Mathematical model and sensor development for measuring energy transfer from wildland fires
Erik A. Sullivan A and André G. McDonald A B
+ Author Affiliations
- Author Affiliations
A Department of Mechanical Engineering, University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, AB, T6G 2G8, Canada. Email: erik@ualberta.ca
B Corresponding author. Email: andre.mcdonald@ualberta.ca
International Journal of Wildland Fire 23(7) 995-1004 https://doi.org/10.1071/WF14016
Submitted: 26 September 2013 Accepted: 27 April 2014 Published: 1 September 2014
Abstract
Current practices for measuring high heat flux in scenarios such as wildland forest fires use expensive, thermopile-based sensors, coupled with mathematical models based on a semi-infinite-length scale. Although these sensors are acceptable for experimental testing in laboratories, high error rates or the need for water cooling limits their applications in field experiments. Therefore, a one-dimensional, finite-length scale, transient-heat conduction model was developed and combined with an inexpensive, thermocouple-based rectangular sensor, to create a rapidly deployable, non-cooled sensor for testing in field environments. The proposed model was developed using concepts from heat conduction and with transient temperature boundary conditions, to avoid complicated radiation and convection conditions. Constant heat flux and tree-burning tests were respectively conducted using a mass loss cone calorimeter and a propane-fired radiant panel to validate the proposed analytical model and sensor as well as test the sensor in a simulated forest fire setting. The sensor was mounted directly beside a commercial Schmidt–Boelter gauge to provide data for comparison. The proposed heat flux measurement method provided results similar to those obtained from the commercial heat flux gauge to within one standard deviation. This suggests that the use of a finite-length scale model, coupled with an inexpensive thermocouple-based sensor, is effective in estimating the intense heat loads from wildland fires.
Additional keywords: fire energy, heat flux measurement, heat transfer, wildland forest fires.
References
Alvarez K, Gomez E (2009) ‘Forest Fires: Detection, Suppression and Prevention.’ (Nova Science Publishers: New York)Anguiano RM (2006) Transient heat transfer through thin fibrous layers. MSc thesis, University of Alberta, Edmonton.
Balling RC, Meyer GA, Wells SG (1992) Relation of surface climate and burned area in Yellowstone National Park. Agricultural and Forest Meteorology 60, 285–293.
| Relation of surface climate and burned area in Yellowstone National Park.Crossref | GoogleScholarGoogle Scholar |
Bova A, Dickinson M (2009) An inverse method to estimate stem surface heat flux in wildland fires. International Journal of Wildland Fire 18, 711–721.
| An inverse method to estimate stem surface heat flux in wildland fires.Crossref | GoogleScholarGoogle Scholar |
Bray J (1990) Aluminum mill and engineered wrought products, properties and selection: nonferrous alloys and special-purpose materials. In ‘ASM Handbook’. Vol. 2, pp. 29–61. (ASM International: Materials Park, OH)
Bryam GM (1959) Combustion of forest fuels. In ‘Forest Fire Control and Use’. (Ed. K Davis) pp. 61–89. (McGraw-Hill: New York)
Butler BW, Cohen JJ, Latham DJ, Schuette RD, Sopko PP, Shannon KS, Jimenez D, Bradshaw LS (2004) Measurements of radiant emissive power and temperatures in crown fires. Canadian Journal of Forest Research 34, 1577–1587.
| Measurements of radiant emissive power and temperatures in crown fires.Crossref | GoogleScholarGoogle Scholar |
Cardarelli F (2008) ‘Materials Handbook: a Concise Desktop Reference’, p.174 (Springer: London)
Carslaw HS, Jaeger JC (1959) ‘Conduction of Heat in Solids’, 2nd edn. (Clarendon Press: Oxford)
Cavanagh JM (2004) Clothing flammability and skin burn injury in normal and micro-gravity. MSc thesis, University of Saskatchewan, Canada.
Çengel YA, Ghajar AJ (2011) ‘Heat and Mass Transfer: Fundamentals and Applications’, 4th edn. (McGraw-Hill: New York)
Chas-Amil M, Touza J, Garcia-Martinez E (2013) Forest fires in the wildland–urban interface: a spatial analysis of forest fragmentation and human impacts. Applied Geography (Sevenoaks, England) 43, 127–137.
| Forest fires in the wildland–urban interface: a spatial analysis of forest fragmentation and human impacts.Crossref | GoogleScholarGoogle Scholar |
Fernandes A, Sousa P, Borges V, Guimaraes G (2010) Use of 3D-transient analytical solution based on Green's function to reduce computational time in inverse heat conduction problems. Applied Mathematical Modelling 34, 4040–4049.
| Use of 3D-transient analytical solution based on Green's function to reduce computational time in inverse heat conduction problems.Crossref | GoogleScholarGoogle Scholar |
Frankman D, Webb B, Butler B, Jimenez D, Forthofer J, Sopko P, Shannon KS, Hiers JK, Ottmar R (2013) Measurements of convective and radiative heating in wildland fires. International Journal of Wildland Fire 22, 157–167.
| Measurements of convective and radiative heating in wildland fires.Crossref | GoogleScholarGoogle Scholar |
Fu CL, Xiong XT, Fu P (2005) Fourier regularization method for solving the surface heat flux from interior observations. Mathematical and Computer Modelling 42, 489–498.
| Fourier regularization method for solving the surface heat flux from interior observations.Crossref | GoogleScholarGoogle Scholar |
Gavin D, Hallett D, Hu F, Lertzman K, Pichard S, Brown KJ, Lynch JA, Bartlein P, Peterson D (2007) Forest fire and climate change in western North America: insights from sediment charcoal recoards. Frontiers in Ecology and the Environment 5, 499–506.
| Forest fire and climate change in western North America: insights from sediment charcoal recoards.Crossref | GoogleScholarGoogle Scholar |
Grine A, Desmons J, Harmand S (2007) Models for transient conduction in a flat plate subjected to a variable heat flux. Applied Thermal Engineering 27, 492–500.
| Models for transient conduction in a flat plate subjected to a variable heat flux.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XhtFWhsrjE&md5=0e91fddf4330b85108df99aa6229ee75CAS |
Häggkvist A, Sjöström J, Wickström U (2013) Using plate thermometer measurements to calculate incident heat radiation. Journal of Fire Sciences 31, 166–177.
| Using plate thermometer measurements to calculate incident heat radiation.Crossref | GoogleScholarGoogle Scholar |
Heyerdahl EK, Brubaker LB, Agee JK (2002) Annual and decadal climate forcing of historical fire regimes in the interior Pacific Northwest, USA. The Holocene 12, 597–604.
| Annual and decadal climate forcing of historical fire regimes in the interior Pacific Northwest, USA.Crossref | GoogleScholarGoogle Scholar |
Hukseflux USA Inc. (2008) ‘SBG01 Water Cooled Heat Flux Sensor 457 According to Schmidt–Boelter’, Specifications Brochure Version 1109. (Hukseflux Inc.: Manorville, NY)
ISO (2013) Fire tests – calibration and use of heat flux meters. Part 2: preliminary calibration methods. ISO 14934–2:2013. (International Organization for Standardization: Geneva, Switzerland)
Jiji L (2003) ‘Heat Conduction’, 2nd edn. (Begell House, Inc.: New York)
Keeley JE (2009) Fire intensity, fire severity and burn severity: a brief review. International Journal of Wildland Fire 18, 116–126.
| Fire intensity, fire severity and burn severity: a brief review.Crossref | GoogleScholarGoogle Scholar |
Keltner NR, Beck JV, Nakos JT (2010) Using directional flame thermometers for measuring thermal exposure. Journal of ASTM International 7, 102280
| Using directional flame thermometers for measuring thermal exposure.Crossref | GoogleScholarGoogle Scholar |
Kremens R, Smith A, Dickinson M (2010) Fire metrology: current and future directions in physics-based measurements. Fire Ecology 6, 13–35.
| Fire metrology: current and future directions in physics-based measurements.Crossref | GoogleScholarGoogle Scholar |
Lam CS, Weckman EJ (2009) Steady-state heat flux measurements in radiative and mixed radiative–convective environments. Fire and Materials 33, 303–321.
| Steady-state heat flux measurements in radiative and mixed radiative–convective environments.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXhtlWlu7%2FJ&md5=5515b2ad74e5df92d7f2ea3a8b261e76CAS |
Lam CS, Weckman EJ (2011) Heat flux measurements and their uncertainty in a large-scale fire test. Journal of Testing and Evaluation 39, 103922
| Heat flux measurements and their uncertainty in a large-scale fire test.Crossref | GoogleScholarGoogle Scholar |
Mansur W, Vasconcellos C, Zambrozuski N, Filho OR (2009) Numerical solution for the linear transient heat conduction equation using an Explicit Green’s Approach. International Journal of Heat and Mass Transfer 52, 694–701.
| Numerical solution for the linear transient heat conduction equation using an Explicit Green’s Approach.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1cXhsFCktb3F&md5=d65be47e3907b712ee129c6a00ed4b8cCAS |
Manzello SL, Park SH, Cleary TG (2010) Development of rapidly deployable instrumentation packages for data acquisition in wildland–urban interface (WUI) fires. Fire Safety Journal 45, 327–336.
| Development of rapidly deployable instrumentation packages for data acquisition in wildland–urban interface (WUI) fires.Crossref | GoogleScholarGoogle Scholar |
Monds J, McDonald A (2013) Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales. Applied Thermal Engineering 50, 593–603.
| Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales.Crossref | GoogleScholarGoogle Scholar |
Morandini F, Perez-Ramirez Y, Tihay VS, Barboni T (2013) Radiant, convective and heat release characterization of vegetation fire. International Journal of Thermal Sciences 70, 83–91.
| Radiant, convective and heat release characterization of vegetation fire.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3sXmt12hsb0%3D&md5=d7a73682b58722de28f8d4a4dfcf02ceCAS |
Nelson RM, Adkins CW (1986) Flame characteristics of wind-driven surface fires. Canadian Journal of Forest Research 16, 1293–1300.
| Flame characteristics of wind-driven surface fires.Crossref | GoogleScholarGoogle Scholar |
OIG (2006) Audit report: Forest Service large fire suppression costs. USDA Office of the Inspector General, Western Region, Report 08601–44-SF (San Francisco, CA)
Peridier V (2006) Estimating transient surface heating using a cellular automation energy-transport model. Complex Systems 16, 139–154.
Pyne SJ, Andrews PL, Laven RD (1996) ‘Introduction to Wildland Fire.’ (Wiley: New York)
Sahoo N, Peetala RK (2011) Transient surface heating rates from a nickel film sensor using inverse analysis. International Journal of Heat and Mass Transfer 54, 1297–1302.
| Transient surface heating rates from a nickel film sensor using inverse analysis.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXhs1Wgu7bE&md5=dcc50748e0bb37c9077446117b3e74b6CAS |
Silvani X, Morandini F (2009) Fire spread experiments in the field: temperature and heat flux measurements. Fire Safety Journal 44, 279–285.
| Fire spread experiments in the field: temperature and heat flux measurements.Crossref | GoogleScholarGoogle Scholar |
Sparrow EM, Cess RC (1978) ‘Radiation Heat Transfer’, Augmented Edn. (Hemisphere: Washington, DC)
Steel Construction Institute (1995) Heat flux loading. In ‘Use of Ultimate Strength Techniques for Fire Resistant Design of Offshore Structures’, FABIG Technical Note 3. pp. 11–13. (Steel Construction Institute: Silwood Park, UK)
Sudheer SS, Kumar L, Manjunath BS, Pasi A, Meenakshi GG, Prabhu SV (2013) Fire safety distances for open pool fires. Infrared Physics & Technology 61, 265–273.
| Fire safety distances for open pool fires.Crossref | GoogleScholarGoogle Scholar |
Sultan MA (2010) Performance of different temperature sensors in standard fire resistance test furnaces. Fire Technology 46, 853–881.
| Performance of different temperature sensors in standard fire resistance test furnaces.Crossref | GoogleScholarGoogle Scholar |
Sutradhar A, Paulino GH, Gray LJ (2002) Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method. Engineering Analysis with Boundary Elements 26, 119–132.
| Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method.Crossref | GoogleScholarGoogle Scholar |
Švantner M, Vacíková P, Honner M (2012) IR thermography heat flux measurement in fire safety applications. Infrared Physics & Technology 55, 292–298.
| IR thermography heat flux measurement in fire safety applications.Crossref | GoogleScholarGoogle Scholar |
Taylor SW, Alexander ME, Pike RG (1996) ‘Field guide to the Canadian Forest Fire Behavior Prediction (FBP) System.’ (Canadian Forest Service: Victoria)
Touloukian YS (1970) ‘Thermophysical Properties of Matter: Thermal Conductivity: Metallic Elements and Alloys.’ (IFI/Plenum: New York)
Westerling AL, Hidalgo HG, Cayan DR, Swetnam TW (2006) Warming and earlier spring increase Western U.S. forest wildfire activity. Science 313, 940–943.
| Warming and earlier spring increase Western U.S. forest wildfire activity.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XotFCitbo%3D&md5=33f81a6860735590a245ddafe692ee24CAS | 16825536PubMed |
Wieczorek CJ, Dembsey NA (2001) Human variability correction factors for use with simplified engineering tools for predicting pain and second degree skin burns. Journal of Fire Protection Engineering 11, 88–112.
| Human variability correction factors for use with simplified engineering tools for predicting pain and second degree skin burns.Crossref | GoogleScholarGoogle Scholar |
