International Journal of Wildland Fire International Journal of Wildland Fire Society
Journal of the International Association of Wildland Fire
RESEARCH ARTICLE

Numerical prediction of size, mass, temperature and trajectory of cylindrical wind-driven firebrands

Luis A. Oliveira A C , António G. Lopes A , Bantwal R. Baliga B , Miguel Almeida A and Domingos X. Viegas A

A ADAI/LAETA, Department of Mechanical Engineering (FCTUC – Polo II), University of Coimbra, PT-3030-201 Coimbra, Portugal.

B Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street, West Montreal, QC, H3A 0C3, Canada.

C Corresponding author. Email: luis.adriano@dem.uc.pt

International Journal of Wildland Fire 23(5) 698-708 http://dx.doi.org/10.1071/WF13080
Submitted: 21 March 2012  Accepted: 20 March 2014   Published: 27 June 2014

Abstract

Mathematical models and numerical solution procedures for predicting the trajectory, oscillation, possible rotation, and mass and size time-evolution of cylindrical wind-driven firebrands are described and discussed. Two test problems and the results, used for validating the mathematical models, are presented. In one, experimental measurements of non-burning cylindrical particles falling in still air are compared to numerical predictions and in the other, predictions of time-evolution of mass and size of stationary burning particles in air flows are compared with experimental results reported in the literature. Results yielded by the proposed models for a demonstration problem involving cylindrical wind-driven firebrands, with the same initial volume, mass and position, but different initial aspect ratios and distinct initial orientations relative to the wind velocity, are then presented. These results show the following: the horizontal distance travelled by the firebrand from release to landing locations is an increasing function of its initial aspect ratio; and the initial orientation of the firebrand, and its subsequent oscillations including possible rotation, have a significant influence on its trajectory, thus it is important to account for them in mathematical models formulated for predicting the spread of fires by spotting.

Additional keywords: horizontal distance travelled, mathematical models, oscillations, rotations, spot fires, total falling time, trajectories.


References

Ahrens CD (2009) ‘Meteorology Today: an Introduction to Weather, Climate, and the Environment’, 9th edn. (Brooks/Cole: Belmont, CA)

Albini FA, Alexander ME, Cruz MG (2012) A mathematical model for predicting the maximum potential spotting distance from a crown fire. International Journal of Wildland Fire 21, 609–627.
A mathematical model for predicting the maximum potential spotting distance from a crown fire.CrossRef | open url image1

Almeida M, Viegas DX, Miranda AI, Reva V (2009) Combustibility of potential embers. In ‘Proceedings of the 18th World IMACS/MODSIM Congress’, 13–17 July 2009, Cairns, Australia. (Eds RS Anderssen, RD Braddock, LTH Newham) pp. 1–7. (Modelling and Simulation Society of Australia and New Zealand: Canberra, ACT) Available at http://www.mssanz.org.au/modsim09/Z1/almeida_m.pdf [Verified 3 June 2014]

Anthenien RA, Tse SD, Fernandez-Pello AC (2006) On the trajectories of embers initially elevated or lofted by small scale ground fire plumes in high winds Fire Safety Journal 41, 349–363.
On the trajectories of embers initially elevated or lofted by small scale ground fire plumes in high windsCrossRef | open url image1

Cheney NP, Bary GAV (1969) The propagation of mass conflagrations in a standing eucalypt forest by the spotting process. In ‘Mass Fire Symposium: Collected Papers’, 10–12 February 1969, Canberra, ACT. Vol. 1, Paper A6. (Commonwealth of Australia, Defence Standard Laboratories: Melbourne)

Ellis PF (2000) The aerodynamic and combustion characteristics of eucalypt bark – a firebrand study. PhD thesis, Australian National University, Canberra.

Ganser GH (1993) A rational approach to drag prediction of spherical and non-spherical particles. Powder Technology 77, 143–152.
A rational approach to drag prediction of spherical and non-spherical particles.CrossRef | 1:CAS:528:DyaK2cXjtVaitLg%3D&md5=d27bdb86759487c36343a886d499812dCAS | open url image1

Goldstein H, Poole C, Safko J (2002) ‘Classical Mechanics’, 3rd edn. (Addison-Wesley: New York)

Himoto K, Tanaka T (2005) Transport of disk-shaped firebrands in a turbulent boundary layer. In ‘Eighth International Symposium on Fire Safety Science’, 18–23 September 2005, Beijing, China. (Eds DT Gottuk, BY Lattimer) pp. 433–444. (International Association for Fire Safety Science: Baltimore, MD)

Hoerner, SF (1965) ‘Fluid-Dynamic Drag.’ (S.F. Hoerner: Bakersfield, CA)

Hölzer A, Sommerfeld M (2008) New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technology 184, 361–365.
New simple correlation formula for the drag coefficient of non-spherical particles.CrossRef | open url image1

Incropera FP, DeWitt DP (1996) ‘Fundamentals of Heat and Mass Transfer’, 4th edn. (Wiley: New York)

Kelbaliyev GI (2011) Drag coefficients of variously shaped solid particles, drops, and bubbles. Theoretical Foundations of Chemical Engineering 45, 248–266.
Drag coefficients of variously shaped solid particles, drops, and bubbles.CrossRef | 1:CAS:528:DC%2BC3MXnsF2gtb4%3D&md5=b117f8ad7799098babfc098aaf0d3d4dCAS | open url image1

Knight IK (2001) The design and construction of a vertical wind tunnel for the study of untethered firebrands in flight. Fire Technology 37, 87–100.
The design and construction of a vertical wind tunnel for the study of untethered firebrands in flight.CrossRef | open url image1

Koo E, Pagni PJ, Weise DR, Woycheese JP (2010) Firebrands and spotting ignition in large-scale fires. International Journal of Wildland Fire 19, 818–843.
Firebrands and spotting ignition in large-scale fires.CrossRef | open url image1

Koo E, Linn RR, Pagni PJ, Edminster CB (2012) Modelling firebrand transport in wildfires using HIGRAD/FIRETEC. International Journal of Wildland Fire 21, 396–417.
Modelling firebrand transport in wildfires using HIGRAD/FIRETEC.CrossRef | open url image1

Kortas S, Mindykowski P, Conslavi JL, Mhiri H, Porterie B (2009) Experimental validation of a numerical model for the transport of firebrands Fire Safety Journal 44, 1095–1102.
Experimental validation of a numerical model for the transport of firebrandsCrossRef | open url image1

Lopes AMG (2003) WindStation – a software for the simulation of atmospheric flows over complex topography Environmental Modelling & Software 18, 81–96.
WindStation – a software for the simulation of atmospheric flows over complex topographyCrossRef | open url image1

Lopes AMG, Sousa ACM, Viegas DX (1995) Numerical simulation of turbulent flow and fire propagation in complex topography Numerical Heat Transfer Part A 27, 229–253.
Numerical simulation of turbulent flow and fire propagation in complex topographyCrossRef | open url image1

Mandø M, Rosendhal L (2010) On the motion of non-spherical particles at high Reynolds number Powder Technology 202, 1–13.
On the motion of non-spherical particles at high Reynolds numberCrossRef | open url image1

Manzello SL, Shields JR, Yang JC, Hayashi Y, Nii D (2007) On the use of a firebrand generator to investigate the ignition of structures in wildland-urban interface (WUI) fires. In ‘Proceedings of 11th International Conference on Fire Science and Engineering (INTERLFAM)’, 3–5 September 2007, London. pp. 862–872. (Interscience Communications: London)

Manzello SL, Shields JR, Cleary TG, Maranghides A, Mell WE, Yang JC, Hayashi Y, Nii D, Kurita T (2008) On the development and characterization of a firebrand generator. Fire Safety Journal 43, 258–268.
On the development and characterization of a firebrand generator.CrossRef | open url image1

Manzello SL, Hayashi Y, Yoneki T, Yamamoto Y (2010) Quantifying the vulnerabilities of ceramic tile roofing assemblies to ignition during a firebrand attack. Fire Safety Journal 45, 35–43.
Quantifying the vulnerabilities of ceramic tile roofing assemblies to ignition during a firebrand attack.CrossRef | open url image1

Manzello SL, Park S-H, Suzuki S, Shields JR, Hayashi Y (2011) Experimental investigation of structure vulnerabilities to firebrand showers. Fire Safety Journal 46, 568–578.
Experimental investigation of structure vulnerabilities to firebrand showers.CrossRef | open url image1

Manzello SL, Suzuki S, Hayashi Y (2012a) Exposing siding treatments, walls fitted with eaves, and glazing assemblies to firebrand showers. Fire Safety Journal 50, 25–34.
Exposing siding treatments, walls fitted with eaves, and glazing assemblies to firebrand showers.CrossRef | open url image1

Manzello SL, Suzuki S, Hayashi Y (2012b) Enabling the study of structure vulnerabilities to ignition from wind driven firebrand showers: a summary of experimental results. Fire Safety Journal 54, 181–196.
Enabling the study of structure vulnerabilities to ignition from wind driven firebrand showers: a summary of experimental results.CrossRef | open url image1

Marchildon EK, Clamen A, Gauvin WH (1964) Drag and oscillatory motion of freely falling cylindrical particles. Canadian Journal of Chemical Engineering 42, 178–182.
Drag and oscillatory motion of freely falling cylindrical particles.CrossRef | 1:CAS:528:DyaF2cXksFeitL8%3D&md5=72585c609aee060801c75d39642345c8CAS | open url image1

McArthur AG (1967) Fire behaviour in eucalypt forests. Commonwealth of Australia, Forest and Timber Bureau, Leaflet number 107. (Canberra, ACT)

McRae GJ, Goodin WR, Seinfeld JH (1982) Development of a second-generation mathematical model for urban air pollution. I. Model formulation. Atmospheric Environment 16, 679–696.
Development of a second-generation mathematical model for urban air pollution. I. Model formulation.CrossRef | 1:CAS:528:DyaL38XktFWju7k%3D&md5=e49abfc443dbb4e9ccbf8ab8b4179c3cCAS | open url image1

Mell W, Maranghides A, McDermott R, Manzello SL (2009) Numerical simulation and experiments of burning douglas fir trees. Combustion and Flame 156, 2023–2041.
Numerical simulation and experiments of burning douglas fir trees.CrossRef | 1:CAS:528:DC%2BD1MXhtV2htb3I&md5=25c9e16593fa9a9d472a78939296eadcCAS | open url image1

Muraszew A, Fedele JB (1977) Trajectory of firebrands in and out of fire whirls. Combustion and Flame 30, 321–324.
Trajectory of firebrands in and out of fire whirls.CrossRef | open url image1

Ohmiya Y, Iwami T (2000) An investigation on the distribution of firebrands and spot fires due to a hotel fire. Fire Science & Technology 20, 27–35.
An investigation on the distribution of firebrands and spot fires due to a hotel fire.CrossRef | open url image1

Oliveira LA, Costa VAF, Baliga BR (2008) Numerical model for the prediction of dilute, three-dimensional, turbulent fluid-particle flows, using a Lagrangian approach for particle tracking and a CVFEM for the carrier phase. International Journal for Numerical Methods in Fluids 58, 473–491.
Numerical model for the prediction of dilute, three-dimensional, turbulent fluid-particle flows, using a Lagrangian approach for particle tracking and a CVFEM for the carrier phase.CrossRef | open url image1

Porteiro J, Míguez JL, Granada E, Moran JC (2006) Mathematical modelling of the combustion of a single wood particle. Fuel Processing Technology 87, 169–175.
Mathematical modelling of the combustion of a single wood particle.CrossRef | 1:CAS:528:DC%2BD2MXht12isr7O&md5=db2860b14bd50a545187c14ae6194e45CAS | open url image1

Porterie B, Consalvi JL, Kaiss A, Loraud JC (2005) Predicting wildland fire behavior and emissions using a fine-scale physical model. Numerical Heat Transfer Part A 47, 571–591.
Predicting wildland fire behavior and emissions using a fine-scale physical model.CrossRef | open url image1

Ren B, Zhong W, Jin B, Lu Y, Chen X, Xiao R (2011) Study on the drag of a cylinder-shaped particle in steady upward gas flow. Industrial & Engineering Chemistry Research 50, 7593–7600.
Study on the drag of a cylinder-shaped particle in steady upward gas flow.CrossRef | 1:CAS:528:DC%2BC3MXmtFyitbc%3D&md5=51bd850f786794d66ddc1a639d8e51ebCAS | open url image1

Roberts AF (1970) A review of kinetics data for the pyrolysis of wood and related substances. Combustion and Flame 14, 261–272.
A review of kinetics data for the pyrolysis of wood and related substances.CrossRef | 1:CAS:528:DyaE3cXktlKks7k%3D&md5=79a04c07073da3c18a04e2d7194135a6CAS | open url image1

Sardoy N, Consalvi JL, Porterie B, Kaiss A (2006) Transport and combustion of ponderosa pine firebrands from isolated burning trees. In ‘First International Symposium on Environment Identities and Mediterranean Area, 2006. ISEIMA ‘06’, 9–12 July 2006, Corte-Ajaccio, France. pp. 6–11. (Institute of Electrical and Electronics Engineers: New York)

Sardoy N, Consalvi JL, Porterie B, Fernandez-Pello AC (2007) Modeling transport and combustion of firebrands from burning trees. Combustion and Flame 150, 151–169.
Modeling transport and combustion of firebrands from burning trees.CrossRef | 1:CAS:528:DC%2BD2sXnsVSrtrY%3D&md5=c4848bd5d072c6c4eb805f08bf27847bCAS | open url image1

Sardoy N, Consalvi JL, Kaiss A, Fernandez-Pello AC, Porterie B (2008) Numerical study of ground-level distribution of firebrands generated by line fires. Combustion and Flame 154, 478–488.
Numerical study of ground-level distribution of firebrands generated by line fires.CrossRef | 1:CAS:528:DC%2BD1cXpt1alsbY%3D&md5=6604c7f975e9ef1147e95f572819240cCAS | open url image1

Sullivan AL (2009a) Wildland surface fire spread modelling, 1990–2007. 1. Physical and quasi-physical models. International Journal of Wildland Fire 18, 349–368.
Wildland surface fire spread modelling, 1990–2007. 1. Physical and quasi-physical models.CrossRef | open url image1

Sullivan AL (2009b) Wildland surface fire spread modelling, 1990–2007. 2. Empirical and quasi-empirical models. International Journal of Wildland Fire 18, 369–386.
Wildland surface fire spread modelling, 1990–2007. 2. Empirical and quasi-empirical models.CrossRef | open url image1

Sullivan AL (2009c) Wildland surface fire spread modelling, 1990–2007. 3. Simulation and mathematical analogue models. International Journal of Wildland Fire 18, 387–403.
Wildland surface fire spread modelling, 1990–2007. 3. Simulation and mathematical analogue models.CrossRef | open url image1

Sullivan AL, Knight IK, Hurley RJ, Webber C (2013) A contractionless, low-turbulence wind tunnel for the study of free-burning fires. Experimental Thermal and Fluid Science 44, 264–274.
A contractionless, low-turbulence wind tunnel for the study of free-burning fires.CrossRef | open url image1

Suzuki S, Manzello SL, Matthew Lage M, Laing G (2012) Firebrand generation data obtained from a full-scale structure burn. International Journal of Wildland Fire 21, 961–968.
Firebrand generation data obtained from a full-scale structure burn.CrossRef | open url image1

Tachikawa M, Fukuyama M (1981) Trajectories and velocities of typhoon-generated missiles. Transactions of Architectural Institute of Japan 302, 1–11. [In Japanese]

Tarifa CS, Del Notario PP, Moreno FG (1965) On the flight paths and lifetimes of burning particles of wood. Proceedings of the Combustion Institute 10, 1021–1037.
On the flight paths and lifetimes of burning particles of wood.CrossRef | open url image1

Tarifa CS, Del Notario PP, Moreno FG, Villa AR (1967) Transport and combustion of firebrands. USDA Forest Service, Final Report of Grant FG-SP-114 and FG-SP-146. (Madrid)

Tse SD, Fernandez-Pello AC (1998) On the flight paths of metal particles and embers generated by power lines in high winds – a potential source of wildland fires. Fire Safety Journal 30, 333–356.
On the flight paths of metal particles and embers generated by power lines in high winds – a potential source of wildland fires.CrossRef | open url image1

Viegas DX (2002) Fire behaviour models: an overview. In ‘Forest Fires: Ecology and Control, Atti del XXXIX Corso di Cultura in Ecologia’, 2–6 September 2002, San Vito di Cadore, Italy. (Eds T Anfodillo, V Carraro) pp. 37–47. (Università Degli Studi di Padova) Available at http://www.incendiboschivi.org/docum/prevenz/fuocoinforest.pdf [Verified 3 June 2014]

Viegas DX (2004) A mathematical model for forest fires blowup. Combustion Science and Technology 177, 27–51.
A mathematical model for forest fires blowup.CrossRef | open url image1

Viegas DX (2006) Parametric study of an eruptive fire behaviour model. International Journal of Wildland Fire 15, 169–177.
Parametric study of an eruptive fire behaviour model.CrossRef | open url image1

Viegas DX, Gabbert W, Figueiredo AR, Almeida MA, Reva V, Ribeiro LM, Viegas MT, Oliveira R, Raposo JR (2012) Report on the Forest Fire of Tavira/São Brás de Alportel, 18–22 July 2012. Centro de Estudos sobre Incêndios Florestais, ADAI/LAETA, University of Coimbra. (Coimbra, Portugal) [In Portuguese]

Woycheese JP, Pagni PJ (1999) Combustion models for wooden brands. In ‘Proceedings of 3rd International Conference on Fire Research and Engineering (ICFRE3)’, 4–8 October 1999, Chicago, IL. pp. 53–71. (Society of Fire Protection Engineers, Boston, MA)

Yin C, Rosendahl L, Kær SK, Sorensen H (2003) Modelling the motion of cylindrical particles in a nonuniform flow. Chemical Engineering Science 58, 3489–3498.
Modelling the motion of cylindrical particles in a nonuniform flow.CrossRef | 1:CAS:528:DC%2BD3sXls1aitbg%3D&md5=a0d56b9d2dff5aae57de6689996b0ec0CAS | open url image1

Yin C, Rosendahl L, Kær SK, Condra TJ (2004) Use of numerical modeling in design for co-firing biomass in wall-fired burners. Chemical Engineering Science 59, 3281–3292.
Use of numerical modeling in design for co-firing biomass in wall-fired burners.CrossRef | 1:CAS:528:DC%2BD2cXlvFynsrg%3D&md5=06136b51c7464d5a4aec673092eedfa7CAS | open url image1

Zastawny M, Mallouppas G, Zhao F, van Wachem B (2012) Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. International Journal of Multiphase Flow 39, 227–239.
Derivation of drag and lift force and torque coefficients for non-spherical particles in flows.CrossRef | 1:CAS:528:DC%2BC3MXhs1Krsb3P&md5=7b65a57ddd9c7c766626338b91abb1bfCAS | open url image1

Zhou X, Mahalingam S, Weise D (2007) Experimental study and large eddy simulation of effect of terrain slope on marginal burning in shrub fuel beds. Proceedings of the Combustion Institute 31, 2547–2555.
Experimental study and large eddy simulation of effect of terrain slope on marginal burning in shrub fuel beds.CrossRef | open url image1



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