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.     

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.     

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).     

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.     

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.     

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.     

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.     

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.     

Flame spread and interactions in an array of thin solids in low-speed concurrent flows

Flame spread in an array of thin solids in low-speed concurrent flows was investigated and numerical solved. A previous steady, two-dimensional flame-spread model with flame radiation was employed and adapted in this work. The flame structures of spreading flames between parallel solids were demonstrated and some of the features were presented, including flow channelling effect and flame radiation interactions. The channelling effect is caused by flow confinement by the presence of the other solids; the flows through the hot combustion gases are accelerated downstream drastically. Radiation interactions between flames and solids contributed to a less heat-loss system, and radiation re-absorption by flames resulted in a larger flame with higher temperature, which increased the conductive heat fluxes to the solids and flame spread rate. Consequently, the extinction limit for the interacting flames is extended beyond the low-speed quenching limit for a single flame. The influence of the separation distance on the flame spread rate was also studied, which exhibits a non-monotonic behaviour. At larger separation distance, the flame spread rate increases with decreasing the separation distance owing to the channelling effect and radiation interactions. However, at very small separation distance, the flame spreading rate decreases with decreasing the distance because of the limited space for thermal expansion and flow résistance between solids.     

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.     

Dimensional scaling of flame propagation in discrete particulate clouds

The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidiser is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modelled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.     

Effect of thermo-hydrodynamic instability on structure and characteristics of filtration combustion wave of solid fuel

Numerical modelling of flame front stability for the inverse wave (with trailing combustion front) of filtration combustion of solid fuel is performed. The problem is treated in terms of dimensionless variables and parameters. It is found that propagation of a plane combustion front becomes unstable under certain conditions. In this case the front spontaneously inclines. The thermo-hydrodynamic mechanism is supposed to be responsible for instability developing. Anisotropic effective mass diffusivity (dispersion) is also taken into account. It turns out that anisotropic diffusivity affects structure and conversion distribution of the inclined combustion front. It is shown that the key parameters determining stability of combustion wave are dimensionless gas flow rate and width of reactor. The range of these parameters corresponding to the stable plane front is determined. It is shown that stability occurs either for small reactor widths (dimensionless values <1), or low gas flow rate (below 0.2). The optimised values of considered dimensionless parameters for maximal productivity are determined.     

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.     

Observation of droplet motion during flame spread on three-fuel-droplet array with a pendulum suspender

Flame spread on a fuel droplet array has been studied as a simple model of spray combustion. A three-fuel-droplet array with a pendulum suspender was employed to investigate interactions between flame spread and droplet motion in the axial direction. Initial droplet diameter was 0.8 mm, and fuel was n-heptane. A silicon carbide pendulum suspender of 15 μm in diameter and 30 mm in length was used for the third droplet. The first fixed droplet was ignited by electric spark. Behavior of the flame and the third droplet was observed using a high-speed video camera with an image intensifier. Particle tracking velocimetry (PTV) measurements were performed to explain the behavior of the third movable droplet. The dimensionless droplet span, which is the average of droplet-to-droplet distances divided by the average initial diameter of the three droplets, was varied from 2.5 to 8 for observing flame spread, and fixed at 5.5 for PTV measurements. It was observed that the third droplet moved away from the second droplet before the flame spread to the third droplet. The displacement of the third droplet is remarkable when the dimensionless droplet span is close to the limit of flame spread. This implies that the movement of the droplet decreases the dimensionless span of the flame spread limit and the flame spread speed near the flame spread limit. Results of PTV measurements suggest that the heat expansion wave, caused by ignition of the premixture which was accumulated around the second droplet, and the burned gas flow from the second droplet pushed away the third droplet; then natural convection, induced by the flames of the first and second droplets, drew the third droplet to the second droplet. The heat expansion wave and the burned gas flow of the second droplet reached nearly 12 in dimensionless span.     

One-dimensional modelling of flame propagation in solid composite fuel with different geometrical configurations

In this paper the propagation of combustion waves in solid composite energetic material consisting of fuel and highly thermal conductive inert elements is investigated using a one-dimensional model with a single step reaction mechanism. The analysis is focused on the study of the effect of the geometrical configuration of the composite material on flame speed and dynamics. Spatial averaging over directions transverse to the propagation direction is performed in such a way as to retain the multidimensional nature of the problem. It is shown that the regimes of combustion depend on the geometry of the composite. The largest possible flame speed enhancement is attained in cases when the heat fluxes along the structural elements are not disrupted. For each configuration selected, there exists an optimal choice of the geometric parameters that maximizes the flame velocity.