Spread of a laminar diffusion flame
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.
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Cited by (347)
Quenching extinction of solid sphere diffusion flames induced by a sudden removal of gravity
2024, Fire Safety JournalThe response of a diffusion flame around a PMMA solid sphere to a sudden transition to zero-gravity is investigated both experimentally and numerically. The initial flame is established in normal gravity with a low speed forced flow in a 17% oxygen by volume atmosphere. An abrupt (step change) normal-to-zero gravity transition occurs when the test package is released in the drop tower. The dynamic flame response is recorded by video and modeled numerically. By the end of the 5.18-s drop, the flame tip retreats, and the flame base may either remain stabilized near the forward stagnation region or extinguish depending on several parameters. The two parameters investigated are: forced flow velocity and the degree of preheating in the surface layer of the solid sample. The amount of preheating or equivalently the conductive flame heat loss rate to the solid interior is varied by controlling the duration of the normal gravity burning before releasing to microgravity. The heat loss is quantified by using embedded thermocouples to measure the solid subsurface temperature gradient near the stagnation point. The detailed numerical model reveals details of the flow field and flame structure including oscillatory extinction and quantifies the various transient gas-solid surface energy balance terms.
Flame spread over a solid surface is a critical metric in assessing the fire hazard of a material. At the core of the flame spread problem is heat transfer to and within the solid fuel. Accurate measurement of surface temperature on the burning solid is necessary to describe the heat transfer mechanisms which drive flame spread. This work employs phosphor thermometry to measure the spatiotemporal surface temperature during downward flame spread over polymethyl methacrylate (PMMA) samples. The phosphor Gd3Ga5O12:Cr,Ce is used to measure the surface temperature in a 23 23 mm2 area with an image resolution of 410 µm/pixel. CH* chemiluminescence imaging is performed alongside phosphor thermometry to measure the flame spread rate and evaluate the surface temperature relative to the flame position. This work investigates the limitations and considerations required to adequately measure surface temperatures in a flame spread scenario using phosphor thermometry. The optimal phosphor coating thickness to prevent interference with the flame spread process is first investigated. Phosphor coating thicknesses of 6 µm and 4 µm impeded flame spread rate and altered the flame shape – thus proving too invasive for this application. A coating thickness of 2 µm, which provided a phosphor to PMMA surface ratio of 0.55/0.45, had no measurable effect on the flame spread behavior and provided reliable 2D surface temperature measurements. The phosphor measurements presented in this work exhibit a similar reliability to a thermocouple, but provide spatially resolved surface temperatures and provide measurement access to the surface underneath the flame sheet. The findings report 2D spatiotemporal surface temperature measurements ahead of the flame front, at the flame’s leading edge, and in the pyrolyzing region immediately beneath the flame. Detailed surface temperature measurements underneath the flame sheet are novel to the use of phosphor thermometry and have not been previously recorded. This study showcases this diagnostic technique in the context of flame spread, and shows the potential of applying these methods to other solid-fuel related research.
Effect of pyrolysis reaction kinetics modified by adding inorganics on flame spread of cellulose
2024, Fire Safety JournalThe influence of pyrolysis reaction parameters on the flame spread rate over a thin cellulose strip was examined for varying additive amounts of an inorganic compound (K2CO3). The increase in the mass fraction of K2CO3 in the sample causes a decrease in the flame spread rate. Above 1.8% in K2CO3, the flame experiences extinction and smoldering occurs. The results of kinetic analysis reveal that the rate of pyrolysis reaction rate is decreased with the increase of K2CO3. To elucidate the decrease in the flame spread rate by the suppression of the pyrolysis reactions, the influence of the change of the flame temperature by various pyrolysis gas compositions or the pyrolysis reaction rate on the flame spread rate is examined theoretically. With regard to the temperature effect, the estimated adiabatic flame temperature decreases weakly with the increase of the K2CO3, which implies a weak contribution of the flame temperature to the flame spread rate. The results of theoretical analysis reveal that the reduction of the flame spread rate comes from the suppression of the pyrolysis reactions by adding K2CO3.
This paper presents experimental and theoretical research on ceiling jet, burn-through, and flame spread behaviors of the combustible ceiling with the impingement of an incipient fire source. Medium-density fiberboard was utilized as the combustible ceiling in experiments, and the ceiling height above the fire source was varied. The flame radial length (rf), ceiling surface temperature, flame shape and spread rate after burn-through, and radiative heat flux were measured. Results showed that rf beneath the combustible ceiling was significantly longer than that of the non-combustible ceiling. Theoretical analysis was conducted for rf based on energy distribution, and an expression of rf beneath combustible ceiling was proposed. The burn-through behavior of the combustible ceiling was explored by combining the ceiling temperature, small-sized experiment and Fourier law. The advancement of char front along the ceiling thickness was calculated, which was the key point during burn-through. Upper surface flame spread in a circular shape after burn-through, and an expression of spread rate was obtained. A three-dimensional radiation model was adopted to calculate the radiative heat flux received by the unburned ceiling surface during the dynamic flame spread process, the calculated results agreed well with the experimental data.
Quantifying the controlling mechanisms of opposed flow flame spread: Influence of orientation, material, and external heating
2024, Fire Safety JournalThe contribution of gas-phase and solid-phase heat transfer on opposed flow flame spread was quantified under a range of experimental conditions. The thermal gradient ahead of the flame front was determined using a temperature reconstruction method from time resolved temperature data. In all conditions tested, both gas phase and solid phase heat transfer displayed significant contributions to heating ahead of the flame front. PMMA samples were tested in three orientations - downward, horizontal, and lateral. It was found that the lateral configuration displayed the highest rate of flame spread (3.54 mm/min) compared to downward (2.67 mm/min) and horizontal (2.54 mm/min). Lateral spread also exhibited a lower magnitude of solid phase heat transfer compared to the other orientations. Trials that were externally heated showed lower contributions of solid phase heat transfer as the applied surface heat flux was increased. Both PMMA and POM samples were used to compare the effects of the presence of a sooting or non-sooting flame. The methodology provided in this work quantifies the relative contributions of gas-phase and solid-phase heat transfer in opposed flame spread scenarios.
The importance of solid phase longitudinal conduction in flame spread over cylindrical and flat fuels: A comparative scale analysis
2024, Fire Safety JournalThis work presents a scale analysis to explore the role played by forward (longitudinal) solid conduction in the mechanism of opposed-flow flame spread over flat and cylindrical fuels. Closed-form expressions in terms of known parameters and properties are derived for a non-dimensional conduction number, which compares solid phase forward conduction with the gas to solid conduction in the preheat zone. The corresponding expressions for cylindrical fuels are related to the flat fuel expressions using a curvature factor that depends on fuel radius and flow velocity. The results of the analysis are compared to existing experimental data for flame spread over thick flat and cylindrical fuels. For thin fuels, a comprehensive numerical model is used to evaluate the conduction number for comparison with the prediction of the analysis. An energy balance at the leading edge, taking into account the longitudinal conduction through solid, produces a spread rate formula that is related to the well-known thermal limit through the conduction number.