Citation

Monod B, Collin A, Parent G, Boulet P. Fire Safety J. 2009; 44(1): 88-95.

Copyright

(Copyright © 2009, Elsevier Publishing)

DOI

10.1016/j.firesaf.2008.03.009

PMID

unavailable

Abstract

aLEMTA, Nancy-Université, CNRS, Faculté des Sciences et Techniques, BP 239, 54506 Vandœuvre lès Nancy Cedex, France bLEMTA, Nancy-Université, CNRS, 2 Avenue de la Forêt de Haye, BP 160, 54504 Vandœuvre lès Nancy Cedex, France An experimental study has been carried out on the radiative properties of six vegetal species. Measurements have been performed in the infrared range on the directional-hemispherical transmissivity and reflectivity. The spectral absorptivity of the various species has been obtained after a pre-processing step, taking into account the porosity of the samples and therefore yielding the characteristics of the plant matter itself. A near constant absorption has been obtained between 2.8 and (3500 and , respectively), showing negligible discrepancies between the species. Some variations are observed in the near infrared range, however. Complementary measurements have been conducted after 40 days on dry species, indicating variations in the characteristics linked to a loss in water content. In parallel, numerical investigations have been also conducted applying a ray-tracing method on the basis of these measured characteristics in order to evaluate the radiative properties of a medium featuring a set of leaves. The absorption of an ensemble of individual vegetation particles has been sought, as a preliminary step before describing a realistic vegetation medium. Comparisons with a classical approximate formula for the extinction of an equivalent medium are discussed. Keywords: Reflection; Transmission; Absorption; Vegetation; Infrared The corresponding extinction coefficient has to be computed prior to the RTE solution. On the basis of pioneer works [7], the corresponding formulation is In the frame of experimental studies, Chetehouna et al. [12] measured the extinction coefficient for Q. coccifera. They showed that the absorption coefficient is proportional to the load and that the proportionality coefficient depends upon the nature of the vegetation. However, the drawback is the required knowledge of all vegetation properties, like the mass density and the surface area to volume ratio. Other works investigated the effects of the extinction coefficient on fire behavior. For example, Pimont et al. [13] showed that the introduction of weak heterogeneities in the vegetation induces important modifications in the fire behavior. This study again demonstrates that the extinction coefficient is a major required parameter in fire science. The present study was conducted considering that the formulation for the extinction coefficient could benefit from a comparison with an experimental investigation based on spectral measurements aimed at its validation, searching for a validation domain and for some controlling parameters. For the application of fire spread, the wavelength range which is relevant is in the infrared. For the vegetation, incident radiation comes from flames. Assuming flame temperatures between 700 and leads to a need for radiative properties from 1.5 to (restricted to in the present study owing to the experimental device used). Studies are available for the radiative properties of the vegetation in the visible range. In particular the reader is referred to the contributions conducted within LOPEX93 (for leaf optical properties experiment) [14] and to the PROSPECT model aimed at the determination of leaf properties in the context of remote sensing applications [15]. The basis was the measurement of hemispherical reflectivity and transmissivity of fresh and dry species. Such a method can be extended to the infrared range, using a Fourier transform infrared (FTIR) spectrometer, an integrating sphere and a specific detector. Some attempts have been reported in the literature in the infrared range (see, for example, [16] and [17]) but very few data are available, in particular beyond the near infrared range. Therefore, the first part of our study was to perform measurements on six available species typical of the vegetation of the south of France: Q. coccifera, A. unedo, Genista, Juniperus oxycedrus, Romarinus officinalis and Pinus halepensis. The experimental characterization has been conducted on fresh species and repeated after 40 days in order to investigate the role of water loss on the radiation absorption in the infrared. Note that this may have two applications: (i) evaluating whether or not caution has to be taken for the exact conditions in which the species are chosen (role of season or meteorological conditions) and (ii) observing if important variations occur in the radiative properties of the vegetation during the drying step before the pyrolysis step itself in case of a fire spread (may be important enough to be taken into account in modeling tools?). Beside this problem of the characterization of the plant matter, the above question of the determination of the radiative property of the equivalent vegetation medium has been investigated. In the past, a method based on ray tracing has been successfully applied in order to determine the radiative properties of heterogeneous media or of an ensemble of particles (see Coquard and Baillis [18] and [19], for example). This method has been used here, considering an equivalent vegetation medium built with individual leaves with known properties taken from our measurements. Transmitted, reflected and absorbed rays are registered. Then, an equivalent extinction coefficient may be identified and the influence of various numerical parameters can be investigated. In the following sections, the first section is devoted to the experimental part of the work, with the description of the experimental setup and the results directly extracted from the measurements. Then the absorption is deduced from a post-processing step taking into account the porosity of the samples. Comparisons are conducted on fresh and dry species. Finally, a numerical investigation is presented for the concept of the equivalent medium property. Directional-hemispherical transmissivity and reflectivity measurements have been carried out in the infrared range. The experimental setup combines an FTIR spectrometer, an integrating sphere and an MCT detector on a classical device for this type of measurements: the sphere is located just after the spectrometer output, the position of the sample (at the inlet or outlet of the sphere) leads to a configuration of transmissivity or reflectivity measurement, and the detector is connected to the sphere and collects a fraction of radiative flux representative of the total radiation inside the sphere. The FTIR spectrometer is an IFS66v/s apparatus by Bruker. This spectrometer is built around a Michelson interferometer with a beamsplitter made of germanium on KBr and a globar as the source. In this configuration the spectral range is 500–. The movable mirror is translated up to a speed that leads to an interferometric signal at a frequency equal to 100 kHz, with the radiation of an He–Ne laser that controls the movement of the mirror. The detector has a sufficient bandwidth (2 MHz) to follow the obtained signal. This leads to a minimal acquisition time for an interferogram, so that a large number of acquisitions (scans) can be performed in order to decrease noise by averaging scans (typically 5000 scans have been performed for the results presented here). The beam exiting from the spectrometer is focused on the sample and collected by the integrating sphere after transmission or reflection by the sample. The sphere is specifically tailored to the infrared range with a gold internal coating warrantying a reflectivity factor equal to 0.9865 (coating referred as infragold). The detector is of MCT type, liquid nitrogen cooled, by Kolmar technologies, working in a photovoltaic mode ensuring a good linearity. Its maximal spectral bandwidth is 850–. Given the spectral bandwidth of the beamsplitter and of the detector, results presented here will be in the 1000– domain, as the signal outside this range is quite small. Samples were prepared two days after gathering. Leaves (Q. coccifera, A. unedo) are simply fastened in a support. Other species with a smaller leaf surface or with needles (Genista, J. oxycedrus, R. officinalis and Pinus halepensis) need a specific preparation. Needles or pieces are carefully placed side by side as to provide a sample with a surface larger than the one intersected by the beam. Despite the care brought to this preparation the sample seen by the beam is not a continuous medium and rather behaves like a porous surface, which leads to an overestimate of transmissivity (where radiation crosses a void fraction of the observed surface) and underestimate of reflectivity (since the same void area does not contribute to the reflection as a continuous surface would) as compared with what the plant matter would provide in reality. This can be easily corrected considering a wavelength where the sample should be opaque, for example, between 1000 and , a range determined thanks to the measurements performed on Q. coccifera and A. unedo for which the samples have been studied without prior conditioning so that no deviation is introduced by the porous nature of the sample. The false transmissivity observed on the other species in this range is characteristic of the porosity of the constructed sample. A threshold correction is performed to decrease the transmissivity to the actual level of the matter of interest (subtracting the so-called false transmissivity), whereas the reflected signal is increased dividing the measured signal by this porosity value. Data are then post-processed with a classical technique taking into account a reference signal (collected in transmission configuration with the sphere without sample) and a zero level signal (sphere used in reflection configuration in the absence of the sample as to detect a possible reflection signal which is not due to the sample itself). Data obtained after the above-mentioned treatment are presented in Fig. 1(a) and (b) for transmission and reflection, respectively. Results are presented with the original spectral resolution ), giving an illustration of the maximum noise observed on the spectra and the related uncertainty: ±1%. The curves only really differ in the range around 4000–. Each curve is referred to its corresponding species in this range where the discrimination can be easily made, except for J. oxycedrus and P. halepensis for which the results are superimposed. A classification ranging from the species with the highest transmissivity or reflectivity to the smallest one can be simply defined around . The same order holds in the whole studied range. Outside this near infrared range, and especially below , the discrepancies between the curves are too small to allow a correct distinction between the species. The non-gray behavior of the species is obvious since important variations may be observed. Transmissivity and reflectivity exhibit similar spectral characteristics. They are very weak below . Then, some variations appear in the rest of the spectrum. Transmissivity reaches a maximum value around 0.3, whereas levels up to 0.35 are obtained in reflection, both in the near infrared range. This observation of spectral dependency of the radiative properties is important considering the fact that the assumption of gray medium is usual in the literature. It appears that this assumption only really holds for wave numbers below (or wavelengths larger than ). Actually, in the case of radiation emitted by flames during fire spread, the maximum of emission could be around this threshold value and a relevant emission probably occurs below this value, where the vegetation behaves like a non-gray medium. One other observation is that the curves exhibit similar variations whatever the considered species. Of course the discrepancies in the optical thicknesses (directly affected by the thickness of the sample itself) yield some differences in the measured levels, but the spectral variations are the same. This leads to the idea that the plant matter has a monotonic behavior whatever the species of interest, with spectral specificities influenced by the components of the leaf itself (for example, water content, cellulose or lignin). The absorptivity is provided applying a straightforward energy balance, simply subtracting above-commented reflectivity and transmissivity from unity. The result is plotted in Fig. 2(a). As a consequence of the observations of the last paragraph, the behavior of the various species is quite the same, with only Q. coccifera and Genista really exhibiting obvious discrepancies in the absorptivity level. Another particularity can be observed on Q. coccifera in the range around . This has to be related to the water content of the studied leaves as will be confirmed hereafter. The lower water content for Q. coccifera probably also explains why its absorptivity is lower than the one of the other species. The plant matter is seen to present a monotonic behavior which is not very different from the one of a blackbody below (absorptivity equal to 0.97 instead of 1). The often used assumption of emissivity equal to 1 for the vegetation is consequently close to the experimental observation, at least in the middle infrared. This is no more true in the near infrared range of course, since the absorptivity is decreasing down to 0.35 in the case of Q. coccifera. To make our experimental characterization complete, the influence of the water content has been investigated by comparing absorptivities obtained on fresh and dry samples (same samples 2 and 40 days after gathering). Results are presented for Q. coccifera and A. unedo in Fig. 2(b). The discrepancy is clear, the loss in water content results in a weaker absorption. One may conclude that during the drying process of the vegetation, when irradiation occurs due to the flame spread, a fine description of radiation propagation could take this change into account. The influence of water is especially observed in the near infrared range and a little around . This singularity in the absorption behavior already noticed for Q. coccifera is observed again. This confirms that this species was probably drier than the others at the early stages of the experimental tests. To the author's knowledge, relation (1) is often used as an empirical formula, sometimes in a modified form, but no mathematical analysis is found in the literature, related to its significance. Starting with a randomly generated vegetation medium and applying an averaging process this relation can be obtained, as demonstrated in the following. The extinction coefficient σe can be estimated thanks to Beer's law with the transmissivity definition: Instead of simply using the above relationship, a numerical study of the properties of a given vegetation medium has been performed, introducing the input data given by our measurements of the vegetation properties. Then, comparisons can be carried out between numerical results and the usual relationship (Eq. (1)). The numerical work developed in this study may be divided into two parts: Once the medium has been randomly built (see Fig. 6), the ray tracing can begin according to the following algorithm: In this first test, the medium is supposed to be made with perfectly absorbing leaves. This configuration allows to compare the numerical predictions with the values obtained by the usual relationship Eq. (1). For the present numerical simulations, the geometrical shapes of two species have been introduced: A. unedo and Q. coccifera (cf. Fig. 5). Several configurations have been considered in varying the leaf density nl from 1000 to . Fig. 7 represents the mean extinction coefficient according to the total leaf area. For each configuration, the confidence intervals regarding statistical uncertainty are given and show that the numerical process ensures the result convergence. Both the results for A. unedo and Q. coccifera are in good agreement with those given by relationship (1). According to the experimental works by Butler [10] and Vaz et al. [11], the usual relationship estimates the mean radiation extinction coefficient with a relative error smaller than 10%, for a volume fraction considered between 0.01 and 0.02. The results presented here show that tiny discrepancies (less than 2%) are obtained when the leaf density is below . Beyond this value, the extinction coefficient starts to be numerically underestimated when compared with the relationship. The explanation comes from an observation stated above: with such a high leaf density non-physical layout of leaves can occur, with non-physical intersections of leaves, leading to an underestimate of the actual obstruction area regarding incident radiation. We have kept the present results as to show the limitation of the numerical simulation in the present form, but we note that small values of leaf densities are currently of interest in reality (for example, observed on available data for chestnut oak). A complementary comparison is now performed for Q. coccifera between relationship (1) and a numerical test involving the measured properties of leaves as presented in the previous section. Indeed, considering the complex non-gray behavior which has been observed, two typical wavelengths have been chosen. Wavelength 1 corresponds to (leaves are close to black surfaces, α=0.97, ρ=0.03 and τ=0) and wavelength 2 to (leaves are absorbing, reflecting and transmitting radiation, α=0.35, ρ=0.33 and τ=0.32). Fig. 8 presents the numerical extinction coefficient as a function of the value given by relation (1) (or what would be obtained numerically for the same leaf density, assuming that leaves are black surfaces). As can be seen, there is no problem with wavelength 1: triangles are quite superimposed on the line corresponding to relationship (1) and no correction is required. On the contrary, the discrepancy becomes obvious when α significantly shifts from 1 (squares deviate from the continuous line). However, a simple correction of relation (1), multiplying by the actual factor (α+ρ) (or 1-τ) yields a very good estimate of the extinction coefficient (see dashed line for the corrected relationship). In a nutshell, the radiative extinction coefficient linearly depends on the complementary part of the transmissivity. The question could be: what are the correct values for α, ρ and τ? The present paper provides information on these properties, on their spectral variations, and finally on their mean values in the following subsection. The spectral treatment of radiative transfer is often avoided for the sake of simplicity and in order to reduce the computational cost. In this frame, an average value for α can be computed involving an integration over the spectral range of interest and taking into account a given incident radiation. Considering the radiation emitted by a blackbody at (of course this is far from the true emission of a flame, but this is a usual approximation of its spectral variation) the average absorptivity of A. unedo has been found equal to 0.90. For Q. coccifera (fresh species) and Genista in the same configuration, absorptivities of 0.84 and 0.93 have been found, respectively. These values are relatively high since the wavelength range of interest for the integration gives a large weight to the domain where the absorptivity is the highest. They are in agreement with the observation of Fig. 2 where Q. coccifera was found to be less absorbing than the other species, for example. Dry species of Q. coccifera and A. unedo as described in Fig. 2(b) exhibit absorptivity equal to 0.80 and 0.83. This decrease in the absorptivity is a consequence of a water loss resulting in a weaker spectral absorptivity as commented above. As a consequence, the absorptivity of the vegetation probably decreases during the first stage of irradiation by flames, but in a weak manner. Finally, the choice of the spectral variation of the incident radiation could also play a role in the average absorptivity computation. For fresh Q. coccifera, considering emission by a blackbody at temperature 400, 700, , absorptivities equal to 0.95, 0.90 and 0.84 are found, respectively. As the temperature rises, the respective weight increases for the spectral range where the absorptivity is lower, thus explaining the evolution of the absorptivity (still approximately remaining in the same range around 0.90, however). All these values are summarized in Table 1 where average coefficients (absorptivity, reflectivity and transmissivity) are presented for the above-mentioned cases. On the whole, this provides an estimate of the correction that should be brought to relationship (1) when predicting the total extinction of the medium: mean absorptivity α is in the range 0.84–0.95, and reflectivity ρ is in the range 0.03–0.10. Consequently, relationship (1) should be multiplied by a factor between 0.94 and 0.98 (for the species investigated here, and submitted to the radiation emitted by a blackbody at high temperature). The extinction coefficient of a vegetation medium has been studied. The transmissivity and reflectivity of six species typical of the south of France have been measured in the infrared range. The corresponding absorptivity has been obtained. The absorptivity is only close to 1 for wavelength larger than , whereas complex variations are observed below this value. Total absorptivity between 0.84 for Q. coccifera and 0.93 for Genista has been obtained. Spectral variations of the various species have been observed to be similar. The water content of the vegetation influences the absorptivity as has been confirmed through measurements carried out on fresh and dry species. Dry species of Q. coccifera have produced lower absorptivities (0.80). A numerical study has been carried out on the validity of the often used relationship by De Mestre when predicting the extinction coefficient of a vegetation medium. A mathematical justification has been found for this relationship. Comparisons have been also carried out with a numerical identification of the corresponding coefficient using a ray tracing method. In the case of a medium made with purely absorbing leaves, the relationship gives very good results. When introducing realistic radiative properties for the leaves, the relationship is less robust but can be easily corrected by multiplying with a correct value of the sum of absorptivity and reflectivity of the leaves. A fine spectral evaluation would involve a complex correction but the multiplication factor for the total extinction can be calculated: the present paper indicates that factors in the range 0.94–0.98 should be used, depending on the species. This study involves a numerical model applied on a simplified virtual medium, where the leaves are randomly located and oriented. This numerical tool should be now extended to more realistic media in which various possible leaf orientation and combination of species will be considered. The experimental part of the study will be also extended to other species and to a finer investigation of the influence of the water content. The authors are grateful to Prof. J.P. Clerc and Prof. B. Porterie of IUSTI (Marseille, France) for the sharing of their experience and for the leaf supply. This research is supported by the French National Research Agency (ANR)—“PIF” project (Protection contre les Incendies de Forêts) through contract 0264-01.