* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Project no. FP6-018505 Project Acronym FIRE PARADOX Project
Survey
Document related concepts
Thermal conductivity wikipedia , lookup
Solar water heating wikipedia , lookup
Space Shuttle thermal protection system wikipedia , lookup
Dynamic insulation wikipedia , lookup
Solar air conditioning wikipedia , lookup
Thermoregulation wikipedia , lookup
Building insulation materials wikipedia , lookup
Heat exchanger wikipedia , lookup
Intercooler wikipedia , lookup
Cogeneration wikipedia , lookup
Copper in heat exchangers wikipedia , lookup
R-value (insulation) wikipedia , lookup
Thermal conduction wikipedia , lookup
Transcript
Project no. FP6-018505 Project Acronym FIRE PARADOX Project Title FIRE PARADOX: An Innovative Approach of Integrated Wildland Fire Management Regulating the Wildfire Problem by the Wise Use of Fire: Solving the Fire Paradox Instrument Integrated Project (IP) Thematic Priority Sustainable development, global change and ecosystems Deliverable 2.5-5-36 Criteria for building material ignition and for burn injuries in wildland fires: final achievements Due date of deliverable: February 2009 Actual submission date: November 2009 Start date of project: 1st March 2006 Duration: 48months Organisation name of lead contractor for this deliverable: The University of Edinburgh Revision (1000) Project co-funded by the European Commission within the Sixth Framework Programme (2002-2006) Dissemination Level PU Public PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services) DX.Y-Z-MM-0100-1 X Page 1 of 43 Authors: Pedro Reszka (P26: UE) José Luis Torero (P26: UE) Executive summary In fire modelling, an accurate prediction of the ignition of solid fuels requires the solution of solid- and gas-phase processes. Methods that decouple the solid from the gas phase would result in significant savings in computational cost. The work described herein presents a novel methodology for this decoupling. It is based on the observation that the time to ignition can be scaled with the square of the time integral of the incident heat flux. This relationship can be readily demonstrated for the classical solutions for time to ignition which consider constant incident heat fluxes. However, some fire applications, in particular situations of wild fires approaching the wildlandurban interface, present time-varying incident heat fluxes which render the classical solutions inaccurate. A new analytical solution for obtaining the time to ignition for ramping incident heat fluxes is presented. The proposed methodology completely decouples the solid and gas phases and is accurate in the prediction of ignition times. The methodology can be applied to both the new and classical analytical solutions. It was validated with tests carried out on PMMA and PA6. The results presented here will be useful for other teams developing forest fire models, especially the team at VTT which is working on the problem of the wildland-urban interface. The second part of the report is concerned with the development of a numerical model for the assessment of the influence of moisture migration in the severity of burn injuries affecting fire fighters. It was proven that this is an important factor affecting the severity of burn injuries. This information will constitute the basis for a research on the physiology of thermal skin burns, and will also help in the development of protective clothing for fire fighters. DX.Y-Z-MM-0100-1 Page 2 of 43 Table of contents: 1. A simple model for the assessment of building material response to wildland fires: Final results. .................................................................................... 4 1.1. Introduction ...................................................................................................... 4 1.2. Solid Fuel Ignition Modelling ............................................................................... 7 1.2.1. Solution for a Ramped Heat Flux ..........................................................................................9 1.2.2. New Analytical Solution .......................................................................................................9 1.2.3. Case when 1.2.4. Comparison of Different Solutions ...................................................................................... 11 q 0 = 0........................................................................................................... 10 1.3. Decoupling of Solid and Gaseous Phases ........................................................... 12 1.4. Experimental Description .................................................................................. 15 1.5. Experimental Results and Discussion ................................................................. 18 1.5.1. Validity of Semi-Infinite Solid Assumption ............................................................................ 18 1.5.2. Benchmark Tests for Constant Incident Heat Flux ................................................................ 20 1.5.3. Ramping Heat Fluxes ........................................................................................................ 20 1.6. Effect of Material Thermophysical Properties ...................................................... 23 1.7. Example of the use of the decoupling methodology ............................................ 24 1.8. Concluding Remarks ........................................................................................ 26 1.9. References ...................................................................................................... 27 2. Criteria for the assessment of wildland fire effect on burn injuries: Model description and experimental results. ........................................................ 29 2.1. Introduction .................................................................................................... 29 2.2. Experimental Procedure ................................................................................... 30 2.3. Experimental Results........................................................................................ 31 2.4. Modelling ........................................................................................................ 37 2.5. Numerical Results ............................................................................................ 38 2.6. Conclusions ..................................................................................................... 41 2.7. Nomenclature.................................................................................................. 41 2.8. References ...................................................................................................... 41 DX.Y-Z-MM-0100-1 Page 3 of 43 1. A simple model for the assessment of building material response to wildland fires: Final results. 1.1. Introduction The prediction of flaming ignition of solid fuels is necessary in many applications of fire safety engineering, ranging from fire modelling to risk assessments and flame spread. Flaming ignition is the result of a series of phenomena occurring simultaneously in the gas and solid phases [1]. To accurately model this process in a practical way, a series of simplifications and assumptions are normally done, conditioning the validity of the results to specific situations. In fire modelling, the differences in scales of the several physical and chemical processes involved makes their resolution become computationally expensive [2, 3]. These scale differences are particularly evident between the solid and gas phases (see Error! Reference source not found. below). A method for decoupling both phases would lessen the computational cost and permit the application of CFD codes to complex geometries. This section will report the work undertaken to develop a methodology for the decoupling of solid and gas phases in the modelling of flaming ignition, and on a new simplified analytical solution of the ignition process, with emphasis on the wildlandurban interface. The objective is to provide a mechanism to assess the potential for ignition without adding an excessive computational burden to CFD or other fire models. DX.Y-Z-MM-0100-1 Page 4 of 43 Type Time Scale (s) Vertical Scale (m) Horizontal (m) Combustion 0.0001 – 0.01 0.0001 – 0.01 0.0001 – 0.01 Fuel particles - 0.001 – 0.01 0.001 – 0.01 Fuel complex - 1 – 20 1 – 100 Flames 0.1 – 30 0.1 – 10 0.1 – 2 Radiation 0.1 – 30 0.1 – 10 0.1 – 50 Conduction 0.01 – 10 0.01 – 100 0.01 – 0.1 Convection 1 – 100 0.1 – 100 0.1 – 10 Turbulence 0.1 – 1,000 1 – 1,000 1 – 1,000 Spotting 1 – 100 1 – 3,000 1 – 10,000 Plume 1 – 10,000 1 – 10,000 1 – 100 scale Table Error! No text of specified style in document.-1: The varying temporal and spatial length scales of the major processes occurring in a forest fire [2]. An ever increasing problem in forest management is the occurrence of fires within the wildland-urban interface (WUI). Here, forest fires interact with buildings, representing a threat to people and property, and the presence of buildings can redefine fire propagation. Major WUI fires have been reported in several countries [4]. It is therefore important to understand the interaction between forest fires and building materials. An overview of this problem has been presented by Rehm [5]. It has become clear that due to the high intensities of the heat fluxes caused by some wildfires, radiant ignition of objects located at the order of tens of metres away from the fire front can be achieved [6]. An approaching fire will impose a time-varying heat flux on a stationary target [4, 6]. The shape of the heat flux can vary, but can normally be regarded as an exponential function of time, as can be seen in the following figures. However, for practical purposes, and given the accuracy level that is being dealt with in the problem, these time-varying heat fluxes can be approximated as linear functions of time after the initial growth stage. DX.Y-Z-MM-0100-1 Page 5 of 43 Figure Error! No text of specified style in document..1. Measured total heat flux at the walls of a shed at the WUI for an approaching prescribed fire (that developed into a crown fire) at New Jersey, USA. Taken from Manzello et al. [4]. DX.Y-Z-MM-0100-1 Page 6 of 43 Figure Error! No text of specified style in document..2. Variation in total incident heat flux with time during the crown fires of the International Crown Fire Modelling Experiment [6] for one of the burnt plots. Given the complexity of this problem, it has become evident that CFD fire models are necessary to study the interaction of wildland fires and buildings. As previously stated, if the gas and solid phases were completely decoupled, ignition times could be predicted without the need to completely resolve the solid phase. This is particularly important in the use of atmospheric wildfire models, where the grid cells are of the order of tens of metres and any building material would lie within the subgrid scale. The decoupling can be readily accomplished using standard analytical solutions to the problem of solid fuel ignition [7, 1], as will be shown in this report. However, the use of these solutions under conditions different to the ones they were obtained for can introduce significant errors [1]. This is the case when modelling the ignition of building materials from approaching wildland fires, because of the time variability of the imposed heat fluxes. The next sections will discuss the modelling of solid fuel ignition and the development of a method for the decoupling of solid and gas phases. Finally, a comparison with experimental results will be presented. 1.2. Solid Fuel Ignition Modelling Classical approaches to ignition [7, 8] obtain analytical solutions to the heat diffusion equation. By considering an ignition temperature at the surface (typically equal to the pyrolysis temperature), times to ignition can be calculated. These methods consider a one-dimensional, semi-infinite, inert solid subjected to a constant incident heat flux and convective heat losses at the exposed surface; the heat diffusion equation being expressed as DX.Y-Z-MM-0100-1 Page 7 of 43 (1) with the boundary and initial conditions given by and The convective coefficient can be made to include radiative losses following standard heat transfer techniques. If the heat flux to the surface is a constant the analytical solution to this equation for the surface temperature is [9, 10] (2) For high incident heat fluxes (i.e. short ignition times), the time to ignition is obtained by performing a Maclaurin series expansion and by making the surface temperature reach a pyrolysis or ignition temperature (Ts=Tpyrolysis). Common solutions are of the form [8, 10]: (3) Where the a is the surface absorptivity, usually taken as unity, k the thermal conductivity, the density, cp the specific heat, q i the incident heat flux, TP the pyrolysis temperature, T∞ the ambient temperature and tP the pyrolysis time, usually considered as being equal to the ignition time [1, 9]. A natural consequence of Equation (3) is that if each material is assumed to ignite at a constant temperature, then it follows that there is a linear dependency between DX.Y-Z-MM-0100-1 and , or that: Page 8 of 43 1.2.1. Solution for a Ramped Heat Flux First, the case of a ramped imposed heat flux will be considered. If no heat losses at the surface are considered, and the incident flux is defined as, (4) a solution for Equation (1) under the new boundary conditions has been presented by Carslaw & Jaeger [11, pp. 75-76]. The solution for x = 0, expressed in a similar form as Equation (3) becomes, (5) 1.2.2. New Analytical Solution A similar expression can be obtained if the same approach is followed for a variable incident heat flux, but this time considering heat losses at the surface. Assuming that the imposed heat flux grows linearly with time, it can be defined as (6) A solution for this problem is not readily available. To obtain it, the Convolution Theorem was applied to the solution of the differential equation in the Laplace space. The new analytical solution for x = 0 is (7) The previous solution was approximated by using a Maclaurin series expansion (for small times): DX.Y-Z-MM-0100-1 Page 9 of 43 (8) Equation (8) constitutes a general solution, incorporating the terms corresponding to a ramping incident heat flux (first term on the RHS of the equation), a constant incident heat flux (second term; cf. with Equation (3)), and the terms multiplied by the convective coefficient, corresponding to the heat losses. It is important to note that in the series expansion that is carried out to obtain the solution presented in Equation (3), the terms containing h are cancelled. This is not the case in the present solution, but it must be pointed out that for the situation of high heat fluxes and short times, as was considered in the solution leading to Equation (3), the terms containing h are not significant, and therefore the solutions presented in equations (3) and (8) are equivalent. 1.2.3. Case when q 0 = 0 For simplicity and the sake of clarity, the analysis will continue assuming that q 0 = 0. Under this assumption, the solution presented in Equation (8) becomes (9) The idea now is to have an expression of a similar form as Equations (3) and (5). So, if in the solution a net heat flux of the form (10) can be generated, then the solution can be expressed in the desired way. To do this, a reference temperature is defined as: (11) The reference temperature represents a time-varying characteristic temperature. A constant reference (or characteristic) temperature cannot be obtained due to the nature of the problem, specifically the time-varying imposed heat flux. Factorizing and dividing by , the solution then becomes DX.Y-Z-MM-0100-1 Page 10 of 43 (12) taking . An expression for an equivalent net heat flux can then be generated: (13) Finally, the solution for the time to ignition considering a ramped incident heat flux and convective surface losses is expressed as (14) 1.2.4. Comparison of Different Solutions The following figure presents a comparison between the different solutions to the ignition problem that have been discussed in this work. A numerical solution of the onedimensional conduction problem with ramping incident heat flux and convective losses at the surface is also plotted. For demonstration purposes, this solution is regarded as being an “exact” solution. The results show the influence of the convective terms. The analytical solution in Equation (7) closely matches the exact solution for all times. The approximate solution, Equation (9), shows good agreement for short times, diverging away from the exact solution at longer times, where the approximation does not hold. The curve corresponding to Equation (5), i.e. the solution for a ramped heat flux and no convective losses, overestimates surface temperatures in a similar way than the solution for a constant heat flux. The constant heat flux intensity used corresponds to the ramp intensity at 100 s., showing that good results can be obtained using this solution if a proper radiant intensity is selected. In the case of h = 0, Equation (7) diverges, but interestingly enough, its approximation (Equation (9)) does not, and becomes equal to Equation (5). If m = 0, Equation (7) behaves in a similar way to the constant heat flux solution, but presents lower surface temperatures due to the presence of terms containing h. DX.Y-Z-MM-0100-1 Page 11 of 43 1000 900 800 Temperature (K) 700 600 Numerical Solution 500 Analytical - Constant (Eq. 3) 400 Analytical - Ramped - No Losses (Eq. 5) 300 Analytical - Ramped - Heat Losses - 1st Order (Eq. 9) 200 Analytical - Ramped - Heat Losses - No Approx. (Eq. 7) 100 0 0 50 100 150 200 250 300 350 400 Time (s) Figure Error! No text of specified style in document..3. Comparison of different analytical solutions. The numerical solution is regarded as being the exact solution in this example. The curves for the numerical solution and Equation (8) are superposed, showing the good agreement of the full analytical solution. Thermophysical properties similar to those of wood were used. In all cases, the ramp used is 83.3 W·m-2·s-1 and the total heat transfer coefficient was 35 W·m -2·s1 . The constant incident heat flux used in Equation (3) was of 8,330 W·m -2, i.e. the level of irradiance of the ramping heat flux at 100 s. 1.3. Decoupling of Solid and Gaseous Phases Beyond all criticism, the methodology originally described in ASTM-E-1321 [12] has shown that independent of the fuel and experimental conditions the linear dependency of with prevails for a wide range of conditions [9, 13-15]. So far there is no complete analysis that shows why this is the case when variables other that the simple thermal model are incorporated. If it is assumed that this functional dependency between external heat flux and time is valid, integration over time shows that time scales with . This dependency can be readily demonstrated if is constant, but showing its validity for a time evolving incident heat flux will be part of the present study. If time can be DX.Y-Z-MM-0100-1 Page 12 of 43 scaled by the squared integral of the incident heat flux, then surface temperature and ignition delay time can be presented as a function of the integral of the heat insult in a single curve that can be used to completely de-couple solid and gas phases in the numerical modelling of the ignition process. The methodology used to demonstrate the dependency of the ignition delay time with the squared integral of the incident heat flux will now be shown. If both sides of Equation (3) are integrated over time, setting the upper integration limit as the time to ignition, (15) the equation becomes (16) Finally, the dependence of the ignition time with the squared integral of the incident energy can be established: (17) In this case, the integral of the incident heat flux is trivial. The following figure shows the scaling of experimental ignition data for PMMA taken from the work of Dakka et al. [14]. Scattering is greater for the lower heat fluxes (i.e. higher ignition times), showing that the magnitude of the surface heat losses compared to the incident heat flux has an effect on the scaling. This will be discussed in more detail in the following sections. DX.Y-Z-MM-0100-1 Page 13 of 43 350 300 Time (s) 250 200 150 100 50 0 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 (Integral q_e)^2 (kJ/m2)^2 Figure Error! No text of specified style in document..4. Scaling of experimental ignition data for PMMA [14]. The scaling was done using Equation (17). In a similar way, the two other analytical solutions are integrated. In both cases the term mt has been taken as . So, for Equation (5) the integral is (18) Then, the time to ignition is expressed as (19) And for Equation (14) the solution is equivalent (following the definition in Equation (10)): (20) For the two previous equations, the heat fluxes are more complex functions of time, but the solutions for both integrals are nevertheless simple. The following table presents the solutions to the integral of the incident heat flux for three cases. DX.Y-Z-MM-0100-1 Page 14 of 43 Table Error! No text of specified style in document.-2. Solution to the time integral of the incident heat flux for the three cases discussed in this report. Thus, if the net heat flux on the surface of the solid as a function of time is known, the integral can be calculated for the elapsed time (i.e. replacing tig by telapsed), and by using the scaling results for the particular material and heating regime (i.e. Figure Error! No text of specified style in document..4 or equivalent), a time to ignition can be calculated. Ignition will be attained when the calculated time to ignition is equal or greater than the elapsed time. An example is provided in Section 1.7 for illustrative purposes. In order to validate the conclusions of this analysis, tests were conducted using ramping heat fluxes. The aim was to compare the different scaling methods applying real cases. The next sections will discuss the experimental procedure and results, to later examine the de-coupling methodologies. 1.4. Experimental Description Three materials, Nylon 6 (PA6), PA6 with ceramic nano fillers, and polymethylmethacrylate (PMMA) were chosen to illustrate the methodology. The materials were tested using the FM Global Fire Propagation Apparatus (FPA) [16]. Piloted ignition tests with in-depth temperature measurements have been carried out on 110 x 110 x 12 mm samples of pure PA6, and of PA6 with nano-composites (Table Error! No text of specified style in document.-3). A sample consists of two 110 x 110 x 6 mm blocks of material bonded together using super glue, with four 2 mm holes drilled from the side at varying depths throughout the sample (Figure Error! No text of specified style in document..5). The specimen is attached to an aluminium block, with heat contact paste applied between the two surfaces to reduce the thermal contact resistance. Type K thermocouples are inserted horizontally through the drilled holes at four depths within the sample and vertically at three depths within the aluminium block (see Figure Error! No text of specified style in document..5). These are connected to a data logger, and temperature readings are taken every second. The specimen is then wrapped with insulation to reduce any effect on the thermocouples of radiation from the sides. Time to ignition is also recorded. Piloted ignition tests were also performed on PMMA samples of dimensions 100 x 100 x 4.9 mm, using a similar methodology. No temperature measurements were carried out. The heat flux ramps ranged from 0.01 to 5.0 kW·m−2·s−1. 36 samples were tested. DX.Y-Z-MM-0100-1 Page 15 of 43 Figure Error! No text of specified style in document..5. Side schematic of the specimen arrangement. The depths of Thermocouples (TCx) for each sample can be found in Table Error! No text of specified style in document.-3. DX.Y-Z-MM-0100-1 Page 16 of 43 Test No. 1 Heat Flux Ramp Thermocouple Depths [kW/m2s] [mm] Material PA6 TC1 = 1.5 TC3 = 6.5 TC2 = 3.1 TC4 = 8.9 TC1 = 1.6 TC3 = 6.0 TC2 = 3.3 TC4 = 9.3 TC1 = 1.9 TC3 = 6.0 TC2 = 3.1 TC4 = 9.0 TC1 = 1.5 TC3 = 6.9 TC2 = 3.2 TC4 = 9.2 TC1 = 2.2 TC3 = 6.9 TC2 = 3.3 TC4 = 9.3 - - 0.1 2 PA6+NC 0.1 3 PA6+NC 0.1 4 PA6+NC 0.2 5 PA6+NC 0.2 6 – 41 PMMA 0.01 – 5.0 Table Error! No text of specified style in document.-3. Experimental conditions. In standard operation, samples tested in the FPA are exposed to constant heat fluxes. Since this study required the samples to be subjected to time-dependent heat fluxes, a MATLAB script was developed to linearly increase the heat flux over time. Figure Error! No text of specified style in document..6 shows ramps that correspond to typical wildland fire heating regimes as the fires approach a target. In all tests, calorimetry was performed; however, for the purpose of this study, only ignition data and in-depth temperature measurements will be presented. DX.Y-Z-MM-0100-1 Page 17 of 43 Figure Error! No text of specified style in document..6. Typical heat flux ramps used during the testing campaign, which are representative of wildland fires. 1.5. Experimental Results and Discussion 1.5.1. Validity of Semi-Infinite Solid Assumption The analytical solutions presented in Section 1.2 are all based on the assumption of a semi-infinite solid behaviour. The in-depth temperature measurements have been used to test the validity of this assumption, thus assessing the applicability of the solutions to the present experimental results. Under ramping incident heat flux conditions, the semi-infinite solid assumption is no longer valid when ignition is attained. The in-depth temperature heating of one sample is presented in Figure Error! No text of specified style in document..7 and Figure Error! No text of specified style in document..8 for two sets of times. It will nevertheless be seen in the following sections that the proposed scaling gives good results, thus it can be inferred that the departure from the semi-infinite solid behaviour is not as considerable. DX.Y-Z-MM-0100-1 Page 18 of 43 Figure Error! No text of specified style in document..7. Initial heating of the sample for PA6. Figure Error! No text of specified style in document..8. Final heating of the sample for PA6, showing the onset of pyrolysis. DX.Y-Z-MM-0100-1 Page 19 of 43 1.5.2. Benchmark Tests for Constant Incident Heat Flux A series of benchmark tests were conducted for a constant heat flux for PA6. The data is presented in Figure Error! No text of specified style in document..9. 0.2 0.18 t_ig^-(1/2) (s^-(1/2)) 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 10 20 30 40 50 60 Incident Heat Flux (kW/m2) Figure Error! No text of specified style in document..9. Ignition delay times as a function of the incident heat flux for PA6. For ease of comparison, the scales are identical to the ones used in Figure Error! No text of specified style in document..10. 1.5.3. Ramping Heat Fluxes Figure Error! No text of specified style in document..10 shows the ignition delay times for the PMMA and PA6 ramping heat flux tests. The heat flux on the abscissa corresponds to the average incident heat flux up to the time of ignition. The observed behaviour is similar to the constant incident heat flux tests. DX.Y-Z-MM-0100-1 Page 20 of 43 0.2 0.18 t_ig^-(1/2) (s^-(1/2)) 0.16 0.14 0.12 0.1 0.08 0.06 0.04 PMMA 0.02 PA6 0 0 10 20 30 40 50 60 Average Incident Heat Flux (kW/m2) Figure Error! No text of specified style in document..10. Ignition delay times as a function of the average incident heat flux (ramping) for PMMA and PA6. However, if the times to ignition are plotted against the total incident energy for both the constant incident heat flux and the ramping incident heat flux cases, it can be seen that both cases follow a trend, as shown in Figure Error! No text of specified style in document..11. This figure shows that for higher heat fluxes and steeper ramps the total energy received by the sample at ignition is less than for lower heat fluxes. Thus, it is not the incident energy but rather the relationship between the net heat flux on the sample and the rate at which that energy is conducted into the sample which controls ignition. In other words, assuming that ignition occurs at a constant temperature, it is the speed at which this temperature is attained that will control the process. DX.Y-Z-MM-0100-1 Page 21 of 43 500 450 400 t_ig (s) 350 300 250 200 150 Ramping 100 Constant 50 0 0 2000 4000 6000 8000 10000 12000 Total Incident Energy (kJ/m2) Figure Error! No text of specified style in document..11. Ignition delay times as a function of the total incident energy for PA6. The results for constant and ramping incident heat fluxes are presented. Because the ramping heat flux tests done for PMMA covered a much wider range than those done for PA6, only the former results will be presented and discussed from this point onwards. Ignition times were plotted against the squared integral of the incident heat flux, for the different analytical solutions presented in this work. Results are shown in Error! Reference source not found. below. The decoupling methodology involves the calculation of the time integral of the net heat flux according to the different scalings discussed previously (Table Error! No text of specified style in document.-2), and the calculated times to ignition will be dependent on the scaling applied. This is demonstrated in Error! Reference source not found., where for a given value of the squared integral of the net heat flux, ignition times present important differences depending on the type of scaling utilized. These differences become less important for the higher values of the ramping heat fluxes. In particular, it is observed that there is no significant difference in the predicted ignition times obtained by the scalings for ramping incident heat fluxes with and without heat losses, which means that for higher heat fluxes, the influence of the surface losses is not important. At less steeper ramps surface heat losses become significant, and the calculated ignition times can present considerable differences. The constant heat flux scaling was carried out for incident heat fluxes corresponding to those at 40% and 60% of the observed ignition time. In the former case, calculated times to ignition will be overestimated. If the constant incident heat flux is set at values above 50% (the latter case), then the ignition times obtained using this method will be DX.Y-Z-MM-0100-1 Page 22 of 43 shorter. For constant incident heat fluxes corresponding to the ramping heat fluxes at 50% of the ignition time, the scaling results match those corresponding to ramping incident heat flux and no losses. This behaviour is easily explained by the fact that for an increase in the incident heat flux, the total amount of incident energy on the surface at the time of ignition decreases (see Figure Error! No text of specified style in document..11). 700 Ignition Time (s) 600 500 400 300 200 Ramping, Surface Losses Ramping, No Surface Losses Constant Heat Flux (40%) Constant Heat Flux (60%) 100 0 0 5 10 15 20 25 Squared Integral of Net Heat Flux (GJ2/m4) 30 35 Figure 1.12. Time to ignition scaling by the squared integral of the incident heat flux, for the different analytical solutions. Results are done for PMMA. The constant heat flux scaling results were carried out for the heat fluxes values corresponding to the irradiance levels of the ramping heat flux at 40% and 60% of the ignition time. The convective coefficient used in the scaling is 25 W·m-2·K-1. 1.6. Effect of Material Thermophysical Properties The effect of material thermophysical properties on the relative magnitude of the incident heat flux and the surface heat losses terms in Equation (9) has been studied. The ratio of the heat losses term to the incident heat flux term was plotted against the surface temperature given by Equation (9) for a ramp of 50 W·m-2·s-1, using properties for several standard building materials [17-20]. Note that the expression in Equation (9) corresponds to an approximation of the analytical expression carried out for small times. Its range of applicability is therefore restricted; see Figure Error! No text of specified style in document..3 for a comparison between this approximation and the exact solution. The results are presented in Figure Error! No text of specified style in document..12. DX.Y-Z-MM-0100-1 Page 23 of 43 0.7 Foam PA6 PE 0.6 Wood PMMA Hardboard Ratio of terms 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 250 300 Surf. Temp. (°C) Figure Error! No text of specified style in document..12. Ratio of the surface heat losses term and the incident heat flux term in Equation (9) as a function of the calculated surface temperature for a ramp of 50 W·m-2·s-1. To calculate the surface temperatures, the same range of times was used in each case, from 10 – 300 s. In the case of Foam, where the value for thermal inertia used was an order of magnitude smaller than the rest of the values, for the given conditions surface temperatures actually started to decrease after 70 s; therefore, the times used ranged from 5 – 60 s. The data was obtained from the following references: Foam [17]; Wood [18]; PA6 [19]; PMMA [20]; PE [20]; Hardboard [17]. This analysis permits testing the validity of performing the scaling using Equation (5), that is without considering the heat losses. For cases of low thermal inertia, as can be seen in Figure Error! No text of specified style in document..12, the term corresponding to surface losses attains significant values compared to the incident heat flux term, thus rendering the assumption of no surface losses invalid. For materials with higher values of thermal inertia this assumption becomes valid, and it will be shown in the next section that for a material with an average thermal inertia, the errors incurred when using this assumption are negligible. 1.7. Example of the use of the decoupling methodology The following example is provided in order to give a more detailed description of the methodology that is proposed in this work. The example is done for PMMA subjected to a ramping incident heat flux. Using experimental ignition data, the scaling is carried out in order to obtain a graph relating the time to ignition to the square of the integral of the incident heat flux. This graph is shown in Error! Reference source not found.. A curve fit is then performed on the data to obtain an expression for that relationship (depending on the scaling employed, the relationship can be linear or of a higher order; see Error! Reference source not found.). DX.Y-Z-MM-0100-1 Page 24 of 43 The time to ignition is calculated by computing the squared integral of the incident heat flux up to the elapsed time, and using the aforementioned expression to obtain a value for an ignition time. The proposed scaling implies that the ignition time at a given incident heat flux (be it ramping or constant) is proportional to the square of the integral of the incident heat flux evaluated between time zero and the time to ignition. This means that ignition will be attained once the calculated time is equal to the elapsed time. Error! Reference source not found. displays the evolution of the calculated times to ignition to the elapsed time. Thus, every ramp will have its own distinct curve for the calculated ignition time. The computed times to ignition compare well with the experimental times to ignition. As was stated before, the difference in the predicted ignition times for the scaling considering surface heat losses as opposed to the scaling without surface losses will depend on the material thermophysical properties. Table Error! No text of specified style in document.-4 shows the differences in ignition times obtained for both cases. Only at very low ramp values the difference becomes appreciable, but these cases can be considered as impractical for fire applications. Figure Error! No text of specified style in document..13 presents the comparison of the ignition times obtained using both scalings for a ramp of 15 W·m-2·s-1. Calculated Ignition Time (s) 700 600 500 400 30.00 (W/m2s) 50.00 (W/m2s) 300 150.00 (W/m2s) 600.00 (W/m2s) 200 100 0 0 100 200 300 400 500 600 700 Elapsed Time (s) Figure 1.14. Calculated ignition time as a function of the elapsed time, for different values of the heat flux ramp. The blue line corresponds to ignition times equal to elapsed times, therefore the intersect of the calculated ignition times for each particular ramp with the blue line will determine the time to ignition. DX.Y-Z-MM-0100-1 Page 25 of 43 Calculated Ignition Time (s) 1200 1000 800 Surface Losses 600 No Losses 400 200 0 0 200 400 600 800 1000 1200 Elapsed Time (s) Figure Error! No text of specified style in document..13. Comparison of the results obtained for the scalings with and without considering surface heat losses. The ramp used in this example is of 15 W·m-2 ·s-1. The blue line corresponds to ignition times equal to elapsed times, therefore the intersect of the calculated ignition times for each particular ramp with the blue line will determine the time to ignition. Table Error! No text of specified style in document.-4. Calculated ignition times for both scalings. The error was calculated using the surface losses case as the base value. 1.8. Concluding Remarks Forest fire models must resolve different phenomena occurring at a wide range of time and length scales, and the application of simplifications to certain events can greatly improve their computational efficiency. The decoupling of the solid and gas phases greatly reduces the computational effort in these models. This decoupling can be readily accomplished using standard analytical solutions for the ignition time, but in some cases like approaching fires in the WUI these solutions are not realistic in terms of boundary conditions. The proposed decoupling methodology aims at providing a more realistic DX.Y-Z-MM-0100-1 Page 26 of 43 approach by considering an incident heat flux linearly growing with time. This methodology incorporates a novel analytical solution for the ignition of solid samples exposed to ramping incident heat fluxes and convective cooling at the exposed surface. This method has been validated for constant and time-varying incident heat fluxes, and has been shown to be accurate. It is recommended that materials with low thermal inertia incorporate the scaling that considers surface heat losses, while it has been shown that materials with higher values of thermal inertia can use the scaling without surface losses. The authors believe this method will prove to be a useful tool in fire modelling, where there is a growing need to model more complex situations, such as those that can be encountered in the wildland-urban interfaces. This contribution will be particularly useful in the scope of the Fire Paradox project, where numerous attempts in forest fire modelling have been proposed. In particular, it is expected to incorporate these results in the work carried out by VTT on W-FDS. In terms of future work, in order for this methodology to be used in real applications, a database of ignition tests of different materials should be compiled. An obvious first choice would be doing the testing on wood, and perhaps study the applicability of the model to predict the ignition of live trees. 1.9. References 1. Torero, J.L., “Flaming Ignition of Solid Fuels”, in: SFPE Handbook of Fire Protection Engineering, 4th Edition, Society of Fire Protection Engineers, 2009. 2. Sullivan, A., “A Review of Wildland Fire Spread Modelling, 1990-Present, 1: Physical and Quasi-Physical Models”, arXiv:0706.3074v1[physics.geo-ph] (2007). 3. Novozhilov, V., “Computational Fluid Dynamics Modeling of Compartment Fires”, Progress in Energy and Combustion Science 27:611–666 (2001). 4. Manzello, S. L., Park, S. H., Cleary, T. G., Shields, J. R, “Developing Rapid Response Instrumentation Packages to Quantify Structure Ignition Mechanisms in WildlandUrban Interface (WUI) Fires”, Fire and Materials 2009. 11th International Conference Proceedings, San Francisco, CA, 2009, pp. 215–224. 5. Rehm, R., “Effects of Winds from Burning Structures on Ground-Fire Propagation at the Wildland-Urban Interface. Final Report”, NIST GCR 06-892, National Institute of Standards and Technology (2006). 6. Cohen, J.D., “Relating flame radiation to home ignition using modeling and experimental crown fires”, Can. J. For. Res. 34:1616–1626 (2004). 7. Quintiere, J., “A Simplified Theory for Generalizing Results from a Radiant Panel Rate of Flame Spread Apparatus”, Fire and Materials 5:52–60 (1981). 8. Lawson, D.I. and Simms D.L., “Reply to Ignition of Wood by Radiation”, British Journal of Applied Physics, 3:394–396 (1952). 9. Quintiere, J., Fundamentals of Fire Phenomena, John Wiley & Sons, Chichester, 2006. 10. Long, R., Torero, J.L., Quintiere, J., Fernandez-Pello, C., “Scale and Transport Considerations on Piloted Ignition of PMMA”, Fire Safety Science, Proceedings 6th International Symposium, Poitiers, France, 2000, pp. 567–578. DX.Y-Z-MM-0100-1 Page 27 of 43 11. Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford University Press, London, 1959. 12. Standard test Method for Determining Material Ignition and Flame Spread Properties, ASTM-E-1321-90, ASTM, Philadelphia, 1990 13. Atreya, A., “Ignition of Fires”, Philosophical Transactions Royal Society London A 356:2787–2813 (1998). 14. Dakka, S., Jackson, G. and Torero, J.L., “Mechanisms Controlling the Degradation of Poly(Methylmethacrylate) Prior to Piloted Ignition”, Proceedings of the Combustion Institute 29: 281–287 (2002). 15. Boonmee, N. and Quintiere, J.G., “Glowing and flaming autoignition of wood”, Proceedings of the Combustion Institute 29: 289–296 (2002). 16. “ASTM E2058-03 Standard Test Method for Measurement of Synthetic Polymer Material Flammability Using a Fire Propagation Apparatus”, ASTM International, West Conshohocken (2003). 17. Quintiere, J., “Surface Flame Spread”, in: SFPE Handbook of Fire Protection Engineering, 3rd Edition, Society of Fire Protection Engineers, 2002. 18. Reszka, P., “In-Depth Temperature Profiles in Pyrolyzing Wood”, PhD Thesis, The University of Edinburgh, 2008. http://hdl.handle.net/1842/2602 19. 19. Steinhaus, T., “Determination of Intrinsic Material Flammability Properties from Material Tests Assisted by Numerical Modelling”, PhD Thesis, The University of Edinburgh, 2009. 20. Tewarson, A., “Generation of Heat and Chemical Compounds in Fires”, in: SFPE Handbook of Fire Protection Engineering, 3rd Edition, Society of Fire Protection Engineers, 2002. DX.Y-Z-MM-0100-1 Page 28 of 43 2. Criteria for the assessment of wildland fire effect on burn injuries: Model description and experimental results. 2.1. Introduction This report is concerned with the development of a numerical model for the assessment of burn injuries affecting fire fighters. For a more detailed discussion on the mechanisms of burn injuries and the state of the art of burn injury prediction and modelling of skin when subjected to heat, please refer to the literature review in IR 2.5-3. A description of the model developed to assess the influence of an impermeable membrane in the degree of burning and a comparison with experimental results is also presented here. Burn injuries when fighting fires are common [1]. Protective fireman clothing is indeed effective in the prevention of burns, but the design requirements and testing procedures do not address all the potential modes of occurrence of burn injuries, and thus protective garments fail in some scenarios. Protective gear can normally fail in three modes during a fire. The first mode is direct impingement from flames or exposure to high heat fluxes for times longer than a critical period of time; a second type of failure occurs when the clothing is compressed, because the fabric significantly reduces its thermal resistance [2], thus increasing the heat flowing from the hot exterior to the skin. This type of injury is caused by direct contact with hot solids or when the fireman kneels or crawls. Finally, steam passing through the clothes and getting into contact with the skin can also cause scalding. For this reason, moisture barriers are included in the protective fabrics [3]. In summary, studies on fire fighter gear have shown that the performance of protective clothing is affected dramatically by three different variables, the structure of the material (thermal properties), the compression level and the water content. The first variable is a design parameter but the other two cannot be specified since they are related to usage. The models developed to predict burn injuries have dealt with the protective clothing as an external boundary condition [4]. The boundary condition imposed on the skin model is normally a heat flux at the inner side of the layer. Although there is general recognition that water transport and latent heat play a significant role in the establishment of a burn injury and in the properties of the protective gear, currently no model exists that incorporates the interaction of the skin with the protective barrier through the transport of water. Water will not only be present as the steam coming from the exterior of the protective barrier, it will also be present in condensed and gaseous phase within the barrier, as a result of perspiration. Water migration from the interior of the barrier can constitute an important mechanism through which heat can be transferred away from the skin, thus being beneficial in terms of the thermal damage to the skin. Thus, the presence of a moisture barrier in the protective layer will prevent this migration. The aim of this study is to analyze the effect of the moisture barrier in the heat insult to the skin. For this reason, a series of simple tests have been performed on water- soaked polyurethane foam exposed to different heat fluxes with and without the presence of an DX.Y-Z-MM-0100-1 Page 29 of 43 impermeable layer. The experimental results were compared to the results of a onedimensional heat transfer model, which includes the migration of water and the presence of the moisture barrier. 2.2. Experimental Procedure Polyurethane foam samples were exposed to a range of incident heat fluxes with two different vapour transfer boundary conditions: an open and impermeable. The test results provided temperature histories at various depths in the simulated skin samples. These temperature histories allow for simple comparison with modelling results. The samples were 100 x 100 x 40 mm blocks of open cell, high porous texture, flexible, non- flame retarded polyurethane foam. Each specimen was placed in a Cone Calorimeter-type sample holder [5], sealed with an unbroken layer of aluminium foil to prevent water escaping through the joint of the base and cover of the holder. The moisture barrier used in the experiments to generate an impermeable moisture boundary condition was a copper plate. The plate was painted black in order to create a definite thermal boundary condition minimizing radiant reflection. The samples were heated using a cone-heating element. The imposed heat flux on the samples ranged from 0 – 20 kW·m-2. Type K thermocouples with 0.25 mm wire diameter were used. Six thermocouples were used in each test, one located 10mm above the surface of the sample and the remaining five were inserted at 5 and 10 mm intervals along the centreline of the sample, starting at 5mm down into sample. The thermocouples were labelled 1 to 6, with thermocouple no. 6 being the one at the surface of the sample and thermocouple no. 1 at the lowest point in the sample. The thermocouple layout is shown in detail on Figure Error! No text of specified style in document..14. 6 5 4 3 1 2 Figure Error! No text of specified style in document..14 Sample thermocouple layout Each hole in the foam specimen was carefully made with a 0.25 mm hole punch. The thermocouples were the inserted to a depth of 50 mm, the centreline of the sample. The sample was inserted into the sample holder and then saturated with approximately DX.Y-Z-MM-0100-1 Page 30 of 43 200 ml of cold water. The initial specimen mass was recorded using an electronic scale. The moisture barrier was put in place before the initial mass was recorded. The selected incident heat fluxes were 3.0, 5.8, 9.8 and 17 kW·m-2, which corresponded to cone heater temperatures of 400, 500, 600 and 700° C respectively. Each experimental condition – incident heat flux and water migration boundary condition – was repeated four times. Temperature (°C) Heat Flux (kW · m-2) 400 3.0 500 5.8 600 9.8 700 17.0 Table Error! No text of specified style in document.-5 Correlation between heater temperature and incident heat flux on the sample. 2.3. Experimental Results The experiments showed good repeatability. As a sample, the following figure presents the results for all four repetitions for thermocouple 5 (closest to the surface) for an external heat flux of 5.8 kW·m-2, with no barrier. DX.Y-Z-MM-0100-1 Page 31 of 43 Comparison of Thermocouple 5 For Each Experiment 120 110 100 90 80 500-1 Temp 70 500-2 60 500-3 500-4 50 Average 40 30 20 10 0 0 500 1000 1500 2000 2500 Time Figure Error! No text of specified style in document..15 Temperature histories for thermocouple #5 (closest to the surface), for an incident heat flux of 5.8 kW·m-2, with no moisture barrier. The average curve is also shown, in red. The first and most noticeable stage corresponds to the preheating stage and took place during the first 500 seconds of the experiments. As the water-saturated sample continued to be heated, water began to migrate freely through the sample. At approximately 1600 seconds into the experiment it was clear that the upper part of the foam had become distinctively dryer than the rest of the sample as the surface began to char slightly, as can be seen in the following figure. DX.Y-Z-MM-0100-1 Page 32 of 43 Figure Error! No text of specified style in document..16 Surface of a foam specimen after 1600 s for an incident heat flux of 5.8 kW·m-2, with no moisture barrier. The effect of the boundary conditions on the temperature histories is clear. Precluding moisture migration from the front face of the specimen will yield higher temperatures in the interior of the foam sample. Moisture migration represents an important source of heat loss from the sample, which helps lower the in-depth temperatures. The comparison of the temperature histories for thermocouple #5, for experiments with and without the presence of the moisture barrier is presented in Figure 1.4. In terms of mass loss, specimens with free moisture migration lose water at higher rates than those with an impermeable barrier. DX.Y-Z-MM-0100-1 Page 33 of 43 Thermocouple No. 5 120 110 100 90 o Temperature ( C) 80 70 500 - No Plate 60 500 - Plate 50 40 30 20 10 0 0 500 1000 1500 2000 2500 Time (seconds) Figure Error! No text of specified style in document..17 Comparison of averaged temperature histories for thermocouple # 5 (closest to the surface), for an incident heat flux of 5.8 kW·m-2;the red curve corresponds to the experiments with a moisture barrier and the blue curve to experiments without any barrier. Figure 1.5 shows the results for thermocouple #5 at various incident heat fluxes and with a permeable boundary condition. Temperature histories vary as expected with the varying heat fluxes. Only in the higher heat fluxes temperatures get close to the water boiling point, but a clear temperature plateau indicating the change of phase is not observed, which indicates that the water mass loss process is mainly by migration and evaporation at the surface. Temperature histories for tests with the moisture barrier in place show faster heating regimes, and an indication that, for the higher heat fluxes, a change of phase is attained, as presented in Figure 1.6. DX.Y-Z-MM-0100-1 Page 34 of 43 TC5 120 400 - No Plate 110 500 - No Plate Benchmark 600 - No Plate 100 700 - No Plate 90 o Temperature C 80 70 60 50 40 30 20 10 0 0 500 1000 1500 2000 2500 Time (sec) Figure Error! No text of specified style in document..18 Comparison of averaged temperature histories for thermocouple # 5 (closest to the surface), for incident heat fluxes of 3.0, 5.8, 9.8 and 17.0 kW·m-2; all the experiments were carried out without a moisture barrier. TC5 120 400 - Plate 110 500 - Plate Benchmark 600 - Plate 100 700 - Plate 90 o Temperature C 80 70 60 50 40 30 20 10 0 0 500 1000 1500 2000 2500 Time (seconds) Figure Error! No text of specified style in document..19 Comparison of averaged temperature histories for thermocouple # 5 (closest to the surface), for incident DX.Y-Z-MM-0100-1 Page 35 of 43 heat fluxes of 3.0, 5.8, 9.8 and 17.0 kW·m-2; all the experiments were carried out with a moisture barrier. The thermal penetration depth is greater for the tests with the moisture barrier, as shown in Figure 1.7 and 1.8. This implies that the thermal damage to the skin will be deeper when the boundary condition at the skin surface prevents an adequate moisture migration. 70 60 Temperature (°C) 50 TC 1 40 TC 2 TC 3 TC 4 30 TC 5 20 10 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time (s) Figure Error! No text of specified style in document..20 Comparison of averaged temperature histories at various depths for an incident heat flux of 5.8 kW·m-2, and no moisture barrier. 120 100 Temperature (°C) 80 TC 1 TC 2 60 TC 3 TC 4 , TC 5 40 20 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time (s) DX.Y-Z-MM-0100-1 Page 36 of 43 Figure Error! No text of specified style in document..21 Comparison of averaged temperature histories at various depths for an incident heat flux of 5.8 kW·m-2, and with moisture barrier. DX.Y-Z-MM-0100-1 Page 37 of 43 2.4. Modelling It has been recognized that the effect of moisture migration on the severity of skin burns plays an important role, and therefore it becomes important to model this process in an accurate way. Modelling the behaviour of the foam samples subjected to heat fluxes representative of those encountered in skin burn accidents with and without the presence of a moisture barrier is a first step in the development of a mathematical model of human skin. As an initial approximation, the model has only included heat and moisture transfer, but has not taken into account any chemical or physical changes on the foam matrix. The model treats the foam specimen as one-dimensional. The model considers three species, foam, liquid water and vapour. The physical phenomena included are rise in control volume sensible heat, conduction, gas convection, and water evaporation. No movement of liquid water or diffusive mass transfer was modelled. These effects are however deemed to be of little importance to the results [6, 7]. The porosity of the foam matrix is given by , and water is considered to be located inside the pores. The energy equation is presented below. (1) Mass conservation is done for water and vapour. Moisture evaporation was modelled as a first order Arrhenius expression. (2) Initial conditions are as follows: (3) At the boundaries, radiative and convective losses from the surface are considered. DX.Y-Z-MM-0100-1 Page 38 of 43 (4) Pressure is calculated by doing a mass conservation equation for vapour and, by assuming ideal gas behaviour, getting an expression for the pressure in terms of the total vapour mass concentration, as shown in Equation (5). The flow of vapour was then calculated using Darcy’s law. (5) The model was solved using the method developed by Crank, Nicolson, Bamford and Malan [8, 9], as formulated by Kung [10]. The temperature for the next time step is assumed to be equal to the temperature at the present time, and with that, new values for densities, solid and gas phase volumes, porosities, permeability, pressure, velocity, effective thermal conductivity, mass fluxes, enthalpies and boundary conditions are calculated. The energy equation is then solved using the updated parameters. With the new temperatures, the previous parameters are calculated again, and after that the energy equation is solved. This loop is repeated until the temperatures converge to a given tolerance value. A Matlab code was developed for the solution of the set of equations. 2.5. Numerical Results The model was compared with two experimental results, namely those for incident heat fluxes of 5.8 and 9.8 kW·m-2. The results are satisfactory, showing close agreement between the measured and predicted results, especially for the time scale of skin burns, which is of the order of minutes. Some numerical instabilities were observed for the case with the presence of the moisture barrier, which is believed to be caused by the solution algorithm. Specifically, the way the vapour velocities are calculated should be reviewed (see Equation (5) above). DX.Y-Z-MM-0100-1 Page 39 of 43 350 340 Temp (K) 330 Model 5 mm 320 Thermocouple 5 Thermocouple 4 310 Model 10 mm 300 290 0 100 200 300 400 500 600 Time (s) Figure Error! No text of specified style in document..22 Comparison of numerical and experimental results at depths of 5 and 10 mm from the exposed surface for an incident heat flux of 5.8 kW·m-2, without moisture barrier. 350 340 Temp (K) 330 Model 5 mm Model 10 mm 320 Thermocouple 5 Thermocouple 4 310 300 290 0 100 200 300 400 500 600 Time (s) Figure Error! No text of specified style in document..23 Comparison of numerical and experimental results at depths of 5 and 10 mm from the exposed surface for an incident heat flux of 5.8 kW·m-2, with moisture barrier. Note that the thermocouple reading for a 10 mm depth shows higher temperatures than the thermocouple located at a 5 mm depth, which can be attributed to experimental error. DX.Y-Z-MM-0100-1 Page 40 of 43 370 360 350 340 Model 5 mm Model 10 mm 330 Thermocouple 5 320 Thermocouple 4 310 300 290 0 100 200 300 400 500 600 Figure Error! No text of specified style in document..24 Comparison of numerical and experimental results at depths of 5 and 10 mm from the exposed surface for an incident heat flux of 9.8 kW·m-2, without moisture barrier. The differences between the model predictions and the experimental results can be due to misplacement of the thermocouple. 370 360 350 340 Model 5 mm Model 10 mm 330 Thermocouple 5 320 Thermocouple 4 310 300 290 0 100 200 300 400 500 600 Figure Error! No text of specified style in document..25 Comparison of numerical and experimental results at depths of 5 and 10 mm from the exposed surface for an incident heat flux of 9.8 kW·m-2, with moisture barrier. Note that the differences for the 10 mm depth thermocouple can be attributed to experimental error. DX.Y-Z-MM-0100-1 Page 41 of 43 2.6. Conclusions It has been shown that the transport of moisture can be a significant factor affecting the severity of skin burns on fire fighters. Thus, if water is allowed to freely exit the skin, the penetration of the heat wave is going to be less important, and the consequent burn less severe. This information can serve as the basis for research on the development of new protective clothes and on the physiology of skin burns. On a shorter timescale, this information can be passed on to fire fighters for them to apply the conclusions and protect the men on the field. 2.7. hfg Nomenclature 2.8. References surface absorptivity latent heat of vaporization (J·kg−1) surface emissivity reaction rate (kg·m−3·s−1) porosity h specific enthalpy (J·kg−1) hc convective heat transfer coefficient (W·m−2·K−1) k thermal conductivity (W·m−1·K−1) K reaction rate coefficient (s−1) L total depth of sample (m) p pressure (N·m−2) density (kg·m−3) R Universal Gas Constant (J·mol−1·K−1) T time (s) T temperature (K) Stefan-Boltzmann constant (5,67x10−8 W·m−2·K−4) u gas velocity (m·s−1) x depth dimension (m) Subscripts f foam vap vapour wat water 1. 2. 3. Karter Jr., M. J. and LeBlanc, P.R., “1996:U.S. Fire Fighter Injuries,” NFPA Journal, November/December, 1997. Lawson, J.R., Twilley, W.H. and Malley, K.S., “Development of a Dynamic Compression Test Apparatus for Measuring the Thermal Performance of Fire Fighters’ Protective Clothing,” NISTIR-6502, National Institute of Standards and Technology, Gaithersburg, Maryland, 2000. NFPA 1971 – “Protective Ensemble for Structural Fire Fighting,” National Fire Codes, 1999. DX.Y-Z-MM-0100-1 Page 42 of 43 4. 5. IR D2.5-3 ISO 5660-1:1993 – “Fire Tests Reaction to Fire Part 1: Rate of Heat Release from Building Products (Cone Calorimeter Method)”, International Organization for Standardization, 1993. 6. Atreya, A., “Pyrolysis, Ignition and Fire Spread on Horizontal Surfaces of Wood”, PhD thesis, Harvard University, 1983. 7. Di Blasi, C., ‘Analysis of Convection and Secondary Reaction Effects Within Porous Solid Fuels Undergoing Pyrolysis’, Combustion Science and Technology 90, 315– 340, 1993. 8. Bamford, C., Crank, J. & Malan, D., ‘The Combustion of Wood. Part 1’, Proc. Cambridge Philosophical Society 42, 166–182, 1946. 9. Crank, J. & Nicolson, P., ‘A Practical Solution for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat-Conduction Type’, Proceedings of the Cambridge Philosophical Society 43, 50–67, 1947. 10. Kung, H., ‘A Mathematical Model of Wood Pyrolysis’, Combustion and Flame 18, 185–195, 1972. DX.Y-Z-MM-0100-1 Page 43 of 43