The dominant mechanism of flame spread is the heat transfer from the flame's reaction zone to the unburnt fuel ahead of the flame. The possible modes of heat transfer are conduction through the solid, and convection, conduction and radiation through the gas. There are many parameters which determine the dominant mode of heat transfer and spread rate. Fuel type, fuel thickness, geometry, orientation with respect to the gravity vector, ambient conditions, flame scale, and strength of gravitational field are some parameters that have been studied.
The four fuel orientations that have been frequently studied are vertical downward, vertical upward, horizontal topside and horizontal underside. For vertical downward and horizontal topside fires, the direction of flame propagation is opposite to the direction of the buoyancy induced gas flow. The forward heat conduction and radiation are balanced by the opposed convective heat transfer, creating a flame that spreads at a constant rate. For vertical upward and horizontal underside fires all modes of heat transfer are in the same direction, creating a rapidly accelerating flame.
To better understand this complicated phenomenon of flame spread, it is best to try to fully understand its most simple cases. A vertical downward spreading flame over a thermally thick vertical slab of polymethylmethacrylate (PMMA) is a case that has been frequently studied. A thermally thick fuel is the limiting case where the flame characteristics become independent of the fuel thickness. PMMA is commonly used because it is a relatively clean burning fuel, and its properties are well known.
Another situation that is commonly studied, is the downward flame spread over a thermally thin sheet of ashless filter paper. A thermally thin fuel is the limiting case where the temperature is constant across the thickness of the solid fuel. For this situation the flame spread rate is dependant on the thickness of the fuel.
Experimental, analytical and numerical methods have been used to find the spread rates, temperature fields, and other flame properties for these two limiting cases. The dominant mode of heat transfer can be deduced from this information. Since each of these three methods of analysis introduces its own source of error, it is necessary to correlate the results as much as possible.
In 1983 Fernandez-Pello and Hirano (13) summarized recent experiments on flame spread over combustible solids. Results from thickness studies on downward and horizontal flame spread over PMMA showed the transition to the thermally thick limit. These results were shown in plots of spread rate and forward heat transfer versus thickness. Experiments on external effects on spread rate were also presented. Effects of surface temperature, external radiant heat flux, opposed flow velocity, and oxygen mass fraction, on spread rate were analyzed. Finally it was shown that these results could be condensed and represented in non- dimensional form.
Williams (18) reviewed concepts in laminar flame spread over solid fuels. Important mechanisms of fire spread were emphasized in this work.
Altenkirch and Bhattacharjee (20) summarized theories in opposed flow microgravity flame spread. Numerical results determining the effect of radiation and opposed flow on spread rate and temperature fields were presented in this work.
Analytical Background
In 1969 de Ris (1) published a mathematical analysis of spreading flames. In this
analysis the velocity of an opposed flow spreading flame was produced for thick and thin fuels.
This was the first time it was shown that the mechanisms of flame spread are different for
thermally thick and thin fuel. This distinction was reexamined often in later works. Although
many simplifying assumptions were made in the analysis, the velocity formulae correlate well
with experimental data for many situations, especially for thin fuels.
Experimental Background
Tarifa et al. (2) used approximate analytical methods and experiments to study
downward flame spread over plexiglass rods. The effects of initial fuel temperature, oxygen
mass fraction, and pressure on spread rate were determined.
Lastrina et al. (3) performed an analytical and experimental study of opposed flow flame spread over thermally thick and thin, PMMA and cellulose fuel samples. The flame- spreading velocity was measured as a function of fuel thickness, pressure, oxygen concentration, radiant heat flux, and opposed flow velocity.
Parker (4) investigated downward flame spread over thin cellulose index cards. A surface temperature profile was obtained using an embedded thermocouple. An artificial flame spread burner was built to emulate a cellulose downward spreading flame. The experimenters used natural gas to create a stationary flame with the same characteristics as a downward spreading flame. From this model it was concluded that the release of pyrolysis gases occurs underneath the flame rather than ahead of it. It was also concluded that the dominant mode of heat transfer to the unburnt fuel was conduction through the gas phase.
Sibulkin et al. (5) did experiments on PMMA rods. The effect of fuel position on the spread rate was studied by varying the angle of inclination of a 1/4" PMMA rod from -90 degrees to +90 degrees. Flame spread rates were measured for rods of varying thickness. Surface and internal temperature distributions were obtained for a 1/2" PMMA rod.
Hirano et al. (6) measured temperature and velocity profiles over thin paper at various positions. Particle tracing methods and fine wire thermocouples were used to collect data. It was concluded that 80% of the heat transfer to the unburnt fuel was in the gas phase within 1 mm of the flame front.
Fernandez-Pello (7) performed extensive studies on laminar flame spread over flat PMMA surfaces. In this work he presented results from thermocouple probing, photography, interferometry, radiometer measurements, gas sample chromatography, and particle-track photography. He concluded that the dominant mode of heat transfer was conduction through the solid.
Downward and horizontal flame spread experiments on paper index cards were performed by Frey (8) et al. These experiments were designed to observe flame spread rates at low pressures and oxygen mole fractions. Gas-phase temperature contour plots were obtained for pressures of 10 (psia) and 3 (psia). The reason for this study was that the assumption of infinite rate chemical kinetics was found to be invalid near flame extinction conditions.
Fernandez-Pello et al. (9) performed downward flame spread experiments on thick PMMA rods to determine temperature and velocity fields. Temperature measurements were made using thermocouple probing. From this data it was concluded that the dominant mode of heat transfer was conduction through the solid.
Thin fuel flame spread experiments were performed in 1980 by Altenkirch et al. (10). With the use of a 15 (m) diameter centrifuge, an increase in effective gravity levels was achieved. The effect of gravity level, oxygen concentration and pressure on downward flame spread rate was determined. It was shown that these results could be represented very concisely in a non-dimensional flame spread rate versus Damk”hler number plot.
Fernandez-Pello, Ray and Glassman (11) performed experiments to determine the effect of opposed forced flow and ambient oxygen concentration on flame spread rate over thick and thin fuels. It was shown that for thick PMMA at high oxygen concentrations, flame spread rate increases as the opposed flow velocity is increased. However, for thin paper sheets at all oxygen concentrations, and thick PMMA at low oxygen concentrations, flame spread rate decreases as the opposed flow velocity increased. The results were also represented in a non- dimensional plot of flame spread rate versus Damk”hler number.
Altenkirch et al. (12) performed experiment to determine the effect of gravity level, pressure and oxygen concentration on downward flame spread rates over thick fuel beds. A centrifuge was used to emulate gravity levels of 1 (g), 2 (g), 3 (g) and 4 (g). These results were also represented in non-dimensional form.
Downward flame spread experiments on thermally thick PMMA slabs were performed by Ito and Kashiwagi (14). Temperature measurements were obtained by counting the interference fringes produced by a holographic image. It was concluded that 57% of the heat transfer to the unburnt fuel was through the gas phase. This result contradicts the previous result by Fernandez-Pello (5).
Bhattacharjee and Altenkirch (15) presented a comparison between experimental and
numerical results in flame spread over thin fuels in microgravity. Experiments to determine
flame spread rates and surface and gas-phase temperature profiles were measured aboard a Space
Shuttle flight. It was concluded that the leading edge flame structure and gas-phase radiation
heat transfer play a significant role in characterizing microgravity flame spread.
Clearly this data acquisition would be simplified if the flame were stationary as opposed to spreading downward. If the fuel sample is moving upward at the same velocity as the flame is spreading downward, a stationary flame can be achieved. For this situation the flame can be characterized in terms of a coordinate system attached to the laboratory, rather than to the surface of the fuel.