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ŠUMARSKI LIST 1-2/2018 str. 81     <-- 81 -->        PDF

releases during flaming combustion. The determination of η depends on two variables, Tf and M, and on several parameters that can be assumed constant. This leads to a somewhat counterintuitive conclusion: the fraction of heat transferred from the flame to the fuel bed does not depend on R or on any aspect of flame geometry. During its heat sink phase, i.e., before igniting and becoming a heat source, fuel can only absorb a fraction of the energy released by combustion corresponding to ignition requirements, which implies that the remaining heat is dissipated elsewhere, regardless of flame configuration or how fast fire spreads. This is similar to what happens when we have a pan with boiling water above a flame: if flame power is increased, a unit mass of water does absorb energy beyond evaporation requirements, there is just a bigger amount of water being vaporized.
To compute η we used experimental data for foliage fuels from Susott (1982) to obtain averaged Qf and ffl values of, respectively, 22111 kJ kg-1 and 0.719. Values of the physical constants in equation (3) were taken as cf = 1.82 kJ kg-1 ºC-1 (Balbi et al. 2014), Ti = 320 ºC, Tv = 100 ºC, Qw = 2260 kJ kg-1 and cw = 4.19 kJ kg-1 ºC-1 (Catchpole and Catchpole 1991). We chose an arbitrary value of Tf = 20 ºC for obtain η as a function of M (Figure 1).
Based on equation (1) we derived equation (6) and inferred that the thermal energy balance presented in (1) is independent from ρb, and thus from w and δ. This does not imply that they do not influence R nor that empirical studies should not use them. But because equation (1) does not give any information on the processes that lead to the establishment of such balance, namely on the mechanisms of heat transfer, effects of those fuel properties on R cannot be directly inferred from Rothermel’s model thermal energy balance. Nevertheless, the model from Rossa (2017) for the ratio between R in the absence of wind or slope and δ, developed based on an extensive laboratory experimental program where fuel bed parameters were varied over a wide range (δ 0.02–0.55 m, w 0.5–3.5 kg m-2, ρb 1.9–30 kg m-3, M 6–179 %), shows that, at least for no-wind and no-slope conditions and constant δ, w and thus ρb do not significantly influence R.
Although we assumed a fixed Tf for obtaining η as a function of M, in real fire-spread situations the relationship between these variables is still approximately linear because Tf has little influence on Qi, when compared to M, and varies within a relatively narrow range. This means that η is nearly constant for constant M values. Thus, high R values, for example in wind-driven fires, are attained because more heat is generated and transferred from the flame to the unburned fuel, despite the ratio between the heat released by the flame and that absorbed by the fuel remains the same.
Empirical models can provide accurate descriptions of fire behaviour by properly combining variables that account for the key influences on fire spread, i.e., weather, topography and fuel complex metrics, even without grasping the fundamental propagation mechanisms. However, because the amount of variables is vast, narrowing them down to a selected few to consider during model development is needed. For such reason researchers usually rely on pre-established knowledge on the physical mechanisms underlying fire spread for making that selection. Thus, the results from the present study are useful to inform future empirical experiments and approaches, in particular the development of R prediction models. One major practical application of accurate R estimates is the obtaining of improved fire size and shape estimates (Anderson 1983), which are key in assisting both prevention and suppression operations.
cf              fuel-specific heat – specifična toplina izgaranja, kJ kg–1 °C–1
cw            water-specific heat – specifična toplina vode, kJ kg–1 °C–1
D             flame depth – dubina plamena, m
δ              fuel bed height – visina ložišta, m
η              fraction of heat transferred from the flame to the unburned fuel – udio topline prenesene od plamena do nesagorijelog goriva
ffl             fraction of fuel consumed in flaming combustion – udio goriva potrošenog u sagorijevanju
M            fuel moisture content – sadržaj vlage goriva, %
Q’’            average horizontal net heat flux through the fuel bed – prosječna količina horizontalnog strujanja topline kroz ložište, kW m–2
Qf           low heat content per unit mass of fuel – donja ogrijevna vrijednost po količinskoj jedinici goriva, kJ kg–1
Qn            power released per unit fireline length – snaga oslobođena po jedinici duljine vatrene linije, kW m–1