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Combustion of forest litters under slope conditions: Burning rate, heat release rate, convective and radiant fractions for different loads
Combustion and Flame 161 (2014) 3237–3248
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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Combustion of forest litters under slope conditions: Burning rate, heat release rate, convective and radiant fractions for different loads Virginie Tihay ⇑, Frédéric Morandini, Paul-Antoine Santoni, Yolanda Perez-Ramirez, Toussaint Barboni SPE – UMR 6134 CNRS, University of Corsica, Campus Grimaldi, BP 52, 20250 Corte, France
a r t i c l e
i n f o
Article history: Received 4 June 2013 Received in revised form 10 October 2013 Accepted 4 June 2014 Available online 8 July 2014 Keywords: Flame spread Slope Heat release rate Radiant and convective fractions Burnt surface variation
a b s t r a c t A set of experiments at laboratory scale was conducted to study the combustion of forest fuel beds in order to quantify the contribution of radiant and convective heat transfer under slope condition. To proceed, a Large Scale Heat Release apparatus was used to measure the heat release rate and fire properties such as the mass loss rate, the geometry of the fire front and the heat transfer were assessed. Because of the slope and the size of the fuel bed, the mass loss rate and the heat release rate do not reach a quasisteady state when the propagation takes place under slope condition. This is due to a V-shape distortion of the fire front, which leads to an increase of the burnt surface rate by the fire over time. The study of this quantity has shown that the heat release over time can be estimated with the fuel load and the time derivative of the burnt surface. The fractions of radiation and convection released by the fire in its environment were calculated. Under a slope of 20°, the convective fraction decreases from 74.9% to 61.1% whereas the overall radiant fraction ranges between 25.1% and 38.9% and increases with increasing fuel loads. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Each year, fires devastate forests from all continents causing casualties and irreparable environmental damages. Determining the parameters that control the spread of wildfires is therefore a major objective for the management and the prevention of these fires. Over the last decades, modeling has been increasingly used for forest management [1], for risk mapping [2] and for studying the fire propagation [3]. However, to implement and test these models, it is necessary to have experimental data that increase the understanding of the phenomena. The effects of slope, wind and vegetation properties on fire behavior have been extensively investigated at laboratory and field scale. In most studies, the researchers have focused on the rate of spread [4–11], the flame geometry [4,9,12], the temperature profile [4,9,11] or the fuel consumption and mass loss [4,7,11]. However, these parameters are not sufficient to completely understand the fire behavior. Increased understanding about the relative roles of radiant and convective heating in fire spread and energy release are essential needs in wildland fire science. In the literature, the radiant fraction has been mainly determined in works devoted to assess the thermal radiation incident ⇑ Corresponding author. Fax: +33 495 450 162. E-mail address: [email protected] (V. Tihay).
upon a target [13]. The point source model has been the method most commonly used. This method relies on the hypothesis that the radiant heat flux emitted by the flames is spherically isotropic [13,14]:
qR ¼
HRRrad cos h 4 p R2
ð1Þ
where qR is the radiant heat flux density, h is the angle between the normal to the target and the line of sight from the target to the point source location, R is the distance between the point source and the target. HRRrad is the radiant power given by the radiant fraction vrad times the heat release rate. This method has been widely applied for the study of liquid hydrocarbon pool fires and for hydrocarbon jet flames [13]. Tihay et al. [15] used also this approach to calculate the radiant fraction of laminar flames obtained from the burning of the vegetative fuels. The obtained values of the radiant fraction varied between 20% and 27%. Kremens et al. [16] conducted also experiments in 8 8 m outdoor plots using preconditioned wildland fuels characteristic of mixed-oak forests. With a two-band infrared radiometer, they studied the radiant power of a fire and found a radiant fraction of 17%. However, the point source model approach is only accurate in the far-field. For measurement at distances within a few fire diameters, this method becomes inadequate because it assumes that all of the radiant energy from the fire is emitted at a single point
http://dx.doi.org/10.1016/j.combustflame.2014.06.003 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
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Nomenclature A a
cross sectional area of the exhaust duct (m2) parameter equals to M_ pdU ðm1 Þ C
Aburnt cp,mix d D
area burnt by the fire front (m2) specific heat of the mixture (J/kg K) duct diameter (0.4 m) distance between the heat flux gauge and the fire front (m) distance covered by the head of the fire front (m) heat release per unit mass of O2 consumed (J/kg) view factor (–) fuel height (m) net heat of combustion (J/kg) effective heat of combustion (J/kg) heat release rate (W) partial derivative of the temperature versus time (K/s) extinction coefficient (m1) constant determined via a propane burner calibration (–) constant of the bi-directional probe (–) length of the fire front (m) distance between the duct entry and thermocouple TK (m) length of the part of the fire front where the flames were the highest (m) flame length (m) flame thickness (m) mass of the fuel (kg) mass flow rate of the chemical compounds–air mixture (kg/s) mass loss rate (kg/s) number of moles (mol) molar flow rates of O2 in incoming air (mol/s) molar flow rates of O2 in the exhaust duct (mol/s) radiant power (W) radiant heat flux density (W/m2) distance between the point source and the target radiant heat flux gauge (–) Rate of spread (m/s) emission surface (m2) total exposed surface area of the material (m2) overall heat transmission coefficient of the duct (W/ m2 K) time (s) temperature (K) total heat flux gauge (–) total heat release (J)
mix p;mix
Dhead E F h Hc,net Heff HRR K Km kt kp L l Lh Lf Lthick m _ mix M MLR n n_ O2 n_ O2 Prad q R RG ROS S Sexp U t T TG THR
rather than distributed over the fire. Conversely, in these situations, the solid flame model can be employed to overcome the inaccuracy of the point source model [13]. This model considers that the flame has an idealized geometrical shape and emits radiant energy uniformly throughout its surface. The thermal radiant heat flux received by an element outside the flame envelope is given by the expression:
qR ¼ F E s
ð2Þ
where F is a geometric view factor, s factor and E is the radiant emittance of flame surface given by E = e r T4 where T is the temperature of the fire, e the emissivity and r the Stefan–Boltzmann constant. As for the point source model, the solid flame model has been mainly used to study the thermal radiation of pool fires and jet fires [13,17,18]. The main difficulty of this approach is the determination of the emissivity and flame temperature.
TK v V_ w W x X
thermocouple in the exhaust duct (–) gas velocity (m/s) standard flow rate in the exhaust duct (m3/s) fuel load (kg/m2) molecular weight (kg/mol) abscissa (m) mole fraction (–)
Greek symbols a expansion factor for the fraction of the air that was depleted of its oxygen (–) b flame angle (°) d angle of the fire front (°) e emissivity (–) DP pressure drop across the bi-directional probe (Pa) DAburnt variation of the area burnt by the fire front (m2) / oxygen depletion factor (–) U heat flux density (W/m2) c slope angle (°) g fuel consumption efficiency (–) q0 density of dry air at 298 K and 1 atm (kg/m3) h angle between the normal to the target and the line of sight from the target to the point source location vconv convective fraction (–) vrad radiant fraction (–) vT sum of the convective and radiant fractions (–) Subscript 0 a air CO2 conv em fl flank g head O2 rad RG tot
initial value ambient air carbon dioxide convective embers flame flank of the fire front gas head of the fire front oxygen radiant radiant heat flux gauge total
Superscript ° incoming air a ambient
Another approach to obtain the radiant heat release rate emitted by the fire is the integration of the measured spatial distribution of radiant flux. This method necessitates several radiometers positioned radially and vertically over a cylindrical control surface surrounding the fire. This method has been especially used for the study of pool fires [19,20] and jet flames of hydrocarbons [21,22]. More recently, several works focused on the determination of the fire radiative energy. For this, a new approach based on the works of Kaufman et al. [23] and Wooster et al. [24] has emerged in the field of biomass fires. This new method determines the fire radiative energy (FRE) by the analysis of fire pixel radiances in the middle infrared spectral region. Freeborn et al. [25] conducted 44 small-scale experimental fires in a combustion chamber by using ponderosa pine needles, Douglas fir twigs and foliage. With two MIR thermal imaging systems, they measured the fire radiative energy and obtained a radiant fraction of 12.4% based on the
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higher heating values of the forest fuels. This method has been criticized by Kremens et al. [16], who indicated the difficulty to determine the total infrared flux accurately by knowing only the sensor-reaching radiance in a single narrow waveband. In the work of Frankman et al. [26], radiant and convective heat fluxes were measured for 13 natural and prescribed wildland fires under a variety of fuel and ambient conditions. From these data, they determined the fraction of the combustion time during which the sensor shows convective heating or cooling. In addition, the fire radiative energy and the fire convective energy were calculated by integrating the measured convective and radiant heat fluxes. The results indicate that the relative contribution of convection and radiation to total energy release is dependent on fuel and environment. Global convection contribution in mixed heat transfer problems can be assessed by the determination of the convective heat release HRRconv. In literature, the convective heat release rate has been generally determined from the gas temperature rise (GTR) calorimetry, by using the following relationship [27]:
HRRconv ¼
Mmix cp;mix _ ðT g T a Þ Sexp
ð3Þ
where cp,mix is the specific heat of the combustion product–air mix_ mix is the total mass flow rate of the ture at the gas temperature, M fire product–air mixture, Tg is the gas temperature, T a is the ambient temperature and Sexp is the total exposed surface area of the material. Freeborn et al. [25] used this method to complete their work on the energy release of biomass fires. They found a convective fraction equal to 52% (based on the higher heating value). Tewarson [27] used also this method to measure the convective heat release rates of various fuels and under different ventilation conditions. As an ASTM E2058 fire propagation apparatus was employed for this study, the heat release rate (HRR) was recorded during the experiments. In systems where heat losses are negligibly small, the heat release rate of a fire consists of a convective and a radiant component. Tewarson [27] deduced from these data the radiant power HRRrad, by using the following relationship:
HRRrad ¼ HRR HRRconv
ð4Þ
The results indicate that the chemical, convective and radiant heat release rates depend on the chemical structures of the materials and fire ventilation. Among the fuels tested, Tewarson reported values for well-ventilated fires of pine wood. For this fuel, a convective fraction of 70.2% was obtained, which leads to a radiant fraction equal to 29.8%. The state of art of these calculation methods points out two main drawbacks. First, these methods calculate only one fraction: either the radiant fraction or the convective fraction. The second one is often derived. Secondly, when the HRR is not measured, there is a considerable uncertainty regarding the quantification of the total heat released during the fire. The heat release rate is commonly assumed to be equal to the product between the mass loss rate and the higher heating values, which leads to potential error in the determination of combustion efficiency of the fire. The knowledge of the HRR is therefore essential. This quantity is not only important to study the heat source but can be also used to classify vegetation, understand the role of transport in porous fuel beds [28] or propose a relationship between line fire intensity and flame length [29]. Given the importance of HRR, we have already performed several studies to measure this quantity and bring better understanding of fire spread behavior under no slope condition. The first one was dedicated to the development of a method based on oxygen consumption calorimetry (OCC) to measure the fireline intensity for spreading fire experiments [30]. A second study was devoted to the evaluation of the fireline intensity
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based on the mass burning rate [31]. A third work concerned the characterization of fires spreading under no slope condition from a point of view of heat release and radiant and convective fractions [32]. Recently, a preliminary study to this work was conducted to investigate the effect of slope on the rate of spread, the heat release rate and the combustion efficiency [33]. As another step of our study, we propose in the present paper to discriminate both radiation and convection that are globally released during fires spreading across pine needles beds under slope condition and for different fuel loads at laboratory scale. To this end, a Large Scale Heat Release (LSHR) apparatus was used to obtain the HRR and the convective power. This article is divided into two main parts. First, an image processing method was used not only to study the geometry of the flame, but also to monitor the surface burnt by the fire during the propagation. These data, taken in conjunction with the heat release rate and heat flux measurements, helped to explain the differences observed between experiments performed under slope and no slope conditions. The second part of the study was devoted to the quantification of radiation and convection during the spread. For this, we calculated the convective fraction from the temperature measured in the exhaust duct, and we derived the overall radiant fraction from these results. Then, a solid flame model was applied to calculate the radiant fraction due to the flame and the radiant fraction due to embers was deduced from these data. The work reported here is from a small unconfined fuel bed that is not intended to simulate a wide fire front. However, some of the results may have application to fires in pine needles in general.
2. Experimental 2.1. Experimental device The fire spread experiments were conducted by using a 1 MW Large Scale Heat Release (LSHR) apparatus. Fire tests were performed on a 2 m long and 2 m wide combustion table with an inclination of 20°. This angle was chosen for two reasons. Firstly, it allowed us to observe a change in fire behavior compared to experiments under no slope conditions. This observation was not visible for angles less than 20°. Moreover, given the length of the combustion table, this angle prevented the flames from impacting the hood. The device was located under a 3 m 3 m hood with a smoke extraction system having a nominal volumetric flow rate of 1 m3/s (Fig. 1). The bench was placed on a load cell (sampling 1 Hz and 1 g accuracy) to record the mass loss over time during the fire spread. Needles of Pinus pinaster oven dried at 60 °C for 24 h were used as fuel. The net heat of combustion Hc,net was equal to 20,411 kJ/kg and was derived from the gross heat of combustion measured in an oxygen bomb calorimeter following the standard AFNOR NF EN 14918. The surface to volume ratio (equal to 3057 m1) and the density (equal to 511 kg/m3) of the needles were measured following the methodology proposed by Moro [34]. Ambient conditions and fuel moisture content on dry basis were measured for each test just before the ignition. The ambient temperature and relative humidity ranged respectively from 18 °C to 21 °C and from 35% to 49% for all the tests. The fuel moisture content ranged between 5.7% and 8.4 % with a mean value equal to 7.0%. The pine needles were distributed uniformly on the table in order to obtain homogenous fuel beds of 1 m width and 2 m long that occupy only the central part of the table. To ensure that the fuel was uniformly distributed on the combustion table, the deposition area of the fuel was cut into 8 squares of 50 cm by 50 cm (2 along the width and 4 along the length of the table). The total mass of pine needles needed for the experiments was separated in 8 portions of equal mass. One portion was then placed on each
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Smoke exhaust 3 (1m /s)
Thermocouple TK
Gas sampling section
Plenum Baffles Filtering and condensing system Hood (3m x 3m) Sample pump Camera1
O2 and CO/CO2 Analyzers
Total (TG) and radiant (RG) heat flux gauges 20 cm
Control volume
Camera 2
Combustion bench (2m x 2m) 20°
Load cell
Fig. 1. Experimental device for the fire spread study.
square. After an initial visual inspection of the uniformity of the distribution of the fuel, the fuel bed height was measured at eight randomly selected positions along the bed of pine needles. Different fuel loads (w) were used: 0.6, 0.9 and 1.2 kg/m2 that correspond respectively to mean fuel beds height (h) of 3, 5 and 7 cm. For each configuration, at least four repetitions were carried out. The fires were ignited along the entire width of the fuel bed by using between 3 and 6 mL of alcohol. Two cameras were used to observe the fire front: one was placed perpendicularly to the fire spread direction (camera 1 in Fig. 1) while the other was located behind the fire front in the direction of propagation (camera 2 in Fig. 1). During the experiments, cameras were automatically controlled to take pictures every 2–4 s, depending on the rate of spread of the fire. Two heat flux transducers cooled with circulating water were also used to measure heat fluxes during the fire spread (Fig. 1). The first one (TG) was a total heat flux gauge (MEDTHERM GTW-10-32-485A) calibrated up to 100 kW/m2. The second (RG) was a radiant gauge (MEDTHERM 64P-02-24T). The radiant heat flux transducer was equipped with a sapphire window with a view angle of 150°. The choice of the sapphire window was motivated by its spectral transmittance, which is between 0.2 and 5.5 lm. Parent et al. [35] and Boulet et al. [36] measured in the infrared the spectral flux emitted by fires from vegetative fuels with FTIR spectroscopy. The measurements clearly exhibited that the main part of the radiation emitted by the fire was between 2 and 5.5 lm, what is included in the spectral transmittance of the sapphire window. The two heat flux gauges (TG and RG) were oriented toward the flame and were placed at the end of the experimental bench, 20 cm above the bed and in the middle of the fire front. The uncertainty for flux measurements was 3%. The response time of the sensors was less than 250 ms, which was adequately addressed with the 10 Hz sampling rate used for this study. Finally, in the exhaust smoke duct, a thermocouple (Fig. 1), called TK, was used to record the temperature of the combustion gases.
2.2. Calorimetric calculation The measurement of exhaust flow velocity and gas volume fractions were used to determine the heat release rate (HRR), using Oxygen Consumption Calorimetry, based on the formulation derived by Parker [37]. Since the calculation procedure was detailed in [30,31], we present only the main steps here. The composition of the pine needles was determined from an ultimate
analysis of CHON. Their combustion is represented by the stoichiometric reaction for the complete combustion of lignocellulosic materials, given by:
C4:15 H6:65 O2:51 þ 4:56ðO2 þ 3:76N2 Þ ! 4:15CO2 þ
6:65 H2 O þ 17:14N2 2 ð5Þ
The amount of energy released by complete combustion per unit mass of oxygen consumed is taken constant. All gases are considered to behave as ideal gases. The analyzed air is defined by its composition in O2, CO2, H2O and N2. All other gases are lumped into N2. The heat release rate is given by the oxygen molar flow rate:
HRR ¼ Eðn_ o2 n_ o2 ÞW o2
ð6Þ
where E is the heat release per unit mass of O2 consumed, n_ O2 and n_ O2 represent respectively the molar flow rates of O2 in incoming air and in the exhaust duct and W O2 is the molecular weight of oxygen. Parker [37] provided a detailed calculation to evaluate the molar flow rate of oxygen based on the volume flow rate in the exhaust _ and the molar fraction of species. He derived the three folduct (V) lowing relations to calculate the HRR:
Eq0 W O2 / 1 X 0H2 O X aO2 V_ ð1 /Þ þ a/ W air sffiffiffiffiffiffiffi k t DP V_ ¼ 22:4A kp T TK xaO2 1 xaCO2 xaO2 1 xaCO2 /¼ xaO2 1 xaCO2 xaO2
HRR ¼
ð7Þ ð8Þ
ð9Þ
where X denotes the molar fraction and q0 is the density of dry air at 298 K and 1 atm. V_ is the standard flow rate in the exhaust duct. a is the expansion factor for the fraction of the air that was depleted of its oxygen. The superscript ° is for the incoming air. A is the cross sectional area of the duct, kt is a constant determined via a propane burner calibration, kp = 1.108 for a bi-directional probe, DP is the pressure drop across the bi-directional probe and TTK is the gas temperature in the duct measured by the thermocouple TK. The HRR is therefore computed from many variables and each variable has a corresponding uncertainty. In this study, the instrumentation is similar to that of the Room Corner Test [38], for which Axelsson et al. [39] analyzed the uncertainty considering individ-
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ual sources of errors for rate of heat release measurements. The combined expanded uncertainty was provided with a coverage factor of 2, giving a confidence level of 95%. Following the same methodology, the combined expanded uncertainty calculated in our case was 3.5%. This value was obtained because of accurate paramagnetic oxygen sensor and calculation of the heat release per unit mass of O2 consumed (E). As the fuel composition was known, we reduced indeed the uncertainty by estimating E with the following expression:
E¼
Hc;net W fuel ¼ 13:98 MJ=kg nO2 W O2
ð10Þ
where nO2 = 4.56 (Eq. (5)) and Wfuel is the molecular weight of the fuel. This value corresponds to an increase of 6.7% compared to Huggett’s constant (13.1 MJ/kg) generally used in calorimetric studies for organic fuels [40].
Table 1 Geometrical properties of the fire front for experiments performed with a slope of 20°. The standard deviations are in parenthesis. Test n°
w (kg/m2)
Lf (cm)
b (°)
d (°)
ROShead (mm/s)
06_1 06_2 06_3 06_4 06_5 09_1 09_2 09_3 09_4 09_5 12_1 12_2 12_3 12_4
0.6 0.6 0.6 0.6 0.6 0.9 0.9 0.9 0.9 0.9 1.2 1.2 1.2 1.2
– 38.7 (9.8) 44.0 (10.7) – 56.4 (12.3) 60.8 (10.0) 76.5 (14.0) 73.4 (14.6) 63.0 (12.8) 78.1 (17.5) 85.6 (16.1) 88.5 (15.2) 92.2 (16.2) 93.3 (15.8)
– 6.7 (5.6) 9.5 (8.0) – 8.2 (6.0) 6.6 (7.4) 5.3 (8.9) 5.7 (7.9) 6.2 (5.6) 3.6 (4.8) 4.4 (5.5) 6.0 (6.5) 5.7 (6.2) 5.4 (6.4)
– 37.0 (6.2) 39.1 (7.1) – 27.5 (5.3) 27.1 (6.2) 22.5 (7.8) 25.5 (8.1) 26.7 (5.3) 23.6 (3.1) 25.9 (4.0) 24.1 (3.2) 26.0 (5.5) 25.5 (4.8)
8.8 9.4 12.5 9.5 10.1 14.3 17.6 15.7 13.4 13.0 16.6 15.8 17.5 14.8
3. Results and discussion 2.3. Fire front descriptors 3.1. Fire front properties The characterization of the fire front was carried out with the following information collected during the experiments (Fig. 2). The rate of spread of the head of the fire front (ROShead) was calculated from the time needed to the head to cover intervals of 0.25 m along the bench. Thus, eight data points were obtained for each experiment and a least-squares regression was used to fit a straight line to the data points in order to obtain ROShead. As the entire fire front did not propagate at the same speed, the rate of spread of the flanks of the fire front (ROSflank) was also calculated through image processing. For this, the pictures taken by the cameras (Fig. 1) were used to determine the rear position of the flanks of the fire front versus time. A least squares regression was then used to fit a straight line to the data points in order to obtain ROSflank. Flame length (Lf), flame angle (b) and the angle of the fire front (d) were determined from photographs taken by camera 1 (Fig. 1) located perpendicularly to the fire spread direction. Lf corresponds to the flame length expressed following the suggestions of Anderson et al. [12]. b is the angle between the flame and the vertical axis. d is defined as the angle between the fire front and the propagation axis. The length of the fire front (L) and the burnt area (Aburnt) were obtained from photographs recorded by camera 2 (Fig. 1) placed behind the fire front. Since the flames on the flanks of the fire front were smaller than in the head and were inclined inwardly of the fire front, we also introduced the length Lh which corresponds to the length of the front, where the flames are the highest (Fig. 2) and inclined outwardly of the front. This measurement was also carried out with camera 2. For each experience, the mean values of Lf, b, d and Lh were computed from 30 to 50 images.
Table 1 shows the geometrical properties of the fire front for each experiment. The variations observed among a same fuel configuration can be explained by the difference of the fuel moisture content and in a lesser extent by a slight variation in the experimental protocol (ignition, fuel distribution or fuel bed height). An average of these values is reported in Table 2, where the mean data obtained for no slope [32] are reported to facilitate the comparison between no slope and upslope fire spread experiments. A brief discussion of these results is presented in the following to facilitate the understanding of the phenomena. By observing the fire front during propagation experiments, two different behaviors were highlighted depending on whether the experiments were carried out with or without slope: For horizontal fire spread, the data have already been published [32]. Only a short summary of results is performed hereafter. The fire front exhibited a nearly linear shape (Fig. 3a). On the edges of the bed, the fire front was however slightly curved and the flame length was lower than at the center. The whole part of the fire front propagated roughly at the same rate of spread (between 3.7 and 5.6 mm/s depending on the fuel load). When the fuel load was multiplied by 1.5 and 2, the mean ROShead increased by 1.3 and 1.5. The fire front was tilted backward with an angle ranging from 12.8° to 17.6° according to the fuel load. The flame lengths ranged between 25.5 and 60.2 cm. Therefore, the flame length increased by a factor 1.7 and 2.4 when the fuel load increases by a factor of 1.5 and 2.
Fig. 2. Geometric descriptors of the flame and fire front (a) lateral view and (b) rear view.
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Table 2 Mean geometrical properties of the fire front. The standard deviation is in parenthesis. w (kg/m2)
Slope (°)
Lh/L (%)
Lf (cm)
b (°)
d (°)
ROShead (mm/s)
ROSflank (mm/s)
0.6 0.9 1.2
0 0 0
100 100 100
25.5 (2.3) 44.4 (9.3) 60.2 (14.9)
12.8 (4.2) 14.1 (5.0) 17.6 (3.6)
90 90 90
3.7 (0.2) 4.7 (0.7) 5.6 (1.4)
– – –
0.6 0.9 1.2
20 20 20
42.5 (8.2) 27.8 (8.7) 28.0 (10.8)
46.4 (7.4) 70.4 (7.1) 89.9 (9.8)
8.1 (1.1) 5.5 (1.0) 5.4 (0.6)
34.5 (5.0) 25.1 (1.8) 25.4 (0.8)
10.1 (1.3) 14.8 (1.7) 16.2 (1.0)
8.0 (1.7) 8.1 (1.2) 10.3 (0.8)
Fig. 3. Picture of the fire front under (a) no-slope condition and (b) 20° upslope condition.
For experiments at a slope of 20°, the fire front had a V-shape (Fig. 3b). The fire head was located in the middle of the fuel bed. This behavior was consistent with the observations reported in literature [6,11,41]. According to Dupuy et al. [11], the entrainment of air from the sides of the fuel bed area explains the distortion of the fire front from the initial straight ignition line. Because of this distortion, the whole fire front did not propagate with the same rate. The head of the fire front had a rate of spread greater than that of the flanks. In addition, ROShead increased with the fuel load. When the fuel load was multiplied by 1.5 and 2, mean ROShead were indeed multiplied by 1.5 and 1.6. For a same fuel load, the rate of spread was about 2.7 times higher for experiments with slope that without slope. These observations are consistent with literature results [4,7,9– 11]. The flame lengths ranged between 46.4 and 89.9 cm. Thus, for a given fuel load, the flames are about 1.6 times higher for the experiments under slope conditions than under no slope conditions. Contrary to the experiments without slope, the flames were inclined forward with an angle between 5.4° and 8.1° depending on the fuel load. For high fuel loads, the flames were less inclined due to greater buoyancy associated with the fuel load. Another difference observed between the experiments under slope and no slope conditions is the evolution of the fire front length. Because of the distortion of the fire front (Fig. 4a), its length increased during the spreading (Fig. 4b). L can indeed be multiplied by a factor up to 3 during the experiments. However, the size of the area where the fire is the
highest (Lh) corresponds only to a length ranging from 27.8% to 42.5% of the total length of the fire front depending on the fuel load. 3.2. General description of HRR Instantaneous heat release rates (HRR) measured during the fire tests are displayed in Fig. 5. The curves obtained under no slope conditions [32] are also provided to facilitate the comparison. Table 3 shows the maximum values obtained under slope conditions. For experiments performed without slope [32], a quasisteady state was reached for all fuel loads. The average heat release rates were 41, 87 and 130 kW for 0.6, 0.9 and 1.2 kg/m2, respectively. The greater the fuel load was, the higher the heat release rate was. The mean HRR were multiplied by 2.1 and 3.2 with the increasing of fuel load by a factor of 1.5 and 2. The increase is not linear with regard to the fuel load. The flameout occurred earlier for higher fuel load due to the increase in the rate of spread (Table 2). For experiments with a slope of 20°, a quasi-steady state was not observed for the heat release, while the rate of spread of the fire head was constant. The heat release rate continued to increase until the fire front reached the end of the table. This observation is related to the size of the fuel bed that did not allow the fire to reach a steady state. At the flameout, the HRR reached about 160 kW, 295 kW and 385 kW for a fuel load of 0.6, 0.9 and 1.2 kg/ m2 respectively. Despite differences between the experiments with and without slope, the total heat released was almost constant for
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Fig. 4. (a) Fireline contours for fire spread and (b) length of the fire front for propagation – for a slope of 20° and a fuel load of 1.2 kg/m2 until the arrival of the fire front head at the table end.
a
b
Fig. 5. Heat release rate versus time for experiments (a) under no slope conditions [32] and (b) for a slope equal to 20°.
Table 3 Properties of the fire spread experiments. Test n°
w (kg/m2)
Peak MLR (g/s)
Peak HRR (kW)
THR (MJ)
Peak Utot (kW/m2)
Peak Urad (kW/m2)
06_1 06_2 06_3 06_4 06_5 09_1 09_2 09_3 09_4 09_5 12_1 12_2 12_3 12_4
0.6 0.6 0.6 0.6 0.6 0.9 0.9 0.9 0.9 0.9 1.2 1.2 1.2 1.2
6.0 6.2 7.7 5.7 8.0 14.1 20.3 17.3 14.7 16.3 22.7 23.4 25.0 22.3
102.0 119.7 154.8 106.5 166.9 244.9 363.5 319.9 255.3 284.8 366.2 380.8 400.2 390.6
21.7 22.9 23.2 21.7 24.6 31.9 33.1 33.1 30.2 27.3 41.8 43.9 44.3 47.8
9.1 11.8 15.2 10.4 11.0 17.4 31.0 28.9 26.4 18.3 26.4 29.7 34.3 18.9
7.6 10.0 13.4 9.1 9.0 13.0 25.6 21.4 22.3 15.7 – 24.5 28.8 16.1
a given fuel load (22.8, 32.2 and 44.5 MJ for 0.6, 0.9 and 1.2 kg/m2 respectively) regardless propagation conditions (Table 4). As the fuel consumption efficiency and the amount of fuel were equal for the two configurations, the combustion efficiency was therefore almost the same under slope and no slope conditions.
The temporal evolution of the mass of the fuel bed is given in Fig. 6 and the corresponding mass loss rate (MLR) versus time in Fig. 7. As for the heat release rate, the results for no slope conditions [32] are also provided. Under no slope conditions, the mass loss rate was almost constant after the ignition stage. The reached value varied according to the fuel load: 2.46 g/s, 4.97 g/s and 8.06 g/s for 0.6, 0.9 and 1.2 kg/m2. Therefore, the mean MLR values were multiplied by 2.0 and 3.3 when the fuel load increases by a factor 1.5 and 2. Under slope conditions, the MLR values were higher than under no slope conditions and increased during the fire spread. These observations are consistent with those reported by Dupuy [7]. They observed indeed that for litters of P. pinaster, experimental fires became unsteady for slopes above 10°. The mass loss rate follows therefore the same trend as the heat released rate (Fig. 5). This is not surprising, since according to previous studies [30–33], the heat release rate and the mass loss rate are linked by the following relationship:
HRR ¼ Heff MLR
ð11Þ
where Heff is the effective heat of combustion.
Table 4 Mean properties of the fire front. The standard deviation is in parenthesis. w (kg/m2)
Slope (°)
THR (MJ)
Peak Utot (kW/m2)
Peak Urad (kW/m2)
vconv (%)
vconv,fl (%)
vrad,em (%)
0.6 0.9 1.2
0 0 0
21.9 (2.3) 33.6 (3.2) 44.2 (2.3)
7.6 (0.5) 10.2 (1.7) 13.9 (3.5)
6.2 (0.4) 8.5 (1.6) 11.3 (3.0)
83.8 (1.9) 80.2 (4.6) 68.5 (7.7)
10.1 (0.8) 9.9 (0.9) 9.1 (0.2)
7.3 (1.9) 9.9 (2) 13.3 (2.2)
0.6 0.9 1.2
20 20 20
22.8 (1.1) 32.2 (1.1) 44.5 (2.1)
11.5 (2.0) 24.4 (5.6) 27.3 (5.6)
9.8 (1.9) 19.6 (4.6) 23.1 (5.3)
74.9 (4.0) 61.1 (2.4) 61.2 (2.9)
13.6 (1.7) 24.1 (2.6) 24.2 (2.7)
11.5 14.8 14.6
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Fig. 8. Comparison between measured and estimated HRR for a fuel load of 0.9 kg/m2 under no slope conditions.
Fig. 6. Mass loss of the fuel beds versus time.
3.3. Calculation of HRR from the burnt surface
According to Eq. (11), the variation of the heat release rate during the propagation is therefore due to the mass evolution of the fuel bed. This quantity can be expressed in terms of the surface burnt by the fire front as follows:
m ¼ m0 wgAburnt
ð12Þ
where m0 is the initial mass of pine needles, w is the fuel load, Aburnt is the burnt surface and g is fuel consumption efficiency equal to 0.97 for our experiments. This value is in agreement with the work of Dupuy [7], in which a combustion efficiency equal to 0.95 was found for P. pinaster litters. The mass loss rate is therefore given by:
MLR ¼ wg
dAburnt dt
ð13Þ
and by using Eq. (11), the heat release rate is given by:
HRR ¼ Heff wg
dAburnt dt
ð14Þ
As the fire front exhibited two different behaviors depending on whether the experiments were carried out under slope or no slope burnt conditions, the expression of dAdt changes. Under no slope conditions, by considering that the fire front was linear during the propagation and kept the same length:
dAburnt;noslope ¼ LROShead dt
ð15Þ
As the rate of spread can be considered constant during the propagation (Table 2), the time derivative of the burnt area remains constant during the fire spread. According to Eqs. (13) and (14):
a
MLRno slope ¼ wgLROShead HRRno slope ¼ Heff wgLROShead
ð16Þ
Under no slope conditions, the mass loss rate and the heat release rate therefore kept roughly the same value during the fire spread, as the rate of spread and the fire front length remained almost constant. This result explains the quasi steady state observed on the curves (Figs. 5 and 7a). An example of the calculation of the heat release rate by using Eq. (16) is given in Fig. 8 for a fuel load of 0.9 kg/m2. For the other fuel loads, same results were obtained. At the beginning of the propagation, the calculation underestimated the HRR whereas at the end, the heat release rate was slightly overestimated. This was due to a slight variation of the rate of spread during the fire spread. At the beginning of the propagation, the rate of spread was indeed a little higher than the mean value due to an ignition effect. At the end, the opposite phenomenon was observed due to the weak distortion of the fire front at the edges. Despite these slight variations, the heat release rate calculated from the time derivative of the burnt area is very close to the measurements obtained by OC calorimetry. For a slope of 20°, the distortion of the fire front (Figs. 3b and 4a) induced an increase of the fire front length during the propagation (Fig. 4b). This was due to the different values of the rate of spread for the head and the flanks of the fire. Given the shape of the fire front, it is difficult to propose an analytical expression of the burnt surface. The time evolution of the surface burnt by the fire front was therefore determined by image processing by using the photographs recorded by camera 2. Figure 9 shows an example of the time evolution of the burnt surface obtained every 40 s for the three fuel loads. For all fuel loads, an increase of the burnt surface per unit of time was noted during the fire spread until the head of the fire front reached
b
Fig. 7. Mass loss rate versus time for experiments (a) under no slope conditions [32] and (b) for a slope of 20°.
V. Tihay et al. / Combustion and Flame 161 (2014) 3237–3248
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Fig. 9. Time evolution of the burnt area for propagation for a slope of 20° and for a fuel load of (a) 0.6 kg/m2, (b) 0.9 kg/m2 and (c) 1.2 kg/m2.
the end of the table. This rise led to an increase of the mass loss rate and heat release rate (Eq. (11)). Figure 10 presents the heat release rate calculated with Eq. (14) for the three fuel loads by using the time derivative of the surface burnt by the fire front. Only the portion on which the image processing was performed is shown in this figure. The heat release rate calculated from the geometrical properties of the fire front is very close to the measurements by OC calorimetry. Although this method did not allow following the rapid fluctuations of HRR, the same tendencies were observed for all fuel loads. These results confirm that for a uniform fuel, HRR can be predicted by the variation of the burnt surface per unit of time using a constant burning efficiency and effective heat of combustion. The rate of spread of the fire front head is not sufficient to understand the dynamics of fire spreading under slope conditions. The rate of spread can be constant during the propagation, whereas the heat release rate increases. To characterize a fire at this scale, it is therefore useful to employ the fireline intensity combined with the rate of spread. Because of the experimental procedure, these results are only applicable to fires of unconfined fuel beds realized at the same scale.
3.4. Convective fraction To estimate the contribution of convection, it is necessary to know the gas temperature at the duct entry (Tg). Through thermocouple TK (Fig. 1), it is possible to know the gas temperature in the exhaust duct (Fig. 11). However, during its passage through the exhaust duct, the gas was cooled. To take into account the heat losses in the duct before the measurements (that is to say, over a length equal to l = 5.576 m), a heat balance was performed in the duct. For a duct section with a length dx:
_ mix cp;mix Tðx; tÞ ¼ M _ mix cp;mix Tðx þ dx; t þ dtÞ þ Uloss M
ð17Þ
where Uloss corresponds to the heat losses modeled by:
Uloss ¼ p d dx UðT Ta Þ
ð18Þ
where d is the duct diameter (0.4 m) and U is the overall heat transmission coefficient of the duct given by:
U¼
_ mix cp;mix aM pd
ð19Þ
where a is a coefficient determined under no slope conditions by using temperature measurements in the duct. The detailed calculation is available in [32].
Fig. 10. Comparison between measured and estimated HRR for a fuel load of (a) 0.6 kg/m2, (b) 0.9 kg/m2 and (c) 1.2 kg/m2 – for a slope of 20°.
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V. Tihay et al. / Combustion and Flame 161 (2014) 3237–3248 30 With a slope of 20°°
Heat fluxes (kW/m2)
25 20
Without slope 15 10 5 0 0
50
100
150
200
250
300
350
400
450
500
Time (s) Total heat flux (TG)
Fig. 11. Temperature measurement in the duct for a fuel load of 0.9 kg/m2 for a slope of 20°.
Radiant Heat flux (RG)
Fig. 12. Total (TG) and radiant heat fluxes (RG) for a fuel load of 1.2 kg/m2 and a slope of 20°.
By combining Eqs. (17)–(19), one obtains:
1 @Tðx; tÞ @Tðx; tÞ þ þ aTðx; tÞ ¼ aT a @t @x
v
ð20Þ
where v is the mean gas velocity in the duct. According to temperature measurements obtained by the thermocouple TK in the extraction duct (Fig. 11), the gas temperature increased quasi-linearly with time. We can thus assume that @Tðx;tÞ ¼ K. The solving of Eq. (20) leads to the gas temperature at @t the duct entry i.e. for x = 0:
Tg ¼ Ta þ
K K al e þ T TK T a av av
ð21Þ
The knowledge of the gas temperature allows the calculation of the convective heat release rate HRRconv with [42]:
_ mix HRRconv ¼ M
Z
Tg
cp;mix ðTÞ dT
ð22Þ
Ta
where Ta is the ambient temperature, cp,mix is the specific heat of the mixture at temperature T taken equal to that of dry air and _ mix is the mass flow rate of the chemical compounds-air mixture. M As the mass flow rate was constant in the duct, it was determined from the volumetric flow rate of the mixture measured in the gas _ TK Þ by the following equation: sampling section VðT
_ mix ¼ VðT _ TK Þ qðT TK Þ M
ð23Þ
where the density of the mixture was taken equal to that of dry air:
298 qðT TK Þ ¼ qair;298 T TK
ð24Þ
The comparison of the heat losses (Eq. (18)) and the convective heat release rate (Eq. (22)) shows that the heat losses in the duct correspond to a mean value of 14.5% of the HRRconv. Then, the convective fraction corresponds to the ratio between the convective heat release rate HRRconv and the heat release rate HRR:
vconv ¼
HRRconv HRR
3.5. Heat flux measurements and overall radiant fraction The time evolution of the heat fluxes received by the two heat flux gauges (TG and RG) located 20 cm above the fuel bed at the end of the experimental bench (Fig. 1) is shown in Fig. 12 for 1.2 kg/m2 without slope [32] and with a slope of 20°. In the preheating zone, the heat fluxes progressively increased up to maximum values which vary according to the fuel loads. The maximal values recorded for the radiant (Urad) and total (Utot) heat fluxes are reported in Table 3. This maximum corresponds to the time when the flames reach the end of the bench, i.e. the closest point of the measurement device. As the total and radiant heat fluxes coincide in the preheating zone, heat transfer is mainly due to radiation. Close to the flame zone, a greater difference appears between both signals. This is characteristic of heat transfer combining radiation and convection. The comparison of the curves obtained under slope and no slope conditions shows two major differences. First, the heat fluxes recorded during experiments under slope conditions are shifted in time. This is due to the higher rate of spread (Table 2). Second, the heat fluxes are higher for upslope fire (Table 4). To characterize the effect of slope on the radiant heat transfer, the overall radiant fraction was firstly calculated. As the sum of the convective and radiant fraction is equal to 100%, the overall radiant fraction corresponds to:
vrad ¼ 100 vconv
ð26Þ
Under a slope of 20°, the overall radiant fractions was therefore equal to 25.1%, 38.9% and 38.8% for fuel loads of 0.6, 0.9 and 1.2 kg/ m2 respectively. For comparison, under no slope conditions, the overall radiant fraction obtained was in the range of 16.2–31.5% [32]. These values are consistent with literature [16,43]. Therefore, for a given fuel load, the overall radiant fraction was higher for upslope fires than under no slope condition. 3.6. Contribution of flames and embers on the radiant fraction
ð25Þ
The mean convective fractions are given in Table 4 for experiments under slope conditions. The mean values obtained under no slope conditions [32] are also provided to facilitate the comparison. For a slope of 20°, the convective fractions were in the range of 61.1–74.9%. Approximately the same value was obtained for fuel loads of 0.9 and 1.2 kg/m2 (about 61%). For 0.6 kg/m2, the convective fraction was higher (about 75%). These values are close to those obtained by Tewarson [27].
To attempt to distinguish the radiant fraction due to the flames and that due to the embers, we first calculated the radiant fraction due to the flames from the radiant heat flux measurements. The radiant fraction corresponds to the ratio between the radiant power (Prad) and the heat release rate (HRR given in Fig. 5 for example).
vrad ¼
Prad HRR
ð27Þ
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To calculate the radiant power, a solid flame model was used by neglecting the atmospheric absorption. For the flames, the radiant power (Prad,fl) was obtained from the heat flux density measurements qRG performed with the radiant heat flux gauge RG (Fig. 12) by considering the view factor (F) and the emission surface of the fire front (Sfl) taking into account the two faces of the flames. In the following, we considered that the radiant energy was emitted uniformly over the flame area. This is of course a strong assumption. However, as the thickness of the flame was almost constant in the continuous flame zone during our experiments, this assumption seems acceptable. Therefore:
qRG ¼
Prad;fl F Sfl
ð28Þ
By combining Eqs. (27) and (28), the radiant fraction of the flames Fig. 13. Diagram describing the modeling of the fire front for the calculation of the view factors.
vrad,fl corresponds to:
vrad;fl ¼
qRG Sfl HRR F
ð29Þ
e ¼ 1 expðK m Lthick Þ
ð30Þ
Therefore, for a constant chemical composition of the flame (i.e. for a same extinction coefficient), the greater the flame thickness is, the higher its emissivity is. Secondly, the flame volume increase leads to an underventilation of the fire. This induces a more signif-
Radiant fraction due to the flames
0.35
The determination of the view factor F was based on the Contour Double Integral Formula (CDIF) method, which calculates the view factor between planar polygons. To simplify the determination of the view factor and the emission surface of the fire front, the geometry of the fire front was approximated by simple shapes. As the flanks of the fire front consisted of small discontinuous flames, inclined inward the fire front, we neglected its contribution to radiation impinging the heat flux sensors. Only the part of the front where the flames are the highest was considered for the calculation of the radiant fraction. Considering the V-shape of the fire front (Figs. 3 and 9), it was modeled by two trapezoids forming an angle d with the propagation axis and having a base of length L2h and a height equals to Lf cos b. Figure 13 shows a sketch of the configuration adopted. This approximation for the fire front is also strong. However, this assumption is fairly good, when the head of the fire front is located between 1.2 and 1.8 m from the ignition edge. On the first meter, the fire front was indeed rounded (Fig. 9). In the following, the calculations were only performed when the fire head was between 1.2 and 1.8 m. Figure 14 presents the evolution of the radiant fraction over time obtained for experiments under slope conditions performed with a fuel load of 0.6 and 1.2 kg/m2. Mean values equal to 13.6%, 24.1% and 24.2% were obtained for 0.6, 0.9 and 1.2 kg/m2 respectively (Table 4). The radiant fraction due to the flames tends therefore to increase with the fuel load even if close values were obtained for fuel loads equal to 0.9 and 1.2 kg/ m2. Table 4 also reports the mean data obtained for no slope [32] to facilitate the comparison. Under no slope conditions [32], the radiant fraction of the flame slightly decreased (from 10.1% to 9.1%) with increasing fuel load. This was due to the inclination of the flame. Although the flame length increased with increasing load, the flames leaned further backward simultaneously (Table 2). This tendency leads to a decrease of the radiant fraction value. The comparison between the experiments under slope and no slope conditions shows that for a given fuel load, the radiant fraction of the flame is higher for a fire front spreading along a slope of 20° than along a flat surface. To explain these differences, it is necessary to consider the influence of two parameters. Firstly, when the fuel load increases or when the propagation takes place with a slope of 20°, the flame thickness increases. The emissivity is related to the extinction coefficient Km and the flame thickness Lthick by the following relationship [44]:
0.3 0.25 0.2 0.15 0.1 0.05 0 0
50
100
150
200
250
Time (s) 0.6 kg/m2
1.2 kg/m2
Fig. 14. Evolution of the radiant fractions due to the flames over time for a slope of 20°.
icant soot production within the flame and an increase of the extinction coefficient, since the extinction coefficient is correlated to the soot volume fraction fv by [45,46]:
K m ¼ 0:1ðX CO2 þ X H2 O Þ þ 1862f v T
ð31Þ
where X CO2 and X H2 O are the mole fraction of CO2 and H2O in the combustion products. Then, the increase of the extinction coefficient leads to an increase of the flame emissivity. Both factors analyzed here above contribute to the increase of the radiant fractions observed during our experiments with fuel load. The contribution of embers to the radiation emitted by the fire front was obtained by deducting from the overall radiant fraction the part due to the flames:
vrad;em ¼ vrad vrad;fl
ð32Þ
Table 4 shows the mean radiant fractions for the embers under slope conditions. The mean data obtained for no slope [32] are also reported to facilitate the comparison. Under no slope conditions [32], the radiant fraction of the embers increases (from 7.3% to 13.3%) when the fuel load ranges from 0.6 to 1.2 kg/m2. For the experiments under slope conditions, the radiant fraction due to embers is equal to 11.5%, 14.8% and 14.6% for the fuel loads of 0.6, 0.9 and 1.2 kg/m2, respectively. Therefore, for a given fuel load, the radiant fractions of the embers were slightly higher for experiments under slope conditions than along a flat surface. This result can be explained by the fact that the volume of embers was larger when experiments were conducted with a slope because the depth of the fire front was greater.
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4. Conclusion In this study, oxygen consumption calorimetry was used to analyze the spreading of fires across pine needles beds for various fuel loads at one slope. The properties of the fire front, the heat release rate, the mass loss rate and the heat transfer were investigated to understand the influence of slope on fire behavior. The main results can be summarized as follows: Conversely to experiments under no slope conditions, the fire front has a V-shape because of a distortion. The length of the fire front and the time derivative of the burnt surface increase during the propagation. This observation is related to the size of the fuel bed that did not allow the fire to reach a steady state. As the time derivative of the burnt area increases for a slope of 20°, the MLR increases hence the HRR also. Under no slope condition, the HRR and the MLR reach a quasi-steady state. The burnt surface increased indeed steadily, leading to almost constant values of MLR and HRR. The comparison between the heat release rate calculated from the geometrical properties of the fire front and the measurements by OC calorimetry confirmed the potential for estimating the heat release rate with the fuel load and the time derivative of the burnt surface. Convection represents between 61.1% and 74.9% of the heat transfer for a slope of 20°. These values are lower than those encountered under no slope conditions. With a slope of 20°, radiation represents between 25.1% and 38.9% of the heat transfer. The main part is due to the flames (between 13.6% and 24.2%). The remaining part comes from the embers (from 11.5% to 14.8%). For both, the radiation rises with the fuel load. These values are higher than those measured under no slope conditions (overall radiant fraction varied between 16.2% and 31.5% depending on fuel loads). The reasons are the increase of the ember volume, the thickening of the flames and a more significant production of soot.
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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Combustion of forest litters under slope conditions: Burning rate, heat release rate, convective and radiant fractions for different loads Virginie Tihay ⇑, Frédéric Morandini, Paul-Antoine Santoni, Yolanda Perez-Ramirez, Toussaint Barboni SPE – UMR 6134 CNRS, University of Corsica, Campus Grimaldi, BP 52, 20250 Corte, France
a r t i c l e
i n f o
Article history: Received 4 June 2013 Received in revised form 10 October 2013 Accepted 4 June 2014 Available online 8 July 2014 Keywords: Flame spread Slope Heat release rate Radiant and convective fractions Burnt surface variation
a b s t r a c t A set of experiments at laboratory scale was conducted to study the combustion of forest fuel beds in order to quantify the contribution of radiant and convective heat transfer under slope condition. To proceed, a Large Scale Heat Release apparatus was used to measure the heat release rate and fire properties such as the mass loss rate, the geometry of the fire front and the heat transfer were assessed. Because of the slope and the size of the fuel bed, the mass loss rate and the heat release rate do not reach a quasisteady state when the propagation takes place under slope condition. This is due to a V-shape distortion of the fire front, which leads to an increase of the burnt surface rate by the fire over time. The study of this quantity has shown that the heat release over time can be estimated with the fuel load and the time derivative of the burnt surface. The fractions of radiation and convection released by the fire in its environment were calculated. Under a slope of 20°, the convective fraction decreases from 74.9% to 61.1% whereas the overall radiant fraction ranges between 25.1% and 38.9% and increases with increasing fuel loads. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction Each year, fires devastate forests from all continents causing casualties and irreparable environmental damages. Determining the parameters that control the spread of wildfires is therefore a major objective for the management and the prevention of these fires. Over the last decades, modeling has been increasingly used for forest management [1], for risk mapping [2] and for studying the fire propagation [3]. However, to implement and test these models, it is necessary to have experimental data that increase the understanding of the phenomena. The effects of slope, wind and vegetation properties on fire behavior have been extensively investigated at laboratory and field scale. In most studies, the researchers have focused on the rate of spread [4–11], the flame geometry [4,9,12], the temperature profile [4,9,11] or the fuel consumption and mass loss [4,7,11]. However, these parameters are not sufficient to completely understand the fire behavior. Increased understanding about the relative roles of radiant and convective heating in fire spread and energy release are essential needs in wildland fire science. In the literature, the radiant fraction has been mainly determined in works devoted to assess the thermal radiation incident ⇑ Corresponding author. Fax: +33 495 450 162. E-mail address: [email protected] (V. Tihay).
upon a target [13]. The point source model has been the method most commonly used. This method relies on the hypothesis that the radiant heat flux emitted by the flames is spherically isotropic [13,14]:
qR ¼
HRRrad cos h 4 p R2
ð1Þ
where qR is the radiant heat flux density, h is the angle between the normal to the target and the line of sight from the target to the point source location, R is the distance between the point source and the target. HRRrad is the radiant power given by the radiant fraction vrad times the heat release rate. This method has been widely applied for the study of liquid hydrocarbon pool fires and for hydrocarbon jet flames [13]. Tihay et al. [15] used also this approach to calculate the radiant fraction of laminar flames obtained from the burning of the vegetative fuels. The obtained values of the radiant fraction varied between 20% and 27%. Kremens et al. [16] conducted also experiments in 8 8 m outdoor plots using preconditioned wildland fuels characteristic of mixed-oak forests. With a two-band infrared radiometer, they studied the radiant power of a fire and found a radiant fraction of 17%. However, the point source model approach is only accurate in the far-field. For measurement at distances within a few fire diameters, this method becomes inadequate because it assumes that all of the radiant energy from the fire is emitted at a single point
http://dx.doi.org/10.1016/j.combustflame.2014.06.003 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
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Nomenclature A a
cross sectional area of the exhaust duct (m2) parameter equals to M_ pdU ðm1 Þ C
Aburnt cp,mix d D
area burnt by the fire front (m2) specific heat of the mixture (J/kg K) duct diameter (0.4 m) distance between the heat flux gauge and the fire front (m) distance covered by the head of the fire front (m) heat release per unit mass of O2 consumed (J/kg) view factor (–) fuel height (m) net heat of combustion (J/kg) effective heat of combustion (J/kg) heat release rate (W) partial derivative of the temperature versus time (K/s) extinction coefficient (m1) constant determined via a propane burner calibration (–) constant of the bi-directional probe (–) length of the fire front (m) distance between the duct entry and thermocouple TK (m) length of the part of the fire front where the flames were the highest (m) flame length (m) flame thickness (m) mass of the fuel (kg) mass flow rate of the chemical compounds–air mixture (kg/s) mass loss rate (kg/s) number of moles (mol) molar flow rates of O2 in incoming air (mol/s) molar flow rates of O2 in the exhaust duct (mol/s) radiant power (W) radiant heat flux density (W/m2) distance between the point source and the target radiant heat flux gauge (–) Rate of spread (m/s) emission surface (m2) total exposed surface area of the material (m2) overall heat transmission coefficient of the duct (W/ m2 K) time (s) temperature (K) total heat flux gauge (–) total heat release (J)
mix p;mix
Dhead E F h Hc,net Heff HRR K Km kt kp L l Lh Lf Lthick m _ mix M MLR n n_ O2 n_ O2 Prad q R RG ROS S Sexp U t T TG THR
rather than distributed over the fire. Conversely, in these situations, the solid flame model can be employed to overcome the inaccuracy of the point source model [13]. This model considers that the flame has an idealized geometrical shape and emits radiant energy uniformly throughout its surface. The thermal radiant heat flux received by an element outside the flame envelope is given by the expression:
qR ¼ F E s
ð2Þ
where F is a geometric view factor, s factor and E is the radiant emittance of flame surface given by E = e r T4 where T is the temperature of the fire, e the emissivity and r the Stefan–Boltzmann constant. As for the point source model, the solid flame model has been mainly used to study the thermal radiation of pool fires and jet fires [13,17,18]. The main difficulty of this approach is the determination of the emissivity and flame temperature.
TK v V_ w W x X
thermocouple in the exhaust duct (–) gas velocity (m/s) standard flow rate in the exhaust duct (m3/s) fuel load (kg/m2) molecular weight (kg/mol) abscissa (m) mole fraction (–)
Greek symbols a expansion factor for the fraction of the air that was depleted of its oxygen (–) b flame angle (°) d angle of the fire front (°) e emissivity (–) DP pressure drop across the bi-directional probe (Pa) DAburnt variation of the area burnt by the fire front (m2) / oxygen depletion factor (–) U heat flux density (W/m2) c slope angle (°) g fuel consumption efficiency (–) q0 density of dry air at 298 K and 1 atm (kg/m3) h angle between the normal to the target and the line of sight from the target to the point source location vconv convective fraction (–) vrad radiant fraction (–) vT sum of the convective and radiant fractions (–) Subscript 0 a air CO2 conv em fl flank g head O2 rad RG tot
initial value ambient air carbon dioxide convective embers flame flank of the fire front gas head of the fire front oxygen radiant radiant heat flux gauge total
Superscript ° incoming air a ambient
Another approach to obtain the radiant heat release rate emitted by the fire is the integration of the measured spatial distribution of radiant flux. This method necessitates several radiometers positioned radially and vertically over a cylindrical control surface surrounding the fire. This method has been especially used for the study of pool fires [19,20] and jet flames of hydrocarbons [21,22]. More recently, several works focused on the determination of the fire radiative energy. For this, a new approach based on the works of Kaufman et al. [23] and Wooster et al. [24] has emerged in the field of biomass fires. This new method determines the fire radiative energy (FRE) by the analysis of fire pixel radiances in the middle infrared spectral region. Freeborn et al. [25] conducted 44 small-scale experimental fires in a combustion chamber by using ponderosa pine needles, Douglas fir twigs and foliage. With two MIR thermal imaging systems, they measured the fire radiative energy and obtained a radiant fraction of 12.4% based on the
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higher heating values of the forest fuels. This method has been criticized by Kremens et al. [16], who indicated the difficulty to determine the total infrared flux accurately by knowing only the sensor-reaching radiance in a single narrow waveband. In the work of Frankman et al. [26], radiant and convective heat fluxes were measured for 13 natural and prescribed wildland fires under a variety of fuel and ambient conditions. From these data, they determined the fraction of the combustion time during which the sensor shows convective heating or cooling. In addition, the fire radiative energy and the fire convective energy were calculated by integrating the measured convective and radiant heat fluxes. The results indicate that the relative contribution of convection and radiation to total energy release is dependent on fuel and environment. Global convection contribution in mixed heat transfer problems can be assessed by the determination of the convective heat release HRRconv. In literature, the convective heat release rate has been generally determined from the gas temperature rise (GTR) calorimetry, by using the following relationship [27]:
HRRconv ¼
Mmix cp;mix _ ðT g T a Þ Sexp
ð3Þ
where cp,mix is the specific heat of the combustion product–air mix_ mix is the total mass flow rate of the ture at the gas temperature, M fire product–air mixture, Tg is the gas temperature, T a is the ambient temperature and Sexp is the total exposed surface area of the material. Freeborn et al. [25] used this method to complete their work on the energy release of biomass fires. They found a convective fraction equal to 52% (based on the higher heating value). Tewarson [27] used also this method to measure the convective heat release rates of various fuels and under different ventilation conditions. As an ASTM E2058 fire propagation apparatus was employed for this study, the heat release rate (HRR) was recorded during the experiments. In systems where heat losses are negligibly small, the heat release rate of a fire consists of a convective and a radiant component. Tewarson [27] deduced from these data the radiant power HRRrad, by using the following relationship:
HRRrad ¼ HRR HRRconv
ð4Þ
The results indicate that the chemical, convective and radiant heat release rates depend on the chemical structures of the materials and fire ventilation. Among the fuels tested, Tewarson reported values for well-ventilated fires of pine wood. For this fuel, a convective fraction of 70.2% was obtained, which leads to a radiant fraction equal to 29.8%. The state of art of these calculation methods points out two main drawbacks. First, these methods calculate only one fraction: either the radiant fraction or the convective fraction. The second one is often derived. Secondly, when the HRR is not measured, there is a considerable uncertainty regarding the quantification of the total heat released during the fire. The heat release rate is commonly assumed to be equal to the product between the mass loss rate and the higher heating values, which leads to potential error in the determination of combustion efficiency of the fire. The knowledge of the HRR is therefore essential. This quantity is not only important to study the heat source but can be also used to classify vegetation, understand the role of transport in porous fuel beds [28] or propose a relationship between line fire intensity and flame length [29]. Given the importance of HRR, we have already performed several studies to measure this quantity and bring better understanding of fire spread behavior under no slope condition. The first one was dedicated to the development of a method based on oxygen consumption calorimetry (OCC) to measure the fireline intensity for spreading fire experiments [30]. A second study was devoted to the evaluation of the fireline intensity
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based on the mass burning rate [31]. A third work concerned the characterization of fires spreading under no slope condition from a point of view of heat release and radiant and convective fractions [32]. Recently, a preliminary study to this work was conducted to investigate the effect of slope on the rate of spread, the heat release rate and the combustion efficiency [33]. As another step of our study, we propose in the present paper to discriminate both radiation and convection that are globally released during fires spreading across pine needles beds under slope condition and for different fuel loads at laboratory scale. To this end, a Large Scale Heat Release (LSHR) apparatus was used to obtain the HRR and the convective power. This article is divided into two main parts. First, an image processing method was used not only to study the geometry of the flame, but also to monitor the surface burnt by the fire during the propagation. These data, taken in conjunction with the heat release rate and heat flux measurements, helped to explain the differences observed between experiments performed under slope and no slope conditions. The second part of the study was devoted to the quantification of radiation and convection during the spread. For this, we calculated the convective fraction from the temperature measured in the exhaust duct, and we derived the overall radiant fraction from these results. Then, a solid flame model was applied to calculate the radiant fraction due to the flame and the radiant fraction due to embers was deduced from these data. The work reported here is from a small unconfined fuel bed that is not intended to simulate a wide fire front. However, some of the results may have application to fires in pine needles in general.
2. Experimental 2.1. Experimental device The fire spread experiments were conducted by using a 1 MW Large Scale Heat Release (LSHR) apparatus. Fire tests were performed on a 2 m long and 2 m wide combustion table with an inclination of 20°. This angle was chosen for two reasons. Firstly, it allowed us to observe a change in fire behavior compared to experiments under no slope conditions. This observation was not visible for angles less than 20°. Moreover, given the length of the combustion table, this angle prevented the flames from impacting the hood. The device was located under a 3 m 3 m hood with a smoke extraction system having a nominal volumetric flow rate of 1 m3/s (Fig. 1). The bench was placed on a load cell (sampling 1 Hz and 1 g accuracy) to record the mass loss over time during the fire spread. Needles of Pinus pinaster oven dried at 60 °C for 24 h were used as fuel. The net heat of combustion Hc,net was equal to 20,411 kJ/kg and was derived from the gross heat of combustion measured in an oxygen bomb calorimeter following the standard AFNOR NF EN 14918. The surface to volume ratio (equal to 3057 m1) and the density (equal to 511 kg/m3) of the needles were measured following the methodology proposed by Moro [34]. Ambient conditions and fuel moisture content on dry basis were measured for each test just before the ignition. The ambient temperature and relative humidity ranged respectively from 18 °C to 21 °C and from 35% to 49% for all the tests. The fuel moisture content ranged between 5.7% and 8.4 % with a mean value equal to 7.0%. The pine needles were distributed uniformly on the table in order to obtain homogenous fuel beds of 1 m width and 2 m long that occupy only the central part of the table. To ensure that the fuel was uniformly distributed on the combustion table, the deposition area of the fuel was cut into 8 squares of 50 cm by 50 cm (2 along the width and 4 along the length of the table). The total mass of pine needles needed for the experiments was separated in 8 portions of equal mass. One portion was then placed on each
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Smoke exhaust 3 (1m /s)
Thermocouple TK
Gas sampling section
Plenum Baffles Filtering and condensing system Hood (3m x 3m) Sample pump Camera1
O2 and CO/CO2 Analyzers
Total (TG) and radiant (RG) heat flux gauges 20 cm
Control volume
Camera 2
Combustion bench (2m x 2m) 20°
Load cell
Fig. 1. Experimental device for the fire spread study.
square. After an initial visual inspection of the uniformity of the distribution of the fuel, the fuel bed height was measured at eight randomly selected positions along the bed of pine needles. Different fuel loads (w) were used: 0.6, 0.9 and 1.2 kg/m2 that correspond respectively to mean fuel beds height (h) of 3, 5 and 7 cm. For each configuration, at least four repetitions were carried out. The fires were ignited along the entire width of the fuel bed by using between 3 and 6 mL of alcohol. Two cameras were used to observe the fire front: one was placed perpendicularly to the fire spread direction (camera 1 in Fig. 1) while the other was located behind the fire front in the direction of propagation (camera 2 in Fig. 1). During the experiments, cameras were automatically controlled to take pictures every 2–4 s, depending on the rate of spread of the fire. Two heat flux transducers cooled with circulating water were also used to measure heat fluxes during the fire spread (Fig. 1). The first one (TG) was a total heat flux gauge (MEDTHERM GTW-10-32-485A) calibrated up to 100 kW/m2. The second (RG) was a radiant gauge (MEDTHERM 64P-02-24T). The radiant heat flux transducer was equipped with a sapphire window with a view angle of 150°. The choice of the sapphire window was motivated by its spectral transmittance, which is between 0.2 and 5.5 lm. Parent et al. [35] and Boulet et al. [36] measured in the infrared the spectral flux emitted by fires from vegetative fuels with FTIR spectroscopy. The measurements clearly exhibited that the main part of the radiation emitted by the fire was between 2 and 5.5 lm, what is included in the spectral transmittance of the sapphire window. The two heat flux gauges (TG and RG) were oriented toward the flame and were placed at the end of the experimental bench, 20 cm above the bed and in the middle of the fire front. The uncertainty for flux measurements was 3%. The response time of the sensors was less than 250 ms, which was adequately addressed with the 10 Hz sampling rate used for this study. Finally, in the exhaust smoke duct, a thermocouple (Fig. 1), called TK, was used to record the temperature of the combustion gases.
2.2. Calorimetric calculation The measurement of exhaust flow velocity and gas volume fractions were used to determine the heat release rate (HRR), using Oxygen Consumption Calorimetry, based on the formulation derived by Parker [37]. Since the calculation procedure was detailed in [30,31], we present only the main steps here. The composition of the pine needles was determined from an ultimate
analysis of CHON. Their combustion is represented by the stoichiometric reaction for the complete combustion of lignocellulosic materials, given by:
C4:15 H6:65 O2:51 þ 4:56ðO2 þ 3:76N2 Þ ! 4:15CO2 þ
6:65 H2 O þ 17:14N2 2 ð5Þ
The amount of energy released by complete combustion per unit mass of oxygen consumed is taken constant. All gases are considered to behave as ideal gases. The analyzed air is defined by its composition in O2, CO2, H2O and N2. All other gases are lumped into N2. The heat release rate is given by the oxygen molar flow rate:
HRR ¼ Eðn_ o2 n_ o2 ÞW o2
ð6Þ
where E is the heat release per unit mass of O2 consumed, n_ O2 and n_ O2 represent respectively the molar flow rates of O2 in incoming air and in the exhaust duct and W O2 is the molecular weight of oxygen. Parker [37] provided a detailed calculation to evaluate the molar flow rate of oxygen based on the volume flow rate in the exhaust _ and the molar fraction of species. He derived the three folduct (V) lowing relations to calculate the HRR:
Eq0 W O2 / 1 X 0H2 O X aO2 V_ ð1 /Þ þ a/ W air sffiffiffiffiffiffiffi k t DP V_ ¼ 22:4A kp T TK xaO2 1 xaCO2 xaO2 1 xaCO2 /¼ xaO2 1 xaCO2 xaO2
HRR ¼
ð7Þ ð8Þ
ð9Þ
where X denotes the molar fraction and q0 is the density of dry air at 298 K and 1 atm. V_ is the standard flow rate in the exhaust duct. a is the expansion factor for the fraction of the air that was depleted of its oxygen. The superscript ° is for the incoming air. A is the cross sectional area of the duct, kt is a constant determined via a propane burner calibration, kp = 1.108 for a bi-directional probe, DP is the pressure drop across the bi-directional probe and TTK is the gas temperature in the duct measured by the thermocouple TK. The HRR is therefore computed from many variables and each variable has a corresponding uncertainty. In this study, the instrumentation is similar to that of the Room Corner Test [38], for which Axelsson et al. [39] analyzed the uncertainty considering individ-
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ual sources of errors for rate of heat release measurements. The combined expanded uncertainty was provided with a coverage factor of 2, giving a confidence level of 95%. Following the same methodology, the combined expanded uncertainty calculated in our case was 3.5%. This value was obtained because of accurate paramagnetic oxygen sensor and calculation of the heat release per unit mass of O2 consumed (E). As the fuel composition was known, we reduced indeed the uncertainty by estimating E with the following expression:
E¼
Hc;net W fuel ¼ 13:98 MJ=kg nO2 W O2
ð10Þ
where nO2 = 4.56 (Eq. (5)) and Wfuel is the molecular weight of the fuel. This value corresponds to an increase of 6.7% compared to Huggett’s constant (13.1 MJ/kg) generally used in calorimetric studies for organic fuels [40].
Table 1 Geometrical properties of the fire front for experiments performed with a slope of 20°. The standard deviations are in parenthesis. Test n°
w (kg/m2)
Lf (cm)
b (°)
d (°)
ROShead (mm/s)
06_1 06_2 06_3 06_4 06_5 09_1 09_2 09_3 09_4 09_5 12_1 12_2 12_3 12_4
0.6 0.6 0.6 0.6 0.6 0.9 0.9 0.9 0.9 0.9 1.2 1.2 1.2 1.2
– 38.7 (9.8) 44.0 (10.7) – 56.4 (12.3) 60.8 (10.0) 76.5 (14.0) 73.4 (14.6) 63.0 (12.8) 78.1 (17.5) 85.6 (16.1) 88.5 (15.2) 92.2 (16.2) 93.3 (15.8)
– 6.7 (5.6) 9.5 (8.0) – 8.2 (6.0) 6.6 (7.4) 5.3 (8.9) 5.7 (7.9) 6.2 (5.6) 3.6 (4.8) 4.4 (5.5) 6.0 (6.5) 5.7 (6.2) 5.4 (6.4)
– 37.0 (6.2) 39.1 (7.1) – 27.5 (5.3) 27.1 (6.2) 22.5 (7.8) 25.5 (8.1) 26.7 (5.3) 23.6 (3.1) 25.9 (4.0) 24.1 (3.2) 26.0 (5.5) 25.5 (4.8)
8.8 9.4 12.5 9.5 10.1 14.3 17.6 15.7 13.4 13.0 16.6 15.8 17.5 14.8
3. Results and discussion 2.3. Fire front descriptors 3.1. Fire front properties The characterization of the fire front was carried out with the following information collected during the experiments (Fig. 2). The rate of spread of the head of the fire front (ROShead) was calculated from the time needed to the head to cover intervals of 0.25 m along the bench. Thus, eight data points were obtained for each experiment and a least-squares regression was used to fit a straight line to the data points in order to obtain ROShead. As the entire fire front did not propagate at the same speed, the rate of spread of the flanks of the fire front (ROSflank) was also calculated through image processing. For this, the pictures taken by the cameras (Fig. 1) were used to determine the rear position of the flanks of the fire front versus time. A least squares regression was then used to fit a straight line to the data points in order to obtain ROSflank. Flame length (Lf), flame angle (b) and the angle of the fire front (d) were determined from photographs taken by camera 1 (Fig. 1) located perpendicularly to the fire spread direction. Lf corresponds to the flame length expressed following the suggestions of Anderson et al. [12]. b is the angle between the flame and the vertical axis. d is defined as the angle between the fire front and the propagation axis. The length of the fire front (L) and the burnt area (Aburnt) were obtained from photographs recorded by camera 2 (Fig. 1) placed behind the fire front. Since the flames on the flanks of the fire front were smaller than in the head and were inclined inwardly of the fire front, we also introduced the length Lh which corresponds to the length of the front, where the flames are the highest (Fig. 2) and inclined outwardly of the front. This measurement was also carried out with camera 2. For each experience, the mean values of Lf, b, d and Lh were computed from 30 to 50 images.
Table 1 shows the geometrical properties of the fire front for each experiment. The variations observed among a same fuel configuration can be explained by the difference of the fuel moisture content and in a lesser extent by a slight variation in the experimental protocol (ignition, fuel distribution or fuel bed height). An average of these values is reported in Table 2, where the mean data obtained for no slope [32] are reported to facilitate the comparison between no slope and upslope fire spread experiments. A brief discussion of these results is presented in the following to facilitate the understanding of the phenomena. By observing the fire front during propagation experiments, two different behaviors were highlighted depending on whether the experiments were carried out with or without slope: For horizontal fire spread, the data have already been published [32]. Only a short summary of results is performed hereafter. The fire front exhibited a nearly linear shape (Fig. 3a). On the edges of the bed, the fire front was however slightly curved and the flame length was lower than at the center. The whole part of the fire front propagated roughly at the same rate of spread (between 3.7 and 5.6 mm/s depending on the fuel load). When the fuel load was multiplied by 1.5 and 2, the mean ROShead increased by 1.3 and 1.5. The fire front was tilted backward with an angle ranging from 12.8° to 17.6° according to the fuel load. The flame lengths ranged between 25.5 and 60.2 cm. Therefore, the flame length increased by a factor 1.7 and 2.4 when the fuel load increases by a factor of 1.5 and 2.
Fig. 2. Geometric descriptors of the flame and fire front (a) lateral view and (b) rear view.
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Table 2 Mean geometrical properties of the fire front. The standard deviation is in parenthesis. w (kg/m2)
Slope (°)
Lh/L (%)
Lf (cm)
b (°)
d (°)
ROShead (mm/s)
ROSflank (mm/s)
0.6 0.9 1.2
0 0 0
100 100 100
25.5 (2.3) 44.4 (9.3) 60.2 (14.9)
12.8 (4.2) 14.1 (5.0) 17.6 (3.6)
90 90 90
3.7 (0.2) 4.7 (0.7) 5.6 (1.4)
– – –
0.6 0.9 1.2
20 20 20
42.5 (8.2) 27.8 (8.7) 28.0 (10.8)
46.4 (7.4) 70.4 (7.1) 89.9 (9.8)
8.1 (1.1) 5.5 (1.0) 5.4 (0.6)
34.5 (5.0) 25.1 (1.8) 25.4 (0.8)
10.1 (1.3) 14.8 (1.7) 16.2 (1.0)
8.0 (1.7) 8.1 (1.2) 10.3 (0.8)
Fig. 3. Picture of the fire front under (a) no-slope condition and (b) 20° upslope condition.
For experiments at a slope of 20°, the fire front had a V-shape (Fig. 3b). The fire head was located in the middle of the fuel bed. This behavior was consistent with the observations reported in literature [6,11,41]. According to Dupuy et al. [11], the entrainment of air from the sides of the fuel bed area explains the distortion of the fire front from the initial straight ignition line. Because of this distortion, the whole fire front did not propagate with the same rate. The head of the fire front had a rate of spread greater than that of the flanks. In addition, ROShead increased with the fuel load. When the fuel load was multiplied by 1.5 and 2, mean ROShead were indeed multiplied by 1.5 and 1.6. For a same fuel load, the rate of spread was about 2.7 times higher for experiments with slope that without slope. These observations are consistent with literature results [4,7,9– 11]. The flame lengths ranged between 46.4 and 89.9 cm. Thus, for a given fuel load, the flames are about 1.6 times higher for the experiments under slope conditions than under no slope conditions. Contrary to the experiments without slope, the flames were inclined forward with an angle between 5.4° and 8.1° depending on the fuel load. For high fuel loads, the flames were less inclined due to greater buoyancy associated with the fuel load. Another difference observed between the experiments under slope and no slope conditions is the evolution of the fire front length. Because of the distortion of the fire front (Fig. 4a), its length increased during the spreading (Fig. 4b). L can indeed be multiplied by a factor up to 3 during the experiments. However, the size of the area where the fire is the
highest (Lh) corresponds only to a length ranging from 27.8% to 42.5% of the total length of the fire front depending on the fuel load. 3.2. General description of HRR Instantaneous heat release rates (HRR) measured during the fire tests are displayed in Fig. 5. The curves obtained under no slope conditions [32] are also provided to facilitate the comparison. Table 3 shows the maximum values obtained under slope conditions. For experiments performed without slope [32], a quasisteady state was reached for all fuel loads. The average heat release rates were 41, 87 and 130 kW for 0.6, 0.9 and 1.2 kg/m2, respectively. The greater the fuel load was, the higher the heat release rate was. The mean HRR were multiplied by 2.1 and 3.2 with the increasing of fuel load by a factor of 1.5 and 2. The increase is not linear with regard to the fuel load. The flameout occurred earlier for higher fuel load due to the increase in the rate of spread (Table 2). For experiments with a slope of 20°, a quasi-steady state was not observed for the heat release, while the rate of spread of the fire head was constant. The heat release rate continued to increase until the fire front reached the end of the table. This observation is related to the size of the fuel bed that did not allow the fire to reach a steady state. At the flameout, the HRR reached about 160 kW, 295 kW and 385 kW for a fuel load of 0.6, 0.9 and 1.2 kg/ m2 respectively. Despite differences between the experiments with and without slope, the total heat released was almost constant for
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Fig. 4. (a) Fireline contours for fire spread and (b) length of the fire front for propagation – for a slope of 20° and a fuel load of 1.2 kg/m2 until the arrival of the fire front head at the table end.
a
b
Fig. 5. Heat release rate versus time for experiments (a) under no slope conditions [32] and (b) for a slope equal to 20°.
Table 3 Properties of the fire spread experiments. Test n°
w (kg/m2)
Peak MLR (g/s)
Peak HRR (kW)
THR (MJ)
Peak Utot (kW/m2)
Peak Urad (kW/m2)
06_1 06_2 06_3 06_4 06_5 09_1 09_2 09_3 09_4 09_5 12_1 12_2 12_3 12_4
0.6 0.6 0.6 0.6 0.6 0.9 0.9 0.9 0.9 0.9 1.2 1.2 1.2 1.2
6.0 6.2 7.7 5.7 8.0 14.1 20.3 17.3 14.7 16.3 22.7 23.4 25.0 22.3
102.0 119.7 154.8 106.5 166.9 244.9 363.5 319.9 255.3 284.8 366.2 380.8 400.2 390.6
21.7 22.9 23.2 21.7 24.6 31.9 33.1 33.1 30.2 27.3 41.8 43.9 44.3 47.8
9.1 11.8 15.2 10.4 11.0 17.4 31.0 28.9 26.4 18.3 26.4 29.7 34.3 18.9
7.6 10.0 13.4 9.1 9.0 13.0 25.6 21.4 22.3 15.7 – 24.5 28.8 16.1
a given fuel load (22.8, 32.2 and 44.5 MJ for 0.6, 0.9 and 1.2 kg/m2 respectively) regardless propagation conditions (Table 4). As the fuel consumption efficiency and the amount of fuel were equal for the two configurations, the combustion efficiency was therefore almost the same under slope and no slope conditions.
The temporal evolution of the mass of the fuel bed is given in Fig. 6 and the corresponding mass loss rate (MLR) versus time in Fig. 7. As for the heat release rate, the results for no slope conditions [32] are also provided. Under no slope conditions, the mass loss rate was almost constant after the ignition stage. The reached value varied according to the fuel load: 2.46 g/s, 4.97 g/s and 8.06 g/s for 0.6, 0.9 and 1.2 kg/m2. Therefore, the mean MLR values were multiplied by 2.0 and 3.3 when the fuel load increases by a factor 1.5 and 2. Under slope conditions, the MLR values were higher than under no slope conditions and increased during the fire spread. These observations are consistent with those reported by Dupuy [7]. They observed indeed that for litters of P. pinaster, experimental fires became unsteady for slopes above 10°. The mass loss rate follows therefore the same trend as the heat released rate (Fig. 5). This is not surprising, since according to previous studies [30–33], the heat release rate and the mass loss rate are linked by the following relationship:
HRR ¼ Heff MLR
ð11Þ
where Heff is the effective heat of combustion.
Table 4 Mean properties of the fire front. The standard deviation is in parenthesis. w (kg/m2)
Slope (°)
THR (MJ)
Peak Utot (kW/m2)
Peak Urad (kW/m2)
vconv (%)
vconv,fl (%)
vrad,em (%)
0.6 0.9 1.2
0 0 0
21.9 (2.3) 33.6 (3.2) 44.2 (2.3)
7.6 (0.5) 10.2 (1.7) 13.9 (3.5)
6.2 (0.4) 8.5 (1.6) 11.3 (3.0)
83.8 (1.9) 80.2 (4.6) 68.5 (7.7)
10.1 (0.8) 9.9 (0.9) 9.1 (0.2)
7.3 (1.9) 9.9 (2) 13.3 (2.2)
0.6 0.9 1.2
20 20 20
22.8 (1.1) 32.2 (1.1) 44.5 (2.1)
11.5 (2.0) 24.4 (5.6) 27.3 (5.6)
9.8 (1.9) 19.6 (4.6) 23.1 (5.3)
74.9 (4.0) 61.1 (2.4) 61.2 (2.9)
13.6 (1.7) 24.1 (2.6) 24.2 (2.7)
11.5 14.8 14.6
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Fig. 8. Comparison between measured and estimated HRR for a fuel load of 0.9 kg/m2 under no slope conditions.
Fig. 6. Mass loss of the fuel beds versus time.
3.3. Calculation of HRR from the burnt surface
According to Eq. (11), the variation of the heat release rate during the propagation is therefore due to the mass evolution of the fuel bed. This quantity can be expressed in terms of the surface burnt by the fire front as follows:
m ¼ m0 wgAburnt
ð12Þ
where m0 is the initial mass of pine needles, w is the fuel load, Aburnt is the burnt surface and g is fuel consumption efficiency equal to 0.97 for our experiments. This value is in agreement with the work of Dupuy [7], in which a combustion efficiency equal to 0.95 was found for P. pinaster litters. The mass loss rate is therefore given by:
MLR ¼ wg
dAburnt dt
ð13Þ
and by using Eq. (11), the heat release rate is given by:
HRR ¼ Heff wg
dAburnt dt
ð14Þ
As the fire front exhibited two different behaviors depending on whether the experiments were carried out under slope or no slope burnt conditions, the expression of dAdt changes. Under no slope conditions, by considering that the fire front was linear during the propagation and kept the same length:
dAburnt;noslope ¼ LROShead dt
ð15Þ
As the rate of spread can be considered constant during the propagation (Table 2), the time derivative of the burnt area remains constant during the fire spread. According to Eqs. (13) and (14):
a
MLRno slope ¼ wgLROShead HRRno slope ¼ Heff wgLROShead
ð16Þ
Under no slope conditions, the mass loss rate and the heat release rate therefore kept roughly the same value during the fire spread, as the rate of spread and the fire front length remained almost constant. This result explains the quasi steady state observed on the curves (Figs. 5 and 7a). An example of the calculation of the heat release rate by using Eq. (16) is given in Fig. 8 for a fuel load of 0.9 kg/m2. For the other fuel loads, same results were obtained. At the beginning of the propagation, the calculation underestimated the HRR whereas at the end, the heat release rate was slightly overestimated. This was due to a slight variation of the rate of spread during the fire spread. At the beginning of the propagation, the rate of spread was indeed a little higher than the mean value due to an ignition effect. At the end, the opposite phenomenon was observed due to the weak distortion of the fire front at the edges. Despite these slight variations, the heat release rate calculated from the time derivative of the burnt area is very close to the measurements obtained by OC calorimetry. For a slope of 20°, the distortion of the fire front (Figs. 3b and 4a) induced an increase of the fire front length during the propagation (Fig. 4b). This was due to the different values of the rate of spread for the head and the flanks of the fire. Given the shape of the fire front, it is difficult to propose an analytical expression of the burnt surface. The time evolution of the surface burnt by the fire front was therefore determined by image processing by using the photographs recorded by camera 2. Figure 9 shows an example of the time evolution of the burnt surface obtained every 40 s for the three fuel loads. For all fuel loads, an increase of the burnt surface per unit of time was noted during the fire spread until the head of the fire front reached
b
Fig. 7. Mass loss rate versus time for experiments (a) under no slope conditions [32] and (b) for a slope of 20°.
V. Tihay et al. / Combustion and Flame 161 (2014) 3237–3248
3245
Fig. 9. Time evolution of the burnt area for propagation for a slope of 20° and for a fuel load of (a) 0.6 kg/m2, (b) 0.9 kg/m2 and (c) 1.2 kg/m2.
the end of the table. This rise led to an increase of the mass loss rate and heat release rate (Eq. (11)). Figure 10 presents the heat release rate calculated with Eq. (14) for the three fuel loads by using the time derivative of the surface burnt by the fire front. Only the portion on which the image processing was performed is shown in this figure. The heat release rate calculated from the geometrical properties of the fire front is very close to the measurements by OC calorimetry. Although this method did not allow following the rapid fluctuations of HRR, the same tendencies were observed for all fuel loads. These results confirm that for a uniform fuel, HRR can be predicted by the variation of the burnt surface per unit of time using a constant burning efficiency and effective heat of combustion. The rate of spread of the fire front head is not sufficient to understand the dynamics of fire spreading under slope conditions. The rate of spread can be constant during the propagation, whereas the heat release rate increases. To characterize a fire at this scale, it is therefore useful to employ the fireline intensity combined with the rate of spread. Because of the experimental procedure, these results are only applicable to fires of unconfined fuel beds realized at the same scale.
3.4. Convective fraction To estimate the contribution of convection, it is necessary to know the gas temperature at the duct entry (Tg). Through thermocouple TK (Fig. 1), it is possible to know the gas temperature in the exhaust duct (Fig. 11). However, during its passage through the exhaust duct, the gas was cooled. To take into account the heat losses in the duct before the measurements (that is to say, over a length equal to l = 5.576 m), a heat balance was performed in the duct. For a duct section with a length dx:
_ mix cp;mix Tðx; tÞ ¼ M _ mix cp;mix Tðx þ dx; t þ dtÞ þ Uloss M
ð17Þ
where Uloss corresponds to the heat losses modeled by:
Uloss ¼ p d dx UðT Ta Þ
ð18Þ
where d is the duct diameter (0.4 m) and U is the overall heat transmission coefficient of the duct given by:
U¼
_ mix cp;mix aM pd
ð19Þ
where a is a coefficient determined under no slope conditions by using temperature measurements in the duct. The detailed calculation is available in [32].
Fig. 10. Comparison between measured and estimated HRR for a fuel load of (a) 0.6 kg/m2, (b) 0.9 kg/m2 and (c) 1.2 kg/m2 – for a slope of 20°.
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V. Tihay et al. / Combustion and Flame 161 (2014) 3237–3248 30 With a slope of 20°°
Heat fluxes (kW/m2)
25 20
Without slope 15 10 5 0 0
50
100
150
200
250
300
350
400
450
500
Time (s) Total heat flux (TG)
Fig. 11. Temperature measurement in the duct for a fuel load of 0.9 kg/m2 for a slope of 20°.
Radiant Heat flux (RG)
Fig. 12. Total (TG) and radiant heat fluxes (RG) for a fuel load of 1.2 kg/m2 and a slope of 20°.
By combining Eqs. (17)–(19), one obtains:
1 @Tðx; tÞ @Tðx; tÞ þ þ aTðx; tÞ ¼ aT a @t @x
v
ð20Þ
where v is the mean gas velocity in the duct. According to temperature measurements obtained by the thermocouple TK in the extraction duct (Fig. 11), the gas temperature increased quasi-linearly with time. We can thus assume that @Tðx;tÞ ¼ K. The solving of Eq. (20) leads to the gas temperature at @t the duct entry i.e. for x = 0:
Tg ¼ Ta þ
K K al e þ T TK T a av av
ð21Þ
The knowledge of the gas temperature allows the calculation of the convective heat release rate HRRconv with [42]:
_ mix HRRconv ¼ M
Z
Tg
cp;mix ðTÞ dT
ð22Þ
Ta
where Ta is the ambient temperature, cp,mix is the specific heat of the mixture at temperature T taken equal to that of dry air and _ mix is the mass flow rate of the chemical compounds-air mixture. M As the mass flow rate was constant in the duct, it was determined from the volumetric flow rate of the mixture measured in the gas _ TK Þ by the following equation: sampling section VðT
_ mix ¼ VðT _ TK Þ qðT TK Þ M
ð23Þ
where the density of the mixture was taken equal to that of dry air:
298 qðT TK Þ ¼ qair;298 T TK
ð24Þ
The comparison of the heat losses (Eq. (18)) and the convective heat release rate (Eq. (22)) shows that the heat losses in the duct correspond to a mean value of 14.5% of the HRRconv. Then, the convective fraction corresponds to the ratio between the convective heat release rate HRRconv and the heat release rate HRR:
vconv ¼
HRRconv HRR
3.5. Heat flux measurements and overall radiant fraction The time evolution of the heat fluxes received by the two heat flux gauges (TG and RG) located 20 cm above the fuel bed at the end of the experimental bench (Fig. 1) is shown in Fig. 12 for 1.2 kg/m2 without slope [32] and with a slope of 20°. In the preheating zone, the heat fluxes progressively increased up to maximum values which vary according to the fuel loads. The maximal values recorded for the radiant (Urad) and total (Utot) heat fluxes are reported in Table 3. This maximum corresponds to the time when the flames reach the end of the bench, i.e. the closest point of the measurement device. As the total and radiant heat fluxes coincide in the preheating zone, heat transfer is mainly due to radiation. Close to the flame zone, a greater difference appears between both signals. This is characteristic of heat transfer combining radiation and convection. The comparison of the curves obtained under slope and no slope conditions shows two major differences. First, the heat fluxes recorded during experiments under slope conditions are shifted in time. This is due to the higher rate of spread (Table 2). Second, the heat fluxes are higher for upslope fire (Table 4). To characterize the effect of slope on the radiant heat transfer, the overall radiant fraction was firstly calculated. As the sum of the convective and radiant fraction is equal to 100%, the overall radiant fraction corresponds to:
vrad ¼ 100 vconv
ð26Þ
Under a slope of 20°, the overall radiant fractions was therefore equal to 25.1%, 38.9% and 38.8% for fuel loads of 0.6, 0.9 and 1.2 kg/ m2 respectively. For comparison, under no slope conditions, the overall radiant fraction obtained was in the range of 16.2–31.5% [32]. These values are consistent with literature [16,43]. Therefore, for a given fuel load, the overall radiant fraction was higher for upslope fires than under no slope condition. 3.6. Contribution of flames and embers on the radiant fraction
ð25Þ
The mean convective fractions are given in Table 4 for experiments under slope conditions. The mean values obtained under no slope conditions [32] are also provided to facilitate the comparison. For a slope of 20°, the convective fractions were in the range of 61.1–74.9%. Approximately the same value was obtained for fuel loads of 0.9 and 1.2 kg/m2 (about 61%). For 0.6 kg/m2, the convective fraction was higher (about 75%). These values are close to those obtained by Tewarson [27].
To attempt to distinguish the radiant fraction due to the flames and that due to the embers, we first calculated the radiant fraction due to the flames from the radiant heat flux measurements. The radiant fraction corresponds to the ratio between the radiant power (Prad) and the heat release rate (HRR given in Fig. 5 for example).
vrad ¼
Prad HRR
ð27Þ
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To calculate the radiant power, a solid flame model was used by neglecting the atmospheric absorption. For the flames, the radiant power (Prad,fl) was obtained from the heat flux density measurements qRG performed with the radiant heat flux gauge RG (Fig. 12) by considering the view factor (F) and the emission surface of the fire front (Sfl) taking into account the two faces of the flames. In the following, we considered that the radiant energy was emitted uniformly over the flame area. This is of course a strong assumption. However, as the thickness of the flame was almost constant in the continuous flame zone during our experiments, this assumption seems acceptable. Therefore:
qRG ¼
Prad;fl F Sfl
ð28Þ
By combining Eqs. (27) and (28), the radiant fraction of the flames Fig. 13. Diagram describing the modeling of the fire front for the calculation of the view factors.
vrad,fl corresponds to:
vrad;fl ¼
qRG Sfl HRR F
ð29Þ
e ¼ 1 expðK m Lthick Þ
ð30Þ
Therefore, for a constant chemical composition of the flame (i.e. for a same extinction coefficient), the greater the flame thickness is, the higher its emissivity is. Secondly, the flame volume increase leads to an underventilation of the fire. This induces a more signif-
Radiant fraction due to the flames
0.35
The determination of the view factor F was based on the Contour Double Integral Formula (CDIF) method, which calculates the view factor between planar polygons. To simplify the determination of the view factor and the emission surface of the fire front, the geometry of the fire front was approximated by simple shapes. As the flanks of the fire front consisted of small discontinuous flames, inclined inward the fire front, we neglected its contribution to radiation impinging the heat flux sensors. Only the part of the front where the flames are the highest was considered for the calculation of the radiant fraction. Considering the V-shape of the fire front (Figs. 3 and 9), it was modeled by two trapezoids forming an angle d with the propagation axis and having a base of length L2h and a height equals to Lf cos b. Figure 13 shows a sketch of the configuration adopted. This approximation for the fire front is also strong. However, this assumption is fairly good, when the head of the fire front is located between 1.2 and 1.8 m from the ignition edge. On the first meter, the fire front was indeed rounded (Fig. 9). In the following, the calculations were only performed when the fire head was between 1.2 and 1.8 m. Figure 14 presents the evolution of the radiant fraction over time obtained for experiments under slope conditions performed with a fuel load of 0.6 and 1.2 kg/m2. Mean values equal to 13.6%, 24.1% and 24.2% were obtained for 0.6, 0.9 and 1.2 kg/m2 respectively (Table 4). The radiant fraction due to the flames tends therefore to increase with the fuel load even if close values were obtained for fuel loads equal to 0.9 and 1.2 kg/ m2. Table 4 also reports the mean data obtained for no slope [32] to facilitate the comparison. Under no slope conditions [32], the radiant fraction of the flame slightly decreased (from 10.1% to 9.1%) with increasing fuel load. This was due to the inclination of the flame. Although the flame length increased with increasing load, the flames leaned further backward simultaneously (Table 2). This tendency leads to a decrease of the radiant fraction value. The comparison between the experiments under slope and no slope conditions shows that for a given fuel load, the radiant fraction of the flame is higher for a fire front spreading along a slope of 20° than along a flat surface. To explain these differences, it is necessary to consider the influence of two parameters. Firstly, when the fuel load increases or when the propagation takes place with a slope of 20°, the flame thickness increases. The emissivity is related to the extinction coefficient Km and the flame thickness Lthick by the following relationship [44]:
0.3 0.25 0.2 0.15 0.1 0.05 0 0
50
100
150
200
250
Time (s) 0.6 kg/m2
1.2 kg/m2
Fig. 14. Evolution of the radiant fractions due to the flames over time for a slope of 20°.
icant soot production within the flame and an increase of the extinction coefficient, since the extinction coefficient is correlated to the soot volume fraction fv by [45,46]:
K m ¼ 0:1ðX CO2 þ X H2 O Þ þ 1862f v T
ð31Þ
where X CO2 and X H2 O are the mole fraction of CO2 and H2O in the combustion products. Then, the increase of the extinction coefficient leads to an increase of the flame emissivity. Both factors analyzed here above contribute to the increase of the radiant fractions observed during our experiments with fuel load. The contribution of embers to the radiation emitted by the fire front was obtained by deducting from the overall radiant fraction the part due to the flames:
vrad;em ¼ vrad vrad;fl
ð32Þ
Table 4 shows the mean radiant fractions for the embers under slope conditions. The mean data obtained for no slope [32] are also reported to facilitate the comparison. Under no slope conditions [32], the radiant fraction of the embers increases (from 7.3% to 13.3%) when the fuel load ranges from 0.6 to 1.2 kg/m2. For the experiments under slope conditions, the radiant fraction due to embers is equal to 11.5%, 14.8% and 14.6% for the fuel loads of 0.6, 0.9 and 1.2 kg/m2, respectively. Therefore, for a given fuel load, the radiant fractions of the embers were slightly higher for experiments under slope conditions than along a flat surface. This result can be explained by the fact that the volume of embers was larger when experiments were conducted with a slope because the depth of the fire front was greater.
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4. Conclusion In this study, oxygen consumption calorimetry was used to analyze the spreading of fires across pine needles beds for various fuel loads at one slope. The properties of the fire front, the heat release rate, the mass loss rate and the heat transfer were investigated to understand the influence of slope on fire behavior. The main results can be summarized as follows: Conversely to experiments under no slope conditions, the fire front has a V-shape because of a distortion. The length of the fire front and the time derivative of the burnt surface increase during the propagation. This observation is related to the size of the fuel bed that did not allow the fire to reach a steady state. As the time derivative of the burnt area increases for a slope of 20°, the MLR increases hence the HRR also. Under no slope condition, the HRR and the MLR reach a quasi-steady state. The burnt surface increased indeed steadily, leading to almost constant values of MLR and HRR. The comparison between the heat release rate calculated from the geometrical properties of the fire front and the measurements by OC calorimetry confirmed the potential for estimating the heat release rate with the fuel load and the time derivative of the burnt surface. Convection represents between 61.1% and 74.9% of the heat transfer for a slope of 20°. These values are lower than those encountered under no slope conditions. With a slope of 20°, radiation represents between 25.1% and 38.9% of the heat transfer. The main part is due to the flames (between 13.6% and 24.2%). The remaining part comes from the embers (from 11.5% to 14.8%). For both, the radiation rises with the fuel load. These values are higher than those measured under no slope conditions (overall radiant fraction varied between 16.2% and 31.5% depending on fuel loads). The reasons are the increase of the ember volume, the thickening of the flames and a more significant production of soot.
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