Fire Safety Science 9780203973493, 1851667199, 9781851667192

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FIRE SAFETY SCIENCEPROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM Editors

Geoffrey Cox Brian Langford Fire Research Station, Borehamwood

INTERNATIONAL ASSOCIATION FOR FIRE SAFETY SCIENCE

f.7\ Taylor & Francis ~

Taylor&FrancisGroup LONDON AND NEW YORK

Published by Taylor & Francis 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN 270 Madison Ave, New York NY 10016 Transferred to Digital Printing 2007 British Library Cataloguing in Publication Data Fire safety science. I. Cox, Geoffrey II. Langford, Brian III. International Association for Fire Safety Science 628.92 ISBN 1-85166-719-9 Library of Congress Cataloging-in-Publication Data Fire safety science: proceedings of the third international symposium /editors, Geoffrey Cox, Brian Langford; International Association for Fire Safety Science. p. cm. 'The Third International Symposium on Fire Safety Science was held at the University of Edinburgh, Scotland from 8-12 July 1991 '-Pref. Includes bibliographical references and index. ISBN 1-85166-719-9 1. Fire prevention-Congresses. 2. Fire-Congresses. I. Cox, Geoffrey. II. Langford, Brian. III. International Association for Fire Safety Science. IV. International Symposium on Fire Safety Science (3rd: 1991: University of Edinburgh) TH9112.F5628 1991 91-30884 626.9'2-dc20 The editors and authors have maintained the highest possible level of scientific and technical scholarship and accuracy in this work, which is not intended to supplant professional engineering design or related technical services, and/or industrial or international codes and standards of any kind. The editors and authors assume no liability for the application of data, specifications, standards, or codes published herein. No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Special regulations for readers in the USA This publication has been registered with the Copyright Clearance Center Inc. (CCC). Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside the USA. should be referred to the publisher. 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.

Publisher's Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original may be apparent

Preface

The Third International Symposium on Fire Safety Science was held at the University of Edinburgh, Scotland, from 8-12 July 1991. There were 326 registrants attending two parallel sessions in which 92 papers were presented. Thirty countries were represented: Australia, Belgium, Brazil, Canada, China, Denmark, Finland, France, Germany, Hong Kong, India, Ireland, Israel, Italy, Japan, Korea, Malaysia, The Netherlands, New Zealand, Norway, Poland, Portugal, Spain, South Africa, Sweden, Switzerland, Union of Soviet Socialist Republics, United Kingdom, United States of America and Yugoslavia. The formal opening ceremony was conducted in the George Square Theatre by Lord James Douglas-Hamilton, Ministerfor Home Affairs and the Environment at the Scottish Office. Welcome addresses were given by Sir David Smith, Principal of the University of Edinburgh and Dr Philip Thomas, Chairman of the International Association for Fire Safety Science. Sir David Smith read a message of welcome from His Royal Highness the Duke of Edinburgh, Chancellor of the University and Patron of the symposium. Following the opening ceremony, Dr P. H. Thomas delivered the Howard W. Emmons Plenary Lecture entitled 'Fire, Flames and Dimensional Analysis'. Papers were accepted on the basis of their quality and originality in the science of fire safety and its applications. Eighty-six papers from the 168 offered were accepted after peer review. In addition to these and the plenary lecture, eight invited papers were also presented during the course of the symposium by Professor T. Hirano, Dr V. R. Beck (delivered by Dr D. Yung), Dr J. McQuaid (delivered by Dr B. Thomson), Professor Y. Uehara, Dr M. Curtat, Mr D. Gross, Professor H. Luck and Dr J. E. Snell. At the Thursday evening dinner, Dr P. H. Thomas was presented by Professor Emmons with the H. W. Emmons Invited Lectureship Award. The plaque recording the names of all Award recipients was passed on to the University of Edinburgh to retain until the next symposium. Professor P. J. Pagni, Chairman of the Awards Committee, presented the Medal of Excellence for the best paper of the Second Symposium. That paper by H. R. Baum and B. J. McCaffrey was entitled 'Fire Induced Flow Field-Theory and Experiment'. The award was received by Dr Baum and by Mrs Carmel McCaffrey on behalf of her late husband. At the committee meeting of the International Association for Fire Safety Science held during the symposium it was agreed that this award be designated the Philip Thomas Medal of Excellence. The chapters that follow are in the order of the ten technical sessions at the symposium with invited papers collected together in an opening section. Three papers accepted but not delivered to the symposium are not included. A new feature of this symposium was the Poster Session. Twenty-four posters were displayed in the foyer of the Appleton Tower where breaks between lectures were taken. Titles and authors of posters are listed towards the end of this volume. iii

The Association would like to record its gratitude to all the committees appointed to organise the various aspects of this successful symposium. It would particularly like to thank Dr D. Drysdale, Chairman of the Arrangements Committee, and his team for their efficient organisation of an enjoyable and technically valuable symposium, and Dr T. Kashiwagi, Professor S. E. Magnusson, Dr J. G. Quintiere and Professor Y. Uehara who coordinated the reviews of manuscripts. The Chairman of the Publications Committee also wishes to thank Lilian Lawson, Pat Walsh and other colleagues at the Fire Research Station for their unstinting support. The Association acknowledges the support of the following organisations for their generous contributions which helped ensure the success of the symposium: ABB Impell Ltd BAA pic Brandforsk, Sweden British Rail pic British Steel pic Courtaulds pic Edinburgh District Council Factory Mutual Research Corporation, USA Fire Research Station Fire Service Research and Training Trust Gent Ltd The Home Office Marks and Spencer pic National Institute for Standards and Technology, USA The Scottish Office The University of Edinburgh

Geoffrey Cox Chairman, Publications Committee

Borehamwood, UK

July 1991

iv

International Association for Fire Safety Science

The International Association for Fire Safety Science (IAFSS) was established in 1985 at the First International Symposium on Fire Safety Science held at the National Institute of Standards and Technology (then the National Bureau of Standards). Gaithersburg, Maryland, USA. It was founded with the primary objectives of encouraging research in the science of preventing and mitigating the adverse effects of fires and of providing a forum for presenting the results of such research. In 1988 the Association acquired the status of a registered charity in England and Wales. Since its inaugural meeting, the Association has grown in stature and influence under the guidance of its officers and Committee. These were: Chairman, Dr P. H. Thomas; Vice-Chairmen, Dr R. Friedman, Professor K. Kawagoe and Professor O. Pettersson; Secretary, Professor T. Hirano; and Treasurer, Professor J. G. Quintiere. Committee members were: Mr G. Cox, Dr M. Curtat, Professor R. W. Fitzgerald, Dr T. Z. Harmathy, Professor S. Horiuchi, Dr M. Kersken-Bradley, Mr H. E. Nelson, Professor P. J. Pagni, Mr K. S. Pedersen, Professor D. J. Rasbash, Professor P. G. Seeger, Dr J. E. Snell, Professor Y. Uehara, Dr J. Unoki, Professor T. Wakamatsu, Professor R. B. Williamson and Dr W. D. Woolley. During the course of the Third Symposium a new committee was nominated and elected at the general meeting of the Association. The new committee was constituted from those above but with the replacement of the retiring members, Dr Harmathy, Professo! Rasbash and Dr Snell. by Dr D. D. Drysdale, Dr G. C. Ramsay and Mr K. Richardson respectively. Dr T. Kashiwagi was also elected to fill an outstanding vacancy. Retiring members were thanked for their contribution by the Chairman Dr P. H. Thomas, himself also retiring as an officer along with Professor K. Kawagoe. New officers elected to serve until new elections in 1994 were: Chairman, Professor J. G. Quintiere; Vice-Chairmen, Dr R. Friedman, ProfessorT. Hirano and Professor O. Pettersson; Secretary, Mr G. Cox; Treasurer, Professor Y. Uehara. This Third International Symposium in Edinburgh completes a cycle of host venues following Gaithersburg and Tokyo in the three geographical regions most active in fire safety science. A new cycle begins again in North America with the next symposium to be held in Ottawa. Papers are accepted on the basis of peer review and an increasing number have been offered to each symposium. The new committee elected at the general meeting during this symposium is of the opinion that some expansion in activity can be entertained without loss of quality and it is proposed that some regional activity can be introduced without impairing the status of the main symposia. This responsibility has been passed to the ViceChairmen to take forward. Developments in the fire research world are moving rapidly. There are new journals, new societies engaged in professional fire safety engineering, new academic educational activities and formal cooperation between research v

managers. The Association intends to expand its activity so as to playa full part in these developments.

Philip Thomas Chairman, International Association for Fire Safety Science Borehamwood, UK July 1991

vi

In Memoriam

Professor Bernard J. McCaffrey

It was with great sadness that the fire research community learned of the death in April 1990 of Professor Bernard J . McCaffrey. He was posthumously a joint recipient of the award for Best Paper at the Second Symposium, and the award was accepted at this Third Symposium by his widow Carmel. Professor McCaffrey was famous for his careful fire research , in particular his fire plume quantification, as described in his award-winning paper. His measurements and analyses provide a standard of excellence by which other plume studies are judged . Professor McCaffrey received his early education in New York City, culminating in a BS from Manhattan College in 1964. He received his MS from the University of Connecticut in 1966, and his PhD in Mechanics from the State University of New York at Stony Brook in 1973 with a thesis on The Oscillatory Behaviour of Carbon Monoxide Oxidation'. He was a Research Fellow in Aeronautics at the University of Southampton in 1974 and a guest worker at the Fire Research Station, Borehamwood, in 1978. From 1974 to 1987 he served as Mechanical Engineer in the Center for Fire Research at the United States National Bureau of Standards. His research included the detailed physics and chemistry of diffusion flames, the design of exquisite fire research instrumentation, the analysis of fire plume mechanics and the growth of fires in enclosures. His innovative extinguishment technique for oil and gas well fires led to a US patent for a new suppression system . He earned the Department of Commerce Bronze Medal in 1983. vii

In 1987 he was appointed Associate Professor at the University of Maryland where he planned to expand his research in combustion and thermoscience fundamentals. He received the Best Teacher award from the College of Engineering at the Baltimore Campus in 1988. At the time of his death, he had nearly completed the establishment of a new fire research laboratory at the University of Maryland. His pioneering work on fire plumes, compartment fire temperatures and diffusion flame extinction has helped lay the foundation for fire safety science. His scientific publications are noted for their reliability, unusual precision and uncompromising integrity. In addition to his technical competence and dedication to fire research, he was noted for his delightful personality and good fellowship. Survived by his wife Carmel and two children, Andrew and Ciara, Professor McCaffrey was an exemplar of the family man, an accomplished violinist and a good vintner. The fire research community will miss both the pleasure of his company and the significant research he left incomplete. Saddened by his loss, we are pleased to be able to award him posthumously the International Association for Fire Safety Science Medal of Excellence.

viii

Symposium Committees ACCOMPANYING GUESTS COMMITTEE

ARRANGEMENTS COMMITTEE D. D. Drysdale (Chair) W. Becker M. Curtat P. Franklin J. Harwood T. Hirano E. W. Marchant F. Nunez-Astray J. G. Ouintiere D. J. Rasbash J. M. Rotter V. Sjolin H. E. Thomson W. D. Woolley

Mrs Judy Drysdale (Chair) Mrs Eileen Marchant Mrs Maureen Rasbash

AWARDS COMMITTEE P. J. Pagni (Chair) T. Hirano D. J. Rasbash J. A. Rockett

PROGRAMME COMMITTEE P. H. Thomas (Chair) T. Hirano T. Kashiwagi O. Pettersson J. G. Ouintiere D. J. Rasbash Y. Uehara

PUBLICATION COMMITTEE G. Cox (Chair) P. J. Pagni P. G. Seeger T. Wakamatsu

ix

Session Chairs TRANSLATION OF RESEARCH INTO PRACTICE

PLENARY SESSION K. Kawagoe

M. Kokkala P. Storey T. Okabe P. Redpath

INVITED LECTURES P. J. Pagni O. Pettersson R. Friedman B. Thomson J. Snell D. J. Rasbash W. D. Woolley V. Sjolin

STRUCTURES R. W. Fitzgerald D. Hosser

PEOPLE AND FIRE FIRE PHYSICS B. Pigott T. Tanaka

T. Kashiwagi T. Suzuki Y. Hasemi J. G. Ouintiere G. Cox P. Joulain F. W. Mowrer K. Satoh T. Hirano S. E. Magnusson

SPECIAL FIRE PROBLEMS P. Beever

SMOKE MOVEMENT E. W. Marchant H. E. Nelson

STATISTICS AND RISK J. A. J. D.

Hall Sekizawa Harwood Yung

DETECTION G. Hekestad P. F. Johnson

FIRE CHEMISTRY

SUPPRESSION

M. Janssens D. D. Drysdale J. R. F. Burdett O. Sugawa A. Atreya G. Camino

R. G. Gann T. P. Sharma

x

Contents

Preface

iii

International Association for Fire Safety Science In Memoriam

vi

Symposium Committees Session Chairs

v

ix

x

Invited Lectures 1991 Howard W. Emmons Lecture Fire, Flames and Dimensional Analysis P. H. Thomas 3 Physical Aspects of Combustion in Fires T. Hirano 27 Fire Safety System Design Using Risk Assessment Models: Developments in Australia V. R. Beck 45 Industrial Fire Problems: An Overview J. McQuaid 61 Fire Safety Assessments in Petrochemical Plants Y. Uehara 83 A Survey of Fire Modelling in France M. R. Curtat 97 Fire Research at NBS: The First 75 years D. Gross 119 Dedicated Detection Algorithms for Automatic Fire Detection H. O. Luck 135 International Fire Research J. E. Snell 149 xi

Fire Physics A Thermal Model for Piloted Ignition of Wood Including Variable Thermophysical Properties M. Janssens 167 Effect of Environmental Variables on Piloted Ignition A. Atreya and M. Abu-Zaid 177 Ignition of Combustible Dust Layers on a Hot Surface C. C. Hwang and C. D. Litton 187 Unsteady-State Upward Flame Spreading Velocity along Vertical Combustible Solid and Influence of External Radiation on the Flame Spread Y. Hasemi, M. Yoshida, A. Nohara and T Nakabayashi 197 An Upward Fire Spread and Growth Simulation M. M. Delichatsios, M. K. Mathews and M. A. Delichatsios

207

Upward Fire Spread: Key Flammability Properties, Similarity Solutions and Flammability Indices M. A. Delichatsios and K. Saito 217 Behavior of the Reverse Flow in Front of the Leading Flame Edge Spreading over Fuel-Soaked Sand in an Air Stream T Suzuki, M. Kawamata, K. Matsumoto and T Hirano 227 A Study of the Fire Performance of Electrical Cables A. C. Fernandez-Pello, H. K. Hasegawa, K. Staggs, A. E. Lipska-Quinn and N. J. Alvares 237 The Ceiling Jet in Fires H. W Emmons 249 Experimental Study of Heat Transfer to Ceiling from an Impinging Diffusion Flame M. A. Kokkala 261 Fire Induced Flow under a Sloped Ceiling H. - C. Kung, R. D. Spaulding and P. Stavrianidis

271

The Transient Ceiling Flows of Growing Rack Storage Fires H. -z. Yu and P. Stavrianidis 281 Analysis of Compartment Fires with Overhead Forced Ventilation C. Beyler 291 xii

Characterizing the Unconfined Ceiling Jet under Steady-State Conditions: A Reassessment V. Motevalli and C. H. Marks 301 Buoyant Convection in an Inclined Enclosure R. G. Rehm, H. R. Baum, D. W. Lozier, H. Tang and J. Sims

313

Predictions of Unsteady Burning of a Fuel Bed W. C. Fan and J. Wang 325 A Study of the Fire Aspect of Atria in Hong Kong W. K. Chow and W. K. Wong 335 Effects of Thermal Radiation on the Fluid Dynamics of Compartment Fires S. Kumar, A. K. Gupta and G. Cox 345 A Numerical Study of Window-to-Window Propagation in High-Rise Building Fires K. Satoh and K. Kuwahara 355 3-D Natural Convection-Radiation Interactions in a Cube Filled with Gas Soot Mixtures T. Fusegi, B. Farouk and K. Kuwahara 365 A Numerical Study of Spontaneous Propane Ignition in a Partially Confined Volume C. R. Kaplan and E. S. Gran 375 Application of a Zone Model to Smoke Control in a Compartment with Exhaust Fan: Comparison with Field Modelling and Experimental Results M. R. Curtat X. E. Bodart J. -L. Tuhault and D. E. Blay 385 Fuel Property Effects on Burning Rate and Radiative Transfer from Liquid Pool Flames J. Gore, M. Klassen, A. Hamins and T. Kashiwagi 395 Burning Characteristics of a Combustible Liquid Soaked in Porous Beds T. Takeuchi, T. Tsuruda, S. Ishizuka and T. Hirano 405 Turbulent Burning of a Flat Fuel Surface L. Zhou and A. C. Fernandez-Pella

415

Pool Fire Plume Flow in a Large-Scale Wind Tunnel V B. Apte, A. R. Green and J. H. Kent 425 xiii

Flame Height from Rectangular Fire Sources Considering Mixing Factor O. Sugawa, H. Satoh and Y. Oka 435 Plume Analysis above Finite Size Fire Sources A. K. Gupta, S. Kumar and B. Singh 445

Statistics and Risk Criteria for Fire Risk Ranking J. M. Watts, Jr. 457 Key Distinctions in and Essential Elements of Fire Risk Analysis J. R. Hall, Jr. 467 Statistical Analyses on Fatalities Characteristics of Residential Fires A. Sekizawa 475 An Expert System to Assess Fire Safety in Dwellings H. A. Donegan, I. R. Taylor and R. T. Meehan 485 On the Rule of Subjective Probabilities in Fire Risk Management Studies F. Noonan and R. Fitzgerald 495 A Probabilistic Approach to the Analysis of Fire Safety in Hotels: MOCASSIN B. Hognon and M. Zini 505 Modelling and Hazard Analysis of Sandia National Laboratories/Underwriters Laboratories' Experiments D. Q. Duong 515

Fire Chemistry Effects of Fire Retardant Addition on the Combustion Properties of a Charring Fuel Y. Chen, A. Frendi, S. S. Tewari and M. Sibulkin 527 Structure-Char Forming Relationship in Intumescent Fire Retardant Systems G. Bertelli, G. Camino, P. Goberti, E. Marchetti, M. P. Luda di Cortemiglia and L. Costa 537 Charring of Wood Based Materials E. Mikkola 547 xiv

In-Situ Heat Release Measurement of Smoldering Combustion of Wood Sawdust H. Ohtani, T. Maejima and Y. Uehara 557 Smoldering Combustion Propagation on Solid Wood T. J. Ohlemiller 565 Characteristics of Large Diffusion Flames Burning in a Vitiated Atmosphere J. H. Morehart, E. E. Zukoski and T. Kubota 575 The Effect of Oxygen Concentration on CO and Smoke Produced by Flames G. Mulholland, M. Janssens, S. Yusa, W. Twilley and V. Babrauskas 585 The Role of Soot Particle Formation on the Production of Carbon Monoxide in Fires R. Puri and R. J. Santoro 595 Heat, CO and Smoke Release Rates of Plywood under a Depleted Oxygen Atmosphere: An Experimental Study Using an OSU Heat Release Rate Apparatus Y. Tsuchiya and J. F. Mathieu 605 Investigation of a Smoke Toxicity Fire Model for Use on Wood M. M. Hirschler and G. F Smith 615 Carbon Monoxide and Soot Emissions from Buoyant Turbulent Diffusion Flames 0. O. K6ylu, Y. R. Sivathanu and G. M. Faeth 625 Fire Retardance Mechanism of Magnesium Hydroxide for Ethylene-Ethylacrylate Copolymers W. Takahashi, 0. Sugawa, H. Yasuda and T. Inoue 635

Translation of Research into Practice A Framework for Utilizing Fire Property Tests T. G. Cleary and J. G. Quintiere 647 Ignition Sources in Room Fire Tests and Some Implications for Flame Spread Evaluation R. B. Williamson, A. Revenaugh and F. W. Mowrer 657 Combustible Wall Lining Materials: Numerical Simulation of Room Fire Growth and the Outline of a Reliability Based Classification Procedure B. Karlsson and S. E. Magnusson 667 xv

Flame Spread Behavior of Char-Forming Wall/Ceiling Insulating Materials J. S. Newman and A. Tewarson 679 Flame Spread Evaluation for Thin Interior Finish Materials F. W. Mowrer and R. B. Williamson 689 Chair Burns in the TB133 Room, the ASTM Room, the Furniture Calorimeter and the Cone Calorimeter W. Parker, K. -M. Tu, S. Nurbakhsh and G. Damant 699 Cabins and Islands: A Fire Protection Strategy for an International Airport Terminal Building P. Beever 709 Comparing Compartment Fires with Compartment Fire Models H. E. Nelson and S. Deal 719 A Study for Performance Based Design of Means of Escape in Fire T. Tanaka 729

Structures Elasto- Plastic-Creep Three- Dimensional Analysis of Steel H - Columns Subjected to High Temperatures T. Okabe, F. Furumura, T. Ave and Y. Shinohara 741 A Simplified Prediction Method of Real Fire Exposure as a Basis for an Analytical Structural Fire Design V. M. Roitman, V. N. Demekhin and M. A. Abdul Majeed 751 Analyses of Composite Beams and Frames at Elevated Temperature T. Morita, T. Wakamatsu, H. Uesugi and H. Saito 761 Fire Resistance of Load- Bearing Reinforced Concrete Walls A. H. Buchanan and V. R. Munukutla 771 Heat and Mass Transfer in an Intensely Heated Mortar Wall K. Harada and T. Terai 781 Glass Breaking in Fires P. J. Pagni and A. A. Joshi

791

People and Fire Optimization Models in Fire Egress Analysis for Residential Buildings M. M. Kostreva, M. M. Wiecek and T. Getachew 805 xvi

EXIT89: An Evacuation Model for High-Rise Buildings R. F. Fahy 815 Defining Care and Residential Buildings with Respect to the Evacuation Capability of Occupants G. Hallberg 825 Evaluation of the Conspicuousness of Emergency Exit Signs T. Jin, T. Yamada, S. Kawai and S. Takahashi 835 To Prevent 'Panic' in an Underground Emergency: Why Not Tell People the Truth? G. Proulx and J. D. Sime 843

Special Fire Problems An Assessment Methodology for the Fire Performance of School Bus Interior Components E. Braun, J. H. Klote, S. Davis, B. C. Levin, M. Paabo and R. G. Gann 855 Experimental Study of Boilover in Crude Oil Fires H. Koseki, M. Kokkala and G. W Mulholland

865

Flame Propagation in the Channel and Flammability Limits G. M. Makhviladze, V. I. Melikhov and V. A. Rabinkov

875

A Study of Underburning in Stands of P. yunnanensis and P. kesiya var. langbianensis D. Wu, F. Yang, S. Yi, C. Yang and P. Wang 885 Analytical Model for Transient Gasification of Noncharring Thermoplastic Materials K. D. Steckler, T. Kashiwagi, H. R. Baum and K. Kanemaru 895

Smoke Movement Investigation of Fire-Induced Smoke Movement in Tunnels and Stations: An Application to the Paris Metro J. P. Vantelon, A. Guelzim, D. Quach, D. K. Son, D. Gabay and D. Dallest 907 Inflow of Air Required at Wall and Ceiling Apertures to Prevent Escape of Fire Smoke G. Heskestad and R. D. Spaulding 919 xvii

Computer Analysis of Smoke Protection of an Atrium Building in a French Business Centre X. E. Bodart M. R. Curtat and P. G. Fromy 929

Detection A Fire Detection Algorithm Using Second Order Statistics J. Klose and R. Siebel 943 Approach to Detection of Fires in Their Very Early Stage by Odor Sensors and Neural Net Y. Okayama 955 A Model of the Population of Fire Detection Equipment Based on the Geometry of the Building Stock S. H. Ellwood and M. Lynch 965 Detection of Smoke: Full-Scale Tests with Flaming and Smouldering Fires D. Meland and L. E. Lrzmvik 975

Suppression Dropwise Evaporative Cooling of a Low Thermal Conductivity Solid M. di Marzo, Y. Liao, P. Tartarini, D. Evans and H. Baum 987 Extinguishment of Enclosed Gas Fires with Water Spray R. Wighus 997 The Role of Active and Passive Fire Protection Techniques in Fire Control, Suppression and Extinguishment 1007 A. Tewarson and M. M. Khan Fire- Fighting Procedure and Estimation of Fire Consequences in Nuclear Plants J. C. Malet C. Casselman J. M. Such and R. Rzekiecki 1019 Posters

1029

Author Index Subject Index

1031 1035

Cumulative Author Index of Papers Presented at the First, Second and 1041 Third Symposia xviii

INVITED LECTURES

1991 Howard W. Emmons Invited Plenary Lecture

Fire, Flames and Dimensional Analysis P. H. THOMAS Kings Cottage 1 Red Road Borehamwood, Herts WD6 4SW, UK

ABSTRACT In the context of the relationship between the fire safety engineer and the fire scientist a few scientific and engineering problems are discussed. Some comments are made about engineering theories of plumes and flames and a dimensionless correlation of the length of flames from a corner source under a ceiling is presented. Fire safety engineers may now be able to exploit a thermal theory of upward flame spread using data obtained by recently developed flammability tests. KEYWORDS:

flames, flame spread, ceilings, compartment fires

INTRODUCTION In pursuing the objectives of understanding fire and its effects, and mitigating the consequent harm, we in this Association seek scientific and quantitative paths. We thereby seek to connect fire safety science with physics and chemistry and other basic sciences. Likewise fire safety engineers seek to connect their discipline with other branches of engineering. These things said in introduction, I wish to explore some of the by-ways of several well known topics involved in the study of compartment fires, particularly those on the boundary of fire safety science and fire safety engineering.

PLUMES AND FLAMES There is much literature on plumes and flames (1 )12) - at least on those which are vertical in an unbounded space and those plumes which become ceiling jets (3 ). Some questions await resolution by computational fluid dynamics, some by the basic physics of turbulence but there are even some problems, unresolved at the engineering level. Before the 'invention' of the entrainment coefficient by Morton, Taylor & Turner (4 ), Taylor lS ) himself, following Schmidt (6 ) and Rouse, Yih and Humphreysl') had studied plumes and jets by exploiting the observation, that far from the source plumes and jets were straight sided in uniform atmospheres, and by recognizing the existence of similarity. FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM, pp. 3-26

3

Experimental data allowed a determination of the angle of expansion '9'; today they determine the entrainment coefficient 'E'. For axi-symmetric plumes, however, a definition is required of an effective radius to which 9 and E are related. The assumption of a Gaussian profile replaces the immediate need for a theory of turbulence but we still have to define 'E' in relation to the assumed distribution. Moreover it is different for axi-symmetric and line plumes. ~ithin these and other limitations velocity and temperature rise at a height 'z' above the source can be expressed as:

We

(z)

ot.rgz.-

Funct

(Q'. B)

(1)

and alTo

ot

Funct

(Q'.

B)

(2)

respectively: where D here is some specified linear size defining the source and Q' is a dimensionless fire power. In the far field defined by z/D » 0, results cannot depend on D separately from the fire power Q' but for real fires where D/z is significant we must expect some influence of the fire size. Moreover some of the conventional boundary layer assumptions (negligible pressure effects, negligible vertical diffusion) may no longer obtain near the source. In the lower reaches of the flame there is a double peaked distribution of velocity and temperature across a horizontal section. Cetegen et al(S) idealised this as in Fig 1.

Figure 1 Lower flame zone, (after Cetegen et al (8))

4

They neglected the inclination and treated the flame as a zone of constant temperature (controlled by the molecular diffusion of air) and so obtained the velocity in the lower combustion zone as (3)

continuity of mass gives: I

d (w b p)

ex

(4)

11.

dz

b

Hence:

(5) and the total entrainment, ie diffusion up to a height 'z' is m=

(6)

C.11.p.z3/4

where C is a constant with respect to z and P is the flame perimeter. 11 is replaced by an eddy diffusivity proportional to: w.b. one

Ot

If

Z3/4

obtains a result given, assuming turbulent entrainment, by Thomas(9). viz m

Ot PZ 3 / 2

(7)

An oddity in contemporary fire engineering circles is that Hinkley(lO) has shown that this form works well for axi-symmetric plumes, ie that for P constant, Z3/2 is a better representation of dm/dz than Q1/3 Z5/3 as an expression of mass flow for 0.2 < Q" < 0.75 kW/m2 and P ~ z/2. Since

Q

ex q"

(8)

p2

where q" is a rate of heat release per unit area:

the ratio of

PZ 3 / 2

1

to

Hinkley acknowledges the limitations to this apparent superiority. It is noteworthy that any slight tendency for E to increase with height would go some way to "explaining" what appears to be a fortuitous result.

5

Unfortunately there is a tendency to exploit this relationship, acknowledging its empiricism and convenience without attempting to resolve the problems and without recognising that even this "superiority" is peculiar to axi-symmetric plumes. For strip and line plumes the Lee & Emmons l l l ) relation is widely used so the empirical preference for the Z3/2 relationship applies to a limited range of shapes and Q*. A peculiarity of these conventional engineering relations may be demonstrated by considering the line plume where the vertical central velocity is constant in the far field. A small restricting disturbance to the vertical flow - such as would be effected by a hypothetical insulated wire gauze - will not affect the new far field velocity but the local reduction in vertical velocity produces less entrainment and less dilution, so higher mean temperatures obtain. Bearing in mind the assumption of similarity one might suspect that this curious conclusion is essentially the consequence of assuming a constancy of the horizontal distribution and of neglecting the role of local eddies. The same result is obtained for a point source axi-symmetric plume but it is easier to see the result with the line plume. The problem may be important when dealing with zone models in which a plume meets a density discontinuity. Does this demonstrate that engineering plume theories are less robust than one perhaps thought they were? There are some other problems. The values of E for two and three dimensional plumes are different though this is a matter of little concern to the engineer. Secondly the transformation effected by Morton ll2 ) which allows the far field strong plume equations to be transformed into those for the weak plume (albeit assuming a top hat profile) does not work for two-dimensional plumes. The modified plume radius:

(9)

B

is necessarily associated with the modification:

E

p

E

(10)

but to effect a simple change of the strong line those of a weak plume one would require: B

plume equations into

(11)

6

which can only be realised easily with: E

Consider based)

E

p

(12) po

the Ricou - Spalding(13) relationship (on which equation (10) 'is

dm dz

(l3)

Because one must employ mass and momentum per unit length m' and M' another dimension is required if 'C' is to remain respectively dimensionless. The variable 0' which incorporates buoyancy (it includes g) has a physical meaning only above the top of the combustion zone. Below that it is a surrogate variable for mass or air flow. Clearly it has limited physical significance because of the combination of g with a horizontal dimension. The relationship: L

ex:

02 /

(14)

5

can perhaps be regarded as an algebraically manipulated expression entrainment surface and velocity of entrainment:

of

(15)

More generally, if a flame shape factor can be defined by fuel supply F = air entrainment

f(LlD)

(= f(L/D»

for a given fuel

(16i)

o

(16ii )

Funct (Q')

(16iii)

one obtains: L

D

7

In the correlation used for characteristic length is:

flames by McCaffrey(14) and

others the

/ ( ~ )2 5

1

poCpTo

g

which is physically related to the distance to a given dilution. The ratio of this length to the size of the source D is 0'2 / 5. The earlier use by Thomas(9) of: mf

emphasised, buoyancy.

for

a

given fuel,

the relative

importance of

momentum to

If the combustion zone is of length H and energy is released uniformly over the height 'H', the plume correlation must be in the form:

a

«Funct

(17i)

To

w

«

.rgz

Funct

(0*,

z,

D

~

)

(17ii)

but in a flame, H is a dependent variable, defined by a degree of dilution eg for a given fuel by a. Then alTo and ware again functions only of 0* and z/D though not the same ones as for a plume.

NON-VERTICAL FLAMES Flames Out Of Openings Plumes and flames out of windows were first studied by Yokoi(15) and several later correlations have been presented. There is a problem in defining the origin of external plumes and flames, since the exit flow is usually a horizontally moving layer, with buoyancy and momentum, often related. In an attempt to decouple this exit flow from the properties of the compartment Morgan and Marshall(16), in a 'zone' model of the emerging plume, have coupled a horizontal flux of buoyancy (potential energy) with a vertical flux of mean kinetic energy. The use of the more accurate mean momentum flux would require estimating a volume determining the buoyancy of the turning flow (see Fig

2).

8

low entrainment

Figure 2 A turning flow

Taking the vertical flux distribution as Gaussian there has to be an 'ad hoc' matching owing to the problems introduced in the description of the turning. Virtually all other attempts to deal with this problem have attached the empiricism to the definition of the position of a virtual source. The connection between plumes and flames was exploited by Yokoi l1SI who identified a mean flame length with the distance to an isotherm. Flames under Ceilings A connection between plumes and flames can be further utilised in correlating the lengths of flames 'L' extending horizontally I 171 from a corner above a burner as in Fig 3.

Figure 3 Flames from corner source below ceiling

For a 'point' source we provisionally might expect, on grounds, a correlation of the form: L

Funct H

[

rgH.

Q

PoC p ToH 2

rgH

"II

H

1

The first term in the brackets defines a Q* in terms of H.

9

dimensional

(18)

The second term must be included to accommodate the wall friction and the damping of turbulence under the ceiling. The effect of a finite source of size 'D' introduces another variable D/H but for small values of D/H we shall assume here a simplification such

as: H

+

C.D

(19)

where C is a constant or for vertical plumes I18 ).

a function of QX as

in Heskestad's correlation

Although in principle we cannot derive the value of C from that of an axi-symmetric plume, we shall begin at the simplest choice, (a neutral plume) devised by Taylor lS ) for axi-symmetric plumes viz 1.5 {AF, where AF is the fire area, which applied to a corner (and a square fire) gives (see Fig 4): H + 3D

(20)

H

o

Figure 4 A corner source

Babrauskas (19 ), using a more detailed argument derived C - 2.94 in calculations interpreting the data of You and Faeth I20 ). Their experiments were on a smaller scale than those of GrossI 21 ). Babrauskas had interpreted flame length as being defined by a degree of air entrainment proportional to the fuel flow but attempted direct calculation. Here we seek only a dimensionless correlation. Two sets of data I21 ,22), based on visual observations, give the correlation shown in Fig 5. Attempting to remove the dependence on H' by plotting L versus Q2/S is unsatisfactory. The correlation: L +

(21)

0.6

10

3~--------------------------------------------------------,

• •

2

L/H*

•

~! Andersson & Giacomelli

~

(22)

!

Gross (21)

O~-L~----~----~--~----~----~--~----~----~--~----~--~

0.00

0.02

0.04

0·06

0.08

0.10

0.12

Figure 5 Correlation of flame lengths under ceilings in a corner configuration

was chosen to correspond with that of Heskested and Delichatsios(23) for a ceiling plume in which we have substituted 40 for their 0 and H* for H. Matching was effected by choosing the isotherm for 1S0 a C. The data of Andersson & Giacomelli(22) also lie in this correlation but the values of L for the You and Faeth data are relatively larger. No residual effect of H* was found, so friction on the walls or viscous forces elsewhere was not manifested in this correlation, though it may have some influence on the data of You and Faeth. A corner is not a quadrant of the full axi-symmetric plume; flames extend near the corner of the wall and ceiling(24) and so extend into what would be the low temperature region if a quadrant. This type of relationship himself exploited.

between plumes and

flames is what

Yokoi

It is an oddity (but an explicable one) that 'g' appears associated with a horizontal dimension for vertical flames and with a vertical dimension for flames under a horizontal surface.

11

THE COMPARTMENT FIRE Although there has been much research in the last 25 years on fire growth the older problem of the fully developed compartment fire is still with us, if only in relation to harmonising design codes in Europe. The purposes of understanding such fires are to improve and cheapen design and to restrict spread, rather than to save lives directly. The compartment fire has not yet been the subject of much computational fluid dynamics so despite the sophistications by structural and heat transfer engineers the compartment fire is still, for design purposes, treated as at uniform temperature with wall surface emissivities sometimes chosen "post-hoc". Paradoxically, the compartment is usually treated as a "well stirred" reactor to provide uniform temperature with no internal flow (no accelerations in calculating the flow in and out of the openings). The simplest heat balance assuming ventilation control terms (eg radiation loss) omitted is:

with small

rna

r

(22)

Illi.

The air flow into the "well stirred reactor" is rather insensitive to temperatures above about 400°C and then for a compartment with a single opening, rna a:

Aw .lHw

(23)

where Aw is the opening area and Hw is its height and h heat transfer coefficient for the whole envelope area AT: Hence if m.

»

is the average

mr:

e

(24)

Cp • [1

+

_h_._A_T__ Cp Aw v1f,;

1

The term

appears extensively in the early literature often without reference to variations in 'h' with which it is associated in a dimensionless variable. A more pressing problem in recent years has been the effect of the fuel properties. The considerable empirical element in structural fire safety design is due to the major use of wood fuel and the prevalence of ventilation controlled fires. There are equations in the literature where both fuel properties and ventilation factors appear; the experiments they describe are not yet interpreted in terms of "state of the art" theory and present a challenge to fire safety engineers.

12

The work described by Tewarson(25), Friedman(26), Babrauskas & Wickstrom(27), B0hm and Hadvig(28), and Bullen and Thomas(29) and others shows how decreasing the heat of pyrolysis or of evaporation produces extra fuel which extends the flame from the opening (and reduces the mean temperature inside the compartment). The assumption of stoichiometry removes the need to calculate the thermal coupling between the fire and the fuel in providing safe design for structures within the compartment but one needs to calculate the thermal coupling in order to assess the severity of the hazard and the propensity for fire spread outside the compartment. The designing facade.

problem became important when structural engineers began buildings with their load bearing elements outside the building

FLAME SPREAD Opposed Flow The spread of flame over flammable solids and the effects of pressure, oxygen etc have been extensively studied for opposed flows, though there was, for a time, a preponderance of data on PMMA. With the theoretical understanding that has been achieved, some "simplification" can be developed for the benefit of the engineer who is mainly interested in the comparative performance of materials in various configurations as floors, ceilings, walls and corners. The principal theoretical simplifications which so far have been exploited are the result of the assumption of a large Damkohler number and the decoupling of the gas phase from the condensed phase so as to treat the heat transfer rate as an experimentally based quantity. This exploits the concept in de Ris's(30) theory for spread over thin materials; gas phase theory enables the value of the heat transfer to the whole of a strip of unit width ahead of the flame to be calculated. There is a characteristic dimension kg/V. in the gas phase (air) which exists as a finite distance only so long as there is relative motion between the heat sources and the medium. It is, for example, the scale of the gradient for a plane thermal wave in an infinite medium where the temperature rise '9', a distance x ahead of the plane moving at V. and at a temperature 90 is: 9 = 90

e V.

xl Kg

(25)

and the heat transfer ahead is: q"

- Ks

(d 9 ) dx 0

Pf

, i g

Cp 90 Va

13

(26)

is not the Note that p as required by a simple energy balance. f , i 9 density of the fuel ahead unless it is uniformly heated, otherwise it is a dependent variable. This equation shows, at its simplest, how the forward conduction is in equilibrium with a convective term. Estimates of the atmosphere(31) give:

Va

(

value

v.g. qf Yox J 1 /

of

Va induced

by a

flame in

a quiescent

3

(27)

r Cpo To

For typical values few mm/sec which is of gases emerging from the flow has, one supposes, Yichman and Agrawal have

of the parameters on the right hand side Va is a the same order of magnitude as that of the fuel pyrolysis zone. This disturbance to the opposed an effect but more behind the pyrolysis front. discussed this in some detail(32).

Most theory has been based on system shown in Fig 6.

a steady velocity of spread.

In the

Thick homogenous solid (opposed flow)

.....- - - - vair (entrained)

----_v

I

- - JI

s raised above Tamb by external heating

tiq =

~

Tiq - Ts

=,},; q'~ ~ Kp~v

,,2

qfl 6 Kpc

is often constant over a useful range of conditions

Figure 6 Opposed flow (after Quintiere)

there appears to be no extra forward conduction (other than that in the forward convection) provided there is no energy loss from the system.

14

However, if radiation losses are allowed for there can be such conduction so it is possible that radiation loss can be a factor in one type of extinction I33 ,34 1 • de Ris incorporated radiation in his models of flame spread and the combination of two strip sources (see Fig 7) gives the temperature rise as: 2

e

(28)

+

.j IIKpCp V

Figure 7 Opposed flow - Iwo strip heating sources

A wide vertical radiator, of height H, and normal to the surface has a view factor ~ of ~, less if the flame is inclined to the rear as in opposed flow. 1, is of order Hand: (29)

where

€

is the flame emissivity and T5 is the surface temperature

«

Tfl

The magnitude of:

I

eig

II

KpCp V

2

" requires the major component to be qfl unrealistically high values of € are required. the dominant one in concurrent spread. In

opposed

flow

theory a

.;s- because otherwise The radiation term may be

pre-heating distance

'0' or

(kg/V.) is

assumed, qfl 0 or (q;i kg/V.) can be shown, by experiments, to be effectively constant over a useful range of conditions (viz a range of T. which can be altered by differences in the pre-heating conditions). This is the basis of the engineering use of spread of flame test data l351 • The insensitivity justification

of qf 1 0 to for the use

the external heating conditions provides a of conventional spread of flame tests by

15

modellers to provide data which can be applied to circumstances other than those used in standard tests. Although tests for wall linings based on opposed flow flame spread are over 40 years old and have been standardised as tests in several countries it is only recently that they can be described as scientifically based tests in the sense of their being subject to quantitative modelling (and recognised as such by the relevant ISO committee). The origin of the British Flame Spread Test - a prototype for several others employing opposed flow flame spread - was a series of experiments on the hazard of spread in a corridor incompletely interpreted as being driven by opposed flow (downward) flame spread. It is fortuitous too that tests of this type should be capable of being modelled long after their adoption on pragmatic grounds. But what other older generation tests have been modelled? In recent times various national standards organisations including the British Standards Institution(36) have formalised the procedure for developing fire tests by declaring that first the hazard be identified and the test be then developed. Ye have discussed Quintiere model) approximately: Ct

Kg

flame spread and

the

as a

total

flux q;l

heat

over a

distance

suppiy

is

qtl

revised

de

Ris's

& (the

& which is,

(Ttl - Tp)

Ct is '0(1). where evaluation and gives:

Delichatsios(37)

theoretical

n Ct=

4

It is interesting that a semi-infinite uniform plane source (see Fig 8) transfers a total of: Ct

Kg

(Ttl -

Tp)

to unit area ahead of the inclined plane where Ttl is here the temperature of the plane at infinity and, for €6n1Z, a>Z/n but falls to zero as e approaches zero. Since most real building materials are not homogeneous, theory must be expected to provide a validated structure for some materials but can hardly be expected to cope with all materials where there may be problems of melting, intumescence and cracking. To sum up, there is valuable progress on the scientific aspects of opposed flow flame spread and on its applica~ion to fire safety engineering and, with some reservation, to fire testing. Upward concurrent flame spread is another matter.

16

Semi infinite plane source

Tt,t temperature at infinity

rTemperature To ~

Figure 8 Moving half plane source

Flame Spread up a Yall Delichatsios et al(38) have recently been making numerical simulations of flame spread. They explicitly require that the input of material properties should be measurable by flammability apparatus*. This in itself implies that the 'properties' - be they basic or effective engineering properties - should be the 'tools' for describing flame spread processes in detail. This is the important link between research and testing, which will, one expects, eventually drive the regulatory system for controlling the hazard from flammable surfaces. Saito, Quintiere and Yilliams(39) have described a model which implies some interesting conclusions.

purely thermal

All models of flame spread up thick solids are so far two-dimensional and the models of Saito et al and of Hasemi(40) are based on quasi-steady flame spread theory. This approximation is clearly less satisfactory near the initiation of the spread than later. However, if we follow Saito et al we identify the heating distance '5' = Xfl - Xp over which the net flux q~l is assumed uniform. Longitudinal conduction was neglected and the classic ignition equation (28) is used. Ye then have: (30)

where T. is the temperature (assumed uniform) ahead of the flame, the ambient temperature or that dependent on external radiation. The heating time 't' was taken as: Xu - Xp

(31)

v

*

state of art equipment, not national standards in general.

17

with:

dX p

v

Xfl - Xp

(32)

dt

where: n

KpCp

(33)

" (Tig - T.)' qf1

4

2

Wichman and Agrawal(32) derive this equation and discuss the theories of Saito et aI, de Ris, and Quintiere in a more general but 2-dimensional context involving the gas phase and pyrolysis. conventionally Xfl is taken as proportional to the 2/3 power of the rate of heat release based on a line or horizontal source but Saito, Quintiere and Williams argued that there was some experimental evidence and some physical argument for a higher power when the source was distributed vertically. Therefore they took, for simplicity, a linear relationship: K (Q'

Xf

+

qm

I

Xp

(34)

m" dx)

where Q' is the convective heat output per unit width of burner and qm is the heat release per unit mass of pyrolized fuel. They constructed a linear integral equation from equations (32) and (34) and discussed the conditions for an asymptotically exponential value of dXp/dt at long times. They did this for two forms of m"(t) viz: m"(t) and m"(t)

mo" cc

11

=

constant

(tiq

I t - tiq

«

tB + tiq)

(35)

(36)

Equations (32) and (34) can be subjected(41) to Laplace transformation to give, respectively: -

Xfl

-

xp

(37)

p Xp - Xpo

where p is the Laplacian operator and the - over the variable denotes the transformed variable, xpo is the initial value of xp

18

and: K

Xfl

(0'

+

(38)

qrniii" p Xp )

from which: KO'/tig

+

xpo

xp p

+ 1/tig -

Kqrn iii"p/tig

(39)

We shall also consider the form used by Magnusson & Sundstrom(42): m"

(40)

and in addition: m"

Ate -

a (t-tig)

(41)

The inverse square root form has a non-finite maximum value and non-finite integral, making it difficult to compare with the others. We shall identify yas 1/tB. These all produce simple forms for iii" which permit simple inversions; Xfl can be evaluated in terms of exponentials. The procedure necessarily gives the same results as does the analysis by Saito, Quintiere and Williams for t~ and the denominator in equation (39) produces a quadratic in 'p, and the roots may be both positive, conjugate or both negative. These three types of solutions correspond respectively to an initial propagation which dies out asymptotically in time, at a finite time (the value of xp unrealistically decreasing after a certain time) or one which accelerates. Each of the propagating fire.

three finite forms of m" defines a requirement for a For the exponential and the step function:

" Funct (tig/tB) Kqrn mo.

> constant

For the third form one has: Kqrn Atig. Funct (tig/tB) The

> constant

differences are partly due to the differences in defining tB and

mo" (and A) and partly due to the real differences in the shapes of the m" (t) curves.

19

For the exponential form the condition is exactly:

Kqm mo"

>

To get some idea of a comparison we define characteristics:

" mch

1

2:

1'"

m" dt

m" dt

so normalising the time scale to the time required to produce half the total mass. Clearly other fractions could be chosen (and perhaps derived by mInImIsIng differences between selected shapes) but the important matter is to recognise that fuel released early plays a greater role in fire growth than that released later. Using this procedure the three forms of m" (t) give requirements for an indefinite propagating flame (see Fig 9).

similar

5~----------------------------------~

4

tV2 is time to release half (1/21 of all heat or mass and m*"tV2 ~ [ t 1h m"dt

i

o

3 2

"Ir _ _ _

m"=m~-,6t

o,L-~~L-~~

05

__

~~

10

__

~-L

1~

____- L__~_

20

2~

30

ti9/'112 Figure 9 Conditions for propagation

" can be defined as Qch " a characteristic rate of heat release. At qmmch this point the engineer may be tempted to abandon theory (which suffers from the defect of being two-dimensional which is inadequate for fires just starting) and recognise that we have a dimensionless criterion

20

between

KQ~h and tig/tl/2 which is amenable to experimentation exploiting

conventional material properties, perhaps with the inclusion of q;~ S. Even the assumption of linearisation of flame length is not crucial for interpreting experiments because the term KQ~h is no more than a characteristic ratio of flame length to pyrolysis length xfo/xpo. Perhaps the shape of the m"(t) charactistic may not be so important as might at first be thought. So far all that has been examined is the condition for indefinite spread (given a flame flux and an external pre-heating condition). Conditions governing limited spread will involve the conditions of ignition, the support given by the burner and the abandonment of the steady state approximation. In practical design these are rather more important than the condition of a propagating fire which has got away. Some aspects of the discussion of upward flame spread are relevant to spread under inclined surfaces or over them if the flames are bent over as was the case in the Kings Cross Underground fire. One would expect the analysis of spread rates of both kinds to involve the correlation of flame length to pyrolysis length. 'Realistic' condition

Ouasi-steady Assumption

(b)

(a) ~

Figure 10

Temperature

Initial temperatures on solid surface

The initial condition shown in Fig lOa ie a finite temperature rise

xp

< x < X!l at t = 0 corresponds to the quasi-steady state.

Clearly for the initial condition shown in Fig lOb which is different theoretically but not necessarily more practical, the more detailed analyses of the type discussed by Delichatsios et al and Wichman and Agrawal are required. If the initial temperature was distributed as a step function there could be no propagation if tB < tig and if tig > tB the initial spread could be discontinuous. Emmons has discussed a different but analagous problem(43) .

21

FIRE TESTING Such procedures - combining theory and experiment - are steps on the road charted by Howard Emmons as the way to develop a rational, scientifically based approach to the control and investigation of fire hazards. No such commitment appears to have been made until recently in Europe except in the Nordic countries, partly perhaps because the average numerically based fire safety record in Europe is perceived to be better than the North American, partly because many of those influential in controlling and devising regulations, be they administrators or fire service officers, are unfamiliar with the engineer's approach to problems, preferring the past prescriptive rules. However there has been an acceptance in principle in the UK of control by design(44). The increased demand in the UK by the fire service for higher educational standards is a new factor so one hopes these attitudes will change even faster. The influence forcing these changes are partly political (deregulation), partly the growth of the subject and partly one hopes, the need for objectivity in European harmonisation. Unfortunately initiatives in 1979( 45 1 by the Commission of the European Communities (CEC) for research on fire growth (to provide a basis for harmonisation of 'reaction to fire' tests) were not supported and now there is a tendency for apparently well thought out solutions to be regarded as long term for the future, so as to justify retaining old solutions as interim solutions. However opposing tendencies have appeared and I hope they will prevail.

CONCLUSION I have discussed a few topics of technical interest to the fire scientist and to the growing profession of fire safety engineers. The Association will endeavour to serve their interests by raising the status of the subject by maintaining, by improving its scientific quality and by responding to their needs.

NOTATION A AT Aw B b C Cp D E F g H Hw H*

constant total envelope area window area modified plume breadth breadth of plume constant specific heat a characteristic distance, eg a burner dimension coefficient of entrainment a ratio acceleration due to gravity a height window height modified height

22

h K k L I M m P p Q Q'

q qm r T t V w x Yox z

average heat transfer coefficient a constant thermal diffusivity flame length a length irradiated momentum mass flow perimeter Laplacian operator flow of convected heat dimensionless Q rate of heat release or transfer heat released per unit mass of fuel air/fuel stoichiometric ratio temperature time veloci ty vertical velocity (plume) distance on solid surface in upward flame spread oxygen mass fraction vertical distance in plumes etc

GREEK SYMBOLS ~ ~

~

£

n

e

K

v p a

coefficient see equation (40) et seq. a heated distance O(kg/V a emissivity viscosity temperature rise, angle thermal conductivity kinematic viscosity density Stefan-Boltzman constant

)

SUFFICES, SUBSCRIPTS a B

ch F

f1

g ig 0

p T

lh w

"

/

air burn centre line characteristic value fire fuel flame gas phase ignition ambient, initial pyrolyis surface total half of total window, opening per unit area per unit width or length

23

REFERENCES 1.

Heskested, G. 'Fire Plumes'. Handbook of Society of Fire Protection Engineers. SFPE Boston 1988, Chapter 1-6, p 107.

2.

McCaffrey, B.

3.

Evans, D.

4.

Morton, B.R., Taylor, G.I. and Turner, J.S. (1956).

5.

Taylor, G.I. The Dispersal of Fog from Airfield Runways, ed Walker, E.G. and Rox, D.A. Min of Supply 1946, p 230 and 'Fire under Influence of Natural Convection', Int Symposium on the use of Models in Fire Research. National Academy of Sciences - National Research Council, Washington DC, publication 786, (1961).

6.

Schmidt, W. Zeit fur Ang Mathematik under Mechanik (1941), 21, 265-278 and 351-363.

7.

Rouse, Hunter, Yih, C.S. and Humphreys, H.W. 201-210.

8.

Cetegen, B.M., Zukoski, E.E. and Kubota, T. Technology (1984), 39, pp 305-331.

9.

Thomas, P.H. Ninth Symposium (International) on Combustion. Combustion Institute, Pittsburgh (1963), p 844.

10.

Hinkley, P.

11.

Lee, S-L., and Emmons, H.W.

12.

Morton, B.L. Tenth Symposium (International) on Combustion. Combustion Institute, Pittsburgh (1965), p 973.

13.

Ricou, F.P. and Spalding, D.B.

14.

McCaffrey, B.J. NBSIR 79-1910 National Bureau of Standards, Washington US, October 1979.

15.

Yokoi, S. 'Study on the Prevention of Fire Spread caused by Upward Current'. Japanese Min of Construction. Building Res Inst. Report No 34, Tokyo, 1960.

16.

Morgan, H.P and Marshall, N.R. 'Smoke Hazards in covered multi-level Shopping Malls. Some studies using a 2-storey Mall'. Current Paper 48/75. BRE, Borehamwood 1975.

17.

Thomas, P.H. and Karlsson, B. 'On the Length of Flames under Ceilings'. SE-LUTVDG/TVBB-3059. Dept of Fire Safety Engineering, Lund University, December 1990.

18.

Heskested, G.

'Flame

'Ceilin~

idem Chapter 1-18, p 298.

Hei~ht'

Jet Flows' idem Chapter 1-9, p 138. Proc. Roy. Soc.

Tellus (1952),

A234, 1

~,

pp

Combustion Science and The

Fire Safety Journal, 10 (1), 1986, p 57. J Fluid Mech,

l!, 1961 p 353. The

J Fluid Mech, 11, 1961, p 21.

Fire Safety Journal (1983),

24

~,

109.

19.

Babrauskas, V.

Fire and Materials,

20.

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21.

Gross, D. 'Measurements of Flame Lengths under Ceilings'. NIST IR88-3835. National Institute of Standards and Technology, Washington DC, 1988.

22.

Andersson, C. and Giacomelli, G. 'Ett Modelrum Fire Safety Engineering, Lund University, 1985.

23.

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24.

Williamson, R.B., Mowrer, F.W. and Fisher, F.L. and Technology (1984), 41, pp 83-99.

25.

Tewarson, A.

26.

Friedman, R. 'The Behaviour of Fires in Compartments' . International Symposium on Fire Safety of Combustible Materials, Edinburgh University (1975), pp 100-113.

27.

Babrauskas, V. and Wickstrom, U.

28.

Behm, B. and Hadvig, S. 201-221.

29.

Bullen, M.L. and Thomas, P.H. (1979). 17th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, p 1139-1146.

30.

de Ris, J.N. (1969). 12th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, p 241-252.

31.

Altenkirch, R.A., Eichorn, R. and Shang, P.C. (1980), 37 p 71-83.

32.

Wichman, I.S. and Agrawal, S. 127-145.

33.

Subulkin, M., Kim, J. and Creeden, J.V. 14, 43, 1976.

34.

Subulkin, M., Kulkarni, A.K. and Annamalai, K. 18th Symposium (International) on Combustion. The Combustion Institute (1981), p 611.

35.

Quintiere, J.G.

36.

British Standard Guide to Development and Presentation of Fire Tests and their use in Hazard Assessment. British Standards Institution BS 6336: 1982.

~(3),

1980, p 119.

Lagor', Dept of

Combustion Science

Combustion and Flame (1972), 19, 363-371.

Combustion and Flame 34, 195, 1979.

Combustion and Flame, 1982, 44 (1-3),

Combustion and Flame

Combustion and Flame 1991, 83, p Combustion Sci & Technology,

Fire and Materials (1981),

25

~,

p 52-60.

37.

Delichatsios, M.A. 257-267.

Combustion Sci and Technology 1986, 44 (5-6) p

38.

Delichatsios, M. M., Mathews, M.K. and Delichatsios, M.A. Upward Flame Spread Simulation Code: Version 1: Non-charring fuels. Factory Mutual Research, November 1990.

39.

Saito, K., Quintiere, J.G. and Yilliams, F.A. Upward Turbulent Flame Spread. International Symposium on Fire Safety Science, Gaithersburg. Hemisphere Publishing Corporation, NY, 1985, P 75.

40.

Hasemi, Y., Yoshida, M. and Nohara, A. Tsukento, Japan 1990.

41.

Thomas, P.H. and Karlsson, B. On Upward Flame Spread. SELUTVDG/TVBB 3058. Dept of Fire Safety Engineering, Lund University, December 1990.

42.

Karlsson, B., Magnusson, S.E. and Andersson, B. Numerical Simulation of Room Fire Growth on Combustible linings and a Rational Classification Model. Interflam '90, p 43-54, London Interscience Communications Ltd 1990.

43.

Emmons, H.Y. Fire in the Forest. Fire Res Abs & Reviews. Sci - Nat Res Council, Yashington DC (1963), ~(3), p 163.

44.

Building Regulations (England and Yales) HHSO, London 1985.

45.

Commission of the European Communities (1979). Protection of Buildings against fire. Draft Research Programme DGIII 827179.

26

Building Research Institute,

Nat Acad

Invited Lecture

Physical Aspects of Combustion In Fires TOSHISUKE HIRANO

Department of Reaction Chemistry The University of Tokyo, Tokyo, Japan

ABSTRACT Present understanding of physical aspects of combustion in fires is summarized in this paper. Following a brief description made on present achievements and remaining problems in fire physics, a comprehensible interpretation is attempted on basic physical phenomena controlling combustion in fires, such as heat and mass transfer, behavior of heat sources, and fire induced flows. Also, a concept of propagation of states is introduced to characterize the fire phenomena. It is emphasized that understanding of fundamental combustion phenomena in fires is essential to enhance the abilities of fire protection engineers.

KEYWORDS:

Combustion, Fire, Fire physics, Review

INTRODUCTION It is clear that reliable prediction of fire processes is indispensable for fire protec tion engineer ing [ 1 ,2]. For the eval ua tion of evacua tion time, the rate of fire development and the smoke behavior during fire development should be predicted. For recommendation of fireproof materials, the difference of ignitabilities of those materials and other ones under fire conditions should be interpreted. For other types of fire hazard assessments, the prediction of aspects, such as smoldering, mass burning, flame radiation, and flashover would be required. Reliabili ty of the prediction of fire processes necessarily depends on the quality and amount of knowledge on the processes. The most basic processes in fires are of combustion and! or closely related to it[1-9]. Thus, a number of studies in fire research have been carried out to explore combustion phenomena, such as ignition, flame spread, smoldering, flame retardation, pool burning, flame radiation, fire plume, fire induced gas flow, and fire behavior. However, it seems rare to utilize appropriately knowledge accumulated throughout the studies on combustion phenomena in fires for protection against fires[2J. Sometimes it can be pointed out that if a person dealing with fire modeling, building design, evacuation planning, detector development, fire suppression system design, or fire fighting tactics FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM, pp. 27 44

27

would have sufficient knowledge of combustion phenomena at fires, he could obtain more reasonable results. On the other hand, in general, the data and models concerning basic combustion phenomena can hardly be involved in the procedure to develop methods for fire protection. Thus, efforts are needed to transfer knowledge obtained throughout basic studies on combustion in fires to practical activities for fire protection, and because circumstances(social and financial conditions as well as scientific and engineering findings) change day by day, such efforts should be continuing. The topics presented in this article are limited to be of physical aspects of combustion in fires. This does not imply a lesser importance of chemical aspects but should be attributed to the author's past experience and present knowledge.

PRESENT ACHIEVEMENT AND REMAINING PROBLEMS IN FIRE PHYSICS Ignition Igni tion is the first process at fire occurrence. A large number of studies have been carried out on this subj ect and the mechanisms of various types of ignition have been revealed[1-12l. Also, quantities representing ignition characteristics, such as ignition temperature, minimum ignition energy, and ignition delay time, have been evaluated or measured. The results of theoretical and experimental studies on this subject were summarized in several review papers[ 10-12]. A large number of data are available. However, most of those data are of ignition under idealized conditions, so that in the processes to predict ignition at a practical situation many problems arise[1,2,12]. Certain effects of initial and boundary conditions on ignition are practically impossible to predict. Some examples will be presented in the latter part of this paper.

Flame Spread The next stage of fire development is flame spread. Flame spread under various conditions has been examined and appropriate models have been proposed. The results of previous studies on this subject have been summarized in several review papers[12-19]. The mechanisms of various types of flame spread have been explored and a large number of data have been accumulated. Studies on this subject seem to be the most advanced of those concerning fire development. The problems in the next step will be of accurate prediction of the phenomena under complicated conditions observed in real fires. To solve such problems, we have to re-examine the available data obtained through experiments, analyses, and numerical simulations. Careful re-examination of data would lead us to appropriate application to practical cases.

Smoldering Smoldering

and smoldering-flaming transition are

28

important phenomena

to understand early stages of fires as pointed out in the previous papers [1,2,20,21]. However , available data concerning this subj ect are scarce. The smoldering-flaming transition is a subj ect in need of more attention because the subsequent process of fire development depends upon it. Another important problem is to examine the relation between the product composition and ambient conditions under which smoldering occurs. Very similar to flame spread, almost the same parameters affect smoldering, such as the thickness, convection, radiation orientation, and physical and chemical properties of the material[20,21].

Mass Burning Knowledge on the rates of combustion and/or resulting product generation must be indispensable for the modeling of fires and prediction of fire hazards[1-9]. A certain amount of data concerning mass burning of liquid and solid combustibles in various configurations and situations have been accumulated. Those data have increased knowledge of mass burning in practical fires and made it possible to predict some fundamental characteristics such as burning rate and radiation intensity for simple cases[1-9, 22-28]. In general, however, prediction of the mass burning rate of real fires is not simple. We have to make efforts to analyze and synthesize previously obtained data and relations and if necessary perform additional experiments for confirming the results. At present, an accurate prediction of burning behavior of a small element, such as a piece of furniture, wall, ceiling, or floor under fire conditions is still not easy.

Smoke Behavior at Fires The fire plume and gas flow inside a compartment are the subjects suitable for computer simulation, so that many studies have been performed on the prediction of these phenomena by using high-speed computers [1-9]. Consequently, a number of excellent programs for the prediction of the fire plume behavior have been established. However, the programs applicable to the prediction of fire induced gas flows in a large size compartment are still very few. The effect of the mixing inside the high temperature zone should be considered as pointed out in previous papers[1,29]' The gas flow behavior in a long corridor or tunnel is also a problem to be solved because it is very important for the fire prevention and protection activities. This problem seems to be worthy of investigation, although it is not easy to include the heat transfer between the flowing gas and the wall.

BASIC PHYSICAL PHENOMENA CONTROLLING COMBUSTION AT FIRES Heat and Mass Transfer Combustion is a type of chemical reaction and necessarily depends on the reactant concentration and temperature, which are closely related to heat and mass transfer processes. Thus, combustion in a fire can be considered to be controlled by the phenomena affecting heat and mass transfer processes in the fire.

29

[ [

IGNITABILITY LIMIT

PERSISTENT IGNITION HORIZONTAL IGNITION

I

VI

\''''''';

100

IGNITION

w ~

I

z

I I

g E z

TRANSIE~

1

>

0

~25 ~

10

IGNITION

I I

I

~

VERTICAL IGNITION

TRANSIENT IGNITION

I

I I

TRANSIENT

~ 0.1L-__ 10

~

____

20

~

____- L_ _ _ _

30

40

~

_ _ _ _L -_ _~_ _ _ _~.

50

RADIANT FLUX.

FIGURE 1

60

70

ao

J/(cm 2 s)

Ignition delay time at radiative ignition of a PMMA piece

As mentioned in the previous section, a large number of data on ignition are available. However, if the initial and boundary conditions are actual ones, the ignition characteristics are not always predictable. It can be found difficult to predict the phenomenon that the ignition delay time at radiative ignition depends on the orientation of the irradiated combustible material surface as shown in Fig. 1[12, 30]. Such a difficulty seems to be attributable to lack of data on heat and mass transfer processes near the irradiated surface[30]. This example seems to indicate that more data on heat and mass transfer processes are needed for predicting ignition processes under various initial and boundary conditions. The results of a large number of previous studies show that the aspects of flame spread under various conditions can be interpreted by exploring heat and mass transfer processes. Based on the variation of dominant heat transfer processes to unburned material from the flame, the variation with the solid thickness of the rate of downward flame spread over solid surface can be interpreted[J1-36]. The accelerating upward flame spread along a solid surface under natural convection is also interpretable based on heat transfer processes to unburned material[37-40], which depends on mass transfer supported by convective gas movement. Typical problems of unsteady flame spread concern the limit of flame

30

( oj

( bJ

(c)

(d)

(e)

(f) SCALE

6

o

2

4

~cm

FIGURE 2

Processes of blow off, regeneration, and development of the burning zone with a curved leading flame edge. Photos were taken every 2 s. Sample: 0.026 cm-thick filter paper; Free stream velocity: 80 cm/s; Light: 360 interruptions/s spread and the transition to extinction [41-44J. Near the limit of flame spread the temperature distribution as well as flow field near the l eading

31

FLAME


=0.092, 6 = 0.1 X 10- 3 , D == 0.27 m, Too == 300 K, T" ==573 K, Q == 0.65 X 108 J/kg, A == 0.25 X 10 10 S-l, E == 0.15 X 109 J/mole.

L = 12.7 mm are shown in Figure 6, along with the experiment.al data [4]. The value of E is taken as 0.9 X 108 J /kmole, which is the value used by Edwards [14J and approximately the average value used by Kansa and Perlee [15J and Davis, d al. [12J. The value of Q used is approximately equal to that of the heating value of Pittsburgh coal: the value of A is adjusted to match t.he experimental data. Agreement between t.he computation and experimental result is good up to the thermal runaway in the mathematical model. The temperature in the experiment. cont.inues to rise beyond the hotplate temperature of 513K and reaches 670K before starting to decrease.

DISCUSSIONS AND CONCLUSION Heating of combustible dust layers by a hot surface comprises a sequence of complex processes. The one-dimensional equation for conduction of heat with a simple Arrhenius reaction expression for heat generation appears to explain many observed features of the processes. A rapid, boundless increase in the local temperature in the layer may be interpreted as ignition. Temperature-time profiles agree with experimental results when appropriate kinetic data are employed. In particular, computations predict the

193

~ '~"

::j

0.08

::.:

-;

'5.,.

]

0.06

~

5 ~

e

~

0.04

i

0

0

0

o

o

0

10) is negligible(Figure 1), this temperature rise is attributed to the heating by the upper invisible part of the intermittent flame(6~ e 3h[Y(2;Ri) m m

(25)

Equations (24) and (25), contain four parameters, Tarr0, Rio, EIH, f/H, and has not yet been fully explored. However, we see by equation (22) that, since the temperature decreases, the first term on the right is negative while the friction and entrainment terms are plus, thus counteracting the effect of heat transfer. THE EFFECT OF FRICTION AND HEAT TRANSFER We now consider, in some detail, the simpler case with E = O. f \

1l

d~

Rio {Ta -+ -Ta) - e _~} e _~ e 3 J0 y(2+Ri) (26) (2 + Ri)3 (2 + Ri o)3 To To The solution is shown in Figures 5 and 6 for the ease of Column I, Table 1, for tranquil flow for Rio = 2. Ignoring, for the moment, the line to point 0, all solutions for various values of f, loop down to Ri = 1 for large f or swoop up to infinity for small f. With more decimal places to f the curves move toward higher ~. To understand this behavior, the differential equation (22), eliminating dT/d~ by equation (3), is put into the form

(1

Ri - -_ --

dRi::; Ri{,*-(2+Ri)(2_ d~

2y

1- Ri

t

)y]

(27)

Then, eliminating y from the nume1ralo(r, using eq)~~tion (20) WI e get } T. 2 T HRi 1l3 (2 + R') dRi::; d~

Ri((~)2e.~)1/3(2_T.)~ 3 (1) e'~ (2--t ~ - fRi~3

2y

To

T H

1- RI

FIGURE 5. Effect of heat transfer and friction on the Richardson Number of a ceiling jet. Initial Richardson Number =2. (Case column I, Table 1)

254

I

(28)

12920

N~)[

j /

/

129

/

/ /

128

FIGURE 6. Effect of heat transfer and friction on a ceiling jet depth. Initial Richardson Number ~ 2. (Case column I, Table I).

.12

From this we see that dRi --=00 at Ri = 1 dS

and

(29)

where HRi l13 (2 + Ri)

r=---'-~-":"

(30)

fRi~3

Figure 7 shows the solutions of Figures 5 and 6 as r vs. S with the additional line on which dr/dS = 0 which depends only upon the thermal properties of the flow. The point 0 at S = 4.683 in Figure 7 is a node. Since the coefficient of the bracket in equation (28) is positive, while both the numerator and denominator are positive below and negative above their respective lines, the solution slopes are as indicated and the node is a saddle point. The slopes of the solution curves passing through the node are found by evaluation of equation (27) as a % form. After considerable algebra we find dRi\ dS •

=1 _ (1 ±-Y3) l

(31)

2Tn

where Tn is the jet temperature at the node position. The corresponding slopes shown

-

.. :f1,': ~-

dr\ de

in Figure 7 are

=~r(I-(l±-Y3)l) 3 n 2Tn

(32)

The solution curves through the node in Figures 5, 6, and 7 were obtained by starting at the node with f = .12920 and the negative slope given by equation (32) integrating toward S = 0, using equation (23) in the form (E = 0) Ri {1+(To/T.-l)e·~}e-~ e 3 Y(::Ri) (2 + Ri)3

27{ 1 + (To / T. -1)e'"

*t

}e'~'

255

(33)

FIGURE 7. Effect of heat transfer and friction on a ceiling jet flow. Initial Richardson Number ~ 2. (Case column 1, Table 1). _ _ line on which solutions have horizontal slope; --/-++ line, Ri ~ 1, on which solutions have vertical slope; +,show sign of slope in region between above lines.

c2 + N

TI-IE CEILING JET In this section, we apply the above theory to an arbitrary fire-produced ceiling jet, in tranquil flow, in an open ended corridor of arbitrary length. Such a case is defined by the p,lrameters Ii1, To, Ta, h, f, L, Rio. We note immediately that Rio may be altered by the Ri = 1 control at the open end. To solve this problem, we first calculate t, at the end.

s,=~. mc

(34)

p

From this, we find the sign of the numerator in brackets of equation (27) in the form f

N=--h I ill c p

0.

and

={ ~2,}l!3 p,g.

(35)

where Ri = 1, and 00 has been canceled out. For Ri > 1 in the corridor, d Ri IdS is opposite in sign to N. If N > 0, the corridor ends before the node is reached. Thus, the solution to equation (33), starting at Ri = 1 at the end, will have a negative slope and Ri will increase back to t, = 0, to the required value of Rio. The velocity and depth of the fluid source will be altered appropriately! If N = 0, the corridor end is at the node and the backward solution to equation (33) starting at t, = t,n must start with the negative slope given by equation (31). Again, Rio will come from the solution and requires source adjustment: If N < 0, the corridor ends after the node and the solution slope for Ri > 1 is positive, the solution starting at the end moves toward S > Se and no solution with the given data exists for t, < Se with Ri = 1 at the end. See the concluding section for further comments on this case. COMPARISON WITH EXPERIMENT Although there are many papers on ceiling jet measurements, [12-14 J few are detailed enough to guide the theory. A recent Ph.D. thesis [15] provides both careful measurements over a narrow range of conditions and a careful boundary layer theory with appropriate velocity and temperature profiles. This theory failed completely to fit the data and was abandoned in favor of the completely unfounded assumption that Ri = 1 everywhere. This assumption agreed fairly well with the data (sec Figures 8 and 9). • "Source adjustment" does not mean any effect on the fire. It means change of depth and velocity after the fire plume reaches the ceiling.

256

I~

Iii

•

FIGURE 8. Richardson Number for Chobotov (15) experiment. 0 Experimental result; _ _ _ Present theory with data column 2, Table 1 and various friction factors; &. Present theory with node at end of experimental channel; - - - - Arbitrary assumption Ri = RiO which gives "best fit" to data.

I.'

I.

0

I

Petillion

010"1 Couldo,

•• Figure 9. Ceiling jet depth for Chobotov (15) experiment. 0 Experimental result; _ _ Present theory with data column 2, Table 1, and various friction factors; & Present theory with node at end of experimental channel; x Arbitrary assumption Ri = RiO which gives "best fit" to data; -it-fI- Chobotov (15) boundary layer theory with arbitrary assumption Ri = 1.

1.0 I

Po_itio" olOft9 Corrido,

FIGURE 10. Effect of heat transfer and friction on the ceiling jet in the Chobotov (15) experiment. _ _ _ Present theory with data column 2, Table 1, and various friction factors; ____ Line on which solutions have horizontal slope; t--I- Lines, Ri = 1 different f, on which solutions have vertical slope; +,show sign of slope in region between above lines; Nt - Node implied by experimental initial data; N2 - Node moved to the end of the experimental channel; - - - - Solution from node at end.

:r---. i>:!;;f '---" :I:I~

257

The top hat theory developed in this paper was applied to the Chobotov experiment computed with the data of Column II, Table 1. The results are shown in Figures 8-10. Computation from 1; = 0 contains a node far short of the end which shows why the boundary layer [15] attempt at solution failed. If the node of the top hat theory is moved to the end of the experiment (by selecting a higher friction coefficient),+ the resulting prediction is shown in Figures 8-10. The agreement with the ceiling jet depth is only fair while the agreement with the measured Richardson Number is very poor. Better agreement is obtained with the completely unfounded assumption that Ri = RiO throughout. CONCLUSIONS The simple top-hat type thcory used in this paper would be expected to yield a COITect qualitative semi-quantitative solution to the flow of buoyant fire gases along a ceiling. So long as the cOlndor is not too long, the heat transfer not too large, or the friction and entrainment not too small, reasonable-looking results are obtained satisfying the open end outlet condition for tranquil flow of Richardson Number = Froude Number = 1. However, for many cases, there appears to be no solution satisfying Ri = 1 at the end. The reason for this is not clear. If the ceiling jet arrives at the open end with Ri > 1, the jet is too deep and the fluid "falls out" with acceleration. Thus, the adjustment could take place beyond the end of the con'idor. If this were the case, the increased velocity and decreased depth would be expected to

0

which is higher than the end fluid velocity, propagate upstream at the wave speed The COITect explanation would appear to be either non top-hat adjustments at and just outside of the end of the cOiTidor, or some non-stcady effects with localized fluid accumulation and discharge suggested by observations of persons fleeing from a fire who state that "the fire came roIling along the ceiling." Another phenomena sometimes intervenes to alter the Ri = 1 problem. As the ceiling jet moves along the corridor and cools off, its buoyancy falls and it is more easily removed from the ceiling by drafts or other disturbances. In the case of fire, there is often a lower layer current of atmospheric air returning into the fire source. This lower level return current can entrain the extra deep, extra cool ceiling jet which, therefore, never reaches the corridor end. It is clear that some scientifically motivated ceiling jet studies are essential to guide further theoretical work on the ceiling jet. The theory of this paper is about the right complexity for use in a general fire model, with some empirical coefficients, if necessary. It needs to be further developed to include partially open or closed con-idors. It needs to be extended to the two dimensional ceiling of a room and needs to include residual fuel which is burning. NOMENCLATURE

Cp

specific heat of ceiling jet gas at constant pressure entrainment coefficient, Equation (I) friction factor, Equation (2) acceleration of gravity

E f

g g' = g

Pa - P P

h H = h 801m c p lil

effective acceleration of gravity, Equation (5) heat transfer coefficient, Equation (3) heat transfer factor, Equation (22) ceiling jet mass flow per unit width, Equation (1)

+ The experimental measurements suggested a very low friction. Thus, the friction factor of f = .046907 required to put the node at the end seems unreasonably large.

258

numerator of

N

H (Ri)\l3 (2 + Ri )

r=

--'---'------'-~~...:..

f (Rio)lJ3 Ri

=

g' o/u 2

dRil

n

dS

,

Equation (35)

useful analysis variable, Equation (30) Richardson Number, Equation (4)

Rio

Richardson Number at jet source, Equation (16)

T

temperature ceiling jet velocity dis tance along corridor [m] ceiling jet depth, Equation (20) ceiling jet depth [m] curve on which dr/dS = 0, Equation (30) ceiling jet density coordinate along corridor

u x

y=O//)o /)

300

~

200

:3

* +

600 500

§

~

0 0

100 0

0

10

20

30

t-t o

Figure 2.

(

40

50

sec )

Convective heat release rates of Tests 1-8.

285

60

At each time instant of concern, the center ofaxisymmetry of the ceiling flow was determined from the gas temperatures measured at locations along the southwest-to-northeast run, and the north-to-south run, as shown in Fig. 1. The methodology to determine the fire axis location based on the spatial temperature variations had been described in Ref. 7. The ceiling flow data of Test 6 were not employed in correlation since the flow departed severely from axisymmetry in the investigation period. Since the location of plume virtual origin changed as the fire grew, the R value for an instrument station varied with time. In this test series, the R values for all the instrument stations ranged from 0 to 4.950 in the investigation period. At each time instant, the normalized ceiling flow data could be grouped into the following seven intervals of R values: 0.0.16 (0.081), 0.17-0.28 (0.217), 0.30-0.50 (0.365),0.500-1.130 (0.787), 1.190-2.500 (1.149), 2.600-3.500 (3.048) and 3.800-4.950 (4.333), where the values in the parentheses are the designated nominal values for the respective intervals. The data obtained at an instrument station may be spl it into two R intervals, depending on the R range at this station. In this paper, the ceiling flow data will be shown only for the following nominal R values: 0.081 (temperature and velocity only), 0.217 (flow depths only), 0.365, 1.149 and 4.333. However, the correlation equations to be presented later were established based on the entire data obtained in this study [9]. Ceiling Gas Temperature Figure 3 presents the normal ized maximum excess gas temperatures versus normalized convective heat release rates for the four selected nominal R values. Since the ambient temperature in this test series ranged from 296

Figure 3.

Correlations of maximum excess ceiling gas temperatures at

r/(H-Z o ) = 0.081, 0.365, 1.149 and 4.333. 286

to 301K, the variation of A in Eqs. (1) and (2) was negligible. suIt, A was not included in the correlation.

As a

re-

The equation, )2 , ( 4) YT = ( L.=.....!? a where YT = a- 1/3 (H-Z ) 1/3 ~T IT and X = a- 1/6 (H_Z )-2/3Q 1/3, was employed to represent the dat.£' pertaill\ng to the individualo nomina1 R value. In Eq. (4), a and b are empirical constants to be determined.

For each nominal value of R, the data were correlated with Eq. (4) using the least-squares method to yield the values of a and b. These determined a and b values were fitted with the following equations: a

=-

0.040R 4

+

0.316R 3 - 0.658R 3

+

3.991R

3.094,

(5)

0.090R 2

+

0.646R - 0.058,

(6)

+

and b

=

O. 118R 4 - 0.066R 3

+

respectively, for 0 < R

4.95.

Ceiling Gas Velocity Figure 4 shows the normalized data of maximum ceiling gas velocity corresponding to the four nominal values of R indicated in the figure. The family of hyperbolic equations, o 'a"

... ..

o 'ts12 ¢ n:s"

Amo,

~.

.::. "J,

+

,.." ,.."

r/(H-IJ-O.0I1

n:.n.

I X

~3

its

2

o

o

'0

-

RtGRESSION

or

DATA

Figure 4. Correlations of maximum ceiling gas velocities at r/(H-Z o ) 0.081, 0.365, 1.749 and 4.333.

287

y 2 = c (X _ X 2) _ d u 0'

(1)

was employed to represent the gas velocity data. Yu = a

-1/6

(H-Z o )

-1/3

In Eq. (1),

Urn' and c, Xo and d are empirical constants.

The values of c, Xo and d for each nominal R were determined by the least-squares method and may be expressed in the following equations: c = 1.0001 (1+R)-2.345 for OsR < 4.950

(B)

40.342R 2 + B.512R - 0.510 for OsR< 0.365 0.040R3 + 0.163R2 + 0.935R - 2.611 for 0.365sRI) at these large r/H values may be the cause of divergence in the ATmax curves. NORMALIZED MAX. TEMPERATURE

LEGEND 6.

Data,

H-l.0

m

o

Data,

H-0.S

m

(1)

.166(r/U)-z+1.2(("/H)-1+ 2 . B

(2)

.BB2Cr/H)-z+1.S(r/Hl- 1+.996

(2)

2.5

o

L-~~~~J-~~~~~~----~~~~--~--~

0.2

0.7

1.2

1.7

2.2

FIGURE 3 - Non-dimensionalized ceiling jet maximum temperature (I) H=I.O m, (2) H=0.5 m The AT*max empirical equation is compared to those obtained by other investigators and data of You & Faeth and Zukoski et. al., as reported by You &Faeth [5], in Fig. 4. Data of You and Faeth are from a very detailed study of a steady-state ceiling jet induced by a 0.25 kW fire. Zukoski et. al.'s data are from study of 1.17 kW and 1.53 kW fires. The general agreement between their data and Eq. (5) indicates that these small-scale experiments correlate quite well. Furthermore, You & Faeth concluded that Alpert's integral model generally underestimates the measured maximum temperature by 20%. Data from this work indicate a 30% to 18% (0.265r/H52.0) underestimation of the measured maximum temperature by Alpert's model. Cooper's model [12] seems to underestimate the maximum temperature even more, especially at r/H>0.75. Heskestad and Delichatsios [6] also show lower temperature in their large-scale experimental results, In the authors' view, the overriding factors in correlating results of ATmax are the actual value of the convective heat release rate used in each investigation, the distance from the virtual origin and differences between heat transfer characteristics in large and small-scale experiments. The convective heat release rate were determined quite accurately for the premixed flames used here. In addition, accurate determination of the 306

location of maximum temperature requires very detailed measurements. While authors and You and Faeth obtained very detailed temperature measurements, data of Alpert & Ward and Heskestad &Delichatsios were not as detailed.

CEILING JET MAXIMUM TEMPERATURE VARIATION 30~----------------------------------------1

a Data (Author) - Carra I at! on .6. You and Faeth

25

o Zukosk I. a t. a I •

M

"';;;'

20

I

:c

\

M

.......

'"0-

16

.......

X

rU

~ 10

, .6.

~.

\-> ~ "-

AIPer·~),··"~' ~~ ... :-:."':.:-;.").",.,~

1. The free jet flow, and thus fT and fv' are effected much more by the buoyancy than the near ceiling flow region. It can also be stated that f is scaled by H since it characterizes the free jet portion of the ceiling jet and it is analogous to the Gaussian thickness of the plume as long as f«H. This explains why fv data has more scatter beyond r/H=0.75 where iy is about 15% of H. The empirical relations defining iv and iT are shown below: fv/H = 0.205 (1-exp[-1.75(r/H)])

0.26~r/H~1.5

(10)

fT/H = 0.112 (1-exp[-2.24(r/H)])

0.26~r/H~2.0

( 11)

The data of fT correlated well for both heights; all fire strengths and at all r/H locations. Aside from a more accurate determination of iT (due to less scatter in the temperature data), f «H holds for this entire range explaining the superior correlation of the {emperature profiles compared to that of the velocity.

310

The empirical equations for iv and iT are compared to those obtained by other investigators in Fig. 8. Note that Alpert and many other investigators have always assumed iv = i, as well as 6vmax=6TTax ' which stems from considering the turbulent Prandtl number, Prt, to be .0. The equation of You and Faeth [5] in figure 8 is based on Alpert's integral model but for a friction factor of 0.3. Cooper's [13J model is again based on the wall-jet theory and data of Alpert. These models indicate a linear growth of i. Retardation in the growth of the ceiling jet seems to be more reasonable. A significant conclusion from comparison of iv and it is that iv > iT' Based on the data presented here, the ratio of ivleT varies between 1.6 to 1.9.

CEILING JET CHARACTERISTIC THICKNESS 0.30

0.25

0.20 :J:

0.15 "'col 0.10

0.05

0.00 0.0

0.5

1.0

1.5

2.0

2.5

r/H

FIGURE 8 - Comparison of models for ceiling jet Gaussian characteristic thickness. Cooper[13], You & Faeth[5] and Alpert[3J. CONCLUSIONS It was concluded that the wall-jet theory for cold flows is inadequate for the prediction of the ceiling jet velocity specially for the 0.2$r/H$0.5 region, and it overestimates the maximum velocity and ceiling jet momentum thickness. The measurements showed that the Gaussian thermal and momentum characteri st i c thi cknesses of the ceil i ng jet are not equal and are a funct i on of r/H. The boundary 1ayer thi cknesses, however, are a function of r alone for Q in the order of tens of kilowatts. The two regimes in the ceiling jet, i.e. near the wall and the free jet portion behave differently where the free jet flow is not strongly effected by the ceil i ng heating. Differences between the small-scale maximum jet temperature and large-scale data may be due to differences in the heat transfer characteristics and accuracy in determination of the convective heat release rates. 311

The effect of buoyancy at r/H~0.75 becomes very significant and interferes with scaling of the ceiling jet parameters solely based on the fire heat release rate and H. REFERENCES 1. Glauert, M.B., J. of Fluid Mechanics, 1, pp. 625-643, 1956. 2. Poreh, M., Tsuei, Y.G. and Cermak, J.E., J. of Applied Mechanics, pp. 457-463, 1967. 3. Alpert, R.L., "Fire Induced Turbulent Ceiling Jet", Technical Report, Factory Mutual Research Corp., FMRC Serial No. 19722-2, 1971. 4. Veldman, C.C., Kubota, T. and Zukoski, E.E., Nat'l Bureau of Stds., NBS-GCR-77-97, 1975. 5. You, H.Z. and Faeth, G.M, Nat'l Bureau of Stads., Rpt. No., NBS-GCR79-188, 1978. 6. Heskestad, G. and Delichatsios, M.A., Proc. of 17th Int'l Symp. on Comb., pp. 1113, The Combustion Inst., 1978. 7. Beyler, C.L., "Fire Plumes and Ceiling Jets", Fire Safety J., 11, pp. 53-75, 1986. . 8. Motevalli, V., Marks, C.H. and McCaffrey, B.J., ASME Winter Annual Meeting, 87-WA-HT-16, 1987. 9. Cox, G., "Gas Velocity Measurements in Fires by the Cross-Correlation of Random Thermal Fluctuations - A Comparison with Conventional Techniques", Comb. and Flames, Vol. 28, pp. 155-163, 1977. 10. Motevalli, V., Ph.D. Dissertation, University of Maryland, College Park, MD, 1989. 11. Motevalli, V., Marks, C.H. and McCaffrey, B.J., "Cross-Correlation Velocimetry for Multi-point Velocity and Temperature Measurements in Lowspeed, Turbulent, Non-Isothermal Flows", submitted to the J. of Heat Transfer, 1990. 12. Cooper, L.Y., J. Heat Transfer, 104, pp. 446, 1982. 13. Cooper, L.Y., "Ceiling Jet-Driven Wall Flows in Compartment Fires", NBSIR 87-3535, 1987. 14. Alpert, R.L. and Ward, E.J., FMRC J.I. No. 01836.20, Factory Mutual Research Corp., 1982.

312

Buoyant Convection in an Inclined Enclosure R. G. REHM. H. R. BAUM. D. W. LOZIER. H. TANG and J. SIMS

National Institute of Standards and Technology Gaithersburg. Maryland 20899. USA

Abstract Equations for a Boussinesq model describing transient buoyant convection driven by a heat source in a rectangular enclosure are presented and solved by finite difference methods. Gravity is allowed to have an arbitrary direction relative to the enclosure so that the enclosure is inclined to horizontal. Computational results for three-dimensional dissipation-free flows and for two-dimensional flows with and without dissipation are presented. The hydrodynamics is based directly on the time-dependent Euler or Navier-Stokes equations. No turbulence model or other empirical parameters are introduced. The previous algorithms had been verified by comparisons with exact solutions to the equations in simple, special cases, and overall predictions of the model when the viscosity and thermal conductivity are zero have been compared with experimental results. The use of Lagrangian particle tracking allows one to visualize the flow patterns. The effects of a fire-induced flow in a corridor, and a stair well (or escalator) are examined. Key Words: Boussinesq; Buoyant Convection; Computational Fluid Dynamics; Enclosure Fires; Finite Difference Methods; Fire-Induced Flows; Transient Flows

1

Introduction

Fires in buildings involve the transport of heat and mass by gravity-induced or buoyant convection. Generally, this convection occurs in rectangular enclosures whf're the direction of gravity is parallel to the surfaces of the enclosure, the walls. However, under certain circum~tances, such as a fire in a stair well or an escalator, the enclosure may be sloped relative to gravity. A very important example of a fire in a sloped enclosure was the devastating fire in the King's Cross underground station in England in 1987, where there was significant loss of life as well as property damage. Numerical simulation of this fire [1] uncovered an unexpected phenomenon which caused a very rapid spread of the fire and led to much of the devastation. This phenomenon was termed "the trench effect," and caused some controversy during investigations of the King's Cross fire in England. The phenomenon was ultimately confirnlf'd hy experiments and additional simulation [2], but transient aspects of the fire simulation FIRE SAFETY SCIENCE- PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM. pp 313--323

313

are still of interest. It is the purpose of this paper to report an examination of this phenomenon using a very different mathematical and computational model than those used in the cited references; our model had been especially constructed to examine time-dependent buoyant convection and has been used to examine fire-driven flows. The authors have previously published descriptions of the mathematical model and algorithm which they developed for computation of the buoyant convection induced by a fire evolving in a room [3], [4], [5], (6). The model is for a dissipation free, thermally expandable fluid, i.e., one for which density and temperature variations can be large, but pressure variations are small (3), and for a Boussinesq model, one in which the density variations are also small. All of the work reported in this paper is for the Boussinesq model only. For the three-dimensional computations, the dissipationfree model described in the papers cited above is used. This model is used because one is unable to resolve both large-scale motions associated with room-scale buoyant convection and motions at the dissipative length scale with computational resources available. However, with the revolution in computational capability currently taking place, an ability to resolve both small scale and large scale features of the flow is now possible in two dimensions. In this document the authors report computational results obtained from a generalization of their model and algorithm, in two dimensions, to include viscous dissipation and thermal conduction. We present a brief description of the algorithm. When the model is restricted to two dimensions, very high resolution computations can be performed, and these computations allow us to resolve both largescale buoyant convection and small scale dissipation for Reynolds numbers of interest for enclosure fires. The two- and three-dimensional results are compared because the "trench effect" phenomenon is essentially two dimensional we believe. First, we present the model of buoyant convection in Section 2, then a description of the finite difference equations used to solve the model is presented in Section 3, and finally, results, together with interpretation of the physical phenomena observed in the numerical computations are described in Section 4.

2

Hydrodynamic Model

Traditionally, two approaches to the computation of fire-induced buoyant convection have been reported: direct integration of the Navier-Stokes equations using molecular values for viscosity and thermal conductivity or integration of these equations using a turbulent viscosity and conductivity to account for fluctuations occurring at the large Reynolds numbers of practical interest. The former approach, although most desirable, is not practically feasible in three dimensions with todays computers, but has become practical in two dimensions. Alternately, the use of a turbulence model in the equations introduces functional forms and empirical constants which do not have a fundamental theoretical basis at this time. Direct simulation of the Navier Stokes equations at Reynolds numbers of practical interest for fire-driven flows is now possible in two dimensions, and these simulations are the subject of this paper. We consider a Boussinesq fluid with constant or zero values of the viscosity and thermal conductivity in a rectangular enclosure driven by a prescribed heat source. The essence of the buoyant convection model is described as follows. We start with the Navier-Stokes equations for a Boussinesq fluid and combine them as described in

314

[3). The nondimensional equations can be written as follows:

8p _ r7 -+u· vp

-

1

2

-Q+ RePr V p

8t 8il -+F+Vp-pg 8t

1 V2Re U

=

(1)

f

where

F W

-ilxw+V(u 2 /2) V x il

f

-V.(F+pg)

Here, all symbols have their usual fluid dynamical meaning: p is density, il is the velocity, p is pressure, g is the vector describing the direction of gravity, Re is the Reynolds number, Pr is the Prandtl number, t is time and Q is proportional to the spatially and temporarily prescribed heat source. All symbols have their meanings in dimensionless form. If we let all variables with tildes denote dimensional quantities and those without denote dimensionless ones, then the dimensional and dimensionless variables are related as follows: it = U il, p = POU2 p ,p = po(U2/gH)p,~ = Hi,l = (H/U)t, where U is the velocity scale, H the height of the enclosure and Po is the ambient density. To define the velocity scale, we introduce the following quantities. Qo is the rate of heat addition in the three dimensional case (energy per time), qo is the heat addition per unit length in the two-dimensional case (energy per length per time), 9 the acceleration of gravity, To is the ambient temperature, and C p is the constant-pressure specific heat. Then, in the three-dimensional and two-dimensional cases respectively,

(2) The Reynolds and the Prandtl numbers are defined as follows: Re = UH/v and Pr = pCp/k, where p is the viscosity, k is the thermal conductivity and v = p/ Po is the kinematic viscosity. See [4) and [7) for more information on the scaling. Boundary conditions used for these equations are that there be no inflow or outflow at boundaries, that either there be a no-slip or free-slip condition at boundary walls and that the walls are either adiabatic or kept at a constant temperature. The initial conditions are that the fluid is quiescent.

3

Numerical Methods

Equations (1) are either a mixed parabolic/elliptic system of partial differential equations, or, if v = k = 0, a mixed hyperbolic/elliptic system; i.e., the equations for the density and for the velocity components are parabolic (hyperbolic), whereas that for the pressure is elliptic. The incompressible equations of hydrodynamics are well known to have this mixed character.

315

When v = k = 0, there is no dissipation in these equations, and it is important not to introduce any through the numerical scheme. Analytical studies of the ability of several candidate finite difference schemes to calculate internal gravity waves [8] led to the conclusion that methods of second order accuracy in space and time would be necessary; the scheme chosen is dispersive, but not dissipative. All time derivatives are replaced by central differences over twice the time step size (a leap-frog scheme). Other terms in the evolution equations (the first two of Eqs. (1)) are in general evaluated at the mid level of the three level leap-frog scheme. An exception arises in the vertical momentum equation, where in the buoyancy term the density is taken to be the average of the density at the top and bottom of the three level scheme; this semi-implicit nature of the scheme is required for stability (see [8], [4] and [6] for details). Small-scale numerical fluctuations arising during computation are removed by stopping periodically the calculations, smoothing and restarting [12]. When viscosity and thermal conductivity are present, a second-order leap-frog (Fronun) method or a lagged-diffusion scheme have been used for temporal updating, causing no additional stability limitations and only a straight-forward generalization of the algorithm discussed in the references cited above. The spatial grid is taken to be uniform in each of the two or three directions, although the mesh length may be different in each direction. Within each mesh cell, a parallelepiped, vector components are evaluated at the faces and scalar quantities at the center of the cell. The staggered grid permits central differences to second order accuracy for all linear operations. The nonlinear terms must be considered separately. The density evolution equation in continuous form is the mass conservation equation minus the expression for the velocity divergence. Each of these two equations is approximated by central differences and then subtracted. The density at all faces is approximated by the mean of the density at the centers of adjacent cells. This procedure ensures global mass conservation as well as second order accuracy. The momentum equation is differenced in the vector invariant form. This ensures nonlinear stability and complete compatibility between the "primitive variable" formulation presented here and a vorticity, stream-function formulation (in the twodimensional case), see [10] for details. When dissipation is absent, the finite difference scheme for the momentum equations is presented in detail in [4] and [10]. The pressure equation is the discretized version of the time derivative of the incompressibility (zero velocity divergence) condition, using the central difference approximation to the divergence of the velocity and with the time difference of the velocity replaced using the discretized momentum equations. Mathematically, the calculation of the pressure requires the solution of an elliptic partial differential equation. The linear algebraic system arising from its discretization has constant coefficients and can be solved by a fast direct method, see [6] for details. The solution to the pressure equation constitutes the bulk of the numerical computation since the density and the velocity are updated explicitly once the pressure gradients are known. Finally, stability of the computational scheme imposes a limit on the time step size relative to the spatial mesh sizes, [4] and [8]. Also, accuracy of the computation is an important consideration, which has been examined in [8], [4] and [6], and verification that the numerical methods solve the partial differential equations, at least in special cases, has been addressed in these references. In addition, the basic features, such as the plume rise-time in a uniform density environment, have been compared with

316

experimental results to verify the predictive capability for the dissipation-free model, [7). With such careful consideration of the basic Euler model and numerical methodology, we have confidence in the predictions of the large-scale phenomena made by these computations, and feel justified in interpreting large-scale physical features arising in them. The computations reported here were performed on the N.I.S.T. Convex C120 obtained for computational combustion. Each computation requires between eight and thirty CPU hours depending upon the conditions of the computation. The most satisfactory means for visualization of the computational output, we have found, is to display the locations of Lagrangian particles introduced into and convected by the flow field. These displays can be dynamically performed using color to show the temperature field for example, an'd have been implemented on Silicon Graphics Personal Irises which are also part of the computational combustion facility. Several frames taken from the screen of the SGI workstations displaying these particles are presented, and the physical interpretation of the results are discussed. It should be emphasized that still pictures cannot convey the sense of movement obtained when the viewer observes the dynamical display on the graphics device. Similarly, depth perception for these three-dimensional calculations and Lagrangian particle plots, which is provided on the graphics device, is diminished in the static figures. Finally, color adds immeasurably to the fluid-dynamical interpretation.

4

Results

Computations of many cases for both two-dimensional and three-dimensional enclosures tilted at a variety of angles have been performed. In the three-dimensional cases and in the 2-D case shown in Figure 3, calculations were performed using the Euler equations (but with periodic smoothing) as described in earlier papers of the authors [3)-[10), [12). In the two-dimensional case, very high resolution computations have been run, using over one quarter million cells in many cases. In most of the 2-D calculations, the Navier-Stokes (N-S) equations were integrated. The Reynolds number is limited by the resolution of the computations; it must be less than, but can be of the order of the number of grid cells. There are two effects of dissipation: there is a smoothing of the flow by viscosity and conduction, which occurs in the interior of the flow field, and there are boundary-layer effects, which can generate small-scale structures at the boundary. In the 2-D N-S computations, dissipative smoothing occurs while changes produced by altering boundary conditions have been examined. The results shown in Figure 3, where the Euler equations have been integrated, are virtually indistinguishable from results computed from the N-S equations with large Reynolds numbers when adiabatic, free-slip BS are imposed. In the following subsections, several results are presented and discussed which show the effects on buoyant convection of inclining an enclosure relative to horizontal.

4.1

3-D Horizontal Corridor

In Figure 1, we present one frame from a sequence generated by the computation of a corridor (four times as long as the height or width of the corridor) flow induced by

317

a heat source (fire) located at a position on the floor one quarter of the length of the corridor and one quarter the width from the end wall and side wall respectively. This calculation shows the full three dimensional nature of the flow. The viewing orientation is from the end of the corridor opposite to where the fire is located and from the wall closest to the fire. The particles rise in a buoyant plume above the fire, hit the ceiling and spread across the width of the corridor and down the side walls, forming a heated gas wedge that overlies the cool ambient gases in the corridor. This heated wedge of gases propagates down the corridor in a gravity current. The undulatory character of the upper layer, as shown in Figure 1, is due to the three-dimensional nature of the flow, a sloshing of the upper layer as internal waves are excited as the corridor is filled by heated gases. Finally, the gravity current hits the back wall, is reflected and returns toward the heat source (not shown here).

Figure 1 The dimensionless time shown is 4.5 units.

4.2

3-D Corridor Inclined 35 Degrees

Figure 2 shows two frames of a corridor flow generated as described for Figure 1 with the heat source similarly placed. In this case, however, the corridor is inclined 35 degrees with respect to horizontal; the end of the corridor opposite to the heat source is higher. The viewing angle is from the side of the corridor, and the time associated with each of the two frames is given in the figure caption. The initial buoyant plume begins to rise above the heat source at a 35 degree angle (opposite to the direction of gravity, which is pointed downward). The plume hits the ceiling and spreads both laterally toward the side walls and up the corridor toward the far wall. Because the corridor is inclined up toward the far end, the heated gases are accelerated toward the back wall as shown in the first frame. At similar times, the heated gases progress much further toward the far end than in the horizontal-corridor case. The high end, or end away from the fire, is filled by the smoke and hot gases, with vigorous mixing taking place in the filling volume as shown in the second frame of Figure 2. These results are essentially as expected for buoyant convection from a heat source in the inclined corridor.

4.3

Corridor at 35 Degrees - 3-D and 2-D Compared

In each of the calculations shown in the preceding figures, there are many interesting fluid-dynamical phenomena occurring; close examination of the results on the dynamical display on the workstation shows these phenomena. However, we will focus on only

318

one phenomenon here, a very curious effect, which we believe is the "trench effect" uncovered and discussed in the Kings Cross investigation.

IJ

Figure 2 A three-dimensional flow in a corridor inclined at 35 degrees; the flow is shown at two dimensionless times, 2.25 and 8.0.

Figure 3 A two-dimensional Euler flow computation in a 35-degree inclined corridor The dimensionless times are 5, 7, 9 and 11.

319

In Figure 3 a collage of four frames from a high resolution 2-D computation of the Euler equations is shown. The resolution of all of the 3-D computations shown in the preceding figures is 144x36x36 (186,624 grid cells) in the 4xlxl corridor; in Figure 3, the resolution is 1024x256 (262,144 grid cells) in the 4xl corridor, a factor of 7 more resolution in each direction. Because the computation shown in Figure 3 is a two dimensional version of the code used to compute the results shown in the preceding figures, the nondimensionalization is different; therefore, the dimensionless times ascribed to the various frames in Figure 3 cannot be compared with the times shown in the preceding figures. In this figure, the plume rises, but is bent back toward the back wall. After the hot gases hit the ceiling, they progress both toward the back wall and up the ceiling toward the high end. However, the hot gases leaving the heat source are pinned along the floor and form a hot gas jet which progresses up along the floor, shedding hot gases near its front; this phenomenon we interpret as the "trench effect" . To confirm this unexpected behavior, we performed a 3-D calculation identical to that shown in Figure 2 except that the heat source was spread across the width of the corridor. In the previous 3-D calculation, the heat source, although spatially distributed, was confined to a small region around its center; the center was located along the floor with its intensity decreasing in an axially symmetric Gaussian fashion with a half-width of one tenth of the width of the corridor. In the 3-D calculation with a 2-D source, the half-width of the Gaussian in the direction across the corridor was increased by three orders of magnitude so that there was essentially no decrease in source intensity across the corridor width. The computation qualitatively showed the same behavior as that shown in Figure 3; hence, we confirmed that the "trench effect" is essentially a 2-D effect, requiring that the heat source be spread across the corridor.

4.4

Corridor at 35 Degrees - Effects of Boundary Conditions

All of the results shown above were computed from a model in which there is no dissipation, i.e., no viscosity or thermal conductivity to diffuse (dissipate) momentum or heat. In the following figures, results will be shown from computations of the model in which viscous and thermal diffusion are included, i.e., the Navier Stokes equations are integrated as described earlier. All computations shown were performed on a 1024 x 256 grid, for a Reynolds number of 0.5 x 10 5 ; this grid allows stable and accurate computations with resolution of the boundary layer at the Reynolds number used. Since previous computations were dissipation free, the boundary conditions used were those appropriate to the Euler equations, namely, no normal momentum and heat fluxes at the boundaries. To determine the effects of changing boundary conditions (B.C.), we performed a series of two-dimensional computations with varying B.C. The B.C. selected were adiabatic, no-slip (ans), cold-wall, free-slip (cfs), cold-wall, no-slip (cns), and a base line computation with adiabatic, free-slip (afs). The degree of realism of the various B.C. for any given physical situation (e.g., fire-driven flows, or salt-water driven flows in fresh water) can be debated, but the comparison between the various cases is of interest because one can imagine scenarios in which each of the B.C. is appropriate. Figure 4 shows a comparison between the computations with the different boundary

320

conditions. It is composed of a frame at the same dimensionless time (5.0) from each of the four computations. The lower left plot is the base line computation with adiabatic, free-slip (afs) boundary conditions; the lower right plot shows adiabatic, no-slip (ans) boundary conditions; the upper left cold boundary, free-slip (cfs); and the upper right shows cold-wall, no-slip (cns) boundary conditions. Figure 5 shows a simliar comparison but at a later dimensionless time (9.0). Note that the plots in the lower left corner, the base-line ones, exhibit vividly the "trench effect", whereas, those in the upper right exhibit a more traditional plume rise above the heat source. The other sets of boundary conditions show intermediate behavior, with the hot gases clinging to the floor of the inclined corridor, interrupted by periodic separation of the hot gases from the floor into the enclosure. We interpret these results as indicating that the buoyant gases will cling to the floor when a fire spreads across the width of an inclined corridor (the trench effect) when boundary layer effects do not disrupt the weak buoyant flows. However, either vorticity generated along the floor by the boundary layer or cooling of the flow by a cold wall tend to break up the "trench effect" . The computations described here are induced by a heat source prescribed as a function of space and time with no combustion model. A very interesting extension of the model would be to include the effects of fire spread, which would affect the flow behavior determined above. This extension can be accomplished by including an appropriate combustion model [11]. We hope in the future to make such an extension.

Figure 4 A composite of frames from four calculations at dimensionless time, 5.0. The computations are similar to those described in Figure 3, except with dissipation (Re = 2 X 10 5 ). The lower left frame is for adiabatic, free-slip BC, lower right for adiabatic, no-slip, upper left for cold-wall free-slip, and upper right for cold-wall noslip BC.

321

Figure 5 A composite of frames at dimensionless time 9.0 from the four calculations described in Figure 4.

References [I] Simcox, S., Wilkes, N.S., and Jones, I.P. "Fire at King's Cross Underground Station, 18th November 1987: Numerical Simulation of the Buoyant Flow and Heat Transfer", Harwell Report AERE-G 4677, May 1988. [2] Cox, G., Chitty, R. and Kumar, S., "Fire Modeling and the King's Cross Fire Investigation", Letter to the Editor, Fire Safety Journal 15, pp 103-106, 1989. [3] Rehm, R.G. and H.R. Baum, "The Equations of Motion for Thermally Driven, Buoyant Flows", Journal of Research of the NBS, Vol. 83, pp 297-308, May-June 1978. [4] Baum, H.R., R.G. Rehm, P.D. Barnett and D.M. Corley, "Finite Difference Calculations of Buoyant Convection in an Enclosure" , SIAM J. Sci. Stat. Computing, Vol. 4, pp 117-135, March 1983. [5] Rehm, R.G., Baum, H.R., Lozier, D.W. and Corley, D.M., "A Model of ThreeDimensional Buoyant Convection Induced by a Room Fire", First National Fluid Dynamics Congress, joint conference sponsored by the A.I.A.A., A.S.M.E., A.P.S. and S.I.A.M., July 24-28, 1988, Cincinnati, Ohio. [6] Baum, H.R. and R.G. Rehm, "Calculations of Three-Dimensional Buoyant Plumes in Enclosures", Combustion Science and Technology, Vol. 40, pp 55-77, Gordon and Breach Science Publishers, 1984. [7] Baum, H.R., Rehm, R.G. and Mulholland, G.W., "Computation of Fire Induced Flow and Smoke Coagulation", Nineteenth Symposium (International) on Combustion/ The Combustion Institute, pp 921-931, Pittsburgh, PA, 1982.

322

[8] Baum, H.R. and Rehm, R.G., Finite Difference Solutions for Internal Waves in Enclosures, SIAM J. Sci. Stat. Comput., Vol. 5, No.4, pp. 958-977 (1984). [9] Baum, H.R. and Rehm, R.G., "Transient Combustion in a Turbulent Fire", 9th Joint Meeting of the U.S. Japan Natural Resources (UJNR) Panel on Fire Research and Safety, Boston, MA, May, 1987. [10] Rehm, R.G., P.D. Barnett, H.R. Baum and D.M. Corley, "Finite Difference Calculations Of Buoyant Convection in an Enclosure: Verification of the Nonlinear Algorithm", Applied Numerical Mathematics, VoU, pp 515-529, North-Holland, 1985. [11] Baum, H.R., Rehm, R.G. and Gore, J.P., "Transient Combustion in a Turbulent Eddy", Twenty Third International Symposium on Combustion, to appear. [12] Rehm, R.G., Baum, H.R. and Barnett, P.D., "Buoyant Convection Computed in a Vorticity, Stream-Function Formulation," Journal of Research of the NBS, Vol. 87, pp 165-185, March-April 1982.

323

Predictions of Unsteady Burning of a Fuel Bed FAN WEICH ENG and WANG JIAN Department of Engineering Thermophysics University of Science and Technology of China Hefei, Anhui 230026, P.R. China

ABSTRACT

Unsteady burning of a fuel bed is often encountered in urban and wildland fires. Two kinds of fuel bed are examined. They are a liquid pool and a porous bed. The fuel bed is ignited at one end by a heat source. The fluid flow, heat and mass transfer, combustion and gasification of the fuel bed, and their interactions in the unsteady burning process of the fuel bed are studied by formulating and solving a set of governing equations. Additional source terms in the governing equations are proposed to represent the transfer processes of mass, momentum, energy and gasified fuel between solid phase and gas phase of the porous bed. Also, porosity is introduced as a concept and an approach to express the blockage within the porous bed. Predicted speed of flame spread along the surface of the Heptane pool is around 2 m / s, which is close to experimental data. Flow field, isotherms and contours of mass fraction of fuel obtained have similar characteristics with typical experimental findings. KEYWORDS: Fire, Modeling and Simulation.

NOMENCLATURE A,B C1,C2 Cp

f H h.. L

m.

constant constant specific heat drag force combustion heat enthalpy of relased gas latent energy vaporization rate per unit area

A. Cd E

gr h k m P

constant drag coefficient activation energy gravitation constant enthalpy turbulence energy mass fraction pressure

FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM. pp. 325-334

325

Po R

S SA T u V

y

p 8

JleCf ub

porosity perfect gas constant source term upwind area of wood temperature axial velocity volume lateral coordinate proportional factor turbulence energy dissipation dependent variable effective viscosity PrandtI number of enthalpy

heat transfer rate from gas to solid chemical reaction rate mass flow rate from solid to gas stoichometric ratio of fuel and oxygen time lateral velocity axial coordinate mass fraction in relased gas heat transfer coefficient density exchange coefficient turbulent viscosity

Qt

R S s t v x ex A. p

r Jlt

Subscripts fu pr y e w v

fuel product lateral coordinate east surface of cell west surface of cell volume dependent variable

oxygen axial coordinate wood south surface of cell north surface of cell node

ox x wo n p

1. INTRODUCTION

Unsteady burning of a fuel bed is a common phenomenon in both urban and wildland fires. In a wildland fire a tract of woods is simplified as a porous fuel bed. The trees are treated as a solid part of the porous bed, while the air between the trees as a gaseous part of the bed. Thus,the fuel loading and its intervals can be simulated by setting porosity appropriately. In order to understand the mechanism and rules of the phenomenon, the fluid flow, heat and mass transfer, chemical reactions and their interaction in the burning processes must be studied. There have been some works on circular pool fire with the surroundings at rest CD , but no numerical predictions of a fire for a rectangular liquid-pool or a porous fuel bed have been reported in the literature. It would be interesting to see the result, if the processes can be formulated and then solved. Burning of the two kinds of fuel bed mentioned above is numerically studied, which are sketched in Fig.2. The interaction between the liquid pool and the fire takes place on the surface of the pool, which can be considered through appropriate boundary conditions. For the porous fuel bed the interactions of the bed and fire exist within the bed as well. The influence of the bed on the fire must be taken into account. In the present study this is done by incorporating appropriate source terms into the governing equations of the gas phase, and by introducing volumetric & surface, porosity in the numerical methods. Source terms added to the continuity, momentum, energy and species equations represent, respectively, the mass transfer from solid to gas, the drag force exerted by the porous surface, the heat transfer from gas to the porous surface, and the production rate of fuel volatiles by pyrolysis. Porosity is a 326

mathematical representation of blockage to fluid flow within the region of interest. These will be described in detail in the Section 2. Wind usually affects the fire. The effects are studied here by setting a certain wind speed as a boundary condition of the momentum equation.

2. MATHEMATICAL DESCRIPTIONS

A. Governin2 Equations

The rectangular fuel bed with infinite length and finite width is placed horizontally. The coming air flows parallel to the fuel bed with an uniform velocity. An ignition source is located at one end of the bed. The main interest in the present study is focused on the unsteady pro· cesses between ignition and steady burning. Accordingly, the following assumptions are made: • the processes are two-dimensional and unsteady; • the flow and combustion are laminar, if the surrounding air is at rest; the processes will be· come turbulent, if the coming flow is turbulent or when the flame covers the whole fuel bed; • the geometry of the fuel bed does not change during the processes studied; • radiation is negligible, since the flame is small and weak, and the temperature of gas is rela· tively low during the unsteady processes. Under these assumptions the governing equations of the gas phase are as follows continuity equation:

(2- I) momentum equation: a(pu) at

+ a(puu) + a(puv) ax

=

_

ap

ax

ay

+ 2.E... ( ax

au)

~errax

+ .E... [ ay

(au + av) ] + ~err ay ax (2 - 2)

{uS - fJ a(pv) at

+ a(puv) + a(pvv) ax

ay

=

_

ap ay

+.E... [

+ au) ] + 2.E... (~ av) _ pg +

(av

ax ~err ax

ay

ay

erray

,

(2 - 3)

{vS - f y } energy equation:

(2 - 4)

species equation: a(pm r)

-at- + a(pm oJ -+ at

a(pum r) a(pvmrJ + ax ay a(pum 0,)

ax

0,) + a(pvm ay

= -

a (

ax a (

=-

ax

am

)

a (

am

).

.

ru ru r ru -ax+ -ay r ru -ay- - R ru + {Cl ru S} am ox ) a (r am 0') r o. - +-- ax ay o. ay

327

R' ox

1 + {s' Cl r o.

(2- 5) (2 - 6)

where the source terms in brackets, f }, are valid only within the porous bed. In the brackets S stands for the total mass flow rate from the solid to the gas; f. and fy are drag forces exerted on the gas phase (2 -7) (2 - 8)

where C cIx and C dy are drag coefficients; SA. and SAy are upwind areas. hjn refers to the enthalpy of the released gas (2- 9)

Q, is the heat transfer rate from gas to solid; ecru is mass fraction of species fuel in the released gas.

These governing equations can be written into a general form. = ~

o(pCll) + o(puCll) + o(pvCll) ot ox oy

ox

(r .2

2~2

[

i\2

dx

]

Poo

Poo

d(b 2 u ) m dx d(b2 APmu 2m)

d(b2 u 2 ) m

[ 1:2i\2] dx

dx

2 deb lIPmUm)

- 2

Poo

i\2

b a u

(17)

m

gb 2 lIP m

(18)

(19)

0

dx Equations (17-19) represent a pseudo one-dimensional mathematical model of a plume originated from a circular fire source. The set of equations (17-19) together with the boundary conditions given by equation (9) complete the model. The solution of model equations are now discussed. Analytical Solution.

By using equation (10), analytical solution of the

model equations (17-19) results the following final forms:

T m T

(20) (b/b )2/n

00

s

(1 - T / T ) 00

s

4C 2 4

(n+2)

(21)

2/n (b/b) s

- 2i\2

where Equations (20) and (21) can be used to compute the centerline values of temperature and velocity. The value of constant ~ will now be determined numerically as has been done earlier. Numerical Solution and Discussion.

Equations

(17-19)

have

been

solved

numerically for different values of source velocities. In order to relate the source conditions, source Froude number given by equation (13) can

450

also be used for circular fire source with CF = A. The solution of the model equations has now been obtained for three values of source Froude number viz., Frs < 1, Frs = 1 and Frs > 1. The results are presented in Figures 4 to 6.

Figure 4 shows the variation of plume width with the height.

It

can

be seen from this figure that applicability of equation (10) is again restricted to Frs = 1. For the case of Frs = 1. the plume expands linearly with height as shown by straight line. The slope of this line is found equal to 1. 1737 IX. Hence, the val ue of 1) comes out to be 1. 1737. The val ue of 1) observed by Morton et al. [21 and Evans [131 is 6/5 or 1.2 i.e., nearly 2% higher than the present value. This may be due to the fact that, we have solved the model equations over an area fire source instead of a virtual point source. For Frs < 1, again the necking of plume is observed,

while for Frs> 1,

the plume expands parabolically near the

source. In all the three cases., the plume expansion becomes parallel to each other asymptotically. Figure 5 shows the variation of plume centerline velocity with height. It has been observed that for Frs 1, the plume velocity at the fire source

is constant upto a very small

height,

1. e.,

dumldx

= O.

Setting dumldx = 0 at x=O for the equation (21), we get the relationship for source Froude number, assumed for circular fire source. For Frs < 1,

the plume centerline velocity first

increases then

becomes constant for a small height and finally contiunes to decrease. For Frs > 1, the centerline velocity goes on decreasing steeply near the source and gradually away from the source. Figure 6 depicts the variation of plume centerline temperature with height for three values of source Froude number. The explanation given in the case of line fire source is equally valid to the present case and is not repeated. Generalization of Explicit Expressions

It has been observed that explicit expressions for line and circular fire sources, obtained analytically to calculate pI ume width and centerl ine temperature and velocity are valid for Frs = 1 only. Hence their use is limited. In order to make these expressions suitable for all cases of Frs' the source condi t ions must be modified in such a way that the modified source is represented by a source Froude number of value one. Let us assume that the temperature of modified and real fire sources are same. The velocity of plume gases at the modified source is usm and its width is b sm

Now irrespective of two sources i.e., real and its modified

version,

mass

the

flux

should

remain the

451

same.

Using

this

concept,

3.0

3.6

2.5

3.0

2.0

.....s::

""

2.4

2

e.

e

3

1.5

Clr"e

.~

1.0 0.5

i,1.8 :z: 1.2

'il

F~

2

0.25 1.00

3

3.00

2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.5 1.0 1.5

2.0

1.5

1.0

3

:~

.J~

0.0 0.0

Frs

I 2

I I

3

0.6

0.0

Curve

I-

2.5

3.5

3.0

4.0

Centerline velocity, m/s

Plume width, m

Figure 2 Vilriiltion of centerline velocity with height (Line fire source)

Figure 1 Variation of plume width with height (Line fire source I 3.6

3.6

3.0

3.0

~---1f---+--+--+-T-crl-c......---+----i

2.4

1--+--+-+-~¥--rlI~--+---I

2.4

1

e

;1.8~--+--+~t:;~'L-+----l-~

2

..... 1.8 .s:: .2'

\

:! 1.2

3

Curw Frs

1 2

\~

0.6

3

0.5 1.0 1.5

""

::!

200 300

0.0

600

3.6

0.1

'1:!I:

1 2 3

1 2 3

,,

e 2.4

l\ t 1\ ~ \

..

~1.8 :z:

1.2 0.6

~'

10

1.5

2.0

3.0

0.5 1.0 2.0

_J...._....I..____1

0.4

0.5

0.6

0.7

:r:

0.6 4.5 5.0

5.5

Centerline velocity, m/s Figure 5 Variation of centerline velocity with height (Circular fire source I

452

Curve Frs 1

2.4

:l:

4.0

0.3

3.0

.~ 1.2

3.5

0.2

Figure 4 Variation of plume width with height ( Circular fire source I

E.1.8

1\\\'-t---

2.5

0.25 1.00

Plume width, m

Curve Frs

....

0.0

L-.-c...J.~_..1.-___t_

0.0

Figure 3 Variation of centerline temperature with height (Line fire source I

3.0

~

1 2

3.00

700 800 900 Centerline temperature, K 400 500

~--I---iI''-+---Ioi''--+----I

0.6 1--1-J'.-.£.+--'--+---1----+--+_---1

~ ~~

0.0

1.2

0.0

f--

1

t----

2

~\-

3

\ 200 300

2 3

0.5 1.0 2.0

~ -..... 400

500

600

700

800

Centerline temperature, K Figure 6 Variation of centerline temper_ ature with height {Circulilr f ire source I

expressions

for

band u have sm sm

been obtained

and

are

given

in

the

following table.

b u

Circular Fire Source

Line Fire Source

Parameter

b

sm

u

sm

s s

Fr

2/3

b

s

1 Fr

2/3

s

Fr

2/5

s

u IFr s s

s

4/5

Thus if Us is replaced by u sm and b s is replaced by b sm in our explicit relationships, we can possibly use them for all types of line and circular fire sources. In order to verify the validity of above modifications, computations have been carried out by using them for the same conditions for which Figures 1 through 6 have been drawn. These computations are shown by dotted lines on the respective figures. It may be noted that the maximum deviation between the two solutions exists near the fire source only, which is expected. The percentage variations for all the parameters are within ± 4 per cent for the locations starting from 0.6 m onwards.

CONCLUSION In the present study pseudo one-dimensional mathematical models have been developed in order to understand the behaviour of a fire plume generated above finite size I ine and circular fire sources. These models can be employed to obtain the steady state values of plume width, centerline velocity and temperature in plumes generated by fire sources of various source Froude numbers. Analytical expressions have also been developed to compute these variables (b, urn and Tm) for a fire source of Frs

1.

With

certain

modifications,

these

expressions

can

also

be

applied to other cases of source Froude numbers, i.e. , Frs < 1 and Frs> 1. ACKNOWLEDGEMENT Authors are grateful to Dr. R. K. Bhandari, Director, and Dr. S. K. Misra, Acting Director, Central Building Research Institute, and Dr. B. S. Varshney, Professor, Chemical Engineering Department, University of Roorkee, for providing necessary facilities for this work.

453

REFERENCES [1]

Rouse, H., Yih, C.S. and Humphreys, H.W., "Gravitational Convection from a Boundary Source", Tellus, ~, 201-210, 1952.

[2]

Morton, B.R., Taylor, G.!. and Turner, J.S., "Turbulent Gravitational Covection from Maintained and Instantaneous Sources", Proc. Roy. Soc. A., 234, 1-23, 1956.

[3]

Yokoi, S., "Study on the Prevention of Fire Spread Caused by Hot Upward Current", Report No. 34, Building Research Institute , Tokyo, Japan, 1960.

[4]

Morton, B.R., "Forced Plumes", J. Fluid

[5]

Lee, S. L. and Emmons, H. W., "A Study of Natural Convection above a Line Fire Source", J. Fluid Mech., 11, 353-368, 1961.

[6]

George, W.K., Alpert, R.L. and Tamanini, F., "Turbulent Measurements in a Axisymmetric Buoyant Plume", Int. J. Heat Mass Tr., 20,

Mech., 5, 151-163, 1959.

1145-1154, 1977. [7]

Heskestad, G., "Virtual Origins of Fire

Plumes", Fire

Safety J.,

~,

109-114, 1983. [8]

Hasemi, Y. and Tokunaga, T., "Flame Geometry Effects on the Buoyant Plumes from Turbulent Diffusion Flames", Fire Sci. & Techno!., 4(1), 15-26, 1984.

[9]

Cetegen, B.M., Zukoski, E.E. and Kubota, T., "Entrainment in the Near and Far Field of Fire Plumes", Combust. Sci. & Techno!., 39, 305-331, 1984.

(10]

Cox, G. and Chitty, R., "Some Source Dependent Effects of Unbound Fires", Combust. Flame, 60, 219-232, 1985.

[11]

Tokunaga, T., Sakai, T., Kawagoe, K., Tanaka, T. and Hasemi, Y., "Mass flow Rate Formula for the Upward Current above Diffusion Flames", Fire Sci. and Techno!., 2(2), 117-125, 1982.

[12] Gupta, A. K., Kumar, S. and Singh, B., "One Dimensional Mathematical Modelling of Enclosure Fire Dynamics", Fire Matrs., 12, 51-60, 1988. [13] Evans, D. D., "calculating Fire Plume Characteristics in a Two-layer Environment", Fire Techno!., 20(2), 47 - 63, 1984.

454

STATISTICS AND RISK

Criteria for Fire Risk Ranking JOHN M. WATTS. JR. Fire Safety Institute Post Office Box 674 Middlebury. Vermont 05753. USA

ABSTRACT Fire risk ranking is evolving as a means of evaluating fire safety that is conducive to the assimilation of research results. This paper sum marizes research into the extent, nature, and criteria for fire risk ranking methods. Concepts of fire risk ranking are presented and examples of the major methods which have been developed are briefly described. The methods have similar basic components of parameters, values, and relationships. The nature and limitations found in application of these components are discussed. Ten criteria are presented as a guide to the development and evaluation of fire risk ranking methods. These criteria apply to the basic. components and to documentation and output of fire risk ranking syste ms. KEYWORDS: decision analysis, decision making, fire risk, fire safety evaluation, risk analysis, risk ranking, systems analysis. INTRODUCTION Fire risk ranking is a link between fire science and fire safety. As we learn more about the behavior of fire, it is important that this new knowledge be implemented to meet fire safety goals and objectives. One of the obstructions to implementation of new technology is the dearth of structured fire safety decision making. Fire risk ranking is evolving as a means of evaluating fire safety that is conducive to the assimilation of research results. As part of an ongoing project to analyze the potential use of fire risk ranking systems, a significant number of approaches have been identified and reviewed [1]. It has been found that while there is wide spread development and use of fire risk ranking techniques there is very little information on methodology or evaluation criteria. This paper is a step toward a protocol for development and evaluation of ranking approaches to fire safety. It presents criteria to be considered in the construction of a fire risk ranking model or in assessment of a specific application. FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM. pp. 457-466

457

Fire Risk

By nature of the circumstances, fire safety decisions often have to be made under conditions where the data are sparse and uncertain. The technical parameters of fire risk are very complex and normally involve a network of interacting components, the interactions generally being non-linear and multidirectional. However, complexity and sparseness of data do not preclude useful and valid approaches. Such circumstances are not unusual in decision making in business or other risk venues. (Exploration of outer space illustrates how success can be achieved when there are little relevant data.) Fire risk analysis involves a large number of multifarious factors which are difficult to assess in a uniform and consistent way. The analysis of such complex systems is difficult but not impossible as evidenced by activities in areas such as nuclear safety and environmental protection. Detailed risk assessment can be an expensive and labor intensive process and there is considerable scope for improving the presentation of results. Ranking can provide a cost-effective means of risk evaluation which is sufficient in both utility and validity. Ranking

Risk ranking is the process of modeling and scoring causal and mitigating parameters to produce a rapid and simple estimate of relative fire risk. The incentive for risk ranking techniques is to provide decision makers with a transparent and defensible way of arriving at decisions. An essential characteristic of ranking alternatives is the aggregation of entities into a single index. The theory behind using a single index to represent many non-com mensurable features is well developed in decision analysis [2]. The sheer mass of input information makes the use of ranking indices attractive. Fire Risk Ranking Fire risk ranking originated with insurance rating schedules in the 19th century. However, in the last few decades, there has been a move to develop more wide spread analytical procedures. 1n general, fire risk ranking assigns values to selected variables based on

professional judgement and past experience. The selected variables represent both positive and negative fire safety features and the assigned values are then operated on by some combination of arithmetic functions to arrive at a single value. This single value can be compared to other similar assessments or to a standard. Fire risk ranking generally has high utility due to the relative ease of application but lacks validity because of the unspecified nature of the selection of variables and their relationships. The relationship of risk ranking techniques to other forms of fire risk analysis is discussed elsewhere [3,4]. EXAMPLES

Numerous schemes for using a weighted combination of parameters to provide a ranking of fire risk have been tried. These include systemic applications to

458

buildings or classes of occupancy and applications to more specific components of the fire risk. Risk ranking approaches have been referred to by various designations such as index systems [5], numerical grading [6], point schemes [7], and rating schedules [3]. Three of the most widely used and most well documented fire risk ranking methods will be briefly described as examples of the approaches taken. They are the US Fire Safety Evaluation System, the Swiss Gretener method and the UK Edinburgh scheme. Fire Safety Evaluation System The Fire Safety Evaluation System (FSES) [6,8] is a method for determining equivalencies to the NFP A Life Safety Code for certain institutions and other occupancies. The technique was developed at the US Center for Fire Research in the late 1970s. It has since been regularly adapted to new editions of the Life Safety Code. The FSES treats risk and safety parameters separately. It begins with a determination of relative risk derived from characteristics of a health care occupancy. Five occupancy risk factors are used; patient mobility, patient density, fire zone location, ratio of patients to attendants, and average patient age. Variations of these factors have been assigned relative weights determined from the experienced judgement of a panel of fire safety experts. Risk is then calculated as the product of the assigned values for the five factors. The system dictates that the calculated risk be offset by safety features. Thirteen safety parameters were selected. These parameters and their respective ranges of values are also products of the same panel of experts. There is no correlation of these fire safety parameters to the previously defined risk factors. Alternative fire safety strategies are identified as containment, extinguishment, and people movement. The expert panel's opinion was again employed to determine in a binary fashion which fire safety parameters apply to each fire safety strategy. Values of the parameters are then summed for each strategy with an adjustment for the value of automatic sprinklers for people movement safety. The resulting sums are considered to be the available level of each fire safety strategy. The calculated level for each fire safety strategy is then compared to predetermined minimum levels. For the category of "general safety" the sum of all available safety parameter values is compared to the occupancy risk previously calculated. Gretener Method M. Gretener of the Swiss Fire Prevention Service developed an arithmetical evaluation of fire risk in buildings [9,10,11]. His premise was that determining fire risk by statistical methods based on loss experience was no longer efficient. The Gretener method is important because of its acceptance for insurance rating and code enforcement and because of its simple mathematical formulation.

459

The Gretener method expresses parameters of ignition and fire spread and parameters of fire protection as empirically derived numerical values. The product of the hazard parameters gives a value for potential hazard, while the product of the fire protection parameters yields a value for protective measures. The ratio of these products is taken as the measure of expected fire severity. It is immediately appealing that the approach begins with the explicit concept

of risk as the expectation of loss, given by the product of hazard probability and hazard severity: R = A x B

where: R = fire risk, A = probability that a fire will start, and B = fire hazard, degree of danger, or probable severity. Thus, the Gretener method is based on these two probabilities and combines them in accordance with probability theory. A further departure from the more popular approaches to fire risk ranking is the calculation of fire hazard as a ratio rather than a sum. Fire Hazard = Potential Hazard / Protective Measures B = P / (N x S x F)

where: B = fire hazard, P = potential hazard, N = standard fire safety measures, S = special fire safety measures, and F = fire resistance of the building. Potential hazard, P, is the product of hazard elements whose magnitudes are influenced on the one hand by the building contents, i.e. materials and merchandise present, and on the other hand by the building itself. As with most other risk ranking approaches, the values for these individual factors are not based solely on statistics, but are empirical quantities resulting from a comparison of analyses of fire risks for which fire protection measures are either common or required by law. Edinburgh Model

A matrix approach to fire safety was developed at the University of Edinburgh, [12,13,14] and has been extended at the University of Ulster [15,16]. The original objective of this work was to improve the evaluation of fire safety in UK hospitals through a systematic method of appraisal. As a logical extension of FSES, consider that there parameters. This suggests levels, that comprise fire

a single fire safety matrix, such as developed in the are more than two categories of fire safety a hierarchy of lists of things, or decision making safety. Such a hierarchy is presented as follows:

460

1. 2. 3. 4.

POLICY OBJECTIVES STRATEGIES COMPONENTS

These represent common levels of fire safety decision making but there may be more or fewer in a particular application. For example, an even lower level dealing with individual hardware items could be added, or intermediate levels could be used to better define certain relationships. This hierarchy of levels of detail of fire safety suggests a series of matrices is appropriate to model the relationships among various fire safety factors, that is, a matrix of policy versus objectives would define a fire safety policy by identifying the specific objectives which are held most desirable. In turn, a matrix of objectives versus strategies would identify the relationship of these factors, and a matrix of strategies versus hardware components would suggest where to use what. Thus, a matrix may be constructed to examine the association of any two adjacent levels in a hierarchy of fire safety factors. An even more appealing aspect of this approach is that two or more matrices may be combined (multiplied) to produce information on the importance of specific details of building ele ments to an overall fire safety policy information which has not here to fore been available. This method is the only such grading of fire safety factors with an explicitly defined relationship to fire safety goals and objectives. Another important contribution of the Edinburgh model is the parameter interaction matrix. Construction of a square matrix of risk parameters provides a systematic approach to the assessment of interdependence of each pair of parameters. This permits adjustment of results to reflect synergisms and other associations of parameters in a consistent manner. COMPONENTS Fire risk ranking methods are found to have three basic components [1,6]; a list of parameters, procedures for assigning values to the parameters, and relationships which define mathematical operations on the parameter values to produce an assessment of hazard or risk. Analysis of the nature of these components in the many different approaches has led to identification of co mmon characteristics. Parameters Parameters of fire risk ranking systems, also referred to as factors, variables, etc., identify the ingredients of fire safety. Fire safety in buildings is a complex system with an inordinately large number of factors which may affect it. It is computationally feasible to deal with only a relatively small number of variables. Therefore, it becomes necessary to reduce the large number of variables to an appropriate subset. It is intuitively appealing to postulate that safety from fire is a Paretian phenomenon in that a relatively small number of factors account for most of the problem. This is supported by general fire loss figures which suggest that a small number of factors are associated with a large proportion of fire deaths.

461

Values The next component of fire risk ranking is the establishment of quantitative measures associating fire risk with the qualitative characteristics of the parameters. Value selection for the parameters is where the existing methods show the greatest range of variation. Sources for these values range from fire test data to hearsay. The approach to determination of values can be either objective or subjective. The main criticism of objective estimates is that historical data may not be relevant to the future conditions being considered. For some decisions the subjective approach may be superior when it takes into account both antecedent data and the decision maker's assessment of present and future influences. There are decision analysis techniques that can be used when, as is most often the case, little or no data are available. Multi-attribute utility theory [17,18] offers a way, through formal questioning, of developing meaningful values. The analytical hierarchy process [15,19,20] is an even more formal technique that produces mathematical measures of consistency. Delphi [21,22] is less formal and has been used in several fire risk ranking projects including the FSES and the Edinburgh model. In all but the simplest approaches, two sets of values are associated with each parameter, intensity and importance. Intensity is a measure of the amount or degree that a parameter is present in a specific application, e.g. number of stories, completeness of automatic detection, etc. Importance is a weight indicating the influence or significance of the parameter to fire safety. Most often these are combined into a single dimensionless value. Relationships

Relationships are the mechanisms by which the parameter values are combined to yield a measure of fire risk. The general expression is given by equation (1).

i=1,2, ...

,n

(1)

where: R = risk Xi = measure of parameter i ai, bi = weights of parameter n = number of parameters In most of the fire risk ranking methods studied, the function (fcn) used is addition. The risk is measured by the weighted sum of the parameter values as indicated in equation (2) where bj = 1 for all i.

n

R

=E

(aixi)

~=1

This expression implicitly assumes the parameters are all independent in their effect on fire risk.

462

(2)

The Gretener method uses multiplication as the function by which fire risk is determined from the parameter values. This is expressed in equation (3) where ai = 1 for all i and bj = +/- 1 depending on whether the parameter represents a potential hazard or a protective measure.

n n

R =

(X:i)

(3)

~=1

Multiplication of parameter values implicitly assumes that all the parameters are completely interactive. That is, the impact on fire risk of any unit change in a single parameter will be dependent on the values of each of the other parameters. Most of the fire risk ranking methods studied do not address the interaction of parameters. Yet it is intuitive that certain combinations of parameters, e.g. smoke detection and automatic suppression, are not simply additive in their associated effect on fire risk. At least two methods do deal explicitly with parameter interaction. The FSES uses exceptions in determining parameter values for certain pairs of parameters in combination. The Edinburgh model uses a parameter interaction matrix to systematically assess potential relationships among all the parameters. Linearity is implicitly assumed by the relationships employed in all the methods studied. CRITERIA

The fire protection community seems to be largely unconcerned with the proliferation of fire risk ranking and how it is being used. The available literature deals only with development and application of a specific method or general descriptions of several selected approaches. Like any analytical techniques, risk ranking methods have their limitations and should not be used uncritically. The purpose of fire risk ranking is to provide a useful aid to decision making. Usefulness requires the methodology to be simple yet credible. It must be easy to apply but sophisticated enough to provide an acceptable minimum of technical validity. Credibility can also be improved through consistency and transparency. The approach should be systematic and clearly discernible to all interested parties that the relevant technical issues have been appropriately covered. Based on the review of numerous fire risk ranking systems, several criteria are proposed as an aid in the development and evaluation of similar approaches. They are qualitative guidelines that do not guarantee a better result but identify minimal requirements for assessment of the credibility of a fire risk ranking. Criterion 1: Development and implementation of the method should be thoroughly documented according to standard procedures. One of the hallmarks of professionalism is that as a study proceeds, a record is made of assumptions, data, parameter estimates and why they were chosen, model structure and details, steps in the analysis, relevant constraints, results, sensitivity tests, validation, and so on. Little of this information is available for most fire risk ranking methods.

463

In addition to facilitating review, there are other practical reasons not to slight the documentation. 1) If external validation is to be conducted, adequate documentation will be a prerequisite. 2) During the life cycle of a fire risk

ranking system the inescapable changes and adjustments will require appropriate documentation. 3) Clear and complete documentation enhances confidence in the method, its absence inevitably carries with it the opposite effect. The value of the documentation will be improved if it follows established guidelines. Standard formats for documentation are primarily directed at lar~e­ scale computer models [23,24] but can be readily adapted in principle to more general applications. Criterion 2: Partition the universe rather than select from it. One of the least well established procedures in fire risk ranking is the choice of parameters. In following a systemic approach e.g. [25] it is best to be comprehensive. In the Edinburgh model, this is achieved by using the NFPA Fire Safety Concepts Tree [26]. The Tree branches out from the holistic concept of fire safety objectives. A cut set on the Tree will then identify a group of parameters which encompasses all possible fire safety features. Criterion 3: Parameters should represent the most frequent fire scenarios. In determining the level of detail of the parameters, it is necessary to look at those factors which are most significant, statistically or by experienced judgement. This criterion may also be used as an alternative to criterion 2, providing the need for systemic comprehensiveness is satisfied. Criterion 4: Provide operational definitions of parameters. If the methodology is to be used by more than a single individual, it is necessary to ensure precise communication of the intent of key terms. Many fire risk parameters are esoteric concepts which have a wide variety of interpretations even within the fire community. Criterion 5: Elicit subjective values systematically. Most fire risk ranking methods rely heavily on experienced judgement. The use of formalized, documented procedures, such as the previously mentioned multi-attribute utility theory, analytical hierarchy process, and Delphi, significantly increases credibility of the system. Similarly, use of recognizable scaling techniques will enhance credibility. Criterion 6: Parameter values should be maintainable. One variable that is not explicitly included in fire risk ranking is time. Yet the influence of time is ubiquitous. It influences the fire risk both internally (e.g. deterioration) and externally (e.g. technological developments). In order for a method to have a reasonably useful lifetime, it must be amenable to updating. This implies that the procedure for generating parameter values must be repeatable. Changes over time and new information dictate that the system facilitate revisions. Criterion 7: Treat parameter interaction consistenUy. In the majority of cases this will consist of an explicitly stated assumption of no interactive effect among parameters. Where interactions are considered, it is important that they be dealt with systematically to avoid bias. The Edinburgh interaction matrix is one approach to this assessment. Criterion 8: state the linearity assumption. While this assumption is universal in fire risk ranking, it is also well known that fire risk variables do not necessarily behave in a linear fashion. It is important to the acceptance of ranking methods

464

and their limitations that such assumptions are understood. Criterion 9: Describe fire risk by a single indicator. The objective of most fire risk ranking methods is to sacrifice details and individual features for the sake of making the assessment easier. Information should be reduced to a single score even in the most complex applications. Techniques have been espoused to combine technical, economic, and socio-political factors [27]. The results should be presented in a manner that makes their significance clear in a simple and unambiguous way. Unless all those involved can understand and discuss the meaning of the ranking, there will not be general confidence in its adequacy. Criterion 10: Validate results. Some attempt should be made to verify that the method does in fact differentiate between lesser and greater fire risks with sufficient precision. The level of accuracy demanded here is not the same as for other engineering purposes, establishing an order of magnitude will generally suffice. REFERENCES 1. Watts, John M., Jr., "Fire Risk Rating Schedules", ASTM Symposium on Fire Hazard and Fire Risk Assessment, San Antonio TX, December 1990. 2. Miser, Hugh J., and Edward S. Quade, eds., Handbook of Systems Analysis, North-Holland, New York, 1985. 3. Watts, John M., Jr., "Fire Risk Assessment Schedules", Section 4, Chapter 11, in The SFPE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy MA, 1988 (pp. 4-89 to 4-102). 4. Hall, John R., Jr., and Ai Sekizawa, "Fire Risk Analysis: General Conceptual Framework for Describing Models", Fire Technology, Vol. 27, No.1, 1991, pp. 33-53. 5. Rosenblum, Gary R., and Steven A. Lapp, The Use of Risk Index Systems to Evaluate Risk, in Risk Analysis: Setting National Priorities, proceedings of the SOCiety for Risk Analysis, Houston TX, 1987. 6. Nelson, Harold E., "Overview: Numerical Grading Systems", report from the 1987 workshop on Analytical Methods for Designing Buildings for Fire Safety Design, National Academy Press, Washington DC, 1988. 7. Rasbash, D.J., Approaches to the Measurement and Evaluation of Fire Safety, Third International Fire Protection Engineering Institute, Wageningen, the Netherlands, February 1980. 8. Nelson, H.E., and A.J. Shibe, 1980, "A System for Fire Safety Evaluation of Health Care Facilities," NBSIR 78-1555, Center for Fire Research, National Bureau of Standards, Washington, DC. 9. Gretener, M., "Evaluation of Fire Hazard and Determining Protective Measures", Association of Cantonal Institutions for Fire Insurance (VKF) and Fire Prevention Service for Industry and Trade (BVD), Zurich, 1973. 10. Gretener, M., "Fire Risk Evaluation", Association of Cantonal Institutions for Fire Insurance (VKF), Society of Engineers and Architects (SIA), and Fire

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Prevention Service for Industry and Trade (BVD), Zurich, 1980. 11. Kaiser, J., "Experiences of the Gretener Method", Fire Safety Journal, vol. 2, 1980, pp. 213-222. 12. Marchant, E. W., "Fire Safety Evaluation (Points) Scheme for Patient Areas Within Hospitals", Department of Fire Safety Engineering, University of Edinburgh, 1982. 13. Marchant, E.W., Fire Safety Engineering - A Quantified Analysis, Fire Prevention No. 210, June 1988, pp. 34-38. 14. Stollard, P., "The Development of a Points Scheme to Assess Fire Safety in Hospitals", Fire Safety Journal, Vol. 7, No.2, 1984, pp. 145-153. 15. Shields, T.J., and G.W. Silcock, An Application of the Analytic Hierarchical Process to Fire Engineering, Fire Safety Journal, Vol. 11, 1986, pp. 235-242. 16. Donegan, H.A., T.J. Shields, and G.W. Silcock, "A Mathematical Strategy to Relate Fire Safety Evaluation and Fire Safety Policy Formation for Buildings", Fire Safety Science - Proceedings of the Second International Symposium, Hemisphere, 1989, pp. 433-441. 17. Raiffa, Howard, Decision Analysis, Addison-Wesley, Reading MA, 1968. 18. Keeny, R.L., and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, Wiley, New York, 1976. 19. Saaty, T.L., The Analytical Hierarchy Process, McGraw-Hill, New York, 1980. 20. Golden, B.L., E.A. Wasil, and P.T. Harker, eds., The Analytic Hierarchy Process, Springer-Verlag, New York, 1989. 21. Linstone, Harold A., and Murray Turoff, eds., The Delphi Method: Techniques and Applications, Addison-Wesley, Reading MA, 1975. 22. Harmathy, T.Z., "The Delphi Method - A Complement to Research", Fire and Materials, Vol. 6" No.2, 1982, pp. 76-79. 23. Gass, SJ., Documenting a Computer Based Model, Interfaces, Vol. 14, No.3, 1984, pp. 84-93. 24. ASTM, Standard Guide for Documentation of Computer Software for Fire Models, ASTM, Philadelphia, 1990 (Draft). 25. Beard, Alan N., ''Towards a SystemiC approach to Fire Safety", Fire Safety Science - Proceedings of the First International Symposium, Hemisphere, 1986, pp. 943-952. 26. NFPA 550, Guide to the Fire Safety Concepts Tree, National Fire Protection Association, Quincy MA, 1986. 27. Chicken, John C., and Michael R. Hayns, The Risk Ranking Technique in Decision Making, Pergamon Press, Oxford, 1989.

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Key Distinctions in and Essential Elements of Fire Risk Analysis JOHN R. HALL, JR. Fire Analysis and Research Division National Fire Protection Association One Batterymarch Park, P.O. Box 9101 Quincy, Massachusetts 02269-9101, USA

ABSTRACT The growing volume of research on fire risk has yet to produce convergence on the meaning of the term "fIre risk" or on closely related concepts like "scenario" and "fire hazard". These differences in tenninology are not simply semantic but often reflect either disagreements or confusion over the essential elements of ftre risk analysis. This paper presents a number of basic concepts and a very general format for fIre risk measures and models. Then the elements of these concepts are discussed to underline key distinctions between appropriate and inappropriate designs for fIre risk analysis. The principal theme is the need to defIne a model to capture all the variations in fIre conditions and other conditions that can affect the fIre involvement of the subject of interest, whatever it may be.

KEYWORDS Risk analysis INTRODUCTION In the past decade, the term "ftre risk analysis" has been used to refer to an everincreasing variety of forms of analysis. Some of this variation occurs because different decisions and problems require different kinds of information. However, much of the variation reflects the use of the term "ftre risk" to refer to a range of fundamentally different types of analysis. Fire risk analysis can encompass every branch of fIre science. Since no one person is likely to have that breadth of knowledge, there is sometimes a tendency for models to be built and labeled as fIre risk analysis models without suffIcient strength in all the requisite areas. In a recent issue of Fire Technology, the author and Dr. Ai Sekizawa of Japan's Fire Research Institute proposed a general framework that could identify the key elements of any ftre risk analysis method [1]. After briefly recapitulating this framework and its key concepts, this paper will focus on key distinctions that tend to be crucial in deciding what models are appropriate for different kinds of problems and decisions. Inappropriate or defIcient modeling approaches will be cited in places to further illustrate the key elements of ftre risk analysis and why they are necessary. FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM. pp. 467-474

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BASIC CONCEPTS AND DEFINITIONS 1. Let U be the universe of all possible flre situations, where each element e of U is defmed by a complete physical description of a flre; the environment in which it began, developed, and ended; and the consequences of its occurrence. The terminology used to describe elements of U is not standardized among researchers, which accoums for the use here of the term "flre situation". 2. Probability Density Function of the Universe of Fire situations. Let p(e) be the probability density function for the universe (U) of all possible flre situations (e). Therefore,

I pee)

(1)

de = 1

U

3. Measure of Severity. Let s be a measure of severity, deflned so that (a) the measure can be calculated for every element e of U and (b) the measure is a monotonic indicator of better and worse outcomes. That is, in comparing two elements of U, if a higher value of s means a worse outcome (a more severe flre) for one pairwise comparison, then in any other pairwise comparison of elements ofU, a higher value of s also will mean a worse outcome. This deflnition does not exclude the use of multiple measures of severity in a single analysis. 4. Probability Distribution for a Measure of Severity. The severity function, s, and the probability density function of the universe of flre situations, pee), jointly deflne a probability density function pes) for the severity measure, s. Here, P(s=s') is given by:

I

P(s=s') =

p(els(e) = s') de

(2)

U

5. Fire Hazard For the purposes of this paper, "flre hazard" is a measure of flre severity for a specifled flre situation. This defmition differs from the usage of "hazard" in conversational English, where "hazard" refers to an object, activity, building, or other item that is a source of danger. (This usage is also common in the technical literature on risk analysis [2].) Here, the term "hazard" is used to refer to the degree of danger and not to the item that poses that degree of danger. 6. Fire Hazard Analysis. A method for analysis of flre hazard is a method for calculating one or more severity measures, given a specifled flre situation, e, from the universe of flre situations. 7. Fire Risk. "Fire risk" is a summary statistic, which may also be called the "outcome measure of flre risk", from a probability density function on a well-deflned flre severity measure (i.e., flre hazard measure). Risk =

-.J

+00

g(s')

P(s=s') ds'

(3)

The function g transforms the severity measure s into the measure of interest for the flre risk analysis. (In fact, g(s) constitutes a severity-measure function itself, but it may be useful to keep this distinction so that a more natural and simple deflnition of severity can be used for s.) For example, let s be defmed as the number of deaths. Then if the measure of interest is simply deaths, g(s) = s. Suppose instead that one is interested only in catastrophic fatal flres, that is, flres that kill flve or more people. Then g(s) = 1 if s is flve or more and zero otherwise. Or, suppose that one is interested in the size of the death toll in catastrophic fatal

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fires only. Then g(s) = s if s is five or more and zero otherwise. These three examples from one simple severity measure should illustrate the point. S. Fire Risk Analysis. Analysis of ftre risk involves the specification of one or more outcome measures, each of which is a well-defined statistic based on the probability density function of a specified severity measure. A method for analysis of fire risk must specify methods for calculating the outcome measure(s).

DEFINING THE SUBJECT OF ANALYSIS The purpose of a fire risk analysis is to calculate and assess the fire risk values obtained when part of the specification of relevant situations includes the specification of some fixed subject of analysis. If the subject of the fire risk analysis is a particular building or type of building, this will imply a series of specifications. The fixed characteristics of that building or the common characteristics of that type of building will be treated as fixed in defining all fire situations to be analyzed. If the subject is a particular product, material, assembly, process, building feature, or fire protection system, than that also will imply a series of specifications. Fires that are not affected by the product, for example, may be excluded from the analysis. In fire risk analysis, it is important not to narrow the specifications any more than is required by the choice of the subject of interest. For example, suppose the subject of interest is upholstered furniture sold for use in private homes. In such a case, it would be appropriate to ignore fires in all manner of commercial or public buildings, but it would not be appropriate to narrow the focus to single-family dwellings, because such a focus would either ignore mobile homes, apartments, duplexes, and the like, or treat them as if their fires developed the same as single dwelling fires. Furthermore, it would not be appropriate to narrow the focus to fires begun by cigarettes igniting upholstered furniture because this is only one of the myriad types of fires that can involve upholstered furniture as a significant contributor. It might, however, be appropriate to ignore fires originating in wall spaces and other places where upholstered furniture is not found, on the theory that the contribution of upholstered furniture would be indistinguishable from other late-stage fuels in such a fire. The common thread here is that for any subject of analysis, the relevant fires are all the fires where that subject of analysis may be involved. Since that will be an infinite number of distinguishable fires, it is necessary to select a manageable number of situations for analysis. Each narrowly defmed situation will therefore have to represent a larger set of similar situations. If instead a fire risk analysis were to be constructed based on one fire situation, for example, that would be equivalent to assuming that the estimated severity of that one fire situation is equal to the average severity in all fire situations. That degree of simplification is likely to be untenable. However, if a large number of very different fire situations are used for analysis, then each can be associated with a relatively homogeneous class of fire situations that are all very much like it. Then the assumption that a particular fire situation is representative of its associated class will become more reasonable.

CHARACTERISTICS OF A FIRE SITUATION The basic defmitions given earlier used a term "fire situation" because more familiar terms, like "scenario", have already been used in so many contradictory ways that they are likely to have misleading special connotations for some people. In particular, most familiar terms have come to refer to specialized subsets of fire situations. For example, in the Fire Risk Assessment Project wolk sponsored by the National Fire Protection Research Foundation, the term "scenario" is used in the same way I have used

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"fIre situation". I favor this usage, but there are points of concern. First, there is the need to use "scenario" to refer to both the individual fIre situation e and to the larger class of fIre situations that e is meant to represent. Probabilities must be estimated based on the class, while severity must be calculated on the individual fIre situation. Dual usage of the term "scenario" can be confusing. More problematically, some analysts use "scenario" to refer only to subsets of fIre situations defmed by the characteristics of initiation, growth and termination of the fIre. This meaning of "scenario" would not include such other characteristics as the number, locations, and characteristics of occupants. Those who use the term "scenario" narrowly often refer to most of the excluded characteristics collectively as "exposure" [3]. In fIre risk analysis for nuclear power plants, one of the most advanced applications at present, there may be the added consideration that plant layouts are so tightly controlled that "exposure" dimensions can be treated as standardized. [4] More often "exposure" is contrasted to "hazard" or "potential for harm," possibly with the view that fIre effects in a space pose a danger that has meaning apart from the presence of people or property who could be harmed.In principle, everyone agrees that fire risk analysis involves all these elements - a product, its environment, a fIre, and exposed people and property - but terminology can become confused because of differing views as to the importance of separating these elements at different stages of analysis. Another term worth introducing is "context of use". In essence, the subject of analysis may be not just a product (such as carpeting) but a product in a particular environment (such as carpeting designed for and sold only for use on floors in offIce building occupancies). For purposes of fIre risk analysis, then, "context of use" refers to characteristics of what I have called fIre situations that shall be fIxed because they are part of the defmition of the subject of analysis but that are not part of the inherent defmition of the product.

It is important to be sure the defInition of the subject of the analysis includes context of use considerations, but it also is important not to assume too much under this heading. For example, it must not be assumed that a product, material, assembly, process, activity, building, feature, or fire protection system will always be used appropriately, installed correctly, maintained regularly, operated properly, or otherwise handled as it should. It may be useful to analyze what its fIre risk would be if it were not subject to such human errors, but it would be a mistake to exclude by definition the many problems that can degrade performance. Also, the context of use will rarely imply any reduction in the range of fIres that may occur and involve the subject of the analysis. Unless the subject's context of use dictates that it can only be found in a very few places, one must proceed on the basis that fIres anywhere in the building(s) could involve and be affected by it. The points made so far may seem merely semantic, so it is worth while to summarize and emphasize the substantive distinctions involved: Fire risk analysis involves development and synthesis of information on the probability and severity of every type of fIre that can include, affect, or be affected by a particular subject of interest. Terminology to refer to a generic type of fIre has not been standardized. In part, this reflects the need to refer to both unique fIre situations and classes of fire situations and the tendency to use the same term for both. In part, it reflects a desire to distinguish among several classes of fIre situation characteristics, such as properties of the fIre vs. building environment vs. people or property exposure, and to do so at the most fundamental level of the design of the analysis. These distinctions can be useful as long as it is recognized

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that every dimension of variation in fire characteristics must be addressed somewhere in the analysis and that the tenns used to do so may not mean the same things to other people. APPROPRIATE OUTCOME MEASURES

While there are many possible outcome measure functions - that is, choices of g(s) in the earlier definitions - it is useful to distinguish those that favor an "average risk" fonn and those that favor an "extreme value" fonn. If g(s) =s, for example, then the measure of risk will be the expected value of loss. This is equivalent to the probability that a fire (of any type) will occur multiplied by the average severity if fire occurs. On the other hand, if g(s) = 1 if s s' and 0 otherwise, for example, then the measure of risk will be the probability that a fire occurs having a severity of s' or greater. An expected loss risk measure is the most natural and appropriate measure in most situations. It provides a measure of predicted loss that is suitable for comparison with the costs of achieving it. Expected loss measures sometimes are invalidly criticized because of confusion between average loss and typica110ss. A true average will give proper weight to very rare, very large losses and may even be dominated by them. A measure of typical loss or a method for calculating the average that does not properly capture extreme values - will not give major events their proper weight.

Extreme-value risk measures, such as measures in the fonn of a "probability of failure" of "probability of large loss", implicitly assume that all fire situations are either major or negligible. There are many specialty areas of engineering where events are either catastrophic (the building loses structural integrity and collapses, the dam breaks, the bridge collapses) or inconsequential (the building, dam, or bridge continues to stand). For many engineers, that view of the world has carried over into fire protection. But for most classes of buildings or products or processes, the majority of fire loss results from an accumulation of small fires. There is simply no justification for a pre-emptive emphasis on major events. However, there are some situations where such a pre-emptive focus can be defended: In some industrial settings, the largest fire or fires of the decade may dominate 1. the overall loss totals. In nuclear power plants, there may be the added factor that controls are extensive enough to justify the assumption that only a very few types of fire situations are even possible. If these conditions hold, expected loss is essentially equivalent to the probability of a large loss, and the latter may be simpler to calculate.

2. For some purposes, an analyst may be interested only in fires whose losses would be so great that they would drive a company out of business. Under those conditions, a fire risk analysis in terms of the probability of unsustainable loss would be justified. 3. The analyst may have been asked to identify not the risk associated with a product - such as a fire protection system or building feature - but its various failure modes, in which case the need for redesign may depend more on the likelihood than on its consequences. Again, if the problem is defmed so that probability of failure is the right measure, it should be used. 4. Recognizing that the press and public tend to place disproportionate emphasis on major fireS, it may be considered appropriate - or even necessary - to focus on those incidents. Even then, however, it may be better to use an approach that captures expected loss in large incidents or that includes all fires but uses a non-linear outcome measure function to give greater weight to more severe incidents while still giving some weight to less severe incidents.

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The common thread in this discussion is that fire risk must be assessed broadly unless it can be positively demonstrated that a narrow focus is valid for the question at issue. There may be inappropriate reasons that tempt analysts to use a narrow focus when it is not appropriate. One is concern over computational burden and the cost of analysis. since expected loss measures often require a large number of scenarios or fire situations. which will tend to involve a very large number of calculations. Another inappropriate reason would be a desire to minimize the use of probabilistic theory and statistics in favor of an emphasis on modeling using physics. chemistry. and laboratory data. An example of a generally inappropriate fire risk formulation that can arise in this way would be a definition of fire risk as the severity of a single event times the probability of that event [3]. While such a definition would satisfy the defmitional requirements given earlier for a measure of fire risk, few if any real problems can be validly addressed by a measure limited to one event. Such a measure would be an appropriate outcome measure only in cases where one and only fire situation was relevant Another example would be the use of the term "frre risk analysis" to refer to a simple listing of major locations of potential concern to fire protection people [5]. Again, the usage of terms like "risk" and "hazard" is far from standardized. Some people use the terms not to refer to relative scales characterizing all objects but rather as category descriptors of selected objects. In other words. they speak: of products or features or buildings as being hazards or risks or as not being hazards or risks rather than as having a certain degree of hazard or risk. The insurance industry's practice of referring to each insured property as "a risk," using the term as a synonym for a customer's property. also adds to the confusion. but this usage is less confusing because it clearly involves no measurement or comparisons. To recapitulate the major point in this section: Just as the previous section warned against defming fire risk analysis too narrowly with respect to the possible dimensions of variation in fire situations, so this section warns against defining fITe risk too narrowly with respect to the level of severity. for example, by focusing on large frres or on cases of established burning. The burden of proof is always on the frre risk analyst to demonstrate positively that any excluded classes of frre situations are truly irrelevant to an assessment of the fire consequences of the subject of interest.

MODELS, DATA AND VALIDATION The scope of many fire risk analyses requires the integration of a wide range of models and data sources. Models developed independently often must be combined. and new modeling components must be developed. Data requirements from the laboratory may go beyond existing standard tests. and data requirements from the field may go beyond existing data bases on actual frres and on the distribution of characteristics in actual buildings. Even a fire risk analysis conducted on a specific building will need to draw on extensive data bases. if only to capture the variations in conditions in that building. Parameter estimates by experts often are needed. One technique that has proven useful in the Fire Risk Assessment Project sponsored by the National Fire Protection Research Foundation involves infening the necessary detail about the starting conditions for fITes from their subsequent development [6]. Such an approach does not attempt to survey large samples of buildings and times to develop a probability distribution for the possible fuel loads and furniture positionings of all rooms in a building. for example, because the cost of such an exercise would be enormous. Instead, a probability is developed for each size a frre might reach. based on the proportion of frres that reached that size during some historical reference period. Then. the description of frre size

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(e.g., flame spread confined to part of room of origin) is converted to physical parameters, based on expert judgment. Then, fire growth curves are set to be consistent with these final sizes and with any other known information, such as initial fuels. These fire growth curves contain all the information needed for modeling and can be used in lieu of more detailed information about the specific combinations of furnishings that produced them. This example illustrates that fire risk analysis models tend to have large data requirements that can only be met by using data sources of widely varying degrees of qUality. All data bases carry significant uncertainties, as do the models, and fire risk analysis requires explicit attention to the degree of uncertainty in the estimates. Validation presents an unusual challenge for fire risk analysis, because there will tend to be no experiment or body of documented experience that can be treated as a better representation of the reality the model seeks to capture than the experiments and data that are part of the model. The few external points of reference will at most serve to partially validate the model, not validate it in its entirety and all its details. Under these conditions, validation becomes indistinguishable from the process of estimating the uncertainty of the risk estimates produced by the model [7]. The two previous sections warned against improperly narrowing a fire risk analysis model based on the exclusion of certain sizes of fires or certain dimensions of variation in fire situations that may be relevant to the subject of interest. This section warns against biasing a fire risk analysis model toward certain favored types of component models or data sources. Also, because conventional validation tends to be possible only for parts of a full-scale fire risk analysis model, it is essential that the uncertainties of the model by explicitly estimated.

CONCLUSIONS The term "fire risk analysis" can be used to refer to any systematic estimation of patterns in the probability and severity of fires involving or affected by a particular subject of interest. However, a valid fire risk analysis needs to encompass all the relevant fires, which dictates considerable care in translating the problem to be solved into model specifications. Both the burdens of computation and the understandable desire of building managers, product manufacturers, and the like for certainty will create pressures to narrow the focus of the fire risk analysis model. Even the terms used to describe elements of fire risk analysis have taken on connotations that reflect this pressure to narrow the focus. It is especially important, therefore, that the design of a fIre risk analysis model for a particular problem, decision, or issue reflect the needs of that situation explicitly and in detail. Sound fire risk analysis depends upon the selection of appropriate severity measures, appropriate outcome functions for those severity measures, and a suitably comprehensive and detailed structuring of the universe of fire situations. By designing fire risk analyses around these key elements and assessing the value of existing models in terms of their choices for these elements, we can produce models that assemble the best information possible for the decision at hand, including a clear sense of the uncertainties attending that information. That is the measure of a fire risk analysis.

REFERENCES 1.

Hall, J.R., Jr. and Sekizawa, A., "Fire Risk Analysis: General Conceptual Framework for Describing Models", Fire Technology, 27:1, 33-53, 1991.

2.

Kaplan, S. and Garrick, B. J., "On the Quantitative Definition of Risk," Risk Analysis, 1:1, 11-27, 1981.

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3.

Roux, H.I. "A Discussion of Fire Risk Assessment," pp. 16-27, in Fire Risk Assessment. American Society for Testing and Materials, Philadelphia, 1982.

4.

Kazarians, M., Siu, N.O. and Apostolakis, G., "Fire Risk Analysis for Nuclear Power Plants: Methodological Developments and Applications," Risk Analysis, 5: 1, 33-51, 1985.

5.

Strickland, B., "Fire Risk Assessment," Fire Command. 34-37, August 1987, and 34-35, September 1987.

6.

Clarke, F.B., Bukowski, R.W., Stiefel, S.W., Hall, I.R., Ir. and Steele, S.A., The National Fire Risk Assessment Research Project: Final Rej)ort. National Fire Protection Research Foundation, Quincy, Massachusetts, Iuly 1990.

7.

Apostolakis, G., "Some Probabilistic Aspects of Fire Risk Analysis for Nuclear Power Plants," in Fire Safety Science: Proceedings of the First International Symposium, ed. C.E. Grant and PJ. Pagni, pp. 1039-1045, Hemisphere Publishing Corporation, New York 1986.

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Statistical Analyses on Fatalities Characteristics of Residential Fires AI SEKIZAWA Fire Research Institute Fire Defense Agency Ministry of Home Affairs 3-14-1, Nakahara, Mitaka-shi, Tokyo 181, Japan

ABSTRACT

Fire death patterns in residences in Japan were examined through the statistical analyses of fire deaths data base made by Fire Defense Agency. It was identified that there are two typical fire death patterns in residences such as "Disaster-Vulnerable People and Daytime Fire" pattern and "Non Disaster-Vulnerable People and Night-time Fire" pattern. The former pattern can be described typically as the case that a person who needs help to move encountered a fire and failed to escape without any help while he was alone during daytime. The latter pattern can be also described typically as the case that a person who has normal physical function was killed in a fire mainly due to delay of detection while he was drunk or asleep at night. For the purpose of fire deaths reduction, the "Disaster-Vulnerable People and Daytime Fire" pattern should be noticed, because the fire death rate of this fire death pattern is much higher than the another fire death pattern and further the population of those disaster-vulnerable people like aged people 65 or older is increasing rapidly in the recent years and the near future in Japan. KEYWORDS: residential fire, fire death, statistics, life loss risk, pattern analysis. INTRODUCTION

Every year, about a half of structure fires occur in residences, and three fourths of fire deaths caused by structure fires are due to residential fires in Japan!1]. Moreover, Japan is facing the problem of the rapid aging of society which is expected to continue to a stage where one fourth of total population will be 65 and older at the beginning of the 21st century!2]. Since almost a half of the total fire deaths are 65 and older, the rapid aging of Japanese society would cause increasing number of fire deaths in the coming near future. Considering these facts, much more concern than before has addressed the residential fire problem in this decade from the viewpoint of fire deaths reduction in Japan. FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM. pp. 475-484

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The purpose of this study is to analyze the characteristics of fatalities due to residential fires for examining what kinds of residential fire protection measures are appropriate in terms of life safety especially for the people with disabilities like aged people.

SOURCE OF FIRE DEATHS DATA USED IN THIS STUDY Every fire death as well as every fire incident is reported systematically in an unified format from municipal fire departments to Fire Defense Agency[3). After those fire death reports are accumulated, the data base is made every year by Fire Defense Agency. The fire deaths data used in this study includes the information of the fire deaths that occurred in residences during five years from 1983 to 1987. However, the fire deaths caused by such fires as incendiary fires and suicide fires are excluded from analysis here, because these kinds of problems should be treated with from other viewpoints such as a crime or a social problem. Then, the total number of residential fire deaths analyzed here is 3,629. The information in a fire death report contains the building features of an origin house or an apartment, the data of a fire profile such as a cause, the first item ignited, extent of fire spread etc., and the fatality's characteristics such as age, sex, physical and mental conditions at a fire including incapacitation due to alcohol.

RESULTS OF ANALYSIS Life Loss Risk by Structure Type of Residences Table 1 shows the comparison of life loss risk by structure type of residences. Six structure types are determined here by combining three construction types ( fire resistive construction, fire proof wooden construction, and ordinary wooden construction) and two housing types ( a single-family dwelling and a multiple-family dwelling ). As can be seen in Table I, the number of fire deaths per year per million units of a corresponding structure type changes mainly according to the change of construction type rather than the change of housing type. For example,

TABLE 1.

The number of residential fire deaths by structure type.

Structure type ( Housing type / Construction type ) Single-family Single-family Single-family Multiple-family Multiple-family Multiple-family

/ / / / / /

wooden fire proof fire rated wooden fire proof fire rated

wooden reinforced concrete wooden reinforced concrete

Total of above

The number of fire deaths per year per million units of house by structure type 35.1 10.2 5.1 33.4 17.1 6.0

21.3

Sources: Number of fire deaths from fire deaths data base, Number of houses from the literature [4].

476

ordinary wooden construction houses have more than twice as high fire death rate as have fire proof wooden construction houses in both housing types of "single-famlly" and "multiple-family". Also, ordinary wooden construction houses have more than five times as high fire death rate as have fire resistive construction houses in both housing types. By contrast, there is not so much difference of fire death raje between two housing types of "single-family" and "multiple-family" in each construction type. Therefore, if characteristics of a fatality itself are omitted from consideration in analysis, fire severity such as an extent and/or rapidity of fire spread is naturally considered to be a dominant factor that affects life loss risk in residential fires. Analysis on Fatalities' Characteristics The items concerning fatalities' physical functions obtained from a fire death report are age, whether one suffers from sickness or not, whether one is handicapped or not, and whether one is bedridden or not. Likewise, the items concerning a level of one's consciousness awakening in terms of ability of fire detection are whether one is drunk or not, and whether one is awake or asleep. Using these items, the fatalities' characteristics are analyzed hereafter. Also, through the analysis of fatalities' characteristics, fire death patterns are discussed. Age of fatality. Figure 1 shows a histogram of the proportion of fire deaths by three age groups as 65 and older, 5 and younger, and 6 to 64. As shown in Figure 1. almost a half ( 47.8 % ) of the total fatalities are 65 and older. By the way. Table 2 gives us another aspect of life loss risk among four high risk groups as 65 and older. 75 and older. handicapped. and bedridden. In terms of the death rate ( the number of fire deaths per year per 100.000 population ). the aged who are 65 and older have 4.5 times as high risk as the average. and the aged who are 75 and older have 8 times higher risk than the average. Handicapped persons. who are given a certificate by the government. have almost the same risk as the aged who are 65 and older. However. the most noticeable fact is that bedridden persons. 82 % of whom are 65 and older. have indeed 41 times as high risk as the average. From this fact. the most difficult condition is considered to be the case of a bedridden person among the groups categorized as the people with disabilities. Although two characteristics of fatalities. aged and bedridden. are likely to overlap each other. a substantial feature of physical functions like bedridden should be given priority for categorization of a high risk group.

65 and older 5 and younger 6 to 64 year

FIGURE 1.

Proportion of residential fire deaths by age classification.

477

TABLE 2. Comparison of residential fire deaths rate among high risk groups

Category of high risk group The The The The

The number of residential fire deaths per year per 100.000 persons

bedridden (>65 handicapped- aged (a) (>65 aged (b) (~75

24.6 4.8

41.0 5.0 4.5 8.0

0.6

1.0

3.0

2.7

Total Population

Ratio of fire death rate to the average ( 1.0 ) of total population

- Handicapped : The people who are given a certificate by the government Sources : Number of fire deaths from fire deaths data base. Number of population by age group from the literature [5). Number of the bedridden from the literature [6). and Number of the handicapped from the literature [71.

Physical Functions. The conditions of physical functions can be sorted out into such seven categories as shown in Figure 2 on the basis of the items in a fire death report. Figure 2 shows a histogram of the proportion of fire deaths ~y these seven category groups. In order to think of a strategy of fire deaths reduction program. it is a considerably important fact that the total percentage of the six groups that have some handicap at some rate in terms of escaping ability reaches almost 70 %. This fact tells us that occurrence of fire death depends not only on severity of a fire itself but also largely on conditions of occupants' physical functions. Therefore, besides fire control measures, we should notice improvement of circumstances of disabled persons and the elderly as well as emergency assistance by their family or neighbors for reducing fire deaths. The Level Of Consciousness Awakening. Combining the two items of drinking status and awakening status, the levels of consciousness awakening of fatalities can be sorted out into such five category groups as shown in Figure 3. From the histogram of the proportion of fire deaths

Bedridden

• •1 13 . 3

Not bedridden but disabled

• • •,1,.11" 19.3

Elderly with sickness Elderly ( Infant

~65

)

(~65

.Ilillllill.

18.9

8.8

(~5)

Persons with sickness Normal

o

10

20

30

40

%

FIGURE 2. Proportion of residential fire deaths by condition of physical functions.

478

by these five groups, about a half ( 53.1 % ) of the total number of fatalities come under such status as drunk or asleep. Figure 4 shows the breakdown by three age groups as described in Figure 1 for each level group of consciousness awakening. In the cases of drunk status to some extent, the proportion of the age group "6 to 64" is over 65 %. On the other hand, the proportion of elderly group "65 and older" exceeds that of "6 to 64" in the cases of sober status.

13.5

Drunk and asleep Awake but heavIly drunk Awake but drunk Asleep and not drunk

._.1lli133.o

Awake and not drunk 60

FIGURE 3. Proportion of residential fire deaths by level of consciousness awakening at a fire.

•

~65

o

~5

~

6-64

Asleep and not drunk Awake and not drunk

o

2\l

40

60

8\l

100

%

FIGURE 4. Breakdown by age classification in each category of levels of consciousness awakening at a fire .

LIving alone

•••1 24 .8

Living alone in a same site Being left alone temporarily Not alone

~;:~2~O~'~91!!!1IIl''.; ~ o

49.2

1111

2111

3111

4111

5111

60

%

FIGURE 5. Proportion of residential fire deaths by situation of presence of others at a fire.

479

Presence of Others at a Fire. Situation of presence of others at a fire, i.e. whether one is staying alone or not at a fire, is also a very important factor as circumstances of fatalities especially for the people who need help to move. The status of staying alone here includes being left alone temporarily and living alone separately from one'~family in the same site, and living alone. Figure 5 shows a histogram of the proportion of fire deaths by the four category groups of presence of others at a fire. A half of the total fire deaths ( 50.8 % ) correspond to the status of staying alone at a fire in any case. Although the living alone case has the most proportion ( 24.8 % ) among the cases of staying alone at a fire, the case of being left alone temporarily has a quite large proportion ( 20.9% ). The number of fire deaths in this case could increase in the future, because there is an increasing tendency for elderly persons to be left alone during daytime, since more and more women go out to work in recent Japan. In either case of staying alone at a fire, emergency communication system for help by neighbors and/or home sprinkler system besides home detectors are needed for disabled persons to be rescued. Fire Deaths Incidence by Time of Day For each of three items such as age grouping, whether one is bedridden or not, and the situation of presence of others at a fire, fire deaths incidence by every two hours in a day is illustrated respectively in Figure 6 through Figure 8. The distribution pattern of each category in these figures can be clearly identified as "more in daytime" type and "more in night-time" type. Namely, as to the categories of the aged, infants, bedridden persons, and being left alone temporarily, fire deaths tend to occur much more during daytime than during night-time. In contrast to above categories, as to "6 to 64" year age group, persons who are not bedridden, and living alone, fire deaths incidence during night-time is considerably higher than that during daytime. Cross Analysis of Fatalities' Physical Functions by Causes of Fire Death Table 3 shows the result of cross analysis between seven categories of fatalities' physical functions and reported causes of fire deaths. Within the fire death causes in Table 3, the causes such as "Difficult to escape" and "Attempt to escape but fail" are considered to relate to fatalities' physical functions. As for these two causes. the physical function category groups such as .. Bedridden ..... Not bedridden but disabled", and "Infant" have considerably high percentages. To the contrary. these three physical function category groups have quite smaller percentages than other groups in the fire death cause of "Delay of detection". The group "Elderly with sickness" has the highest percentage (23.3%) in the fire death caURe of "Wearing apparel ignited" among seven category grollps of physical function. On the other hand. as for the fire death cause of "Delay of detection" which is not related directly with physical function, the group "Normal" has the highest percentage (43.6%) and the group "Persons(6-64) with sickness" has the secondary high percentage (36.6%). And, the group "Normal" has lowest percentage (4.9%) in the fire death cause of "Difficult to escape".

480

18

'. 14

.5. 5 i',

12

x

~I

,....,

HI 8

--.. ,

6

, -;-L I___ "

/'"

-.-

'.I

/1 '/

~65

"L

~.-.

4

6-64

2 0 0

6

2

10

8

12

14

I

I

I

I

I

I

I

I

2

4

6

8

10

12

14

16

hour

22

16

18 I

I

I

18

20

22

20

24

FIGURE 6. Fire deaths incidence by time of day for each category of age classification. 16 14

.... ....

12

V Bedridden

,,

X

,

,

'\

10

\

8

\

\

6

~

----'1//

4

1

,----,-

/

1 _/

1

Not bedridden

2 0 0

2

4

I

I

I

2

4

6

6

8

8

10

10 I

I

12

12

14

I

I

14

16

16 I

18

22

20

18 I

I

I

20

22

24

hour

Fire deaths incidence by time of day for each category of the "bedridden" and the "not bedridden".

FIGURE 7.

Being left alone tempor ar ily

18

I.

16 14 12

X

/

Not alone

10 8

'y _-~'J ---/~:'

---"

6

.. --

-"

I,

.-' /' - .-'..... ~.----_/\

-

-.:

4

Living alone

2 0 0

2

4

6

8

I

!

t t l

2

4

6

8

10

10

12

I

I

12

14

14

16

18 I

I

I

16

18

20

20 22

24

22

hour

FIGURE 8. Fire deaths incidence by time of day for each category of presence of others at a fire.

481

TABLE 3.

Cross analysis of fatalities' physical functions by cause of fire deaths.

Physical function category Bedridden Not bedridden but disabled Elder ly (;::.65) with sickness Elderly (;::.65) Infant

(,::5)

Persons (6-64) with sickness Normal Column total

I I I Delay of I detection I I 66 I 13.7% I I 140 I 20.0% I I 30 I 21.1% I I 193 I 28.2% I I 48 I 15.0% I I I 71 I 36.6% I 476 I 43.0% I I 1,024 I 28.2% I

Cause of Fire Death Difficult to escape

Attempt to escape but fall

269 55.8%

88 18.3%

Wearing apparel ignited

Others

Row total

44 9.1%

15 3.1%

482 13.3%

148 21.2%

184 26.3%

109 15.6%

118 16.9%

699 19.3%

15 10.6%

17 12.0%

33 23.2%

47 33.1%

142 3.9%

37 5.4%

88 12.8%

112 16.4%

255 37.3%

685 18.9%

218 68.3%

16 5.0%

6 1.9%

31 9.8%

319 8.8%

31 16.0%

16 8.2%

15 7.7%

61 31.4%

194 5.3%

54 4.9%

146 13.2%

42 3.8%

390 35.2%

1.108 30.5%

772 21.3%

555 15.3%

361 9.9%

917 25.2%

3,629 100.0%

Sources : fire deaths data base.

TABLE 4.

Two typical fire deaths patterns derived from study of fire deaths incidence by time of day. Fire Death Pattern

Disaster-Vulnerable. People & Daytime Fire

Distinctive Features from the Viewpoint or fire protection • Victims are people who are disabled, elderly, or infant. * There are relatively few victims who are drunk or asleep. • There are many such cases that victims are left alone at a fire during other family members' absence . • For this pattern, home sprinkler system and/or neighbor's assistance is needed.

* Most of victims are people who are 6 to 64 years old and

Non Disaster-Vulnerable People & Night-time Fire

* Disaster-Vulnerable

with normal physical functions.

* There are many victims who are drunk or asleep.

*

Many cases of living alone as well as staying with other family members at a fire come under this pattern * For this pattern, efficient fire detection system would save many lives. The people who are vulnerable to disaster

482

CONCLUDING REMARKS Considering fire deaths incidence by time of day described above, residential fire deaths can be grouped as "the Disaster-Vulnerable People & Daytime Fire" pattern and "Non Disaster-Vulnerable People & Night-time Fire" pattern. Table 4 gives a summary of the distinctive features of these two typical fire death patterns. The former pattern can be described typically as the case that a person, who needs help to move, encountered a fire alone and was killed while other family member(s) was absent for work or shopping. On the other hand, the latter pattern could be the probable case that a person, who has normal physical functions, was killed in a fire mainly due to the delay of detection while he was drunk or asleep at night. Towards the goal of reduction of fire deaths, "Disaster-Vulnerable People & Daytime Fire" pattern is more important than "Non DisasterVulnerable People & Night-time Fire" pattern, because the death rate as well as the number of deaths in the former pattern is quite high and further the population of such a high risk group corresponding to this pattern like aged people is increasing rapidly in Japan. Similar fire death patterns in residences in the United States are introduced in the report entitled "Patterns of Fire Deaths Among the Elderly and Children in the Home" by Karter, M.J.[8). However, there is one big difference between the United States and Japan. It is the fire death rate of preschool children. From the former analysis by the author [9) and the analysis by Hall, J. of NFPA, preschool children (ages 0-5) in the United States are a high risk group with a fire death rate per million population nearly twice the average for all ages. On the other hand, preschool children in Japan have about the same risk as the overall average. As one reason for this difference, the study entitled "Fatal Fires and Unsupervised Children" by Fahy, Rita [10] suggested that many of the children in the United States were either unattended or unsupervised at the time of their fire deaths probably because there is a higher incidence of single-parent families in the United States. In the end, this kind of pattern classification of fire deaths makes it easy to understand what kinds of fire protection measures such as a smoke detector, home sprinkler system, and emergency communication system, and their combination would be appropriate for a specified target group like the aged, the handicapped, or the persons who tend to be left alone during daytime. In addition, on the basis of statistics on the proportion of some fire death pattern and the population of the corresponding target high risk group, an estimation of the effect of a specified fire protection measure would be possible when fully equipped for the target group. Also, international fire comparison studies using the same pattern classification would be very helpful to understand what kind of situation is a common problem and/or a distinctive problem in each country. ACKNOWLEDGMENTS

This study was conducted as a part of the research project study on fire protection measures in residences during 1987-1989 financed by Fire Defense Agency. Also, the author wishes to thank Dr. John Hall of NFPA in the United States for the discussion on this paper.

483

REFERENCES

1.

Fire Defense Agency, Ministry of Home Affairs of Japan, White Book on Fire Service in Japan, 1983-1987.

2.

National Association for Social Welfare of Japan, White BooK on Aged People, 1988.

3.

Fire Defense Agency, Ministry of Home Affairs of Japan, Hand Book for Reporting System of Fire Incident and Fire Death.

4.

Ministry of Construction of Japan, Summary of the Results of 1983 Housing Survey of Japan, 1986.

5.

Statistics Bureau, Management and Coordination Agency of Japan, Japan Statistical Year Book, 1983-1987.

6.

Ministry of Health and Welfare of Japan, Report of Basic Survey on Public Administration of Health and Welfare, 1985.

7.

Ministry of Health and Welfare of Japan, Survey on the Circumstances of the Physically Handicapped, 1987.

8.

Karter, M.J., "Patterns of Fire Deaths Among the Elderly and Children in the Home", Fire Journal, pp. 19-25, March-April, 1986.

9.

Sekizawa, A., "Comparison Analysis on the Characteristics of Residential Fires Between the United States and Japan", Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, 1988. .

10.

Fahy, R., "Fatal Fires and Unsupervised Children", Fire Journal, pp. 19-24, January-February, 1986.

484

An Expert System to Assess Fi re Safety in Dwellings H. A. DONEGAN. I. R. TAYLOR and R. T. MEEHAN Institute of Informatics University of Ulster Shore Road, Newtownabbey BT37 DaB, UK

ABSTRACT

This paper describes the application of an expert system to the evaluation of fire safety in dwellings based on the body of knowledge developed by the Fire Engineering Research Group at the University of Ulster. The background and philosophy of the evaluation procedure together with the associated reasoning with respect to the choice of system and its implementation are outlined in some detail. This demonstration system is intended as a pilot study for a more ambitious programme. A discussion relating to problems with the system and future developments concludes the paper.

KEYWORDS:

Fire safety evaluation, expert system, Delphi, points scheme.

J:N'l'RODUCTJ:ON

In recent years the notion of fire safety evaluation with respect to buildings has become inextricably bound up with the perception of the prioritisation of those entities which taken together comprise the fire safety components of a specific building type. The prioritisations, often but not exclusively the result of expert opinion, are used in the development of points schemes. These are essentially research into practice devices which facilitate the economical allocation of scarce resources in the design and refurbishment of buildings. The philosophy is clearly extendible to any form of shelter, e.g. ships, planes and trains, where life safety and property protection are paramount. This paper will focus on dwelling fire safety with specific reference to the determination of a fire safety quality measure which can be optimised interactively using the expert system shell Xi Plus in a PC environment. The level of optimisation achieved is a function of the user's requirements and resources given the existence of acceptable norms. The chronology of events leading to this work began with the study by Nelson and Shibe [1] who produced a system for the Fire Safety Evaluation FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM, pp. 485-494

485

of health care facilities in the USA. Following these developments, the Department of Health and Social Services (DHSS) sponsored the Fire Engineering Department at the University of Edinburgh to produce a fire safety evaluation points scheme for patient areas within hospitals. The work was conducted by Marchant (2) and completed in 1982. Stollard [3] reported on the development of the points scheme at Edinburgh and outlined the procedures which were used. In 1983 a pilot study (4) based on the methodology of Marchant was undertaken to consider the application of the DHSS scheme to dwellings. This led to a programme of work in 1984 at the University of Ulster, funded by the Science and Engineering Research Council. The theoretical consequences (5) and practical considerations (6) which followed provide the immediate environment for the present expert system. The motivation for the expert system derives from the complexity of the total fire safety scheme and the need to create a 'what i f ' environment for the user. The ideas in [2] and [4] are directed towards the production of a weighted ranking, referred to as a priority vector, of fire safety components. Typical components might be management, occupants and visitors, contents, fire brigade, detection systems, fire fighting equipment and so on. The weighted rankings for n such components (w 1 ,w 2 ,w 3 , ••. wn ) emerge from the consensus of expert opinion generally obtained through an application of the Delphi process (7). Notwithstanding certain shortcomings of the latter [8) and assuming that a priority vector can be arrived at, the fundamental and as yet unanswered question is not with regard to its existence, but with regard to its significance in the field of application. More particularly its optimal effectiveness - can it be used to minimize safety maintenance costs or to allocate scare resources in the pursuit of maximum safety? The authors would contend that such issues in the environment of fire safety analysis are the driving force behind research into practice. On the premise that total safety while being a desirable objective is something which can only be approximated within technological development periods, the approximation is presumably the stability of professional expert opinion within each time period. Fire safety history provides a wealth of examples of connected time periods, each new period arising as a result of at least one catastrophe at the conclusion of or within a previous time period. The overall effect has been the production of more and more prescriptive legislation whi·ch inhibits an engineering approach to the solution of many problems. At the present time, within the constraints of existing legislation, consideration is being given to engineering strategies which will facilitate a degree of trade-off between passive and active fire safety measures. This is where the application of an expert system capable of logical repeatability has a distinct advantage in that it provides a basis for uniformity in the decision making process. It is clear from Figure 1 that an expert system which provides the user with a 'what i f ' environment fits comfortably as part of a generalisation of the simple fire safety framework proposed in [5] .

Prior to the introduction of the expert system the procedure in using a points scheme involved taking the scalar product of the priority vector V' (w 1 ,w 2 ,w 3 , ••• wn ) with each of two corresponding sets of component

486

IDELPHI INFORMATION I ANALYTICAL MODEL

r--------------- ----------------,I NORM VECTOR

SURVEY VECTOR

ve

I I I IE IX I p IE IR

IT

I I S

NORM SCOREQ

CHARACTERISTIC SCORES

IY S T

E M

E N

V I R

o N M

I WHAT IF SURVEY VECTOR VC CHANGES I

E N

~

T

OUTPUT ANALYSIS I

--------------------------------~ IrIG.l

GI~Nm{ALiSED

FI{AMI!:WORK FOR nRJ£ SAFE1Y I!:VALUATION

487

vN

points score allocations - a norm set dwelling category and a

survey

set

c V

(sl,s2,s3'"

.sn)

for

an

actual

dwelling in the category [4]. The corresponding products, the norm score Q and characteristic score S were then compared. The advantage of the above generalisation became apparent when it was realised that it was quite feasible for a dwelling to satisfy the overall criterion, viz: S > Q and yet fail in one or more subsets of the components. Given that there are 2 n - 1 mathematically possible subsets for the n components this can lead to a large number of possibilities for large n. However in this case with n = 11, [6], it was decided to cluster the components from a fire engineering point of view as follows: A: Human measures B: Building specific or passive measures and C: Supportive or active measures. Table 1 exemplifies the categorisation used in this study.

TABLE 1. Fire Safety Component Clustering

A: Human

B:Passive

C:Active

Occupants and Visitors Contents Management

Internal Design Survey Volume Means of Escape Hazard Protection External Envelope

Fire Brigade Detection Systems First Aid Fire Fighting Equipment

An important feature of the conceptualisation was to distinguish the notions of passive/active safety from passive/active measures. Literature on safety [9] defines active safety as accident prevention and passive safety as accident protection, with the proviso that every critical event is a series of casual events within which it is possible to practice accident prevention (active safety). Once the critical event occurs it is only possible to practice accident protection (passive safety). Given the situation of a critical event (an unwanted fire), fire engineering literature refers to active and passive measures designed to combat the event. It is clear that trade-off between active and passive measures is possible but there is no potential for trade-off between active and passive safety. Figure 2 shows the fundamental relationship between these variables. From this diagram it is possible to see that total fire safety will only arise as a result of complete active safety or total prevention whereas within a technological time period passive safety is the limiting state of prevailing expert opinion. The implicit assumption is that as technological time periods progress there should be a statistically observable decrease in fatalities and in property destruction. The efficiency of any system can only be measured in the future. Meanwhile the present approach is a contribution to the organised thinking which is essential for any level of improved safety. The next sections will describe the choice of application and its implementation.

488

(PROTECTION)

HUMAN MEASURES

FrGURB 2 passive/Active Safety and Passive/Active Measures

CHorCE OF SYSTEM

Bearing in mind the above considerations the resultant expert system must be capable of: 1 - deciding overall if a dwelling is adequate for fire safety, 2 - allowing some trade off between active and passive measures, 3 - suggesting acceptable requirements on each of the measures A,B and C and of 4 - allowing changes in the dwelling specification to test 'what i f ' questions. It was decided to investigate if an· expert system could meet the above requirements with the possibility that such a system could also answer "why" questions, justifying its conclusions. Such a computer system should also be consistent in its answers and allow a variety of people in different locations to access its expertise. By building in help information at various levels, the system can be employed by more users, allowing them to learn from the inbuilt expertise. To aid such use, information about the dwelling under consideration must be input, with the system asking appropriate questions and using default values if no information is available. To test its feasibility the authors have applied the expert system to the study of the previously mentioned points system for evaluating fire safety in dwellings, [4,6,10]. The eleven components of fire safety, as identified by the Delphi technique, are clustered into the A, Band C categories described above. The expertise of the system includes identification of the eleven components, their relative weighting as given by the vector V' and the norm score Q for which a particular kind of dwelling would be deemed to satisfy fire safety requirements. An expert system requires a knowledge base within which such expertise is represented, an inference engine to process the knowledge and an interface to users and developers. Within an expert system shell the latter two facilities are already provided allowing the user to concentrate on the development of the knowledge base. Since the shell is 'domain-free' and SO contains no information on fire safety, the knowledge base must contain all

489

the expertise of the system, which as well as rules and facts includes appropriate questions and help for the user. For this investigation the PC based shell xi Plus was chosen, in which the knowledge is represented in a rule-based form. The shell allows links to, for example, databases, spreadsheets and C programs and this was utilised for some of the data. The shell provides a comprehensive set of tools for developing and testing the knowledge base, within a user friendly environment. While it does not allow for probabilities within the data this was not required in the present project. Relatively little work on the application of expert systems within fire safety has been published, with most of it on the compliance of buildings with fire regulations. The best known example is the commercial program BRIGADE [11], a system with 4000 rules based on the shell Level 5, while there are discussions of ongoing work in [12].

:IMPLEMENTAT:ION In developing an expert system the main problems are obtaining the expertise and then deciding how to represent it within the knowledge base. In basing this expert system on the work of [4,6], the acquisition of knowledge using the Delphi technique has been performed and it remains to represent it within the shell. The components of Table 1 are structured as illustrated as in figure 3, with appropriate questions, on-line help and corresponding rules for each component.

F:IRE SAFETY

Occupants and Visitors

Management

Contents

Fire Brigade

F:IGURB 3 External Knowledge Structure

490

Detection Systems

Fire Fighting Equipment

In the system as described in [6], worksheets were used to assess each of the eleven components with a rating on a scale from 0-5. Each component set was then weighted by the priority vector v' to give an overall score, S in a scale 0-500. Expert opJ.nJ.on indicates that for the house type considered in the investigation an overall score of 375 or 75% would be sufficient for the dwelling to satisfy fire safety standards. This equates with norm scores for each measure of (A, 154), (5,154) and (C, 67), each being 75% of the corresponding maximum allocations of (A,205), (5,205) and (C,90). To allow for trade-off between the different measures the selected norm scores for A, 5 and C must be less than 75% of the overall maximum allocation. This is illustrated in the Results section below. Within the expert system, separate knowledge bases were constructed for the three measures A, 5 and C, aiding separate development and testing. The information required is obtained by prompting the user with various questions. The answers are tested by the inbuilt rules of the knowledge base and along with other information stored as data the program decides on an overall score for the dwelling. Unlike the manual system, the expert system can allow different levels of trade-off between A, 5 and C by setting separate norms for these measures. For example in obtaining a rating for "occupants and visitors" the information considered is the number of occupants compared with the number of bedspaces, the number of floors and the ratio of adults to dependents. A screen of the form of figure 4 is used to request information, with help available if required. Within this component there are rules such as IF THEN

number of occupants occupant score = 1.7

IF THEN

dwelling is two storey survey score = 1.3

bed spaces

with a total of 17 rules for the first component. Under A for human measures there are 46 rules, in 5 on building specific measures there are 80 rules with 34 rules in C. To test a system with a total of 160 rules, as many as possible paths through the system must be tried. A set of test cases representing standard and extreme situations was developed, to probe the system for potential limitations and weaknesses.

RESULTS

Applying the program to an actual dwelling, typical output might be

A: Human Measures 5: 5uilding Specific Measures C: Supportive Measures OVERALL

491

actual score 170 165 50 385

selected norm score 141 135 58 375

pass/fail P P

f P

r-----~~o·ccupants

Application: Fire Safety Knowledgebase: Human Measures and Visitors--------------------------------------------,

How many occupants in dwelling?

3

How many bed spaces in dwelling?

2 single storey *two storey greater than two storey

What size is dwelling?

How many able adults in dwelling?

1

How many dependants in dwelling?

2

PRESS Fl FOR HELP

ESC cancel FIGURE 4: measures.

II

CTRL+Rtn end

II

F3 why

II

Tab/Backtab

next/previous field

Information requested on occupants and visitors,

within human

To allow trade-off the selected norm scores in this example are (A, 141) , (B,135) and (C,5a). The overall required score is of course 375 (75% of 500) . Trade-off is occuring between C, below standard, and A and B to give an overall pass for the dwelling. In contrast for another dwelling the results may be

A: Human Measures B: Building Specific Measures C: Supportive Measures OVERALL

actual score 145 140 70 355

selected norm score 141 135 58 375

pass/fail P P P f

so that the dwelling fails to reach the required standard even though it passes in each of A, Band C. If trade-off is allowed, by setting the norms for A, Band C below the overall standard required, then inevitably some dwellings will pass each aspect but fail to reach the required overall standard, as in this example. By setting the required norm scores for A, B and C at 154,154 and 67 respectively, ie 75% of each maximum possible score of 205,205 and 90, no trade-off would be allowed between the measures. The philosophy of trade-off is discussed further in [13]. If a dwelling fails to reach the overall standard, the expert system allows a 'what i f ' type investigation to be performed to ascertain what improvements may be made to bring the house up to specification. With the addition of some financial information the. alternate cost of a range of possible alterations to the building may be explored using the expert system. The program can be easily adjusted to allow trade-off only between the passive and active measures, Band C.

492

CONCLUSIONS

This paper shows that a points scheme for the fire safety evaluation of dwellings may be computerised using an expert system. The program illustrates the merits of using an expert system shell to encapsulate the knowledge, especially in comparison to using a conventional programming language. The program can be run at all stages of development with a built-in user friendliness. On any consultation, context sensitive help is available to the user at the level required, the user may ask the system why some information is required and explore 'what i f ' type situations. When loaded in a portable PC, the system could be employed on-site to assess the status of a dwelling and, if required, to suggest options for improving its level of fire safety to any required level. The program allows trade-off between different aspects of fire safety, but the amount of trade-off may be adjusted. The system could be developed to assess the fire safety of for example public assembly buildings as discussed in (141. On the basis of this pilot study the authors are convinced that subject to appropriate funding, the expert system incorporating a points scheme could be extended to more complex buildings where the risk factors are likely to be much higher.

REFERENCES

1. 2.

3. 4. 5.

6. 7. 8.

9.

10.

11. 12.

Nelson, H.E., and Shibe, A.J.,"A system of Fire Safety Evaluation of Health Care Facilities", Report NBSIR 78-1555-1, NBS, 1978. Marchant, E.W., (ed), "Fire Safety Evaluation (Points) Scheme for Patient Areas within Hospitals", A report on its origins and development sponsored by DHSS Department of Fire Safety Engineering, University of Edinburgh, 1982. Stollard, P., "The Development' of a Points Scheme to Assess Fire Safety in Hospitals", Fire Safety Journal, 7, 145-153, 1984. Shields, T.J. Silcock, G.w. and Bell Y., "Fi;e Safety Evaluation of Dwellings", Fire Safety Journal, 10 , 29-36, 1986. Donegan, H.A., Shields T.J., and Silcock G.W., "A Mathematical Strategy to Relate Fire Safety Evaluation and Fire Safety Policy Formulation for Buildings" in Fire Safety Science - Proceedings of the 2nd International Symposium, Tokyo, pp. 433-441, 1988. Shields, T.J, Silcock G.W. and Donegan, H.A., "Assessing Fire Risk in Dwellings", University of Ulster, 1989. Linstone, H.A. and Turoff, M., (eds), The Delphi Method, Techniques and Applications, Addison Wesley, 1975. Shields, T.J., Silcock, G.W. and Donegan, H.A., "Methodological Problems Associated with the Use of the Delphi Technique", Fire Technology, 23, 175-186, 1987. Wilson, G.A., "Techniques of Safety and Risk Management", Proc. One Day Seminar, Dept. of Mech. and Ind. Eng., University of Ulster and Plant Safety, 22, 2, 1990. Shields, T.J., Silcock, G.W. and Donegan, H.A., "The Development of a Fire Safety Evaluation Points Scheme for Dwellings, Part I - Some Theoretical Considerations", Fire Safety Journal, 15, 313-324, 1989. Peregrine Expert Systems Ltd, "Brigade", Dublin, 1988. Hamilton G., Harrison A.P., PascalI J.R., Directory of Research and development of expert systems in the construction and building

493

13. 14.

services industries Vol III, BSRIA Ref 7177, 1983. Shields T.J., Silcock G.W. and Donegan H.A., "A Philosophy for Trade Off", Report for Department of Environment, NI, 1989. Shields, T.J., Silcock G.W. and Donegan, H.A., " Towards the development of a fire safety systems evaluation for public assembly buildings", Construction Management and Economics, !, 147-158, 1990.

494

On the Role of Subjective Probabilities in Fire Risk Management Studies FRANCIS NOONAN and ROBERT FITZGERALD Fire Protection Engineering Worcester PolytechniC Institute Worcester, Massachusetts 01609, USA

ABSTRACT

If risk management studies in fire protection are to be implemented on a quantitatiVe basis, it becomes necessary to estimate probability loss models for each risk management alternative. While actuarial data may exist for quantifying the risk of situations similar to the alternatives under review, there are usually enough di fferences or envi ronmenta 1 uncerta i nt i es that direct substitution is considered to be inappropriate, and dependency on subjectively assessed probability loss models is a reality to be recognized. In our opinion, a common perception by practitioners in fire protection engineering is that subjective probabilities are "just guesses" and not to be used in any serious or rigorous fire protection risk management study. This paper points out that subjective probability assessments are valid representat ions of knowl edge, and we seek to communicate guide 1i nes from decision analysis for generating subjective probabilities within fire risk management studi es. Keywords: Fi re Ri sk Assessment, Subject i ve Probabilities; Probability Loss Models. INTRODUCTION

Risk management for fire protection often reduces to a basic decision making problem. Given that certain assets have an identified fire risk exposure, then a choice may exist between accepting the current level of risk (i.e. the status quo alternative) or spending certain dollars in an effort to transfer, prevent or control the risk, and thereby reduce the likelihood of future loses. To make choices on a quantitative and systematic basis, it is necessary to perform quantitative risk assessment and generate probability loss models for each ri sk management alternative. The probl em is that probability loss models are usually not known for the specific alternatives. While actuarial data may exist for quantifying the risk of situations similar to the alternatives under review, there are usually enough differences or envi ronmental uncertai nt i es that di rect subst i tut ion is cons idered to be inappropriate. FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM, pp. 495-504

495

The fire protection engineering literature contains excellent surveys on fire risk modeling ([1], [2]). The literature reveals a variety of methods for modeling fire and assessing probability loss models ([3], [4] [5]). Despite the diversity that exists among these methods they share common ground in their dependence on subjective probabilities as inputs to the modeling process. A common perception by practitioners in fire protection engineering is that subjective probabilities are "just guesses" and not to be used in any seri ous or ri gorous fi re protect i on ri sk management study. Th is paper addresses the role of subjective probabilities in fire risk assessment. Our position is that, in the pragmatic world of risk management decision making, subject i ve probabil ity is a val i d representat i on of knowl edge, and in the practice of fire protection engineering there will always be risk management studies which require the use of subjective probabilities. While criticism for risk assessment methods which fail to explain how model inputs should be obtained or criticism for studies which employ subjective probabilities in a casual manner is certainly well justified, the reaction of either doing nothing or falling back to performing only qualitative risk assessment is inappropriate. The discipline of decision analysis has made considerable progress in understanding how humans process information for making subjective probability assessments; guidelines for making subjective assessments more effectively have been identified. This paper reviews these results and interprets them for application in risk management studies. We hope that this improved understanding of subjective probability assessment will enable the fi re protect i on community to practice quant itat i ve ri sk assessment more frequently and more effectively. PROBABILITY VIEWPOINTS There are three viewpoints for probability. The objectivist viewpoint regards the probability of an event as the limit of the frequency with which the event occurs as the number of tri a1s increases without 1imit. The objectivist considers the probability of an event to be a property of the event, and their concern is how to make an actuarial estimate of the event probability. The objectivist views the actuarial estimate as a measure of the empirical evidence. The subjectivist viewpoint, on the other hand regards the probability of an event as a number which represents a person's degree of belief that a statement about an event is true. The subjectivist considers a probability to be an attribute of the person making the assessment, and thereby disallows the notion of the assessment as being right or wrong. However, the subjectivist does require that encoded probabilities adhere to the basic axioms of probability and that evidence or knowledge be used in a rational and consistent manner. The mathematical viewpoint on probability works from assumptions of symmetry (on underlying elementary events) in conjunction with a rational or logical model in order to deduce the probability of higher level events. To understand the conflict between the first two viewpoints, consider the probability of a fire next year in the building that you are in right now and, if there is a fire, consider the probability that the severity will exceed a specified level. There is a large volume of actuarial data On fire frequency and severity levels for various types of buildings. Also, there is a growing number of rational deterministic models for predicting fire growth over time. Can these different sources provide the information to answer relevant risk management questions? In general, One finds that as you seek data which provides good association with a specific building, the availability of

496

objective data quickly dwindles, and may well vanish. Suppose the building is a warehouse and one must evaluate the cost effectiveness of a sprinkler system installation. The evaluation requires estimates on the frequency of fire and the expected severity for the warehouse in question. For discussion purposes, focus on frequency. There is a good chance that you will be able to get an actuarial estimate on fire frequency for warehouses in general, but you may not be comfortable in assuming that this warehouse is typical with respect to frequency. Empirical evidence exists which shows that fire frequency in warehouses depends on a number of factors (e.g. type of building, type of materials stored), and, considering these factors, you feel that the warehouse in question presents greater than average risk. Consequently, you may wish to stratify the actuarial data on frequency, and focus on a data subgroup. It should be noted that frequency estimates require two types of actuarial data, fire incidence data and exposure level data. Therefore, we are really talking about being able to stratify two data bases. It is necessary to do this on each of the frequency relevant factors if one is to retrieve an actuarial estimate which is representative of the specific occupancy being assessed. However, the feasibility for stratification diminishes as the number of relevent factors increases because there is a progressively greater chance that either the data base of fire incidence or the one on exposure level will not contain the information that is necessary to perform stratification. Suppose one is unable to stratify the actuarial data to obtain a subgroup which is representative of the warehouse in question. The pure objectivist will say that the frequency estimate is not available since representative actuarial data is not available. A subjectivist who understands the basic principles of decision analysis would recommend using an integration of the available objective (i .e. actuarial) and subjective data (i.e. expert opinion) with appropriate weights assigned to each data source. In this manner, an estimate of the frequency of a fire for the warehouse may be constructed. Later in this paper, some quidelines for doing this are provided. When using any type of probabilistic analysis, subjective judgment and objective data are always linked. When actuarial statistics are used directly in risk assessment, one must make the judgment that the particular facility (or class of facilities) under study presents substantially the same experiment upon whi ch the actuari a1 data was based. Thi sis a subject i ve judgment. Fire science models are deterministic and, by themselves, cannot yield probability loss models. Nevertheless, they also represent a source of objective data that can be linked to subjective judgement. For example, if a fire growth model predicts that a certain physical loss outcome will occur under a given set of conditions, then one can assess subjectively a degree of bel ief in how well the model represents the actual condition being assessed. Also, if the fire science model requires a set of input conditions, and these conditions are not known with certainty, then subjective (or actuarial) probabilities on the conditions can be introduced to generate a probability loss model. The statement is sometimes made that, given enough time and effort, improvements in actuari a1 data bases and fi re sci ence models wi 11 make subjective assessments no longer necessary in risk management studies. This is mi s 1eadi ng . Although advances wi 11 continue to improve the scope and accuracy of fire science models and actuarial data bases, change~ also will continue in building designs and fire protection technology. For many risk 497

management studies a gap will always persist, and subjective probability assessments wi 11 cont i nue to play a key role. The process of us i ng fi re science models to generate probability loss models is illustrated in more detail later in the paper.

GUIDELINES IN SUBJECTIVE PROBABILITY ASSESSMENT Although subjective probabilities are opinions and cannot be viewed as right or wrong, one still may judge the qual ity of the assessment. A consideration of decision analysis refers to normative and substantive goodness in assessments made by experts ([6]). Substantitive goodness refers to the amount of knowledge that the experts bring to the assessment process while normative goodness refers to the skill in translating the expert's knowledge base into probabilities. That is, does the expert fully utilize his or her knowledge and do they adhere to the basic axioms of probability? All probabilities are ultimately conditional, and it should be reasonable that if substantive and normative goodness are to exist, then the event (and its qualifying conditions) should be defined clearly. This advice may seem trivial. However, recently we participated in an experiment for integrating subjective judgment and output from a fire science model to estimate the probabi 1ity of compartment full room i nvo 1vement. Duri ng the experi ment, approximately half of the interaction time among the three experts was spent on trying to get agreement on what constitutes full room involvement. As an analyst seeking to assure substantive goodness when eliciting subjective assessments from an expert, one must clearly understand the nature of the expert's knowl edge base and construct an interface to access the expertise effectively. Procedurally, this means that one should avoid asking an expert to assess highly aggregate events. A fundament a1 pri nc i p1e of decision analysis is to exploit decomposition fully to more effectively solve a decision making problem [7]. In probability assessment, decomposing an event into subevents can provide the key to unlock the expert's knowledge base. Event trees, fault trees and inference trees are establ ished decomposition techniques. An event tree uses inductive logic to go from an initiating event to a set of possible final or complete events. For example, given that established burning has occurred in a building, one may wish to assess directly the probability of various loss levels. Alternatively, one may utilize an event tree to consider various scenarios for outcomes after establ i shed burni ng. Each scenari 0 is a sequence of subevents that occur through time. The subevents address issues of fi re growth, i ntervent ion response times and suppression effectiveness (see Figure 1). Presumably, the expert's knowledge base for assessing a probability loss model will be more fully utilized using the event tree rather than asking the expert to assess the likelihood for loss directly.

498

ESTABLISHED BURNING

DETECTION! SUPPRESSION RESPONSE SUPPRESSION TIME EFFECTIVENESS

PRE-INTERVENTION FIRE GROWTH OUTCOMES

SEVERITY OUTCOME($)

LOW r - - - - - - - - O ------------

FAST r--------

0 ------------

HIGH INITIATING EVENT

MODERATE

AVERAGE

MODERATE LOW

27 EVENT SCENARIOS FROM INITIATING EVENT

SLOW ' - - - - - - - - - 0 -------------

HIGH o --------------

FIGURE 1 EVENT TREE FOR MODELING SEVERITY (3 EVENT CATEGORIES FOR DECOMPOSITION)

A fault tree uses deductive logic to decompose the system by going from a complete or final event and branching backwards to consider all possible ways that the final event could occur. Inference trees allow one to explain an unobserved event (i.e. a hypothesis) in terms of observable events (i.e. data). Inference trees are commonly used in the insurance industry under the heading of risk scoring models [8], but their potential value in assisting Quant itat i ve ri sk assessment is probably not fully appreci ated. Fi gure 2 illustrates one type of inference tree. HYPOTHESIS

PROBAB I LITY OF FLASHOVER

WEIGHTS

DATA

20%

COMPARTMENT VOLUME

15%

COMPARTMENT FLOOR AREA

15%

COMPARTMENT CEILING HT.

20%

BOUNDARY MATERIAL

30%

AMT. &TYPE OF FUEL PKGS.

FIGURE 2 - INFERENCE TREE (i.e. SCORING MODEL) FOR ASSESSING A COMPARTMENTS PROBABILITY FOR FULL ROOM INVOLVEMENT

499

After decompos it i on one is confronted wi th a vari ety of probabil ity assessment tasks. In each case, one is either dealing with a single event or with a random variable. To provide for normative goodness some guidelines are available. When assessing probabilities of single events (e.g. probability of ignition or probability of full room involvement), one should avoid asking experts to assess probabilities directly. The expert should use a reference event whose probability of occurrence is known (e.g. an actuarially known event), and then proceed to assess a rel at i ve probabil i ty. For assess i ng probability models of random variables (e.g. response time or severity of fire loss), the method of fract il es is recommended [9]. If there...-is a random variable, RV and the Probability {RV~x} = p, then x is called the p-th fractile of RV. Under the method of fractiles, the expert assesses a discrete approximation to the random variable's probability distribution function by focusing on a few special fractile values, namely the .01, .25, .5, .75 and .99 fract il es. The assessor shoul d not be asked to speci fy fract il es directly. The 0.5 fractile is determined by varying the x-value until indifference is assessed between the RV being above or below that value. The .01 and .99 fractiles are set by finding approximate lower and upper bounds. Research has shown that assessors tend to be overconfident or over conservative and not set the .01 and .99 fractiles as wide as possible. By making the assessor aware of this tendency, one can neutralize it to some extent. To continue, by conditioning the RV to be above the 0.5 fractile, one again can find an x-value which probabilistically divides that subrange evenly; the value is the 0.75 fractile. The 0.25 fractile can be assessed in a similar manner. The method of fractiles is similar to the quideline for assessing single event probabilities in that the procedure avoids assigning probability values directly. Figure 3 illustrates how the five fractile va 1ues can be smoothed to generate a cumul at i ve probabil ity di stri but ion function for the RV in question.

0.99r-----------------------------------------------~

........ ., ............. ...

F

R

-------------;rc:~:::=::::::-::-~:---

0.75

A

C

;/'

T

I L E

I

"

--------~,~/-------

0.50

L E V

E L S

0.25

.....................................................................".~ .........................................................................................-................ .

O.OO~--~--=~_6L"_'_"_"_/L/_"_"-'-'L----L--~L---~--~----~--~RV __

o

2

3

5

4

6

7

8

9

RESPONSE TIME (MIN.) - FRACTILE VALUES

FIGURE 3 - CUMULATIVE PROBABILITY DISTRIBUTION ON RESPONSE TIME 500

10

Experimental research in subjective assessment has shown bias on the part of human decision makers [10]. Humans display overconfidence in scientific knowledge, understate how human error can occur and have great difficulty in est i mat i ng rare events. To understand better the nature of human bi as in performing subjective assessment tasks, we consider two types of information or data which experts utilize in applying subjective judgment ([11]). Singular information is case specific. It distinguishes the specific case from others in the same category. Distributional information is base rate data and concerns outcomes for a 1arger general cl ass of s ituat ions. Subject i ve assessments require experts to draw upon both types of information. However, humans do not integrate this information well. Humans employ a number of heuristics to process information. Unfortunately, the heuristics can entail bi as and detract from normative goodness. Under the representativeness heuri st i c, the probabi 1ity of an outcome is approxi mated by the degree to which the outcome represents the essential features of the evidence. This can lead to overemphasizing singular information and ignoring prior or base rate statistics. Using our previous example, suppose one needs to estimate the frequency of a fire in a warehouse which has no sprinkler system. Suppose that on an act uri a1 bas is the probabil ity of a reportabl e fi re duri ng a year in any warehouse (i .e. sprinklered or not) is 1%. Also, 90% of all reported warehouse fires had no sprinkler system and 75% of all warehouses have no sprinkler systems. If F denotes the event of having a reportable warehouse fire and NS denotes the event of a warehouse having no sprinkler system then Bayes Rule for probabilities can be used to determine precisely the probabi 1 i ty of a fi re ina warehouse wi th no spri nkl er system (i. e. the conditional event, F/NS). Using P(·) to denote probability, then Bayes Rule gives P(F/NS)

= [P(NS/F) P(NS)

1P(F)

= [90%] 75%

x 1%

= 1.2%

( 1)

The frequency of fires for all warehouses, P(F), is an example of distributional or base rate information. while P(NS/F), the evidentiary data linking reportable fires and the lack of sprinkler systems is an example of singular (i.e. more site specific) information. If actuarial probabilities on the events NS/F, NS and F are available, then Bayes Rule is the mechanism for integrating the singular and distributional information and, thereby, estimating P(F/NS). However, if P(NS) is not known, then one must estimate P(F/NS) subjectively. The represent at i veness heuri st i c warns us that, as i nformat ion processors, assessors may overemphas i ze the evi dence 1i nki ng fi res to the absence of sprinklers and ignore the base rate data by estimating P (F/NS) to be much greater than the value of 1. 2%. In the extreme, the representativeness heuristic is called the Bayesian fallacy where one equates the likelihood of a fire for a certain type of occupancy to the likelihood of finding that occupancy type, given there was a fire (i.e. P(F/NS) ~ P(NS/F». The anchoring heuristic can introduce bias in the opposite sense. Under the anchoring heuristic, assessments are formed by using a reference class for which outcome probabilities are known (i.e. distributional information) and, then adjusting the probabilistic value to include singular information. Bias

501

occurs when conservatism and fear of uncertainty leads to underadjustment in utilizing singular information. Another heuristic in subjective assessments is the availability heuristic which leads to approximating the probability of an outcome by the degree to which one can imagine the event. This can lead to bias toward retrievability of instance and improperly ignoring the longer term distributional information. For example, if a highly catastrophic fire recently occurred, one might overestimate the likelihood of such a fire occurring in a current risk management study. By understanding which type of bias which can exist, and by focusing on the two distinct types of information (i.e. singular and distributional), a risk analyst can do a better job in bringing normative goodness to the process of subjective probability assessment. More practical guidelines follow. First, the concept of substantive goodness for risk assessment should be interpreted in the pragmatic worl d of ri sk management dec is i on maki ng. Substantive goodness is relative; it is maximized when one uses all information that is available within the time and monetary constraints of the particular risk management study. If there is interest in making a greater conversion of qualitative risk assessment studies over to quantitative risk assessment, it may be more reasonable to focus first on low cost assessment methodology which has a greater chance for adoption. In any event, fire risk analysts should recognize that one could have two widely differing ri sk assessment methodologies, each of which may offer a similar degree of substantive goodness even though a commensurate difference in the time and cost requirements for the two methods may exist. Whatever methodology is uded, an awareness for the two types of knowledge or information available to the probabil ity assessment task is necessary. Di stri but i ona 1 i nformat i on wi 11 include actuarial data and usually can be formatted in term of probability loss model parameters. Singular information concerns site specific observations or data for the particular subject of the risk management study. It is less likely that singular information can be formatted directly as probability loss model parameters. When assessing the parameter of a probability loss model subjectively, one must first select a reference class for which actuarial or fire science data is available. While it is desirable to relate the reference class as closely as possible to the specific case under investigation, tradeoffs must be made between the similarity of the reference class to the specific assessment task and the quality of the actuari a1 or fi re sci ence data available for the reference class. Using an actuarial risk parameter estimate as an anchor, one must focus on the singular information that is available (i .e. information which distinguishes the specific case from the general characteristics of the reference class), and subjectively assess how much the actuarial risk parameter should be adjusted (i.e. subjective assessment (adjustment factor) x (actuarial risk parameter». The adjustment factor can be determined by a direct subjective judgment, or it can be enhanced by exploiting decomposition and the use of scoring models (i .e. inference trees). For the latter case, one can examine the available singular information and identify a set of observable factors (Fi' i = 1, ... 1) which can be scored for both the specifi c s i tuat i on and the reference cl ass. The factors chosen should be explanatory with respect to the value of the risk parameter. The relative importance of the factors for predicting the risk parameter can be assessed subjectively, and then calibrated to conform to the reference class. That is,

502

Subjective Assessment

t

= {i=l Wi Fi }

I

where .E

wiFj = 1

and

(2)

X {Actuarial Risk parameter}

(Fj, i =1, ..·

I)

denotes the factors scored for the

~=1

reference class. When the source of objective data is not an actuari a1 probabil i ty but output from a fire science model, the adjustment process is different. The fire science model will simulate the physical conditions for some stage of a fire process over time (e.g. a compartment's upper layer temperature before i ntervent i on, T). I f one can defi ne the cri t i cal event (s) in terms of threshold conditions on the physical variables being modeled (e.g. FL denotes flashover which occurs when T ~ T*), then one can use the fire science model to estimate the probability of flashover (i.e. P(FL». The human expert makes a subjective judgment on how well the fire science model represents reality. If the representation is not perfect, then the model either understates or overstates the physical variables and the expert must come to terms with the nature of this approximation. When T ~ T* and you believe that the model understates T then P(FL)=I. However, if you believe that the model overstates T, then one must integrate that opinion subjectively with the difference, T-T*, in order to estimate a value for P(FL) between (0, I). Conversely, if T < T* and you bel ieve the model understates T, the expert agai n must integrate the objective knowledge, T*-T, with the subjective judgment on the model's quality in order to generate an estimate on P(FL). Uncertainty can be appended to fire science models in a second way. If the model requires specifying a set of input conditions (denoted by I) and these conditions are not known with certainty, one then must consider a probability model where (In' n=l, ...• N) denotes the set of N possible input conditions. For each condition. one has an objective or subjective probability, Pn'

The final result. P(FL) can be given by

N

E P(FLn ) P n •

n=l

The discipline of decision analysis has made considerable progress in understandi ng how humans process i nformat i on for maki ng subject i ve probabil ity assessments. Guidelines for making more effective subjective assessments have been presented wi th the hope that improved understandi ng of subject i ve probability assessments will enable the fire protection community to use this tool more effectively in research and practice.

503

REFERENCES 1.

Ling, W-C.T., Williamson, R.B., "Modeling Fire Spread Through Probabilistic Networks", Fire Safety Journal, 2: 287-300, 1985.

2.

Elms, D.G., "Model ing Fire Spread in Buildings", Fire Technology, 20: 1, 11-19 , 1984.

3. Yeh, Kwan-Nan "Ignition Risk Analysis - Cigarette Ignition of Upholstered Furniture", Fire Technology, 21: 2, 105-121, 1985. 4.

CONCAWE's Ad-Hoc Risk Assessment Group, "Methodologies for Hazard Analysis and Risk Assessment in the Petroleum Refining and Storage Industry", Fire Technology, 20: 3, 23-56, 1984.

5.

Watts, J.M., "Dealing with Uncertainty: Some Applications in Fire Protection Engineering", Fire Safety Journal, ll: 127-134, 1986.

6.

Winkler, R.L., Murphy, A.H., "Good Probability Assessors", Journal of Applied Meteorology, I: 751-758, 1968.

7.

Von Winterfeldt, Detlof, Edwards Ward, Decision Analysis and Behavioral Research, pp. 45-62, Cambridge University Press, Cambridge, Massachusetts, 1986.

8.

Kaiser, J. "Experiences of the Gretener Method", Fire Safety Journal,

Z: 213-222, 1980.

9. P. Vatter, Bradley, S.P., Sherwood C.F. Jr. and Jackson, B.B, Quantitative Methods in Management, pp. 165-183, Richard D. Irwin, Inc., Homewood, Illinois 1978. 10. Tversky A. and Kahneman D., "Uncertainty: Heuristics and Biases", Science, 185: 1124-1131, 1974. 11. Kahneman, D., Slovic, P. and Tversky, A., Judgement Under Uncertainty, pp. 414-421, Cambridge University Press, Cambridge, Massachusetts, 1982.

504

A Probabilistic Approach to the Analysis of Fire Safety in Hotels: MOCASSIN B. HOG NON and M. ZINI Centre Scientifique et Technique du Biitiment Champs sur Marne, BP 02 77421 Marne La Vallee Cedex 02, France

ABSTRACT After defining a quantifiable criterion i.e. the probability of a fire causing multiple victims, an explanation is given of the advantage of using event-oriented modelling! to which a simulation technique can be applied. The MINHOTAURE model aeveloped to represent the possible functioning of the system being considered, is a temporized, stochastic Petri net. After reviewing the rules which govern the o~ration of this typ'e of network, the contents of the moael, its possibilities and limits are briefly described. Scenarios are automatically created by a software package which uses a Monte-Carlo simulation to choose the valid transition delays. This soHware enables groups of scenarios to be simulated, different in both number and time. It supplies information concerning the marking of places and conditions reached during or at the end of scenarios. Finally', in order to illustrate the advantage of and the p'ossibilities offered by this approach, the probabilities of 4 events are given, two of whic correspond to the presence of multip.le victims at the end of the simulated scenarios. The results concern 6 projects which, for the same hotel, differ with regards to the safety equipment used.

KEYWORDS : Fire safety analysis - Fire safety level - Deadly fire - Mutltiple victims -

Probability - System - Simulation - Event-oriented modelling - Probabilist approach Petri net - Place - Transition - Message - Marking - State - Action delay - Stochastic network - Monte-Colo simulation technique - Random variable. INTRODUCTION The need for an analysis method to p.redict the fire safety level of buildings open to the public is largely sahred by' the public authorities, architects and engineers in numerous countries. This is a particulary so in France where the Department of Civil Defence (DSq would like to eventually comp'lete the current regulations based on obligation of means, by new regulations basea on obligation of results. The success of this approach should satisfy an urgent demand expressed for a number of years now by the designers of buildings for public use. To do this, the FIRE SAFETY SCIENCE-PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM, pp.

505~513

505

DSC has asked the CSTB (Centre Scientifique et Technique du Batiment) and CEPS (Contr6le et Prevention Systemes) to conduct a feasibility study and produce a model for hotels, based on the hypothesis of a fire breaking out in a guest room.

FIRE SAFETY LEVEL Choice of a qualitive criterion The expression "level of safety" is a convenient term to use but it must be formally defined in order to be determined quantitatively. In the case of hotels, what the public authorities are concerned with is preventing deadly fires causing victims other than the occupants of the room in which the fire originateo, which is considered to be a rrivate space and does not concern collective safety. During a hotel fire, the death 0 several people indicates the insufficiency or failure of the safety measures applied to the establishment. With regards to the aim of collective safety, regulated by the public authorities, it is an unwanted event the occurrence of which can oe used as a criterion for evaluating the safety level. It is the use of this type of criterion which directed us towards the choice of event-oriented modelling.

Quantitative definition of criterion With regards to the safety analysis practice, the statement that absolute safety does not exist is a basic assumption. Thus, we will try and determine, by calculation, the probability of unwanted events occurring. Br transposing this type ot approach to our problem, the fire safety level of a hote can be defined oy calculating the prop'ability of occurrence i.e. the probability that a fire, having been declared, will leaCl to multiple victims. The lower the prooability of this critical event occurring, the higher the fire safety level of the establishment. It should be noted that this approach does not include calculating the probability of a fire occurring in a hotel room, since it is considered a private area and is thus not covered by preventive measures of a regulatory order. Working out a methodology for calculating the p.robability of a fire causing multiple victims and its application to various types of public establishments, will eventually p.rovide the public authorities with the possibili!y of determining an obligation of result, expressed in the form of a maximum value which must not be exceeded, so that an establishment can be considered reasonably safe for the people in it.

METHODOLOGY USED Simulation In order to determine the probability of an unwanted event occurring during the functioning of a system, it must be possible to study a large number of developments for the system concerned. The system which we are concerned with here is a hotel, in one of the rooms of which accidental ignition occurs for an undetermined reason. This leads to incorrect functioning of the system, to varying degrees. Since it is impossible to examine in real world a large number of examples of incorrect functioning, either by observation or by testing the system itself, a simulation

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technique must be used. Simulation is a method used to study complex systems and phenomena which consists in replacing them with a simpler model with similar behaviour, on which the experiment is carried out and not on the system. Simulation can be applied to either an existing system or a system still being designed. It can therefore be perfectlY incorporated into the different stages ot building design and the examination of building/ermits. It means that a preCliction analysis of tile effectiveness of measures designe to protect users from deadly fires can be carried out, thus meeting the demand of the public authorities. Event-oriented modelling The system to be studied here is far too complex to derive proper equations on the physics of all its aspects which include the following : • the development of fire and the propagation of produts of combustion and smoke inside a hotel, • the behaviour of the occupants of the hotel, both guests and staff, • triggerring of fire safety equipment and the effect thereof, • the contribution of external aid - fire fighting, rescuing of occupants who were not able to leave the premises and are in danger trom the fire, etc. The computer mathematical models wich are available today do not cover all these aspects. Due to their elaborate forms, these models are too unwieldy to use for them to be currently incorporated into a coherent set of programs. Also, since these models are of the deterministic ty:pe, they can only p.roduce a single scenario, based on an given initial situation{ ana a single end result. The calculation time required using work stations currenny available to the engineer is often far longer than the actual physical time of the simulated scenario. This is a considerable deterrent to using tlie probabilistic aprroach, since it means increasing the number of scenarios, bas8d on the same initia condition of a system, in order to arrive at various end results~ some of which can include the unwanted event - the presence of many victims in the notel after the fire. We must therefore direct our attention towards methods for modelling the dynamic behaviour of discrete systems. CEP Systemes has thus examined the possibility of representin.9 the problem with methods conventionally used for the safety of systems. This has led to selecting an event-oriented model of all the aspects of the system using the temporized stochastic Petri net. Temporized stochastic Petri net This type of model consists in describing the system and its potential functions using four sets of objects - places, transitions, arcs and messages. Places represent the basic ~ssible states of the various components of the system. Tokens are used to demarcate the Rnished set of places. The places marked at any given time deRne the state of the system at that time. l