A Simplified Theory

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Limitations of the classic de Ris [1] formula for opposed-flow flame spread rate of thick solid fuels in the thermal regime are explored in the works [2][3] listed below. While several assumptions of the de Ris theory have been found to be justified in the thermal regime, the assumption of an Oseen (slug) flow and constant properties have been found to be non-negligible. Such assuptions result in the de Ris formula being in error by as much as a factor of 10.

A spread rate formula, derived from a semi-empirical solution of a simplified problem, is shown in [3] to overcome the drawbacks of the de Ris formula while retaining its simpliciity. The formula developed here, which can be written as in which V_eqv contains the hydrodynamic information and the factor in front of it contains the chemical information, performs significantly better than the de Ris formula when tested against availble data and extensive computational results for different flow configurtions, opposed-flow velocities, oxygen levels and ambient pressures.

The unique aspect of this theory is that the structure of the flame is also obtained, unlike previous theories[1][4]. This aspect was not explored to completion in [3] because the printed medium did not lend itself to communicating this information effectivly. However, the introduction of the World Wide Web and dynamic extensions such as JAVA has made widespread 'publishing' of such information possible in a manner that is platform independent. To this end a JAVA applet has been written to dynamically plot the flame structure from information entered in the applet interface.

The applet is located below the reference list if you are interested in experimenting with it. A some-what rigourous documentation of the the mathematics of the simplified theory is under preparation. The applet source is available for download for the more curious viewers. I am open to suggestions and constructive criticism on how this page could be improved. (See "feedback" at the bottom of this page).

References
1)"Spread of a Laminar Diffusion Flame", de Ris, J., N., Twelvth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1969, pp.241-252.

2)"A Simplified Theory for de Ris Flame Over Thick and Thin Fuel Bed", Bhattacharjee, S., West, J. and Dockter, S., 1996, Accepted for Publication, Combustion and Flame.

3)"Determination of the Spread Rate in Opposed-Flow Flame Spread Over Thick Solid Fuels in the Thermal Regime", Bhattacharjee, S., West, J., and Altenkirch, R.,A., Twenty-Sixth Symposium(International) on Combustion, Accepted for Presentation, July 1996, Naples, Italy.

4)"Flame Spread in an Opposed Flow with a Linear Velocity Gradient ", Wichman, I., S., Combustion and Flame, 1983, V50, pp. 287-304.