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SFPE Handbook of Fire Protection Engineering pp 396–428Cite as

Fire Plumes, Flame Height, and Air Entrainment

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Abstract

Practically all fires go through an important, initial stage in which a coherent, buoyant gas stream rises above a localized volume undergoing combustion into surrounding space of essentially uncontaminated air. This stage begins at ignition, continues through a possible smoldering interval, into a flaming interval, and may be said to end prior to flashover. The buoyant gas stream is generally turbulent, except when the fire source is very small. The buoyant flow, including any flames, is referred to as a fire plume.

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Notes

  1. 1.

    As a further aid in assessing variations in A, Tewarson [44], in his Table 3–4.12, lists values of ΔH O for complete combustion of many fuels, the lower heat of combustion per unit mass of oxygen consumed. From these values, H c /r (kJ/kg) can be easily calculated, the lower heat of combustion per unit mass of air (of standard composition) consumed and, hence, the coefficient A.

  2. 2.

    For normal atmospheric conditions (T ∞ = 293 K, g = 9.81 m/s2, c p  = 1.00 kJ/kg K, ρ∞ = 1.2 kg/m3), the factor \( 9.1{\left[{T}_{\infty }/\left(\Big(,g{c}_p^2\ {p}_{\infty}^2\right)\right]}^{1/3} \) has the numerical value 25.0 K m5/3 kW–2/3, and the factor 3.4[g/(c p ρ∞ T ∞)]1/3 has the numerical value 1.03 m4/3 s−1 kW–1/3.

  3. 3.

    A ratio L/D = 0.02 can be calculated from Equation 13.7 assuming H c /r = 3470 kJ/kg, an average for silicone oils from values reported by Tewarson [63] and assuming a convective heat fraction \( {\dot{Q}}_c/\dot{Q}=0.7 \). If a value of H c /r near the bottom of the reported range [63] is selected, 3230 kJ/kg, the observed value L/D = 0.14 is reproduced; slight changes in the assumed convective fraction will also reproduce the measured value.

  4. 4.

    Without specific knowledge, \( {\dot{Q}}_c/\dot{Q} \) may usually be assumed at 0.7. However, methyl alcohol produces a fire of low luminosity and radiation, for which \( {\dot{Q}}_c/\dot{Q}=0.8 \) is a good estimate.

  5. 5.

    In addition to convective heating, which depends on gas temperature and velocity, radiative heating would also be important in such cases and might even dominate over convective heating if the structure is immersed in flames.

References

  1. Rehm, R.G, Baum, H.R., “The Equations of Motion for Thermally Driven, Buoyant Flows,” J. Res. Nat. Bur. Stand. 83, pp. 297–308 (1978).

    Article  MATH  Google Scholar 

  2. H.R. Baum, K.B. McGrattan, and R.G. Rehm, “Mathematical Modelling and Computer Simulation of Fire Phenomena,” Fire Safety Science-Proceedings Fourth International Symposium, International Association of Fire Safety Science, London, UK (ed. T. Kashiwagi), pp. 185–193 (1994).

    Google Scholar 

  3. T.G. Ma and J.G. Quintiere, “Numerical Simulation of Axi-Symmetric Fire Plumes: Accuracy and Limitations,” Fire Safety Journal, 38, pp. 467–492 (2003).

    Article  Google Scholar 

  4. Y. Xin, J.P. Gore, K.B. McGrattan, R.G. Rehm, and H.R. Baum, “Fire Dynamics Simulation of a Turbulent Buoyant Flame Using Mixture-Fraction-Based Combustion Models,” Combustion and Flame, 141, pp. 329–335 (2005).

    Article  Google Scholar 

  5. Xin, Y., Filatyev, S.A., Biswas, K., Gore, J.P., Rehm, R.G., and Baum, H.R., “Fire Dynamics Simulations of a One-Meter Diameter Methane Fire,” Combustion and Flame, 153, pp.499–509 (2008).

    Google Scholar 

  6. Tieszen, S.R., O’Hern, T.J., Schefer, R.W., Weckman, E.J. and Blanchat, T.K., “Experimental Study of the Flow Field In and Around a One Meter Diameter Methane Fire,” Combustion and Flame, 129, pp. 378–391 (2002).

    Article  Google Scholar 

  7. FireFoam, released by FM Global, available from < http://code.google.com/p/firefoam-dev/>

  8. OpenFoam, produced by OpenCFD Ltd, available from < http://www.openfoam.com/>

  9. Wang, Y, Chatterjee, P. and de Ris, J.L., “Large Eddy Simulation of Fire Plumes,” Proceedings of the Combustion Institute, 33, pp. 2473–2480 (2011).

    Article  Google Scholar 

  10. Olenick, S.M. and Carpenter, D. J., “An Updated International Survey of Computer Models for Fire and Smoke,” Journal of Fire Protection Engineering, 13, pp. 87–110 (2003).

    Article  Google Scholar 

  11. G. Heskestad, “Engineering Relations for Fire Plumes,” Fire Safety Journal, 7, pp. 25–32 (1984).

    Article  Google Scholar 

  12. B.J. McCaffrey, “Purely Buoyant Diffusion Flames: Some Experimental Results,” NBSIR 79–1910, National Bureau of Standards, Washington, DC (1979).

    Google Scholar 

  13. G. Cox and R. Chitty, “A Study of the Deterministic Properties of Unbounded Fire Plumes,” Combustion and Flame, 39, pp. 191–209 (1980).

    Article  Google Scholar 

  14. G. Heskestad, “Peak Gas Velocities and Flame Heights of Buoyancy-Controlled Turbulent Diffusion Flames,” 18th Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 951–960 (1981).

    Google Scholar 

  15. H.C. Kung and P. Stavrianidis, “Buoyant Plumes of Large-Scale Pool Fires,” 19th Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 905–912 (1983).

    Google Scholar 

  16. E. Gengembre, P. Cambray, D. Karmed, and J.C. Bellet, “Turbulent Diffusion Flames with Large Buoyancy Effects,” Combustion Science and Technology, 41, pp. 55–67 (1984).

    Article  Google Scholar 

  17. G. Heskestad, “A Fire Products Collector for Calorimetry into the MW Range,” Report OC2E1.RA, Factory Mutual Research Corp., Norwood, MA (1981).

    Google Scholar 

  18. A. Tewarson, “Physico-Chemical and Combustion/Pyrolysis Properties of Polymeric Materials,” NBS-GGR-80-295, National Bureau of Standards, Washington, DC (1982).

    Google Scholar 

  19. C.L. Beyler, “Fire Hazard Calculations for Large, Open Hydrocarbon Fires,” The SFPE Handbook of Fire Protection Engineering, 3rd ed., Society of Fire Protection Engineering and National Fire Protection Association, Quincy, MA (2002).

    Google Scholar 

  20. B. Hägglund and L.E. Persson, “The Heat Radiation from Petroleum Fires,” Försvarets Forskningsanstalt, Stockholm, FDA Report C20126-D6(A3) (1976).

    Google Scholar 

  21. F. Tamanini, “Direct Measurements of the Longitudinal Variation of Burning Rate and Product Yield in Turbulent Diffusion Flames,” Combustion and Flame, 51, pp. 231–243 (1983).

    Article  Google Scholar 

  22. E.E. Zukoski, T. Kubota, and B. Cetegen, “Entrainment in Fire Plumes,” Fire Safety Journal, 3, pp. 107–121 (1980–81).

    Google Scholar 

  23. E.E. Zukoski, B.M. Cetegen, and T. Kubota, “Visible Structure of Buoyant Diffusion Flames,” 20th Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 361–366 (1985).

    Google Scholar 

  24. B. McCaffrey, “Flame Height,” The SFPE Handbook of Fire Protection Engineering, 2nd ed., Society of Fire Protection Engineers and National Fire Protection Association, Quincy, MA, pp. 2-1–2-8 (1995).

    Google Scholar 

  25. H.A. Becker and D. Liang, “Visible Length of Vertical Free Turbulent Diffusion Flames,” Combustion and Flame, 32, pp. 115–137 (1978).

    Article  Google Scholar 

  26. G. Cox and R. Chitty, “Some Source-Dependent Effects of Unbounded Fires,” Combustion and Flame, 60, pp. 219–232 (1985).

    Article  Google Scholar 

  27. G. Heskestad, “Luminous Heights of Turbulent Diffusion Flames,” Fire Safety Journal, 5, pp. 103–108 (1983).

    Article  Google Scholar 

  28. G.T. Kalghatgi, “Lift-Off Heights and Visible Lengths of Vertical Turbulent Jet Diffusion Flames in Still Air,” Combustion Science and Technology, 41, pp. 17–29 (1984).

    Article  Google Scholar 

  29. F.R. Steward, “Prediction of the Height of Turbulent Diffusion Buoyant Flames,” Combustion Science and Technology, 2, pp. 203–212 (1970).

    Article  Google Scholar 

  30. P.H. Thomas, “The Size of Flames from Natural Fires,” Ninth Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 844–859 (1963).

    Google Scholar 

  31. W.R. Hawthorne, D.S. Weddel, and H.C. Hottel, “Mixing and Combustion in Turbulent Gas Jets,” Third Symposium on Combustion, Williams and Wilkins, Baltimore, pp. 288–300 (1949).

    Google Scholar 

  32. E.E. Zukoski, “Fluid Dynamic Aspects of Room Fires,” Fire Safety Science—Proceedings of the First International Symposium, Hemisphere, New York, pp. 1–30 (1984).

    Google Scholar 

  33. E.E. Zukoski, “Convective Flows Associated with Room Fires,” Semi-Annual Progress Report to National Science Foundation, California Institute of Technology, Pasadena (1975).

    Google Scholar 

  34. G. Heskestad, “On Q* and the Dynamics of Turbulent Diffusion Flames,” Fire Safety Journal, 30, pp. 215–227 (1998).

    Article  Google Scholar 

  35. G. Heskestad, “A Reduced-Scale Mass Fire Experiment,” Combustion and Flame, 83, pp. 293–301 (1991).

    Article  Google Scholar 

  36. H. Vienneau, “Mixing Controlled Flame Heights from Circular Jets,” BSc Thesis, Dept. Chem. Eng.,Univ. New Brunswick, Fredericton, N.B., 1964.

    Google Scholar 

  37. M.V. D’Souza and J.H. McGuire, “ASTM E-84 and the Flammability of Foamed Thermosetting Plastics,” Fire Technology, 13, p 85–94 (1977).

    Article  Google Scholar 

  38. V.I. Blinov and G.N. Khudiakov, “Certain Laws Governing Diffusive Burning of Liquids,” Dokl. Acad. Nauk SSSR, 113, p 1094–1098 (1957).

    Google Scholar 

  39. B. Hägglund and L.E. Persson, “The Heat Radiation from Petroleum Fires,” Försvarets Forskningsanstalt, Stockholm, FDA Rep. C20126-D6 (A3), 1976.

    Google Scholar 

  40. B.D. Wood, P.L. Blackshear, Jr. and E.R.G. Eckert, “Mass Fire Model: An Experimental study of the Heat Transfer to Liquid Fuel Burning from a Sand-Filled Pan Burner,” Combust. Sci. Technol., 4, p. 113 (1971).

    Article  Google Scholar 

  41. K.S. Mudan, “Thermal Radiation Hazards from Hydrocarbon Pool Fires,” Prog. Energy Combust. Sci., 10, pp. 59–80 (1984).

    Article  Google Scholar 

  42. G. Heskestad, “Flame Heights of Fuel Arrays with Combustion in Depth,” Fire Safety Science—Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, pp. 427–438 (1998).

    Google Scholar 

  43. Huggett, C., “Estimation of Rate of Heat Release by Means of Oxygen Consumption Measurements,” Fire Mater. 4, pp. 61–65 (1980).

    Article  Google Scholar 

  44. Tewarson, A.,” Generation of Heat and Gaseous, Liquid, and Solid Products in Fires,” The SFPE Handbook of Fire Protection Engineering, 4th ed, Society of Fire Protection Engineers and National Fire Protection Association, Quincy, MA, pp. 3-109–3-194 (2008).

    Google Scholar 

  45. B.S. Grove and J.G. Quintiere, “Calculating Entrainment and Flame Height in Fire Plumes of Axisymmetric and Infinite Line Geometries,” Journal of Fire Protection Engineering, 12, pp. 117–137 (2002).

    Article  Google Scholar 

  46. Newman, J.S. and Wieczorek, C.J., “Chemical Flame Heights,” Fire Safety Journal, 39, pp. 375–382 (2004).

    Article  Google Scholar 

  47. de Ris, J, Wu, P. and Heskestad, G., “Radiation Fire Modeling,” Proceedings of the Combustion Institute, 118, pp. 51–60 (1999).

    Google Scholar 

  48. T.R. Blake and M. McDonald, “An Examination of Flame Length Data from Vertical Turbulent Diffusion Flames,” Combustion and Flame, 94, pp. 426–432 (1993).

    Article  Google Scholar 

  49. T.R. Blake and M. McDonald, “Similitude and the Interpretation of Turbulent Diffusion Flames,” Combustion and Flame, 101, pp. 175–184 (1995).

    Article  Google Scholar 

  50. M.A. Delichatsios, “Transition from Momentum to Buoyancy-Controlled Turbulent Jet Diffusion Flames and Flame Height Relationships,” Combustion and Flame, 33, pp. 349–364 (1993).

    Article  Google Scholar 

  51. H.A. Becker and S. Yamazaki, “Entrainment, Momentum Flux and Temperature in Vertical Free Turbulent Diffusion Flames,” Combustion and Flame, 33, pp. 123–149 (1978).

    Article  Google Scholar 

  52. N. Peters and J. Göttgens, “Scaling of Buoyant Turbulent Jet Diffusion Flames,” Combustion and Flame, 85, pp. 206–214 (1991).

    Article  Google Scholar 

  53. G. Heskestad, “Turbulent Jet Diffusion Flames: Consolidation of Flame Height Data,” Combustion and Flame, 118, pp. 51–60 (1999).

    Article  Google Scholar 

  54. A.H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1, The Ronald Press Company, New York (1953).

    Google Scholar 

  55. W. Schmidt, “Turbulente Ausbreitung eines Stromes erhitzer Luft,” Zeitschrift für Angewandte Mathematik und Mechanik, 21, pp. 265–278 (1941).

    Article  MATH  Google Scholar 

  56. H. Rouse, C.S. Yih, and H.W. Humphreys, “Gravitational Convection from a Boundary Source,” Tellus, 4, pp. 201–210 (1952).

    Article  Google Scholar 

  57. B.R. Morton, G.I. Taylor, and J.S. Turner, “Turbulent Gravitational Convection from Maintained and Instantaneous Sources,” Proceedings of the Royal Society A, 234, pp. 1–23 (1956).

    Article  MathSciNet  MATH  Google Scholar 

  58. B.R. Morton, “Forced Plumes,” Journal of Fluid Mechanics, 5, pp. 151–163 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  59. B.R. Morton, “Modeling of Fire Plumes,” 10th Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 973–982 (1965).

    Google Scholar 

  60. W.K. George, R.L. Alpert, and F. Tamanini, “Turbulence Measurements in an Axisymmetric Buoyant Plume,” International Journal of Heat and Mass Transfer, 20, pp. 1145–1154 (1977).

    Article  Google Scholar 

  61. S. Yokoi, “Study on the Prevention of Fire-Spread Caused by Hot Upward Current,” Report No. 34, Building Research Institute, Japan (1960).

    Google Scholar 

  62. G. Heskestad, “Fire Plume Simulator,” Report 18792, Factory Mutual Research Corp., Norwood, MA (1974).

    Google Scholar 

  63. A. Tewarson, “Experimental Evaluation of Flammability Parameters of Polymeric Materials,” in Flame-Retardant Polymeric Materials, Plenum, New York, pp. 97–153 (1982).

    Google Scholar 

  64. G. Heskestad, “Note on Maximum Rise of Fire Plumes in Temperature-Stratified Ambients,” Fire Safety Journal, 15, pp. 271–276 (1989).

    Article  Google Scholar 

  65. G. Heskestad, “Dynamics of the Fire Plume,” Philosophical Transactions of the Royal Society of London A, 356, pp. 2815–2833 (1998).

    Article  Google Scholar 

  66. G. Heskestad, “Fire Plume Behavior in Temperature Stratified Ambients,” Combustion Science and Technology, 106, pp. 207–228 (1995).

    Article  Google Scholar 

  67. J-I. Watanabe and T. Tanaka, “Experimental Investigation into Penetration of a Weak Fire Plume into a Hot Upper Layer,” Journal of Fire Sciences, 22, pp. 405–420 (2004).

    Google Scholar 

  68. G. Heskestad, “Virtual Origins of Fire Plumes,” Fire Safety Journal, 5, pp. 109–114 (1983).

    Article  Google Scholar 

  69. Y. Hasemi and T. Tokunaga, “Flame Geometry Effects on the Buoyant Plumes from Turbulent Diffusion Flames,” Fire Science and Technology, 4, pp. 15–26 (1984).

    Article  Google Scholar 

  70. B.M. Cetegen, E.E. Zukoski, and T. Kubota, “Entrainment in the Near and Far Field of Fire Plumes,” Combustion Science and Technology, 39, pp. 305–331 (1984).

    Article  Google Scholar 

  71. C.-S. Yih, “Free Convection Due to a Point Source of Heat,” Proceedings of the U.S. National Congress of Applied Mechanics, New York, pp. 941–947 (1952).

    Google Scholar 

  72. B.M. Cetegen, E.E. Zukoski, and T. Kubota, “Entrainment and Flame Geometry of Fire Plumes,” Report G8-9014, California Institute of Technology, Daniel and Florence Guggenheim Jet Propulsion Center, Pasadena (1982).

    Google Scholar 

  73. G. Heskestad, “Fire Plume Air Entrainment According to Two Competing Assumptions,” 21st Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 111–120 (1986).

    Google Scholar 

  74. C.L. Beyler, Development and Burning of a Layer of Products of Incomplete Combustion Generated by a Buoyant Diffusion Flame, Ph.D. Thesis, Harvard University, Cambridge, MA (1983).

    Google Scholar 

  75. M.A. Delichatsios and L. Orloff, “Entrainment Measurements in Turbulent Buoyant Jet Flames and Implications for Modeling,” 20th Symposium on Combustion, Combustion Institute, Pittsburgh, PA (1985).

    Google Scholar 

  76. M.A. Delichatsios, “Air Entrainment into Buoyant Jet Flames and Pool Fires,” The SFPE Handbook of Fire Protection Engineering, 2nd ed., Society of Fire Protection Engineers and National Fire Protection Association, Quincy, MA, pp. 2-20–2-31 (1995).

    Google Scholar 

  77. J.Q. Quintiere and B.S. Grove, “A Unified Analysis for Fire Plumes,” 27th Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 2757–2766 (1998).

    Google Scholar 

  78. G. Heskestad and T. Hamada, “Ceiling Jets of Strong Fire Plumes,” Fire Safety Journal, 21, pp. 69–82 (1993).

    Article  Google Scholar 

  79. P.H. Thomas, P.L. Hinkley, C.R. Theobald, and D.L. Sims, “Investigation into the Flow of Hot Gases in Roof Venting,” Fire Technical Paper No. 7, H. M. Stationery Office, Joint Fire Research Organization, London (1963).

    Google Scholar 

  80. P.L. Hinkley, “Rates of ‘Production’ of Hot Gases in Roof Venting Experiments,” Fire Safety Journal, 10, pp. 57–65 (1986).

    Article  Google Scholar 

  81. M.A. Delichatsios, “Fire Growth Rates in Wood Cribs,” Combustion and Flame, 27, pp. 267–278 (1976).

    Article  Google Scholar 

  82. Zukoski, E.E., Kubota, T. and Cetegen, B., “Entrainment in the Near Field of Fire Plumes,” California Institute of Technology, Daniel and Florence Guggenheim Jet Propulsion Center, August 1981

    Google Scholar 

  83. D.J. Rasbash, Z.W. Rogowski, and G.W.V. Stark, “Properties of Fires of Liquids,” Fuel, 35, pp. 94–107 (1956).

    Google Scholar 

  84. B.M. Cetegen and T.A. Ahmed, “Experiments on the Periodic instability of Buoyant Plumes and Pool Fires,” Combustion and Flame, 23, pp. 157–184 (1993).

    Article  Google Scholar 

  85. G.M. Byram and R.M. Nelson, Jr., “The Modelling of Pulsating Fires,” Fire Technology, 6, pp. 102–110 (1970).

    Article  Google Scholar 

  86. T. Tanaka, T. Fujita, and J. Yamaguchi, “Investigation into Rise Time of Buoyant Fire Plume Fronts,” International Journal of Engineering Performance-Based Fire Codes, 2, pp. 14–25 (2000).

    Google Scholar 

  87. G. Heskestad, “Rise of Plume Front from Starting Fires,” Fire Safety Journal, 36, pp. 201–204 (2001).

    Article  Google Scholar 

  88. L.H. Hu, Y.Z. Li, R. Huo, L. Yi, and C.L. Shi, “Experimental Studies on the Rise-Time of Buoyant Fire Plume Fronts Induced by Pool Fires,” Journal of Fire Sciences, 22 pp. 69–84 (2004).

    Article  Google Scholar 

  89. Y. Hasemi and T. Tokunaga, “Some Experimental Aspects of Turbulent Diffusion Flames and Buoyant Plumes from Fire Sources Against a Wall and in a Corner of Walls,” Combustion Science and Technology, 40, pp. 1–17 (1984).

    Google Scholar 

  90. J. Back, C. Beyler, and P. DiNenno, “Wall Incident Heat Flux Distributions Resulting from Adjacent Flames,” Proceedings of the Fourth International Symposium on Fire Safety Science, International Association for Fire Safety Science, London, UK, pp. 241–252 (1994).

    Google Scholar 

  91. T. Mizuno and K. Kawagoe, “Burning Rate of Upholstered Chairs in the Center, Alongside a Wall and in a Corner of a Compartment,” Fire Safety Science—Proceedings of the First International Symposium, Hemisphere, New York, pp. 849–857 (1984).

    Google Scholar 

  92. M.A. Kokkala, “Characteristics of a Flame in an Open Corner of Walls,” Interflam 1993, Interscience Communications Limited, London (1993).

    Google Scholar 

  93. M. Poreh and G. Garrad, “A Study of Wall and Corner Fire Plumes,” Fire Safety Journal, 34, pp. 81–98 (2000).

    Article  Google Scholar 

  94. B.Y. Lattimer and U. Sorathia, “Thermal Characteristics of Fires in a Noncombustible Corner,” Fire Safety Journal, 38 pp. 709–745 (2003).

    Article  Google Scholar 

  95. J.R. Welker and C.M. Sliepcevich, “The Effect of Wind on Flames,” Technical Report No. 2, NBS Contract XST 1142 with University of Oklahoma, Norman (1965).

    Google Scholar 

  96. S. Attalah and P.K. Raj, “Radiation from LNG Fires,” Interim Report on Phase II Work, Project IS-3.1 LNG Safety Program, American Gas Association, Arlington, VA (1974).

    Google Scholar 

  97. K.G. Huffman, J.R. Welker, and C.M. Sliepcevich, “Wind and Interaction Effects on Free-Burning Fires,” Technical Report No. 1441–3, NBS Contract CST 1142 with University of Oklahoma, Norman (1967).

    Google Scholar 

  98. T.A. Brzustowski, S.R. Gollahalli, and H.F. Sullivan, “The Turbulent Hydrogen Diffusion Flame in Cross-Wind,” Combustion Science and Technology, 11, pp. 29–33 (1975).

    Google Scholar 

  99. O.K. Sönju and J. Hustad, “An Experimental Study of Turbulent Jet Diffusion Flame,” 9th ICODERS, American Institute of Aeronautics and Astronautics, Poitiers, France (1984).

    Google Scholar 

  100. H.A. Becker, D. Liang, and C.I. Downey, “Effect of Burner Orientation and Ambient Airflow on Geometry of Turbulent Free Diffusion Flames,” 18th Symposium on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1061–1071 (1981).

    Google Scholar 

  101. Newman, Jeffrey S. and Croce, Paul A., “A Simple Aspirated Thermocouple for Use in Fires,” Journal of Fire and Flammability, 10, pp. 326–336 (1979).

    Google Scholar 

  102. Burgess, D.S., Grumer, J., and Wolfhard, H.G., “Burning Rates of Liquid Fuels in Large and Small Open Trays,” International Symposium on the Use of Models in Fire Research, Publication 786, National Academy of Sciences - National Research Council, Washington, DC, 1961, p68.

    Google Scholar 

  103. NFPA 92B, Standard for Smoke Management Systems in Malls, Atria, and Large Spaces, National Fire Protection Association, Quincy, MA (2005).

    Google Scholar 

  104. R.L. Alpert and E.J. Ward, “Evaluation of Unsprinklered Fire Hazards,” Fire Safety Journal, 7, pp. 127–143 (1984).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Retired from FM Global in 2004 as a Consulting Research Scientist, Norwood, USA

    Gunnar Heskestad

Authors
  1. Gunnar Heskestad
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Editor information

Editors and Affiliations

  1. Aon Fire Protection Engineering, Greenbelt, MD, USA

    Morgan J. Hurley P.E., FSFPE (Editor-in-Chief) (Editor-in-Chief)

  2. Hughes Associates, Baltimore, USA

    Daniel Gottuk Ph.D., P.E.

  3. National Fire Protection Association, Quincy, USA

    John R. Hall Jr. Ph.D.

  4. Kyoto University, Kyoto, Japan

    Kazunori Harada Dr. Eng.

  5. National Institute of Standards and Technology, Gaithersburg, USA

    Erica Kuligowski Ph.D.

  6. Worcester Polytechnic Institute, Worcester, USA

    Milosh Puchovsky P.E., FSFPE

  7. The University of Queensland, St Lucia, Australia

    José Torero Ph.D.

  8. The Fire Safety Institute, Quincy, USA

    John M. Watts Jr. Ph.D., FSFPE

  9. FM Global, Johnston, USA

    Christopher Wieczorek Ph.D.

Nomenclature

A

Defined in Equation 13.6 (m⋅kW–2/5)

B

Buoyancy flux defined in Equation 13.15 (m4⋅s−3)

b

Plume radius (m)

b ΔT

Plume radius to point where ΔT/ΔT 0 = 0.5 (m)

b u

Plume radius to point where u/u 0 = 0.5 (m)

b um

b u at level of maximum gas velocity near flame tip (m)

c

Adjustable constant, Equation 13.35

c p

Specific heat of air at constant pressure (kJ/kg⋅K)

D

Diameter (m)

F

Function (c p , T ∞, ρ∞, g); see Equation 13.31 (m⋅kW–2/5)

f

Frequency (s−1)

g

Acceleration due to gravity (m/s2)

H c

Actual lower heat of combustion (kJ/kg)

ΔH O

Tewarson’s [44] lower heat of combustion per unit mass of oxygen consumed (kJ/kg)

I

Intermittency

k

Ratio of specific heats, constant-pressure versus constant-volume

L

Mean flame height above base of fire (m)

L B

Buoyancy controlled flame height (m)

L I

Intermittency length scale

L M

Momentum controlled flame height (m)

ṁ ent

Entrained mass flow rate in plume (kg/s)

ṁ ent,L

ṁ ent at the mean flame height, L(kg/s)

ṁ f

Mass burning rate (kg/s)

N

Nondimensional parameter defined in Equation 13.4

p s

Pressure in source gas discharge stream (Pa)

p s0

Pressure in source gas reservoir (Pa)

\( \dot{Q} \)

ṁ f H c total heat release rate (kW)

\( {\dot{Q}}_c \)

Convective heat release rate (kW)

\( {\dot{Q}}^{*} \)

Radiative heat release rate (kW)

\( {\dot{Q}}^{*} \)

Nondimensional parameter defined in 13.1

R

Radius (m)

r

Actual mass stoichiometric ratio, air to fuel volatiles

R M

Momentum parameter defined in Equation 13.8

T

Mean temperature (K)

T 0

Mean centerline temperature in plume (K)

T ∞

Ambient temperature (K)

T ′

rms temperature fluctuation (K)

T a (z)

Ambient temperature at level z (K)

T a1

Ambient temperature at source level (K)

T L

T 0 at mean flame height (K)

ΔT

T − T ∞, mean temperature rise above ambient (K)

ΔT 0

Value of ΔT on plume centerline (K)

ΔT L

T L  − T ∞(K)

t

Time (s)

t g

Growth time; see Equation 13.49 (s)

t R

Rise time of plume front (s)

t * R

Nondimensional rise time of plume front, see 13.62

u

Mean axial velocity (m/s)

u 0

Mean axial velocity on centerline (m/s)

u 0m

Maximum value of u 0, near flame tip (m/s)

u′

rms velocity fluctuation in axial direction (m/s)

W f

Fire perimeter (m)

z

Height above base of fire (m)

z 0

Height of virtual origin above base of fire (m)

z m

Maximum vertical penetration of plume fluid in stratified ambient (m)

α

Entrainment coefficient

ξ

Nondimensional parameter defined in Equation 13.26

v m

Kinematic viscosity of flame gases at maximum flame temperature (m2 ⋅ s−1)

ρ

Mean density (kg/m3)

ρa1

Ambient density at source level (kg/m3)

ρ fe

Mean density in flames (kg/m3)

ρ s

Density of source gas discharge stream (kg/m3)

ρs0

Density of source gas in reservoir (kg/m3)

ρs∞

Density of source gas at ambient temperature and pressure (kg/m3)

ρ∞

Ambient density (kg/m3)

Δρ

ρ∞ − ρ, mean density deficiency (kg/m3)

σΔT

Plume radius to point where ΔT/ΔT 0 = e−1 (m)

σ u

Plume radius to point where u/u 0 = e−1 (m)

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Heskestad, G. (2016). Fire Plumes, Flame Height, and Air Entrainment. In: Hurley, M.J., et al. SFPE Handbook of Fire Protection Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2565-0_13

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  • DOI: https://doi.org/10.1007/978-1-4939-2565-0_13

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