Influence of edge propagation on downward flame spread over three-dimensional PMMA samples

This systematic experimental study measures the effect of flame propagation along vertical edges on the overall downward spread of flames using Polymethyl Methacrylate (PMMA). Samples with a wide range of regular cross-sections – from triangular through octagonal – as well as irregular ones, have been used to test a large variation of internal angles. A MATLAB-based tool was used to calculate instantaneous spread rate for central and edge flames. The edge flame is shown to significantly enhance the spread rate, as much as five times, in respect to samples with no edges. This amplification is shown to depend primarily on the internal angle at the edge (the smaller the angle, the faster the flame) and fuel thickness, and not on other factors such as aspect ratio or cross-sectional area. Using a phenomenological argument, the edge propagation rate is correlated to the spread rate over an equivalent cylindrical fuel (the limiting shape with infinite edges) with an effective radius obtained from the geometry of the edges and the diffusion length scale of the solid phase. A formula for flame spread over cylindrical fuel from the literature is used to link the new results to existing models. Both thick and thin limits are shown to encompass the wide range of three-dimensional spread rate data within the effective radius (the independent variable), which can be determined from the known parameters. Based on these results, different types of cross-sectional areas can be sorted in the order of their inherent fire safety characteristics.     

Opposed flow flame spread over an array of thin solid fuel sheets in a microgravity environment

In this work a numerical study has been carried out to gain physical insight into the phenomena of opposed flow flame spread over an array of thin solid fuel sheets in a microgravity environment. The two-dimensional (2D) simulations show that the flame spread rates for the multiple-fuel configuration are higher than those for the flame spreading over a single fuel sheet. This is due to reduced radiation losses from the flame and increased heat feedback to the solid fuel. The flame spread rate exhibits a non-monotonic variation with decrease in the interspace distance between the fuel sheets. Higher radiation heat feedback primarily as gas/flame radiation was found to be responsible for the increase in the flame spread rate with the reduction of the interspace distance. It was noted that as the interspace distance between the fuel sheets was reduced below a certain value, no steady solution could be obtained. However, at very small interspace distances, steady state spread rates were obtained. Here, due to oxygen starvation the flame spread rate decreased and eventually at some interspace distance the flame extinguished. With fuel emittance (equal to absorptance) reduced to ‘0’ the flame spread rate was nearly independent of the interspace distance, except at very small distances where the flame spread rate dropped due to oxygen starvation. A flame extinction plot with the extinction oxygen level was constructed for the multiple-fuel configuration at various interspace distances. The default fuel with an emittance of 0.92 was found to be more flammable in the multiple-fuel configuration than in a single fuel sheet configuration. For a fuel emittance equal to zero, the extinction oxygen limit decreases for both the single and the multiple fuel sheet configurations. However, the two flammability curves cross over at a certain fuel separation distance. The multiple-fuel configurations become less flammable compared to the single fuel sheet configuration below a certain separation distance.     

Correlating flame geometry in opposed-flow flame spread over thin fuels

Numerical analysis and scale analysis are combined in a novel manner in this work to develop closed-form expressions for flame geometry in opposed-flow flame spread over condensed fuels. A scale analysis is used to relate different geometric attributes to appropriate non-dimensional parameters. A comprehensive numerical model is then used to generate a large set of numerical data for flame height, flame length, and pyrolysis length as functions of different fuel and oxidizer parameters for flame spread in the thermal, kinetic, and radiative regimes. The numerical data is then correlated to scaled expressions and the unknown coefficients are numerically determined. It is shown that flame length, flame height, and pyrolysis length can be expressed in terms of the preheat length in different regimes of flame spread. An experimental approach is outlined to measure the preheat length necessary for accurately predicting the flame structure. Experimental images obtained from interferometry in two different regimes – downward spreading configuration and quiescent microgravity environment – are consistent with the proposed flame height correlation.     

Steady and oscillatory flame spread over liquid fuels

The flow induced in a layer of liquid fuel at sub-flash temperature by the thermocapillary forces associated with the spreading of a flame that heats and vaporizes the liquid is analysed numerically and asymptotically, for large values of the Marangoni number and of the Reynolds number based on the propagation speed. Upstream heat convection in a recirculating region moving with the flame front is described for a steady model problem and for uniform and pulsating flame spread. A possible mechanism triggering flow oscillations entirely dependent on the liquid phase is identified and discussed.     

Appearance of cool flame in flame spread over fuel droplets in microgravity

This research conducted microgravity experiments to investigate phenomena appearing around a droplet existing outside the flame-spread limit. n-Decane droplets are tethered at intersections of SiC fibers. The flame spreads to two- or three-interactive droplets to heat a droplet placed outside the flame-spread limit of the interactive droplets. The cool-flame appearance during the flame spread over droplets was detected using different methods. The droplet diameter was measured with a back illumination to evaluate the vaporization-rate constant and to judge whether the cool flame appears or not. The temperature around the droplet was measured by the thin-filament pyrometry using a near-infrared camera to detect the temperature rise due to cool-flame appearance. The infrared radiation distribution from the combustion products was measured using a mid-wave infrared camera to judge the cool-flame appearance. The results show that a cool flame appears around the droplet existing outside the hot-flame-spread limit and the vaporization completes with the cool flame if the heat input from the hot flame is sufficiently large. This type of flame spread is called hot-to-cool flame spread. The definition of flame spread should be extended considering the cool flame.     

Scaling and instability analyses on flame spread over liquids

Stability and scaling analyses were applied to experimental data obtained by this group and other researchers on pulsating flame spread over liquids. Data to be analyzed include recent findings of cyclic appearance of a cold temperature valley at the liquid surface-created surface-wave ahead of the spreading flame, and main-pulsation of 0.5–2 Hz and sub-pulsation of 5–10 Hz. Our stability analysis is performed to understand the mechanism of instability on the liquid surface ahead of a flame’s leading edge, which is thought of as the major cause for pulsating flame spread. The scaling analysis is performed to explore the role of four independent (gravity, surface-tension, viscose, and inertia) forces on the mechanisms of flame spread. These four forces form three independent pi-numbers: Marangoni (Ma) number, Weber (We) number, and Froude (Fr) number, all of which include the critical length scale ratio: (height of sub-surface circulation)/(horizontal length of preheated liquid surface). We combined the wave equation obtained from the stability analysis, the three pi-numbers, and the critical length scale ratio, and used them as a universal formula to describe flame spread over liquids. Using this formula, flame spread mechanism over four different types of alcohols was divided into two separate regimes: the thin liquid pool and the thick-liquid pool. For the thin liquid pool, the flame spread rate was correlated with (Fr/Ma^0.5)^−1.0, while for the thick-liquid pool it was correlated with (Fr/Ma^0.5)^−1.5. Change of flame spread pattern from the uniform to the pulsating can be described with temperature difference between the flash point and bulk liquid temperature. For the thin liquid pool this temperature difference is correlated with Ma^−0.5, while for the thick-liquid pool it is correlated with Ma⁻¹. The frequency of pulsation is correlated with We^−1.0 for the thin liquid pool, while it is correlated with We^−1.5 for the thick-liquid pool.     

Pattern formation in flame spread over thin solid fuels

The fingering char pattern emerging on the surface of thin cellulosic sheets burning against an oxidizing wind is discussed. Employing collocation-based averaging, the assumption of diffusive-thermal equilibrium, the strong temperature dependence of the reaction rate, and the strong disparity between the densities of the solid and gaseous phases, an elementary two-dimensional free-interface model for the flame spread is formulated. It is shown that the pattern-forming dynamics is functionally akin to the well-studied cellular instability occurring in low Lewis number premixed gas flames.     

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.     

Effects of fuel Lewis number on flame spread over solids

Using a detailed two-dimensional numerical model, a systematic investigation has been made to study the effect of fuel Lewis number (Le_F = α/D_F) and mass transfer on flame spread over thin solids. The fuel Lewis number affects the flame spread rates for both concurrent and opposed flames over thin fuels. The dependence of the flame spread rate on Le_F for these two spreading modes is, however, not the same. In opposed flame spreads (zero-gravity, self-propagation, and normal gravity downward propagation), the flame spread rate vs. Le_F curve is non-monotonic with a maximum value occurring at an intermediate value of Le_F = 0.5. In steady, concurrent spread in zero-gravity with low-speed flow and a constant flame length, the flame spread rate decreases with Le_F in a monotonic manner. By using the computational model as a tool, the effects of fuel mass diffusion perpendicular to and parallel with the solid surface are isolated to obtain more physical insight on the two-dimensional aspect of fuel mass transfer on flame spread. In addition, the model has also been used to decouple the solid evaporation process so that the fuel diffusion effect in the gas-phase can be isolated. Both of these theoretical exercises contribute to the understanding of mass transfer effects on the flame spreading phenomena over solids.     

Gravity modulation study on opposed flame spread over thin solid fuels

In this work a numerical investigation has been carried out to study the effect of g-jitter on zero-gravity (0g_e) opposed flow spreading flame over thin solid fuels. For comparison simulations have also been carried out for normal gravity (1g_e) downward spreading flames. G-jitter is emulated by gravity modulation of sinusoidal (A_ge sin(2πt/T_ge)) gravity perturbation (g-perturbation) of a particular time-period (T_ge) and amplitude (A_ge) over a selected base gravity level (0g_e or 1g_e). The response of flames at 0g_e base gravity and at 1g_e base gravity was different to the imposed g-perturbation. While at 0g_e the mean and the amplitude of the oscillatory flame spread rate (FSR) magnified with increase in the time period of g-perturbation, interestingly for the 1g_e flame a maximum mean FSR and oscillation amplitude occurs at certain perturbation time period. Further, at very small perturbation time-periods (T_ge) the FSR at 1g_e was lower than the steady state FSR. The amplitude of oscillatory FSR increased with increase in perturbation amplitude (A_ge). However, the 0g_e flame which is little affected (compared to 1g_e flame) at small perturbation amplitude (A_ge) is affected severely at large perturbation amplitude (A_ge). Both the gas phase and fuel pyrolysis (or fuel response) follow perturbation signal with a lag but fuel pyrolysis is more sluggish and lags behind gas phase. The phase lag between fuel pyrolysis and gas increases at smaller time-periods (T_ge) and tends to enhance the effect of external perturbation whereas at larger time-periods (T_ge) this lag inhibits the effect of external perturbation.     

Flame structure and flame spread rate over a solid fuel in partially premixed atmospheres

We have investigated the downward flame spread over a thin solid fuel. Hydrogen, methane, or propane, included in the gaseous product of pyrolysis reaction, is added in the ambient air. The fuel concentration is kept below the lean flammability limit to observe the partially premixing effect. Both experimental and numerical studies have been conducted. Results show that, in partially premixed atmospheres, both blue flame and luminous flame regions are enlarged, and the flame spread rate is increased. Based on the flame index, a so-called triple flame is observed. The heat release rate ahead of the original diffusion flame is increased by adding the fuel, and its profile is moved upstream. Here, we focus on the heat input by adding the fuel in the opposed air, which could be a direct factor to intensify the combustion reaction. The dependence of the flame spread rate on the heat input is almost the same for methane and propane/air mixtures, but larger effect is observed for hydrogen/air mixture. Since the deficient reactant in lean mixture is fuel, the larger effect of hydrogen could be explained based on the Lewis number consideration. That is, the combustion is surely intensified for all cases, but this effect is larger for lean hydrogen/air mixture (Le < 1), because more fuel diffuses toward the lean premixed flame ahead of the original diffusion flame. Resultantly, the pyrolysis reaction is promoted to support the higher flame spread rate.     

A three-dimensional model of steady flame spread over a thin solid in low-speed concurrent flows

Athree-dimensional model of a steady concurrent flame spread over a thin solid in a low-speed flowtunnel in microgravity has been formulated and numerically solved. The gas-phase combustion model includes the full Navier-Stokes equations for the conservation of mass, momentum, energy and species. The solid is assumed to be a thermally thin, non-charring cellulosic sheet and the solid model consists of continuity and energy equations whose solution provides boundary conditions for the gas phase. The gas-phase reaction is represented by a one-step, second-order, finite-rate Arrhenius kinetics and the solid pyrolysis is approximated by a one-step, zeroth-order decomposition obeying an Arrhenius law. Gas-phase radiation is neglected but solid radiative loss is included in the model. Selected results are presented showing detailed three-dimensional flame structures and flame spread characteristics.

In a parametric study, varying the tunnel (solid) widths and the flow velocity, two important three-dimensional effects have been investigated, namely wall heat loss and oxygen side diffusion. The lateral heat loss shortens the flame and retards flame spread. On the other hand, oxygen side diffusion enhances the combustion reaction at the base region and pushes the flame base closer to the solid surface. This closer flame base increases the solid burnout rate and enhances the steady flame spread rate. In higher speed flows, three-dimensional effects are dominated by heat loss to the side-walls in the downstream portion of the flame and the flame spread rate increases with fuel width. In low-speed flows, the flames are short and close to the quenching limit. Oxygen side diffusion then becomes a dominant mechanism in the narrow three-dimensional flames. The flame spreads faster as the solid width is made narrower in this regime. Additional parametric studies include the effect of tunnelwall thermal condition and the effect of adding solid fuel sample holders.     

Realizing microgravity flame spread characteristics at 1 g over a bed of nano-aluminum powder

Nanoscale aluminum (nAl) powders demonstrate relatively fast counter-flow flame spread rates compared to typical fuels such as Poly(methyl methacrylate) or cellulose at similar conditions. This allows for the dominant forward heat transfer mechanism to be through the solid fuel at higher applied oxidizer velocities, and flame structure characteristics typically observed in microgravity to be realized at 1 g conditions. Because of the porosity of the nAl powder, the gaseous oxidizer can diffuse into the bed and reactions within the solid phase become important. Using an energy balance applied to only the solid phase, an analytical model is developed which predicts the experiments for flame spread over a nAl bed. Moreover, an explanation for fingering phenomenon is established based on the effective Lewis and Damköhler numbers. This allows for an explanation of why flame spread over a bed of nAl will demonstrate this fingering instability in a quiescent, 1 g environment without a top plate to hinder buoyant flows.     

On the role of radiation and dimensionality in predicting flow opposed flame spread over thin fuels

In this work a flame-spread model is formulated in three dimensions to simulate opposed flow flame spread over thin solid fuels. The flame-spread model is coupled to a three-dimensional gas radiation model. The experiments [1] on downward spread and zero gravity quiescent spread over finite width thin fuel are simulated by flame-spread models in both two and three dimensions to assess the role of radiation and effect of dimensionality on the prediction of the flame-spread phenomena. It is observed that while radiation plays only a minor role in normal gravity downward spread, in zero gravity quiescent spread surface radiation loss holds the key to correct prediction of low oxygen flame spread rate and quenching limit. The present three-dimensional simulations show that even in zero gravity gas radiation affects flame spread rate only moderately (as much as 20% at 100% oxygen) as the heat feedback effect exceeds the radiation loss effect only moderately. However, the two-dimensional model with the gas radiation model badly over-predicts the zero gravity flame spread rate due to under estimation of gas radiation loss to the ambient surrounding. The two-dimensional model was also found to be inadequate for predicting the zero gravity flame attributes, like the flame length and the flame width, correctly. The need for a three-dimensional model was found to be indispensable for consistently describing the zero gravity flame-spread experiments [1] (including flame spread rate and flame size) especially at high oxygen levels (>30%). On the other hand it was observed that for the normal gravity downward flame spread for oxygen levels up to 60%, the two-dimensional model was sufficient to predict flame spread rate and flame size reasonably well. Gas radiation is seen to increase the three-dimensional effect especially at elevated oxygen levels (>30% for zero gravity and >60% for normal gravity flames).     

Experimental study on downward/opposed flame spread and extinction over electric wires in partial gravity environments

Downward/opposed flame spread over laboratory wire samples under varied gravity conditions were investigated in the range from 0 G to 1 G. Reduced gravity experiments are conducted by parabolic flights of an airplane. Limiting oxygen concentrations (LOCs) and flame spread rates ($V_{\mathrm{f}}$) are obtained as a function of gravity level, with oxygen concentration, forced flow velocity, and wire characteristics such as insulation thickness and core material as experimental variables. The samples used in this study consist of low-density polyethylene (LDPE) insulation over metallic cores. Copper (Cu) and nickel-chrome (NiCr) were selected as core materials. It is found that the effect of gravity on the insulation flammability varies with the thermal conductivity of the wire core; the LOCs of the Cu sample are less affected by gravity, while those of the NiCr sample decrease with decreasing gravity level. On the other hand, $V_{\mathrm{f}}$ increase monotonically with increasing gravity level in the Cu sample, while $V_{\mathrm{f}}$ of the NiCr sample show a peak value under the low gravity conditions. It is suggested that these differences in the response of LOCs and $V_{\mathrm{f}}$ to the gravity level due to the difference in core materials are controlled by the fuel concentration in the reaction zone, which is a function of $V_{\mathrm{f}}$. It is also found that the molten LDPE produced during the flame spread process shows unique behaviors depending on the gravity levels and wire characteristics. Some characteristics of the dynamic motion of the molten LDPE during the flame spread process, such as deformation and dripping, are also summarized in this paper. The experimental data obtained in this study provide useful information on the flammability of materials in a partial gravity environment and will serve as a database for fire safety design in future space exploration.     

Analysis of skew plate problems with various constraints

This paper presents the application of the modified Rayleigh-Ritz method with Lagrange multipliers to analyze skew plate problems with various constraints. By this procedure one can satisfy both geometric and natural boundary conditions of skew plates. To demonstrate the accuracy and versatility of the method, several examples of bending, vibration and buckling of skew plates are solved, and results are compared with those obtained by other approximate methods.