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Journal ArticleDOI

Energy Balance Models of Downward Combustion of Parallel Thin Solid Fuels and Comparison to Experiments

09 Sep 2013-Combustion Science and Technology (Taylor & Francis Group)-Vol. 185, Iss: 12, pp 1820-1837
TL;DR: In this article, the authors analyzed the flame front speed in the downward combustion of multiple parallel samples of thermally thin fuels at normal gravity and far from extinction conditions and derived an analytical approximation for the burning rate that generalizes the classical de Ris formula for those cases where radiative effects cannot be neglected.
Abstract: We analyze the flame front speed in the downward combustion of multiple parallel samples of thermally thin fuels at normal gravity and far from extinction conditions. In contrast with the single sample case, where conduction through the gas-phase is the dominant heat transfer mechanism, in the multiple parallel samples case, radiative heat fluxes may become very relevant, which compromises the application of the well-known formula of de Ris for determining the burning rate. Here we study the downward combustion of multiple parallel sheets by (1) obtaining new experimental data at different oxygen atmospheric levels; (2) generalizing a previous comprehensive energy balance model now expected to be valid for a wide range of scenarios; and (3) deriving an analytical approximation for the burning rate that generalizes the classical de Ris formula for those cases where radiative effects cannot be neglected. The comparison with own as well as with external data reveals the strengths and weaknesses of these type...
Citations
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Journal ArticleDOI
TL;DR: In this article, the orientation effects during inclined downward flame spread processes were thoroughly investigated by experimental and theoretical methods, and the mechanism of orientation effect during the flame spread process was qualitatively analyzed in detail, and simplified expressions of flame spread rate of the two insulation materials with different orientations were deduced.

83 citations

Journal ArticleDOI
TL;DR: In this paper, an experimental investigation of diffusion flames spreading along thin solid fuels in concurrent and opposed configurations in a gravity induced flow is presented, where the multiple fuel sheets (2 and 3 sheets) are kept parallel to each other with the separation distance between them varied from 0.5 to 3 cm.

19 citations

Journal ArticleDOI
TL;DR: Thermal structure inside flame front during downward flame spread was experimentally measured and indicated that the distribution of the molten layer in the direction perpendicular to the plane of the XPS sheet is a significant factor for dripping and collapsing.

8 citations

Journal ArticleDOI
TL;DR: In this article, numerical simulations of flame spread along parallel, combustible plates are performed to identify the occurrence conditions of a symmetry-breaking phenomenon, and two-dimensional, time-dependent cons...
Abstract: To identify the occurrence conditions of a symmetry-breaking phenomenon, numerical simulations of flame spread along parallel, combustible plates are performed. Two-dimensional, time-dependent cons...

5 citations


Cites background from "Energy Balance Models of Downward C..."

  • ...Since Kurosaki and Itoh’s model requires several parameters to predict the spread rate, Comas et al. attempted to generalize the model to be applicable for various situations by evaluating the flame geometry (Comas and Pujol, 2013)....

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  • ...attempted to generalize the model to be applicable for various situations by evaluating the flame geometry (Comas and Pujol, 2013)....

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Journal ArticleDOI
TL;DR: In this paper, a 2D numerical model based on OpenFOAM is used to simulate the flame spread in a natural convective environment under normal gravity, and the model is validated with detailed experimental data involving spatial distributions of temperature and species, and flame spread rates.

4 citations

References
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Journal ArticleDOI
01 Jan 1969
TL;DR: In this article, a theoretical description of a laminar diffusion flame spreading against an air stream over a solid- or liquid-fuel bed is presented, where both a thin sheet and a semi-infinite fuel bed are considered.
Abstract: A theoretical description is presented for a laminar diffusion flame spreading against an air stream over a solid- or liquid-fuel bed. Both a thin sheet and a semi-infinite fuel bed are considered. The burning process is described as follows: The hot flame heats the unburned fuel bed, which subsequently vaporizes. The resulting fuel vapor reacts with the oxygen supplied by the incoming air, thereby producing the heat that maintains the flame-spread process. The formulated model treats the combustion as a diffusion flame, for which the details of the reaction kinetics can be ignored by assuming infinite reaction rates. The model includes the chemical stoichiometry, heat of combustion, gas-phase conductive heat transfer, radiation, mass transfer, fuel vaporization, and fuel-bed thermal properties. The radiation is mathematically treated as a heat loss at the flame sheet and a heat gain at the fuel-bed surface. The calculated flame-spread formulas are not inconsistent with available experimental data. These results reveal much of the physics involved in a spreading, flame. For instance, the flame-spread rate is strongly influenced by (1) the adiabatic stoichiometric flame temperature, and (2) the fuel-bed thermal properties, except for the fuel-bed conductivity parallel to the propagation direction.

356 citations


"Energy Balance Models of Downward C..." refers background or methods in this paper

  • ...In these cases, a model beyond the classical de Ris (1969) one is needed since radiation may play an important role....

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  • ...The analytical model (A model in Figure 4), which generalizes the de Ris expression by including radiation, predicts higher values of the spread rate due to the positive contribution of the radiative terms in Eq. (15), as already expected. This analytical model matches the data at XO21⁄4 50% but fails to reproduce the observed behavior at greater atmospheric concentrations, underestimating by 19% the flame front speed at XO21⁄4 100%. The generalized model gives slightly greater values of Vf than the analytical model, but not higher enough to correctly report the measured data at high XO2. In comparison with de Ris Eq. (1), and for a single sheet, the differences with the generalized (I-G) model arise from the radiative flux from the flame (qrf1) and the radiative losses from the paper (qrs). This radiative correction may lead to a negative value for losses higher than the gain from the flame. However, this is not observed in our model due to the assumed flame shape. In our model, the flame is a rectangle parallel to the paper, separated from it by a length Lh (see Figure 3). This provides a view factor of the flame to a differential element of the preheated zone of the paper greater than it would be if a more realistic shape was assumed, which overestimates qrf1. Note also that the qrf1 value predicted by the I-G model is greater than the value obtained from the A model since it applies the Vf value instead of the Vf,deRis for determining the geometrical flame parameters. In contrast, Kurosaki et al. (1979) and Itoh and Kurosaki (1985) models clearly underestimate the experimental observations at moderate–high values of XO2, only correctly predicting the flame spread rate at environmental values XO21⁄4 21%, which correspond to the conditions that they were developed. Both K and I models shown in Figure 4 adopt a variable value of the flame temperature Tf as a function of XO2, being the same as that employed in A and I-G models. Figure 4 Downward burning rate Vf as a function of the oxygen molar fraction XO2 for a single sheet. Our experimental data is compared with the Kurosaki et al. (1979) model (K model), Itoh and Kurosaki (1985)...

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  • ...For a single sample, the downward flame front speed in the thermal regime of a thin solid fuel follows the well-known de Ris’s expression (de Ris 1969): Vf ;deRis ¼ p 4 kg Tf;ad Tvap s=2ð Þcsqs Tvap T1 ð1Þ Received 21 June 2013; revised 25 August 2013; accepted 26 August 2013....

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  • ...In contrast with the previous subsection, values of the parameters dg, Lh, Lf, and Le needed in qcv, qrf1, qrf2, and qre have been evaluated at Vf, deRis instead of at Vf. This makes Eq. (15) fully explicit. Note that in Eq. (15) we have neglected the contribution of the qrp term due to its small relevance in the total heat transfer rate as noted in Kurosaki et al. (1979). We point out that Eq....

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  • ...The analytical model (A model in Figure 4), which generalizes the de Ris expression by including radiation, predicts higher values of the spread rate due to the positive contribution of the radiative terms in Eq. (15), as already expected. This analytical model matches the data at XO21⁄4 50% but fails to reproduce the observed behavior at greater atmospheric concentrations, underestimating by 19% the flame front speed at XO21⁄4 100%. The generalized model gives slightly greater values of Vf than the analytical model, but not higher enough to correctly report the measured data at high XO2. In comparison with de Ris Eq. (1), and for a single sheet, the differences with the generalized (I-G) model arise from the radiative flux from the flame (qrf1) and the radiative losses from the paper (qrs). This radiative correction may lead to a negative value for losses higher than the gain from the flame. However, this is not observed in our model due to the assumed flame shape. In our model, the flame is a rectangle parallel to the paper, separated from it by a length Lh (see Figure 3). This provides a view factor of the flame to a differential element of the preheated zone of the paper greater than it would be if a more realistic shape was assumed, which overestimates qrf1. Note also that the qrf1 value predicted by the I-G model is greater than the value obtained from the A model since it applies the Vf value instead of the Vf,deRis for determining the geometrical flame parameters. In contrast, Kurosaki et al. (1979) and Itoh and Kurosaki (1985) models clearly underestimate the experimental observations at moderate–high values of XO2, only correctly predicting the flame spread rate at environmental values XO21⁄4 21%, which correspond to the conditions that they were developed....

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Journal ArticleDOI
TL;DR: In this paper, the steady-state flame spread over a thermally thin solid fuel is investigated, and qualitative agreement is obtained with experimental results in the near-extinction limit region.

183 citations


"Energy Balance Models of Downward C..." refers background in this paper

  • ...The opposed flow gas velocity Vg is assumed to vary accordingly to the expression (Frey and T’ien, 1979) Vg=Vg,ref1⁄4 [ag(Tf,ad T1)]=[ag,ref (Tf,ad,ref T1)], where the reference values correspond to those at XO21⁄4 21% with Vg,ref1⁄4 0....

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  • ...The opposed flow gas velocity Vg is assumed to vary accordingly to the expression (Frey and T’ien, 1979) Vg=Vg,ref¼ [ag(Tf,ad T1)]1=3=[ag,ref (Tf,ad,ref T1)]1=3, where the reference values correspond to those at XO2¼ 21% with Vg,ref¼ 0.3ms 1....

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Journal ArticleDOI
01 Jan 1981
TL;DR: In this article, the velocity of flame propagation over the surface of thick PMMA and thin paper sheets has been measured as a function of the velocity and oxygen concentration of a forced gas flow opposing the direction of the flame propagation.
Abstract: The velocity of flame propagation over the surface of thick PMMA and thin paper sheets has been measured as a function of the velocity and oxygen concentration of a forced gas flow opposing the direction of flame propagation. It is shown that although for thin fuels the flame spread rate always decreases as the opposed flow velocity increases, for thick fuels the dependence of the spread rate on the gas velocity is also a function of the ambient oxygen concentration. For low oxygen concentrations the flame spread rate decreases as the velocity of the gas flow increases. For high oxygen concentrations, however, the spread rate increases with the flow velocity, reaches a maximum and then decreases as the gas velocity increases. The velocity of the opposed flow at which the maximum occurs is a function of the oxygen concentration, decreasing as the concentration decreases. Following phenomenological considerations and simplified descriptions of the primary mechanisms occurring during the flame spread process, the experimental results are correlated by two non-dimensional parameters, one describing the gas phase kinetic effects and the other describing the process of heat transfer from the flame to the fuel. Such a correlation provides a powerful means of predicting the flame spread prcess as well as physical insight into the mechanisms controlling the propagation of the flame.

173 citations


"Energy Balance Models of Downward C..." refers background in this paper

  • ...(1) with a wide variety of experimental data (see, e.g., Fernández-Pello et al., 1981) corroborates that conduction through the solid-phase as well as radiative heat fluxes are of secondary importance when burning thin solid fuels far from the extinction limits....

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Journal ArticleDOI
TL;DR: In this paper, the exact solution for the rate of creeping flame spread over thermally thin materials based on de Ris' (1969) formulation of the problem was presented, which was prompted by a recent paper by Wichman and Williams (1984).
Abstract: In this work we present the exact solution for the rate of creeping flame spread over thermally thin materials based on de Ris' (1969) formulation of the problem. The publication of the present work was prompted by a recent paper by Wichman and Williams (1984). These authors noted that de Ris (1969) obtained theoretical values for flame spread rates which are by a factor of two larger than recent experimental data (Fernandez-Pello et at., 1981). Wichman and Williams (1984) correctly suggested that this discrepancy between the theory and the experiment may have resulted from an approximation by de Ris(1969) of an irrational kernel by a rational function. The substitute kernel used by de Ris (1969) allowed him to obtain an analytical solution of the flame spread rates; however, this approximation may have introduced errors in the calculation of proportionality constants. The exact solution for creeping flame spread rates, which we present in the final analysis, agrees with the experimental data. In...

79 citations


"Energy Balance Models of Downward C..." refers methods in this paper

  • ...…# Taylor & Francis Group, LLC ISSN: 0010-2202 print=1563-521X online DOI: 10.1080/00102202.2013.839556 1820 where the p=4 term has been included after the exact solution derived by Delichatsios (1986) (see the Nomenclature for the description of the variables and parameters)....

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Journal ArticleDOI
01 Jan 2005
TL;DR: In this paper, a simplified analysis leading to the development of closed-form expressions for spread rate for both thin and thick fuels in the microgravity regime of opposed-flow flame spread is presented.
Abstract: The spread rate formulas of de Ris in the thermal regime of opposed-flow flame spread are inarguably the most well-known formulas in the flame spread literature. Similar easy-to-use formulas are lacking in all other regimes of flame spread. This paper presents a simplified analysis leading to the development of closed-form expressions for spread rate for both thin and thick fuels in the microgravity regime of opposed-flow flame spread. The resulting formulas, expressed in terms of the thermal limit of spread rate and a radiation number that can be evaluated from the known parameters of the problem, are shown to reproduce the experimentally and numerically observed trends quite well at both limits of fuel thickness. These formulas are utilized to develop quantitative criterion to delineate thin and thick fuels in the microgravity and thermal regimes. The transition between the microgravity and thermal regimes is also explored. The flammability maps, derived from the spread rate expressions, are the first of their kind, establishing fuel thickness as one of the critical parameters.

53 citations


"Energy Balance Models of Downward C..." refers background or methods in this paper

  • ...On the other hand, flame Lf, ember Le, and separation from flame to paper Lh lengths are calculated using Bhattacharjee et al.’s (2011) work:...

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  • ...We assume that the relevant length scale where the convective heat flux qc is important corresponds to dg ag=(VgþVf), as it was determined in Bhattacharjee et al. (2005)....

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  • ...In this case, the flame spread rate strongly depends on radiative effects (Bhattacharjee et al., 2005)....

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  • ...We assume that the relevant length scale where the convective heat flux qc is important corresponds to dg ag=(VgþVf), as it was determined in Bhattacharjee et al. (2005). Therefore, we state that d1⁄4 dg in the exponential shape for the convective flux qc1⁄4 be ....

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  • ...Our generalization of the I model employs the parameterizations of the flame geometrical dimensions of Bhattacharjee et al. (2011) and a variable convective flux (I-G model)....

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