There are two objectives in this paper on applying fire modelling techniques for designing fire safety provisions with symbolic mathematics. The first is to review key equations for a two-layer zone model and simplification to a simpler model. There are eleven equations on the mass, volume, temperature, density and internal energy for the upper hot layer and lower cool layer; and the pressure of the compartment. In addition, there are seven constraints and so only four equations are required to be solved. By following the assumptions made in the ASET type of two-layer zone model, these four equations can be further reduced to only two ordinary differential equations. Both the ASET model itself and its modification to FIRM in a compartment with a vertical vent were considered.
The second objective is to solve the two ordinary differential equations in the simplified model by symbolic mathematics. The advantages of using symbolic mathematics are discussed. It is proposed that symbolic mathematics is suitable for use by the Authority on assessing fire safety design based on performancebased fire codes where fire modelling technique has to be used.
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References
1.
1. Chow, W.K. (1999). A Preliminary Discussion on Engineering Performancebased Fire Codes in the Hong Kong Special Administrative Region , International Journal on Engineering Performance-Based Fire Codes, 1(1): 1–10 .
2.
2. Practice Note for Authorized Persons and Registered Structural Engineers: Guide to Fire Engineering Approach, Guide BD GP/BREG/P/36, Buildings Department, Hong Kong Special Administrative Region , March (1998).
3.
3. Hadjisophocleous, G.V., Benichou, N. and Tamim, A.S. (1998). Literature Review of Performance-based Fire Codes and Design Environment , Journal of Fire Protection Engineering, 9(1): 12–40 .
4.
4. Society of Fire Protection Engineers (2001). SFPE Engineering Guide to Performance-based Fire Protection Analysis and Design of Buildings, Society of Fire Protection Engineers, Bethesda, Maryland, USA .
5.
5.Sheppard, D. and Meacham, B.J. (2000). Acquisition, Analysis, and Reporting of Fire Plume Data for Fire Safety Engineering , In: Curtat, M. (ed.), Proceedings of 6th International Symposium, International Association for Fire Safety Science (IAFSS), pp. 195–206 , 5–9 July 1999, Poitiers, France, Intl. Assoc. for Fire Safety Science, Boston, MA.
6.
6. Babrauskas, V. (1996). Fire Modelling Tools for FSE: Are they Good Enough? , Journal of Fire Protection Engineering, 8(2): 87–96 .
7.
7. Friedman, R. (1992). An International Survey of Computer Models for Fire and Smoke , Journal of Fire Protection Engineering, 4(3): 81–92 .
8.
8. Birk, D.M. (1991). An Introduction to Mathematical Fire Modeling, 1st edn. Technomic Publishing Co. Inc., Lancaster, USA .
9.
9. Cox, G. (1996). Combustion Fundamental of Fire, Academic Press, London .
10.
10. Janssens, M.L. (2000). An Introduction to Mathematical Fire Modeling, 2nd edn. Technomic Publishing Co. Inc., Lancaster, USA .
11.
11. Abbott, M.B. and Basco, D.R. (1989). Computational Fluid Dynamics: An Introduction for Engineers, Longman Scientific & Technical, London .
12.
12. Versteeg, H.K. and Malalasekera, W. (1995). An Introduction to Computational Fluid Dynamics, The Finite Volume Method, Longman Scientific, London .
13.
13. Yang, K.T. (1999). Role of the Fire Field Models as a Design Tool for Performance-based Fire-code Implementation , International Journal on Engineering Performance-Based Fire Codes, 1(1): 11–17 .
14.
14. Quintiere, J. (1989). Fundamentals of Enclosure Fire ‘Zone’ Models , Journal of Fire Protection Engineering, 1: 99–119 .
15.
15. Forney, G.P. and Moss, W.F. (1992). Analyzing and Exploiting Numerical Characteristics of Zone Fire Models, NISTIR 4763, National Institute of Standards and Technology, Gaithersburg, Maryland, USA .
16.
16. Forney, G.P. and Moss, W.F. (1994). Analyzing and Exploiting Numerical Characteristics of Zone Fire Models , Fire Science& Technology, 14(1): 49–60 .
17.
17. Quintiere, J. (1995). Compartment Fire Modeling, Fire Protection Engineering, Section 3, Chapter 3, pp. 3–125–3–133, National Fire Protection, Battery, Ma .
18.
18. Tanaka, T., Fujita, T. and Yamaguchi, J. (2000). Investigation into rise time of buoyant fire plume fronts , International Journal on Engineering Performance-Based Fire Codes, 2(1): 14–25 .
19.
19. Kanury, A.M. (1987). On the Craft of Modelling in Engineering and Science , Fire Safety Journal, 12(1): 65–74 .
20.
20. Cooper, L.Y. (1982). A Mathematical Model for Estimating Available Safe Egress Time in Fires , Fire and Materials, 6(2): 135–150 .
21.
21. Cooper, L.Y. and Stroup, D.W. (1985). ASET-A Computer Program and User’s Guide , Fire Safety Journal, pp. 29–45 .
22.
22. Walton, W.D. (1985). ASET-B: A Room Fire Program for Personal Computer, NSSIR 85-3144-1 National Bureau of Standards, Washington DC, USA .
23.
23. Rehm, R.G. and Forney, G.P. (1992). A Note on the Pressure Equation used in Zone Fire Modelling, NISTIR 4906, National Institute of Standards and Technology, Gaithersburg, Maryland, USA .
24.
24. Chow, W.K., Wong, L.T., Chan, K.T., Fong, N.K. and Ho, P.L. (1999). Fire Safety Engineering: Comparison of a New Degree Programme with the Model Curriculum , Fire Safety Journal, 32(1): 1–15 .
25.
25. Chow, W.K., Chao, T.Y., Fong, N.K. and Chan, K.T. (2001). Engineering Mathematics for Degree Programmes in Building Services Engineering , International Journal on Architectural Science, 2(2): 23–34 .
26.
26. Heal, K.M., Hansen, M.L. and Richard, K.M. (1996). Maple V Release 5: Learning Guide, Waterloo Maple Zone, Waterloo, London .
27.
27. Chow, W.K. (2000). Building Fire Zone Models, The Hong Kong Polytechnic University, Hong Kong, China .
28.
28. Chow, W.K. (1997). Studies on Flashover Criteria for Compartmental Fires , Journal of Fire Sciences, 15(2): 95–107 .
29.
29. Jones, J.C. (1999). Difficulties with the Principles and Application of a Zone Model of Flashover , Journal of Fire Sciences, 17(2): 91–96 .
30.
30. Chow, W.K. and Jones, J.C. (1999). Rebuttals from Chow and Jones , Journal of Fire Sciences, 17(3): 171–174 .
31.
31. Jones, J.C. (1998). On the Measurement of Temperatures in Simulated Room Fires , Journal of Fire Sciences, 16(2): 3–14 .
32.
32. Cetegen, B.M., Zukoski, E.E. and Kubota, T. (1982). Entrainment and Flame Geometry of Fire Plumes, PhD Thesis, California Institute Technology, Pasadena, USA.
33.
33. NFPA 92B (1991). Guide for Smoke Management Systems in Malls Atria and Large Areas.
34.
34. Atkinson, K.E. (1978). An Introduction to Numerical Analysis, New York .
35.
35. Schwalbe, D. (1993). ‘‘Rungekuttahf’’ ODE file of the share library of Maple at e-mail: schwalbe@macalstr.edu, Macalester College, USA .
36.
36. ‘‘BRANZFIRE: Version 2001.4’’ Building Research Association of New Zealand, Willington, New Zealand (2001).
37.
37. Ho, D.C.W., Lo, S.M., Yiu, C.Y., Cheng, W.Y. and To, M.Y. (2002). Building Official’s Perception on the Use of Performance-based Fire Engineering Approach in Building Design – A Second Stage Study , International Journal on Engineering Performance-Based Fire Codes, 4(4): 119–126 .
