminate earlier if the end of the fire file is reached, flashover occurs and the user instructs the program to stop, or the layer interface drops below the fuel surface or the sill. The unit for this variable is seconds. Heat release rate, Q. If the user decides not to use an existing fire file, heat release rate data must be entered. Except at time zero, the heat release rate data are entered in pairs. Each data pair consists of the time and the corresponding heat release rate. The unit for time is seconds, and heat release rate is in kW (S.I. and mixed) or Btu/s (US. engineering). The user must also specify the heat of combustion of the fuel, in kJkg (S.L) or Btunb (U.S. engineering and mixed).

6.7 EXTERNAL DATA FILES FIRM-QB (and ASET-QB) requires the user to specify the heat release rate of the f i e . Heat release rate information is stored in external ASCII

Output Information

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data files, i.e., f i e files. These files have the extension ".FIR," and consist of numerical data in three parallel columns, followed by two lines of text. The first c o l m is the time in seconds, the second column is the heat release rate in kW at the corresponding time in the first column, and the third column is the mass loss rate in g/s. The latter is equal to the heat release rate divided by the heat of combustion, which is supplied by the user. The mass loss rate is not used by FIRM-QB (and ASET-QB), but it is needed for compatibility with FPETool. The values in the last row of the three columns are equal to -9, to designate the end of the numerical data. The first line of text contains the name of the fde, and the date it was created. The second line is a description of the fire file entered by the user. Fire fdes can be created directly fiom FIRM-QB. However, it is recommended to use HRR-QB, because it was written specifically for creating f ~ files, e and offers more options (see Section 4.4.5). 6.8 SYSTEM CONTROL REQUIREMENTS It is recommended that the user press the CAPS LOCK key before starting a FIRM-QB session. Thus, all character strings will be in uppercase letters, resulting in a consistent and uniform output format. Instructions for running FIRM-QB can be found in Appendix C. 6.9 OUTPUT INFORMATION

The results of a run are displayed on the screen, saved to a file, and, if requested by the user, sent to the printer. The format is nearly identical for the three output media. A header is shown at the top of the screen, the start of the data file, and the top of each printed page. The results are printed in parallel columns below the header. Figure 6-2 shows the output from a m with input data in Figure 6-1. The fust nine columns contain time in seconds, upper layer temperature in "F and "C, layer interface height in ft and m, heat release rate fiom the fire in Btds and kW, and upper layer vent flow in lb/s and kg/s. The last two columns indicate which vent flow regime is in effect (see Section 4. l), and whether the fire is oxygen-starved (see Section 4.2).

FIRM-QB VERSION 1.00 - JULY 1999 ACETONE DIP TANK SIMULATION OUTPUT DATA FILE : c:\FIRM\DATA\DIPTANK.FOF : 139.35 m A 2 ( 1500.00 ftA2) FLOOR AREA : 4.57 m (15.00 ft) ROOM HEIGHT : 3.66m (12.00ft) WIDTH OF VENT : 0.00 m ( 0.00 ft) VENT SILL HEIGHT : 3.05 m (10.00 ft) VENT SOFFIT HEIGHT : 1.22 m ( 4.00 ft) FIRE BASE HEIGHT RADIATIVE FRACTION : 0.250 : 0.550 HEAT LOSS FRACTION 900 S MAXIMUM RUN TIME HEAT RELEASE RATE DATA FILE : C:\FIRM\DATA\DIPTANK.FIR

END OF INPUT FIRE

FIGURE 6-2. Output from typical FIRM-QB run

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At the end of a run, the user has the option to view screen plots of upper layer temperature, layer interface height, heat release rate and upper layer vent flow vs. time. The plotted variables are in units that depend on the system of units chosen by the user on input.

6.10 PERSONNEL AND PROGRAM REQUIREMENTS Anybody who is somewhat familiar with personal computers should have no difficulties installing and operating the FIRM-Q software. It is essential that the user have a background in fire science or fue protection engineering, so that he fully understands the limitations of the model, and can determine whether FIRM-QB is suitable to solve a particular problem. In addition, the user must know how to obtain appropriate values for the different input parameters, and must be capable of interpreting the results of a simulation. Any changes to the source code shall be documented by adding comment lines. It is helpful to include, in addition to a description of the purpose of the change, the name of the person who made the change, and the date when it was made. Any publication of results obtained with a modified version of the model shall include a description of the changes, so that others can verifL the technical basis for the changes, and can reproduce the results. Execution speed varies greatly depending on the type of machine, and the version of the program. The time needed to simulate the acetone dip tank fire described in Section 6.11.3 is given in Table 6- 1 for four different machines, and the two versions of the FIRM-QB program. Table 6-1. FIRM-QB Execution Time on Different Personal Computers Environment Machine 25 MHz 386SW387SX 33 MHz 486 60 MHz Pentium 333 MHz Pentium

QBasic

DOSIWindows

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6.11 SAMPLE PROBLEMS The following examples are intended to provide an indication of the use of FIRM-QB, both in application and execution. The first example is a reconstruction of an actual fire. The second example is intended to demonstrate the use of the model in building design for fire safety. The third example provides an indication of the use of the model for evaluating an existing hazard. 6.11.1 Reconstruction of the Westchase Hilton Hotel Fire On March 6, 1982, a fire occurred in the Westchase Hilton Hotel located in Houston, Texas [77]. As a result of this fire, twelve people lost their lives and three others were seriously injured. The fire, which originated in the early morning hours, was reported to the Houston Fire Department at 2:25 A.M. The fire originated in a guest room on the fourth floor of the guest tower. Although reaching Minvolvement, the fire did not spread fiom the room of origin with any severity. However, hot gases and smoke traveled extensively throughout the fourth floor, and to varying degrees throughout the entire guest tower. As with many fires, the cause of death was generally due to toxic gas poisoning. TnQcations of the fire were first reported as early as 2:00 A.M.,when an odor of smoke was detected on the tenth floor. At 2: 10 A.M. light smoke was observed on the eighth floor in a room located directly above the fire. The fire was not actually discovered until 2 2 0 A.M.when one of the two occupants returned to the room of fire origin. Finding the guest elevators inoperable, this guest used a service elevator and upon entering the fourth floor, observed smoke in the corridor. Opening the door to his room, this guest was met by a heavy smoke concentration and later reported a glow near the bed closest to the window. When this guest observed the fire, he attempted to extinguish it by beating it with what was believed to be a pillow. Being unsuccessful in his attempts, this guest searched for and found his fiiend between the two beds, and removed him from the room. The two then traveled to the west exit stairwell (see Figure 6-3).

Sample Problems VWlCAL EXTERIOR FIRE,EXTENSION

t

129

HOTEL REAR

AREA OF FIRE DAMAGE

VICTIM LOCATIONS E ELEVATORS

FIGURE 63. Westchase Hilton Hotel floorplan of the floor of fire origin (reprinted with permission fiom NFPA Investigation Report Number LS-7, Westchase Hilton Hotel Fire, copyright 01982, National Fire Protection Association, Quincy, MA, 00269)

Thinking the rescued occupant's date was still in the room, the second occupant returned to the room in an attempt to search for the date. (Note, occupant one is identified as the guest who was in the room of origin at the time of the fire's inception, and who was subsequentlyrescued. Occupant two is identified as the guest who returned to the hotel to find the fire and rescue his roommate.) At this time, occupant two was unaware that his roommate's date had left the hotel. Regardless, due to the rapidly deteriorating conditions within the room of origin, guest two could not reenter the room. The two guests then exited the hotel. The two guests who occupied the room of origin survived the fire with minor injuries. At postfire interviews, these guests reported that during the course of the day, when the door leading to the hallway was open, the door failed to completely close by itself due to interference by the carpeting in the room. This corroborates the fire investigator's belief that, after the rescue of occupant number one, the door was left open during the course of the fire. Estimates suggest that the door may have been open between 6 and 18 inches. At approximately 2:31 A.M.,the district fire chief arrived on the fire scene and observed fire projecting out of the windows fiom the room of origin, which indicated that room flashover had occurred some time after 2:20 A.M. and before 2:31 A.M. Fire department representatives estimate first water was applied to the fire at about 2:38 A.M., and resulted in fire extinguishment at Z:4 1 A.M.

130

FIRM-QB USER'S MANUAL

Summary time lines are commonly used for fire investigations. Time lines can also prove beneficial for comparing model predictions with eyewitness accounts and other reference data. Table 6-2 contains the time line that was constructed ftom the information obtained in the investigation. It is clear ftom the time line that the fire had smoldered for over twenty minutes. Based on the rapid deterioration of the conditions within the room of origin after the returning guest rescued his roommate, it appears that the f ~ may e have been limited due to the depleted oxygen within the room, or perhaps the chair was just attaining a flaming state. After the overcome guest was removed ftom the room, the door was left partially open, which provided a new source of oxygen for the fire. From this point on, the fue grew rapidly resulting in flashover. From information provided by the occupants of the room of origin, it is known that at about 2:20 AM., one guest rescued his roommate, assisted him down the hallway, and returned to search for a second occupant who was believed to be in the room. However, when the guest attempted to reenter the room, conditions had deteriorated to the point where he could no longer enter. The FIRM-QB model will be used to predict the f i e development within the room of origin. It will be assumed that the first he1 ignited was an upholstered chair, as shown in Figure 6-4. This assumption was based on fire investigators attributing the cause of the fire to be a smoldering cigarette in the chair. As a result of the fire, the Consumer Products Safety Commission and the National Institute of Standards and Technology tested hrniture removed from the hotel that was similar to the f.umiture located Table 6-2. Time Line of Important Events for Westchase Hilton Hotel Fire

2:OOA.M.

Odor of smoke on 10th floor.

2110 A.M.

Light smoke noticed in room 804.

220 A.M.

Room 404 (room of fire origin) occupant returns. Smoke in 4th floor corridor. Fire discovered in room 404. Unconscious guest rescued by roommate.

2:25 A.M.

Telephone alarm to Houston Fire Department.

2:27 A.M.

Fire apparatus dispatched.

2:31 A.M.

District fire chief on scene. Fire showing from 4th floor window, indicating flashover occurred between 2:20 A.M. and 2:31 A.M.

to ble

ORIGIN

bed

bed

FIGURE 6-4. Floor plan of room of origin showing fuel location

in the room of origin. The data in Table 6-3 describe the measured heat release rate history of the chair. HRR-QB was used to create a fire file for the chair. The name of this file is CH6-AO1.FIR. If the chair releases sufficient energy to cause flashover, then the model can be run using the heat release rate of the chair. If the chair does not, the cumulative energy release rate of the chair and boxspring-mattress must be combined. It can be assumed that ignition of the mattress would occur as the chair heat release is peaking, especially when considering the rapid rise to peak heat release once the chair begins to flame. The room dimensions and f i e specifications are shown in Table 6-4. Based on these data, the model predicts a heat loss kaction of L, = 0.66 (see Figure 6-5). The default value for L,(L, = 0.35) was selected since this value is typically used for modeling upholstered h t u r e [78]. It is assumed that minimal fbel had been consumed during the smoldering period and that upon opening the door to the room, the smoke in the room cleared appreciably. This assumption allows for the established (flaming) burning of the fbel (chair) to begin just after the door is opened. Due to the rapidity that the conditions within the room deteriorated right after the door was opened, this assumption appears to be justified. The data input screen with prompts and responses for this simulation, with the door opening set at 18 inches, is shown in Figure 6-5 and the FIRM-QB computer model output is shown in Figure 6-6. Table 6-3. Heat Release Rate History of Chair Time (seconds)

Heat Release Rate (kW)

Sample Problems

133

Table 6-4. Room of Fire Origin - Westchase Hilton Hotel 177 Room Floor Area

263.8 ft?

Room Ceiling Height

8.00 R

Door (Vent) Sofit

6.56 ft

Vent Width (Varied)

6-18 in.

Fire Height (Estimated)

3.0 ft

PATH FOR OUTPUT FILE? C:\FIRM\DATA\ OUTPUT FILE NAME (WITHOUT PATH AND EXTENSION)? CH6-A05 DO YOU WANT TO PRINT THE RESULTS (Y/N)? Y S.I., ENGINEERING, OR MIXED UNITS (S, E, M) ? M RUN TITLE? WESTCHASE HILTON FIRE RECONSTRUCTION: 1.5 FT DOOR ROOM FLOOR AREA (ftA2)? 263.8 ROOM CEILING HEIGHT (ft)? 8 WIDTH OF THE VENT (ft)? 1.5 VENT SILL HEIGHT (ft)? 0 VENT SOFFIT HEIGHT (ft)? 6.56 FIRE BASE HEIGHT ( ft) ? 3 MAXIMUM TIME (sec)? 1200 RADIATION HEAT LOSS FRACTION (DEFAULT=0.35)? DO YOU WANT TO PREDICT THE HEAT LOSS FRACTION (Y/N)? Y IS THE CEILING SMOOTH, MODERATE, OR ROUGH (S/M/R)? M ROOM LENGTH TO WIDTH ASPECT RATIO? 1.41 TOTAL HEAT LOSS FRACTION (DEFAULT=0.660)? HEAT RELEASE FILE NAME (WITHOUT PATH AND EXTENSION)? CH6-A01

FIGURE 6-5. Example of FIRM-QB input for Westchase Hilton fire reconstruction

Figures 6-7 and 6-8 show the predicted location and temperature of the hot layer in the room, after established burning has commenced, for various vent widths. The various vent widths reflect the estimated door opening range of 6 to 18 inches based on information documented during the fire investigation. Additional opening widths are included for comparison purposes. The simulation for a closed door was performed with ASET-QB, and the corresponding data file on the accompanying CD-ROM is CH6-AO1.AOF. FIRM-QB was used for the other simulations,with door widths between 3 and 36 inches. The corresponding data fdes are CH6-A02.FOF to CH6-A07.FOF.

FIRM-QB VERSION 1.00 - JULY 1999 WESTCHASE HILTON FIRE RECONSTRUCTION (1.5 FT DOOR WIDTH) SIMULATION OUTPUT DATA FILE : C:\FIRM\DATA\CH6-A05.FOF FLOOR AREA : 24.51 m A 2 ( 263.80 ftA2) ROOM HEIGHT : 2.44 m ( 8.00 ft) : 0.46 m ( 1.50 ft) WIDTH OF VENT VENT SILL HEIGHT : 0.00m (0.00ft) VENT SOFFIT HEIGHT : 2.00m (6.56ft) FIRE BASE HEIGHT : 0.91 m ( 3.00 ft) : 0.350 W I A T I V E FRACTION HEAT LOSS FRACTION : 0.660 MAXIMUM RUN TIME : 1200 S HEAT RELEASE RATE DATA FILE : C:\FIRM\DATA\CH6-AO1.FIR

FZASHOVER OCCURRED - RUN TERMINATED BY USER. FIGURE 6-6. Example of FIRM-QB output for Westchase Hilton fue reconstruction

I

I

I

I

closed door 0.25 ft door 0.50 ft door 1 .OO ft door .....,....... 1.50 ft door 2.00 ft door 3.00 ft door m - - - - - -

- - - - - m -

width width 1 width : width 1 width : width I

-

I

I

I

I

Time (S)

FIGURE 6-7. Layer interface height vs. time for various door widths

,.pH-

v

closed door 0.25 ft door ------- 0.50 f t door -----. - 1.OO ft door ............. 1.50 ft door -.-.-.m 2.00 ft door -,.-..-... 3.00 ft door

P

-----

Time

width width width width width width

(S)

FIGURE 6-8. Upper layer temperature vs. time for various door widths

136

FIRM-QB USER'S MANUAL

From the time versus temperature plots (Figure 6-8) it can be noted that vent widths from 1 to 3 feet result in flashover being achieved in a rather narrow time frame of 122 seconds (2.03 min) to 142 seconds (2.37 min). It is interesting to see that the time to flashover decreases from 142 seconds (2.37 min) to 125 seconds (2.08 min) when the door width is changed from 1 to 2 ft, and increases back to 140 seconds (2.33 min) for a door width of 3 ft. This can be explained by the fact that the fire is not oxygenstarved prior to flashover for door widths of 2 ft or greater. In that case, the heat losses associated with the upper layer vent flow are greater for larger widths, resulting in longer flashover times. Below 2 ft, the fire becomes oxygen-starved prior to flashover, and the resulting heat release rate reduction compensates for the decreasing vent flow heat losses. The reader is encouraged to review the data files to verify this. Flashover, for the minimal reported door opening width of 6 inches (0.5 feet), occurs at 199 seconds (3.32 min), and at 299 seconds (4.98 min) for a door opening of only 0.25 feet. Thus, the time to flashover begins to differ appreciably for door openings greater than approximately 1 foot. With the door closed, the simulation was terminated before flashover occurred, i.e., when the layer interface dropped below the fuel height. If it is assumed that the door was left open at least one foot, then flashover can be predicted to have occurred approximately at 2-2.5 min past established burning. As noted, the prediction of the time to flashover is extremely dependent on the true opening of the door. The interface prediction (see Figure 6-7) is less affected by the door opening width. The interface height is between 1.2 and 1.5 m (4 and 5 ft) when flashover occurs, and decreases with increasing door width. Based on values presented by Cooper and Stroup, untenability in enclosure fres is assumed to occur when the hot layer reaches 183°C (361°F) when the hot layer is above eye level, or when the hot layer reaches l OO°C (2 12°F) when the hot layer descends below eye level [35]. The selection of 183°C is based on the fact that the radiant flux fiom a black body (i.e., a perfect radiator, see Section B.3.3.1) at this temperatwe is 2.5 kw/m2,which is near the threshold of human tenability. The 100°C (i.e., the boiling point of water) is based on the damages suffered by the respiratory system due to the inhalation of hot gases and due to irritation of the skin and eyes. Using 5 feet (1.5 m) as an estimation of eye level, it can be noted fiom Figures 6-7 and 6-8 that the eye level criterion is not important since the hot layer drops below that level when the upper layer temperature is already much higher than 183°C. Between 50 and 55

Sample Problems

137

seconds into the fire, regardless of the door width, the hot layer is above the 183°C untenability limit. Therefore, there is less than one minute for occupants to safely exit the hotel room after the onset of flaming combustion. If it took approximately I minute for the rescuing guest to assist his roommate to the west exit stairwell and then return to the room of origin, the conditions within the room would have deteriorated to the point where reentry to the room was impossible. In another minute and a half, flashover in the room would occur based on the model predictions. This would correspond to a real time of about 2:23 A.M. This is about 8 minutes prior to the arrival of the district chief, who reported observing flames h m the window of the room of origin. Flashover predictions based on the minimal door openings of one-quarter and one-half of a foot would also result in flashover times prior to the arrival of the district chief. The f i e development predicted by the model appears to be reasonable. In particular, the time to flashover is predicted within the allowable range based on eyewitness accounts. The time elapsed between flashover and the time of the district chief S arrival is unknown. Also, the error associated with the times provided by the eyewitnesses is unknown. Within these limitations, the true time to flashover cannot be more adequately quantified As such, an evaluation of the model predictions versus the true event time line cannot be more specific. However, the predictions do appear to be acceptable. The results could be used to further study the fue and to evaluate the effect of varying input data, such as fuel loading, and first fuel ignited, i.e., bed versus chair. An indication of the effects of varying door widths has already been provided. Several limitations must be considered with studies such as the actual fire reconstruction just provided. The difficulty associated with the incomplete time lines for comparison has already been mentioned. Also, the effect and importance of varying the heat loss fractions will be demonstrated in Chapter 7. This was not included in this study. An assumption of the study was that when the door was opened to the room of origin, the smoke present quickly cleared, and the fxe then began as a small flame on the chair. The effect of varying the input data to account for varying initial conditions would also be beneficial. Also, it was assumed that the first fuel ignited (the chair) was the only fuel appreciably contributing to the fue up to flashover. In the same regard, it is not known for sure that the fire actually originated in the chair; it could have originated in the bed near the chair.

138

FIRM-QB USER'S MANUAL

To summarize, fire modeling can be an effective tool for assisting in the reconstruction of actual fire incidents. However, a great deal of information is required, and numerous simulations should be run to account for variations in input data. The uncertainty associated with input data and the time lines used for comparison must also be evaluated. Once the model predictions have been tested and accepted, the model input can be varied to investigate the effect of altering the $re scene on model predictions. It should be clear that the above example does not reflect a complete reconstruction using fire modeling. It only demonstrates an approach, and presents some of the difficulties and limitations associated with the application of fire modeling to the reconstruction of actual fire incidents. 6.11.2 The FIRM-QB Model as a Design Tool Chapter 13 of the 1997 edition of the National Fire Protection Association document NFPA 101, The Life Safety Code [79], covers requirements for existing health care facilities. Paragraph 13-3.6.1 states that corridors must be separated from all other areas by rated partitions and protected openings. Exception No. 6 of that paragraph states that certain spaces may be open to the corridors and unlimited in area, provided the non-separated area is either protected by automatic sprinklers, or "the furnishings and fiuniture in combination with all other combustibles within the area are of such a minimum quantity and are arranged so that a fully developed fire is unlikely to occur." Other requirements must also be met before this exception may be taken. A design team may wish to take this exception, but not want to install sprinklers. Alternatively, they may wish to determine which is the most functional and cost-effective:providing sprinkler protection or limiting the combustibles. One possible approach for evaluating the combustibles permitted in the space would be to use computer fue modeling to evaluate different he1 scenarios within the space. For example, consider a hospital waiting area that is located on a patient wing and opens directly into a corridor. The floor area is 400 square feet, with an 8-foot high ceiling. The entrance into the space is through a large opening that is 7 feet high and 9 feet wide. The architect's interior design section has selected two types of sofas, both of which come in three sizes: full, one-half, and one-quarter. The ody difference between

the two types of sofas is the cover fabric. One has a polyolefm cover, the other is primarily cotton. The proposed sofas are described in Table 6-5. The sofa selection, and the number to be used, will be based on the requirement that the sofas must not be capable of causing flashover in the waiting area. The geometric data of the space in question, and the data provided on the proposed sofas will be used to predict the fire development within the waiting area. The triangular heat release prediction model will be used to provide an estimate of the heat release rate history of the sofas. The approach will be to model the fire development resulting fiom involvement of a single sofa, to determine if the single piece is capable of causing flashover. It will be assumed that the single pieces will be placed such that ignition of a secondary fuel item cannot occur due to heat transferred fiom the f ~ sfuel t ignited. Methods to evaluate the required separation can be found in the literatwe [go]. As a conservative approach, since life safety is the primary concern, low heat loss fiactions were selected because low values would result in higher predicted hot-layer temperatures. With L, = 0.30, a moderately rough ceiling, and a compartment length to width ratio of 1, FIRM-QB suggests a value of 0.63 for L,. Therefore, an L, value of 0.30 and L, of 0.55 were selected as being reasonable, but below the expected values. This affords a factor of safety in the analysis. The sofas with polyolefm-based cover fabrics were evaluated first. According to the FIRM-QB model, all three sizes would cause flashover in the waiting area. Therefore, the use of these sofas would be prohibited (see CH6-B0l .FOF through CH6-B03.FOF on the CD-ROM for the actual model outputs). The cotton-covered sofas were then evaluated. The fullTable 6-5. Sofa Selection Data

Frame:

Wood

Padding:

Polyurethane Foam

Cover Fabric:

Polyolefin or Cotton

Total Weight:

5 1.50 kg (M1 size) 26.75 kg (Xsize) 12.86 kg (% size)

Heat of Combustion:

18,000 kJ/kg (Polyolefin) 14,600 kJkg (Cotton)

140

FIRM-QB USER'S MANUAL

size cotton-covered sofa resulted in flashover. The one-half size sofa f i e approached flashover near the peak heat release, but did not reach it. The one-quarter size sofas did not cause flashover by a large margin (see CH6-B04.FOF through CH6-B06.FOF for the actual model outputs). A sensitivity analysis in Section 7.3.4.3 will show that relatively minor changes of some critical input variables would result in flashover for the one-half size sofa fre. Therefore, the smallest size cotton-covered sofa is the only design that should be safely permitted for use in the waiting area (without sprinklers). The peak heat release rates, and times to flashover for the various sofa designs are shown in Table 6-6. Since the predictions are based on conservative input, the use of cotton-covered sofas of the one-quarter size appear to be safe for use in the waiting area. As mentioned above, there still remains the need to safely locate the fuels (sofas) apart from each other such that flaming or radiative ignition cannot occur. Obviously, numerous other sofas could be considered. For example, sofas with cotton batting are not likely to cause flashover for the situation considered, and may be a candidate for use in full-size sofas within the waiting area. Figure 6-9 shows the effect of altering the composition of upholstered furniture on the rate of heat release. 6.113 The Firm-QB Model as a Hazard Analysis Tool

As an example of the evaluation of an existing hazard, a fictitious s fimiture and uses an facility will be considered. The facility r e f ~ s h e old acetone dip tank for stripping old paint and finishes off of the furmture. Table 6-6. Heat Release Rates and Times to Flashover of Various Sofa Designs Computed by FIRM-QB Sofa Full Polyolefin %-Polyolefin %-Polyolefin Full Cotton %-Cotton %-Cotton

Peak Heat Release Rate

Time to Flashover (S)

Sample Problems

14 1

FURNITURE WIMETER

TME (S)

FIGURE 6-9. Effect of varying fuel composition on heat release rate [72]

The dip tank is a square tank with Cfoot sides, and the top of the acetone is approximately 4 feet above the floor. The dip tank is located in a large room that measures 30 by 50 feet, with a 15-foot ceiling. On each end of the room are 10-foot high by 6-foot wide openings, where the fiuniture passes through. Since the model allows for a single vent only, it will be assumed that a single vent, tvvice the width of the two equal-area vents, will result in vent flows equivalent to that of the two single vents. Thus, the vent will be modeled as being 10 feet high by 12 feet wide. The authority having jurisdiction (AHJ) is concerned that the unprotected acetone tank poses an unacceptable hazard to the life safety of the workers, due to the threat of spreading fire caused by flashover. Predictive modeling can be used to evaluate the threat posed by the acetone tank. For the present analysis, the primary concerns will be, "Can the acetone tank cause flashover?'and "How much time is available for safe egress?" From measurements of the facility, the geometric data required for input is available. Based on the information on page 3-78 of Reference [H], the radiative heat loss fiaction for acetone can be estimated to be 27%. With L, = 0.27, LIW = 1.67, and a moderately rough ceiling,

FIRM-QB suggests a value of 0.62 for L,. Again, since life safety is a primary concern, low heat loss fractions will be used to afford a factor of safety, i.e., L, = 0.25, and L, = 0.55. An estimation of the rate of heat release fiom the burning acetone tank is required. The acetone tank can be adequately modeled as a pool fire. From Equations (4.35) and (4.36), and Table 4-3, the heat release rate can be predicted by

where, from Table 4-3 0.041 kg/m2*s =1.91/m Ah,, = 25,800 kJ/kg

"zil kp

The heat release rate, which is considered to be a constant until the fuel is consumed, is found to be 1457.8 kW. Note that the diameter of the pool, D, must be specified in meters. A data input screen similar to that for the acetone dip tank example is shown in Figure 6-1. For this example, different names were used for the data and fire files, i.e., CH6-Col.* instead of DIPTANK.", and a maximum simulation time of 900 seconds was specified. The results for the first 150 seconds of the simulation are identical to those in Figure 6-2. To review the complete results of the simulation, the reader can browse through the data file, CH6-CO1.FOF. Figures 6-10 and 6- 11 show the predicted layer interface height and hot-layer temperature as a function of time for the acetone fire. Based on a hot-layer temperature of 600°C, the FIRM-QB model shows that flashover does not occur (see Figure 6-11). The available safe egress time can be determined on the basis of untenability criteria, such as the ones proposed by Cooper and Stroup (see Section 6.1 1.1). Using 5 feet (1.5 m) as an estimation of eye level, it can be noted fiom Figure 6-10 that the interface never drops below eye level, since the hot layer becomes steady at 8.5 fi (2.6 m) above floor level. However, at 35 seconds into the fire, the hot layer temperature is equal to 183OC. Therefore, there is less than one

1

'

"

'

I

"

"

ceiling

soffit

0

300

600 Time

900

(S)

FIGURE 6-10. Layer interface height for acetone dip tank hazard analysis

0

300

600 Time

900

(S)

FIGURE 6-11. Hot layer temperature for acetone dip tank hazard analysis

144

FIRM-QB USER'S MANUAL

minute for all occupants to safely exit the room containing the acetone dip tank. If someone is injured and requires assistance, the time available for safe egress may be insufficient. If occupants delay egress, for whatever reason, they could be subjected to untenable conditions. Furthermore, since acetone has a boiling point of only 56S°C, ignition of other acetone tanks, if present, is quite likely. Based on this analysis, the AHJ may have sufficient cause to require some form of suppression system protecting the dip tank (if not already required), or may prevent the continuation of dipping operations. In other situations, the analysis may suggest that a variance in the code requirements is permissible, although this would require a more extensive analysis to verify the effect of uncertainties in the input data on the results of the predictions. 6.12 RESTRICTIONS AND LIMITATIONS

FIRM-QB will run on virtually any IMB compatible PC. The source code can be loaded and executed fiom the QBasic environment. The QBasic interpreter is included with DOS (version 5.0 and higher) and Windows 95. The executable can be run directly fiom DOS or Windows. Therefore, there are no significant hardware or software restrictions. FIRM-QB predicts the consequences of a user-specified fire in a compartment with a single vent in one of the vertical walls of the compartment. Therefore, the application of FIRM-QB is limited to certain types of problems. The predctive capability of FIRM-QB has been verified for compartments with a floor area of 100 m2 (or 1000 fl?) or less and a height of the order of 3 m (or 10 ft), and fires of a few Megawatts (see Chapter 7). If FIRM-QB is used to simulate a much bigger fire and/or a fue in a much larger compartment, it is strongly recommended that the user evaluate the predictive capability of the model according to the guidelines in ASTM E 1355. 6.13 ERROR MESSAGES

FIRM-QB has limited error-handling capabilities. When executed fi-om the QBasic environment or fiom DOS, the program will prompt the user if a disk error (disk Ml, disk not ready, etc.) or a printer problem (out of paper, printer off-line, etc.) occurs. A message is displayed explaining the

Error Messages

145

problem, and requesting corrective action. When executed from Windows, the operating system provides this type of error-handling. The program does not check whether input parameter values are physically possible. For example, if the soffit height exceeds the room height, the program will not detect the error and will crash. In other cases, input data errors may lead to unexpected or unphysical results. It is the user's responsibility to check the input data for this type of errors. The FIRM-QB source code can be easily expanded to include tests to verifl that input data are within a valid range.

Evaluation of the Predictive Capability of FIRM-QB

CHAPTER 7

7.1 INTRODUCTION Once a model has been developed, it must be rigorously tested to assure the model yields acceptable results, regardless of its simplicity or complexity. This "testingy7of the model is commonly referred to as "evaluation of the predictive capability of a model." Without this evaluation, the results of a model will be suspect. The subject of this chapter is the evaluation of the predictive capability of FIRM-QB. This evaluation is performed following the guidelines in ASTM E 1355, "Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models" [75]. The evaluation process, according to ASTM E 1355, consists of the following four steps:

1 2 3 4

Defme the scenarios for which the evaluation is to be conducted. Validate the theoretical basis and assumptions used in the model. Verify the mathematical and numerical robustness of the model. Evaluate the mode, i.e., quantify its uncertainty and accuracy.

Step 4 is usually based on a comparison between model output and experimental data, and provides an indirect method for validation (step 2) and verification (step 3) of a model for the scenarios of interest (step 1). It is generally assumed that the model equations are solved correctly, and the terms validation and evaluation are therefore often used interchangeably. Khoudja stated that model validation/evaluation "is the process of determining how appropriate a model is for possible use" [81]. Davies reported that "Model validation is essentially a reviewing or auditing function with a bias towards the user's viewpoint" [82]. Bukowski

148

EVALUATION OF THE PREDICTIVE CAPABILITY OF FIRM-QB

described validation~evaluationas "establishing the statistical accuracy of the predicted quantities" [83]. Peacock et al. refer to the validation/evaluationactivity as "the accuracy assessment process" where, "for complex models, the question to be answered is not does the model agree with experiment, but rather how close does the model come to the experiment" [5 l]. Interestingly, Watts has stated that "no model can be validated in an absolute sense; i.e., a model can never be proved correct, it can only be proved wrong. . . . Thus, in practice, validating a fire model is really a problem of invalidation" [84]. 7.2 PREDICTIVE CAPABILITY OF FIRE MODELS

The four steps in the model evaluation process as described in ASTM E 1355 are discussed in some detail below.

7.2.1 Documentation The f i s t step of the process consists of a review of the model documentation, and a description of the fire scenarios for which the evaluation is to be conducted. Sufficient documentation is necessary to determine whether the model is suitable for the intended use, i.e., the simulation of frre scenarios of interest. ASTM E 176, "Standard Terminology of Fire Standards" [85], defiesfie scenario as "a detailed description of conditions, including environmental, of one or more stages from before ignition to the completion of combustion in an actual fire, or in a full scale simulation." Model documentation prepared according to the guidelines in ASTM E 1472 [74] contains all the elements needed for a proper evaluation.

7.2.2 Validation Ideally, a model should be validated by an independent expert who has not been associated with the development of the model. In practice, often only the model developer has enough incentive to conduct such a tedious and time consuming task. The validation process consists of a detailed review of the theoretical basis of the model, and an assessment of the

Predictive Capability of Fire Models

149

correctness of the assumptions that are made and the approaches that are used.

7.2.3 Verification A model is verified by assessing its mathematical and numerical robustness. Verification can be performed by comparing model output to analflcal solutions of simple problems for which such solutions exist (e.g., steady problems), by checking the computer source code for irregularities and inconsistencies, andlor by investigating the accuracy and convergence of the numerical solutions of the model equations. 7.2.4 Evaluation

A model is evaluated on the basis of a comparison between its output and experimental data for the scenarios of interest.

7.2.4.1 Types of Evaluations A distinction can be made between 3 types of evaluations:

Blind Evaluation. The person performing the evaluation is provided with a basic description of the problem, and must develop appropriate inputs &om the limited information that is provided. A blind evaluation does not only assess the model, but also tests the ability of a user to develop appropriate input data. SpeczJed Evaluation. The person performing the evaluation is provided with a detailed description of all model inputs. A specified calculation is primarily an evaluation of the underlying physics of the model. Open Evaluation. The person performing the evaluation is provided with the most complete information, including experimental data and the results of blind and specified calculations. least one of the three types of evaluations should be performed to compare different models, and to determine which model is most suitable

150

EVALUATION OF THE PREDICTIVE CAPABILITY OF FIRM-QB

for simulating a particular scenario. Working Commission 14 of the Conseil International du Biitiment (CIB W 14) conducted a major program that involved the three types of evaluations to compare more than two dozen models in their ability to simulate a series of single compartment fire tests that were conducted at the Technical Research Center of Finland (VTT) [86]. 7.2.4.2 Sources of Eqerimental Data for Model Evaluation There are 4 major sources of experimental data for model evaluation: 1 Standard tests. Standard test data are useful for the evaluation of models that predict how a material or assembly performs in the test. Only a few standard test procedures involve a room, and most standard test data are therefore not applicable for the evaluation of compartment fire models. ASTM E 603, "Standard Guide for Room Fire Tests" [87] provides general guidelines for conducting full-scale fire experiments, and is perhaps the most useful standard test procedure in terms of generating data suitable for compartment fire model validation. 2 Tests conducted speclJicallyfor thispurpose. Due to the high cost, it is very unusual that full-scale tests are conducted specifically to provide data for evaluation of a particular model. If experiments are conducted, they should be designed judiciously to assure the data produced by the tests affords the best data for comparison. For example, a model that does not calculate layer species concentrations certainly would not require any experiments where these data are measured. 3 Test data in the literature. For obvious reasons, the open literature is by far the most common source of data for model evaluation. 4 Fire experience. Fire risk assessment involves a very large number of deterministic computer fire model runs, and can be used to evaluate the model by comparing the results of the risk assessment to fire statistics. Compartment fire models are usefd tools in the reconstruction of fires, and can be evaluated by checking whether model predictions are consistent with the time line and other pieces of information in the fire investigation report (e.g., see Section 6.11.1).

Predictive Capability of Fire Models

151

7.2.4.3 Accuracy and Uncertainty of Fire Models

Two factors contribute toward the uncertainty and accuracy of fire models when quantified, by comparing model predictions with experimental data: l Model Uncertainty. This is primarily due to the uncertainty of model inputs. Sensitivity analyses are used to identify the critical input parameters, i.e., parameters for which small deviations result in large changes in model output. The critical input parameters must be specified with much greater care than the parameters to which the model is relatively insensitive. A sensitivity analysis of a complex model might involve a very large number of runs to assess the effect of all input parameters individually, and of possible interactions between different parameters. Peacock and Breese reported that a study involving the systematic variation of the input parameters of the Harvard Fire Code would require up to 3 192 computer runs [88]. This is clearly an effectively impossible requirement. Fortunately, special mathematical techniques, such as Latin Hypercube Sampling [89], can be used to drastically reduce the number of computer model runs without losing much information. 2 Experimental Uncertainty. Full-scale fire test data are generally accepted without question. However, such data are subject to uncertainties. Therefore, discrepancies between model predictions and experimental data might be, at least partly, due to measurement errors. There are procedures to determine the precision of standard test methods on the basis of interlaboratory trials or round robins [90,91]. Custom non-standard full-scale fire experiments are usually not repeated for cost reasons. However, the uncertainty of custom test data must be comparable to that of standard full-scale f i e tests. Round robins of standard .111-scale fire test methods have shown that the uncertainty of some measurements may be as high as %30%[92]. 7.2.4.4 Comparing Model Ou@ut to Experimental Data

There are many problems in comparing the results from fire model simulations to data fiom full-scale fire experiments. Some of the problems are due to the differences between the form of the recorded experimental

data and the form needed for comparison with model predictions. For zone models, the compartment is divided into two distinct zones, a lower cool layer and a hot upper layer. In reality, there is no such clear and sharp change distinguishing the lower and upper layers. A typical temperature profile inside a f i e compartment is shown in Figure 7-1. Also shown in Figure 7-1 is the corresponding idealized temperature distribution for a two-zone situation. The difference between actual and ideal is obvious. To use experimental data for comparison with zone model results requires that the experimental data be cast into an idealized form, i.e., isothermal upper and lower layers separated by a sharp interface. This is commonly accomplished by identifying the ideal interface level, and then simply averaging the temperatures within the hot layer based on thermocouple data. Thus the problem is one of identifying the ideal interface level. A common procedure to determine the location of the layer interface on the basis of vertical temperature profile measurements was developed by Cooper et al., and is referred to as the NO/o rule [93]. According to this rule, the interface is located at a height at which the gas temperature rise above ambient is some percent of the temperature rise (10, 15, or 20 percent, for example) of the top-most thermocouple in the test room. The dependence on the selection of the interface on the data used for comparison is evident. A lower value for the interface will likely lead to a lower hot-layer

l

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l

-

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-

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P

1.5-

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U-

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3 ........................................................... - 1 .o C* Neutral plane height t

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.

100

I

150

.

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200

Temperature

.

I

250

.

I

300

.

0.0 350

(OC)

FIGURE 7-1. Typical two-layer and measured room temperature profiles

Predictive Capability of FIRM-QB

153

temperature due to averaging in the relatively cooler temperatures of the lower portions of the hot layer. Intuitively, the opposite is true for the selection of a higher (evaluation) interface level. This effect must be considered when comparing experimental and model results. A more detailed discussion on the subject of transforming room fire test data so that they are suitable for comparison with results fiom zone model shulations can be found in Reference [94]. Perhaps the most common method for comparing experimental data and model results is through graphical methods. Two variables are plotted against each other for both the experimental data and model predictions. Graphs of layer temperatures, interface location, and vent flows as a function of time are the most widely used. Since it is difficult to quantify the agreement between two curves, evaluations based on this type of comparison are usually subjective. For graphs plotting values against time, a common technique is that of time shifting. Time shifting refers to the sliding of data along the time axis to get key events to match, thus providing a reference point for comparing the entire graph. For example, an experimental procedure that utilizes a cigarette as a smoldering ignition source may not result in flaming ignition for extended time periods [72]. The period of smoldering can be ignored and the comparison between model and experiment can be initiated at a reference heat release rate, i.e., one indicative of flaming ignition of the fuel being modeled. Examples of data that have been time-shifted for comparison between data sets are provided by Figures 4-9 and 4-10 in Section 4.5.2.

7.3 PREDICTIVE CAPABILITY OF FIRM-QB 7.3.1 Documentation The fire scenario simulated by FIRM-QB is that of a single item burning in a compartment with a vent in a vertical wall. The fire is specified by the user in the form of a heat release rate vs. time curve. FIRM-QB predicts the consequences of the fire in t e r n of the average upper layer temperature, layer interface height, and mass flows through the vent. The documentation for FIRM-QB was developed according to the

154

EVALUATION OF THE PREDICTIVE CAPABILITY OF FIRM-QB

guidelines of ASTM E 1472 1741, and can be found in Chapters 5 and 6, and in Appendices C and D.

7.3.2 Validation Validation of FIRM-QB by an independent expert is not provided. The reader is encouraged to validate the model by assessing the completeness of the documentation, by reviewing the scientific basis for the model equations, and by checking constants and default values that are used by the model.

7.3.3 Verification The numerical algorithms that are used to solve the non-linear algebraic and ordinary differential equations are discussed and verified in Appendices B and D. 7.3.4 Evaluation

7.3.4.1 Type of Evaluation

Since the evaluation of the predictive capability of FIRM-QB in this book is provided by the developer of the model, it is by definition a speclJied evaluation. 7.3.4.2 Eqerimental Data for Evaluation of FIRM-QB

Unfortunately, funds for full-scale experiments to evaluate FIRM-QB were not in the author's or publisher's budget for the production of this book. Suitable well-documented compartment fne test data were obtained fiom the literature to evaluate the predictive capability of FIRM-QB.

Predictive Capability of FIRM-QB

155

7.3.4.3 Accuracy and Uncertainty of FIRM-QB

A limited sensitivity analysis was conducted to illustrate the uncertainty of the FIRM-QB model. The example in Section 6.11.2 of a one-half size cotton-covered sofa in a hospital waiting area was selected as the base case for this analysis. This case was chosen because flashover was approached, but not reached. A slight change in the right direction of a critical parameter is expected to tip the scale and result in flashover, while changes in other parameters will hardly affect the predictions. FIRMQB simulations were performed with one input parameter increased or decreased by 20% from the base case value, and the remaining values unchanged from the base case. Table 7-1 shows the effect of the changes on the occurrence of flashover. The reader is encouraged to review the complete results of the simulations. The output file names (without the .FOF extension) for the different runs are given in Table 7-1. These fdes are copied to the data directory (or folder) during the installation process (see Appendix C). The model seems to be insensitive to changes in room area and he1 height. Reductions of 20% in room height, soffit height, vent width, or total heat loss fraction all result in flashover. Increased radiative heat losses, or a higher heat release rate also result in flashover. Table 7-1. Effect of Input Parameter Changes on the Prediction of Flashover Parameter

-20%

" time to flashover (S)

flashover did not occur

t,,"

FileName

+20%

t,,

FileName

156

EVALUATION OF THE PREDICTIVE CAPABILIlY OF FIRM-Q9

FIRM-QB appears to be most sensitive to the soffit height, because a 20% decrease of 2,results in the shortest time to flashover (254 S). A lower soffit height, with the remaining input parameters unchanged, results in a more rapid descent of the neutral plane and layer interface, and, therefore, reduced entrainment and a higher hot layer temperature. A 20% increase of 2, has a similar effect, and leads to a slightly delayed flashover. As expected, FIRM-QB is also very sensitive to a reduction of the total heat loss fkaction, and to an increase in the heat release rate. These changes have a similar effect, and result in a higher rate of energy transfer to the hot layer. A smaller vent width results in a slight reduction of the vent flows and a corresponding increase of the hot layer temperature. The latter is relatively small, but sufficient to create flashover conditions when the heat release rate of the fire is near its peak. A lower ceiling height has a very similar effect. Because the distance between the soffit and the ceiling is very small, the duration of flow regimes 1 and 2 is very short. This accelerates the descent of the layer interface, and the corresponding reduction of entrainment and hot layer temperature rise. It is perhaps surprising that a 20% increase of L, results in flashover. Increased radiative heat losses, with the remaining input parameters unchanged, result in reduced entrainment into the fie, and a higher hot layer temperature. In practice, radiative heat losses and total heat losses are coupled. Higher radiative losses result in higher total losses, and, consequently, lower temperatures. 7.3.5 Comparison of FIRM-QB Predictions with Experimental Data

In this section, a comparison is presented between FIRM-QB predictions and experimental data tiom two series of room tests that were carefdly conducted at the National Institute of Standards and Technology (NIST, previously the National Bureau of Standards or M S ) . 7.3.5.1 Single Room with Furniture

The first data set was reported in a paper by Peacock et al. in the Journal of Research of the National Institute of Stamkwds and Technology [95].This paper provides an extensive discussion on the subject of room

Predictive Capability of FIRM-QB

157

fire testing and accuracy assessment of room fire models. Five sets of experimental data, which can be used to evaluate the predictive capability of zone-based fire models, are described in detail. The data are available fiom MST on a CD-ROM as "Fire Data Management System" (FDMS) ASCII data files [96]. The first set, referred to as "Single Room with Furniture" was chosen to evaluate FIRM-QB, primarily because the test scenario is identical to that simulated by the model, i.e., a single furniture item in a room of fixed size but with varying vent sizes and shapes. The upholstered furniture items were tested previously in the furnitwe calorimeter. The description of the tests in the following paragraphs is largely taken fiom the aforementioned journal article.

Test Room. An experimental room, 2.26 X 3.94 X 2.3 l-m, with a window opening in a narrow wall was constructed inside the large-scale fire test facility. The dimensions of the window openings for the various tests are given in Table 7-2. The sofit depth of the window opening was the same in all cases. For tests 1 and 2, the opening height (and therefore the ventilation parameter AV=) only was varied. For test 6, the same A ~ J H , was retained as in test 2, but the shape of the opening was changed. Test 5 resembled test 6, except that the fuel was an armchair instead of a loveseat. Thus, for specimen type, ventilation factor, and opening aspect ratio, a pair of tests each was provided where these variables were singly varied, the other two being held constant. The walls and ceiling materials in the room were 16 mm thick Type X gypsum wallboard, fiured out on steel studs and joists. Floor construction was normal weight concrete. The test room was conditioned before testing by gas burner fires, where the paper facing was burned off the gypsum wallboard, and the surface moisture driven off The room was allowed to cool overnight and between tests. The room was equipped with an instrumented exhaust collection system outside the window opening that can handle fires up to 7 MW size. Table 7-2. Chairs and Vent Sizes for NIST Single Room Tests with Furniture

Test #

Chair

5 (m)

5

armchair (F21)

0.00

Zt (m) Hv(m) W , (m)

2.00

2.00

1.29

AVJH(mm)

3.65

158

EVALUATION OF THE PREDICTIVE CAPABILITY OF FIRM-QB

Instrumentation. Two mays of thermocouples, each consisting of 15 vertically spaced thermocouples, were installed in the room. The top and bottom thermocouples were at the ceiling and on the floor, respectively. In addition, a load cell for mass loss and a Gardon heat flux meter for measuring radiation to the floor were installed on the centerline of the room. Fifteen closely spaced velocity probes, with companion thermocouples, were located evenly spaced along the vertical centerline to facilitate accurate measurements of mass and heat flow through the vent. Initial calibrations with gas burner flows showed adequate agreement, to within 10 to 15 percent, of window inflows and outflows, after an initial transient period of about 30 S. Similarly, during the final, smoldering stages of the furniture fires, a reasonable mass balance was obtained. During peak burning periods in the upholstered furniture tests, such agreement, however, was not obtained. Two gas samphg probes were also located along the upper part of the opening centerline. The exhaust system had an array of velocity probes and thermocouples, together with 0,, CO,, and CO measurements to permit heat release to be determined according to the oxygen consumption technique [65,66]. Experimental Conditions. The test furniture for four of the six tests is listed in Table 7-2, and included a 28.3 kg armchair (F21) and a similar 40.0 kg loveseat (F3 1). A description of these items is provided in Table 4-4. A single piece of test furniture and the igniting wastebasket were the only combustibles in the test room. The furniture items were tested previously in the furniture calorimeter (see Section 4.4.4). The tests in the furniture calorimeter [64] made use of a gas burner simulating a wastebasket fire as the ignition source. Because of practical difficulties in installing that burner in the test room, actual wastebasket ignition was used. This involved a small polyethylene wastebasket filled with 12 polyethylene-coated paper milk cartons. Six cartons were placed upright in the wastebasket, while six were tom into six pieces and dropped inside. The total mass of the wastebasket was 285 g, while the 12 cartons together weighed 390 g, for a total mass of 675 g. The gross heat of combustion was measured to be 46,320 kT/kg for the wastebasket and 20,260 W/kg for the cartons, representing 2 1.1 MJ in all. Using an estimated correction, this gives a heat content of 19.7 MJ, based on the net heat of combustion. To characterize this ignition source, a constant mass loss rate of 1.8 g/s (equivalent to 52.5 kW) was assumed for the fxst 200 S.The mass loss rate of the ignition source was considered negligible thereafter.

Predictive Capability of FIRM-QB

159

Comparison with FIRMQB Predictions. Two sets of FIRM-QB simulations were performed. The first set used the heat release rate curves that were measured in the room fire tests. The second set used the triangular approximations described in Section 4.4.4.1. However, the triangular heat release rate approximations were shifted in time so that the peak of the triangle occurs at the same time as the maximum heat release rate in the tests. The default value of 35% was used for the radiative heat loss fraction. The simulations were performed with L, = 0.606, as calculated by FIRM-QB for a moderately rough ceiling. The names of the fue files and output data files for the different runs are given in Table 7-3. Figures 7-2, 7-6, 7-10, and 7-14 provide a comparison between the measured and predicted hot layer temperatures. The measured temperatures are based on an average of the readings of the thermocouples in one of the vertical arrays that are located between the layer interface and the ceiling. The NO! rule by Cooper et al. was used to define the location of the layer interface [93]. The predicted maximum temperatures are higher than the measured peaks. This can be explained by the fact that during the peak burning period flames emerged through the vent, and part of the heat was released outside the compartment. The measurements in the exhaust duct account for all the heat that is released, including that from combustion outside the compartment. FIRM-QB assumes that the heat release rate specified by the user is generated inside the compartment, and only applies a reduction to account for oxygen starvation. Thus, FIRM-QB will overpredict the hot layer temperature if part of the heat is released outside the compartment. Figures 7-3,7-7,7-11, and 7-15 show a comparison of predicted and measured layer interface heights. The predictions agree quite Table 7-3. Fire and Output Files for Single Room with Furniture Tests Measured Heat Release Rate --

Test #

Fire Filea

Outnut Fileb

B CH7-B04 CH7-B04 " Fire file names have extension .FR Output files have extension .FOF

Triangular Heat Release Rate Fire File"

Output Fileb

CH7-B04T

CH7-B04T

Single Room with Furniture: Test # l (CH7-BO1) 1

'

"

'

I

"

"

I

"

"

-----

............. FIRM-Q (Triangle HRR)

0

300

600 Time

900

1200

(S)

FIGURE 7-2. Upper layer temperature measurements and predictions for test 1

Single Room with Furniture: Test # l (CH7-€301)

----- FIRM-Q

............. FIRM-Q

(Measured HRR) (Triangle HRR)

FIGURE 7-3. Layer interface height measurements and predictions for test 1

Single Room with Furniture: Test #l(CH7-BO1)

FIGURE 7-4. Heat release rate curves for test 1

Single Room with Furniture: Test # l (CH7-BO1)

0

300

600 Time (S)

900

1200

FIGURE 7-5, Upper layer vent flow measurements and predictions for test 1

Single Room with Furniture: Test #2 (CH~-B02)

1-

Experiment

----- FIRM-Q (Measured HRR)

0

300

.........

.,,.

FIRM-Q (Triangle HRR)

600 Time (S)

900

11

1200

FIGURE 7-6. Upper layer temperature measurements and predictions for test 2

Single Room with Furniture: Test #2 (CH~-B02)

0

300

600 Time (S)

900

1200

FIGURE 7-7. Layer interface height measurements and predictions for test 2

162

Single Room w i t h Furniture: Test #2 (CH7-602)

0

300

600 Time (S)

900

1200

FIGURE 7-8. Heat release rate curves for test 2

Single Room w i t h Furniture: Test

0

300

600 Time (S)

#2 (CH7-B02)

900

1200

FIGURE 7-9. Upper layer vent flow measurements and predictions for test 2

163

Single Room with Furniture: Test #5 (CH7-B03)

0

300

600 Time

900

1200

(S)

F'IGtTRE 7-10. Upper layer temperature measurements and predictions for test 5

0

300

600 Time

900

1200

(S)

FIGURE 7-11. Layer interface height measurements and predictions for test 5

Single Room with Furniture: Test #5 (CH7-€303)

Time

(S)

FIGURE 7-12. Heat release rate curves for test 5

Single Room with Furniture: Test #5 (CH7-B03)

300

600 Time (S)

900

1200

FIGURE 7-13. Upper layer vent flow measurements and predictions for test 5

Single Room with Furniture: Test #6 (CH7-004)

0

300

600 Time

900

1200

(S)

FIGURE 7-14. Upper layer temperature measurements and predictions for test 6

Single Room with Furniture: Test #6 (Ci47-804)

Experiment FIRM-Q (Measured HRR) ,,,.......... FIRM-Q (Triangle HRR)

FIGURE 7-15. Layer interface height measurements and predictions for test 6

Single Room with Furniture: Test #6 (CH7-B04)

FIGURE 7-16. Heat release rate curves for test 6

Single Room with Furniture: Test #6 (CH7-B04)

1.2 1.0

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FIGURE 7-17. Upper layer vent flow measurements and predictions for test 6

well with the measurements, except during the peak burning period, when the measured interface height drops down temporarily to 0.5 m (or less) from the floor. Figures 7-4, 7-8, 7-12, and 7-16 provide a comparison between the measured heat release rates, and those used by the model. There is a slight reduction of the heat release rate due to oxygen starvation around the peak burning rate in tests 2 and 6. The triangular approximation is quite good in test 1, but appears to be rather crude for the remaining tests. However, the model does not seem to be very sensitive to the exact shape of the heat release rate curve, and the triangular model seems to be adequate for engineering analyses. The calculated upper layer vent flows are shown in Figures 7-5,7-9,7- 13, and 7- 17. The measured flows are not shown because Peacock et al. concluded on the basis of the tests' data that the arrangement of velocity probes spaced along the centerline of the window opening leads to serious errors in computed mass flows.

7.3.5.2 Steady Vent Flow Experiments. The second data set is from a NIST report detailing a study of fre-induced vent flows measured during m-scale experiments. The report is titled "Fire Induced Flows through Room Openings- Flow Coefficients" [49]. The data presented in this report allow for a twofold comparison of model versus experiment. Firstly, measurements of the temperature and location of the hot layer during the experiments can be compared to the results presented by the model simulation. Secondly, the report provided detailed data regarding the vent flows recorded during the steady-state regime of the experiments. These data will be compared to the predictions of FIRM-QB.

Test Room. The experiments were conducted in the test room depicted in Figure 7- 18. The dimensions of the test room were 2.8 X 2.8 X 2.13-m. The vent (opening) configurations that were used for the various tests are shown in Figure 7-19. The ceiling and walls of the test room were lined with ceramic fiber insulation. The thickness of the linings were not provided in the report documenting the experiments, nor was a description of the floor material included.

Predictive Capability of FIRM-QB

169

MOVABLE B I m c T I o N A 1 ,VUOCRY PROBES AND THERMOCOUPLES ASPIRATED THERMOCOUPLE

FIGURE 7-18. Set-up for steady vent flow experiments

Instrumentation.An array of aspirated thermocouples was located in one of the front corners to measure the vertical gas temperature profile inside the room. A vertical array of thermocouples and bi-directional probes was positioned in the centerline of the vent to determine temperatures and velocities of gas flows into and out from the compartment. Experimental Conditions. A large number of experiments were conducted to evaluate the effect of f i e size, fre location, and opening configuration on fie-induced vent flows. The fire was a circular (0.3 m diameter) gas burner, with methane supplied at a constant rate. The porous burner surface in most of the experiments was flush with the floor. A few experiments were conducted with the burner surface raised 0.3 m above the floor. Heat release rates were either 3 1.6 kW, 62.9 kW, 105.3 kW, or 158.0 kW, based on the fbel consumed. The majority of the experiments were conducted with the burner in the center of the room, but some tests were repeated with the burner in a different location. Because the room was very well insulated, steady conditions were reached in a few minutes after the start of a test. The test duration was 10 minutes.

6/6

7/6

8/6

DOOR OPENINGS

WINDOW OPENINGS FIGURE 7-19. Vent configurations for steady vent flow experiments

170

Predictive Capability of FIRM-QB

171

Comparisonwith FIRM-QB Predictions. The FIRM-QB model was used to simulate the experiments with the bumer in the center of the room, and the burner surface flush with the floor. The output and frre file names and some information about the test conditions are given in Table 7-4. A value of 0.25 was used for L, since methane has a characteristically low radiative heat loss fraction. Since the walls and ceiling of the compartment were very well insulated to obtain steady conditions as quickly as possible, Table 7-4. Data Files and Test Conditions for Steady Vent Flow Tests Test P Output Fileb Fire Filec

Vent Configuration

Q

(kW)

216 Door 316 Door 416 Door 416 Door 516 Door 616 Door 616 Door 616 Door 616 Door 7/6 Door 816 Door

Full Window 213 Window 213 Window 113 Window 616 Door 616 Door 616 Door " Numbers are for reference purposes, and are not in original report Fire file names have extension .FIR Output files have extension .FOF

it was expected that the total heat losses were very low. Therefore, instead of using a generic value, L, was estimated for each test on the basis of the steady-state energy conservation equation for the compartment (Equation 7-l),and measured gas temperatures and vent flows reported in Reference [49]. The data and resulting total heat loss fractions are given in Table 7-5.The steady-state energy conservation equation is as follows

Table 7-5. Selected Test Data and Calculated L, values

Predictive Capability of FIRM-QB

173

where c, is 1.004 kT/kg-K. Table 7-6 provides a comparison between the measured and calculated steady-statevalues of interface height, upper layer temperature rise over ambient, and upper layer vent flow. The simulation of test 15 was terminated at 11 seconds, when the layer interface dropped below the sill of the vent. Table 7-6 reveals that the predicted interface height is close to the upper limit of the measured range. Predicted upper layer temperatures are significantly higher than the measured temperatures (up to 99OC or 50%), while the calculated vent flows are consistently lower than the measured flows (up to 0.26 kg/s or 40%). Table 7-6. Comparison of Vent Flow Test Data and FIRM-QB Predictions

FIRM-QB Predictions

Measurements Test #

& (m)

T,- T,('C)

m,,(Ws)

Zi (m)

T,- T, ('C)

% (k@)

174

EVALUATION OF THE PREDICTIVE CAPABILITY OF FIRM-QB

Steckler et al. observed that the flame was pushed over by the flow of air entering the room through the lower part of the vent. This phenomenon was discussed in more detail by Quintiere et al. in Reference [97]. In this paper, average flame angle measurements based on video recordings are presented for some of the tests conducted by Steckler et al. Quintiere et al. suggested increasing the vertical distance between the fuel surface and the layer interface in Zukoski's equation to bring the calculated entrainment rates in better agreement with the vent flow measurements. The PlumeFlow subprogrm in FIRM-QB was modified to account for the flame and plume angle. The modified source code is shown in Figure 7-20. The distance between the kel surface and the layer interface is simply divided by the sine of the flame angle. If the centerline of the tilted flame hits a wall before it reaches the layer interface, the increased entrainment height is set equal to the distance between the fuel surface and the w d . The variable Theta is the flame angle, which was added to the list of global variables that are shared between the main program and all subprograms through a COMMON SHARED statement in the main program. A few lines were added to the InputData subprogram to allow the user to input the flame angle fiom the keyboard. The measured flame angles reported in Reference [97], the flame angle values used for the calculations with the modified FIRM-QB program, and the results of the calculations are given in Table 7-7. The layer interface quickly dropped below the sill in tests 13, 14, and 15, leading to termination of the modified FIRM-QB program. A comparison of the calculated results in Table 7-7 and the measurements in Table 7-6 shows that the inclusion of the flame angle effect greatly improved agreement between FIRM-QB predictions and the experimental data. Figures 7-2 1, 7-22, and 7-23 provide the same comparison in graphical form. 7.4 CONCLUSIONS

The comparisons between FIRM-QB simulations and experimental room fire test data presented in this and the previous chapter should give the reader a good feel for the predictive capability of the model. Whether FIRM-QB is suitable for a particular use, and whether its accuracy is suficient for a certain application still must be determined by the user.

I

FUNCTION PlumeFlow (Q, Z i ) Calculates plume mass flow based on Zukoskils equation Parameter values passed to function Q : heat release rate of the fire (kW) Zi : interface height (m) Value returned by function PlumeFlow : plume flow (kg/s) Global variables used in function : radiative fraction of heat losses ( - ) Lr Theta : flame angle (rad) Zf : height of the base of the flame (m) Global constants used in function K : constant in Zukoskils plume flow equation Change to FIRM-QB:

the following four lines were added

DeltaZi = (Zi - Zf) / SIN(Theta) I E COS(Theta) * DeltaZi > S Q R ( A ) / 2 THEN DehtaZi = S Q R ( A / 4 + (Zi Zf) 2) END I F

-

I

Zukoski's plume flow equation (Equation 2.12)

l

'

l'

( ( 1 - Lr) IFme Zi= KZf* THEN ELSE me = 0 END IF

* Q * DeltaZi

A

5)

A

(1 / 3 )

Entrainment-controlled burning (Equation 4.28)

IF me > 55 * K

I

A

me = 55 END IF

* K

PlumeFlow

=

A

1.5 * (1 - Lr) 1.5 * ( 1 - L r )

A

A

.5 * DeltaZi .5 * DeltaZi

A

A

2.5 THEN 2.5

me

END FUNCTION

FIGURE 7-20. Modified version of Zukoski's plume flow model for a tilted plume

One of the limitations of FIRM-QB is due to the fact that the lower layer is assumed to be at ambient temperature. However, this results in higher, and therefore conservative predictions of the hot layer temperature. A major strength of FIRM-QB is that the source code is provided and can easily be modified to address a particular circumstance or problem, as was illustrated in Section 7.3.5.2. Table 7-7. FIRM-QB Predictions with Tilted Flames Test #

Data File'

Measured 0 (")

" Output files have extension .FOF

Used 0 (")

Z (m)

2'"-T, (OC)

m, (Ws)

Averoge meosured Zi (m)

FIGURE 7-21. Calculated vs. measured Zi for steady vent flow tests 250..

-

;---.

I

.

I

.

.

I

v,....

............ Line of perfect ogreement

h

P

200

0

-

W

'

l-

o&00

150 3

ZI

0

8

O

.

.."a

..:'

,,$..,'

,./

. '

1000

0 0

8

.,. . .

8&.....a

-U Q,

0

50 -

m,. :..' ,......"

....."'

0 Without flame angle correction

-

With flame angle correction

O ; . . ~ . ; . . . l s . . . l . . . l m . m m l . , ~ m 0 50 100 150 200 250 Meosured T,,-To ("C)

FIGURE 7-22. Calculated vs. measured T, - T,for steady vent flow tests

-

Line of perfect agreement

.............

;.m"

.a ,.""

,..."'

.. "' ..

*

0, 0

"'

.'i 0

0

@

0 ...'

.aa. m

,go

,,. 0'

-

0

0 Without flame angle correction

With flame angle correction I

I

I

I

I

I

I

Measured mu (kg/s)

FIGURE 7-23. Calculated vs. measured m, for steady vent flow tests

-

Conclusion

CHAPTER 8

Congratulations! If you made it to this chapter (without too much cheating), you should have a fairly detailed understanding of the inner workings of compartment zone fue models. You are now ready to apply your newly acquired knowledge in your professional activities. The tools provided in this book will be usell in the solution of many practical problems that face fze scientists and f r e protection engineers. However, chances are that you will soon need a more sophisticated set of fire modeling tools to address increasingly complex problems. One option is to customize FIRM-QB by adding new features so that the resulting enhanced model is capable of simulating the scenario and fire phenomena of interest. The flame angle correction discussed in Section 7.3.S .2 provides an example of this approach. It must be stressed that any changes must be clearly documented by adding clarifying comment statements to the source code, and by providing an extensive discussion of the changes in any report or publication of the model calculations. This discussion must be detailed enough so that others can reproduce the results. It is important that significant changes to the model be validated and verified, and that the predictive capability of the enhanced model be re-evaluated. Chapter 7 illustrates how the evaluation should be conducted. A second option is to switch to a more sophisticated model. In this case, the model user takes advantage of existing knowledge and avoids duplication of effort, but gives up control over the approach that is used. Often this second option is preferred, because it is more cost-effective and less time-consuming. Readers who want to pursue this option are strongly advised to obtain NIST Special Publication 921, "A User's Guide for FAST: Engineering Tools for Estimating Fire Spread and Smoke Transport'' fiom the Building and Fire Research Laboratory (BFRL) at the National Institute of Standards and Technology (NIST) in Gaithersburg, MD. This publication includes a CD-ROM with the latest versions of the

180

CONCLUSION

FAST and FASTLITE programs, and older fire modeling software such as FIRST, FPETool, and LAVENT Alternatively, the same programs (as well as data, publications, and other bits of information that may be of interest to the fire modeler) can also be downloaded fiom the MST BFRL web site OJRL: http ://fiie.nist.gov/). NIST also developed a CFD model to predict smoke and air flow movement caused by fire, wind, ventilation systems, etc. This model is referred to as the FIRE DYNAMICS SIMULATOR (FDS). A separate program, called SMOKEVIEW, visualizes the predictions generated by FDS. These programs (as well as a user's guide and example data files) can be downloaded fiom the aforementioned MST BFRL web site. SMARTFIRE is another popular CFD-based fire model. The SMARTFIRE program was developed by the Fire Safety Engineering Group at the University of Greenwich in the UK. SMARTFIRE is user friendly, and appears to be an excellent educational tool for the novice CFD fire modeler. It is continuously being improved and expanded. For the latest information on SMARTFIRE, it is recommended the reader consult the FSEG web site OJRL: http://fseg.gre.ac.uk/). It is hoped that the reader, who might have avoided using models in the past because of the potentially intimidating mathematical equations and computer programs, will start to appreciate and enjoy mathematical fire modeling as a result of this book.

APPENDIX A

Conversion Factors and Constants Table A-l. Conversion Factors Acceleration 1 ft/s2= 0.3048 m/$ 1 d s 2= 3.2808 ft/s2 Area 1 ff = 0.09290 m2 1 m2= 10.764 ff Density 1 l b / e = 16.019 kg/m3 1 kg/m3= 0.06243 l b / e Dzflusivity (heat dzflwzvity and kinematic viscosity) 1 ffls = 0.09290 m2/s 1 m2/s= 10.764 ft2h Energy 1 Btu = 1.OS0 kJ = 1.O%O kNm 1 kJ = 0.9478 Btu Heat flux 1 Btu/s*ft2= 11.353kW/m2 1 kw/m2= 0.08808 Btu/s*ff Heat of combustion 1 Btullb = 2.3259 kJ/kg l kJAg = 0.4299 Btuflb Heat transfer coeflcient 1 Btu~h-fl?*~F = 5.6781 W/m2K 1 W/m2*K= 0.176 1 Btu/h.fI?*OF Length 1 A = 0.3048 m 1 m = 3.2808 R Mass 1 lb = 0.4536 kg 1 kg = 2.2046 lb Mass ftwc 1 lb/ft% = 4.8825 kg/m2*s 1 kg/m2.s = 0.2048 lblft2.s

l81

Table A-l. Conversion Factors (Continued) Pressure 1 in. H20= 249 Pa 1 psi = 6894.8 Pa = 6894.8 N/m2 1 bar = 105Pa = 14.504 psi 1 atm = 1.013bar = 14.692 psi Power 1 Btu/h = 0.293 1 W = 0.2931 J/s 1 W = 1 J/s = 3.4122 Btu/h Specrfic heat 1 Btu/lb*"F= 4.1867 kJ/kgK 1 kJ/kg*K= 0.2389 Btu/lb."F Temperature T (OF) = 32 + 1.8 X I'("C) T ("R) = 460 + T (OF) T ("C) = [T ("F) - 32]/1.8 T (K) = 273.15 + T("C) Temperature dzflerence AT(OF)= 1.8 X AT(OC)= 1.8 X AT@) AT ("C) = AT (K) = AT ("F)/1.8 T h e m 1 conductivity 1 Btu/h.fk°F = 1.7303 W/mK 1 W1rn.K = 0.5779 Btu/h.fk°F Velocity 1 ft/s = 0.3048 m/s 1 m/s = 3.2808 ft/s Viscosity 1 1bIft.s= 1.4882 Pass = 14.882 P 1 kPa.s = 10 P = 0.6720 lb/R-S Volume 1 ft3 = 0.02832 m3 1 m3 = 35.315 ft3 Table A-2. Constants Avogadro 'S number n = 6.0222-1023molecules per mole Acceleration of gravity g = 32.174 Ws2= 9.8066 m/s2 Boltzmann constant a = 0. 1714*104~ t u I h . f f - = " ~5.6697-1 ~ 0-8w / ~ ~ * K ~ Speed of light in vacuum c, = 9.8357.108ftjs = 2.9979*108m/s Universal gas constant R = 8314.4 J h o 1 . K

APPENDIX B

Review of Fundamentals of Engineering for Fire Modeling B.l FLUID MECHANICS Fluid mechanics is the branch of physical science dealing with the behavior of fluids under the action of force. A fluid is either a liquid or a gas, and can be distinguished from a solid because of a fluid's inability to resist shear forces. The shear force on a body is the component of the total force tangential to the surface of the body. The subject of fluid mechanics consists of two parts: fluid statics, and fluid dynamics. The former is concerned with the equilibrium of fluids at rest. The latter involves the study of fluids in motion, and the forces that produce this motion.

B.1.1 Properties at a Point The following properties describe the state of a fluid, and may vary from point to point.

Density, p. The density of a fluid at a point is equal to the mass per unit volume at that point. Density is expressed in kilograms per cubic meter or kg/m3(S.I. unit), and in pounds per cubic foot or lb/ft' (U.S. engineering unit). Pressure, P. The pressure at a point is equal to the normal force at that point divided by the area upon which it acts. The pressure at a point in static equilibrium is the same in all directions. Pressure is expressed in Pascals or Pa (S.I. unit), and in pounds per square inch or psi (U.S. engineering unit). One Pascal is equal to 1 Newton per square meter, or 1 Pa= 1 ~ / r n ~ . Temperature, T. The temperature at a point characterizes the thermal state of the fluid at that point. Absolute temperature is proportional to 183

184

APPENDIX B

the mean kinetic energy of the translational motion of the fluid molecules, and is expressed in Kelvin or K (S.I. unit), and in degrees Rankine or "R (US. engineering unit). Practical variants of the absolute temperature scales are the Centigrade ("C) and Fahrenheit ("F) scales. Equations to convert temperature values between the different scales are given in Table A-l of Appendix A. Density, pressure, and temperature are related by the equation of state. For all practical purposes, liquids can be considered incompressible, i.e., density and temperature are related but independent of pressure. The equation of state for an ideal gas takes the following form

where

R M

= =

universal gas constant (83 14.4 Jkmol-K) molecular mass of the gas (kgh.101)

An ideal gas is a hypothetical gaseous substance for which the intermolecular forces and the volume occupied by the molecules are negligible. Fortunately, Equation (B.l) is also valid for real gases at low to moderate pressures, provided the absolute temperature is at least twice the critical temperature. As will be demonstrated in Section B.2.1, deviations from the ideal gas law are minor for gases at pressures and temperatures in the range that the f i e modeler is concerned with. Density, pressure, and temperature describe the state of a fluid at a point. Additional properties are needed to describe the flow of a fluid in motion. These flow properties are the components of the velocity vector. In a steady flow field, fluid and flow properties vary as a fimction of location only. If the flow is unsteady, properties vary with time as well.

B.1.2 Fluid Statics As mentioned before, the pressure at a point is identical in all directions. This is referred to as Pascal 'S law,and is a consequence of the

Review of Fundamentals of Engineering for Fire Modeling

185

absence of shear stresses. In a fluid at rest under gravity, the pressure is uniform over any horizontal cross section. The pressure difference between two points, respectively at heights Z, and Z , is equal to the weight of a fluid column with unit cross-sectional area and a height Z,- 2,.

where

AP

=

pressure difference (Pa)

P(2)= pressure at height Z (Pa)

Z p g

= = =

height (m) density (kg/m3) acceleration of gravity (9.8066 m/s2)

This is referred to as the hydrostatic pressure difference. The difference of hydrostatic pressures inside and outside the f i e room dnves the flow of gases through a vertical vent (see Section 2.6.2.2). An object that is submerged in a fluid with a different density, is subjected to a force due to hydrostatic pressure differences. If the density of the object is greater than that of the fluid, the object will sink; if the fluid density is higher, the object will rise. This phenomenon is referred to as buoyancy. Buoyant forces cause hot fue gases to rise.

B.1.3 Fluid Dynamics To determine how the fluid and flow properties change as a function of position and time in a given region, a set of equations must be solved that express the conservation of mass, momentum, and energy. The equation that results from applying the fundamental physical law of mass conservation is called the continuity equation. The conservation equations of momentum are derived from Newton's second law of motion. The energy conservation equation is based on the first law of thermodynamics, and will be discussed in more detail in Section B.2.2. There are five conservation equations for a three-dimensional flow field: one for mass, three for momentum (X, y, and z direction), and one for energy. Because there are six variables (density, pressure, temperature, and

the three velocity vector components), an additional relationship between the fluid and/or flow properties is needed to close the system of equations. This relationship is provided by the equation of state. A useful concept in the description of a fluid in motion is the streamline. It is defined as a line that is tangent to the velocity vector at each of its points.

Although a fluid at rest is unable to sustain shear forces, this is not the case with a fluid in motion. Furthermore, it has been observed experimentally that a moving fluid is at rest immediately adjacent to a stationary solid boundary. Therefore, there must be a region close to the solid boundary where the velocity changes from zero to the main stream value. Figure B-l shows a typical velocity profile in this transition region, which is referred to as the boundary layer. The shear stress at a point for most fluids of practical interest is proportional to the rate of deformation due to shear forces at that point:

I

Velocity v

/

I

Free S t r e a m

Layer

Solid Boundary

FIGURE B-l. Boundary layer flow

Review of Fundamentals of Engineering for Fire Modeling

187

where 'G

p v y

= = =

=

shear stress (Pa) viscosity (Pa-S) velocity (mls) distance from the solid boundary (m)

Fluids for which Equation (B.3) is valid are called Newtonian. The viscosity, p, is a physical property of the fluid. It is related to the transverse transfer of flow momentum due to molecular motion. Viscosity is therefore a function of temperature, composition, and pressure of the fluid. The ratio of viscosity to density occurs often in engineering problems. This ratio, pip, is referred to as the kinematic viscosity, v. To distinguish p from v, the former is called the dynamic viscosity. The units of p are Pa-S(S.I. unit) and lb/ft=s(U.S. engineering unit). The kinematic viscosity, v, is expressed in m2/s(S.1. unit) and ft2/s (U.S. engineering unit). B.1.3.2 Laminar and Turbulent Flow It has been observed experimentally that there are two very different types of fluid motion. Under certain conditions, the flow will be regular or laminar. Equation p . 3 ) is valid for this type of flow. Under other conditions, however, the flow appears to be irregular with transverse eddies. When this type of flow prevails, Equation (E3.3) has to be modified to account for the transverse transfer of momentum due to eddy movement. The modified equation can be written as follows

where his the turbulent viscosity, associated with the momentum transfer due to eddy movement, which is usually much greater than the molecular viscosity, p. Unfortunately, p, is not a physical property of the fluid, but a function of the flow itself. Therefore, in order to characterize a turbulent flow field, the conservation equations need to be complemented by one or more additional equations that describe the dissipation of turbulent energy.

With a few exceptions (very small fires), the flows associated with enclosure fires are turbulent.

B.l.3.3 Conservation of Mass Consider a control volume that consists of a bundle of streamlines, as shown in Figure B-2. A control volume is a region in space through which fluid flows. Application of the fundamental law of conservation of mass to the control volume leads to an equation that describes the continuity of the flow. If the flow is steady, the law of mass conservation requires that the mass flow of fluid entering the control volume through surface 1 is equal to the mass flow leaving the control volume through surface 2. The continuity equation can therefore be written as

For unsteady flows, this equation has to be modified to account for changes in the total amount of fluid accumulated inside the control volume.

B.l.3.4 Conservation of Momentum Application of Newton's law of motion to a control volume in a steady flow expresses that the net sum of forces acting on the volume is equal to the net efflux of momentum fiom the control volume. If the flow is unsteady, the equation has to be modified to account for the rate of accumulation of momentum inside the control volume.

FIGURE B-2. Conservation of mass

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189

The set of differential equations that express Newton's second law of motion for a compressible Newtonian fluid are referred to as the NavierStokes equations.The derivation of these complex equations is beyond the scope of this review. The reader is referred to a textbook on fluid mechanics for a more detailed treatment. Euler's equations are a simplified fom of the Navier-Stokes equations for an inviscid fluid (p is negligible). Integration of Euler's equations along a streamline lead to the following expression, known as Bernouilli 'S equation

P

+

1 -pv2 + pgh 2

=

constant

(B4

where h is the height above a fuced datum level (m). Bernouilli's equation can be used to describe the flow through a sharp-edged orifice plate, commonly used to measure fluid flow through a pipe (see Figure B3).The stream emerges fiom the orifice as a jet. The jet converges to a vena contracta just downstream of the orifice plate, and then breaks up into a turbulent flow region. Application of the continuity equation between sections 1 and 2, assuming the fluid is incompressible, leads to

FIGURE B-3. Orifice flow meter

Note that A, is slightly smaller than the area of the orifice plate opening. Bernouilli's equation can be written as follows

Combination of Equations (B.7) and (B.8) leads to

This equation is used in Section 2.6.2.2 to determine the mass flow through a vent in a vertical wall of an enclosure that contains a fie.

B.1.3.5 Dimensional Analysis To enable analysis of complex fluid flow problems, and to allow a systematic interpretation of the results, it is necessary to minimize the number of variables. This is accomplished by grouping variables into a number of dimensionless parameters. This procedure is called dimensional analysis. The following dimensionless groups are commonly used in formulating and presenting the results of (fire-related) fluid dynamics problems.

1 The Reynolds number, Re

where

l

=

characteristic length of the geometry under consideration (m)

Review of Fundamentals of Engineering for Fire Modeling

v

=

191

kinematic viscosity (m2/s)

The Reynolds number is the ratio of inertial to viscous forces. The transition between laminar and turbulent flow is often characterized by a critical Reynolds number. The characteristic length varies with the geometrical configuration of the problem. For example, in the case of forced flow through a duct, the characteristic length is usually the diameter of the pipe. 2 The Froude number, Fr

The Froude number is the ratio of inertial to gravity forces. Fr is, for example, used to correlate experimental data fiom gas burner jet fires.

8.2THERMODYNAMICS Thermodynamics is the science of the relation between heat, work, and the properties of systems. A system is hereby defined as any prescribed and identifiable collection of matter. B.2.1 Equation of State

The density, pressure, and temperature of an ideal gas are related by the equation of state, (B.l), which can also be written as

where

c = compressibility factor

APPENDIX B

Temperature ("C) FIGURE B-4. Compressibility factor of some gases

This equation is also applicable to real gases at temperatures and pressures observed in fires. This is illustrated by Figure B-4, which shows C of some important gases at atmospheric pressure (or saturation pressure for water vapor below 100°C), and temperatures between 0 and 1200°C. The C values for water vapor were determined fi-omthe steam tables, while those for the other gases were calculated with the truncated virial equation (see Reference [98], p.50). It can be observed in Figure B-4 that the largest deviation of from unity is 1.5% (for water vapor at 100°C). However, agreement is generally much better, in particular at higher temperatures, which are of greater interest to the fire modeler. In f ~ e sas , in many other areas of thermal engineering, we are usually dealing with mixtures of gases, e.g., air, products of combustion, etc. Each gas in a mixture behaves as if it alone occupied the entire volume containing the mixture. The pressure exerted by a component in the mixture is the partial pressure of that component. According to Dalton's law, the pressure of the mixture is equal to the sum of the partial pressures of its N components.

Review of Fundamentals of Engineering for Fire Modeling

193

The composition of a mixture is usually specified in terms of mass fractions, denoted by the symbol Y, or in the form of mole (or volume) fractions, denoted by the symbol X. By defmition, the sum of the mass or mole fractions in a gas mixture is equal to one.

(B.l4b)

Under the conditions of pressure and temperature that are normally encountered in fues, the equation of state is also valid for each component in a mixture.

where

R,

=

gas constant of species i (Jkg-K)

Unlike the universal gas constant R, which is expressed on a molar basis and is the same for any type of gas or gas mixture, R, is expressed on a mass basis and varies fi-om one gas species to another. 4 is equal to R divided by the molecular mass of species i. Summation of Equation (B.15) over all components in the mixture, and in combination with Equation (B.13), leads to

194

APPENDIX B

(B.16)

Equation (B. 16) shows that the equation of state can also be applied to a mixture of gases, whereby the gas constant of the mixture is related to the gas constants of its components by the following expression

B.2.2 First Law of Thermodynamics B.2.2.1 Work Consider the piston-cylinder mechanism shown in Figure B-5.The gas mixture inside the cylinder forms a thermodynamic system. When the system is in equilibrium, the force exerted on the piston due to the gas pressure is equal in magnitude, and opposite in direction to the external force F exerted on the piston. The former is equal to the gas pressure, P, times the area of the piston, A. Suppose now that the external force is suddenly increased. As a result, the gas inside the cylinder will be compressed and the volume of the system will decrease until the internal and external forces are again in equilibrium. If the fi-iction of the piston is negligible, the work done by the system during this process is given by

Review of Fundamentals of Engineering for Fire Modeling

195

FIGURE B-5. Piston-cylinder mechanism

Subscript 1 refers to the original state (prior to the increase of F), and subscript 2 refers to the fmal state after compression to the new equilibrium. The value of W,, is a h c t i o n of the process, i.e., the path of successive states passed through between the initial and fmal states. For example, if the cylinder is water-cooled to keep its temperature constant, the work done by the system can be calculated fiom

Wl, =

i

PdV

1

=

im~mix' 1

v

Note that W,, is negative for a compression process (V, is smaller than V,), and positive for an expansion process. The type of work described in this section is referred to as displacement work. Many other types of work are important in engineering thermodynamics, for example, work associated with fluid friction, stirring, electrical effects, etc. B.2.2.2 Heat Consider two systems at different temperatures. Provided there is a mechanism for it (in other words, provided the two systems are not thermally isolated fiom each other), heat will be transferred fiom the system at higher temperature to the system at lower temperature. Heat can be transferred via conduction through matter, convection of fluids, and thermal radiation. The three modes of heat transfer are discussed in more detail in Section B.3. A system that is perfectly isolated to eliminate any heat transfer through the system boundaries is called an adiabatic system.

A thermodynamic process that does not involve heat transfer is referred to as an adiabaticprocess.

B.2.2.3 Internal Energy The internal energy of a thermodynamic system, U, is the kinetic energy associated with molecular motion and interaction of the molecules comprising the system. It is very common to use the specific internal energy, U,i.e., the internal energy expressed per unit mass of the system. Since there is no molecular interaction in an ideal gas, its internal energy is a function of temperature only. Consequently, the change of internal energy of an ideal gas due to a particular process depends only on the initial and final states of the system. It can be demonstrated that this is also valid for systems of real gases. Suppose the volume of a system is kept constant, and heat is transferred to the system to raise its temperature. This also increases the internal energy of the system by an amount that is proportional to the temperature rise. The relationship between increase of internal energy and temperature rise can be written as

where c,, is the specific heat at constant volume of the gas, which is a material property that varies with temperature. The specific heat at constant volume of a gas mixture can be calculated ffom the specific heat of its components using the following relationship.

B.2.2.4 Enth a@y The enthalpy, H, of a system is defmed as follows

Review of Fundamentals of Engineering for Fire Modeling

197

Enthalpy is also most commonly used on a per-mass-unit basis. Since both U and P V are a function of temperature, H varies with temperature also. The change of the specific enthalpy of a system is also proportional to the system's temperature change, and is given by

where c, is the specific heat at constant pressure of the gas (the reason for this name will be explained in Section B.2.2.6). As with c,, the specific heat at constant pressure is a material property that varies with temperature. Equation (B.23) is valid only for very small temperature changes. To calculate the enthalpy change for a large temperature difference, the temperature-dependency of c, must be accounted for. Denoting the temperature difference by AT = T2 - Tl, the corresponding specific enthalpy change follows fiom

where 5 is the average specific heat between Tl and T2. The average specific heat of most gases does not vary strongly with temperature, and a cubic temperature function fits the data quite well:

The polynomial constants for gases that are of primary interest to the fire modeler are provided in Table B- l. These constants are for T in "C, with 0°C as the reference temperature (Tl = O°C). The resulting equations are valid for temperatures between 0 and 3000°C.

Table RI. Polynomial Constants to Calculate c,(T) of Some Gases M Species (kglkmol)

A (kJ/kg°C)

Ar

39.95

0.5207

Air

28.96

1.0009

B C (kJ/kg.oC2) (kJ/kg°C3)

0

0

8.454~10-~ 4.941-10-9

D (kJ/kg°C4)

0

-3.242-10-l2

The average specific heat between two arbitrary temperatures, T, and T, can be calculated from

where the subscripts and superscripts are the lower and upper limits respectively, of the temperature interval over which the average specific heat is calculated. The specific heat at constant pressure of a gas mixture is equal to the mass-weighted average of the specific heats of the components.

For example, dry air consists of 1.28% Ar by mass, 0.05% CO,, 75.53%

NZ,and 23.14% 0,. The reader can verify that the constants in Table B-l are identical to the mass-weighted averages of the component constants.

Review of Fundamentals of Engineering for Fire Modeling

199

B.2.2.5 First Law for Closed Systems The frst law of thermodynamics expresses the conservation of energy. The heat transferred to a closed system during a process, g,,, minus the work done by the system, W,, is equal to the increase of its internal energy, U, - U,.The corresponding equation is as follows

B.2.2.6 First Law for Open Systems In an open system, matter flows through the system boundaries. If the inflow is equal to the outflow, and the kinetic and potential energy are negligible, the first law can be expressed as follows: the heat transferred to the system in a process, g,,, minus the work done by the system, W,,, is equal to net the outflow of enthalpy, or

In the case of an open system, the subscript 1 refers to the state of the fluid when it enters the system, and 2 refers to the state of the fluid when it leaves the system. Since an open system control volume is (usually) fued, work is not associated with a change in volume, but with a change in pressure. If the process is isobaric, i.e., the pressure in the open system is constant and P, = P,, no work is performed on or by the system. In this case, Equation (B.29) indicates that the heat transferred to the system is equal to the enthalpy rise of the fluid flowing through the system. This is the reason why c,, as defmed by Equation (B.23), is referred to as the specific heat at constant pressure. B.3 HEAT TRANSFER Heat is transferred by conduction, convection, and radiation. These three modes of heat transfer are discussed in some detail below.

200

APPENDIX B

B.3.1 Conduction Energy is transferred in the form of heat from molecules that have a higher kinetic energy to adjacent molecules with a lower kinetic energy. This type of heat transfer, called heat conduction, occurs when a temperature gradient exists in a solid, liquid, or gas. Another mechanism for heat conduction is associated with the flow of free electrons through metals. Therefore, good electrical conductors are also good thermal conductors. The rate of heat transferred by conduction in a particular direction is proportional to the temperature gradient in that direction, and the area through which heat is transferred. This is commonly known as Fourier 's Law, and can be expressed as follows

where q" is the rate of heat transfer per unit area in the X direction. There is a minus sign on the right hand side of the equation, because heat is transferred fiom a point at higher temperature to a point at lower temperature, i.e., in the opposite direction of the temperature gradient. The proportionality constant is called the thermal conductivity, and is a material property. Insulating solids have a thermal conductivity of the order of 0.1 WImK, while metals have a thermal conductivity that is 100 to 1000 times greater. Thermal conductivity generally increases as a function of temperature. If conduction is the only mode of heat transfer, as, for example, in an opaque solid, the conservation of energy leads to the following general heat conduction equation

where p is the density (in kg/m3),and c, is the specific heat (in Jkg-K), T is temperature (in 'C or K), t is time (in S), and k is the thermal conductivity (in W/mK). In a Cartesian coordinate system, Equation (B.31) has the following form

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The left hand side of this equation is equal to the amount of energy that is stored in the solid, per unit time and volume. The right hand side is a summation of the gradients of conduction heat flux in the three directions, X , y, and z. If the thermal conductivity is constant, i.e., does not vary with temperature (and, therefore, with location), Equation (B.32) simplifies to

where a is the thermal diffusivity of the solid (m2/s). To determine the temperature distribution in a spatial region, the heat conduction equation must be solved in conjunction with a set of algebraic equations that specify the conditions at the boundaries of the region. The boundary conditions must prescribe either temperature, heat flux, or a combination. These are referred to as boundary conditions of the fist, second, and third kind respectively. B.3.2 Convection When a fluid flows over a solid surface, heat will be transferred between the fluid and the solid, provided they have a different temperature. This mode of heat transfer is referred to as convection. If the flow is driven by external forces, as, for example, in the case of ceiling jet flow, the convection is calledforced. If the flow is driven by the heat transfer itself, the mechanism is referred to asfree, or natural convection. An example of free convection is that of a cold fluid in contact with a vertical hot wall surface. The fluid adjacent to the wall will be heated by the wall, and will rise due to buoyancy.

202

APPENDIX B

B.3.2.1 Newton's Law of Cooling To simplify convective heat transfer calculations for engineering applications, a heat transfer coefficient h, is defmed by the following equation

where q" is the rate of heat transfer per unit area fiom the solid to the fluid, T, is the solid surface temperature, and Tf is the fluid's fiee stream or bulk temperature. If T, is higher than Tf, heat is transferred from the solid to the liquid and Q" is positive (by convention). If T, is higher than T,, q" is negative. Equation (B.34) is referred to as Newton 'S Law of Cooling. B.3.2.2 Dimensional Analysis As in the case of pure fluid flow without heat transfer, the systematic analysis of convection problems is greatly facilitated by the use of dimensionless parameters.

1 The P r d t l number, Pr. The boundary layer concept was discussed in Section B. 1.3.1. There is also a thermal boundary layer, i.e., a region in the fluid close to the solid boundary where the temperature gradually changes fiom the solid surfsce temperature, T,, to the free stream fluid temperature, Tp There is a similarity between the equations that describe conservation of momentum and energy in the boundary layers. The characteristic dimensionless parameter that describes this similarity is the Prandtl number, which is defined as

where v = kinematic viscosity of the fluid (m2/s) a = thermal diffusivity of the fluid (m2/s)

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The fluid properties in Equation (B.35) have to be evaluated at the mean film temperature T,, i.e., the average of the surface and fluid free stream temperatures. The Prandtl number is equal to the ratio of velocity and temperature boundary layer thicknesses. For gases, Pr is close to unity. 2 The Nusselt number, Nu. The Nusselt number is a dimensionless form of the convection coefficient, and has the form

where l k

= =

a characteristic length (m) thermal conductivity of the fluid at T, (W/mK)

3 The Grashof number, Gr. Forced flow is characterized by its velocity, or in dimensionless form the Reynolds number (see Equation B. 10). If the flow is natural, the Grashof number is used instead. It represents the ratio of the buoyancy forces to the viscous forces on the fluid, and is defined as

where p is the volumetric coefficient of thermal expansion of the fluid, i.e, the relative change of the fluid density due to a temperature increase of one Kelvin. For ideal gases, P is equal to the reciprocal of the absolute temperature of the gas. For liquids P cm be calculated from the density vs. temperature relationship. Empirical correlations have been developed between the Nusselt number and combinations of other dimensionless parameters for a large number of geometries and flow conditions (forced and natural convection,

204

APPENDIX B

laminar and turbulent flow). For example, the Nusselt number for natural convection over a vertical flat plate at constant temperature is given by [29]

Nu

=

{

0.59(Gr*pr)lA for lo4 S Gr-PT<109 O . ~ O ( G ~ * P ~ ) ' "f o r 1 0 ~ ~ G r = P r < l 0 ' ~(B-38)

The characteristic length, I, in this case is the height of the plate. Once the Nusselt number is known for the geometry and flow conditions at hand, the heat transfer coefficient (Equation B.36), and rate of convective heat transfer pquation (l3.34)] can be calculated. B.3.3 Thermal Radiation Thermal radiation is the transmission of energy by electromagnetic waves. Electromagnetic waves are characterized by their wavelength, h, or frequency, v. The relationship between h and v is given by

where c is the speed of propagation of the wave. Matter is not required for radiant heat transfer, and c in a vacuum is equal to the speed of light (approximately 300,000 kmh). A body at a temperature greater than absolute zero emits thermal radiation over a range of wavelengths fiom 0.1 to 100 pm. This includes the visible region, which extends from 0.38 to 0.76 pm. Thermal radiation at longer wavelengths than the upper limit of the visible range is called infared. In ffires, radiation heat transfer occurs primarily at wavelengths in the hfkared region. Thermal radiation that falls upon a body is partly absorbed, partly reflected, and partly transmitted through the body, or in equation form

where

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p = reflectivity, or fiaction of incident radiation that is reflected a = absorptivity, or fiaction of incident radiation that is absorbed z = transmissivity, or fraction of incident radiation that is transmitted Most solid materials absorb all radiation within a very thin surface layer. These materials are called opaque, and have a transmissivity equal to zero ('G = 0). In fire modeling applications, solid surfaces can generally be considered diffuse, i.e., they reflect and emit radiation uniformly in all directions. Gases do not reflect (p = O), but absorb andor transmit thermal radiation. B.3.3.1 Blackbody Radiation A blackbody is defined as an object that absorbs all incident radiation, fiom all directions, and at all wavelengths, i.e., a = 1 and p = z = 0. It can be demonstrated on the basis of thermodynamic principles that a blackbody emits the maximum possible amount of radiation as a function of its temperature. An expression for the monochromatic emissive power of a blackbody, as a fimction of blackbody temperature T (in K) and wavelength h (in m), was derived by Planck. The monochromatic emissive power, EM,is the rate at which energy is radiated from a unit area of the surface at a single wavelength to the hemisphere of space above it. Planck's equation, with E, in w/m3, can be written as follows

where

C,

=

a constant (3.7401 0-19W-m2)

C, = a constant (1.439.1O5 m=K)

Figure B-6 shows the monochromatic emissive power of a blackbody at different temperatures. Planck's equation indicates that the wavelength at which maximum radiation is emitted is proportional to the inverse of absolute temperature. This is known as Wien's displacement law:

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APPENDIX B

0

2

1

3

4

5

Wavelength, h (pm) FIGURE B-6. Blackbody monochromatic emissive power

where C,

=

a constant (2.940-' mK)

Wien's displacement law explains why the color of a hot metal surface changes to bright red as its temperature increases above 600°C. The total ernissive power (in w/m2) fiom a blackbody, 4,at a given temperature is equal to the area under the spectral distribution at that temperature, and is given by the following remarkably simple relationship

where

o = Boltzmann constant (5.67010-*w/m2K4)

B.3.3.2 Grey Surfaces A real body generally does not absorb all incident radiation, i.e., part of the incident radiation is reflected at the surface. A real surface also emits less radiation than a blackbody at the same temperature. The ratio of the monochromatic emissive power of a real body to that of a blackbody at the same temperature is referred to as the emissivity, E*. The emisivity of a real body varies with wavelength. For engineering purposes, it is often assumed that the emissivity is independent of wavelength. A surface with this property is referred to as a grey surface. The emissive power of a grey surface is related to its temperature by

where E is the total (all wavelengths) hemispherical (all directions) emissivity. It can be shown that the emissivity and absorptivity of a grey surface are identical. B.3.3.3 Radiative Heat Transfer between Grey Surfaces The fraction of radiation emitted by a grey surface S, at uniform temperature T,, that strikes another grey surface S, at uniform temperature T, is only a function of the geometry. This fiaction is commonly referred to as the geometricalfactor or view factor, Fiji,. Methods for calculating view factors are mathematically involved, and view factor equations for common geometries can be found in textbooks on heat transfer and thermal radiation (see for example References [27] and [29]). View factors obey the following reciprocity relation

where A, and A, are the surface areas of surfaces S, and S, respectively. Furthermore, for an enclosure consisting of N isothermal surfaces, the sum

of the view factors between one swface and all surfaces in the enclosure (including its own surface) is equal to one, or

These simple algebraic relationships, in conjunction with Equations (B.40) and (B.44) can be used to derive a set of radiation transfer equations, which describe the relationship between the temperatures of and radiative heat fluxes to all surfaces in an enclosure. The use of these transfer equations in zone models to calculate radiative heat transfer in enclosure fires is discussed in Section 2.6.3.1. The equations presented in Section 2.6.3.1 also account for the effect of absorbing/emitting gases (partially) filling the enclosure. The subject of gas radiation is briefly discussed below. B.3.3.4 Radiation Heat Transfer through Gases

AU gases, except those with diatomic molecules, absorb (and also emit) thermal radiation. However, they do not absorb radiation at all wavelengths, but only over specific bands. A graph of the absorptivity of a gas as a function of wavelength is referred to as its absorption spectrum. The absorption spectrum of a gas mixture is equal to the sum of the absorption spectra of its components (each weighed on the basis of the component's concentration in the mixture), except at wavelengths where component spectra overlap. Rather complex corrections are necessary to determine total absorptivity at overlapping wavelengths. Smoke from fres nearly always contains significant amounts of soot particles. The absorption spectrum of a soot cloud is continuous, and must be combined with the discrete spectrum of the carrying gas mixture to determine the radiation characteristics of the smoke. Despite the fact that the resulting spectrum has discrete peaks at wavelengths where one or several gas components absorb, an approximate grey gas assumption is often used for engineering calculations of radiation heat transfer through smoky fire gases. The absorptivity of a grey gas volume is a fhction of the length of the path that a beam has to travel to cross the volume. If the path length is denoted as L, the absorptivity is given by

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where k is the extinction coefficient in llm. The extinction coefficient is a function of the temperature and concentration of absorbing gas species and soot in the mixture (a method for calculating k of smoke is presented in Reference [28]). The absorptivity of a grey gas is different for each beam, because of the varying path length. Consequently, the presence of an absorbing gas greatly complicates radiation heat transfer calculations in an enclosure, even if the gas and surfaces are assumed to be grey. This problem can be alleviated by the assumption that all beams travel the same distance. This distance is referred to as the mean beam length, L,, and is purely a function of the geometry. Equations to determine L, for common geometries can be found in the aforementioned textbooks. For a gas volume V with an enveloping area A, L, can be estimated from

B.4 COMBUSTION

B.4.1 Combustion Chemistry B.4.l .l Elements, Compounds, and Mixtures

Elements are the basic materials of matter, which cannot be subdivided into any other substances. Hydrogen and oxygen are examples of elements. Compounds are substances that are made from elements. For example, water is a compound made fiom hydrogen and oxygen. A mixture is created when elements andor compounds are mixed together without the formation of a new substance. Moist air is a mixture of gases: primarily oxygen, nitrogen, and water vapor. Note that a vapor, as opposed to a gas, is the giiseous form of a substance that under normal conditions of pressure and temperature occurs as a liquid.

210

APPENDIXB

B.4.1.2 Atoms and Molecules

Matter is made up of very small particles of elements, called atoms. Atoms of different elements have a different mass. To identifl thls difference, a relative scale of atomic mass was created. The lightest of all elements is hydrogen. Its relative atomic mass is slightly greater than one. The relative atomic mass of some important elements involved in combustion and fire phenomena are listed in Table B-2. The common symbols for these elements are also listed. Compounds also consist of small particles. These particles contain more than one atom, and are called molecules. The chemical formula of a compound consist of a combination of the symbols of all elements represented in the compound, each followed by a subscript denoting the number of atoms of the element in the molecule. For example, a water molecule consists of two hydrogen atoms, and one oxygen atom. The corresponding chemical formula is H,O. Since a molecule consists of atoms, its mass can be expressed on the same scale as the relative atomic mass. The molecular mass of water, for example, is equal to 2 X 1.O1 + 16.00 = 18.02. A convenient quantity used in combustion calculations is the mole (abbreviated as mol). One mole of a compound is equal to the number of grams of the compound equal to its molecular mass. One kilomole (kmol) of a compound is equal to 1,000 moles. For example, one mole of water is equal to 18.02 grams of water, and one kilomole is 18.02 kilograms. Based on Avogadro's hypothesis, the volume of one mole of an ideal gas (mixture) at a given pressure and temperature is constant, and independent of the type of gas (or composition of the mixture). At atmospheric pressure (1.Ol3 bar) and O°C, this volume is equal to 0.02241 m3. Table B-2. Relative Atomic Mass of Some Elements Element

Symbol

Atomic Mass

Hydrogen

H

1.01

Carbon

C

12.01

Nitrogen

N

14.01

Oxygen

0

16.00

Argon

Ar

39.95

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B.4.1.3 Chemical Reactions and Stoickiornetry

A chemical reaction between two or more substances mixed together results in the formation of one or more different substances. The starting substances are called reactants. The substances that are formed are referred to as products. In a chemical reaction, the molecules of the reactants are broken apart, and the resulting atoms (or groups of atoms) are rearranged into the molecular structure of the products. The number of atoms of each element involved in the reaction is conserved. Chemical reactions are either exothermic (generating heat) or endotherrnic (absorbing heat). Combustion is an exothermic reaction that generally involves oxygen as one of the reactants. A chemical reaction is described by an equation, which consists of a summation of the reactant symbols on the leR side and a summation of the product symbols on the right side, separated by an arrow pointing from left to right. The symbols of reactants and products are each preceded by a number (usually an integer) that indicates, on a relative basis, how many molecules of the compound are involved in the reaction. Equation (13.49) describes the complete combustion of methane in oxygen.

CH, + 20,

-

CO, + 2 H 2 0

One molecule of methane reacts with two molecules of oxygen to form one molecule of carbon dioxide, and two molecules of water. The total number of carbon (l), hydrogen (4), and oxygen (4) atoms is the same on both sides of the equation. Most combustion reactions take place in air, instead of pure oxygen. The mole (or volume) fi-action of oxygen in dry air is 20.95%. The balance consists of nitrogen (78.09%) and small amounts of other non-reacting gases, primarily argon (0.93%) and carbon dioxide (0.03%). For engineering calculations, dry air is assumed to consist of 2 1% by volume oxygen, and 79% by volume nitrogen. Hence, complete combustion of methane in air is described by the following equation, which can be derived from Equation (B.49)

CH, + 20, + 7.52N2

-

CO, + 2 H 2 0 + 7.52N2

(l3.50)

The nitrogen term is the same on both sides of the equation, indicating that nitrogen does not participate in the combustion reactions and only acts as an inert diluent. Equation (B.50) is also referred to as the stoichiometric equation for methane combustion in air. To have enough oxygen available for complete combustion of all methane, air and methane must be mixed in proportions that correspond to the right hand side of the stoichiometric equation. Such a stoichiometric mixture consists of 141 + 2 + 7.52) = 9.5 1% by volume methane, and 90.49% air. The molecular mass of this mixture is equal to 0.0951 X 16.05 + 0.9049 X 28.96 = 27.73. Hence, the composition of the mixture by mass is 9.51 X 16.05127.73 = 5.50% methane, and 90.49 X 28.96127.73 = 94.50% air. If the concentration of fuel in a fuellair mixture exceeds the stoichometric concentration (5SO% for methane), the mixtwe is called rich (in fuel). I f there is more air present than needed to burn the fuel, the mixture is lean (in fuel). The composition of a fuellair mixture is often expressed in terms of its equivalence ratio, Q,. The equivalence ratio is defied as follows

where the numerator is the ratio of the mass fraction of air to the mass fraction of fuel in a stoichiometric mixture, and the denominator is the same ratio for the actual mixture. Q, of a fuel-rich mixture is greater than one. is less than one when the mixture is fuel-lean. A stoichiometric fuellair mixture, by d e f ~ t i o nhas , an equivalence ratio equal to one. B.4.1.4 Reaction Rate and Equilibrium

Suppose reactants a .mixed in a container, and a chemical reaction is initiated. The reaction will continue until an equilibrium condition is reached. Equilibrium is defined on the basis of a constant, K, which is unique for a given reaction, and varies with temperature. Consider the following generic reaction equation

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This equation states that a molecules of substance A react with b molecules of substance B, to form c molecules of substance C and d molecules of substance D. Equilibrium is reached when the following expression is valid

where square brackets are used to denote concentrations. Equation (l3.53) is referred to as the Z m of mass action. In the case of methane combustion, the equilibrium condition can be written as follows

The equilibrium constant for combustion reactions is much greater than one. This implies that the residual amount of unreacted fuel will be neghgible if the initial reactant mixture is fuel-lean (Q < l), and that nearly all oxygen will be consumed if the initial mixture is fuel-rich (Q,> 1). The fact that a chemical reaction has a large equilibrium constant does not ensure that it will occur. For example, consider a fuel-lean mixture of propane (C,H,) and air, with an equivalence ratio iP = 0.8. The mixture is stored inside a vessel at ambient temperature and pressure. Under these conditions, the mixture will not react. However, a glowing wire or an electric spark introduced into the vessel will initiate the reaction due to the local temperature increase. The heat generated by the reaction will cause a temperature increase at adjacent locations in the vessel, resulting in propagation of combustion through the entire mixture. The Swedish scientist Arrhenius discovered that the rate of a chemical reaction is proportional to exp(- EJRT), where E, is the reaction activation energy (in kJ/kmol), R is the universal gas constant (8.3144 W/kmolK), and T is the absolute temperature (in K). The reaction rate is also a futlction of the concentration of the reactants. Westbrook et al. reported the following expression for the reaction rate of propane [99]

where the concentrations are expressed in kmoVm3.The reader can verify that the concentrations of propane and oxygen in the aforementioned propane mixture are approximately given by [C3H8]= 0.00151 kmoVm3, and [O,] = 0.00906 kmoVm3. The reaction rate calculated from Equation (B.55) at T = 300 K is equal to 1S*10-l6kmoVm3.s. At this rate, it would take more than three thousand centuries to convert all propane in the mixture. Although the calculated rate is probably not accurate because it is obtained by extending Equation (B.55) outside its valid temperature range, it can still be concluded that the reaction rate at ambient temperature is indeed negligible. At a glowing wire temperature of 1,000 K, the reaction rate increases to 0.3 kmoVm3-S.At this rate it would take 5 d s e c o n d s to consume all propane. In reality it will take longer, because the reaction will slow down as the reactants are being consumed. At an electric spark temperature of 2,000 K, the reaction rate increases by another three orders of magnitude to 267 kmoVm3-S,reducing the time to less than three microseconds.

B.4.1.5 The Simple Chemically Reacting System (SCRS) A chemical reaction is much more complex than reactants breaking apart into atoms, which then recombine into products. The combustion of methane, for example, has been demonstrated to consist of as many as 149 transition reactions in which numerous intermediate species (such as H, H, HCHO, HCO, CH,, CO, 0, and OH) are formed and destroyed [loo]. The overall reaction rate is a fizllction of the rate at which the transition reactions take place. However, the transition species are unstable and shortlived, and never obtain concentrations of the same order as the reactants (initially) and products (when equilibrium has been reached). For many engineering applications, including zone fire modeling, the intermediate steps and reactions are of little interest, and only the "big picture" needs to be considered. To describe the main features of a combustion system, Spalding introduced the concept of a Simple Chemically Reacting System (SCRS) [loll. "The SCRS involves a

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reaction between two reactants (fuel and oxidant) in fixed proportions by mass, to produce a unique product." An SCRS can be described as follows

r kg 0,

-

( 1 + r) kg product

@.W

1 kg fuel + s kg air

-

( 1 +S) kg product

(33.57)

1 kg fuel

+

In the case of stoichiometric combustion of methane in oxygen, Equation p.49) indicates that r is approximately equal to (2 X 32)/16 = 4 kg r,,, Equation (B.50) shows that s is equal to (2 X 32 + 7.52 X 28)/16 = 17.2 kg sstoich. The ratio between s and r is equal to the mass fiaction of oxygen in air, i.e., 0.232. Hence, s is 4.3 times greater than r. Often excess air is supplied, so that s (and r) are larger than the stoichiometric values sdoi, (and rstoich). Theoretically, at 0 = 1 there is enough oxygen for complete combustion of the fuel. In reality, an equivalence ratio smaller than 1 is needed for complete combustion. This is because at 0 = 1 it is unlikely that each fuel molecule will f i d the oxygen gas molecules it needs to react with. Results fi-omgas burner experiments reported in the SFPE Handbook (see Reference [15], p. 2-68) show that the combustion reactions of a stoichiometric mixture of propane and air (Q = 1) can be approximated by

In this case, the reactants consist of propane and air, mixed in stoichiometric proportion of s = sstoich = 15.6 kg air per kg propane. The product consists of a mixture of CO2 (approximately 14% by mass), CO (1% by mass), H,O (approximately 10% by mass), 0, ( approximately 3% by mass), and N2 (approximately 72% by mass).

B.4.2 Heat of Combustion and Adiabatic Flame Temperature Consider the steady combustion process shown in Figure B-7.Fuel at temperature T, is supplied to an open combustion chamber at a rate m, Air at temperature T, is supplied at a rate m, exceeding the stoichiometric rate, so that combustion is complete. Fuel and air mix inside the chamber, and react to form combustion products that are removed at a rate rir, = m, + m,. Heat is extracted fkom the combustion chamber at a rate Q, so that the products of combustion exit the chamber at a temperature Tp. Application of the first law of thermodynamics to this system leads to the following equation

This energy balance can be expressed on a fuel mass basis by dividing each side of the equation by m, Denoting the ratio of the rate of heat extracted to the rate of fuel supplied as q, this leads to

If fuel and air were supplied at a reference temperature, To, and if heat were extracted at the exact rate to cool the products down to the same temperature, Equation (E3.60)would take the following form

CHAMBER

FIGURE B-7. Steady combustion process

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Ah, is equal to the amount of heat generated by the combustion reactions per mass unit of fuel burnt, and is called the gross heat of combustion of the fuel. This quantity is independent of the air to fuel ratio (provided the air supply rate is high enough so that combustion is complete), because the enthalpy of the excess air at temperature Toappears in the second and third term on the right hand side of Equation (B.61), but with a different sign. However, Ahc,mssis a function of the reference temperature. Since Tois typically 20 or 25"C, the reference enthalpy of the products of combustion includes that of water in the liquid state. The net heat of combustion, &,,(To) is also defined by Equation (B.61), except that all products of combustion are assumed to be in the gaseous state. Ahc,netis lower than Ahc,~oss, the difference being the product of the latent heat of vaporization of water (2.44 MJ/kg at 25°C) and the amount of water formed per mass unit of fuel burnt. For example, MC,,, (25°C) of propane is 50.4 MJ/kg. Since 1.65 kg of water is formed per kg of propane burnt (this can be determined fkom the stoichiometry of the combustion reactions), Ah,, (25°C) of propane is equal to 50.4 - 1.65 X 2.44 = 46.4 MJ/kg. The net heat of combustion is more u s e l l and practical in combustion calculations. Ah,, (25OC) values of different fuels can be found in Table 4- 1. Equation (B.60) can now be rewritten by subtracting the modified version of Equation @.61), and using Equation (13.26) to express enthalpy differences as a function of temperature. This leads to

The combustion products attain their maximum temperature when the process is adiabatic, i.e., when there are no heat losses fkom the combustion chamber (q = 0). In this case, the entire energy generated by the combustion reactions is used to raise the sensible enthalpy, and therefore the temperature, of the combustion products. This maximum is referred to as the adiabaticflame temperature. If fuel and air are supplied at the reference temperature, the adiabatic flame temperature is given by

APPENDIX B

2600

1

Equivalence Ratio, @

FIGURE B-8. Adiabatic flame temperature of methane and propane

This is in fact a non-linear equation, because c;, is a (weak) function of temperature. The higher the S, the lower the adiabatic flame temperature, because excess air acts as a diluent, which increases the total mass of combustion products that must be heated. Figure B-8 shows the adiabatic flame temperature of methane and propane as a h c t i o n of the equivalence ratio. The lower limit of the @-axis range (Q, = 0.5) approximately corresponds to the lower flammability limit (LFL) of the two gases. For methane in air, the LFL (at 25OC and 1.0l 3 bar) is 5% by volume (see Reference [15], p. 2-150), which is equivalent to Q, = 0.48. The LFL for propane is 2.1%, corresponding to = 0.52. If the fuel concentration is below the LFL, there is not enough fuel to sustain combustion. Actual flame temperatures are lower than adiabatic temperature, primarily due to radiative heat losses from the flame. Incomplete combustion, in particular if Q! is close to or greater than 1 and partial dissociation of CO, (into CO and 0,) and H,O (into H, and 0,) also reduce the flame temperature. Dissociation reactions are endotherrnic, and are significant at temperatures exceeding 1800 K. Flame temperatures in fires are typically lower, so that dissociation can be ignored.

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B.4.3 Diffusion Flames In flaming fires, combustion occurs predominantly in the gas phase. Liquid and solid fbels are heated by their own flame and/or heat transfer fi-om external sources (hot gas volumes, high temperature surfaces, etc.) Combustible volatiles are generated by evaporation of liquid hels, and pyrolysis of solids. The volatiles mix with air that is entrained into the flame, and react with its oxygen. Because the air is not premixed with the h e 1 but is supplied by mass transfer processes, the resulting reaction zone is referred to as a dzflusionflame. Diffusion flames have been studied extensively. For example, many different correlations have been developed to estimate the height of a diffusion flame as a hction of its heat release rate and the geometry of the fuel. The following convenient expression was developed by Heskestad (see Reference [ lS ] , p. 2- 10)

where

H,

mean flame height (m) heat release rate of the fire (kW) D = effective diameter of the fire (m)

0

=

=

This expression, in conjunction with Zukoski's plume flow correlation Rquation 2.1O), can be used to calculate the amount of air that is entrained over the entire flame height of a free-burning fire. Use of the virtual origin correction specified in Equation (2.13), and the fact that the amount of heat released by stoichiometric combustion per kg of air supplied is approximately constant and equal to 3030 kJ (see Section 4.2.2), leads to the following remarkable result

220

APPENDIX B

This indicates that if a free-burning f i e loses 25% of its heat output by radiation, air is entrained in the flame at nine times the stoichiometric rate. For a flame that loses half of its heat output by radiation, the entrainment drops slightly below eight times the stoichiometric rate.

B.5 NUMERICAL METHODS Even the simplest fire models (such as the ones presented in this book), consist of a collection of relatively complex equations, which cannot be solved analytically. Numerical methods must be used to obtain approximate solutions. Two such methods are discussed in this section. First, however, it is important to provide some discussion concerning computer accuracy.

B.5.1 Computer Accuracy Computers store numbers in the form of binary digits, or bits. A bit can have a value of 0 or 1.Bits are combined into groups of eight, called bytes. Numbers are represented using a binary, or base 2, numbering system. An integer can be represented exacly, as long as its value does not exceed the range that can be represented. The highest number that can be represented is a function of the number of bits (or bytes) that are used. For example, the maximum value that can be represented in one byte is 1111 1 111 in binary. The corresponding decimal number is given by

Negative integers can be represented by using the first bit as a sign bit (0 for positive numbers, 1 for negative numbers). In this case, numbers between - 128 and 127 can be represented in one byte. More sophisticated methods are needed to represent real (or floatingpoint) numbers. A single precision representation of real numbers consists of a group of four bytes, divided into portions. The first portion, the mantissa, holds the base value of the number. The second portion, the exponent, indicates to what power the mantissa must be raised to obtain the final value of the number. As with integers, as sign bit is used to distinguish between positive and negative numbers. The most common

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format is that promulgated by the Institute of Electrical and Electronics Engineers (JEEE). The IEEE format consists of a sign bit in the most significant position, followed by eight exponent bits, and 23 bits for the mantissa. The real numbers that can be represented this way range fiom approximately - 3.4010"' to 3.4-1Ot3'.. More importantly, a maximum of only seven significant digits can be represented in lEEE format. Consequently, the representation of a number that has more than seven significant digits is not exact. For example, the number 0.123456789 is rounded to 0.1234568. The diff~encebetween the actual number, and that corresponding to its representation in the computer is called the roundoff error. The relative roundoff error is the smallest floating-point number that added to 1.0, results in a number different from 1.0 [44]. It is a characteristic of the computer hardware, and is commonly referred to as the machine accuracy, E,. The single precision floating-point machine accuracy of B M compatible PCs is 1.19-10-' (see Reference [44], p. 883). Arithmetic operations result in an accumulation of roundoff errors. The cumulative roundoff error after N operations is typically between dN and N times E,. This means that after one million operations, the fractional roundoff error can exceed l%! Roundoff errors cannot be eliminated. However, good numerical methods minimize the cumulative error by optimizing (reducing) the number of operations, and by avoiding the use of unstable algorithms, which unnecessarily amplify roundoff errors. Even if a perfect machine were available (i.e., machines without roundoff error), numerical methods would still produce approximate solutions. The difference between the true and calculated solutions is referred to as the truncation error. This type of error is generally due to truncation of an infinite series (which yields the true solution) to a finite number of most significant terms (so that the result can be calculated in a f i t e time). Unlike roundoff errors, truncation errors can be controlled by the programmer. A good numerical method provides an estimate of the truncation error, and includes measures to reduce it to a tolerable level (e.g., by increasing the number of terms in a truncated series).

B.5.2 Solution of Algebraic Equations The bisection method is a simple, but powerful method to solve algebraic equations. Truncation errors are not an issue. The method is used

222

APPENDIX B

in FIRM-QB (and FIRM-VB) to solve the vent flow equations (see Section 4.1.6). An equation can always be written in the following form

The problem is to fmd a root, i.e., a value X, of x that fiilfills Equation (B.67). Assume we know that the root we are seeking falls between two Xvalues, denoted as X, and X., Furthermore, assume that there is only one and X-. With these root, and that f is continuous between X,, assumptions,f ( X - )andf ( x a must have opposite signs. Now, let X, be halfway between X,, and xma.If the sign off(xmg) is the same as that of f ( X - ) ,then we know that the root lies between X, and X-. If the sign of f (xmJ is the same as that off ( x a , then the root must be between X, and X., In either case, we reduced the interval that brackets the root to one half of its original width. We can repeat this process, reducing the interval to 114, 118, ... of its original width, until we have bracketed the root to whatever accuracy required. The bisection method is computationally not very efficient, but it will always find the root (provided the assumptions concerning the bracketing interval limits, uniqueness of the root, and function continuity are valid). Moreover, the number of iterations can be a priori determined, and is equal to the smallest integer n that WfAs the following criterion X,,-X

mm .

2"

S

accuracy

@.W

It is surprising, however, how quickly this algorithm leads to the solution. For example consider a temperature function that is known to have a single root between 0 and l,OOO°C. If the desired accuracy is k0.0l0C, it will take only 17 function evaluations to fmd the root! For relatively simple problems consisting of one, or only a few algebraic equations, the "slow" bisection method is perfectly acceptable. In more complex cases involving large sets of equations, and requiring many iterations, the speed of the bisection method (or lack thereof) might become a problem. The use of a more efficient method, such as the

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Newton-Raphson method, would alleviate this. The Newton-Raphson method is more complex, but also much faster than the bisection method.

B.53 Solution of Ordinary Differential Equations (ODEs) The subject of this section is the numerical solution of an ordinary differential equation (ODE). The Runge-Kutta method presented here can easily be extended to solve sets of ODEs, and is used in ASET-QB and FIRM-QB (and their Visual Basic counterparts) for the solution of a set of two equations to determine the layer interface height and upper layer temperature as a function of time. The ODE problem can be described as follows (B.69a)

where y is the dependent variable, x is the independent variable, andf is a function of x and y. The problem is referred to as an initial value problem, because x is usually time. Equation (B.69b) is called an initial condition, because X, is equal to the time at the start of the period for which a solution is to be obtained. The solution consists of finding a h c t i o n y(x) that meets the initial condition, and that fulfills Equation (B.69a) for the range of x values of interest. This range is referred to as the solution domain. To obtain a numerical solution, the solution domain is first subdivided into N steps. The step size is denoted as h, and the upper limit of each interval is given by xi X, + i h, with i = 1 ... N. Instead of a continuous solution, a numerical method frnds a discrete solution in the form of estimates of y at X,,X,, ..., X,. The simplest approach to numerically solve an initial value problem is the Euler or tangent method. Since X, and y, are known, the slope of the tangent line to the solution at x = X, can be calculated fiom the differential Equation (B.69a). If h is small, the slope can be used to obtain a reasonable estimate of y, as illustrated in Figure B-9. This process can be repeated at the estimated (X,, y,) to obtain an estimate of y,, subsequently at (X,,y,) to

-

224

APPENDIX B

FIGURE B-9. Euler method for the solution of an ODE obtain an estimate of y,, etc. The general Euler formula is as follows

If we denote the exact solution of the initial value problem as @(X), then, a Taylor series expansion to express @(xi+ h) as a function of @(xi)leads to

Comparison of Equations (B.70) and (B.72) leads to the conclusion that the local truncation error of the Euler method, i.e., the error of the numerical solution when advancing one step h in the solution domain, is proportional to h2. It can be shown that the cumulative error over the entire solution domain is proportional to h. Therefore, to reduce the cumulative truncation error by a factor of 2, h must be halved. However, besides doubling the computation time, this also increases the cumulative roundoff error, often to a point that it defeats the purpose of using a smaller stepsize. Because

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its accuracy is limited by the roundoff error, the Euler method is generally not recommended for the numerical solution of initial value problems. Around the turn of the 19th century, the German mathematicians Runge and (later) Kutta developed some improvements to the Euler method. The basic idea was to estimate the slope at an intermediate point inside the step interval, instead of using the slope at the start of the interval to advance the solution to the end of the interval. The most frequently used Runge-Kutta method is the fourth-order method described below. Derivation of these equations is beyond the scope of this book, and can be found in many textbooks on numerical analysis (see, for example, Chapter 8 in Reference [102]).

where

The local truncation error is proportional to h5,while the cumulative error is proportional to h4 (reason why it is called a fourth order method). It is obvious that, compared to the Euler method, truncation error improvements by stepsize reduction are much less likely to be offset by increased roundoff errors. The local truncation error can be controlled by comparing two solutions for y,,. The first solution is obtained by using the Runge-Kutta equations two times, each time with a stepsize equal to h. The first time, yi+, is estimated fiom xi and y,. The second time, yi+, is obtained from and yi+l. If the local truncation error is denoted as E, the cumulative truncation error ofy,+,obtained as explained above is 2 ~ ,The . second approach consists of solving the Runge-Kutta equations with a stepsize equal to 2h, to estimate yi+, from xi and y, in one step. Since the local truncation error is proportional to the stepsize raised to the fifth power, the truncation error

of yi+, estimated directly fkom xi and yi is equal to 326,. Therefore, the difference of the two estimates of yi, is equal to approximately 30 times E,, or, conversely, E, is one thirtieth of the difference. If the error estimate is within the user-specified tolerance, the estimates of yi+,and yi+,based on the h t solution are acceptable, and we can proceed to the next step. If the error exceeds the tolerance, a smaller stepsize must be used. The stepsize that is needed to bring the local truncation error within the desired bounds can be estimated fiom

The stepsize control algorithm described above is implemented in the ASET and FIRM programs presented in this book.

APPENDIX C

Installing and Running the Software C.1 INTRODUCTION The accompanying CD-ROM contains the three QBasic programs discussed in the main text: HRR-QB, ASET-QB, and FIRM-QB. This appendix provides instructions for installing and running these programs, and their Visual Basic counterparts. All fire and output files that were created during the sample calculations presented in the book are also on the CD-ROM, and are copied to the reader's hard disk during installation of the QBasic programs. The Visual Basic programs use the same data files. Even if the reader does not intend to use the QBasic programs, it is recommended that they be installed, so that the data files will be available.

C.2 QBASIC SOFTWARE C.2.1 System Requirements The system requirements for the QBasic programs are minimal by today's standards. Any IBM compatible PC with at least 640 K of conventional RAM should work. A VGA display adapter is needed to view the screen plots of the output variables, but this is optional. A printer must be connected to the computer to obtain a printout of the results. C.2.2 Installation of the QBasic Software

The QBasic program and data files on the CD-ROM are not compressed. The software is therefore installed by copying all fdes to the 227

hard disk. It is recommended that the program files be copied to C:\FIRM\, and the data fdes be kept in C:WIRMUIATA\. The latter is the default directory where the Visual Basic programs expect to fmd all fire and output files. In Windows 95/98, the installation can be performed as follows: 1 2 3 4 5 6 7

Place the CD-ROM in the drive. Click the Start button, then choose Programs and Windows Explorer. Click the CD-ROM drive icon in the left side of the Explorer window. Click the FlRM folder in the right side of the Explorer window. Select Copy from the Edit menu in the Explorer window. Click the C: drive icon in the left side of the Explorer window. Select Paste from the Edit menu.

If the reader intends to customize the QBasic programs, it is recommended to copy QBASKEXE and QBAS1C.W to C:V;IRM\ as well. These two files can be found on the Windows 95 CD-ROM in the \OTHER\ODDMSDOS directory, or can be downloaded from the Internet (e.g., from http://neozones.quickbasic.com,see Section D.3). C.2.3 Running the QBasic Software

QBasic executables can be started fiom the DOS prompt by first changing to the directory where the programs reside, and then entering the program name (HRR-QB, ASET-QB, or FIRM-QB) on the DOS command line. To display the DOS command prompt from within Windows 95/98, click the Start button, then choose Programs and MS-DOS prompt. This starts a windowed DOS session. To switch to a full-screen DOS session, press Alt + Enter. At the end of a session, enter EXIT on the command line to return to Windows. Alternatively, to start a DOS program from within Windows 95/98, follow these steps: 1 Double-click the My Computer icon on the Windows 95/98 desktop. 2 Locate the program file. 3 Double-click the program file, i.e., HRR-QB.EXE, ASET-QB.EXE, or FIRM-QB.EXE..

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229

There are several other ways to run DOS programs from within Windows. The reader is referred to the Windows user's guide for more details. To run the source programs, the QBasic interpreter must first be loaded. Follow the aforementioned instructions for starting a DOS program to run the interpreter. In the QBasic environment, choose the Open command from the File menu. Then switch to the directory where HRRQB.BAS, ASET-QB-BAS, and FIRM-QB reside, and double-click on the desired program name. Alternatively, scroll down until the name is highhghted, and press Enter or click OK. The source code is loaded in the QBasic environment, and can be edited and executed fi-om this environment.

C.3VISUAL BASIC SOFTWARE C.3.1 System Requirements

To run the Visual Basic programs, the reader must have a system that meets the following requirements: IBM PC or 100% compatible computer 486166 or higher processor (Pentium or higher recommended) Windows 95/98 16MBofRAM 2 MB of available hard disk space CD-ROMdrive VGA or higher-resolution monitor (Super VGA recommended) C.3.2 Installing the Visual Basic Software

The setup routine on the CD-ROM must be used to install the Visual Basic software. The installation can be performed as follows: l Place the CD-ROM in the drive. 2 Double-click the My Computer icon on the Windows 95198 desktop. 3 Double-click the icon for the CD-ROM drive. 4 Double-click SETUP.EXE, and follow the instructions on the screen.

230

APPENDIX C

The setup routine decompresses the files on the CD-ROM, creates the necessary directories on the user's hard drive (if needed), copies the programs and Windows DLL files fiom the CD-ROM, updates the Windows registry, and creates a FIRM-VB program group. If the reader intends to customize the Visual Basic programs, it is recommended that the source code be copied fkom the \FIRM\ directory on the CD-ROM to the hard disk. This is not necessary if the QBasic software already has been installed (see Section C.2.2). C3.3 Running the Visual Basic Programs There are two ways to run the Visual Basic software. The fust way consists of running the compiled Visual Basic programs. Click the Start button, then choose Programs and FIRM-VB, and click on the desired program name, i.e., HRR-VB, ASET-W, or FIRM-W. The QBasic executables can also be started from the FIRM-VB program group. A special icon was created for each of the three Visual Basic programs. It is recommended that the same icons be associated with fire files (*.FIR extension), ASET output files (*.AOF extension), and FIRM output files (*.FOF extension) respectively. This can be done by clicking the Start button, then choosing Settings and Folder Options, and selecting the File Types tab. After pressing the New Type button, the user can specify an extension and select the corresponding icon. Select HRR-VB.EXE, ASET-W.EXE, or FIRM-VB.EXE as the source file for the icon. The second way must be used if the reader wants to modify the Visual Basic source code. In this case, the program (*.WP extension) must be loaded into the Visual Basic programming environment. There are several books on the market that come with a working model of Visual Basic 6.0 (e.g., Perry, G. and S. Hettihewa, 1998. Teach Yourself Visual Basic 6 in 24 Hours, Sams, Indianapolis, IN), which provides the reader with an inexpensive way for exploring the source programs (retail prices are as low as $20). Working models do not allow the creation of stand-alone compiled programs. Readers who wish to compile and perhaps distribute their modified programs should consider the Visual Basic 6.0 Deluxe Learning Edition, published by Microsoft Press. With a list price of $130, the Deluxe Learning Edition is much more expensive than any of the working models. However, it comes with two books, and a multimedia tutorial on CD-ROM. If the reader requires more advanced capabilities, he may need to obtain the Professional or Enterprise Edition of Visual Basic 6.0.

APPENDIX D

QBASIC Programmer's Notes

D.l INTRODUCTION The computer software presented in this book, i.e., the HRR-QB.BAS, ASET-QB.BAS, and FIRM-QB.BAS programs, are written in QBasic, a powerfbl BASIC interpreter fist released in 1991 by Microsofi as part of MS-DOS 5.0. This appendix provides some useful information for QBasic programmers who want to customize the programs to suit their particular needs. The reader is encouraged to do this, because it will allow him to get the most benefit fiom this book. The next two sections provide some general information on the history and use of QBasic. Programmer's notes for HRR-QB, ASET-QB, and FIRM-QB are presented in the remaining three sections. The reader should generate a printout of the source code of the programs before reviewing the notes. The source code of the three programs is provided on the accompanying CD-ROM, and is copied to the user's hard drive during the installation process (see Appendix C). The source programs are plain text files that can be imported by any word processing program. It is best before printing to set the page orientation to landscape, the font to 10 point Courier, and the left and right margins to 0.5 inch so that statements fit on a single line. It is much harder to read the source code when long statements wrap around to another line, because this disturbs the indentation scheme used to identify blocks of code that form a logical entity. Between the programmer's notes in this appendix and the extensive number of comments in the source code, the reader should have more than enough information to understand how the programs work.

D.2 A BRIEF HISTORY OF QBASIC The BASIC programming language was developed by John Kemeny and Thomas Kurtz at Dartmouth College in the mid-1960s, as a learning tool for beginning programmers. BASIC is an acronym for Beginner 'S Allpurpose Symbolic Instruction Code. It is a high-level language, i.e., it uses common English words to instruct the computer to perform certain tasks, as opposed to machine language which does not have any meaning to humans (except machine or assembly language programmers). In the 1970s, when rnicrocomputers first became available, a BASIC interpreter was supplied with each microcomputer. (An interpreter translates the source code to machine language, and executes the resulting instructions statement by statement.) In 1981, IBM introduced the Personal Computer (PC). The operating system of the IBM PC was developed by Microsoft, and included a BASIC interpreter, called BASICA. On clones of the IBM PC it was called GW-BASIC. The programs developed in the fust edition of this book were written in GW-BASIC. In 1982, Microsoft released its frst BASIC compiler for the IBM PC, called BASCOM 1.0. (A compiler translates the entire source code to machine language prior to execution. A compiled BASIC program runs much faster than a BASIC interpreter.) In subsequent years, Microsoft continuously improved its BASIC compiler. The next version of Microsoft BASIC compilers was named QuickBasic 2.0. It was a major breakthrough, because it included an integrated editing environment that greatly facilitated program development. Early in 1990, Microsoft released its most powerful BASIC compiler for MS-DOS computers: the Professional Development System (or PDS) version 7.1. It was an extended version of the popular QuickBasic 4.5 compiler released in 1988. A major reason for the success of QuickBasic 4.5 was its price (less than $loo), which put the compiler within anybody's reach. In 1991, Microsoft started shipping a completely revised BASIC interpreter, called QBasic, with version 5 of its MS-DOS operating system. QBasic has essentially not changed since its fust release (the most current version is 1.1). QBasic has a user interface similar to QuickBasic 4.5, and has many of the same features. However, QBasic has some important limitations compared to QuickBasic 4.5. For example, QBasic is not capable of generating an executable program (it is an interpreter, and not a compiler), and supports only one module. QuickBasic 4.5 can handle

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233

programs consisting of multiple modules, each stored in a separate file. Despite its limitations, and the fact that it is a DOS program (and therefore somewhat obsolete), QBasic still has an extensive following. Some of the reasons are that it is easy to learn, allows structured programming at a rock-bottom price (it's free!), is suitable for relatively complex calculations, and an e*ensive number of programs are available in the public domain (which can be used as is, or can serve as a basis for new programs). The author believes that the reader can gain much more from this book by actually modifying the programs that are provided. Based on its capabilities and price, QBasic appears to be the ideal programming tool to facilitate this process. D.3 USING QBASIC The reader is referred to the numerous excellent books on QBasic for detailed information concerning its use. The author recommends the following two references: l Feldman, P., and T. Rug, 1993. Using Basic (2nd Edition), Que

Corporation, Cannel, IN. 2 Dyakonov, V., V. Munerman, E. Yemelchenkov, and T. Sarnoylova, 1996. The Revolutionary Guide to QBasic, Wrox Press, Birmingham,

m.

The first book is a tutorial and reference for beginning to intermediate QBasic programmers. The second book addresses more advanced topics and discusses the development of professional QBasic applications. A quick search through the world wide web shows that there still is an extensive following of die-hard QBasic afficionados, despite the fact that QBasic is a somewhat obsolete DOS-based programming tool. The following two web sites are among the most frequently visited: 1 http://neozones.quickbasic.com 2 http://www.qbasic.com Both sites offer book reviews, tutorials, tons of sample programs, links to other QBasic web sites, and much more.

The QBasic interpreter is needed if the reader wants to modify the source code provided with this book. It can be copied from the \OTHER\OLDMSDOS folder on the Windows 95 CD, or can be downloaded fiom the neozones web site. A compatible compiler is much harder to find. The executable QBasic programs on the accompanying CD-ROM were generated with Microsoft PDS 7.1. However, Microsoft discontinued its support of the Professional Development System, and legal copies of QuickBasic 4.5 are no longer available either. There are a few BASIC compilers that can be downloaded from the neozones web site, but none of these compilers are fdly compatible with QBasic. The efforts to convert the source code are probably not worth the trouble, since execution in the QBasic environment is quite fast (in particular on Pentium class PCs, which are very common nowadays, see Section 6.1O), and the interpreter can handle much more complex programs than the ones presented in this book.

D.4 HRR-QB HRR-QB allows the user to create fire files that are read by ASET-QB and FIRM-QB. The f i e name extension (*.FIR) and file format are identical to those of the fire files in FPETool3.2 [4 l]. Therefore, if the user already has a database of FPETool fire fdes, there is no need to reenter the data to conduct simulations with ASET-QB or FIRM-QB. The fire files consist of numerical data in three parallel columns, followed by two lines of text. The first column is the time in seconds, the second column is the heat release rate in kW at the corresponding time in the first column, and the third column is the mass loss rate in g/s. The latter is equal to the heat release rate divided by the heat of combustion, which is supplied by the user. The mass loss rate is not used by ASET-QB and FIRM-QB, but it is needed for compatibility with FPETool. The values in the last row of the three columns are equal to -9, to designate the end of the numerical data. The first line of text contains the name of the fde, and the date it was created. The second line is a description of the fire file entered by the user. HRR-QB allows the user to create fire fdes for 3 fires as described in Section 4.4.1, a semi-universal fire as described in Section 4.4.2, pool fires as discussed in Section 4.4.3, and upholstered firrnitwre fires based on Babrauskas' triangle model described in Section 4.4.4.1. The program

QBASIC Programmer's Notes

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offers the user the option to enter a series of (t, 0 )data points on a curve, which can also be done directly fkom within ASET-QB and FIRM-QB. The main program code starts with a declaration section where functions, subroutines, and global variables are declared; constants are defied; and dimensions of m y s are specified. Next, an error trapping routine is enabled to handle disk and file errors. This is followed by the screen display of the main menu, which gives the user six choices: 1. create a ? fire fie, 2. create a semi-universal f i e file, 3. create a pool fire me, 4. create a fiuniture f i e fie, 5. create a custom fire file, or 6. exit. If the user selects the last option, the program terminates. If the user selects any of the fist five choices, he is prompted to do the following: Speczfi the jirejile name and path. Select the units. This only pertains to the input parameters or data subsequently specified by the user. Fire f i e data are always in S.I. units. Enter a description. This will be the last line of the fire file. Enter the heat of combustion ofthefuel. The default is 12,000 W/kg i.e., the effective heat of combustion of wood. Enter the ignition delay time. Provide the parameters or &a points for the type offrre selected. For example, for a P fire the user must specify the growth factor a, the time to maximum heat release rate t,, and the duration of the fire ten& Each type of fire is associated with a different block of code. The user is prompted for the required fire parameters (e.g., a,t,, and tend.for a fire), or data (for a custom fire), and data points are calculated and stored on disk. A Select Case ... End Select structure is used to activate the block of code corresponding to the main menu selection. The subroutine XYPlot is called to display a graph of the heat release rate curve on the screen. XYPlot in turn calls the DrawAxes and LinePZot subroutines. DrawAxes draws the x-axis and y-axis on the screen; with tick marks,labels, and titles. The description of the f i e is printed at the top of the graph. The Side Write subroutine writes the title of the y-axis vertically. The range for each of the axes is determined by a call to the MaxValue function, which finds the highest value in a one-dimensional array (also called a vector). Lineplot finally draws a line on the screen that connects all the data points. When the user is done viewing the graph, he is taken back to the main menu.

236

APPENDIX D

D.5 ASET-QB

ASET-QB is a QBasic version of the ASET model. The physical basis and limitations of the model, and the use of the program are discussed in Chapter 3. Here, some additional information is provided for QBasic programmers who want to customize the code. ASET-QB is more structured than HRR-QB. The main program is much shorter, and the major tasks are performed by subroutine or function calls. The program flow of ASET-QB is shown schematically on the chart in Figure D-l. The main program code again starts with a declaration section where functions, subroutines, and global variables are declared; constants are defined; and dimensions of arrays are specified. Next, an error trapping routine is enabled to handle printer errors, as well as disk and f i e enors. This is followed by a call to the InputData subroutine. InputData takes the user through a series of prompts to obtain the path for data files, the names of the output file (default extension *.AOF, which stands for ASET Output File) and fire (*.FIR) file, and the input data for the m (a brief description, and the values of A, H, 2, L, and Q). The heat release rate data can be read fiom a fire file, or can be specified by the user in the form of a series of (t, Q) data points (the same way as a custom fire file is created in HRR-QB). M e r initialization of all variables, headers and initial values are written to disk, displayed on the screen, and sent to the printer (the latter only if a hardcopy was requested). All data output is handled by the OupzitData subroutine. When the output of headers and initial values is completed, the program loops through a set of instructions to obtain the solution of the model equations at one second intervals. The subroutine ODESolve is called to advance the solution of the ODEs (3.2) and (3.7) by one time step. The time step used in ASET-QB is initially set at one second, but may be reduced by the ODE solver. ODESoZve performs the stepsize control described in Section B.5.3, and, if necessary, the stepsize is reduced according to Equation (B.74) to obtain the desired accuracy. The tolerances for the layer interface height and the upper layer temperature are set at kO.OO 1 m and kO.3"C respectively. They are identical to the rather high tolerances specified by Walton in ASET-B [3]. The basic Runge-Kutta equations are actually coded in a separate subroutine, called RungeKuttn. The values of the functions on the right hand side of the ODEs are calculated in subroutine Derivatives. This

Declare functions, subroutines, global variables; Define constants; Specify dimensions of arrays

l ~ n a b l eerror trapping 1

e et input data (lnputData subroutine)/

6 Initialize variables

Print headers and initial values (OutputData subroutine)

t

l solve ODES ( O ~ ~ S o l vsubroutine) e /

Update screen/file/printer

+

Z E n d of s i m u l a t i o n ' ? ?

Close files

FIGURE D-l. Flow chart of ASET-QB

subroutine is called by ODESoZve to determine the function values at (xi,yi),where x is the time, and y is the upper layer temperature or the layer interface height. RmgeKutta calls Derivatives to obtain the values at (xi + 0.5h,yi + OSk,), (xi + 0.5h,yi + 0.5k2), and (xi + h, yi + k,), where h is the stepsize, and k,, 4, and k; are defined in Equation p.73). The reader is referred to Section B.5.3 for a discussion of the fourth-order RungeKutta method. Derivatives in turn calls the QDod and PlumeFZow functions to determine the heat release rate at a given time (by interpolation of fire file data), and the rate of entrainment into the flame and fire plume (according to Zukoski's correlation) respectively. Every five seconds, OutputData is called to update the disk fde, screen display, and printer output. OutputData calls the VentFlows subroutine to obtain the outflow of air from the compartment. The sequence outlined in this paragraph is repeated until the specified end of simulation or the end of the fire file is reached, or until an event occurs that invalidates the model assumptions (for example, the upper layer drops below the fuel surface). At the end of the run, the user has the option to perform another simulation, in which case the program returns back to the line where InputData is called, to obtain a new set of input data.

D.6 FIRM-QB FIRM-QB is a QBasic version of the FIRM model developed in this book. The physical basis of FIRM-QB, the use of the program, and the predictive capability of the model are discussed in Chapters 5, 6, and 7 respectively. Here, some additional information is provided for QBasic programmers who want to customize the code. The structure of FIRM-QB is very similar to that of ASET-QB. In fact, FIRM-QB was created fiom ASET-QB, by changing or adding statements to include the additional features of FIRM-QB. The "document compare" feature in word processors, such as Wordperfect and Word, can be used to quickly determine what the differences are between the two programs. The declaration section of FIRM-QB is longer due to the additional futlctions, subroutines, global variables, constants, and arrays. Output data files generated by FIRM-QB have the extension *.FOF, which stands for FIRM Output File. The function HeatLossFraction was added to estimate the heat loss fiaction as described in Section 4.3.1. The user has the option to accept the estimated heat loss fraction, or to specify a different value.

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The Derivatives subroutine in FIRM-QB calls the VentFlows subroutine, because the vent flows are needed to calculate the function values on the right hand side of the ODEs. The VentFlows subroutine is much more complex in FIRM-QB, because the calculation of vent flows requires the solution of a non-linear algebraic equation (see Section 4.1.6). The bisection method is used to solve this equation. The code that performs these calculations is embedded into the VentFlows subroutine, instead of in a separate stand-alone subroutine (as for numerical solution of the ODEs). This approach has the advantage that it is easier to program, and the drawback that it is more difficult to reuse the code for the solution of the same type of problem in another application. XYPlot is called at the end of the main FIRM-QB program, allowing the user to view graphs of the upper layer temperature, layer interface height, heat release rate, and vent flow (outflow) versus time. XYPlot and the subroutines and functions that are called fiom XYPlot (DrawAxes, Lineplot, and indirectly SideWrite and MaxValue) are identical to those in HRR-QB, except for a menu that was added in XYPlot so that the user can select the variable to be plotted. When the user is done viewing the graphs, he can terminate the program, or start a new simulation.

---

Visual Basic Programs p

--

APPENDIX E --

E.l INTRODUCTION In 1991, Microsoft released a new graphics-oriented, event-driven BASIC compiler for Windows, called Visual Basic. The objective was to provide a programming tool that is largely compatible with BASIC, has much of the simplicity of BASIC, but is powerful enough so that it can be used to develop Windows applications. Shortly after the release of the Windows version, Microsoft introduced Visual Basic for MS-DOS. The DOS version operated in a similar way as the Windows version, but with windows (calledforms in Visual Basic) in text mode instead of graphics mode. Support for the DOS version of Visual Basic was quickly dropped, as Windows became the opcrating system of choice for IBM and compatible PCs. There are major fundamental differences between QBasic and Visual Basic. In a QBasic program, the sequence of events is a priori determined by the programmer. For example, a QBasic program that first gets some input values from the user, will always go through the same sequence of input variable prompts. It is not possible at any point during the sequence to change a variable that was specified earlier in the sequence. The only option is to restart the program. In Visual Basic, the user would be presented with a window (form) that has various input data entry fields, and be allowed to enter the data in any order. This is obviously much more user-fi-iendly. Rather than going through a sequence of instructions, Visual Basic programs respond to events, such as entering data in a text box, pressing a button, etc. The user dictates the sequence of events, not the programmer. The three QBasic programs presented in this book were rewritten in Visual Basic 6.0 (the current version at the time of this writing). The source code and compiled programs are installed on the user's hard drive

during the setup process discussed in Section C.3.2. The following three sections provide a brief tutorial of the compiled Visual Basic programs HRR-VB, ASET-VB, and FIRM-VB. The final section provides some useful information to readers who wish to customize the Visual Basic source code to meet specific needs.

E.2 RUNNING HRR-VB In this section the reader will be shown how to use HRR-VB to create a fire file. Walton's ASET-B example case f r e (see Section 3-5) will be used. To start HRR-VB, follow the instructions in Section C.3.3. A welcome screen is displayed with the graphic image, the name of the program (KRR-VB), the version number, and some copyright information. This is commonly referred to as a splash screen (see Figure E-l). If the user clicks on the Quit button, the program terminates. Clicking on the Continue button (or pressing Enter) leads to the main data input screen. Figure E-2 shows the input screen, with the description field already completed. Because HRR-VB is not a very complex program, there is no extensive help feature. Some assistance is provided in the form of ToolTips, i.e., informative text boxes that pop up when the user points at

FIGURE E-l. HRR-VB splash screen

Visual Basic Programs

243

FIGURE E-2. HRR-VB main input data screen

a control on the screen. Figure E-2 shows the ToolTip that appears when the user points at the U.S. Engineering Units option button. The U.S. engineering units for length, area, mass, temperature, and energy are displayed in the text box. When the user clicks on, or moves the cursor to the Fire File Name Field, a dialog box pops up that allows the user to select a file name (see Figure E-3). A separate dialog box minimizes the risk that an existing file name is specified and overwritten by mistake, because the user can verify whether the fde already exists and will be asked to confm overwriting any existing file. Figure E-3 shows that the specified file, APPE-A0 1, does not exist. This will not be the case if the user copied the data files fiom the CD-ROM as specified in Section C.2.2. The extension .FIR is automatically appended to the file name. Note that C:\FIRMU>ATA\is the default directory for fire files. To go back to the main input data menu, click on the Save button. Since we will enter heat release rates in kW, there is no need to change the units. The Heat of Combustion field can also be left unchanged, because it is only needed to calculate mass loss rates, and does not affect the fire data that are used by ASET-VB and FIRM-VB. The user can enter a delay time in the text box in the lower left corner of the main data input screen. This may be useful toaccount for delayed ignition of the fuel. For example, for the furniture fire simulations discussed in Section 7.3S.1, an ignition delay was added to synchronize the triangular heat release curves

244

APPENDIX E

FIGURE E-3. Dialog box to specifl the fire file name

based on Babrauskas' model with the experimental data. We are now ready to enter the heat release rate curve, so click on the Custom Fire command button (or press the Tab key several times until the Custom Fire button is highlighted and press Enter, or press Alt + C). The program verifies that the delay time is indeed zero, and returns to the main data input screen if a delay time has to be specified. If no delay time is needed, the program displays the custom fue parameter screen. Figure E-4 shows the screen after the data points of Walton's ASET-B example case fue curve have been entered. If there are more than 10 data points on the curve, the user can click the Next 10 Points command button when the first screen is completed. A second blank screen is then presented. This process can be repeated until 1800 data pairs have been entered. In our case we only have four data pairs, so we can click the OK button. The next screen is a graph of the heat release curve (see Figure E-5). If the user is satisfied with the curve, he can click the Save button to write the data to disk. A File Save dialog box is displayed to give the user a fmal opportunity to change the fde name, and avoid possible data loss by overwriting an existing file. After the data are saved, the program returns to the graph screen. The Save button is disabled to indicate that the data were indeed saved. Clicking the Close button takes the user back to the main input data screen. If the Close button is clicked before the Save button, the user is asked to confirm that he does not want to save the data.

FIGURE E-4.HRR-VB custom fire parameter screen

FIGURE E-5. Graph of Walton's ASET-B example case fire curve

245

246

APPENDIX E

While HRR-VB is running, it is recommended that the reader create a fire fde for the acetone dip tank example described in Sections 6.5,6.9, and 6.11.3. The main data input and pool fue parameter screens are shown in Figures E-6 and E-7.

FIGURE E-6.Main HRR-VB input data screen for acetone dip tank fire

FIGURE E-7.Pool fire parameters for acetone tank

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E.3 RUNNING ASET-VB To start ASET-VB, follow the instructions in Section C.3.3. A welcome screen is displayed that is identical to the HRR-VB splash screen, except for the program name (ASET-VB in this case). Clicking the Continue button leads to the main input data screen, fkom where all input variables are specified. This can be done in two ways. The fust way is by moving through the input fields and entering the necessary information in each field. The second approach consists of retrieving the variables fkom an existing output file, and modifying the input fields as needed. The second approach can save the user a lot of time, in particular if a sensitivity study needs to be conducted (see Section 7.3.4.3). To illustrate this approach, perform the following steps to prepare ASET-VB for Walton's ASET-B example case. It is assumed that the reader installed the QBasic program and data fdes to the default directories on the hard disk, as specified in Section C.2.2. Choose Open fkom the File menu. Select CH3-A0 l .AOF fkom the Open File dialog box. Change the description to "ASET-VB SAMPLE RUN OF WALTON'S ASET-B EXAMPLE CASE," i.e., change ASET-QB to ASET-W. Change the output data file name to APPE-A01 .AOF. Change to U.S. engineering units, and correct the geometric data. (ASET-QB and ASET-VB work internally in S.I. units, and conversions back and forth between the two unit systems result in slight roundoff errors). The correct values for A, H, and 2, are 225 ft2, 9 ft, and 1 A respectively. Change the fue file name to APPE-A0 1.FIR. The completed input data screen is shown in Figure E-8. Clicking Run initiates the calculations. An output data screen is displayed, as shown in Figure E-9. Only seven lines of results fit inside the window, and the vertical scroll bar allows the user to go through and inspect the entire data set. The results on this screen are identical to the ASET-QB data presented in Table 3- 1, and those stored in CH3-A0 1.AOF.

FIGURE E-8. Completed ASET-VB input data screen

FIGURE E-9. Sample output data screen generated by ASET-VB

248

Visual Basic Programs

249

E.4 RUNNING FIRM-VB

Running FIRM-VB is similar to naming ASET-VB and HRR-W. The main input screen has more controls, and allows the user to specifl all input variables (see Sections 6.5 and 6.6.2 for a list of the variables, and a brief description). Figure E-10 shows the completed input data screen for the acetone dip tank example described in Sections 6.5, 6.9, and 6.11.3. Provided the geometric data have been entered, the user can request that the program estimate the total heat loss coefficient, L,, by clicking the command button below the L, field. Figure E-l l shows the FIRM-VB output screen for the acetone dip tank example. The results on this screen are identical to the FIRM-QB data presented in Figure 6-2, and stored in CH6-CO1.FOF. Clicking the Graph button on the output screen leads to a new screen that allows the user to view graphs of the upper layer temperature, layer interface height, heat release rate, and vent flow as a b c t i o n of time.

FIGURE E-10. FIRM-VB input data screen for acetone dip tank example

250

APPENDIX E

FIGURE E-11. FIRM-VB output data screen for acetone dip tank example

E.5 CUSTOMIZING THE VISUAL BASIC PROGRAMS If the reader wants to modifi the Visual Basic source code, he will need to load the source program (*.VBP extension) into the Visual Basic programmitlg environment. As a minitnum, the reader will need a working model of Visual Basic 6.0 to run the programs. There are several books on the market that come with a working model of Visual Basic 6.0 (see Section C.3.3). If the reader wants to compile his programs, he will need more than a working model. Microsoft released different versions of Visual Basic 6.0, to suit the needs of any programmer, ranging fiom the novice to the professional. All changes to the Visual Basic programs must be clearly documented by adding clarifying comment statements to the source code, and by providing an extensive discussion of the changes in any report or publication of the model calculations. This discussion must be detailed enough so that others can reproduce the results. If the changes are extensive, the predictive capability of the modified model may have to be re-evaluated (see Chapter 7).

REFERENCES

1. Mitler, H. E. 1987. "User's Guide to FIRST, A Comprehensive Single-Room Fire Model," NBSIR 87-3595, National Bureau of Standards, Washington, DC. 2. Peacock, R. D., G. P. Forney, P. Reneke, R. Portier, and W. W. Jones. 1993. "CFAST, the Consolidated Model of Fire Growth and Smoke Transport," NIST Technical Note 1299, National Institute of Standards and Technology, Gaithersburg, MD. 3. Walton, W. D. 1985. "ASET-B: A Room Fire Program for Personal Computers," NBSlR 85-3144-1, National Bureau of Standards, Washington, DC. 4. Kanury, A. M. 1987. "On the Craft of Modeling in Engineering and Science," Fire Safety Journal, 1265-74. 5. Friedman, R. 1992. "An International Survey of Computer Models for Fire and Smoke," Journal of Fire Protetction Engineering, 4:8 1- 92. 6. Cooper, L. Y. 1980. "Estimating Safe Available Egress Time from Fires," NBSIR 80-2172, National Bureau of Standards, Washington, DC. 7. Steckler, K. D., H. R. Baum, and J. G. Quintiere. 1986. "Salt Water Modeling of Fire Induced Flows in Multi-Compartment Enclosures," NBSIR 86-3326, National Bureau of Standards, Washington, DC. 8. Prahl, J. and H. W. Emmons. 1975. "Fire Induced Flow through an Opening," Combustion and Flame, 25:369-385. 9. 1992. Fire Protection Handbook. 17th Edition. National Fire Protection Association: Quincy, MA. 10. Fitzgerald, R. W. 1982. The Anatomy of Building Firesafety. Worcester Polytechnic Institute, Worcester, MA. 11. Berlin, G. N. 1982. "A Simulation Model for Assessing Building Fire Safety," Fire Technology, 18. 12. Galea, E. 1988. "On the Field Modeling Approach to the Simulation of Enclosure Fires," Journal of Fire Protection Engineering, 1:11-22. 13. Emmons, H. W. 1983. "The Calculation of a Fire in a Large Building," Journal of Heat Transfer, 105:151- 158. 14. Zukoski, E. E. 1978. "Development of a Stratified Ceiling Layer in the Early Stages of a Closed-Room Fire," Journal of Fire and Materials, 7:54-62. 15. DiNenno, P. J., ed 1995. The SFPE Handbook of Fire Protection Engineering. Second Edition. Boston, MA: Society of Fire Protection Engmeers.

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16. Klote, J. H., and J. W. Fothergill. 1983. "Design of Smoke Control Systems for Buildings," NBS Handbook 141, National Bureau of Standards, Washington, DC. 17. Butcher, E. G. and A. C. Parnell. 1979. Smoke Control in Fire Safety Design. London: E. & F. N. Spon Ltd. 18. 1986. "Measured Air Leakage in Buildings," STP 904, ASTM, West Conshohocken, PA. 19. Beyler, C. L. 1986. "Fire Plumes and Ceiling Jets," Fire Safety Journal, 11:53-75. 20. Forney, G. P. 1994. "Analyzing and Exploiting Numerical Characteristics of Zone Fire Models," Fire Science & Technology, 14:49-60. 2 1. Zukoski, E. E., T. Kubota, and H. Cetegen. l98OA98 1. "Entrainment in Fire Plumes," Fire Safety Journal, 3: 107- 121. 22. Morton, B. R., G. F. Taylor, and J. S. Turner. 1956. "Turbulent Gravitational Convection from Maintained and Instantaneous Sources," in Proceedings of the Royal Society, A234: 1- 23. 23. Yokoi, S. 1960. Building Research Report No. 34, Ministry of Construction, Tokyo, Japan. 24. Kawagoe, K. 1958. "Fire Behavior in Rooms," Report No. 27, Building Research Institute, Ministry of Construction, Tokyo, Japan. 25. Thornton, W. 1917. "The Relation of Oxygen to the Heat of Combustion of Organic Compounds," Philosophical Magazine and J. of Science, 33. 26. Huggett, C. 1980. "Estimation of the Rate of Heat Release by Means of Oxygen Consumption," J. of Fire and Flammability, l2:6 1- 65. 27. Siegel, R. and J. Howell. 1981. Xhermal Radiation Heat Transfer.New York, NY: Hemisphere Publishing Company. 28. Modak, A. T. 1979. "Mation from Products of Combustion," Fire Research, 1:339-361. 29. Oziqk, M. N. 1985. Heat Transfer.A Basic Approach. New York, NY: McGraw Hill Book Company. 30. Cooper, L. Y. 1993. "Fire-Plume-Generated Ceiling Jet Characteristics and Convective Heat Transfer to Ceiling and Wall Surfaces in a Two-Layer Fire Environment: Uniform Temperature Walls and Ceiling," Fire Science & Technology, 13:1- 17. 31. Beller, D. K. 1987. "Alternate Computer Models of Fire Convection Phenomena for the Harvard Computer Fire Code," M.S. Thesis, Worcester Polytechruc Institute, Worcester, MA. 32. Satterfield, D; B. and J. R. Barnett. 1990. "User's Guide for WPUFire Version 2 Compartment Fire Model," Worcester Polytechnic Institute, Worcester, MA. 33. Sarnarskii, A. A., and P. N. Vabishchevich. 1995. Computational Heat Transfer (2 Volumes).Chichester, England: John Wiley & Sons Ltd. 34. Petzold, L. R. 1982. "A Description of DASSL: A DifferentiaVAlgebraic System Solver," Technical Report 8637, Sandia National Laboratories, Albuquerque,

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35. Cooper, L. Y., and D. W. Stroup. 1982. "Calculating Safe Egress Time (ASET) - A Computer Program and User's Guide," NBSIR 82-2578, National Bureau of Standards, Washington, DC. 36. Cooper, L. Y. 1983. "A Concept for Estimating Available Safe Egress Time in Fires," Fire Safely Journal, 5:135- 144. 37. Cooper, L. Y. 1982. "A Mathematical Model for Estimating Available Sale Egress Time in Fires," Fire and Materials, 6:135- 144. 38. Cooper, L. Y. and D. W. Stroup. 1985. "ASET - A Computer Program for Calculating Safe Egress Time," Fire Safety Journal, 9:29- 45. 39. DiNenno, P. J. 1985. "ASET-B: A Room Fire Program for Personal Computers," Software Review, Fire Technology, 2 1:322- 323. 40. Walton, W. D. 1985. 'ASET-B: A Room Fire Program for Personal Computers," Fire Technology, 2 11293-309. 41. Deal, S. 1995. "Technical Reference Guide for FPETool Version 3.2,"NISTIR 5486-1, National Institute of Standards and Technology, Gaithersburg, MD. 42. Cooper, L. Y. 1983. "The Development of Hazardous Conditions in Enclosures with Growing Fires," Combustion, Science and Technology, 33:279-297. 43. Boyce, W. E. and R. C. DiPrima. 1977. Elementary D~flerentialEquations and Boundary Value Problems. New York, NY: John Wiley & Sons. 44. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. 1992. Numerical Recipes in Fortran - The Art of Scientrfic Computing. Second Edition. Cambridge, England: Cambridge Universty Press. 45. 1997. "Standard Guide for Use and Limitations of Deterministic Fire Models," ASTM, West Conshohocken, PA. 46. Birk, D. Personal Communication with G. Heskestad. 47. Milke, J. A. 1989. "Smoke Management Design Considerations for Covered Malls and Atria," International Fire Protection Engineering Institute, Ottawa Ontario, Canada. 48. Babrauskas, V. 1983. "Upholstered Furniture Heat Release Rates: Measurements and Estimations," Journal of Fire Sciences, 1 :9-32. 49. Steckler, K. D., H. R. Baurn and J. G. Quintiere. 1984. "Fire Induced Flows through Room Openings - Flow Coefficients," NBSIR 83-2801. National Bureau of Standards, Washington, DC. 50. Nakaya, I., T. Tanaka, M. Yoshida, and K. Steckler. 1986. "Doorway Flow Induced by a Propane Burner," Fire Safety Journal, 10:185- 195. 5 1. Peacock, R. D., S. Davis, and B. T. Lee. 1988. "An Experimental Data Set for the Accuracy Assessment of Room Fire Models," NBSIR 88-3752. National Bureau of Standards, Washington, DC. 52. Lawson, J. R. and J. G. Quintiere. 1985/1986. "Slide Rule Estimates of Fire Growth," Fire Technology, 2 1 :267-292, and 22:45- 53. 53. Nelson, H. E. 1986. "FIREFORM- A Computerized Collection of Convenient Fire Saftety Computations," NBSIR 86-3388, National Bureau of Standards, Washington, DC. 54. Rockett, J. A. 1976. "Fire Induced Flow in an Enclosure." Combustion Science and Technology, 12:l65 - 175.

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55. Mitler, H. E. 1978. "The Physical Basis for the Harvard Computer Fire Code," Home Fire Project Technical Report No. 34, Harvard University, Cambridge, MA. 56. Babrauskas, V. 1984. "Upholstered Furniture Room Fire Measurements. Comparison with Furniture Calorimeter Data and Flashover Predictions," Journal of Fire Sciences, 2:2- 19. 57. Drysdale, D. 1985. An Introduction to Fire Dynamics. New York, NY: John Wiley & Sons. 58. 1996. "National Fire Alarm Code," NFPA 72, National Fire Protection Association, Quincy, MA. 59. 1998. "Guide for Smoke and Heat Venting," NFPA 204, National Fire Protection Association, Quincy, MA. 60. Babrauskas, V. 1996. "Fire Modeling Tools for FSE: Are They Good Enough?" Journal of Fire Protection Engineering, 8:97-96. 61. Schifiliti, R. P. 1986. "Alternate Computer Models of Fire Convection Phenomena for the Harvard Computer Fire Code," M.S. Thesis, Worcester Polytechnic Institute, Worcester, MA. 62. Babrauskas, V. 1986. "Free Burning Fires," Fire Safety Journal, 11. 63. Babrauskas, V. 1983. "Estimating Large Pool Fire Burning Rates," Fire Technology, 19:251- 26 1. 64. Babrauskas, V., J. R. Lawson, W. D. Walton, and W. H. Twilley. 1982. "Upholstered Furniture Burning Rates as Measured with a Furniture Calorimeter," NBSIR 82-2604, National Bureau of Standards, Washington, DC. 65. Parker, W. J. 1982. "Calculations of the Heat Release Rate by Oxygen Consumption for Various Applications," NBSIR 8 1-2427, National Bureau of Standards, Washington, DC. 66. Janssens, M. L. 1991. "Measuring Rate of Heat Release by Oxygen Consumption," Fire Technology, 27:234-249. 67. 1996. "Standard Test Method for Fire Testing of Real Scale Upholstered Furniture Items," ASTM E 1537, ASTM, West Conshohocken, PA. 68. 1987. "Upholstered Furniture Fire Behavior - Full-scale Test," NORDTEST NT Fire 032, NORDTEST, Helsinki, Finland. 69. Krasny, J. F., V. Babrauskas, and W. J. Parker. 1998. "Fire Behavior of Upholstered Furniture Items," in press. 70. 1997. "Standard Test Method for Heat and Visible Smoke Release Rates for Materials and Products Using an Oxygen Consumption Calorimeter," ASTM E 1354, ASTM, West Conshohocken, PA. 71. Babrauskas, V. and W. D. Walton. 1986. "A Simplified Characterization of Upholstered Furniture Heat Release Rates," Fire Safety Journal, 11:18 1- 192. 72. Babrauskas, V. and J. Krasny. 1985. "Fire Behavior of Upholstered Furniture," NBS Monograph 173, National Bureau of Standards, Washington, DC. 73. Peacock, R. B. and J. N. Breese. 1982. "Computer Fire Modeling for the Prediction of Flashover," NBSIR 82-2516, National Bureau of Standards, Washington, DC. 74. 1992. "Standard Guide for Documenting Computer Software for Fire Models," ASTM E 1472, ASTM, West Conshohocken, PA.

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75. 1997. "Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models," ASTM E 1355, ASTM, West Conshohocken, PA. 76. Siirdqvist, S. 1993. "Initial Fires: HRR, Smoke and CO Generation from Single Items and Room Fire Tests," LUTVDGtTVBB-3070-SE, Lund University, Department of Fire Technology, Lund, Sweden. 77. Bell, J. R., T. J. Klem, and A. W Willey. 1982. "Investigation Report Westchase Hilton Hotel Fire," NFPA No. LS-7, National Fire Protection Association, Quincy, MA. 78. Mitler, H. E. and H. W. Ernrnons. l98 1. "Documentation for CFC V, The Fifth Harvard Computer Fire Code," NBS-GCR-81-244, National Bureau of Standards, Washington, DC. 79. 1997. "Code for Safety to Life from Fire in Buildings and Structures," NFPA 101, National Fire Protection Association, Quincy, MA. 80. Babrauskas, V. 198111982. "Will the Second Item Ignite?" Fire Safety Journal, 4:281-292. 81. Khoudja, N. 1988. "Procedures for Quantitative Sensitivity and Performance Validation Studies of a Deterministic Fire Safety Model," NBS-GCR-88-544, National Bureau of Standards, Washington, DC. 82. Davies, A. D. 1985. "Applied Model Validation," NBSIR 85-3154-1, National Bureau of Standards, Washington, DC. 83. Bukowski, R. W. 1985. "The Application of Models to the Assessment of Fire Hazards from Consumer Products," NBSIR 85-3219, National Bureau of Standards, Washington, DC. 84. Watts, J. M., Jr. 1987. "Validating Fire Models," Fire Technology, 23:93-94. 85. 1999. "Standard Terminology of Fire Standards," ASTM E 176, ASTM, West Conshohocken, PA. 86. Keski-Rahkonenen, 0 . 1996. "CIB W l 4 Round Robin of Code Assessment: A Comparison of Fire Simulation Tools," in Proceedings of the Conference on Fire Safety Design of Buildings and Fire Safety Engineering, Oslo, Norway, August 19-20,l- 14. 87. 1999. "Standard Guide for Room Fire Experiments," ASTM E 603, ASTM, West Conshohocken, PA. 88. Peacock, R. B. and J. N. Breese. 1982. "Computer Fire Modeling for the Prediction of Flashover," NBSIR 82-25 16, National Bureau of Standards, Washington, DC. 89. Iman, R. L. and Shortencarier. 1984. "A FORTRAN 77 Program and User's Guide for the Generation of Latin Hypercube and Random Samples for Use with Computer Models," NUREGICR-3624, SAND83-2365, Sandia National Laboratories, Albuquerque, NM. 90. 1997. "Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method," ASTM E691, ASTM Standards on Precision and Biasfor Various Applications, 5" Edition, ASTM, West Conshohocken, PA. 91. 1986. "Precision of Test Methods - Determination of Repeatability and Reproducibility for a Standard Test Method by Inter-Laboratory Tests," IS0 5725, International Origanization for Standardization,Geneva, Switzerland.

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INDEX

Absorption coefficient, 92 Absorptivity, 204 Adiabatic flame temperature, 2 16-218 Air Composition, l98,2 11 Density, 27 Equivalence ratio, 2 15 Hydrostatic pressure, 15 Specific heat, 54,198 ASET fire model Assumptions, 54 Derivation of equations, 54- 57 Limitations, 63- 67 Model runs, 61-63,133 Numerical solutions, 58- 59 Programmer's notes, 236- 238,250 Running the software, 228-230 Software installation, 227-230 Atom, 2 10 Available safe egress time, 8,5 1,65, 142 Avogadro's hypothesis, 2 10 BASIC, 8-9,232-234,250 Bernouilli's equation, 24, 189 Bisection method, 78, 116- 117, 22 l-223,239 Blackbody radiation, 205 Boltzmann constant, 182,207 Boundary layer, 186,202- 203 Buoyancy, l85,2O 1,203 Burning rate Pool fire, 92- 94 Upholstered furniture, 95- 102

Ceiling jet, 2,42,84-87,201 CFAST fire model, ix, 8,12 Closed system, l99 Compartment fire, 1-4 Computer language, 8 BASIC, see BASIC FORTRAN, see FORTRAN QBASIC, see QBASIC Visual Basic, see Visual Basic Conduction, 42-43,200-201 Conservation equation Energy, 37-48,199 Mass, 20- 34, 188 Momentum, 188- 190 Species, 34-37 Continuity equation, see Conservation equation of mass Control volume, 13, 188, 199 Convection, 4 1-42,2O 1- 204 Density, 183 Deterministic fire model, 7,9 Diffusion flame, 2 19 Dimensional analysis, 190,202 Dynamic viscosity, 187 Emissivity, 38-40,207 Enthalpy, 196- 197 Entrainment, 20- 24,174- 175 Euler method, 58- 59,224-225 Extinction coefficient, 39- 40,209 FAST fire model, 179- 180 FASTLITE fire model, 179- 180

258

Index

FIRE DYNAMICS SIMULATOR, 180 Fire model Field, 7, 180 Stochastic, 4 Zone, 7- 8 Fire plume, 51, 105, 112,238 FIRM fire model Assumptions, 113 Derivation of equations, 114- 116 Documentation, 154 Evaluation of predictive capability, 154- 156 Limitations, 144 Model runs, 128- 144,155- 178 Numerical solutions, 116- 117 Programmer's notes, 238-239,250 Running the software, 228-230 Software installation, 227- 230 Validation, 154 Verification, 154 FIRST fire model, xi, 8, 12- 13,40,42, l80 Flame height, 2 19 Flame temperature, 2 16-218 Flammable liquid, see Pool fire Flashover, 2, 104- 110, 129- 137, 139- 142,155- 1S6 Fluid, 183 Fluid dynamics, 185- 191 Fluid statics, 184- 185 FORTRAN, 8,5 1- 52 Fourier's law, 200 FPETool fire model, 53,95, 100, 117, 122,125,180,234 Free convection, 20 1 Free-burning fire, 2 19-220 Froude number, 191 Furniture calorimeter, 95-96 Grashof number, 203 Grey surface, 207

HARVARD fire model, 8,71, 15 1

Health care facilities, l38 Heat conduction, 200- 20 1 Heat flux, 39,41-42,49, 106,201

Heat loss fraction Estimate, 6 1 Limitations, 67 Prediction, 83- 87 Sensitivity analysis, 155- l56 Heat of combustion, 82,93- 94, 103, 216-217 Heat release rate predictions, 87- 103 Heat transfer Conductive, see Conduction Convective, see Convection Radiative, see Thermal radiation Heat transfer coefficient, 181,202,204 Hotel fire, 128-130 Hot-layer, 2-6,56,65-66,70 Hydrostatic pressure, 15,24,25, 185 Ideal gas, 184 Ignition delay, 159 Incomplete combustion, 4 2 18 Interior finish, 89 Internal energy, l96 Isobaric, 199 Isothermal, 41, 152,207 Kinematic viscosity, 181, 187, 191, 202

LAVENT fire model, 180 Layer interface height, 19 Life safety code, 138 Lower flammability limit, 2 18 Mass action, 2 13 Mass loss rate, 13,20,34,92,100, 122,125,158,234 Mathematical fire modeling, 7, l l, 4, 53,180 Mean beam length, 39,40,92,209 Methane, 82, 169, 171,211-215,218 Mole, 182, 193,210-21 1 Molecular mass, 184,193,2 10,212 Molecule, 210-21 1,215 Momentum, 7- 8,42,185,187- 188, 202

Index

Natural convection. 41,201,203,204 Navier-Stokes equations, 189 Neutral plane, 20,25-27,30,72, 156 Newton-Raphson method, 223 Newton's law, 188,202 Numerical solution techniques, 52 Nusselt number, 4 1,203-204 Orifice flow, l89 Oxygen starvation, 54,66, 113-115, 159,168 Partial pressure, 192 Pascal's law, 184 Planck's equation, 205 Plume, l-3,20-24 Pool fire, 92, 142,235,246 Pressure, 183 Products, 2 11 Propane, 82,213-215,217,218 Pyrolysis, 2 19

Radiation, see Thermal radiation Radiative fraction, 54, 126, 134, 175 Reactants, 2 11-215 Reflectivity, 205 Reynolds number, 190- 191,203 Runge-Kutta method, 59, 116,223, 225 Sensitivity analysis, 140, 151, 155 Shear stress, 186, 187 Simple Chemically Reacting System, 35,214 SMARTFlRE fire model, 180 Species conservation, 34,48 Specific heat, 197- 198 Stack effect, 70,7 1 Stoichiometry, 36,37,2 11,2 17 Stratification, 54,64,65, 113 Streamline, 186,189 System, 191 fire, 88, 100,234

259

Thermal diffusivity, 20 1,202 Thermal radiation, 38- 4 1,204- 209 Thermodynamics, 191- 199 Time shifting, 153 Transmissivity, 40,205 Truncation error, 22 1,224-226 Turbulent flow, 187,189,19 1,204 Turbulent viscosity, l87 Universal gas constant, 182, 184, 193, 2l 3 Untenability, 136, 137, 142 Upholstered fiuniture, 95- 103 Validation of fire models, 147- 148, 150,154 Vena contracts, 189 Vent flow, 24- 32,69- 79 Vent flow regimes, 7 1- 72 Verification of fire models, 147, 149, 154 View factor, 207 Viscosity, 186- 187 Visual Basic, 230,240-241 Westchase Hilton hotel fire, 128-130 Wien' s displacement law, 205- 206 Work, 194- 195